Re: measure problem
Juergen Schmidhuber
in this particular universe it's going well, thank you!
As promised, I had a look at your paper. I think
it is well written and fun to read. I've got a few comments
though, mostly on the nature of math vs computation,
and why Goedel is sexy but not an issue
when it comes to identifying possible mathematical
structures / universes / formally describable things.
I think some of the comments are serious enough to affect
the conclusions. Some come with quotes from papers in
http://www.idsia.ch/~juergen/computeruniverse.html
where several of your main issues are addressed.
Some are marked by "Serious".
I am making a cc to the everythingers, although it seems
they are mostly interested in other things now - probably
nobody is really going to read this tedious response which
became much longer than I anticipated.
1. An abstract "baggage-free" mathematical structure
does not exist any more than a "baggage-free"
computer - the particular axiomatic system you choose
is like the set of primitive instructions of the computer
you choose. Not very serious, since for general computers
and general axiomatic systems there are invariance theorems:
changing the baggage often does not change a lot, so to speak.
But it should be mentioned.
2. p 11: you say that data sampled from Gaussian random variables
is incompressible - NOT true - give short codes to probable events
(close to the mean), long codes to rare events (Huffman
coding).
3. same sentence: how to test what inflation predicts?
How to test whether the big bang seed was really random,
not pseudo-random? The second million bits of pi look
random but are not. We should search for short programs
compressing the apparent randomness:
http://www.idsia.ch/~juergen/randomness.html
4. p 15: Mathematical structure (MS)
"just exists". Is that so? Others will look at
your symbols and say they are just heaps of chalk
on a blackboard, and you need a complex,
wet pattern recognition system to interpret them.
Here's where beliefs enter...
5. p 18: "mathematical structures, formal systems and
computations are aspects of one underlying
transcendent structure whose nature we don't fully understand"
But we do! I'd say there are NO serious open problems with
your figure 5 - formal systems vs math vs computation
is a well-explored field. More about this below.
The 2000 paper (your nr 17) exploits
this understanding; it turns out the most convenient way to deal
with the measure problem is the computer science way (right
hand corner of your figure 5).
As I wrote in the 2000 paper:
http://arxiv.org/abs/quant-ph/0011122
The algorithmic approach, however, offers several conceptual
advantages: (1) It provides the appropriate framework for issues of
information-theoretic complexity traditionally ignored in pure
mathematics, and imposes natural complexity-based orderings on the
possible universes and subsets thereof. (2) It taps into a rich source
of theoretical insights on computable probability distributions
relevant for establishing priors on possible universes. Such priors are
needed for making probabilistic predictions concerning our own
particular universe. Although Tegmark suggests that ``... all
mathematical structures are a priori given equal statistical weight''
[#!Tegmark:98!#](p. 27), there is no way of assigning equal
nonvanishing probability to all (infinitely many) mathematical
structures. Hence we really need something like the complexity-based
weightings discussed in [#!Schmidhuber:97brauer!#] and especially the
paper at hand. (3) The algorithmic approach is the obvious framework
for questions of temporal complexity such as those discussed in this
paper, e.g., ``what is the most efficient way of simulating all
universes?''
6. Serious: run the sim, or just describe its program?
Are you sure you know what you want to say here?
What's the precise difference between program bitstrings
and output bitstrings? The bitstrings generated by the programs (the
descriptions) are just alternative descriptions of
the universes, possibly less compact ones. You as
an external observer may need yet another program
that translates the output bits (typically a less compressed
description) into video or something, to obtain the
description your eyes want.
Note that the 2000 paper and the 2002
journal variant don't really care for time
evolution, just for descriptions - within
the bitstrings maybe there is an observer
who thinks he knows what's time, but
to the outsider his concept of
time may be irrelevant. (Unlike the
1997 paper, the 2000/2002 papers do not focus on a
one to one mapping between physical
and computational time steps, otherwise we'd
miss all the universes where the concept
of time is irrelevant.) Here's what I wrote at the end:
"After all, algorithmic theories of the describable do
encompass everything we will ever be able to talk
and write about. Other things are simply beyond description."
7. Serious: p 18 CUH: what's your def
of computable? You mean by halting
programs? In theoretical CS there are these famous
computability hierarchies, and one should understand them
to see the relation between math and computability (also
in your figure 5):
Halting-computable is just a tiny part of
what's limit-computable, but limit-computable
still means constructively describable. This was a
major motivation of the 2000 paper, which
identified all the constructively describable
mathematical structures, i.e., those whose
descriptions can be generated by (possibly
non-halting) finite programs such that each
description prefix does not change any more
after finite time. (But you cannot predict when
it will cease to change, otherwise you could
solve the halting problem - but that's not an issue,
just like the whole Goedel stuff is fun but not at all
an issue - more on that below).
8. Serious: p 19 your cite of 13, 17 (the
97 paper and the 2000 paper) is misleading:
Yes, I do mention halting universes in the 1997 paper
(mostly because of the sexy coding theorem for
halting programs), but even then I emphasize the
importance of non-halting programs (since you'd miss
out on a lot of constructively describable
universes without them). And the
2000 paper is really driven by a few new insights
about the nature of compressibility through non-halting
programs, clarifying which universes and math structures
are constructively describable,
and which are not (and thus cannot exist even under
the most relaxed constructive perspective).
(Less relevant to what you are discussing:
in certain algorithmic TOEs computation time plays a
major role - the harder something is to compute, the smaller
its probability. This is more restrictive (and perhaps
more interesting) than the general case above
which is discussed at length. Novel
insights concerning the general case eventually
ended up in the 2002 IJFCS article
novel insights concerning
computation time in the 2002 COLT paper
http://www.idsia.ch/~juergen/speedprior.html )
9. p 19/20: careful with Goedel - inconsistent is not
the same as omega-inconsistent.
BTW, inconsistent axiomatic
systems correspond to systematic theorem provers
(programs) listing all possible theorems, halting
once the first contradiction is discovered. Desirable
alternative: this search program does not halt.
Non-halting programs can be good...
10. Serious. p 20 conclusion of C: IMO this focus on halting
computations is missing the point. Non-halting
computations are still constructive. If you want
to talk about all constructive MS / universes
you don't want to ignore universes compactly
describable by NON-halting programs! One of the main
points of the 2000 paper.
11. Serious. p 21 item 4: Goedel-undecidability:
the 2000 paper is full of Goedel-undecidable
yet limit-computable examples of mathematical structures / computable
universes. Note that you don't really need infinitely many
steps to compute any prefix of any limit-computable
universe - you can do it in finite time, you just don't
know at which point you're done! That's essentially
all Goedel & Turing say. That's why Goedel does not
pose any obstacles whatsoever when the question is:
which are the formally describable universes?
Some of those universes do allow for observers
formulating undecidable questions - so what?
As I wrote in the 1997 paper:
http://www.idsia.ch/~juergen/everything/
"Although we live in a computable universe, we occasionally chat about
incomputable things, such as the halting probability of a universal
Turing machine (which is closely related to Gödel's incompleteness
theorem). And we sometimes discuss inconsistent worlds in which, say,
time travel is possible. Talk about such worlds, however, does not
violate the consistency of the processes underlying it."
12. Serious. p 21 item 5: "even more general structures" - but you
cannot describe them constructively at all! For example,
most real numbers don't exist in the sense that you cannot describe
them formally. Even the uncountability of the entire set of real numbers
is not a formal consequence of the axioms of the real numbers
but just a matter of interpretation - the axioms do not imply
uncountability! They also have a countable model.
As I wrote in the 2000 paper:
Much of this paper highlights differences between countable and
uncountable sets. It is argued (Sections 6, 7) that things such as
uncountable time and space and incomputable probabilities actually
should not play a role in explaining the world, for lack of evidence
that they are really necessary. Some may feel tempted to counter this
line of reasoning by pointing out that for centuries physicists have
calculated with continua of real numbers, most of them incomputable.
Even quantum physicists who are ready to give up the assumption of a
continuous universe usually do take for granted the existence of
continuous probability distributions on their discrete universes, and
Stephen Hawking explicitly said: ``Although there have been suggestions
that space-time may have a discrete structure I see no reason to
abandon the continuum theories that have been so successful.'' Note,
however, that all physicists in fact have only manipulated discrete
symbols, thus generating finite, describable proofs of their results
derived from enumerable axioms. That real numbers really exist in a way
transcending the finite symbol strings used by everybody may be a
figment of imagination -- compare Brouwer's constructive mathematics
[#!Brouwer:07!#,#!Beeson:85!#] and the Löwenheim-Skolem Theorem
[#!Loewenheim:15!#,#!Skolem:19!#] which implies that any first order
theory with an uncountable model such as the real numbers also has a
countable model. As Kronecker put it: ``Die ganze Zahl schuf der liebe
Gott, alles Übrige ist Menschenwerk'' (``God created the integers, all
else is the work of man'' [#!Cajori:19!#]). Kronecker greeted with
scepticism Cantor's celebrated insight [#!Cantor:1874!#] about real
numbers, mathematical objects Kronecker believed did not even exist.
13. Serious: p 21 conclusion of D: "a mathematical object does
not exist unless it can be constructed from natural numbers in
a finite number of steps - this leads to item 3".
Careful here! Any finite thing can be computed
by a halting program, of course. But do you want
to forbid infinite descriptions whose every prefix
is limit-computable in finite time?
Then you'll lose many constructive mathematical
structures of the 2000 paper!
The most general constructive way to
handle all descriptions really is the one mentioned above:
Universe descriptions can be finite or infinite,
but their shortest descriptions have to be finite.
These shortest descriptions, however, may correspond
to NON-halting programs that compute each prefix of
the possibly infinite "unfolded" description in finite
time, such that it remains stable thereafter, although
you may never know WHEN it's converged (because
of Goedel, but that's not at all important here). Ah,
I am in a loop, repeating myself...
14. p 21 E: "no aspect of our universe is undecidable..."
This does not seem true: build a computer in our universe,
feed it with programs - it's generally undecidable by
a halting program which ones will halt - so there are undecidable
aspects of our universe. My old point: so what? This won't
destroy our universe.
15. Serious. p 22 measure of computer programs: "they depend
on the representation of structures or computations
as bitstrings, and no obvious candidate currently
exists for which rep to use". This is misleading.
The measures for different but fundamentally
equivalent computers /
programming languages / axiomatic systems are the
same save for multiplicative constants independent of
the objects to be measured, because of the invariance
theorems!
16. p 22 G: equivalence classes - measure problem:
This is why those famous coding theorems are essential.
A good coding theorem says: ok, there are many
descriptions of a particular universe, but its measure
is dominated by the probability of the shortest
programs. Coding theorems for halting programs
and certain types of non-halting ones differ a bit though.
One must carefully state one's assumptions:
which computable universe descriptions are acceptable as TOEs?
Just the halting ones? Certain types of limit-computable
ones (there are various more or less general classes)?
Then check the corresponding coding theorem
to deal with the measure problem.
17. p 23 main results: "we found it important
to define mathematical structures precisely."
well, that's a main motivation of the 2000 paper:
what precisely does it mean to be formally
describable? Answer (see above): the
constructively describable mathematical structures
(or formally describable things) are those whose
descriptions can be generated by (possibly
non-halting) finite programs such that each
description prefix does not change any more
after finite time. (I told you I am in a loop...)
18. p 23 "it is unjustified to identify
the 1-dim comp sequence with 1 dim time."
Sure - who's arguing against that?
Ok, that's much more than I wanted
to write originally. Hope it will help!
Cheers,
Juergen
http://www.idsia.ch/~juergen/computeruniverse.html
On Apr 14, 2007, at 2:49 AM, Max Tegmark wrote:
> Hi Jürgen,
>
> I hope the universe is treating you well.
> If you're looking for a new and better sleeping pill, you'll be
> pleased to know that, after 11 years of procrastination, I've finally
> finished http://arxiv.org/pdf/0704.0646. It's the sequel to that old
> Level IV multiverse paper of mine, attempting to flesh out the ideas
> and elaborate on implications. I've tried to elaborate on the many
> interesting connections with your ideas, and I'd very much appreciate
> any comments you may have - especially since you're one of the very
> few people I imagine may read it!
>
> Cheers,
> Max
> ;-)
Bruno Marchal
Le 26-avr.-07, à 16:31, Juergen Schmidhuber a écrit :
> Hi Max,
>
> in this particular universe it's going well, thank you!
>
> As promised, I had a look at your paper. I think
> it is well written and fun to read. I've got a few comments
> though, mostly on the nature of math vs computation,
> and why Goedel is sexy but not an issue
> when it comes to identifying possible mathematical
> structures / universes / formally describable things.
> I think some of the comments are serious enough to affect
> the conclusions. Some come with quotes from papers in
> http://www.idsia.ch/~juergen/computeruniverse.html
> where several of your main issues are addressed.
> Some are marked by "Serious".
>
> I am making a cc to the everythingers, although it seems
> they are mostly interested in other things now - probably
> nobody is really going to read this tedious response which
> became much longer than I anticipated.
Don't worry, we are used to some long posts in this list. I am not sure
you follow the list because the "other things" you are mentioning are
just the follow up of the search of the theory of everything, except
that since you leave the list, denying the 1-3 distinction, some years
ago, most people who continue the discussion now are aware of the
necessity to take into account that distinction between first and third
person points of view, and more generally they are aware of the mind
body problem (or of the 1-person/3-person pov relations). I think most
of them, except new beginners, have no more any trouble with the first
person indeterminacy in self-duplication experiments, etc.
I have already made this clear: the hypothesis that there is a physical
computable universe (physicalist-comp) is just untenable.
Let me recall you the reason: obviously physicalist-comp entails what
we are calling comp in this list, that is, the hypothesis that "we" are
locally emulable by a digital universal machine. I will call it
"indexical comp" to insist on the difference. So:
PHYSICALIST-COMP => INDEXICAL-COMP
Then the Universal Dovetailer Argument shows that comp entails that
the physical appearances have to be justified *exclusively* by a
self-duplication like first person (plural) indeterminacy: see the pdf:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf
The main idea is that INDEXICAL-COMP entails that we don't know which
computations support our local states, and that they are a continuum of
computational histories (computations + possible "real" oracles) going
through those states. It can be argued that the first person "physical"
appearances does emerge from a "sum" on all those computational
histories, but only *as seen from those 1-person views*. But this
entails that "apparent physical universe" are not necessarily
computable objects. Actually, indexical comp entails it exists
"exploitable" internal indeterminacies. A priori:
INDEXICAL-COMP entails NOT PHYSICALIST-COMP.
It gives to physics a more key role than in Tegmark's idea that the
physical universe is a mathematical structure of a certain type. Comp
(indexical comp) relate somehow physics to almost all mathematical
structures (in a certain sense).
This constitutes the main critic of both your approach and Tegmark's
one in the search of a TOE. You still talk like if the mind body
relation was a one-one relation, when the mind can only be associated
to infinities of states/worlds. With indexical-comp there is no obvious
notion of "belonging to an universe". This has been discussed many
times on the list with different people.
And then, once you realize the fundamental importance, assuming comp,
of keeping distinct the possible views that a machine has to have about
arithmetical or mathematical reality, and that physics emerges from one
such points of view, then it is hard not to take into account the fact
that any universal machine looking inward cannot not discover those
points of view; indeed they appear as inevitable modal or intensional
variant of the godelian provability predicate. This makes Godel's
theorems (and Lob's generalization, and then Solovay's one) key tools
for extracting physicalness from number's extensions and their (lobian)
intensions. And, and this is a major technical point, it makes this
form of comp testable, by comparing the comp-physics with the empirical
physics.
Now I have discovered that those modal variant offer a transparent
arithmetical interpretation of Plotinus hypostases. You are welcome in
Siena in June where I will present my paper "A purely Arithmetical, yet
empirically falsifiable, Interpretation of Plotinus' Theory of Matter":
http://www.amsta.leeds.ac.uk/~pmt6sbc/cie07.html
I can send you a copy of the paper later for copyright reason. You can
also consult my preceding paper:
Marchal, B., Theoretical Computer Science & the Natural Sciences,
Physics of Life Reviews, Elsevier, Vol 2/4 pp 251-289, 2005. Available
here:
http://linkinghub.elsevier.com/retrieve/pii/S1571064505000242
Max, Juergen, you are still under the Aristotelian physicalist spell,
and you are still putting the "mind-body" problem under the rug, I'm
afraid. But I am aware it is a tradition since about 1500 years, when
scientists, without much choice alas, did abandon theology to
"politicians" ...
(scientific theology = theology done with the usual doubting procedure
of the modest interrogating scientist).
Juergen, are you still denying the 1-3 distinction (like in our old
conversations)? Are you still thinking that there is no 1-first
person indeterminacy, or that such an indeterminacy has no role in the
emergence of the physical laws? Could you tell me at which step of the
UDA you are stuck? (cf the UDA version of the SANE paper, ref above).
I will asap try to explain the arithmetical version of the UDA, the one
based on Godel and which can be seen as an arithmetical interpretation
of Plotinus' main "hypostasis" (in case you prefer to read Plotinus
instead of doing the duplication thought experiment, UDA, ...).
Some people asks me to do this without too much technics and I have to
think about how to do that. I recall the UDA is already the "non
technical" (yet rigorous) argument. The interview of the machine is of
course formal and technical, and its only need (beside illustrating the
UDA) comes from the desire to *explicitly*extracts the physical from
numbers.
Bruno
PS This list, wisely unmoderated by Wei Dai, welcomes, for obvious
reason giving the hardness and originality of the subject, both
professional and non professional. By professional I just mean people
submitting theses, papers or books from time to time, even rarely. So,
don't hesitate to send us "call of paper" related with comp and or
everything-like or Everett-like TOEs. Thanks. And don't hesitate to
participate, 'course!
Brent Meeker
Exactly how do you mean "continuum"? Do you mean an uncountably infinite number (the power set of the integers)? Is it a realized infinity or a potential one?
>It can be argued that the first person "physical"
> appearances does emerge from a "sum" on all those computational
> histories, but only *as seen from those 1-person views*. But this
> entails that "apparent physical universe" are not necessarily
> computable objects. Actually, indexical comp entails it exists
> "exploitable" internal indeterminacies. A priori:
>
> INDEXICAL-COMP entails NOT PHYSICALIST-COMP.
>
> It gives to physics a more key role than in Tegmark's idea that the
> physical universe is a mathematical structure of a certain type. Comp
> (indexical comp) relate somehow physics to almost all mathematical
> structures (in a certain sense).
>
>
> This constitutes the main critic of both your approach and Tegmark's
> one in the search of a TOE. You still talk like if the mind body
> relation was a one-one relation, when the mind can only be associated
> to infinities of states/worlds. With indexical-comp there is no obvious
> notion of "belonging to an universe". This has been discussed many
> times on the list with different people.
>
>
> And then, once you realize the fundamental importance, assuming comp,
> of keeping distinct the possible views that a machine has to have about
> arithmetical or mathematical reality,
What is a machine? Am I to think of it as one of the continuum of histories corresponding to a 1st person viewpoint?
Brent Meeker
John Mikes
I look at your 'chat' with Max and Juergen with "awe": some words do sound as if representing some meaning to me, too, from my earlier accumulation of readings.
My idea about your uncertainty of the application of 'comp' (and 'physical') could be (poorly) worded in your 'logician', Max's 'physicalistic' and Juergen's '???(maybe arithmetical)?" positions, all pertaining to a comp in our so far developed human sense.
The TOE etc. questions are way beyond that, and we all want to draw conclusions on them from experience AND methodology acquired within.
'We" FORCE conclusions that are not due. The efficient 'comp', serving right the purpose sought, is 'somewhere' above the numberific etc. simplification of the features still unknown to us. Both the features and 'that' comp-quality. ((In "meaning" computation e.g.: Concept x function = idea? where x is not 'arithmetical' multiplying))
I tend to see the mind-body problem on this so far unachieved plane:
mind is (mentality of) the unlimited TOE and its vision(s), while body (the somehow limited contraption including the tool for our thinking - call it brain tissue, physical, digital comp, or - horribile dictu: arithmetical - anyway within our limited mentality) is an aspect (partial) of it. Problem: to reach the total from the limitational part - without the possession (understanding) of the missing rest of it.
This is an idea from the outskirts of your discussion, I do not vouch for it, just stated -
perhaps provides some good. If not, let it fade away.
John M
Bruno Marchal
Le 30-avr.-07, à 20:57, John Mikes a écrit :
> mind is (mentality of) the unlimited TOE and its vision(s), while body
> (the somehow limited contraption including the tool for our thinking -
> call it brain tissue, physical, digital comp, or - horribile dictu:
> arithmetical - anyway within our limited mentality) is an aspect
> (partial) of it.
I asked you this before: what do you mean by *our* in *our* limited
mentality?
Do you mean the Hungarians?
The Americans?
The Humans?
The Apes?
The Animals?
The inhabitants of Earth?
The inhabitants of the Solar System?
The inhabitants of the Milky Way galaxy? (they are so much Milky Way
Minded, you know!)
or
The sound lobian machines?
The omega-consistent lobian machines?
The consistent lobian machines?
The lobian machines?
...
The lobian entities?
... ?
> Problem: to reach the total from the limitational part - without the
> possession (understanding) of the missing rest of it.
This is exactly, if I get your point, what I think can be done about
the lobian entities, which, thanks to the mathematically describable
gap between what the machine can know and what the machine can hope for
(of fear for, bet, etc.) it is possible to get some large and testable
overview of the comp consequences for any TOEs based on the comp hyp.
Including "physical consequences".
Hope this can motivate you for the "interview" of the L machine (or L
entity), but be patient, thanks;
Best,
Bruno
John Mikes
Bruno Marchal
Le 02-mai-07, à 17:49, John Mikes a écrit :
> One wisdom above all others consists of formulating questions which by
> their wording eliminate the answers. Your question starts:
> "What do you mean by "...our..."?
> The classic reply: "Who is asking?" -- It is you and me and all "who"
> we can consider normal minds to converse with.
> *
> I try to be patient as long as I am around, but cannot take seriously
> a "LM" that 'knows' everything 'unknowable' and TELLS US all in an
> interview. It is all still in 'our' mind (imagination?) content.
> Why do you not 'extract' everything at once? Why piecemeal small
> portions of epistemic enrichment? All questions discussed on this and
> any other forum could be answered. Why are we so shy? (Maybe life
> would be intolerably boring knowing all the answers at once?)
> (I got it:
> it is the 'mathematically discernible' gap ...so is it a limitation?
Yes. But the L machine can see its own limitations. The UD Argument
explains why we have to expect physics rising from some geometry
bearing on that limitation.
> and only its 'fears', 'hopes', (=suggestions, fantasies?) we(?) in our
> feeble mind work/content can produce similar unreal ideas.)
> Is the 'mathematical' included to justify the imperfections of a LM?
Yes.
> - No, I did not really ask that.
> *
> Why did a LM not disclose 'itself' 3000 years ago?
I guess that happens. There are some relations between so-called
mystics or inward-looking truth researchers and lobian machine.
> with ALL the answers?
Certainly not.
> Why still teasing us even now? A Sadist Loebian Machine!
> Does it have 'rules' on 'how much' to disclose in an interview? Who's
> rules? the Allmighty? but that is the LM itself!
> You see, I am confused. (ha ha) good for me.
I will come back on the interview. I have to answer Mark Geddes'
question on Tegmark little three-diagram first, and this could help to
relate the interview and the search for a TOE. Indeed I have to explain
the many nuances between the notion of computability, provability,
knowability, observability, etc. All that in the arithmetical frame,
... and without being too much technical! The problem is that those
nuances *are* technical! I am using technics here because our
intuitions are misleading.
Just note this. No Lobian Machine, even sound and ultra-powerful can
ever be "Allmighty". The contrary is true: the machine is somehow
extremely modest. If you ask a sound (lobian) machine if she will ever
say a bullshit, she answers that [either she will say a bullshit or she
*might* say a bullshit]. This is a form of Godel's theorem. Lob's
theorem shows in a deeper way that the L machine is really
modesty-driven all along. The machine can also prove to herself that
the more she learns, the less she knows. Her science makes her more
ignorant, and lead her to bigger doubts, and thus also to bigger
possibilities (relatively to her most probable computational history).
Also, I use the term Lobian machine, in honor of Löb, but also as a
shorter expression for "a self-referentially correct machine having
enough beliefs in elementary arithmetic".
I remind you that in some older post you were willing to accept the
idea that either you are yourself lobian, or that you can identify a
lobian machine living in you (as far as you accept enough elementary
arithmetical truth).
Recall also I am not defending the comp hyp., I am just trying to show
that the comp hyp. has (startling) observable and thus testable
consequences (cf also both the UDA and the neoplatonists like
Plotinus).
>
> Wishing you the best
The best for you too. Hope this will help you to keep patient, thanks,
Bruno
John Mikes
.....
BM:
Yes. But the L machine can see its own limitations. The UD Argument
explains why we have to expect physics rising from some geometry
bearing on that limitation.
At the 1989(?) German Complexity Conference Rainer Zimmermann had a paper on
"Pre-Geometrical" world-origin. This instigated my idea about (MY) Plenitude, which is neither (pre?)geometrical, nor preceding a 'time' - nonexistent in it. Geometry is a consequence of spatial order, so it has to be 'invented' in a post-BigBang universe of at least spatial arrangements. In congruence with your later remark that physics stems from geometry. At least 2nd phase in my narrative. Consequence of things I am looking for.(and still predecessor to physics as you stated).
*
JM..:..
> Is the 'mathematical' included to justify the imperfections of a LM?
Yes.
JM now: that was a trap. Sorry. (see my next line that I did not 'really' ask that) -
You probably did not realize that "mathematical" was said to be 'included' into something not containing it. Or is "numbers-based" not (really) mathematical?
((See my confusion?))
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> Why did a LM not disclose 'itself' 3000 years ago?<
I guess that happens. There are some relations between so-called
mystics or inward-looking truth researchers and lobian machine.
*
JM now:
when I condoned the chance to be a LM it was not in your presently spelled out way:
(I still do not know what to understand as such) it is at the - or before - 'geometrical' level, however definitely - as you said - pre-physical. But consequential - subsequent to the level I used to the formulation of universes. Generatee, not generator.
John M
PS: Bruno, I submit my ideas to you only to show a different position - not to "beat" yours. To "round up' your theory in a discussion with a different stance.
If you find it useless, tell me: I will stop sending them. J
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