is induction unformalizable?
Wei Dai
Ben Goertzel
Ben Goertzel
> Correct me if wrong, but isn't the halting problem only
> undecidable when the length of the program is unbounded? Wouldn't the AI assign non-zero
> probability to a machine that solved the halting problem for
> programs up to size S? (S is the number of stars in the sky, grains of sand,
> atoms in the universe, etc...) As an aside, this would actually be my best guess as to
> what was really going on if I were presented with such a box (and I'm not
> even programmed with UD+ASSA, AFAIK). Any sufficiently advanced
> technology is indistinguishable form magic (but not actual magic) and all that ;->...
>
> Moshe
Wei Dai
>> undecidable when the length of the program is unbounded? Wouldn't the AI assign non-zero
>> probability to a machine that solved the halting problem for
>> programs up to size S? (S is the number of stars in the sky, grains of sand,
>> atoms in the universe, etc...) As an aside, this would actually be my best guess as to
>> what was really going on if I were presented with such a box (and I'm not
>> even programmed with UD+ASSA, AFAIK). Any sufficiently advanced
>> technology is indistinguishable form magic (but not actual magic) and all that ;->...
>>
>> Moshe
Ben Goertzel
Hal Finney
> One day, Earth is contacted by a highly advanced alien civilization, and
> they tell us that contrary to what most of us think is likely, not all of
> the fundamental physical laws of our universe are computable. Furthermore,
> they claim to be able to manufacture black boxes that work as oracles for
> the Halting Problem of Turing machines (one query per hour). They give
> us one free sample, and want to sell us more at a reasonable price. But
> of course we won't be allowed to open up the boxes and look inside to
> find out how they work.
> So our best scientists test the sample black box in every way that they
> can think of, but can't find any evidence that it isn't exactly what
> the aliens claim it is. At this point many people are ready to believe
> the claim and spend their hard earned money to buy these devices for
> their families.
So in terms of induction, the situation is that we do test after test
to see if this box acts as a halting-problem oracle (HPO, we always
need more 3 letter acronyms around here). And it passes all the tests.
So then we apply induction and say, since it's acted like an HPO in our
tests, we will go ahead and assume that it really is an HPO.
The problem is that HPOs are theoretically impossible. We have a proof
of it, in fact we have a lot of proofs. So how do we reconcile this?
Well, one possibility is that the proof is invalid. It's a pretty
simple proof so we look at its assumptions. Fundamentally it assumes
that computation is a finitary process. We can only do a finite amount
of computation in a finite time.
To act as a real HPO it would seem to be necessary for the box in some
way to deal with infinities. There would have to be an actual infinity
in there somewhere.
But again, we generally assume that there are no actual infinities.
In physics they are called singularities, which means places where the
laws of physics break down. In fact even the prospect of an actual
infinity in a theory is seen as a sign that the theory is wrong or
incomplete. Relativity puts singularities at the center of black holes,
but it is assumed that quantum gravity will fix these, in fact this is
one of the main motivations for work on quantum gravity.
Disbelief in actual infinities, like disbelief in HPOs, is not really
rooted in observation and induction. We don't disbelieve in them simply
because our universe seems to be devoid of them. In fact, on the face
of things there is evidence that actual infinities may really exist in
our universe. Relativity theory has its infinites; there are quantum
models which hint at the possibility as well, and even old fashioned
Newtonian gravitation on point particles, like is studied in high school
physics, implicitly embeds infinities and can construct an HPO. But still,
nobody believes that this stuff will work. It's always assumed to be
a mistake which future work will correct. (Google hypercomputers or
super-Turing computers for some theoretical models of HPOs.)
So where does our disbelief come from? Why are we so skeptical? We don't
have very good grounds from observation. The mere fact that we've never
seen X isn't strong evidence that X doesn't exist. We discover new things
all the time, amazing things. Why should HPOs be any different?
It seems that our disbelief in HPOs and in other manifestations of
infinity is somehow rooted in mathematics itself. We have an instinctive
aversion to the possibility of an actual infinity existing as something
we can interact with. We believe that mathematics is essentially a
finite endeavor, at least in terms of how it manifests in the real world.
And yet there are plenty of mathematical models of infinities.
The study of transfinites is a very active part of set theory, in
fact it is entirely what makes set theory non-trivial. Likewise, with
the super-Turing work people have constructed hierarchies of ever more
powerful infinity machines. So there is no dearth of mathematical models
to deal with infinities.
In response to early work on transfinites the mathematical school called
constructivism arose. Constructivists reject most of mathematics that
deals with infinities. I am not too familiar with the history but I
believe that they were concerned about the many potential paradoxes
and the possibility that our intuition was a poor guide to truth in the
treacherous waters of the transfinites.
Constructionism has not gained much ground among mathematicians; I get the
impression that it's just not that much fun to do math that way. But it
seems to accord well with our instincts about the world. Perhaps we
could say that it is all very well for the mathematicians to construct
their transfinite castles in the air, but when it comes to reality,
we are constructionists.
> Fortunately, the Artificial Intelligence in charge of
> protecting Earth from interstellar fraud refuses to allow this. Having
> been programmed with UD+ASSA (see Hal Finney's 7/10/2005 post for a
> good explanation of what this means), it proclaims that there is zero
> probability that Halting Problem oracles can exist, so it must be pure
> chance that the sample black box has correctly answered all the queries
> submitted to it so far.
> The moral of this story is that our intuitive notion of induction is not
> fully captured by the formalization of UD+ASSA. Contrary to UD+ASSA, we
> will not actually refuse to believe in the non-existence of uncomputable
> phenomena no matter what evidence we see.
Our theories say that it can't happen. Yet in this case we have an
observation where it seems like it does happen. So what do we do?
It helps in the analysis to distinguish what people actually do from
what they "should" ideally do. People are imperfect reasoning machines
and there is no fundamental or theoretical interest in explicating every
detail of what they believe and what they don't. No doubt it would be
possible to build up a complete formal theory and model of a given human
brain that would fully explain how it does induction, full of complicated
rules and contradictions. That's not the interesting question.
The harder question is, what *should* we do, in this situation? I see
two possibilities.
One is to hold to our theories. No matter how many times we see
this machine work, we disbelieve it. We assume it is a trick.
Others have suggested ways the trickery might be done. It would be
extremely difficult and technologically challenging, but not impossible.
These tricks require effort that would be characterized by extremely
large numbers, but not infinities. If we are skeptical that they could
put such large numbers together, we should be infinitely more skeptical
that they can manage infinities.
The other possibility is to change our theories, and apply induction.
Faced with the evidence of a machine that seems to work, we accept that
maybe it really does work. And if so, then our theories are wrong and
we need new ones.
This is a hard course because of the peculiar grounding of the theories
involved. As described above, they aren't based on observation. They are
much more fundamental. They have to do with our deepest beliefs about the
nature of reality and perhaps even the nature of logic and mathematics.
It's questionable to me whether any finite set of observations in the real
world has the standing, the philosophical strength, to change our beliefs
about the nature of something as ethereal and unphysical as mathematics.
But maybe it's the right thing to do. After all, our imperfections,
our existence as creatures of a mundane reality, make us prone to error.
We might be wrong about anything. Arguably, an optimal induction engine
stands ready to change any and every one of its pre-existing beliefs,
when they are strongly enough contradicted by the evidence. So perhaps
we really should change our minds about mathematics, forget about that
constructionism nonsense, and accept that infinities exist and are real,
and here's one that we can touch and poke at.
> What can we do to repair this flaw? Using a variant of UD, based on a
> more powerful type of computer (say an oracle TM instead of a plain TM),
> won't help because that just moves the problem up to a higher level of
> the computational hierarchy. No matter what type of computer (call it C)
> we base UD' on, it will always assign zero probability to the existence of
> even more power types of computer (e.g., ones that can solve the halting
> problem for C). Intuitively, this doesn't seem like a good feature.
> Earlier on this mailing list, I had proposed that we skip pass the
> entire computational hierarchy and jump to the top of the set theoretic
> hierarchy, by using a measure that is based a set theoretic notion of
> complexity instead of a computational one. In this notion, instead of
> defining the complexity of an object by the length of its shortest
> algorithmic description, we define its complexity by the length of
> its shortest description in the language of a formal set theory. The
> measure would be constructed in a manner analogous to UD, with each
> set theoretic description of an object contributing n^-l to the measure
> of the object, where n is the size of the alphabet of the set theory,
> and l is the length of the description. Lets call this STUM for set
> theoretic universal measure.
Are you confident that this is well defined? I understand Schmidhuber's
approach: pick an arbitrary UTM, run a random program through it, and take
the bit pattern that comes out as the information object. The fraction
of programs that produce a given information object is the measure.
Is there a similarly mechanical way of understanding the concept of
object description in the language of set theory? Can you sketch how
that would work?
> STUM along with ASSA does a much better job of formalizing induction, but
> I recently realized that it still isn't perfect. The problem is that it
> still assigns zero probability to some objects that we intuitively think
> is very unlikely, but not completely impossible. An example would be a
> device that can decide the truth value of any set theoretic statement. A
> universe that contains such a device would exist in the set theoretic
> hierarchy, but would have no finite description in formal set theory,
> and would be assigned a measure of 0 by STUM.
> I'm not sure where this line of thought leads. Is induction
> unformalizable? Have we just not found the right formalism yet? Or is
> our intuition on the subject flawed?
The mainstream view, I gather, is that induction is indeed unformalizable.
The contrary claim, that induction can be formalized, would be considered
controversial.
Another way to express the problem is to think of trying to build an
optimal induction machine. It could use Bayes theorem to update its
beliefs, but what about the priors? Same problem. We could use the
Universal Prior but it gives probability 0 to HPOs. Then there are all
those other priors that implicitly assume infinite computation, so where
does it stop? There are no end to infinities, and as Wei's example shows,
there is apparently no place to stand once you start down that road.
It would be absurd to suggest, say, that everything up to Aleph-23
has Platonic existence, while infinities from Aleph-24 on up are mere
mysticism. Likewise, building a universe out of a UTM+HPO doesn't make
sense because as Wei says, there is a 2nd-order HPO, an HPO2, which is
beyond the scope of UTM+HPO, so what if the aliens show up with one
of those? For a multiverse model to make sense it has to be simple,
distinctive and (ideally) unique. We don't quite achieve uniqueness
with the UDist (due to the arbitrary choice of a UTM which creates a
multiplicative constant difference on measure), which is a major flaw.
But adding oracles makes the problem infinitely worse.
Here's what I conclude. If we really believe in the Universal
Distribution, then we ascribe probability zero to HPOs. That means
that in Wei's story, indeed the aliens are tricking Earth. If we try to
imagine a universe where the aliens are legitimate and have real HPOs,
that is impossible. We are just confusing ourselves if we think such a
universe could be real. There is no point in even considering thought
experiments based on it, any more than imagining what would happen if
aliens showed up with a logical formula which was obviously simultaneously
true and false. So given that we stand upon the UDist, there is no need
to pay much attention to these kinds of thought experiments.
I would suggest that evidence for or against the UDist should come
more from the fields of mathematics and logic than from any empirical
experience. My hope is that further study will lead to a computational
model which is distinguished by its uniqueness and lack of ambiguity.
That seems necessary for this kind of explanation of our existence to
be successful.
Hal Finney
Bruno Marchal
I make a comment on Wei Dai, as quoted by Hal Finney, and then I Hal
Finney's answer.
Le 14-juil.-05, à 23:03, Hal Finney a écrit :
> Wei Dai writes:
>> One day, Earth is contacted by a highly advanced alien civilization,
>> and
>> they tell us that contrary to what most of us think is likely, not
>> all of
>> the fundamental physical laws of our universe are computable.
I recall that the comp hyp (I am a machine) entails that the apparent
universe cannot be the result of a computation (but can appear (first
personally) *through* the infinite execution of a non terminating
computation like UD* (the infinite trace of the Universal Dovetailer).
I have discussed this at length with Schmidhuber on this list, but he
dismissed the 1-3 difference so we were not able to progress.
>> Furthermore,
>> they claim to be able to manufacture black boxes that work as oracles
>> for
>> the Halting Problem of Turing machines (one query per hour). They give
>> us one free sample, and want to sell us more at a reasonable price.
>> But
>> of course we won't be allowed to open up the boxes and look inside to
>> find out how they work.
>
>> So our best scientists test the sample black box in every way that
>> they
>> can think of, but can't find any evidence that it isn't exactly what
>> the aliens claim it is. At this point many people are ready to believe
>> the claim and spend their hard earned money to buy these devices for
>> their families.
>
> Hal Finney:So in terms of induction, the situation is that we do test
> after test
> to see if this box acts as a halting-problem oracle (HPO, we always
> need more 3 letter acronyms around here). And it passes all the tests.
> So then we apply induction and say, since it's acted like an HPO in our
> tests, we will go ahead and assume that it really is an HPO.
>
> The problem is that HPOs are theoretically impossible. We have a proof
> of it, in fact we have a lot of proofs. So how do we reconcile this?
I guess you mean that "testing HPO" is theoretically impossible. I
agree with comp. But some "hyperturing" thesis we could test HPO (the
fact that nobody can give a protocol for testing HPO in a finite time
suggests that "hyperturing thesis" could be non plausible.
>
> Well, one possibility is that the proof is invalid. It's a pretty
> simple proof so we look at its assumptions. Fundamentally it assumes
> that computation is a finitary process. We can only do a finite amount
> of computation in a finite time.
This is equivalent to the comp hyp.
>
> To act as a real HPO it would seem to be necessary for the box in some
> way to deal with infinities. There would have to be an actual infinity
> in there somewhere.
.. and in "our head" to understand the HPO. Note that a test exists in
the limit by computing the OMEGA Chaitin number (through an infinite
always self-correcting procedure which stabilize in a non constructive
way).
>
> But again, we generally assume that there are no actual infinities.
> In physics they are called singularities, which means places where the
> laws of physics break down. In fact even the prospect of an actual
> infinity in a theory is seen as a sign that the theory is wrong or
> incomplete. Relativity puts singularities at the center of black
> holes,
> but it is assumed that quantum gravity will fix these, in fact this is
> one of the main motivations for work on quantum gravity.
OK.
>
> Disbelief in actual infinities, like disbelief in HPOs, is not really
> rooted in observation and induction. We don't disbelieve in them
> simply
> because our universe seems to be devoid of them. In fact, on the face
> of things there is evidence that actual infinities may really exist in
> our universe. Relativity theory has its infinites; there are quantum
> models which hint at the possibility as well, and even old fashioned
> Newtonian gravitation on point particles, like is studied in high
> school
> physics, implicitly embeds infinities and can construct an HPO.
That is right. Mathematically HPO and actual infinities are not
obviously inconsistent. They are obviously consistent for those who
believe in the consistency of ZF (Zermelo Fraenkel Set Theory).
> But still,
> nobody believes that this stuff will work. It's always assumed to be
> a mistake which future work will correct. (Google hypercomputers or
> super-Turing computers for some theoretical models of HPOs.)
(Note, in passing, that G and G* remains sound and complete for those
hyper-turing machine. Actually what I call comp could be called in that
contest omega-comp. I think (but don't have a full detailed proof of
it) that for all constructive (Church-Kleene) ordinal alpha, the logic
of self-reference (G and G*) remains stable for alpha-comp. Solovay's
proof makes it possible to get proper extensions of G and G* for
strong, non constructivist generalization of provability, like "being
true in all *transitive* models of ZF".
Of course ""being true in just all models of ZF", is equivalent, by
Godel's COMPLETENESS (not incompleteness) theorem to provable in ZF,
and this leads to completeness and soundness of G and G*.
Let me quote the footnote 28 of mùy sane paper:
[G and G* are sound and complete for larger systems, and can be
enriched for providing non-comp notion of belief, for example Solovay
got that G together with the formulas B(BX->BY) v B(BY->(BX&X)) gives a
system which is sound and complete for the (set theory) propositions
which are true in all transitive models of ZF (Zermelo Fraenkel set
theory). For a proof see Boolos 1993. Solovay got also that G together
with the formulas B(BX->Y)vB((BY &Y)->X) captures in the same way the
propositions true in all models VKappa with kappa an inaccessible
(rather big) cardinal. In case we find, as a measure on the consistent
histories, a consistent subset of physics, but don’t find all of
physics, making comp false, similar Solovay extensions of G and G*
could provide psychologies of some “non machine” notions. See R. M.
Solovay (1976): “Provability Interpretation of Modal Logic,” Israel
Journal of Mathematics, 25:287-304.]
>
> So where does our disbelief come from? Why are we so skeptical? We
> don't
> have very good grounds from observation. The mere fact that we've
> never
> seen X isn't strong evidence that X doesn't exist. We discover new
> things
> all the time, amazing things. Why should HPOs be any different?
>
> It seems that our disbelief in HPOs and in other manifestations of
> infinity is somehow rooted in mathematics itself. We have an
> instinctive
> aversion to the possibility of an actual infinity existing as something
> we can interact with. We believe that mathematics is essentially a
> finite endeavor, at least in terms of how it manifests in the real
> world.
Note that you talk a little bit as you were (again?) postulating the
existence of a real world, when in other post you acknowledge the
interest of deriving it from the observer-moments.
>
> And yet there are plenty of mathematical models of infinities.
> The study of transfinites is a very active part of set theory, in
> fact it is entirely what makes set theory non-trivial.
> Likewise, with
> the super-Turing work people have constructed hierarchies of ever more
> powerful infinity machines. So there is no dearth of mathematical
> models
> to deal with infinities.
>
> In response to early work on transfinites the mathematical school
> called
> constructivism arose. Constructivists reject most of mathematics that
> deals with infinities. I am not too familiar with the history but I
> believe that they were concerned about the many potential paradoxes
> and the possibility that our intuition was a poor guide to truth in the
> treacherous waters of the transfinites.
>
> Constructionism has not gained much ground among mathematicians;
The problem for the constructionist is that the work they do find
terribly interesting applications in non-constructive mathematics!
There is a fertile back and forth between constructive and
non-constructive mathematics.
> I get the
> impression that it's just not that much fun to do math that way. But
> it
> seems to accord well with our instincts about the world. Perhaps we
> could say that it is all very well for the mathematicians to construct
> their transfinite castles in the air, but when it comes to reality,
> we are constructionists.
This is *very* debatable.
1) A down to earth problem on the braids group has been solved by using
large cardinals.
2) Girard succeeds in blurring the distinction between constructive/non
constructive. In some sense classical linear or quantum logics are
more constructive than constructive linear logics.
3) George Boolos, commenting a solution of a puzzle by Smullyan, shows
that decision theory needs non classical thought (like the excluded
middle principle).
>
>
>> Wei Dai: Fortunately, the Artificial Intelligence in charge of
But concerning the HPO I don't think we can do the test at all. We
cannot know if the machine does the trick. If the machine solves and
give the proof for the first 2^64 math problems corresponding to the 64
first digit of Chaitin OMEGA, all we can conclude is that they are very
advanced in math. Testing an HPO box just measure the advance of the
extraterrestrial math. Even if they open the box and show us it is not
just a summary (-la-OMEGA-Chaitin's way) of their "annals of
mathematics", we will not been able to understand it, or if we do, then
the extra-terrestrial will indeed refute Church thesis and comp.
> Others have suggested ways the trickery might be done. It would be
> extremely difficult and technologically challenging, but not
> impossible.
> These tricks require effort that would be characterized by extremely
> large numbers, but not infinities. If we are skeptical that they could
> put such large numbers together, we should be infinitely more skeptical
> that they can manage infinities.
>
> The other possibility is to change our theories, and apply induction.
> Faced with the evidence of a machine that seems to work, we accept that
> maybe it really does work. And if so, then our theories are wrong and
> we need new ones.
>
> This is a hard course because of the peculiar grounding of the theories
> involved. As described above, they aren't based on observation. They
> are
> much more fundamental. They have to do with our deepest beliefs about
> the
> nature of reality and perhaps even the nature of logic and mathematics.
> It's questionable to me whether any finite set of observations in the
> real
> world has the standing, the philosophical strength, to change our
> beliefs
> about the nature of something as ethereal and unphysical as
> mathematics.
I agree, at least for a large part of math.
Well, Tegmark tried but did not succeed. Of course you can list the
definition of set object or of set of proof. But then "computationnaly"
is it like working in very weak theory, and concerning proof, well this
is not "closable" for the diagonalization procedure so this is
"forever" a relative concept. Formally, if the proofs are checkable (in
finite time) the invariant you can capture is already given by G and
G*.
>
>
>> STUM along with ASSA does a much better job of formalizing induction,
>> but
>> I recently realized that it still isn't perfect. The problem is that
>> it
>> still assigns zero probability to some objects that we intuitively
>> think
>> is very unlikely, but not completely impossible. An example would be a
>> device that can decide the truth value of any set theoretic
>> statement. A
>> universe that contains such a device would exist in the set theoretic
>> hierarchy, but would have no finite description in formal set theory,
>> and would be assigned a measure of 0 by STUM.
>
>> I'm not sure where this line of thought leads. Is induction
>> unformalizable? Have we just not found the right formalism yet? Or is
>> our intuition on the subject flawed?
>
> The mainstream view, I gather, is that induction is indeed
> unformalizable.
> The contrary claim, that induction can be formalized, would be
> considered
> controversial.
Right, but this does not prevent mathematical analysis.
>
> Another way to express the problem is to think of trying to build an
> optimal induction machine. It could use Bayes theorem to update its
> beliefs, but what about the priors? Same problem. We could use the
> Universal Prior but it gives probability 0 to HPOs. Then there are all
> those other priors that implicitly assume infinite computation, so
> where
> does it stop? There are no end to infinities, and as Wei's example
> shows,
> there is apparently no place to stand once you start down that road.
Mmh..., Prior, Bayes, ... required ASSA. But comp needs RSSA. (old
discussion).
>
> It would be absurd to suggest, say, that everything up to Aleph-23
> has Platonic existence, while infinities from Aleph-24 on up are mere
> mysticism. Likewise, building a universe out of a UTM+HPO doesn't make
> sense because as Wei says, there is a 2nd-order HPO, an HPO2, which is
> beyond the scope of UTM+HPO, so what if the aliens show up with one
> of those?
This rejoins my critics of Tegmark.
> For a multiverse model to make sense it has to be simple,
> distinctive and (ideally) unique. We don't quite achieve uniqueness
> with the UDist (due to the arbitrary choice of a UTM which creates a
> multiplicative constant difference on measure), which is a major flaw.
> But adding oracles makes the problem infinitely worse.
>
> Here's what I conclude. If we really believe in the Universal
> Distribution, then we ascribe probability zero to HPOs.
I agree, except that methodologically, once we accept Church thesis,
this is not something we can decide, we must prove that there is no
other choice.
> That means
> that in Wei's story, indeed the aliens are tricking Earth.
Most probably (unless not comp).
> If we try to
> imagine a universe where the aliens are legitimate and have real HPOs,
> that is impossible. We are just confusing ourselves if we think such a
> universe could be real. There is no point in even considering thought
> experiments based on it, any more than imagining what would happen if
> aliens showed up with a logical formula which was obviously
> simultaneously
> true and false. So given that we stand upon the UDist, there is no
> need
> to pay much attention to these kinds of thought experiments.
Nor with the UD ;)
>
> I would suggest that evidence for or against the UDist should come
> more from the fields of mathematics and logic than from any empirical
> experience.
Yes.
> My hope is that further study will lead to a computational
> model which is distinguished by its uniqueness and lack of ambiguity.
> That seems necessary for this kind of explanation of our existence to
> be successful.
ASSA + Udist: I doubt it can work. But who knows?
RSSA + UD: they are "concrete" evidence it works. No?
Bruno
Hal Finney
supposed halting-problem oracle (HPO) box?
In particular I wonder, suppose it turns out that P=NP and that further
there is an efficient algorithm to solve any NP problem. For those
unfamiliar with this terminology P means polynomial time, and we say
that problems in P can be solved efficiently. NP means nondeterministic
polynomial time, and essentially this means that for problems in NP, we
can efficiently test a purported solution for correctness. Whether P
is equal to NP or merely a subset of it is one of the major unsolved
problems of computer science.
But what if the aliens have solved it, and (somewhat to our surprise)
the answer is that every NP problem can be efficiently solved. And they
have embedded this NP solving algorithm (along with some other ones)
in the HPO box.
My concern is that to test the HPO box we could for example give it
a problem we have solved and see if it gets the answer. But success
might just imply that the HPO had substantially (but not astronomically)
greater computing power than the human race can bring to bear. Or we
could give it a problem we can't solve and then check the answer the
HPO gives, but if the answer is testable that would mean it is in NP,
and so even success in this area could be explained if P=NP as above.
It is much less philosophically challenging to imagine that P=NP than
to imagine that a true HPO could exist. Things would be different if
we ever get a proof that P < NP but we aren't in that situation now.
Are there other tests we could give, harder ones, that could give us
evidence that it was a true HPO, that could not be fooled by an NP solver?
My knowledge of these areas is pretty spotty. The only non NP problem I
know of offhand is the travelling salesman problem, finding the shortest
path visiting everyone of a set of cities with specified distances
between each pair. Proposed solutions cannot be tested efficiently,
as far as I know. If the box solved travelling salesmen problems for
us, it might be a boon to salesmen but we would not necessarily know if
we were getting truly optimal paths.
So in Wei's story, when the scientists go to test the HPO box, how strong
is the evidence that they can reasonably expect to get for it being a
real HPO? And I suppose a practical point arises as well; even if it
is not a true HPO, if it is nevertheless able to solve every problem we
give it, it's probably worth the money!
Hal Finney
scerir
> but this doesn't mean induction is unformalizable,
> it just means that the formalization of cognitive-science
> induction in terms of algorithmic information theory
> (rather than experience-grounded semantics) is
> flawed...
Imo, induction only works when the complexity
of the data is not larger than the complexity
of the theorem (or the model, or the theory,
etc.) we wish to prove. In other words, if those
data are special, induction does not work.
Isn't this another parameter for that formalization?
-serafino
Bruno Marchal
Le 15-juil.-05, à 20:55, scerir a écrit :
Actually this is a subject of a whole sub-branch of theoretical
computer science called Computational Learning Theory.
You are right that automated induction cannot work on sequences as
complex as they minimal description, but you are optimist if you think
the reverse is true, at least in term of class of sequences
recognizable by a unique machine. (An individual computable sequence is
always trivially inferable if only by the stupid machine which knows
only the program of that sequence, so the interesting notion in
learning theory is the learning of class of sequences (or of computable
total function). A class of sequence is learnable by a machine if for
any sequence taken from that class and presented by finite pieces the
machine eventually (after a finite time) output a program predicting or
computing the sequence.
The class of ALL computable sequences (or the set of computable total
functions) cannot be recognized in that sense by any learning machine.
By using genuinely the notion of "dovetailing" it is not hard to show
that all Recursively (Mechanically) Enumerable set of computable total
function can be learned.
By weakening the criteria of identification, some hierarchies of
learnable class can be studied.
Putnam and Popper have wrote some important prehistorical papers.
Important works by BLUM. But also by Blum and Blum. Blum wrote with her
husband the paper on the "NON UNION THEOREM", which, roughly speaking,
says that if you evaluate intelligence of machine by the learnable
class, then (in a sense) What is uncomputably more intelligent than a
machine? Two machines! (where a sequence is recognize if one of the two
machine get the correct predicting program).
BLUM L. & BLUM M., 1975, Toward a Mathematical Theory of Inductive
Inference. Information and Control 28,.pp. 125-155.
My favorite paper (a classical one):
CASE J. & SMITH C., 1983, Comparison of Identification Criteria for
Machine Inductive Inference. In Theoretical Computer Science 25,.pp
193-220.
A book (there is a new edition quite augmented by I have not the
reference):
OSHERSON D.N., STOB M.and WEINSTEIN S., 1986, Systems that Learn, MIT
press.
See also:
http://www.cis.udel.edu/~case/colt.html and links therein,
See perhaps a short summary of the main result by Case & Smith in the
section 5.2 of:
http://iridia.ulb.ac.be/~marchal/publications/M&PI_15-MAI-91.pdf
Bruno
http://iridia.ulb.ac.be/~marchal/
Wei Dai
1. P=?NP is a purely mathematical problem, whereas the existence of an HPO
box is an emperical matter. If we had access to a purported HPO box while
P=?NP is still unsolved, we can use the box to exhaustively search for
proofs of either P=NP or P<NP.
2. I think it's very unlikely that P=NP, but in case it is, we can still
test an HPO box by generating random instances of hard problems with known
solutions. (That is, you generate a random solution first, then generate a
random problem with that solution in mind.) For example here's a page about
generating random instances of the Traveling Salesman Problem with known
optimal solutions.
http://www.ing.unlp.edu.ar/cetad/mos/FRACTAL_TSP_home.html
----- Original Message -----
From: ""Hal Finney"" <h...@finney.org>
To: <everyth...@eskimo.com>
Sent: Saturday, July 16, 2005 12:29 AM
Subject: Re: is induction unformalizable?
Hal Finney
> 1. P=?NP is a purely mathematical problem, whereas the existence of an HPO
> box is an emperical matter. If we had access to a purported HPO box while
> P=?NP is still unsolved, we can use the box to exhaustively search for
> proofs of either P=NP or P<NP.
I've seen many speculations that P=?NP may be undecideable under our
current axioms. I guess this is because people are tired of looking
for proofs and PhD students don't want to get assigned this problem.
I'm not sure whether both of the following possibilities would be
consistent with the issue being undecideable:
A: There actually exists a polynomial-time algorithm to solve all
NP problems, but we can't prove that it always works, even though it
always does.
B: There is no polynomial time algorithm that solves all NP problems,
but we can't prove that no such algorithm exists.
I wonder if we could ask the HPO (halting problem oracle) box any harder
questions, that might help resolve the issue if it turned out that P=NP
is undecideable. Could we use it to directly ask whether the algorithm
in case A above exists, and perhaps even to find it?
> 2. I think it's very unlikely that P=NP, but in case it is, we can still
> test an HPO box by generating random instances of hard problems with known
> solutions. (That is, you generate a random solution first, then generate a
> random problem with that solution in mind.) For example here's a page about
> generating random instances of the Traveling Salesman Problem with known
> optimal solutions.
>
> http://www.ing.unlp.edu.ar/cetad/mos/FRACTAL_TSP_home.html
That's a good idea, but is it known that this subset of problems is
still NP-hard? I would worry that problems like these, where a fractal
or space-filling curve type of path is the right solution, might turn
out to be easier to solve than the general case.
Hal Finney
Stephen Paul King
One question: Does it not make sense that if there did exist an instance
of a P=NP computation within our physical universe that Nature would not
have found a way to implement it widely? The fact that the folding of
proteins, a known NP complete problem, takes a relatively long time to
actually occur tells me that such a computation, at best, only occurs is
very special situations in our universe, situations that can not be
converted (via a polynomial transformation) to solve problems in other
situations.
There is an old saying: What ever Man can do, Nature is already doing,
better.
Nature is performing computations all the time and what we experience is
the best computation possible.
It is only our failure of imagination that leads us to endlessly follow
rabbit trails. ;-)
Kindest regards,
Stephen
----- Original Message -----
From: ""Hal Finney"" <h...@finney.org>
To: <everyth...@eskimo.com>; <h...@finney.org>; <wei...@weidai.com>
Sent: Friday, July 22, 2005 12:43 PM
Subject: Re: is induction unformalizable?
Brent Meeker
computation to exist in nature. What it would mean in computer
science is that there was an algorithm for translating any NP
algorithm into a P algorithm for the same problem. This refers
to classes of algorithms for classes of problems. If you observe
a certain instance of protein folding - that's not an algorithm.
If you study many instances of protein folding you may develop an
algorithm that will predict how a class of proteins will fold and
that may scale as NP. Someone else might find another algorithm
that scales as P. But that's not the same as finding a way of
translating any NP algorithm into a P one. And neither one shows
that nature is using an algorithm. Nature isn't predicting how a
class of proteins is going to fold - it's just folding a few
specific examples.
Brent Meeker
On 22-Jul-05, you wrote:
> Hi Brent,
>
> You make a very good point and I agree with you completely!
> But I am arguing that it is the distinction between physical and
> abstract systems that seems to require some closer examination,
> and a slightly different point. If we are going to use arguments
> that are only "in principle"based to make decisions about
> situations in the physical world, does it not follow that we
> might be making serious errors?
> My claim stands!
>
> "... if there did occurs an instance of a P=NP computation
> within our physical universe then it follows that Nature would
> have found a way to implement it widely."
>
> If "P=NP Oracles" are allowed at all in our physical
> universe, then it follows that some evidence could be found of
> their occurance. If they can only exist in the very special case
> of an abstract universe, what connection do they have with
> physics or anything other than metaphysics?
>
> Stephen
>
> PS. Please cc your reply to the Everything List, I am sure that
> others are interested in this thread.
>
> ----- Original Message -----
> From: "Brent Meeker" <meek...@rain.org>
> To: "Stephen Paul King" <step...@charter.net>
> Sent: Friday, July 22, 2005 3:07 PM
> Subject: Re: is induction unformalizable?
>
>
>> On 22-Jul-05, you wrote:
>>
>>> Dear Brent,
>>
>> Could you name some examples? In the real world,
>> computations obey the laws of thermodynamics, among other
>> things, thus for problems with the same number of independent
>> degrees of freedom, the P problems can be computed faster
>> than
>> the NP. Of course this is just an average, but baring some
>> counter-examples I fail to understand your point.
>>
>> Stephen
>>
>> The laws of thermodynamics apply to physical processes, not
>> abstractions like algorithms. Of course computations are
>> physical processes - but P and NP are classes of algorithms,
>> not
>> computations. I'll see if I can find some specific examples,
>> but
>> the general point is that a polynomial algorithm may have a
>> large
>> fixed cost and then scale, say, linearly with the size of the
>> problem; while another algorithm for the same class of problem
>> may have a small fixed cost yet scale exponentially. Then up
>> to
>> some size (which may be very large) the latter will be faster
>> than the former. It is only in the limit of infinite size that
>> a
>> P algorithm is necessarily faster than an NP one. Since all
>> examples from Nature are finite, you can't infer that Nature
>> must
>> have found P algorithms for problems we think are NP.
>>
>> Brent Meeker
>>
>
>
Regards
--
Brent Meeker
Stephen Paul King
Ok, I am rapidly loosing the connection that abstract models have with
the physical world, at least in the case of computations. If there is no
constraint on what we can conjecture, other than what is required by one's
choice of logic and set theory, what relation do mathematical models have
with reality?
Is this not as obvious as it appears?
BTW, Scott Aaronson has a nice paper on the P=NP problem that is found here:
http://www.scottaaronson.com/papers/npcomplete.pdf
I recommend this paper as well:
http://www.scottaaronson.com/papers/are.ps
Kindest regards,
Stephen
Brent Meeker
> Hi Brent,
>
> Ok, I am rapidly loosing the connection that abstract models
> have with the physical world, at least in the case of
> computations. If there is no constraint on what we can
> conjecture, other than what is required by one's choice of logic
> and set theory, what relation do mathematical models have with
> reality?
>
> Is this not as obvious as it appears?
Here's my $0.02. We can only base our knowledge on our experience
and we don't experience *reality*, we just have certain
experiences and we create a model that describes them and
predicts them. Using this model to predict or describe usually
involves some calculations and interpretation of the calculation
in terms of the model. The relation of the model to reality, if
it's a good one, is it gives us the right answer, i.e. it
predicts accurately. Their are other criteria for a good model
too, such as fitting in with other models we have; but prediction
is the main standard. So in my view, mathematics and theorems
about computer science are just models too, albeit more abstract
ones. Persis Diaconsis says, "Statistics is just the physics of
numbers." I have a similar view of all mathematics, e.g.
arithmetic is just the physics of counting.
Brent Meeker
cha...@bigpond.net.au
A formal logic (an arbitrary calculus) is defined by 4 basic constituents:
1) signs
2) rules of formation
3) rules of inference
4) rules of transformation
Basically it's a formally specific grammar of signs.
A formal proof is a collection of (3) transformed according to (4) that takes the original inference from a starting state to an end state. Whatever state results is necessarily true according to the language.
The concept that I have found useful is that if you imagine that in some context in the universe, the natural behaviour of it happens to correspond to a virtual definition of items 1, 2, 3, 4 above, then what will be found is the universe behaving like formal logic of a certain type. Voila, mathematical decriptions are found to be 'unreasonably effective' ways of characterising the universe.
In different contexts in the natural world, difference sets of formal logic happen to be 'virtually reified' by the circumstances. In each case a different set of rules will be found. A slithly differrent set of mathematical rules will be found and we will tend to think that the 'laws' thus 'discovered' are somehow driving the universe.
In formal mathematics, though, one set of formalities can be transformed into anouther. Arithmetic can be done using formal logic, for example. Extraordinalrily tedious..but can be done...In a sense there is no 'native tongue', there are only 'tongues'.
When you think about it this way you end up wondering what is the 'calculus' of the natural world, which is selectively mapped into other calculii we find so useful? This brings in the idea of the universe as a reified calculus. Indeed the _only_ reified calculus. If it is, then what are its signs, rules of formation, inference, transformation?
I have been looking into this and I have been able to make on. I wonder if others can. Try it. I called mine 'entropy calculus'.
The idea brings with it one unique aspect: none of the calculii we hold so dear, that are so wonderful to play with, so poweful in their predictive nature in certain contexts, are ever reified. None of them actually truly capture reality in any way. They only appear to in certain contexts. The only actual mathematics that captures the true nature of the universe is the universe itself as a calculus. It doesn't invalidate the maths we love. It just makes it merely a depiction in a certain context. Very useful but thats all.
But there's a further subtlelty to this.
In mathematics there is a cultural assumption born of the history of mathematics.
..imagine Leibniz or Newton sitting there with their new toy calculus. They start with one set of symbols and work in a single line, transformation after transformation. A single linear proof emerges. Wonderment ensues.
If the universe is a calculus, how many Newtons and Leibniz's are there _All_ working at once? How many 'proofs' are being evaluated at once, all with direct relationships to each other?
Nobody ever thinks about that. If 100,000,000,000,000 leibnizs all started with their own sign and then connected with each other, formed, inferred transformed, each finding the results of the other 99,999,999,999,999 Leibniz's results in some way available to use in their own next transformation, what would the resulting calculus look like? What would it be like to 'be' one the proofs being enacted by Leibniz 145,735,365,268?
Leibniz 145,735,365,268's proof could be an electron. Leibniz 567,145,735,365,268's proof could be Bruno Marchal.
Our mathematics, as we see it, thinking about it from this perspective, is rather lame, n'est pas? Food for thought, anyway.
That's my handle on the relationship between mathematical models and reality. It's been a useful way of thinking for me and I commend it to you for a little amusement.
cheers
colin hales
Hal Finney
> The idea brings with it one unique aspect: none of the calculii we
> hold so dear, that are so wonderful to play with, so poweful in their
> predictive nature in certain contexts, are ever reified. None of them
> actually truly capture reality in any way. They only appear to in
> certain contexts. The only actual mathematics that captures the true
> nature of the universe is the universe itself as a calculus. It doesn't
> invalidate the maths we love. It just makes it merely a depiction in a
> certain context. Very useful but thats all.
You might like this quote from John Wheeler, in his textbook Gravitation written
with Charles Misner and Kip Thorne, which perhaps expresses a similar idea:
: Paper in white the floor of the room, and rule it off in one-foot
: squares. Down on one's hands and knees, write in the first square
: a set of equations conceived as able to govern the physics of the
: universe. Think more overnight. Next day put a better set of equations
: into square two. Invite one's most respected colleagues to contribute
: to other squares. At the end of these labors, one has worked oneself
: out into the door way. Stand up, look back on all those equations,
: some perhaps more hopeful than others, raise one's finger commandingly,
: and give the order `Fly!' Not one of those equations will put on wings,
: take off, or fly. Yet the universe 'flies'.
My current view is a little different, which is that all of the equations
"fly". Each one does come to life but each is in its own universe,
so we can't see the result. But they are all just as real as our own.
In fact one of the equations might even be our own universe but we can't
easily tell just by looking at it.
Hal Finney
cha...@bigpond.net.au
>
> : Paper in white the floor of the room, and rule it off in one-foot
> : squares. Down on one's hands and knees, write in the first square
> : a set of equations conceived as able to govern the physics of the
> : universe. Think more overnight. Next day put a better set of equations
> : into square two. Invite one's most respected colleagues to contribute
> : to other squares. At the end of these labors, one has worked oneself
> : out into the door way. Stand up, look back on all those equations,
> : some perhaps more hopeful than others, raise one's finger commandingly,
> : and give the order `Fly!' Not one of those equations will put on wings,
> : take off, or fly. Yet the universe 'flies'.
>
> My current view is a little different, which is that all of the equations
> "fly". Each one does come to life but each is in its own universe,
> so we can't see the result. But they are all just as real as our own.
> In fact one of the equations might even be our own universe but we can't
> easily tell just by looking at it.
>
> Hal Finney
Hi Hal,
Your 'flying equations' sound a bit like the idealist 'a-priori'... interesting but different topic for another day. :-) Thanks for the wheeler link....
On that note I'm not sure Wheeler's description is the same. In my idea of the calculus all there is is the sheets of paper. There are no symbols (no intrinsic representation). There are intrinsic rules of formation and transformation that relate and associate the bits of paper. If the bits of paper were jigsaw pieces with implicit connective rules then it is more like my idea.
If you try an build a universe as a monism from an enormous quantity of only one thing (a primitive sign - piles of little bits of paper :) ) then you can construct space and the leftovers become the stuff we call matter. Deep down it's all the one thing, however. It's been a fascinating mental exercise for me.
The problem is to let go of all the maths in a symbolic sense. We have this huge and very historically justified tendency to think the linear maths is the 'real stuff' of the natural world. I have been able to think of ways in which that is not the case, but that look 'as if' it was. It doesn't invalidate our maths, it just makes it look like it's not justified to ascribe anything more to the existence of our maths than that of a useful limited description.
The main thing is to get used to the idea of ridding your preconceptions of symbolic 'aboutness'. There is no intrinsically meaningful sign. However an intrinsic event: the expression of the sign (any sign), can literally be a truth in itself. The fact of the utterance of the sign itself is a truth. From that all other truths can be expressed through meaningless signs combining through intrinsic properties (affinities) for other signs.
It's more like a reified mega-dimensional cellular automata, actually. Not a traditional computational one. It took me a long time to be able to let go of my symbolic mathematical tendencies when I needed to.
You can make our universe out of hierarchically structured noise starting from nothing. The 'sign' in the calculus is basically the elemental noise event of the entropy calculus I have played with. Stuff that looks like the rules of quantum mechanics appears well up the hirearchy. Waaaaaay up the hierarchy it looks ontological but with structure all the way down to the elemental signs. The one that makes us is somewhere between 15? and 40? organisational layers deep. Very busy, these Leibniz's !!
Lots of fun! Don't know what to make of it but at least it has enabled me to post to this thread with a little bit of novelty!
cheers
colin
Stephen Paul King
Subject: Re: what relation do mathematical models have with reality?
> On 22-Jul-05,Stephen P. King wrote:
>
>> Hi Brent,
>>
>> Ok, I am rapidly loosing the connection that abstract models
>> have with the physical world, at least in the case of
>> computations. If there is no constraint on what we can
>> conjecture, other than what is required by one's choice of logic
>> and set theory, what relation do mathematical models have with
>> reality?
>>
>> Is this not as obvious as it appears?
> [BM]
> Here's my $0.02. We can only base our knowledge on our experience
> and we don't experience *reality*, we just have certain
> experiences and we create a model that describes them and
> predicts them. Using this model to predict or describe usually
> involves some calculations and interpretation of the calculation
> in terms of the model. The relation of the model to reality, if
> it's a good one, is it gives us the right answer, i.e. it
> predicts accurately. Their are other criteria for a good model
> too, such as fitting in with other models we have; but prediction
> is the main standard. So in my view, mathematics and theorems
> about computer science are just models too, albeit more abstract
> ones. Persis Diaconsis says, "Statistics is just the physics of
> numbers." I have a similar view of all mathematics, e.g.
> arithmetic is just the physics of counting.
[SPK]
Ok, I would agree completely with you if we are using Kant's definition
of *reality*- Dasein: existence in itself, but I was trying to be point out
that we must have some kind of connection between the abstract and the
concrete.
One thing that I hope we all can agree upon about *reality* is that what
ever it is, its properties are invariant with respect to transformations
from one point of view to any other. It is this trait that makes it
"independent", but the problems with realism seem to arise when we consider
whether or not this *reality* has some set of properties to the exclusion of
any others independent of some observational context.
QM demands that we not treat objects as having some sharp set of
properties independent of context and thus the main source of
counterintuitive aspects that make QM so difficult to deal with when we
approach the subject of Realism. OTOH, we have to come up with an
explanation of how it is that our individual experiences of a world seem to
be confined to sharp valuations and the appearance of property definiteness.
Everett and others gave us the solution to this conundrum with the MWI. Any
given object has eigenstates (?) that have eigenvalues (?) that are sharp
and definite relative to some other set of eigenstates, but as a whole a
state/wave function is a superposition of all possible.
So, what does this mean? We are to take the a priori and context
independent aspect of *reality* as not having any one set of sharp and
definite properties, it has a superposition of all possible. The trick is to
figure out a reason why we have one basis and not some other, one
partitioning of the eigenstates and not some other.
What does this have to do with mathematics and models? If we are going
to create/discover models of what we can all agree is sharp and definite-
our physical world, we must be sure that our models agree with each other.
This, of course, assumes that there is some connection between abstract and
concrete aspect of *reality*.
Stephen
Brent Meeker
MWI is *a* solution. But it is also possible to regard QM as a theory of
what we know or can say about a system. Have you read Bohm's
interpretation of QM? MWI seemed very promising when it seemed to solve
the Born problem. But since it has been shown that the Born postulate is
independent, then one might as well postulate that only one thing happens -
as in consistent histories, or Bohm's intepretation.
>Any given object has eigenstates (?) that have eigenvalues
> (?) that are sharp and definite relative to some other set of eigenstates,
> but as a whole a state/wave function is a superposition of all possible.I
I'm not sure what you mean by "object". In general an object, such as an
electron, has different eigenvalues depending on how it is
prepared/measured. So they are not necessarily properties of the object
alone.
> So, what does this mean? We are to take the a priori and context
> independent aspect of *reality* as not having any one set of sharp and
> definite properties, it has a superposition of all possible.
That's not how I'd take it.
>The trick is
> to figure out a reason why we have one basis and not some other, one
> partitioning of the eigenstates and not some other.
That's the decoherence program of Zeh, Zurek, Joos, Schlosshauer, et al.
>
> What does this have to do with mathematics and models? If we are going
> to create/discover models of what we can all agree is sharp and definite-
> our physical world, we must be sure that our models agree with each other.
> This, of course, assumes that there is some connection between abstract
> and concrete aspect of *reality*.
Or that we pick out those parts of our experience which we can describe by
models indpendent of viewpoint. The rest we call subjective experience.
Brent Meeker
Aditya Varun Chadha
Here's my Rupee 1 on the connection between "abstract models" and "reality";
Although it is ofcourse debatable, I hold that what we call reality is
our minds' "understanding" of our sensory perceptions. Thus the notion
of (our) reality depends on:
1. The nature of mind
Let's assume that the mind is simply the brain + the processes the
brain is capable of + the information it stores/processes. Then the
nature of the mind is the (sub)set of data-structures and computations
that the brain is capable of.
2. The process of "understanding"
Using the above informal definition of the mind, understanding is
simply the following process:
a. organize incoming data into data-structures that the brain is
capable of storing and processing (itself a brain-process),
b. process these data structures (computation) to make
"predictions" (just more data),
c. compare these predictions with more incoming feeds from our
senses (experiment/testing),
d. and finally re-adjust the organization of data in our brain
(data-structures) to accommodate the differences in prediction data
and sensory data.
The above process continues iteratively, thus the iterative
refinements in our theories of reality, aka physics.
3. Our sensory perceptions
The data that comes in to the brain. This clearly depends on the
instruments of perception (senses) themselves. For example a person
born with a microscope attached to his eyes will transfer very
different data to the brain than most of us, and thus may have a very
different "understanding of reality".
In other words, our understanding of reality depends on brains and our
senses. It can never be any more "real" or "imaginary".
[SPK]
> we have to come up with an
> explanation of how it is that our individual experiences of a world seem to
> be confined to sharp valuations and the appearance of property definiteness.
response:
This is simply because of the similar constitution of our sensory
organs and brains (closeness in genotype and therefore phenotype if
you may). A fly's understanding of reality is probably very very
different (may or may not be sharp)
[SPK]
> What does this have to do with mathematics and models? If we are going
> to create/discover models of what we can all agree is sharp and definite-
> our physical world, we must be sure that our models agree with each other.
> This, of course, assumes that there is some connection between abstract and
> concrete aspect of *reality*.
response:
If we presume to take my above description of the nature of mental
models (mathematical/physical/etc.) as physical reality, then physical
reality itself guarantees that our models will always depend on not
only "objective reality" but also the "nature of our mind" and our
"sensory perceptions", which themselves form a subset of reality.
It is much easier to make other humans "understand" (have their brains
recalibrated to) a new model or theory than to attempt the same with a
fly (unless the fly is given a human brain and human sensory organs).
Thus this "agreement" is NOT a certificate of validity for our models.
But this does NOT imply that there is no connection between abstract
and physical "reality".
Abstract reality is a "parallel universe" created by extrapolation on
a very limited (finite?) subset of "concrete reality", namely our
brain, sensory perceptions and the computations therein. The purpose
of creating and refining this "abstract reality" (aka
mathematical/physical models) is to recalibrate the brain and senses
so that the abstract models it can hold predict incoming data
(concrete reality) with increasing accuracy.
Yet this accuracy itself is limited by laws like those given by QM
(that limits the power of our senses). This suggests that we are close
to the best we can do, although we may continue coming monotonically
closer to the asymptotic optimum that we are limited to.
--
Aditya Varun Chadha
adi...@gmail.com
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Hal Finney
> Here's my $0.02. We can only base our knowledge on our experience
> and we don't experience *reality*, we just have certain
> experiences and we create a model that describes them and
> predicts them. Using this model to predict or describe usually
> involves some calculations and interpretation of the calculation
> in terms of the model. The relation of the model to reality, if
> it's a good one, is it gives us the right answer, i.e. it
> predicts accurately. Their are other criteria for a good model
> too, such as fitting in with other models we have; but prediction
> is the main standard.
This makes sense but you need another element as well. This shows up
most explicitly in Bayesian reasoning models, but it is implicit in
others as well. That is the assumption of priors.
When you observe evidence and construct your models, you need some
basis for choosing one model over another. In general, you can create
an infinite number of possible models to match any finite amount of
evidence. It's even worse when you consider that the evidence is noisy
and ambiguous. This choice requires prior assumptions, independent of the
evidence, about which models are inherently more likely to be true or not.
This implies that at some level, mathematics and logic has to come before
reality. That is the only way we can have prior beliefs about the models.
Whether it is the specific Universal Priori (1/2^n) that I have been
describing or some other one, you can't get away without having one.
> So in my view, mathematics and theorems
> about computer science are just models too, albeit more abstract
> ones. Persis Diaconsis says, "Statistics is just the physics of
> numbers." I have a similar view of all mathematics, e.g.
> arithmetic is just the physics of counting.
I don't think this works, for the reasons I have just explained.
Mathematics and logic are more than models of reality. They are
pre-existent and guide us in evaluating the many possible models of
reality which exist.
Hal Finney
Russell Standish
>
> On that note I'm not sure Wheeler's description is the same. In my idea of the calculus all there is is the sheets of paper. There are no symbols (no intrinsic representation). There are intrinsic rules of formation and transformation that relate and associate the bits of paper. If the bits of paper were jigsaw pieces with implicit connective rules then it is more like my idea.
>
> If you try an build a universe as a monism from an enormous quantity of only one thing (a primitive sign - piles of little bits of paper :) ) then you can construct space and the leftovers become the stuff we call matter. Deep down it's all the one thing, however. It's been a fascinating mental exercise for me.
>
> The problem is to let go of all the maths in a symbolic sense. We have this huge and very historically justified tendency to think the linear maths is the 'real stuff' of the natural world. I have been able to think of ways in which that is not the case, but that look 'as if' it was. It doesn't invalidate our maths, it just makes it look like it's not justified to ascribe anything more to the existence of our maths than that of a useful limited description.
>
> The main thing is to get used to the idea of ridding your preconceptions of symbolic 'aboutness'. There is no intrinsically meaningful sign. However an intrinsic event: the expression of the sign (any sign), can literally be a truth in itself. The fact of the utterance of the sign itself is a truth. From that all other truths can be expressed through meaningless signs combining through intrinsic properties (affinities) for other signs.
>
> It's more like a reified mega-dimensional cellular automata, actually. Not a traditional computational one. It took me a long time to be able to let go of my symbolic mathematical tendencies when I needed to.
>
> You can make our universe out of hierarchically structured noise starting from nothing. The 'sign' in the calculus is basically the elemental noise event of the entropy calculus I have played with. Stuff that looks like the rules of quantum mechanics appears well up the hirearchy. Waaaaaay up the hierarchy it looks ontological but with structure all the way down to the elemental signs. The one that makes us is somewhere between 15? and 40? organisational layers deep. Very busy, these Leibniz's !!
>
> Lots of fun! Don't know what to make of it but at least it has enabled me to post to this thread with a little bit of novelty!
>
> cheers
>
> colin
>
Hi Colin, Have you written up your "entropy calculus" in a paper, so
we could have a more detailed look at it? I know you sent me a paper
of yours recently (and apologies - I haven't read your latest draft
yet either :( ), but it doesn't seem to connect with what you are
saying here.
Cheers
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A/Prof Russell Standish Phone 8308 3119 (mobile)
Mathematics 0425 253119 (")
UNSW SYDNEY 2052 R.Sta...@unsw.edu.au
Australia http://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
----------------------------------------------------------------------------
Stephen Paul King
I do not see anything in your reasoning that I would disagree with. ;-)
It seems that you subscribe to a concrete interpretation of mathematics,
which is one that I take on occasion. I merely wish to comprehend the ideas
of those that take a Pythagorean approach to mathematics; e.g. that
Mathematics is "more real" than the physical world - "All is number".
One thing that I have learned in my study of philosophy is that no
single finite model of reality can be complete. Perhaps that asymptotic
optimum involves the comprehension of how such a disparate set of models can
obtain in the first place.
Kindest regards,
Stephen
----- Original Message -----
From: "Aditya Varun Chadha" <adi...@gmail.com>
To: <everyth...@eskimo.com>
Sent: Sunday, July 24, 2005 2:20 AM
Subject: Re: what relation do mathematical models have with reality?
snip
Hal Finney
> On 24-Jul-05, you wrote:
>
> > Brent Meeker writes:
> >> Here's my $0.02. We can only base our knowledge on our experience
> >> and we don't experience *reality*, we just have certain
> >> experiences and we create a model that describes them and
> >> predicts them. Using this model to predict or describe usually
> >> involves some calculations and interpretation of the calculation
> >> in terms of the model. The relation of the model to reality, if
> >> it's a good one, is it gives us the right answer, i.e. it
> >> predicts accurately. Their are other criteria for a good model
> >> too, such as fitting in with other models we have; but prediction
> >> is the main standard.
> >
> > This makes sense but you need another element as well. This shows up
> > most explicitly in Bayesian reasoning models, but it is implicit in
> > others as well. That is the assumption of priors.
> >
> > When you observe evidence and construct your models, you need some
> > basis for choosing one model over another. In general, you can create
> > an infinite number of possible models to match any finite amount of
> > evidence. It's even worse when you consider that the evidence is noisy
> > and ambiguous. This choice requires prior assumptions, independent of the
> > evidence, about which models are inherently more likely to be true or not.
>
> that kind of constraint we may have trouble finding even one candidate
> theory. We begin with an intuitive physics that is hardwired into us by
> evolution. And that includes mathematics and logic. Ther's an excellent
> little book on this, "The Evolution of Reason" by Cooper.
>
>
> >
> > This implies that at some level, mathematics and logic has to come before
> > reality. That is the only way we can have prior beliefs about the models.
> > Whether it is the specific Universal Priori (1/2^n) that I have been
> > describing or some other one, you can't get away without having one.
> >
> >> So in my view, mathematics and theorems
> >> about computer science are just models too, albeit more abstract
> >> ones. Persis Diaconsis says, "Statistics is just the physics of
> >> numbers." I have a similar view of all mathematics, e.g.
> >> arithmetic is just the physics of counting.
> >
> > I don't think this works, for the reasons I have just explained.
> > Mathematics and logic are more than models of reality. They are
> > pre-existent and guide us in evaluating the many possible models of
> > reality which exist.
>
> conditions on our models of reality. They are attempts to avoid talking
> nonsense. But note that not too long ago all the weirdness of quantum
> mechanics and relativity would have been regarded as contrary to logic.
>
>
> Brent Meeker
janos nagyapu
I kept out of it (not the least because of computer
troubles still unresolved) now I have some remarks:
How do you (all) imagine experience/knowledge WITHOUT
experience and knowledge to absorb/create it? It is a
(vicious?) circle. Do we start with a blank form to
fill in? What empty lines? what relations? where from?
You all use the word "reality" - who's and who knows
what is 'behind' it? We interpret some figment by our
own (1st mostly, but applying 3rd pers. info as well -
to the extent how we absorbed it as our own 1st pers
compliance) We are part of the "reality"-word, can't
see it in its totality (from the inside). Can a
deepsea fish describe water? A blind the colors deaf
the sound?
Then again 'computer sci (whatever) is a "more
abstract model"?' what is a non-abstract one? It comes
by abstraction limiting the topic we visualize between
OUR homemade boundaries.
I kept out from topics beyond (beneath?) my common
sense, like the Q immortality related fantasms,
because WHAT may 'live on' if the COMPLEXITY of
mentality (call it as you wish, consciousness, spirit,
soul, mind etc.) TOGETHER with the bodily aspect we
visualize (and live ???) falls apart? Who are you
without your body? Who are you without your mind? The
reincarnationists have not resolved that: nobody (in
the next life) remembers anything about the former
bodily existence (have you been an ant? an eagle? or
an elephant?) so WHAT is that reincarnational (or
Q-transfer) item? Superstitious (my slogan on
religion-based belief - including the post Q
thoughts).
Evidence? a model based figment that supports my
model.
Quantizing? the human mind invented numbers (Bohm) and
'counting' within the items chosen to be included in
our actual model. Go beyond it? That's highly
"unscientific" (which tells something about our terms
of the sciences).
Granted: in "wholism" we are vague, even ignorant,
because our knowledg-base is limited and our working
mind (still not understood what it may be) does think
(work) only in those model-terms we can account for.
Which does not mean to accept the model-based talk.
Please excuse me for misusing the moment when a
mailbox was willing to forward my remarks.
John Mikes
Hal Finney
> BTW, Scott Aaronson has a nice paper on the P=NP problem that is found here:
> http://www.scottaaronson.com/papers/npcomplete.pdf
That describes different proposals for physical mechanisms for efficiently
solving NP-complete problems: things like quantum computing variants,
relativity, analog computing, and so on. He actually looked at a claim
that soap bubble films effectively solve NP complete problems and tested
it himself, to find that they don't work.
He also discusses time travel and even what we call quantum suicide,
where you kill yourself if the machine doesn't guess right.
I am skeptical though about something he says in conclusion: "Even many
computer scientists do not seem to appreciate how different the world
would be if we could solve NP-complete problems efficiently.... If such
a procedure existed, then we could quickly find the smallest Boolean
circuits that output (say) a table of historical stock market data,
or the human genome, or the complete works of Shakespeare. It seems
entirely conceivable that, by analyzing these circuits, we could make
an easy fortune on Wall Street, or retrace evolution, or even generate
Shakespeare's 38th play. For broadly speaking, that which we can compress
we can understand, and that which we can understand we can predict....
if we could solve the general case - if knowing something was tantamount
to knowing the shortest efficient description of it - then we would be
almost like gods."
This doesn't seem right to me, the notion that an NP solving oracle
would be able to find the shortest efficient description of any data.
That would require a more complex oracle, one that would be able to
solve the halting problem.
I think Aaronson is blurring the lines between finding the smallest
Boolean circuit and finding the smallest efficient description. Maybe
finding the smallest Boolean circuit is in NP; it's not obvious to me
but it's been a while since I've studied this stuff. But even if we
could find such a circuit I'm doubtful that all the rest of Aaronson's
scenario follows.
Hal Finney
Hal Finney
> [Hal Finney wrote:]
> > When you observe evidence and construct your models, you need some
> > basis for choosing one model over another. In general, you can create
> > an infinite number of possible models to match any finite amount of
> > evidence. It's even worse when you consider that the evidence is noisy
> > and ambiguous. This choice requires prior assumptions, independent of the
> > evidence, about which models are inherently more likely to be true or not.
> In practice we use coherence with other theories to guide out choice. With
> that kind of constraint we may have trouble finding even one candidate
> theory.
Well, in principle there still should be an infinite number of theories,
starting with "the data is completely random and just happens to
look lawful by sheer coincidence". I think the difficulty we have in
finding new ones is that we are implicitly looking for small ones, which
means that we implicitly believe in Occam's Razor, which means that we
implicitly adopt something like the Universal Distribution, a priori.
> We begin with an intuitive physics that is hardwired into us by
> evolution. And that includes mathematics and logic. Ther's an excellent
> little book on this, "The Evolution of Reason" by Cooper.
No doubt this is true. But there are still two somewhat-related problems.
One is, you can go back in time to the first replicator on earth, and
think of its evolution over the ages as a learning process. During this
time it learned this "intuitive physics", i.e. mathematics and logic.
But how did it learn it? Was it a Bayesian-style process? And if so,
what were the priors? Can a string of RNA have priors?
And more abstractly, if you wanted to design a perfect learning machine,
one that makes observations and optimally produces theories based on
them, do you have to give it prior beliefs and expectations, including
math and logic? Or could you somehow expect it to learn those? But to
learn them, what would be the minimum you would have to give it?
I'm trying to ask the same question in both of these formulations.
On the one hand, we know that life did it, it created a very good (if
perhaps not optimal) learning machine. On the other hand, it seems like
it ought to be impossible to do that, because there is no foundation.
> > Mathematics and logic are more than models of reality. They are
> > pre-existent and guide us in evaluating the many possible models of
> > reality which exist.
> I'd say they are *less* than models of reality. They are just consistency
> conditions on our models of reality. They are attempts to avoid talking
> nonsense. But note that not too long ago all the weirdness of quantum
> mechanics and relativity would have been regarded as contrary to logic.
I guess we could agree that they are "other" than models of reality?
It still strikes me as paradoxical: ultimately we have learned our
intuitions about mathematics and logic from reality, via the mechanisms
of evolution and also our own individual learning experiences. And yet
it seems that at some level a degree of logic, and certain mathematical
assumptions, are necessary to get learning off the ground in the first
place, and that they should not depend on reality.
I'm pretty confused about this right now.
Hal Finney
Brent Meeker
An RNA string, arising naturally in a particular envirionment, can be modelled
as expressing a prior about the probability of such RNA strings.
>
> And more abstractly, if you wanted to design a perfect learning machine,
> one that makes observations and optimally produces theories based on
> them, do you have to give it prior beliefs and expectations, including
> math and logic? Or could you somehow expect it to learn those? But to
> learn them, what would be the minimum you would have to give it?
You'd have to give it the ability to reproduce and an environment in which it
competed with other reproducing learners.
>
> I'm trying to ask the same question in both of these formulations.
> On the one hand, we know that life did it, it created a very good (if
> perhaps not optimal) learning machine. On the other hand, it seems like
> it ought to be impossible to do that, because there is no foundation.
Why aren't elementary particles and entropy gradients enough foundation?
>
>
>>>Mathematics and logic are more than models of reality. They are
>>>pre-existent and guide us in evaluating the many possible models of
>>>reality which exist.
>
>
>>I'd say they are *less* than models of reality. They are just consistency
>>conditions on our models of reality. They are attempts to avoid talking
>>nonsense. But note that not too long ago all the weirdness of quantum
>>mechanics and relativity would have been regarded as contrary to logic.
>
>
> I guess we could agree that they are "other" than models of reality?
> It still strikes me as paradoxical: ultimately we have learned our
> intuitions about mathematics and logic from reality, via the mechanisms
> of evolution and also our own individual learning experiences. And yet
> it seems that at some level a degree of logic, and certain mathematical
> assumptions, are necessary to get learning off the ground in the first
> place, and that they should not depend on reality.
Why should they be any more independent of reality than say evolution or
folk-physics? I highly recommend Cooper's book.
Brent Meeker
Lee Corbin
> Although it is of course debatable, I hold that what we call reality is
> our minds' "understanding" of our sensory perceptions.
It's just amazing on this list. Does no one speak up for
realism? The *default* belief among *all* people up until
they take their first fatal dive into a philosophy book
is that there is an ordinary three-dimensional world that
we are all running around in.
(Yes---one *may* look at it as a model, but is this *really*
necessary? It prevents accurate understanding as well as
fosters terrible misunderstandings.)
When 99% of the human race use the word "reality", they mean
the world outside their skins.
If you sacrifice our common understanding of "reality", then
you'll find yourself in a hole out of which you'll never climb.
Janos wrote later
> How do you (all) imagine experience/knowledge WITHOUT
> experience and knowledge to absorb/create it? It is a
> (vicious?) circle. Do we start with a blank form to
> fill in? What empty lines? what relations? where from?
>
> You all use the word "reality" - who's and who knows
> what is 'behind' it? We interpret some figment by our
> own (1st mostly, but applying 3rd pers. info as well -
> to the extent how we absorbed it as our own 1st pers
> compliance) We are part of the "reality"-word....
See? This is what happens.
Look, it's VERY simple: take as a first baby-step the notion
that the 19th century idea of a cosmos is basically true, and
then add just the Big Bang. What we then have is a universe
that operates under physical laws. So far---you'll readily
agree---this is *very* simple conceptually.
Next, look at this picture after 14.7 billion years. Guess
what has evolved? Finally, there is intelligence and there
are entities who can *perceive* all this grandeur.
So, don't forget which came first. Not people. Not perceptions.
Not ideas. Not dich an sich. Not 1st person. Not 3rd person.
NOT ANY OF THIS NONSENSE. Keep to the basics and we *perhaps*
will have a chance to understand what is going on.
And have a common language with which to describe it.
Lee
Lee Corbin
> > I'd say they are *less* than models of reality. They are just consistency
> > conditions on our models of reality. They are attempts to avoid talking
> > nonsense. But note that not too long ago all the weirdness of quantum
> > mechanics and relativity would have been regarded as contrary to logic.
>
> I guess we could agree that they are "other" than models of reality?
What do you mean by "reality", by the way, since it's seems to be confounding
so many here?
> It still strikes me as paradoxical: ultimately we have learned our
> intuitions about mathematics and logic from reality, via the mechanisms
> of evolution and also our own individual learning experiences.
That's exactly right!
> And yet it seems that at some level a degree of logic, and certain
> mathematical assumptions, are necessary to get learning off the
> ground in the first place, and that they should not depend on reality.
"In the first place?" What does that mean? It sounds like you're using
English tenses and even English time-ordering adjectives.
If so, then that takes us, by the hand, back before the big bang,
and I'm not so sure that our English temporal vocabulary and grammar
are really of much use there.
Yes, there indeed are mysteries about the relationship between physics
and mathematics. But a lot of the math is now in our genes, because it
turns out that it really is a feature of the real physical universe.
And it had to be learned if we wanted to survive.
On a much more abstruse level are our philosophical meanderings about
Tegmark and Tipler universes. I'm just writing this so that we keep
the basics firmly in mind as we explore.
Lee
Stephen Paul King
I am trying to speak up for Realism! I feel your exasperation! The
problem is that our language is demonstrably NOT any good at giving us a
basic set of tools to make sense of our common "world outside their skins"!
The closer we look at this world of ours, including what is inside our
skins, we find that our naive ideas simply are wrong. If we are to have any
hope of finding models and methods to make sense of our universe we
absolutely must take into consideration all of the empirical data that we
have so far found. I would really like to see a version of realism that can
handle the implication of the "delayed choice" experiments!
http://www.bottomlayer.com/bottom/basic_delayed_choice.htm
Stephen
Russell Standish
> Aditya writes
>
> > Although it is of course debatable, I hold that what we call reality is
> > our minds' "understanding" of our sensory perceptions.
>
> It's just amazing on this list. Does no one speak up for
> realism? The *default* belief among *all* people up until
> they take their first fatal dive into a philosophy book
> is that there is an ordinary three-dimensional world that
> we are all running around in.
>
> (Yes---one *may* look at it as a model, but is this *really*
> necessary? It prevents accurate understanding as well as
> fosters terrible misunderstandings.)
>
> When 99% of the human race use the word "reality", they mean
> the world outside their skins.
>
> If you sacrifice our common understanding of "reality", then
> you'll find yourself in a hole out of which you'll never climb.
>
Sadly, your wish for the common sense understanding of "reality" to hold
will be thwarted - the more one thinks about such things, the less
coherent a concept it becomes.
For most of us in this list, the 3+1 dimensional spacetime we inhabit,
with its stars an galaxies etc is an appearance, phenomena emerging
out of constraints imposed by the process of observation.
For Kant, the noumenon, or Ding an Sich is "reality", and it could be
completely unlike what we observe, or phenomenon. For most on this
list, "reality" might refer to the laws of quantum mechanics, or the
Multiverse, or even the various "Plenitudes" proposed. My particular
Plenitude is the simplest possible object, it should really be called
Nothing. If I were to use "reality", I'm more likely to be referring to the
Multiverse, or an individual (observer relative) universe of
phenomena. Consequently, I will mostly dispense with the term reality
altogether, its too confusing.
I may sometimes use the term "realism" to refer to the proposition
that there exists an unexplainable noumenon to which phenomena can be
causally related. "Idealism" contrasts this by asserting no such thing
exists. This is largely how these terms are used in philosophy. I
would usually say my "ontology of bitstrings" is idealistic, but
then again, one could argue that the Plenitude _is_ the noumenon. This
often manifests itself with Platonism being described as realist. So
you could say these terms are incoherent too - perhaps I shall have to
stop using them, oh bother!
Cheers.
Lee Corbin
> Sadly, your wish for the common sense understanding of "reality" to hold
> will be thwarted - the more one thinks about such things, the less
> coherent a concept it becomes.
Well, all that I ask is that the *basics* be kept firmly in mind
while we gingerly probe forward.
The basics (basic epistemology, that is) include
1. the map is not the territory, and perception is not reality
2. the words we have for things are not the things themselves,
but only labels
3. we must *not* use basic language and terminology that conflicts
with that used by twelve-year olds
> For most of us in this list, the 3+1 dimensional spacetime we inhabit,
> with its stars and galaxies etc is an appearance, phenomena emerging
> out of constraints imposed by the process of observation.
Right there is the problem. Let's focus on what you are *referring*
to in your first sentence: "the 3+1 spacetime with its stars and
galaxies". We must keep clear the difference between what you are
*referring* to and our observations of it, or our perceptions of it.
They're not at all the same thing.
So when you use the dread "is" and write "For most of us... the
spacetime *is* an appearance", we've already gone over the edge.
No. The spacetime that you probably meant is *not* an appearance,
and we should not talk about it as if it is an appearance. *It*
is whatever is out there. Yes, our understanding of it may be poor.
Yes, it may not be at all as we *think*. In fact, it cannot in
in any literal sense *be* what we *think*.
I'm just urging everyone to keep in mind this key difference,
that's all. If we lose the language of realism, we lose our
real ability to communicate. There is no longer any constraint
at all that keeps one's words having meaning to others.
I understand and appreciate your remaining remarks.
Lee
> For Kant, the noumenon, or Ding an Sich is "reality", and it could be
> completely unlike what we observe, or phenomenon. For most on this
> list, "reality" might refer to the laws of quantum mechanics, or the
> Multiverse, or even the various "Plenitudes" proposed. My particular
> Plenitude is the simplest possible object, it should really be called
> Nothing. If I were to use "reality", I'm more likely to be referring to the
> Multiverse, or an individual (observer relative) universe of
> phenomena. Consequently, I will mostly dispense with the term reality
> altogether, its too confusing.
>
> I may sometimes use the term "realism" to refer to the proposition
> that there exists an unexplainable noumenon to which phenomena can be
> causally related. "Idealism" contrasts this by asserting no such thing
> exists. This is largely how these terms are used in philosophy. I
> would usually say my "ontology of bitstrings" is idealistic, but
> then again, one could argue that the Plenitude _is_ the noumenon. This
> often manifests itself with Platonism being described as realist. So
> you could say these terms are incoherent too - perhaps I shall have to
> stop using them, oh bother!
>
> Cheers.
Stephen Paul King
Are you the continuer of Niels Bohr? Seriously! The argument that your
making is very similar to the argument that lead to the Copenhagen
Interpretation. ;-) This is not a crtitisism, you are making some very good
points.
My problem is that I agree with both you and Russell and am having a
hardtime finding the middle ground. ;-)
Onward!
Stephen
----- Original Message -----
From: "Lee Corbin" <lco...@tsoft.com>
To: <everyth...@eskimo.com>
Cc: "EverythingList" <everyth...@eskimo.com>
Sent: Monday, July 25, 2005 10:06 PM
Subject: RE: what relation do mathematical models have with reality?
Russell Standish
>
> > For most of us in this list, the 3+1 dimensional spacetime we inhabit,
> > with its stars and galaxies etc is an appearance, phenomena emerging
> > out of constraints imposed by the process of observation.
>
> Right there is the problem. Let's focus on what you are *referring*
> to in your first sentence: "the 3+1 spacetime with its stars and
> galaxies". We must keep clear the difference between what you are
> *referring* to and our observations of it, or our perceptions of it.
> They're not at all the same thing.
>
> So when you use the dread "is" and write "For most of us... the
> spacetime *is* an appearance", we've already gone over the edge.
> No. The spacetime that you probably meant is *not* an appearance,
> and we should not talk about it as if it is an appearance. *It*
> is whatever is out there. Yes, our understanding of it may be poor.
> Yes, it may not be at all as we *think*. In fact, it cannot in
> in any literal sense *be* what we *think*.
>
The trouble is, _is_ is exactly what I do mean. 3+1 spacetime is an
appearance, an emergent thing, an illusion perhaps (although I detest
that term). Whatever the "territory" may be, what most people think of
as reality is the "map", not the territory.
Cheers
--
*PS: A number of people ask me about the attachment to my email, which
is of type "application/pgp-signature". Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.
----------------------------------------------------------------------------
A/Prof Russell Standish Phone 8308 3119 (mobile)
Mathematics 0425 253119 (")
UNSW SYDNEY 2052 R.Sta...@unsw.edu.au
Australia http://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
----------------------------------------------------------------------------
Stathis Papaioannou
>It's just amazing on this list. Does no one speak up for
>realism? The *default* belief among *all* people up until
>they take their first fatal dive into a philosophy book
>is that there is an ordinary three-dimensional world that
>we are all running around in.
>
>(Yes---one *may* look at it as a model, but is this *really*
>necessary? It prevents accurate understanding as well as
>fosters terrible misunderstandings.)
>
>When 99% of the human race use the word "reality", they mean
>the world outside their skins.
>
>If you sacrifice our common understanding of "reality", then
>you'll find yourself in a hole out of which you'll never climb.
Yes, but what *is* this 3D world we can all stub our toe on? If we go back
to the start of last century, Rutherford's quaintly pre-QM atom, amazingly,
turned out to be mostly empty space. Did this mean that, suddenly, it
doesn't hurt when you walk into a brick wall, because it isn't nearly as
solid as you initially thought it was? Of course not; our experience of the
world is one thing, and the "reality" behind the experience is a completely
different thing. If it is discovered tomorrow beyond any doubt that the
entire universe is just a game running in the down time on God's pocket
calculator, how is this fundamentally different to discovering that,
contrary to appearances, atoms are mostly empty space, or subatomic
particles have no definite position, or any other weird theory of modern
physics? And how could, say, the fact that brick walls feel solid enough
possibly count as evidence against such an anti-realist theory?
--Stathis Papaioannou
_________________________________________________________________
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Lee Corbin
> > When 99% of the human race use the word "reality", they mean
> > the world outside their skins.
> >
> > If you sacrifice our common understanding of "reality", then
> > you'll find yourself in a hole out of which you'll never climb.
>
> Yes, but what *is* this 3D world we can all stub our toe on?
Korzybski would warn: beware the "is" of identity :-)
> If we go back to the start of last century, Rutherford's
> quaintly pre-QM atom, amazingly, turned out to be mostly
> empty space. Did this mean that, suddenly, it doesn't hurt
> when you walk into a brick wall, because it isn't nearly as
> solid as you initially thought it was? Of course not; our
> experience of the world is one thing, and the "reality"
> behind the experience is a completely different thing.
That's *exactly* right. We *could* have been designed by
evolution not to hurt when we walked into a wall. For certain
reasons, we were not designed that way.
> If it is discovered tomorrow beyond any doubt that the
> entire universe is just a game running in the down time
> on God's pocket calculator, how is this fundamentally
> different to discovering that, contrary to appearances,
> atoms are mostly empty space, or subatomic particles have
> no definite position, or any other weird theory of modern
> physics?
Good analogy! The world surprises us all the time, especially
the more we learn about it. It would be bizarre if it did not,
(we'd probably have to abandon most of our theories).
> And how could, say, the fact that brick walls feel solid enough
> possibly count as evidence against such an anti-realist theory?
Occam's razor. We go with the simplest theory. Imagine
that you and I believe we are standing next to a wall.
Our conjecture is that it has certain properties. We
may need it to protect us. If we're wrong, nature will
make short work of us. That we have survived this long
is a strong indication that the wall really is there.
In fact, on some level of practicality, it is foolish
to debate the existence of the wall. Samuel Johnson
did refute Berkeley.
Lee
Bruno Marchal
Hi Stephen,
> I merely wish to comprehend the ideas of those that take a Pythagorean
> approach to mathematics; e.g. that Mathematics is "more real" than the
> physical world - "All is number".
> One thing that I have learned in my study of philosophy is that no
> single finite model of reality can be complete. Perhaps that
> asymptotic optimum involves the comprehension of how such a disparate
> set of models can obtain in the first place.
I agree with you that no single finite "theory" of reality can be
complete. Actually Godel's incompleteness theorem just proves that in
the case of arithmetical truth. And that was an argument for realism in
math (platonism).
You should not confuse a theory (like Peano Arithmetic, or Zermelo Set
theory) and its intended reality (called model by logician), which by
incompleteness, are not fully describable by finite theory (or by any
machine).
About the idea that math (or just arithmetic) is more real than the
physical worlds is a logical consequence of comp. And comp is testable,
it entails quite strong constraints on the "observable" propositions
(like being necessarily not boolean for example).
Regards,
Bruno
Bruno Marchal
Le 23-juil.-05, à 08:14, Hal Finney a écrit :
> My current view is a little different, which is that all of the
> equations
> "fly". Each one does come to life but each is in its own universe,
> so we can't see the result. But they are all just as real as our own.
> In fact one of the equations might even be our own universe but we
> can't
> easily tell just by looking at it.
This is so true that we cannot even localize ourself in *one*
universe/history.
What we call "a universe" emerges from the interference of an infinity
of (similar) histories.
(Are you not dismissing the first and third person distinction?).
Bruno
http://iridia.ulb.ac.be/~marchal/
Bruno Marchal
Le 23-juil.-05, à 06:20, cha...@bigpond.net.au (Colin Hales) a écrit :
> That's my handle on the relationship between mathematical models and
> reality. It's been a useful way of thinking for me and I commend it to
> you for a little amusement.
Just a subtle point: if you say "YES" to the comp-doctor, the
artificial brain you get is supposed not to model you, but to emulate
you. This asks for a quite strong act of faith, making comp closer to
theology than science in the usual sense of the word. But then it gives
a rational theology in which you can make sharable reasonings and
derive testable propositions (and that's also called sciences,
traditionally).
Bruno
http://iridia.ulb.ac.be/~marchal/
Bruno Marchal
Le 26-juil.-05, à 02:17, Lee Corbin a écrit :
> Look, it's VERY simple: take as a first baby-step the notion
> that the 19th century idea of a cosmos is basically true, and
> then add just the Big Bang. What we then have is a universe
> that operates under physical laws. So far---you'll readily
> agree---this is *very* simple conceptually.
>
> Next, look at this picture after 14.7 billion years. Guess
> what has evolved? Finally, there is intelligence and there
> are entities who can *perceive* all this grandeur.
>
> So, don't forget which came first. Not people. Not perceptions.
> Not ideas. Not dich an sich. Not 1st person. Not 3rd person.
> NOT ANY OF THIS NONSENSE. Keep to the basics and we *perhaps*
> will have a chance to understand what is going on.
But both the quantum facts, and then just the comp hyp are incompatible
with that type of naive realism.
You are reifying Nature, like those who confuses Aristotle's
methodology and its metaphysical questions.
It seems to me you are confusing the map and the territory, like you
ask us not to do in your other recent posts. I'm confuse about what you
really think (about fundamental matters).
Bruno
http://iridia.ulb.ac.be/~marchal/
Bruno Marchal
Le 26-juil.-05, à 04:06, Lee Corbin a écrit :
> Well, all that I ask is that the *basics* be kept firmly in mind
> while we gingerly probe forward.
>
> The basics (basic epistemology, that is) include
>
> 1. the map is not the territory, and perception is not reality
This is ambiguous. A trivial example is that for someone who studies
*maps*, maps are the territory. Also: "perception of x" is not "reality
of x". But perception itself is more probably real (unless we are all
zombies), so perception is a reality (independently of the gap between
perceiving and the things at the origin of perception).
>
> 2. the words we have for things are not the things themselves,
> but only labels
NOT ALWAYS. I agree that *in general* we must not confuse the word and
what they are intended for. But here too we can study the words
themselves, and, with comp, we can even make some non trivial
identification.
>
> 3. we must *not* use basic language and terminology that conflicts
> with that used by twelve-year olds
I agree. It is an important point.
Actually I am willing to believe that we can go much further in that
direction. We should NOT use basic language and terminology that we
are unable to translate in a language interpretable by any Lobian
Machine.
>
>> Russell: For most of us in this list, the 3+1 dimensional spacetime
>> we inhabit,
>> with its stars and galaxies etc is an appearance, phenomena emerging
>> out of constraints imposed by the process of observation.
>
> Right there is the problem. Let's focus on what you are *referring*
> to in your first sentence: "the 3+1 spacetime with its stars and
> galaxies". We must keep clear the difference between what you are
> *referring* to and our observations of it, or our perceptions of it.
> They're not at all the same thing.
>
> So when you use the dread "is" and write "For most of us... the
> spacetime *is* an appearance", we've already gone over the edge.
> No. The spacetime that you probably meant is *not* an appearance,
> and we should not talk about it as if it is an appearance. *It*
> is whatever is out there. Yes, our understanding of it may be poor.
> Yes, it may not be at all as we *think*. In fact, it cannot in
> in any literal sense *be* what we *think*.
Come on. What Russell said was the fact that many in this list could
imagine that the very idea of "out there" could be part of the
perception, like in a simulation (real, virtual or even just
arithmetical but I will not insist too much here).
Besides, please take comp seriously (if only just for one week), but it
makes almost "literally" the sky out there be what we think! Only *we*
denotes something much larger than usual. We, the (hopefully)
consistent Machine.
Please correct me, but I have the feeling you take physicalism (the
doctrine that physics is necessarily the fundamental science, or that
physics cannot be reduced to another body of knowledge) as so obviously
true that we should not even *doubt* about it.
Thanks to your conversation with Stathis, and our last posts, I know
you are ready to tackle the fourth step of the Universal Dovetailer
Argument (UDA) ...
My point is that if we take comp seriously enough then it is not a
matter of choice: physics has to be reducible to computer science, and
this in a verifiable way (already partially verified).
I think it is up to you to find an error in the argument (of course you
can wait someone else find it if you have not the time ;).
The UDA is not technical, and *is* the proof.
Only the translation of UDA in the language of a (Lobian) Machine is
obviously technical (like assembly language can be). The goal of that
translation does not consist in making the UDA more rigorous, but only
more constructive (and indeed it gives the shortest path to derive
physics from computer science).
Bruno
PS And all what I say here is compatible with both the ASSA
Schmidhuberian view (a-la Hal Finney) and the RSSA view (Levy,
Standish, me, ...). Our discussion is internal on how we structure the
OMs. I think (well, some like Schmidhuber explicitly invokes some
physicalist predicate at some points, and I could argue the very notion
of "prior" is basically physicalist, but we have already discussed this
..).
http://iridia.ulb.ac.be/~marchal/
Lee Corbin
> > Look, it's VERY simple: take as a first baby-step the notion
> > that the 19th century idea of a cosmos is basically true, and
> > then add just the Big Bang. What we then have is a universe
> > that operates under physical laws. So far---you'll readily
> > agree---this is *very* simple conceptually.
> >
> > Next, look at this picture after 14.7 billion years. Guess
> > what has evolved? Finally, there is intelligence and there
> > are entities who can *perceive* all this grandeur.
> >
> > So, don't forget which came first. Not people. Not perceptions.
> > Not ideas. Not dich an sich. Not 1st person. Not 3rd person.
> > NOT ANY OF THIS NONSENSE. Keep to the basics and we *perhaps*
> > will have a chance to understand what is going on.
>
>
> But both the quantum facts, and then just the comp hyp are incompatible
> with that type of naive realism.
At this level of discourse, dear Bruno, I don't give a _______
for your *hypothesis*.
Moreover, please google for "naive realism". You'll find that this
is the world view of children who have *no* idea of the processes
by which their brains are embedded in physical reality.
Since no one claims to be a naive realist, this rises to the level
of insult.
But then, I'm not too surprised that the most *basic* understanding
of our world has been forgotten by some who deal everyday with only
the most high level abstractions.
Lee
Aditya Varun Chadha
Our perception of reality is limited by the structure and composition
of brains. (we can 'enhance' these to be able to perceive and
understand 'more', but at ANY point of time the above limitation
holds). I think this is closer to what Lee wants to say, and I totally
agree with it. This is what I have tried to elaborate on in my earlier
(my first here) email.
But the very fact that this limitation is absolutely inescapable
(observation and understanding is ALWAYS limited to the observer's
capabilities) gives us the following insight:
That which cannot be modelled (understood) cannot figure in ANY of our
"models of reality". Therefore although our models of reality keep
changing, at any given time instance there is no way for us to
perceive anything beyond the model, because as soon as something
outside our current model is perceived, we have moved to a future
instance, and can create a model that includes it. Thus it is kind of
senseless to talk of a reality beyond our perception. In other words,
we can call something "reality" only once we perceive it. In this
sense "models may be more real than reality" to us. This is an
argument of the "Shroedinger's Cat" kind.
In fact if I am correct about what both Bruno and Lee want to say,
then Lee's arguments are a prerequisite to understanding to what Bruno
is hinting at.
Quantum Physics says that an observer and his observation are
impossible to untangle.
>From the above fact,
A Realist (Lee) would conclude that "absolute reality" is unknowable.
(follows from heisenburg's uncertainty also btw:-) ). But for this the
realist assumes that this "absolute reality" exists.
A Nihilist (Bruno) would conclude that since this tanglement of
observer and observation is inescapable, it is meaningless to talk
about any "absolute reality" outside the perceived and understood
reality (models).
None of the views is "naive". In fact neither view can ever disprove
the other, because both belong to different belief (axiomatic)
systems. apples and oranges, both tasty.
P.S.:
If what I have said above sounds ok and does help put things in
perspective, then I would like to think that in this WHOLE discussion
there is NO NEED of invoking terms like "comp hyp", "ASSA", "RSSA",
"OMs", etc. I, being clearly a lesser being in this new domain of
intellectual giants at eskimo.com, would highly appreciate if atleast
the full forms are given so that I can google them and put them in
context.
Stephen Paul King
I find your attempt to reconcile the arguments to be very good! I most
appresiate that you point out that our notion of Realism must include both
the invariants with respect to point of view and an allowance for novelity.
I do agree that we could use a FAQ defining the strange terms that we
use. ;-)
Kindest regards,
Stephen
----- Original Message -----
From: "Aditya Varun Chadha" <adi...@gmail.com>
To: <everyth...@eskimo.com>
Bruno Marchal
Thanks for answering all my mails, but I see you send on the list only
the one where you disagree. Have you done this purposefully? Can I
quote some piece of the mail you did not send on the list? I will
answer asap.
Also, for this one, I did not intend to insult you. Sorry if it looks
like that,
Bruno
Le 26-juil.-05, à 23:31, Lee Corbin a écrit :
http://iridia.ulb.ac.be/~marchal/
Bruno Marchal
Le 27-juil.-05, à 00:12, Aditya Varun Chadha a écrit :
> I think a reconciliation between Bruno and Lee's arguments can be the
> following:
Thanks for trying to reconciliate us :)
>
> Our perception of reality is limited by the structure and composition
> of brains. (we can 'enhance' these to be able to perceive and
> understand 'more', but at ANY point of time the above limitation
> holds). I think this is closer to what Lee wants to say, and I totally
> agree with it. This is what I have tried to elaborate on in my earlier
> (my first here) email.
>
> But the very fact that this limitation is absolutely inescapable
> (observation and understanding is ALWAYS limited to the observer's
> capabilities) gives us the following insight:
>
> That which cannot be modelled (understood) cannot figure in ANY of our
> "models of reality".
Why ? (I have explicit counterexamples, like the notion of knowledge
for machine).
Logic has evolved up to the point we are able to build formal theory
bearing on non formalizable notions (like truth or knowledge). Amazing
and counterintuitive I agree.
> Therefore although our models of reality keep
> changing, at any given time instance there is no way for us to
> perceive anything beyond the model, because as soon as something
> outside our current model is perceived, we have moved to a future
> instance, and can create a model that includes it. Thus it is kind of
> senseless to talk of a reality beyond our perception.
Why? We can bet on some theories and derive consequences bearing
indirectly on some non perceivable structure.
> In other words,
> we can call something "reality" only once we perceive it. In this
> sense "models may be more real than reality" to us. This is an
> argument of the "Shroedinger's Cat" kind.
>
> In fact if I am correct about what both Bruno and Lee want to say,
> then Lee's arguments are a prerequisite to understanding to what Bruno
> is hinting at.
Actually I agree with it. I do think Lee is close to what I want to
say, at the level of our assumptions. But Lee is quite honest and
cannot not be sure that my conclusion must be non sense (which means
that he grasped them at least).
>
> Quantum Physics says that an observer and his observation are
> impossible to untangle.
OK. But I don't use this. Actually I don't use physics at all. Physics
is emergent, not fundamental (once we assume seriously enough "digital
mechanism" (or computationalism).
>
>> From the above fact,
>
> A Realist (Lee) would conclude that "absolute reality" is unknowable.
> (follows from heisenburg's uncertainty also btw:-) ). But for this the
> realist assumes that this "absolute reality" exists.
>
> A Nihilist (Bruno) would conclude that since this tanglement of
> observer and observation is inescapable, it is meaningless to talk
> about any "absolute reality" outside the perceived and understood
> reality (models).
Actually I am a platonist, that is, a mathematical realist. I do also
believe in physical reality. My point is just that if you make some
hypothesis in the cognitive science (mechanism, computationalism) then
physics is 100% derivable from mathematics. The physical laws are
mathematical (even statistical) laws emerging from what any machine can
correctly bet concerning invariant feature of their most probable
computational history.
Nihilism is what happens when you believe in both computationalism and
materialism. This has been illustrated by La Mettrie and mainly Sade
(but also Heidegger and Nietsche in a less direct way, and then perhaps
Hitler or Bin Laden in in very more indirect way).
I am not at all a nihilist. I just show that the computationalist
hypothesis makes the physical world emerge from the truth on numbers. I
take those truth as being independent of me.
I am not a physical realist perhaps, although I do believe in an
independent physical world. I just don't physical reality is primitive.
Like Plato I take what we see and measure as some shadows of something
quite bigger, and non material ...
>
> None of the views is "naive". In fact neither view can ever disprove
> the other, because both belong to different belief (axiomatic)
> systems. apples and oranges, both tasty.
>
>
> P.S.:
> If what I have said above sounds ok and does help put things in
> perspective, then I would like to think that in this WHOLE discussion
> there is NO NEED of invoking terms like "comp hyp", "ASSA", "RSSA",
> "OMs", etc. I, being clearly a lesser being in this new domain of
> intellectual giants at eskimo.com, would highly appreciate if atleast
> the full forms are given so that I can google them and put them in
> context.
OK, but I think those you mention are used in so many posts that I
suggest you to remember them:
ASSA = A SSA = Absolute Self-Sampling Assumption,
RSSA = R SSA = Relative Self-Sampling Assumption,
comp hyp = Computationalist Hypothesis (or digital mechanism, ...)
OM = Observer-moment
Bruno
http://iridia.ulb.ac.be/~marchal/
chris peck
The main thrust of Berkley's argument is to show that sensory perception is
indirect, and therefore the existance of a material cause for those
perceptions is an unjustified inference in contravention of Occam's razor.
The argument that the look, texture, smell, taste and sound of an object are
apprehended indirectly is successful in my opinion, and I dont feel any need
to defend it unless someone really thinks a defence is required. Aterall, on
any view there is a translation of 'signals' of many different forms (light
waves, sound waves) , into various 'signals' of the same form (neurons
firing) which become synaesthetically unified into a whole, such that we
associate the smell, taste, colour and texture of say an orange, as being
qualities of the same object. That kicking a rock hurts, for example, does
not establish that the 'material world' is apprehended directly, or that the
concept of a material world is anything more than an inference.
I dont think this is really what Johnson meant, but the only challenge his
'refutation' genuinely offers is with regards to extension. How is the size
of an object, or its ability to exist and move (by being kicked) in a 3
dimensional realm, derived from perception alone? Our grasp of a 3
dimensional world is dependent on our stereoscopic perception. Its only when
there are two seperate perceptions of the world of the same type (eg. left
and right eye) that we apprehend a properly 3 dimensionally world, each of
these perceptions is however intrinsically 2 dimensional. It is the mental
combination of these slightly different images from which we derive an
extended world. This is probably more controversial, but Berkley's move here
is to insist that it we have enough information now to create the appearance
of a 3 dimensional world out of elements that are not intrinsically
extended. By Occam then, we should not infer something for which there is no
requirement - however firmly that inference has been imbedded in us. We
should stick to using what we can know directly. Perception.
In otherwords, dualists and materialists contravene Occam, not idealists. i
dont see how Johnson refuted that.
regards.
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Bruno Marchal
Le 27-juil.-05, à 15:55, chris peck a écrit :
I agree ontologically. But I disagree epistemologically. It is like
with Mendeleev classification of the elements (atoms). It was wise to
infer the existence of "unknown atoms" from the holes provided by the
classification. So a view-point should always to be completed as much
as possible. This makes it possible to get in a quicker way some
possible contradiction (internal or with facts). Remember that Occam
was proposing the razor for the number of hypotheses. In this list most
people tend to agree that we should have as few postulates as possible.
This makes the set of possibilities bigger and we take it as face value
(most are inspired or encouraged by Everett quantum mechanics (the
"many world").
> Perception.
Oops! Mhhh... Tricky word which has a foot in "knowing" (first person)
and a foot in some infered third person describable "reality".
>
> In otherwords, dualists and materialists contravene Occam, not
> idealists. i dont see how Johnson refuted that.
Very well said. But idealist are not necessarily solispsist, and once
you can acknowledge the existence of one "other", or even just this set
{1, 2, 3, 4, ...} (in the company of addition and multiplication),
then there is a vast realm full of ... surprises (counter-intuitive
truth which we can "know" but only indirectly. (A little like you need
two eyes to imagine 3D, you need two brains to make a genuine proof or
a genuine bet).
Bruno
http://iridia.ulb.ac.be/~marchal/
chris peck
There are problems with Berkley to be sure, but I dont think Johnson had
much of a grasp of them. Are there good objections to Berkley? Certainly.
Did SJ propose any? Not really.
>I agree ontologically. But I disagree epistemologically. It is like with
>Mendeleev classification of the elements (atoms). It was wise to infer the
>existence of "unknown atoms" from the holes provided by the classification.
I have a similar approach to Berkley which revolves around Occam's principle
of sufficiency. With regards to perception being the essence of existance,
what happens when things are not percieved? A perception or idea must exist
in a mind, right? Furthermore, in some sense a mind must be concieved of (by
Berkley) in terms of ideas too, So what are minds percieved by? Gaps like
these in my opinion, break Occam's principle of sufficiency. It leads to
Berkley positing a God which percieves all ideas (unpercieved things and
percieving minds). This enables 'the dark side of the moon' to exist
unpercieved and for percieving minds themselves to exist. However, I think
in satisfying the sufficiency principle, Berkley now breaks Occam's appeal
for simplicity.
In a way he has been forced to make a non empirical deduction which should
really be abhorrent to him. Perhaps an ad hoc invention might be more
accurate, in so far as God is invoked for theoretical difficulties
primarily.
>So a view-point should always to be completed as much as possible.
As shown, Berkley arguably does complete his theory. However, not in a way
that 'makes it possible to get in a quicker way some possible contradiction
(internal or with facts).'.
At this point then, Berkley is on unsteady ground, because we want some
means of falsification, I feel cheated that there isnt one, especially from
an empiricist. Internally though, I think he is largely consistant.
>>Perception.
>
>Oops! Mhhh... Tricky word which has a foot in "knowing" (first person)
Firstly, I use the word in the sense that this is what Berkley would have
used. I think there is a problem with how Berkley uses it. I think he plays
on a similarity between 'idea', 'mind' and 'perception'. I think you can
trap Berkley into a position where he has to admit that ideas are percieved,
which suggests again a two part process, an indirection. A translation.
However, with regards to :
>and a foot in some infered third person describable "reality".
Berkley has a third person describable reality. It is just not a material
one. Berkley is no solipsist. He does not deny objective reality. He basis
reality on a different substance and preserves it in the mind of God. Like
Leibniz. This is why Johnson is wrong, he thinks that Berkley is denying the
existance of things. Its a consequence of thinking dualistically. Dualists
naturally regard 'mentality' as less substantial than matter, Idealists
dont. It is their substance of choice in a sense. Materialism and Idealism
are very similar. Its monism really, as opposed to dualism. Think of the way
Marx (materialism) flips Hegel (idealism).
>>
>>In otherwords, dualists and materialists contravene Occam, not idealists.
>>i dont see how Johnson refuted that.
>
>
>Very well said. But idealist are not necessarily solispsist, and once you
>can acknowledge the existence of one "other", or even just this set {1, 2,
>3, 4, ...} (in the company of addition and multiplication), then there is
>a vast realm full of ... surprises (counter-intuitive truth which we can
>"know" but only indirectly. (A little like you need two eyes to imagine 3D,
>you need two brains to make a genuine proof or a genuine bet).
Not quite sure what you are getting at here.... The truth is always
incomplete from a single perspective?
Many Regards
Chris.
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Lee Corbin
> >>Samuel Johnson did refute Berkeley.
>
> The main thrust of Berkley's argument is to show that sensory perception is
> indirect, and therefore the existence of a material cause for those
> perceptions is an unjustified inference in contravention of Occam's razor.
> The argument that the look, texture, smell, taste and sound of an object are
> apprehended indirectly is successful in my opinion, and I don't feel any need
> to defend it unless someone really thinks a defence is required.
Do *you* contend that the existence of material causes for your
perceptions is unjustified? Good grief.
As for your other statement, these senses are indeed, just as you
say, apprehended indirectly. (That's the difference between realists
and naive realists, e.g., children.) Of course there is no need for
you to defend that, because no one here would disagree.
> Afterall, on any view there is a translation of 'signals' of many
> different forms (light waves, sound waves) , into various 'signals'
> of the same form (neurons firing) which become synaesthetically
> unified into a whole, such that we associate the smell, taste,
> colour and texture of say an orange, as being qualities of the
> same object.
Of course.
> ...Berkley's move here is to insist that it we have enough
> information now to create the appearance of a 3 dimensional
> world out of elements that are not intrinsically extended.
I'm not sure what you mean. By elements already in the brain?
Yes, that's true. But they got into the brain by the aforementioned
processes, as you know. Don't lose sight of the fact that almost
all the information came from outside.
> By Occam then, we should not infer something for which there is no
> requirement - however firmly that inference has been imbedded in us.
> We should stick to using what we can know directly. Perception.
You don't know all this complicated crap (neurons, perception,
inference, the whole nine yards) nearly as well as you know
the monitor in front of you. The problem is the word "know".
The first things you knew consciously, and knew well, were things
outside your skin: your mother and father, and tables and chairs.
Let's resist the temptation to begin using words in other ways.
Much, much later you ceased being a naive realist and became a
realist. You understood that there can be things like optical
illusions, and altered states of consciousness. You even understood
that your own exalted consciousness is not anything to be utterly
depended upon, because one can be sick or crazy. (If it hasn't
happened to you yet, then just stay around a few more decades.)
Build carefully upon what is simple and knowable, and keep the
wild theories to a minimum. Even then, the world is hardly
simple, but at least we've got a chance.
> In other words, dualists and materialists contravene Occam, not
> idealists. I don't see how Johnson refuted that.
Materialists do not contravene Occam. The simplest explanation is
that there is a world "out there" and that our brains are survival
machines designed by evolution to thrive in it. The phantasms that
occasionally infest our awareness and consciousness causally arise
as side-effects of how our brains work, that's all.
The simplest explanation does *not* start with perceptions and
all the rest of that stuff, for a number of reasons. The primary
reason is that you can't truly communicate them to others---after
all, your brain may not work the same as theirs. As Wittgenstein
said, "Of what we cannot speak thereof we must be silent".
Lee
chris peck
You see Samuel Johnson as a realist?
I think I started off a naive realist, became a realist and quickly became
confounded by the absurdity of the position. If I 'understood that there can
be things like optical illusions', I did so honestly, they told me something
very clear about the nature of perception which makes realism look as naive
as naive realism.
We have strong perceptions when we dream, we dont always know we are
dreaming. Sense data is what we are directly aware of, mental
representations. When we are not dreaming, we are still only directly aware
of sense data. However justifiable, the external world is an inference from
these representations whatever they are instantiated in. How can I on the
one hand be told that light falls upon my retina creating an image that is
upside down, then be told that I see things directly and as they are? It
makes no sense. Its blind hope and is obviously wrong. The world does not
look upside down. The very fact the image gets flipped the right way up is
enough to demonstrate I am in the grip of a cognitive representation. No.
Berkley is right on that score.
with regards to the question of whether Johnson refuted Berkley. I cant see
how he did.
many regards
Chris.
>From: "Lee Corbin" <lco...@tsoft.com>
>Reply-To: <lco...@tsoft.com>
_________________________________________________________________
It's fast, it's easy and it's free. Get MSN Messenger 7.0 today!
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Lee Corbin
> Brent Meeker wrote:
> > In practice we use coherence with other theories to guide out choice. With
> > that kind of constraint we may have trouble finding even one candidate
> > theory.
> Well, in principle there still should be an infinite number of theories,
> starting with "the data is completely random and just happens to
> look lawful by sheer coincidence". I think the difficulty we have in
> finding new ones is that we are implicitly looking for small ones, which
> means that we implicitly believe in Occam's Razor, which means that we
> implicitly adopt something like the Universal Distribution, a priori.
An intriguing way of putting it; yes, the amount of data compression
possible is necessarily related to both Occam's Razor and the UDist.
> > We begin with an intuitive physics that is hardwired into us by
> > evolution. And that includes mathematics and logic. There's an
> > excellent little book on this, "The Evolution of Reason" by Cooper.
>
> No doubt this is true. But there are still two somewhat-related problems.
> One is, you can go back in time to the first replicator on earth, and
> think of its evolution over the ages as a learning process. During this
> time it learned this "intuitive physics", i.e. mathematics and logic.
> But how did it learn it? Was it a Bayesian-style process? And if so,
> what were the priors? Can a string of RNA have priors?
I would say that the current state of the RNA string at any
given time can be regarded as its prior. After all, it survived
up to now, eh? The idea that evolution has to be pretty conservative,
---that is, the mechanisms must not allow too many new guesses---
also follows at once.
> And more abstractly, if you wanted to design a perfect learning machine,
> one that makes observations and optimally produces theories based on
> them, do you have to give it prior beliefs and expectations, including
> math and logic? Or could you somehow expect it to learn those? But to
> learn them, what would be the minimum you would have to give it?
>
> I'm trying to ask the same question in both of these formulations.
> On the one hand, we know that life did it, it created a very good (if
> perhaps not optimal) learning machine. On the other hand, it seems like
> it ought to be impossible to do that, because there is no foundation.
I strongly urge you to read the new book "What is Thought", by
Eric Baum. He very insightfully and carefully attends to these
questions.
Lee
Bruno Marchal
Le 27-juil.-05, à 20:11, Lee Corbin a écrit :
> Build carefully upon what is simple and knowable, and keep the
> wild theories to a minimum. Even then, the world is hardly
> simple, but at least we've got a chance.
I agree completely.
>
>> In other words, dualists and materialists contravene Occam, not
>> idealists. I don't see how Johnson refuted that.
>
> Materialists do not contravene Occam.
Subtance-materialists does. Imo. (but we can go back on this latter).
> The simplest explanation is
> that there is a world "out there" and that our brains are survival
> machines designed by evolution to thrive in it.
I agree. But it is just the recent "logical" path. Atoms and waves also
are "survival" machines, then eventually the laws of physics themselves
emerge from simpler things (like immaterial relations between prime
numbers for example).
> The phantasms that
> occasionally infest our awareness and consciousness causally arise
> as side-effects of how our brains work, that's all.
I disagree completely. Take a physicist of mass M, and another one of
mass m. physicists obey to the laws of physics, all right? (It is *the*
Everett motto). So the physicists will attract each other proportionaly
to mM/r^2 (r being the distance between the two physicists). Believe me
but that attraction is negligible compared to the usual psychological
repulsions and attraction among colleagues!
Consciousness is the most powerful force in the multi ... multiverses.
It entails the biggest self-speeding up of self-organisation of
information possible. Fears can transform itself into bombs, cathedral
or libraries.
And then, just defining "consciousness" by unconscious (automated)
inference of self-consistency, not only explains this self-speeding up
process, but it can explain why matter or consciousness *looks*
epiphenomenal.
(The self-speeding up is related to theorems by Godel and Blum in logic
and computer science.)
(This can also be related to works by I.J. Goods on a modelisation of
"free-will" in term of relative computations speed).
>
> The simplest explanation does *not* start with perceptions and
> all the rest of that stuff, for a number of reasons. The primary
> reason is that you can't truly communicate them to others---after
> all, your brain may not work the same as theirs. As Wittgenstein
> said, "Of what we cannot speak thereof we must be silent".
Well, apparently, either Wittgenstein missed the opportunity to remain
silent, or we have the right to ask him "What are you really talking
about, M. Wittgenstein?". But I agree with Wittgenstein: there exists
propositions which although true cannot be communicated or justified.
(And, as a reminder, I recall that Dt or equivalently ~Bf, are such
proposition in the near death OMs of the Papaioannou's multiverses.
This at least gives a picture capable of making Wittgenstein
consistent. Good because with such sentences (also said by Lao Tseu
btw) we are playing near ... inconsistency.
Bruno
http://iridia.ulb.ac.be/~marchal/
janos nagyapu
below
John Mikes
--- Bruno Marchal <mar...@ulb.ac.be> wrote:
>
> Le 27-juil.-05, à 20:11, Lee Corbin a écrit :
>
> > Build carefully upon what is simple and knowable,
> and keep the
> > wild theories to a minimum. Even then, the world
> is hardly
> > simple, but at least we've got a chance.
>
> I agree completely.
>
Only 'that much' is knowable, especially simple, so we
have no choice. Wild theories? Who is to label it?
>
> >
> >> In other words, dualists and materialists
> contravene Occam, not
> >> idealists. I don't see how Johnson refuted that.
> >
> > Materialists do not contravene Occam.
>
> Subtance-materialists does. Imo. (but we can go back
> on this latter).
>
Occam principlised our human knowledge based model. It
may well be that there are much more simple solutions
beyond our horizon of knowability. Even our present
level of epistemicly supplied cognitive inventory is
VERY limited - to say it mildly.
>
> > The simplest explanation is
> > that there is a world "out there" and that our
> brains are survival
> > machines designed by evolution to thrive in it.
>
> I agree. But it is just the recent "logical" path.
> Atoms and waves also
> are "survival" machines, then eventually the laws of
> physics themselves
> emerge from simpler things (like immaterial
> relations between prime
> numbers for example).
>
Simplest...see above. "out there"? we are 'out there'.
There is no "US and the rest of the world out there".
What are we so special ABOVE(?) those figments we call
"atoms" etc. to put our 'mentality' (ideational basis)
into a special box? It may be different (for us),
maybe we see more complexity in ourselves because we
know more about ourselves.
>
> > The phantasms that
> > occasionally infest our awareness and
> consciousness causally arise
> > as side-effects of how our brains work, that's
> all.
>
> I disagree completely. Take a physicist of mass M,
> and another one of
> mass m. physicists obey to the laws of physics, all
> right? (It is *the*
> Everett motto).
Snip the enjoyable monolog about physicists as
objects.
*
I cannot 'disagree completely' untill we agree in the
elusive phantasm called consciousness. No such
'thing'.
> Consciousness is the most powerful force in the
> multi ... multiverses.
SNIP
> And then, just defining "consciousness" by
> unconscious (automated)
> inference of self-consistency, not only explains
> this self-speeding up
> process, but it can explain why matter or
> consciousness *looks*
> epiphenomenal.
"epi" (or endo) to what?
*
> >
> > The simplest explanation does *not* start with
> perceptions and
> > all the rest of that stuff, for a number of
> > reasons. The primary
> > reason is that you can't truly communicate them to
> others---after
> > all, your brain may not work the same as theirs.
> As Wittgenstein
> > said, "Of what we cannot speak thereof we must be
> silent".
>
>
> Well, apparently, either Wittgenstein missed the
> opportunity to remain silent,
BRAVO
> or we have the right to ask him "What are
> you really talking
> about, M. Wittgenstein?". But I agree with
> Wittgenstein: there exists
> propositions which although true cannot be
> communicated or justified.
SNIP
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
>
Remark: ever since we have a way of communication we
try to complete (verb) our feeble imagination about
the world according to the ever increasing level of
the knowables. Our models (so far) have always been
totally boundary-enclosed and we did not even think
beyond them
"Natural laws". "logical laws", ONE cause, the axioms
and givens to make such views work AND math as the
main adjuvant of that fantastic and fruitful edifice
we have built called "scientific worldview". All human
thought.
Only lately (½ c.?) do some looked-down minds attempt
to 'look beyond' - even violating the Witgenstein
norm.
J.M.
>
Jesse Mazer
>
>Chris writes
>
> > >>Samuel Johnson did refute Berkeley.
> >
> > The main thrust of Berkley's argument is to show that sensory perception
>is
> > indirect, and therefore the existence of a material cause for those
> > perceptions is an unjustified inference in contravention of Occam's
>razor.
> > The argument that the look, texture, smell, taste and sound of an object
>are
> > apprehended indirectly is successful in my opinion, and I don't feel any
>need
> > to defend it unless someone really thinks a defence is required.
>
>Do *you* contend that the existence of material causes for your
>perceptions is unjustified? Good grief.
How do you define "material causes"? It seems to me you are conflating
idealism with solipsism, or the idea that the outside universe doesn't have
any existence outside of my perception of it, and that there are no
objective truths about external reality outside of my subjective ideas about
it. But even though I lean towards idealism, I certainly believe that other
minds (or 'observer-moments') have an independent existence outside of my
perceptions of them when I interact with them (with 'interactions' explained
in terms of different oberver-moments affecting one another's measure,
perhaps); I see other minds "from the outside", but they have an independent
experience of themselves "from the inside". And I also lean towards
panpsychism, which would imply that everything we label as a physical
process can really be understood as just another observer-moment (perhaps a
very simple one) viewed "from the outside". So rocks, stars, quarks, etc.
would have just as much of an independent existence as other people, in
terms of this hypothesis. I suggest checking out the article on
"Naturalistic Panpsychism" at http://www.hedweb.com/lockwood.htm which gives
a pretty good summary of the idea, although I don't agree with every aspect
of his version of it.
Jesse
Lee Corbin
> Lee Corbin wrote:
> >
> >Chris writes
> >
> > > >>Samuel Johnson did refute Berkeley.
> > >
> > > The main thrust of Berkley's argument is to show
> > > that sensory perception is
> > > indirect, and therefore the existence of a
> > > material cause for those perceptions is an
> > > unjustified inference in contravention of
> > > Occam's razor. The argument that the look,
> > > texture, smell, taste and sound of an object
> > > are apprehended indirectly is successful in
> > > my opinion, and I don't feel any need
> > > to defend it unless someone really thinks
> > > a defence is required.
> >
> > Do *you* contend that the existence of material
> > causes for your perceptions is unjustified? Good grief.
>
> How do you define "material causes"?
I stay clean away from definitions, sorry. I gave
reasons earlier why definitions don't work.
I expect that you want to know what was meant when
Chris and I were writing.
I'll get to that.
> It seems to me you are conflating idealism with
> solipsism, or the idea that the outside universe
> doesn't have any existence outside of my perception
> of it, and that there are no objective truths about
> external reality outside of my subjective ideas about
> it.
Well, no, I understand the difference, and agree with
the characterization of it you gave. It sounds as though
you believe in the existence of things "out there"
independent of your perceptions of it. That is, if
you were given a drug that cut off your senses, then
you'd figure that the outside world was still there
even though you could no longer sense it. We agree
on that.
Customarily (whether people like you and me are sensing
that outside world or not), we believe that for the most
part here on Earth, at least, there are a lot of material
objects around. Tables, chairs, rocks, and cars for
instance.
We can then go further and say that in this model, even
peoples bodies are material objects, and obey the usual
high school laws of physics. (They have mass, often
reflect light, and so forth.)
So by
> > Do *you* contend that the existence of material
> > causes for your perceptions is unjustified?
I meant that your perceptions have physiological causes
because your brain is a part of an obviously successful
survival machine designed by evolution.
Lee
Jesse Mazer
Sure, but all of this is compatible with an idealist philosophy where
reality is made up of nothing but observer-moments at the most fundamental
level--something like the "naturalistic panpsychism" discussed on that
webpage I mentioned. So does this mean you have no problem with idealism per
se, as long as it does not claim that there is no external reality
independent of *my* perceptions of it (even if this external reality
consists of nothing but other observer-moments, with some sort of measure
attached to each)? Is there anyone on this list who disagrees with the idea
of such an external reality? If not, then who are your criticisms aimed at?
Jesse
Lee Corbin
> > I meant that your perceptions have physiological causes
> > because your brain is a part of an obviously successful
> > survival machine designed by evolution.
>
> Sure, but all of this is compatible with an idealist philosophy where
> reality is made up of nothing but observer-moments at the most fundamental
> level--something like the "naturalistic panpsychism" discussed on that
> webpage I mentioned.
The disagreement I have with what you have written
is that I do *not* see observer-moments as the most
fundamental entities. It's just so much *clearer*
to me to see them arising only after 13.7 billion
years or so (locally) and that they obtain *only* as
a result of physical processes.
When in the laboratory we examine the concepts mice
have of the world, we can easily see their limitations.
What would we think of mice who attempted to found all
of reality on "mouse observer moments"? Unfortunately
for the ultimate survival prospects of mice, they're
not capable of understanding evolution and their own
highly contingent appearance in it.
We are, and we should be talking as though we do understand.
> So does this mean you have no problem with idealism per
> se, as long as it does not claim that there is no external reality
> independent of *my* perceptions of it (even if this external reality
> consists of nothing but other observer-moments, with some sort of measure
> attached to each)? Is there anyone on this list who disagrees with the idea
> of such an external reality? If not, then who are your criticisms aimed at?
It all depends on which way you think the explanations gain
the most mileage. You can start with these "human observer
moments"---which are in principle not comparable from one
entity to another and about which anyone's opinion is as
good as anyone else's, or you can start from what we have
learned so far about the universe we're embedded in.
Lee
Jesse Mazer
>
>Jesse writes
>
> > > I meant that your perceptions have physiological causes
> > > because your brain is a part of an obviously successful
> > > survival machine designed by evolution.
> >
> > Sure, but all of this is compatible with an idealist philosophy where
> > reality is made up of nothing but observer-moments at the most
>fundamental
> > level--something like the "naturalistic panpsychism" discussed on that
> > webpage I mentioned.
>
>The disagreement I have with what you have written
>is that I do *not* see observer-moments as the most
>fundamental entities. It's just so much *clearer*
>to me to see them arising only after 13.7 billion
>years or so (locally) and that they obtain *only* as
>a result of physical processes.
Ok, but even if you don't agree with this speculation about observer-moments
being the most fundamental entities, criticizing this speculation on the
basis of it being anti-realist seems misguided. Also, as I said, my idea is
that *all* possible causal patterns qualify as "observer-moments", not just
complex ones like ours. And I don't disagree that complex observer-moments
are generally the result of a long process of evolution in the physical
universe, it's just that I think at a most fundamental level the "physical
universe" would be reducible to an enormous pattern of causal relationships
which can be broken down into the relationships between a lot of
sub-patterns, each of which is an observer-moment. The idea that physics
should ultimately be explainable in terms of nothing more than causal
relationships between events, and that higher-order concepts like
"particles" and "spacetime" would emerge from this level of explanation, is
an idea that some approaches to quantum gravity seem to favor, like loop
quantum gravity--it's at least not out of the question that a final
"physical" ToE would be about nothing more than causal relationships between
events. If so, it would just be a different "interpretation" of this theory
to say that each sub-network in this universal causal network would be an
observer-moment of some kind, and my "meta-physical" speculation would be
that you could *start* by looking at all possible finite causal networks and
finding a unique measure on them, and the appearance of the huge causal
network we call the "physical universe" could be derived from the
relationships between all the sub-patterns implied by this unique measure.
Obviously I don't expect you to agree with this speculation, but I'm just
pointing out that it isn't anti-realist, nor does it contradict your
statement about our particular type of consciousness being the result of a
long process of evolution.
>
>When in the laboratory we examine the concepts mice
>have of the world, we can easily see their limitations.
>What would we think of mice who attempted to found all
>of reality on "mouse observer moments"?
Since there is nothing specifically human about my idea of
"observer-moments" this analogy doesn't really work.
Jesse
Aditya Varun Chadha
---------- Forwarded message ----------
From: Aditya Varun Chadha <adi...@gmail.com>
Date: Jul 30, 2005 8:47 PM
Subject: Re: What We Can Know About the World
To: Jesse Mazer <laser...@hotmail.com>
At the risk of barging in once again,
> Since there is nothing specifically human about my idea of
> "observer-moments" this analogy doesn't really work.
>
> Jesse
I agree more with this version of "observer-moments". An assumption
that an "observer" is a human or even a "biological" entity is being
narrow-minded IMO.
I think a common error that we make is to assume some vague concept of
"consciousness" and then limit our notion of observation as a process
that only "conscious" entities can undertake/undergo.
We only believe we are conscious, we have no "proof" or "physical
evidence", because ALL our thought-systems ASSUME consciousness, it is
just a human axiom. Or taken another way, conscious is a human-made
word representing just the way we (and our "close relatives" for the
relatively liberal) work. Nothing special about it.
Why not allow "observation" to be any event in which any set of
entities (even the most "fundamental" entities) interact among each
other in any way? After all, human observation can be explained as the
"physical" interactions of our senses/brain with "other" entities.
(i.e. just events)
Notice that this "definition" (or description, for the
"definition"-averse) cuts through a WHOLE lot of assumptions,
ultimately revealing (at least to me) the IDENTITY (sameness) of the
terms "Event" and "Observer-Moment".
Further, no version of "Observation" adopted by any Idealists violates
this definition. Also, the converse is not hard to accept if we are
just a bit more open minded (doing away with the "speciality" of human
thought).
In the system that emerges, yes, Observer-Moments alone ARE a
candidate for giving us a ToE, but for this, they cannot be
differentiated from our simple notion of "Event". (The realist favours
the term Event, the Idealist favours Observer-Moment)
I have been tilted towards what this list seems to call "realism"
since the start, but I maintain that digging deep enough, the realism
and idealism being discussed here aren't that different if we just use
a "Realish-Idealish, Idealish-Realish" dictionary, and I believe all
terms in either "language" have equivalent translations in the other.
I think Mazer has put this across quite nicely, so I pause here.
--
Aditya Varun Chadha
adichad AT gmail.com
http://www.adichad.com
____________________
Stephen Paul King
I must interject!
----- Original Message -----
From: "Jesse Mazer" <laser...@hotmail.com>
To: <lco...@tsoft.com>; <everyth...@eskimo.com>
Sent: Saturday, July 30, 2005 9:32 AM
Subject: RE: What We Can Know About the World
> Lee Corbin wrote:
snip
>> [LC]
>>The disagreement I have with what you have written
>>is that I do *not* see observer-moments as the most
>>fundamental entities. It's just so much *clearer*
>>to me to see them arising only after 13.7 billion
>>years or so (locally) and that they obtain *only* as
>>a result of physical processes.
> [JM]
[SPK]
It is my deep suspicion that this idea that there exists a "unique
measure" on the equivalence class (?) of "all possible finite causal
networks" is fallacious because it is equivalent to a observational P.o.V.
that instantiates the *true* state of motion/rest of a system.
For this measure to exist (in the a priori sense) then there must be an
a priori instantiation and mutual comparison of all possible finite
networks, a diffeomorphism matching. This is Barbour fallacy, the assumption
that the results of a Process can obtain independent of the implementation
of the Process.
Unless one is going to make the leap of faith that it is possible for a
computation to occur in zero time and necessitating zero resourse
consuption - the ultimate "everything from nothing" violation of
thermodynamics - this idea rapidly is seen to be absurd.
When will you guys learn the lesson of Relativity: There is no prefered
frame; there are only invariances.
>>[LC]
>>When in the laboratory we examine the concepts mice
>>have of the world, we can easily see their limitations.
>>What would we think of mice who attempted to found all
>>of reality on "mouse observer moments"?
> [JM]
> Since there is nothing specifically human about my idea of
> "observer-moments" this analogy doesn't really work.
[SPK]
Nice try, Jesse! If our idea of an Observer Moment is to be coherent at
all, there must exist OMs for *any* possible entity, including that of Mice
and Men.
Onward!
Stephen
PS, my critique is missing something but I don't have the time to correct it
now. :_(
Bruno Marchal
Le 30-juil.-05, à 17:18, Aditya Varun Chadha a écrit :
>
> I think Mazer has put this across quite nicely, so I pause here.
I agree with you and Jesse Mazer. Except that Jesse points on a
"speculation on the observer-moments", where I find enough to speculate
on the truth on the comp hypothesis which is implicitly or explicitly a
common hypothesis in both physics and cognitive science.
>
>> Since there is nothing specifically human about my idea of
>> "observer-moments" this analogy doesn't really work.
>>
>> Jesse
>
> I agree more with this version of "observer-moments". An assumption
> that an "observer" is a human or even a "biological" entity is being
> narrow-minded IMO.
OK. Many people tend to forget that rather key point.
Bruno
http://iridia.ulb.ac.be/~marchal/
Wei Dai
> No doubt this is true. But there are still two somewhat-related problems.
> One is, you can go back in time to the first replicator on earth, and
> think of its evolution over the ages as a learning process. During this
> time it learned this "intuitive physics", i.e. mathematics and logic.
> But how did it learn it? Was it a Bayesian-style process? And if so,
> what were the priors? Can a string of RNA have priors?
I'd say that biological evolution bears little resemblance to Bayesian
learning, because Bayesian learning assumes logical omniscience, whereas
evolution cannot be viewed as having much ability to make logical
deductions.
> And more abstractly, if you wanted to design a perfect learning machine,
> one that makes observations and optimally produces theories based on
> them, do you have to give it prior beliefs and expectations, including
> math and logic? Or could you somehow expect it to learn those? But to
> learn them, what would be the minimum you would have to give it?
>
> I'm trying to ask the same question in both of these formulations.
> On the one hand, we know that life did it, it created a very good (if
> perhaps not optimal) learning machine. On the other hand, it seems like
> it ought to be impossible to do that, because there is no foundation.
Suppose we create large numbers of robots with much computational power, but
random programs, and set them to compete against each other for limited
resources in a computable environment. If the initial number is sufficiently
large, we can expect that the ones that survive in the end will approximate
Bayesian reasoners with priors where actual reality has a significant
probabilty. We can further expect that the priors will mostly be UDist
because that is the simplest prior where the actual environment has a
significant probabilty. Thus we've created foundation out of none. Actual
evolution can be seen as a more efficient version of this.
Now suppose one of these suriviving robots has an interest in philosophy. We
might expect that it would notice that its learning process resembles that
of a Bayesian reasoner with UDist as prior, and therefore invent a
Schmidhuberian-style philosophy to provide self justification. I wonder if
this is what has happened in our own case as well.
Bruno Marchal
Le 30-juil.-05, à 08:53, Lee Corbin a écrit :
> When in the laboratory we examine the concepts mice
> have of the world, we can easily see their limitations.
> What would we think of mice who attempted to found all
> of reality on "mouse observer moments"?
Give them time! Mice will probably discover that reality is made of
mice observer moments the day they will bet on identifying mice with
hopefully consistent machine.
Bruno
http://iridia.ulb.ac.be/~marchal/
chris peck
Im dont know. Im in two minds now. I think my own objection to Sam Johnsons
'refutation' is based on a very strict definition of knowledge which entails
some notion of certainty. To be only 99% certain is not enough on this
definition to know something. Its a little sceptical isnt it? We lock people
away on a weaker definition that that. We dont require certainty to inhibit
someones freedom, why then in philosophy or science? Certainly the
consequences of relaxing such a definition of knowledge are only a fraction
as serious in those disciplines. Well, infact in science too we dont apply
that much rigour, theories are corroborated or not to a certain degree. They
stand or fall on pragmatic grounds. People use Newton's math in many
circumstances, whilst knowing Einstein's math reflects reality more
accurately. It doesnt matter when Newton's math are suffiecient practically
speaking.
Logically in kicking the stone SJ doesnt raise a counterargument many
rationalists are going to worry about, but he does make a powerful appeal to
our intuition that ought to have worried an empiricist like Berkley - any
empiricist really. The very fact he invokes a God (unempirically) leads one
to argue why such an inference is permissable, but the inference of a
genuinely extended world is not. They both serve the same purpose, to
maintain the existance of things when unpercieved.
Beyond the impressive and dazzling display of mathematics here and beyond
Berkley's almost pathological suspicion of perceptual inference, any theory
that denies extension is deeply unintuitive. Clearly the onus is on
Idealists - of whatever ilk - to present an explanation of non - extended
extension that makes some sense, rather than just make the mind boggle. It
does feel sometimes as though Idealists are sophists tinkering with logic
more than reality - how things could have been, rather than are.
Why, I feel like asking, would the cause of my perceptions be so different
from the picture of the world effected? Doesnt it make more sense to say
that the world appears extended, material and not 'ideal' because that is in
fact how it is, there must be a symmetry between what is percieved and what
causes those perceptions even if we can not probe that symmetry to any
satisfaction. Im not sure that a reaist would be happy by transcendental
argument like that, but it makes a little sense to me.
Perhaps there is something in Sam Johnson's quip afterall.
Many Regards
Chris.
>From: "Lee Corbin" <lco...@tsoft.com>
>Reply-To: <lco...@tsoft.com>
>To: "EverythingList" <everyth...@eskimo.com>
>Subject: RE: What We Can Know About the World
_________________________________________________________________
Lee Corbin
> At the risk of barging in once again,
Oh, please forget about all that! No one should apologize for it. Ever.
I (Lee) had written
> > When in the laboratory we examine the concepts mice
> > have of the world, we can easily see their limitations.
> > What would we think of mice who attempted to found all
> > of reality on "mouse observer moments"?
and Jesse wrote
> Since there is nothing specifically human about my idea of
> "observer-moments" this analogy doesn't really work.
I meant only to say that it's obvious how limited the ideas
of biological machines can be, *especially* when they consult
their subjective ideas.
Aditya continues
> I agree more with this version of "observer-moments". An assumption
> that an "observer" is a human or even a "biological" entity is being
> narrow-minded IMO.
Quite right.
> I think a common error that we make is to assume some vague concept of
> "consciousness" and then limit our notion of observation as a process
> that only "conscious" entities can undertake/undergo.
That sounds so sensible.
> We only believe we are conscious, we have no "proof" or "physical
> evidence", because ALL our thought-systems ASSUME consciousness, it is
> just a human axiom. Or taken another way, conscious is a human-made
> word representing just the way we (and our "close relatives" for the
> relatively liberal) work. Nothing special about it.
I *think* that that has to be right.
> Why not allow "observation" to be any event in which any set of
> entities (even the most "fundamental" entities) interact among each
> other in any way? After all, human observation can be explained as the
> "physical" interactions of our senses/brain with "other" entities.
> (i.e. just events)
>
> Notice that this "definition" (or description, for the
> "definition"-averse) cuts through a WHOLE lot of assumptions,
> ultimately revealing (at least to me) the IDENTITY (sameness) of the
> terms "Event" and "Observer-Moment".
I suspect that we will be driven to accept this just as you
have written it.
> Further, no version of "Observation" adopted by any Idealists violates
> this definition. Also, the converse is not hard to accept if we are
> just a bit more open minded (doing away with the "speciality" of human
> thought).
Well, taken literally your statement cannot be correct. There
will be versions of the concept "Observation" that will be
adopted by some idealists that indeed violate your definition.
> In the system that emerges, yes, Observer-Moments alone ARE a
> candidate for giving us a ToE, but for this, they cannot be
> differentiated from our simple notion of "Event". (The realist
> favours the term Event, the Idealist favours Observer-Moment)
By "event" do you mean an event that leaves a record? Just
wondering. Meanwhile, yes: if we have observer moments,
and mice have observer moments, then so will ants and even
thermometers. (A thermometer observes the temperature and
its mercury expands or contracts accordingly.)
Thanks for a nice try at clearing up what Jesse, at least,
and I were discussing.
Lee
Lee Corbin
> Im dont know. Im in two minds now. I think my own objection to Sam Johnsons
> 'refutation' is based on a very strict definition of knowledge which entails
> some notion of certainty. To be only 99% certain is not enough on this
> definition to know something. Its a little sceptical isnt it? We lock people
> away on a weaker definition that that. We dont require certainty to inhibit
> someones freedom, why then in philosophy or science?
*Certainty* is a bug-a-boo. It is a great and dreadful siren call
that must be ignored. Certainty does not exist. All our claims
are only conjectural. While it may be argued that for each of
us Descartes' "I think therefore I am" is pretty certain, it
just doesn't carry much information and is kind of useless.
Have you studied any PCR? That is, "Pan-Critical Rationalism"?
A number of us here would highly recommend it. It really seems
to be the best overall philosophy. It's powered by the single
most powerful idea in science, evolution.
> Beyond the impressive and dazzling display of mathematics here and beyond
> Berkley's almost pathological suspicion of perceptual inference, any theory
> that denies extension is deeply unintuitive. Clearly the onus is on
> Idealists - of whatever ilk - to present an explanation of non - extended
> extension that makes some sense, rather than just make the mind boggle. It
> does feel sometimes as though Idealists are sophists tinkering with logic
> more than reality - how things could have been, rather than are.
Well, that's how it *feels* to me too. Unfortunately, if things could
be *proven*, then either the realists or the idealists would have given
up centuries ago. Sure, sometimes the advocates in one camp or the other
really are ignorant, or you can show that there are some facts that as
individuals they've really not taken into account in their thinking.
But abandon all hope that any philosophical movement can be shown to
be incorrect.
This is not to say that progress is impossible. Consider an idea
like Aditya has: what is the real difference between an event
and an observer-moment? In trying to answer that question, many
of us may learn something (at least for our own purposes).
> Why, I feel like asking, would the cause of my perceptions be so different
> from the picture of the world effected?
I guess you mean "what could cause my perceptions that would
be different from the picture of the world influenced or affected?".
> Doesnt it make more sense to say that the world appears extended,
> material and not 'ideal' because that is in fact how it is, there
> must be a symmetry between what is perceived and what causes those
> perceptions even if we can not probe that symmetry to any
> satisfaction?
Yeah, I'd say so. "The *fact* that the world is material" is
a wonderful first approximation, and I heartily endorse it.
Of course, Eternal Truth #2 intercedes ("every statement must
be further modified") and so it has to be qualified.
First, it's not a fact, really. We're best off to *regard*
it as a fact, of course, for many reasons (chiefly because
you don't go to jail when you fail to pay your bills, etc.).
But it could be that we're just processes within some
unimaginable substrate. E.g., we could be computer
simulations. But I expect you know all this.
Second, it's so *close* to being a fact, given our theories
of physics, that every other alternative I know of pales
into improbable (but not impossible) insignificance. Even
if we were a computer simulation, for example, chances are
very good that MWI is true, and that sometime somewhen
there really was a good old Milky Way galaxy with versions
of us in it.
> Im not sure that a realist would be happy by transcendental
> argument like that, but it makes a little sense to me.
>
> Perhaps there is something in Sam Johnson's quip afterall.
Well, *this* realist finds it palatable, (if it turns out that
it's really right to call me a realist, I guess it is).
Lee
Aditya Varun Chadha
A simple question that just opened up SO many things in my mind!
(maybe a few screws too:-) ) Blabber on I shall!
[LC]:
> By "event" do you mean an event that leaves a record? Just
> wondering.
"leaves a record" is the same as saying "affects/causes/interferes
with other events".
Side Note: Beware the pitfalls of visualizing this as a temporal
cause-effect relationship though, we are talking of events, which
happen in space-time, not space. Better to understand it as
"interference".
I think that if we consider an ENTIRE intricate interference-connected
web of events, we are in fact considering one equivalence class from
the partition called "multiverse". The equivalence relation creating
this partition is the "interferes with" relation. And each equivalence
class is a "universe".
Side Note: If you are following till here, then please help me a bit
with the reflexive part of the "interferes with" equivalence. How does
an event interfere with itself? I am going the base the rest of the
post on this assumption, and unfortunately I currently cannot
substantiate it.
But now this is a perfect example of something that our brain can
"define" but not model. Because from our perspective, until and unless
an event "interferes with" our universe, it is in "some other
universe" which we have no way of describing.
Therefore yes, for us the "knowable universe" at any time can only
have events that leave records in our universe, or events that form
part of our interference web.
BUT, since "coming to know" is itself only an event, it is ALWAYS
possible that even our notion of "knownable universe" is incomplete.
This is because we ALWAYS have the potential to be "unlucky enough" to
not "feel" some interference from an event that we currently believe
is in "some other universe" and therefore "unknowable". It is just a
matter of not being in the right place at the right time.
So although I cannot say for sure whether there even exist events that
"do not leave a record", but if they do exist, then they are
unknowable. By their very definition they do not "affect" us in ANY
way, and therefore can be ignored in a ToE. But the problem is, we
have NO way of knowing that an event SURELY does NOT leave a record!
Having said this, the universe seems to be at BEST only recursively
enumerable to us, not recursive. Because while we CAN observe what's
INSIDE it, we have NO way of saying what's OUTSIDE (yet INSIDE the
"multiverse"). So my concluding claim is this: We may some day have a
ToE that is in fact Consistent and Complete (finally TRUE), but we
will NEVER be sure that it is so.
[LC]
> Thanks for a nice try at clearing up what Jesse, at least,
> and I were discussing.
Maybe now I have managed to complicate things again:-)
--
Aditya Varun Chadha
adichad AT gmail.com
http://www.adichad.com
________________________________
Russell Standish
>
> This is not to say that progress is impossible. Consider an idea
> like Aditya has: what is the real difference between an event
> and an observer-moment? In trying to answer that question, many
> of us may learn something (at least for our own purposes).
>
Err, an event is a particular set of coordinates (t,x,y,z) in 4D
spacetime. This is how it is used in GR, anyway.
An observer moment is a set of constraints, or equivalently
information known about the world (obviously at a moment of time). It
corresponds the the "state" vector \psi of quantum mechanics.
Perhaps you have different definitions of these terms, but it seems
like chalk and cheese to me.
Cheers
--
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Aditya Varun Chadha
On 7/31/05, Russell Standish <r.sta...@unsw.edu.au> wrote:
> On Sat, Jul 30, 2005 at 12:25:48PM -0700, Lee Corbin wrote:
> >
> > This is not to say that progress is impossible. Consider an idea
> > like Aditya has: what is the real difference between an event
> > and an observer-moment? In trying to answer that question, many
> > of us may learn something (at least for our own purposes).
> >
>
> Err, an event is a particular set of coordinates (t,x,y,z) in 4D
> spacetime. This is how it is used in GR, anyway.
>
> An observer moment is a set of constraints, or equivalently
> information known about the world (obviously at a moment of time). It
> corresponds the the "state" vector \psi of quantum mechanics.
>
> Perhaps you have different definitions of these terms, but it seems
> like chalk and cheese to me.
>
Lets not constrain an "event" to mean something only in 4-space. Take
any N-Space and you can define it in terms of a set of N-dim. events.
Ofcourse I agree with your definition, am just making it scale over
dimensions.
Now consider an "observer moment" to be exactly what you are defining
it to be: information KNOWN about the world at a moment of time. The
"coming to know" of any information corresponds to an "event". Thus an
"observer moment" is well-defined if and only if "event" is defined.
In other words, an Observer-Moment exists iff it's corresponding
"coming to know" event exists for "some" observer. In terms of light
cones, OMs are the Events at and "after" the crossing over of light
cones.
I think the distinction is not a qualitative one between the two, only
those events which interfere with the set of events "observable" by
"us" (who are also just sets of events) correspond to
"observer-moments" in "our universe". So the set of OMs is simply a
subset of the set of all events.
refer to my previous mail about the multiverse as a partition with
equivalence classes which are maximal sets of connected "observer
moments", in other words, maximal sets of "mutually interfering
events". visualize this as connected components of a graph.
Defining entities in more than one different sets of words does not
rule out their qualitative identity. Every Observer-Moment is an
event. Every event is an Observer-Moment in some universe.
Hal Finney
> as I said, my idea is
> that *all* possible causal patterns qualify as "observer-moments", not just
> complex ones like ours. And I don't disagree that complex observer-moments
> are generally the result of a long process of evolution in the physical
> universe, it's just that I think at a most fundamental level the "physical
> universe" would be reducible to an enormous pattern of causal relationships
> which can be broken down into the relationships between a lot of
> sub-patterns, each of which is an observer-moment. The idea that physics
> should ultimately be explainable in terms of nothing more than causal
> relationships between events, and that higher-order concepts like
> "particles" and "spacetime" would emerge from this level of explanation, is
> an idea that some approaches to quantum gravity seem to favor, like loop
> quantum gravity--it's at least not out of the question that a final
> "physical" ToE would be about nothing more than causal relationships between
> events. If so, it would just be a different "interpretation" of this theory
> to say that each sub-network in this universal causal network would be an
> observer-moment of some kind, and my "meta-physical" speculation would be
> that you could *start* by looking at all possible finite causal networks and
> finding a unique measure on them, and the appearance of the huge causal
> network we call the "physical universe" could be derived from the
> relationships between all the sub-patterns implied by this unique measure.
This is a very interesting speculation which raises some random questions
and comments:
1. One problem I have is with the notion of causality. Do you view this as
something that is well defined, the degree and/or kind of causality that
one node in a causal network applies to another? Would it be merely a
boolean (node A either does or does not have a causal influence on node
B) or would it be more complex (node A promotes B while inhibiting C)?
I realize that these are detailed questions to be asked of an embryonic
theory but it would help to understand what your notion of causality is.
One of my concerns is that some universes may not have causality as well
defined as ours does, and I wonder how well your theory would work there.
In fact, even in our universe one can certainly imagine situations and
relationships between events where the existence or degree of causality
is not at all well defined. I'm worried about basing a model for
consciousness on something as abstract and ill defined as causality.
Are we replacing one mystery with another?
2. If we think of the "causal pattern" which corresponds to a conventional
observer-moment, say your experience of eating a particular bite of cherry
pie, would you imagine that this is something which could in principle
be diagrammed, and/or represented in some kind of canonical form?
So we could point to this picture and say, this *is* that particular
experience of eating that byte of cherry pie. That would be pretty
cool, and I do think that ultimately any theory of consciousness is
going to have to be able to do something like this.
3. Presumably the actual causal patterns of our conscious moments are
very large. We have trillions of neurons each with tens of thousands
of synapses, firing at hundreds or thousands of times per second.
That's a lot of activity, all of it intricately linked into what might
well be called a causal network, although the "causality" involved is
quite complex and involves integration over time. But assuming that we
could in fact imagine representing that in canonical form, clearly the
representation would be very large.
We could imagine successively simpler "causal patterns" until we got
down to quite trivial ones. Calling them "observer moments" seems to
be a bit of a stretch, given the enormous number of orders of magnitude
difference between what we would normally recognize as a conscious OM and
one of these trivial ones. But on the other hand I agree that we could
probably not draw a line in this succession of causal patterns and say
this half are conscious, this half are unconscious. Presumably we are
talking about shades of gray here, degrees of consciousness. It never
completely goes away, although it certainly gets close enough to zero
for all practical purposes.
4. Another point is that for a "causal pattern" to actually be
recognizably conscious requires more than complexity. One can imagine
any number of causal networks of perhaps tremendous complexity that would
not seem particularly likely to correspond to what we would recognize
as conscious experience. (In terms of the "shades of gray" analogy,
even though the networks are at least slightly conscious by definition,
there would still be virtually no "gray" there.)
5. To me, this points to the problem with panpsychism theories like this.
On the one hand, everything is conscious (at least a little bit).
This saves us from the Sorites paradox, that it's impossible to draw a
line among shades of gray and try to separate white from black. But on
the other hand, in practice only brains are noticeably conscious (and
probably only big brains; the nematode with its 302 neurons can't have
much consciousness). Even though our stomachs and earlobes are causal
networks and have their little slivers of consciousness, only our brains
manage to really count. It just seems strange that if consciousness is,
in the metaphysical sense, so easy that it's omnipresent, then why do
so few systems actually exhibit it?
Hal Finney
Stephen Paul King
A possibly related question. Given your definition of events and OMs,
does it not seem that they complement each other, assuming that events have
more quatities associated, such as 4-momentum-energy?
Onward!
Stephen
Saibal Mitra
Observers are defined by the programs that generate them. If we identify
universes with programs then observers are just embedded universes. An
observer moment is just a qualia experienced by the observer, which is just
an event in the observer's universe.
I don't think that Hal's idea of identifying brain patterns with OMs will be
successful. The brain is just the hardware that runs a program (the
observer). If I run a simulation of our solar system on a computer, then the
relevant events are e.g. that Jupiter is in such and such a position. This
is associated with the state of the transistors of the computer running the
program. But that same pattern could arise in a completely different
calculation. You would have to extract exactly what program is running on
the machine to be able to define OMs like that. To do that you need to feed
the program with different kinds of input and study the output, otherwise
you'll fall prey to the famous ''clock paradox'' (you can map the time
evolution of a clock to that of any object, including brains).
Saibal
Stephen Paul King
Let me add a question to your insightful post. Could we consider the
"hardware: itself to be a simulation as well?
Onward!
Stephen
Hal Finney
> I agree with the notion of OMs as events in some suitably chosen space.
> Observers are defined by the programs that generate them. If we identify
> universes with programs then observers are just embedded universes. An
> observer moment is just a qualia experienced by the observer, which is just
> an event in the observer's universe.
I can agree with the thrust of this, but let me break it down a bit.
I agree that, "Observers are defined by the programs that generate them."
One complication is that any output, including an observer, may be
produced by multiple programs, which leads to Bruno's first-person
indeterminacy. But that's not important here.
I pretty much agree that, "If we identify universes with programs then
observers are just embedded universes." However I think the terminology
is being stretched quite a bit here, calling observers embedded universes.
What I would say is, programs produce every possible kind of information
structure. We could call all of these structures "universes", although
the word is going to be more applicable in some cases than others.
For example, there is a program which outputs the sequence of integers.
Is that sequence a "universe"? It's a stretch, but okay, we can call
it that.
But there are also programs which output the dynamic information patterns
that recognizably correspond to observers. The structure of such programs
is a key part of the "book" which Lee Corbin suggests I have been in
effect writing. If we stick to the definition that all outputs are
(in some sense) "universes" then yes, I agree with your statement that
observers can be thought of as embedded universes.
Actually I'm not sure I fully agree about the "embedded" part. I'm not
sure what you mean by that. Maybe you mean that the observer (whom we
have defined as a universe) is himself embedded in a larger universe,
the world we see around us. I agree that this will often be the case.
"An observer moment is just a qualia experienced by the observer,
which is just an event in the observer's universe." I think I see what
you're saying here. If we focus on the observer as a "universe" we can
think of him as being sort of self-contained. Yes, in practice he is
probably embedded in a larger world, but we can restrict our attention
to the observer himself, as an abstract process that is going through
a sequence of states. These momentary states are what you are calling
the "events" of the observer "universe", and these would correspond
to observer-moments.
In our space-time we have a notion of "events" as the four dimensional
points out of which space-time is built. But you are saying that the
internal structure of an observer as a sort of self-contained universe is
not really four-dimensional. Maybe it's trillion-dimensional. It is an
abstract structure which, while embedded in our space-time, exists on its
own terms with its own internal data representation. You are defining
"events" within that data structure, that self-contained universe.
They don't have a direct correspondence with four dimensional space-time
events in the larger universe that the observer is embedded in.
This reminds me of Jesse Mazer's conjecture about consciousness as a
causal pattern. I asked whether he could imagine an abstract causal
network as capturing the essence of a given moment of consciousness.
I could see that concept as being closely related to your idea of the
observer as a universe, embedded in a larger structure. However I may
be merely projecting both of your ideas into my own framework.
> I don't think that Hal's idea of identifying brain patterns with OMs will be
> successful. The brain is just the hardware that runs a program (the
> observer).
I don't think we necessarily disagree about this. In
http://www.escribe.com/science/theory/m7453.html I wrote:
"To apply this concept to observers, we first need to think of an observer
as an information pattern. I adopt a block universe perspective and think
of time as a dimension. Then we can see the dynamic activity that is
part of an observer's thinking as producing a pattern in space and time."
So I have an observer as being a *dynamic* pattern in space and time.
It is not just the hardware, it is the temporal pattern of activation of
the neural network. I then went into painstaking albeit crude detail in
the rest of that message to try to estimate just how much information
it would take to capture a certain number of seconds of firing of the
neural network. Again, this is a pattern of activity, a series of
related events, not just a static snapshot.
I also discussed in detail in that message how an observer as a self
contained information pattern could be considered to be embedded in a
larger universe, and how that would affect the measure of the observer.
That seems very much like your conception above, if I understood it
correctly.
> If I run a simulation of our solar system on a computer, then the
> relevant events are e.g. that Jupiter is in such and such a position. This
> is associated with the state of the transistors of the computer running the
> program. But that same pattern could arise in a completely different
> calculation. You would have to extract exactly what program is running on
> the machine to be able to define OMs like that. To do that you need to feed
> the program with different kinds of input and study the output, otherwise
> you'll fall prey to the famous ''clock paradox'' (you can map the time
> evolution of a clock to that of any object, including brains).
I'm not sure I fully understand this, but I'll make two comments. First,
a simulation of the solar system is vastly simpler than the calculation
needed to create an observer. Intuitions based on the first case will
fail when applied to the other. It may be plausible that two different
calculations could create matching representations of Jupiter's orbit.
But it's completely implausible that two calculations could accidentally
both create the same sequence of observer moments. I estimated in the
message above that the chance of that happening would be one in 2^(10^18).
No human alive can even begin to grasp the impossibility of such an event.
Think of the most absolutely, totally, completely impossible event you
could ever imagine, and you won't be anywhere near as improbable as that.
It is beyond human comprehension.
Second, this clock paradox has been discussed before. Years ago Jacques
Mallah on this list pointed out that algorithmic complexity disposes of
it neatly. Sure, you can map any two calculations together, but if the
map becomes bigger than the calculations, then all the correspondence
is in the map and none in the calculations.
In measure terms, it still comes down to how short a program you can
write to produce the output that corresponds to an observer. Go ahead
and write your clock or counter program, but its output does not match my
canonical representation of an observer moment. The challenge is to write
a translation program that turns the output of your clock into the OM's
canonical representation (which is 10^18 bits in size!). Such a program
is going to be as big as the OM data itself. The clock is of no help.
On the other hand consider a program which (we would agree) really
does output or create the observer-moment, but perhaps not in the nice
canonical representation I might have defined. Then we can write
a mapping program which will be relatively short, to turn one data
representation into another. Even though we have 10^18 bits of data,
the mapping program will still be much smaller than this, because its
complexity does not depend on the size of the data to be translated.
This shows that the program really did create the observer-moment, because
there was little extra data in the map program. The correspondence was
in the calculation, not in the map.
With such large data sets as observer-moments, the point becomes
very clear. There is effectively no ambiguity about whether a given
calculation instantiates an OM or not. Clocks don't do it; neural network
simulations can do it (with proper input); universe simulations can do it
(using a subset of their output).
Hal Finney
Lee Corbin
> I agree with the notion of OMs as events in some suitably chosen space.
> Observers are defined by the programs that generate them. If we identify
> universes with programs then observers are just embedded universes. An
> observer moment is just a qualia experienced by the observer, which is just
> an event in the observer's universe.
Is there a possible confusion here on the one hand between
"event" as a witnessed event by extensive systems like observers,
and on the other hand event as used in, say, spacetime physics?
("Observers" are *usually* taken to be rather complex systems.)
One interpretation of what Aditya was saying (and which I know Stephen
sometimes entertains) is that every film in a camera, or even anything
whatsoever on which a record can be made could be thought of as an
observer. That is---perhaps---anything that can be influenced at all.
So I'm not sure what you mean by "observer". Could you put some limits
on it?
Lee
Quentin Anciaux
Le Dimanche 31 Juillet 2005 19:06, Hal Finney a écrit :
> SNIP
>
> This shows that the program really did create the observer-moment, because
> there was little extra data in the map program. The correspondence was
> in the calculation, not in the map.
In all of these discussion, it is really this point that annoy me... What is
the calculation ? Is it a physical process ? Obviously a calculation need
time... what is the difference between an abstract calculation (ie: one which
is done on a sheet of paper or just in your head) with an "effective"
calculation ? What is the meaning of "instantiating" in a block universe
view ?
Quentin
John M
since I missed hundreds of posts in this list - now
extremely proliferous and sweeping through "subjects"
making backtracking a bore,
do we have an agreement on
WHAT do we call an EVENT? Also: To OBSERVE?
In my lay common sense I am inclined to call a step in
a change an event, and the acknowledgment (absorption
acceptance, incorporation) of information an
observation - by anything, photon, universe or G. B.
Shaw.
In such semantics an OM may be a qualifier in events.
Not the event proper.
I know this is splittin hair, but we may fix what we
are talking about. Just to keep our sanity.
Best regards
John Mikes
Lee Corbin
> An event is a particular set of coordinates (t,x,y,z) in 4D
> spacetime. This is how it is used in GR, anyway.
>
> An observer moment is a set of constraints, or equivalently
> information known about the world (obviously at a moment of time).
> It [the observer moment] corresponds the the "state" vector \psi
> of quantum mechanics.
and Stephen inquires
> Hi Russell,
> A possibly related question. Given your definition of events and OMs,
> does it not seem that they complement each other, assuming that events have
> more quatities associated, such as 4-momentum-energy?
Well, Russell did also say that OMs and events seemed to him about as
alike as chalk and cheese. It's starting to look that way:
I quote Hal:
Calling them [causal patterns] "observer moments" seems
to be a bit of a stretch, given the enormous number of
orders of magnitude difference between what we would
normally recognize as a conscious OM and one of these
trivial ones [e.g. a 302-neuron nematode OM].
So, alas, it seems that the firmly established meanings of
"event" and "observer moment" can't really be said to be at
all the same thing. (Folks like Russell and Hal have been
using the term "OM" for years and years, and "event" has
a pretty standard meaning in physics.) Observer moments have
to do with something conscious (and, evidently, pretty complex).
And of course, as Hal wrote later on, consciousness exists on
a gray scale.
Lee
P.S. In normal physics an event, as Russell says, is associated
with coordinates. Nonetheless I, for one, had always supposed
that indeed something was happening there, e.g., a photon was
emitted. Well, in familiar physics we may also say that in the
usual three-space there is quantum activity at each point. This,
at least for me, makes the terms a little more meaningful.
John M
I believe if we are up to identifying concepts with
common sense content as well, we should not restrict
ourselves into the model-distinctions of (any) physics
but generalize the meanings beyond such restrictions.
Of course: I am no physicist. My apologies.
To Russel's 4 coordinates of (any?) event: how come
the occurrence (event!) of a 'good idea' in my mind -
(mind: not a thing, not a place, not time-restricted)
should have t,x,y,z coordinates?
Naively yours
John Mikes
--- Lee Corbin <lco...@tsoft.com> wrote:
Lee Corbin
> [Lee writes]
> > [Jesse wrote]
> > > Sure, but all of this is compatible with an idealist philosophy where
> > > reality is made up of nothing but observer-moments at the most
> > > fundamental level--something like the "naturalistic panpsychism"
> > > discussed on that webpage I mentioned.
> >
> > The disagreement I have with what you have written
> > is that I do *not* see observer-moments as the most
> > fundamental entities.
>
> There are two distinct kinds of "fundamental". OMs may be epistemologically
> fundamental, but not ontologically fundamental.
We'll see about that! :-)
> Starting with what we think we know, we develop a model
> of reality which goes beyond what we directly experience.
> It's the best explanation of our experience that
> there is a reality not dependent on our thoughts.
I can't argue with that. Yes, indeed, whether individually
as we develop from childhood, or historically, as we develop
away from primitive concepts, (but NOT philologically, as we
develop from early life forms), we fashion all these complicated
explanations of what lies beyond what we directly experience,
e.g., other parts of the light spectrum.
Key is the fantastic accuracy of these models. Fifteen or
more decimal places of accuracy! Let us never forget this!
But I'd suggest that even the stance of a tiger is that of
an explorer who's ready to learn about some aspect of his
environment which has so far escaped him (like lunch). So
the tiger too in a sense understands that there is a reality
not dependent on his thoughts.
I would say that *epistemologically* fundamental are the
usual objects of childhood, which we still regard as
primary most of each day. You know there's a keyboard
in front of you, and about other practical realities
that do not permit you to post all day long on the
Everything list.
Lee
> > It's just so much *clearer* to me to see them arising
> > only after 13.7 billion years or so (locally) and that\
> > they obtain *only* as a result of physical processes.
>
> That seems to be the most parsimonious explanation.
>
> Brent Meeker
Russell Standish
relationship (note: mathematical term employed here) between observer
moment and event, appropriately defined, however it is unclear how one
might adjust the definitions I gave to illuminate such a duality.
Cheers
On Sun, Jul 31, 2005 at 10:44:17AM -0400, Stephen Paul King wrote:
> Hi Russel,
>
> A possibly related question. Given your definition of events and OMs,
> does it not seem that they complement each other, assuming that events have
> more quatities associated, such as 4-momentum-energy?
>
> Onward!
>
> Stephen
>
--
Russell Standish
> I salute Lee's new subject designation.
>
> I believe if we are up to identifying concepts with
> common sense content as well, we should not restrict
> ourselves into the model-distinctions of (any) physics
> but generalize the meanings beyond such restrictions.
> Of course: I am no physicist. My apologies.
>
> To Russel's 4 coordinates of (any?) event: how come
> the occurrence (event!) of a 'good idea' in my mind -
> (mind: not a thing, not a place, not time-restricted)
> should have t,x,y,z coordinates?
>
> Naively yours
>
> John Mikes
>
I would say that the event occurs in your brain (the neural correlate
of whatever is going on in your mind). Whatever is going on in your
mind is something else - an "observation" perhaps.
I'm only pointing to my understanding of these terms - I'm willing to
change terminology if its useful to do so.
Lee Corbin
> John M. wrote
>
> > I believe if we are up to identifying concepts with
> > common sense content as well, we should not restrict
> > ourselves into the model-distinctions of (any) physics
> > but generalize the meanings beyond such restrictions.
I agree: that is, so long as we can smoothly extend the
concepts from daily life without conflict with other areas
of knowledge.
> > To Russell's 4 coordinates of (any?) event: how come
> > the occurrence (event!) of a 'good idea' in my mind -
> > (mind: not a thing, not a place, not time-restricted)
> > should have t,x,y,z coordinates?
>
> I would say that the event occurs in your brain (the neural correlate
> of whatever is going on in your mind). Whatever is going on in your
> mind is something else - an "observation" perhaps.
Interesting note about "mind": there is no German language
equivalent for it. Another reason to be *very* careful when
employing it. <Sarcastic comment about the possibility of
Teutonic zombies elided.>
In a very deep (but non-mathematical) book, "What is Thought?"
by Eric Baum, the author decides to use "mind" as the name of
the program the brain runs, and it seems to work out well.
Lee
Russell Standish
>
> Interesting note about "mind": there is no German language
> equivalent for it. Another reason to be *very* careful when
> employing it. <Sarcastic comment about the possibility of
> Teutonic zombies elided.>
>
I am surprised about that! The word "der Geist" sprang immediately to
mind as the translation.
According to my German/English disctionary, the relevant words were:
die Seele (psychology)
der Geist (intellect)
das Gemuet (feelings)
das? Lust (desire/inclination) (bsp ich habe Lust zu es machen)
So Geist or Seele would in fact be the closest translations to how I
used mind above. Similarly in French, the word esprit would be
used. In English, these two words have become corrupted to Ghost and
Spirit, meaning much the same thing as each in English, but somewhat
different to the original language meanings. In Seele becomes Soul in English.
cha...@bigpond.net.au
>Interesting note about "mind": there is no German language
>equivalent for it. Another reason to be *very* careful when
>employing it. <Sarcastic comment about the possibility of
>Teutonic zombies elided.>
>
>by Eric Baum, the author decides to use "mind" as the name of
>the program the brain runs, and it seems to work out well.
>
>Lee
What is going on? Another book is quoted and it too is right in front of me. I conclude there is a hidden web cam somewhere in my office.... I love causality. :)
As regards the book contents. I have to go through it in more detail but at first run through he makes precisely the same mistakes as all the other functionalists outlined so well in ...
Searle J. R. 1992. The rediscovery of the mind. Cambridge, Mass.: MIT Press.
Chapter 2
Once again: Baum formulates a metaphor based on a lack of imagination. The fallacy: that because our mind is so adept at constructing ontologies that therefore there is such things as 'things' in the universe. There are ways of constructing 'thought' that have no need for prescription of an ontology of any sort but where it can appear to be that way. Including Germans!
Baum cannot make any empirical predictions of brain matter. Nice read...but no progress has been made except to shoehorn the received view into the limelight.
Are we ever going to get past this?
Cheers
Colin
cha...@bigpond.net.au
>Interesting note about "mind": there is no German language
>equivalent for it. Another reason to be *very* careful when
>employing it. <Sarcastic comment about the possibility of
>Teutonic zombies elided.>
>
>In a very deep (but non-mathematical) book, "What is Thought?"
>by Eric Baum, the author decides to use "mind" as the name of
>the program the brain runs, and it seems to work out well.
>
>Lee
What is going on? Another book is quoted and it too is right in front of me. I conclude there is a hidden web cam somewhere in my office.... I love causality. :)
As regards the book contents. I have to go through it in moiré detail but at first run through he makes precisely the same mistakes as all the other functionalists outlined so well in
Searle J. R. 1992. The rediscovery of the mind. Cambridge, Mass.: MIT Press. xv, 270 p.
Once again: A metaphor based on a lack of imagination. The fallacy: that because our mind is so adept at constructing ontologies that therefore there is such things as 'things' in the universe. There are ways of constructing 'thought' that have no need for prescription of an ontology of any sort yet appears to be so. Including Germans!
Hal Finney
> In all of these discussion, it is really this point that annoy me... What is
> the calculation ? Is it a physical process ? Obviously a calculation need
> time... what is the difference between an abstract calculation (ie: one which
> is done on a sheet of paper or just in your head) with an "effective"
> calculation ? What is the meaning of "instantiating" in a block universe
> view ?
I am generally of the school that considers that calculations can be
treated as abstract or formal objects, that they can exist without a
physical computer existing to run them.
The goal is to model the universe (among other things) as such a
calculation. If we demand that a calculation exists in a universe, and
a universe is also a calculation, then we have an infinite regression.
One might postulate a God who is infinite himself and is the endpoint
of the regression, but absent such supernatural entities, the model
otherwise doesn't work.
Why model the universe as a calculation? Well, for one reason, because it
seems to work. It appears that physical law is essentially mathematical,
implying that it should be feasible in principle to construct a program
which could simulate the entire universe to any degree of accuracy.
It would seem odd, given that the universe can be a calculation, if it
weren't a calculation.
If it seems objectionable to have a calculation without a calculator,
perhaps simpler examples can support the intuition. You can imagine a
triangle without a triangulator. You can imagine a number without someone
who counts. Perhaps you can even imagine a mathematical proof without
a prover. Mathematical objects may have virtually unlimited complexity
and internal structure, and can be said to exist independently of anyone
who thinks about them or discovers them. Computations seem to fit very
comfortably into this framework.
If we allow ourselves to imagine calculations as having mathematical
reality, and further to imagine that our universe is such a calculation,
then we have unified mathematical and physical reality. There is no
longer a difference. Things which are physically real are merely a
subset of the things which are mathematically real.
If we don't take this step, we have two kinds of reality, mathematical
and physical, which makes for a more awkward (IMO) philosophical position.
However I certainly understand that all these arguments are only
persuasive and indicative and certainly do not amount to a proof.
Nevertheless it is my hope that by pursuing these ideas we can construct
testable propositions which, if verified, will add weight to the
possibility that this is the nature of reality.
Hal Finney
cha...@bigpond.net.au
Aditya Varun Chadha
> alike as chalk and cheese. It's starting to look that way:
> So, alas, it seems that the firmly established meanings of
> "event" and "observer moment" can't really be said to be at
> all the same thing. (Folks like Russell and Hal have been
> using the term "OM" for years and years, and "event" has
> a pretty standard meaning in physics.) Observer moments have
> to do with something conscious (and, evidently, pretty complex).
> And of course, as Hal wrote later on, consciousness exists on
> a gray scale.
Then dare I say that any Theory based on this "restricted" definition
of OMs (happening to observers with consciousness/intelligence
"comparable" to ours) can never be as complete as a theory based on
the much simpler (and encompassing) notion of events.
Ok, the above sounds a bit arrogant on my part, but its just that when
I think of Big things like ToEs, I am much more comfortable without
the burden of assuming that I am special in some way. If it were so,
It would either be too much of a coincidence, or some act of a God
that I can never hope to explain to myself.
I can only agree to disagree by saying that any theory that explains
consciousness in terms of something more than just "interference of
events" on a HUGE scale, is pretty much the same as explaining away
coincidents as acts of a God: that unreachable, unfathomable "entity".
John M
I would try "Vernumft" (which may as well be similarly
inaccurate for 'consciousness'). There were some
German speaking souls(!) who used it quite effectively
<G>.
I try for'mind':the mentality aspect of the living
complexity which says not much more if 'mentality'
is not properly identified. However referring to the
complexity of the 'living creatures' it points to a
function which is inseparable from the substrate it
goes together with (brain and the rest of the world).
So I would not agree with Baum as to the 'brain'
running the program for thinking, which is a tool in
the complexity 'running' in concert with the rest of
it. Also simulating menatlity from computer
expressions seems reversing the fact that in comp (AI
etc.) the computer science attempts to simulate
certain and very limited items we already discovered
from our "mind".
"Living" I use instead of "human", of course. But that
comes from my generalization trend of terms beyond our
human only pretension.
To Searle's book-title: it implies that we already
HAVE discovered what the 'mind' is. Well, we did not.
At least not to the satisfaction of the advanced
thinking community.
John M
--- "cha...@bigpond.net.au" <cha...@bigpond.net.au>
wrote:
Lee Corbin
> [LC]:
> > Well, Russell did also say that OMs and events seemed to him about as
> > alike as chalk and cheese. It's starting to look that way:
>
> > So, alas, it seems that the firmly established meanings of
> > "event" and "observer moment" can't really be said to be at
> > all the same thing. (Folks like Russell and Hal have been
> > using the term "OM" for years and years, and "event" has
> > a pretty standard meaning in physics.) Observer moments have
> > to do with something conscious (and, evidently, pretty complex).
> > And of course, as Hal wrote later on, consciousness exists on
> > a gray scale.
>
> Then dare I say that any Theory based on this "restricted" definition
> of OMs (happening to observers with consciousness/intelligence
> "comparable" to ours) can never be as complete as a theory based on
> the much simpler (and encompassing) notion of events.
I am hugely sympathetic to the point of view you are proposing, namely that theories based on OMs do have inherent weaknesses, and
are quite out of line with the progress sciences has shown historically.
Most of the proponents of OM-based theories will succumb to the temptation to resort to introspection as an investigation tool. Yes,
some will at all times keep flexibly in mind the realization that any OM explanation must be totally consistent with its dual
event-based explanation.
However, it's the eternal search for ever simpler more unifying explanation that fuels the search for a way to avoid another dualism
(so it seems to me), the idea that mathematics and physics are separate. That is, they want to derive everything about physics from
the platonic existence of mathematical patterns.
> Ok, the above sounds a bit arrogant on my part, but its just that when
> I think of Big things like ToEs, I am much more comfortable without
> the burden of assuming that I am special in some way. If it were so,
> It would either be too much of a coincidence, or some act of a God
> that I can never hope to explain to myself.
Yes, some of Wheeler's theories (e.g. an observer created universe) have this very characteristic: the observer (to me an immensely
complicated machine, a johnny-come-lately in evolution) is placed at the center and deemed fundamental. But to be fair, the
time-deniers (the math Platonists who seek everything explained by patterns) allow that all conscious, complex entities have
non-trivial OMs.
> I can only agree to disagree by saying that any theory that explains
> consciousness in terms of something more than just "interference of
> events" on a HUGE scale, is pretty much the same as explaining away
> [coincidence] as acts of a God: that unreachable, unfathomable "entity".
Yeah, well said.
Lee
John M
--- Lee Corbin <lco...@tsoft.com> wrote:
> Russell writes
>
> > John M. wrote
> >
> > > To Russell's 4 coordinates of (any?) event: how
> come
> > > the occurrence (event!) of a 'good idea' in my
> mind -
> > > (mind: not a thing, not a place, not
> time-restricted)
> > > should have t,x,y,z coordinates?
> >
[Russell?]
> > I would say that the event occurs in your brain
> (the neural correlate
> > of whatever is going on in your mind). Whatever
> is going on in your
> > mind is something else - an "observation" perhaps.
>
[JM]:
I guess whatever is observable in your brainfunctions
is not the event but its reflection. The event itself
is the 'occurrence' what you deem 'observation', while
you observe it only as it happenned.
It is quite clear as you call the brain a "neural
correlate", which makes it clear that it is not the
originating, neither executing factor, just a
correlate of such. Exactly the 'hard problem' since
Kohler's Gestalt.
I like the "correlate", it is pointing to the
inseparability of the functions as we try to decipher
them.
To the translations in Russell's other post: I take
translation = transfiguration, I read in 5 languages
and saw 'good' translations with different meanings.
Nothing beats the 'original' written in a
mother-tongue
John M
Quentin Anciaux
Le Lundi 01 Août 2005 05:32, Hal Finney a écrit :
> Quentin Anciaux writes:
> > In all of these discussion, it is really this point that annoy me... What
> > is the calculation ? Is it a physical process ? Obviously a calculation
> > need time... what is the difference between an abstract calculation (ie:
> > one which is done on a sheet of paper or just in your head) with an
> > "effective" calculation ? What is the meaning of "instantiating" in a
> > block universe view ?
>
> I am generally of the school that considers that calculations can be
> treated as abstract or formal objects, that they can exist without a
> physical computer existing to run them.
I completely agree with that... but I have problem with the word
"instantiating" in front of an abstract calculation, because if the
calculation is abtract that means the calculation just is, no need of
instantiation. On the other hand I have still problem with abstract
calculation... take for example a mathematic demonstration written on a sheet
of paper, it doesn't mean anything if there is no observer to read it and
understand it (thereby "instantiating" the calculus in his own mind), what do
you think of that ?
Quentin
Lee Corbin
> I did mention the question of whether a given calculation
> instantiated a given OM. Maybe "instantiate" is not the
> right word there. I meant to consider the question of whether
> the first calculation added to the measure of the information
> structure corresponding to the OM.
I think that both the word and the meaning are clear.
Consider the following "gentle seduction" approach. One
day instead of artificial hearts, people get---piece by
---piece, artificial brains; and let us, just for the
purpose of clarifying the above, suppose that this happens
without much protest (say in the year 2100). Of course,
*many* here do protest, but let's just imagine that it
becomes accepted anyway.
Then a lot of "people" are walking around with very complicated
programs for minds. Since they act and talk just as we do, let's
inquire as to how they would report on the above discussion.
While someone's body is undergoing repair, it may happen that
he or she can rent a replacement body. It may even happen that
for the duration of the operation, their program (i.e. what we
think of as their mind) is temporarily halted. This too would
seem unobjectionable given the original premise above that in
2100 people have artificial brains made of silicon.
Finally, instead of just being unconscious, that is, absent,
during the operation, it might be that they could download
their program into some small device that furnished only
virtual reality. This too would be equally unobjectionable,
given the aforesaid premise.
So while some very small machine somewhere was "hosting" them,
we could very well say that that particular machine was
*instantiating* them, could we not? This is how I would use
the terms. One could even go further and say that a person
could be instantiated in more than one place at a time.
After all, today we speak of your computer being able to
instantiate a program (give runtime to), while my computer
can do the same thing with a different instance of the
same program.
So the big "Everything" claim, or Schmidhuber conjecture, (or
I don't know what to call it) is that you and I are *already*
being instantiated by abstract mathematical patterns (the
UDist, for Universal Distribution). This conjecture, of course,
is hotly debated, but I think that what is being claimed
is clear. Does anyone disagree with the *clarity* of
what I have written, or can anyone have a problem with any
of the *words* I used?
(We must before anything else make sure that we are communicating.)
Lee
Bruno Marchal
Le 01-août-05, à 16:57, John M a écrit :
> Also simulating menatlity from computer
> expressions seems reversing the fact that in comp (AI
> etc.) the computer science attempts to simulate
> certain and very limited items we already discovered
> from our "mind".
Except that since Turing, Church, Godel ... we know that we don't know
what is a computer. There are no theory capable of completely
describing what they can or cannot do.
Remember I insist that comp entails we cannot even know which machine
we are, although we can bet on some substitution level in front of the
doctor (for the worst or for the best).
The discovery of computers makes us much more ignorant.
Computers will make our lives much less easy. Hopefully more funny too
but it depends in part from us (the human, here).
Kind Regards,
Bruno
http://iridia.ulb.ac.be/~marchal/
Hal Finney
> Le Lundi 01 Août 2005 05:32, Hal Finney a écrit :
> > I am generally of the school that considers that calculations can be
> > treated as abstract or formal objects, that they can exist without a
> > physical computer existing to run them.
>
> I completely agree with that... but I have problem with the word
> "instantiating" in front of an abstract calculation, because if the
> calculation is abtract that means the calculation just is, no need of
> instantiation.
I agree, and if I used that terminology then it was probably a
mistake. Looking back at the message you replied to, I did not talk of
instantiating an abstract calculation. I did mention the question of
whether a given calculation instantiated a given OM. Maybe "instantiate"
is not the right word there. I meant to consider the question of whether
the first calculation added to the measure of the information structure
corresponding to the OM. If you can find any other place where I used
the word confusingly, let me know.
> On the other hand I have still problem with abstract
> calculation... take for example a mathematic demonstration written on a sheet
> of paper, it doesn't mean anything if there is no observer to read it and
> understand it (thereby "instantiating" the calculus in his own mind), what do
> you think of that ?
I can interpret your question in two ways. One is, does a mathematical
proof written on paper has an intrinsic meaning, or is the meaning
in the mind of the reader? And the other is, do mathematical proofs
have abstract, logical/mathematical existence, in the same way that,
say, numbers or geometric figures might be said to abstractly exist?
As far as the first question, I would analyze it by asking whether someone
who did not know the language it was written in, not even recognizing
the symbols, would be able to deduce what the proof was. I believe the
answer is yes, for reasonably long proofs. There would be no ambiguity.
As a concrete way to understand this, suppose we want to ask the question,
does this string of symbols represent proof X, where X is some valid
mathematical proof. We could write a translation program which, given the
symbols, would output proof X. If the string of symbols is reasonably
long and actually does match proof X, the translation program will be
short, much shorter than the proof itself. However if the string of
symbols is not a proof of X, then the translation program will have to
be long. By the same type of argument I have used repeatedly, this gives
us a tool for evaluating whether a string has a given "meaning". If the
translation program is short, then the meaning is in the string. If the
translation program is long, then the meaning is in the translation.
I believe that this shows that it is in fact reasonably to suppose that a
complex proof written on paper does in fact have intrinsic meaning and it
is not just a matter of how it is interpreted in the mind of the reader.
In terms of the other question, whether proofs have abstract mathematical
existence just as (we suppose) integers and triangles do, again I think
that the answer is yes. Proofs are merely more complex. They have
relationships amongs their parts. They depend on an axiom system.
The implicit "causality" and "time ordering" among steps of the proof
could be represented graphically, by colored arrows leading from one
step to another. I could imagine a representation where valid proof
steps would be as apparent and obvious as the question of whether a set
of lines in a geometric figure all meet at a common point.
In short, I do think that proofs, and for that matter computations,
can be sensibly thought of as having abstract existence just like other
complex mathematical objects. Some of the constructions of set theory
are far more complex than any humanly understandable proof, yet it is
reasonable to say that sets exist in the abstract. The fact that a
proof has many parts and has complex relationships between the parts is
no obstacle to its having abstract mathematical existence.
Hal Finney