PARADISE LOST: Debunking Cantor's theory
david petry
In this article, "Cantor's theory" refers to the ideas about infinity
and infinite sets introduced into mathematics by Cantor. The claim
here is that Cantor introduced an element of make-believe into
mathematics, and we'd all be better off without it.
PHILOSOPHICAL PRINCIPLES
Our technologically advanced society needs mathematics. Ultimately,
the purpose of mathematics is to meet the needs of society. When
thinking about the foundations of mathematics, we should ask the
question of just why it is that mathematics is so useful, and then we
can define mathematics in terms of the answer to that question.
Mathematics is part of mankind's quest for truth. Truth informs us
about reality. Reality is what we observe and interact with. We all
observe and interact with the same reality, and we can come to an
agreement about what we observe and about the nature of our
interactions with reality, and that agreement is what we call "truth".
Truth necessarily has observable and testable implications. Truth is
unique. The meaning of a statement may be equated with its observable
and testable implications, and statements having no such implications
are meaningless. Mathematics is not meaningless.
DEFINITION OF MATHEMATICS
The reality underlying mathematics is computation. It's useful to
think of the computer as the mathematicians' laboratory instrument.
The computer serves as a microscope which helps mathematicians peer
deeply into the world of computation, and it serves as a test tube
which allows mathematicians to perform experiments within the world of
computation. So we can observe the world of computation, and we can
interact with it. So it's real. The world of computation is worthy of
study because phenomena observable within the world of computation can
serve as models for phenomena in the physical world.
Mathematics is the science of the phenomena observable within the
world of computation. Mathematical statements must make falsifiable
predictions about the outcomes of possible computational experiments.
If we want to assert that some object exists within the world of
computation, we must be able to say how to observe the object. All of
the mathematics that has the potential to help us understand the world
in which we live fits within the scope of that definition.
WHAT IS WRONG WITH CANTOR'S THEORY?
If we accept Cantor's theory as part of the foundation of mathematics,
then the notion of "existence" becomes meaningless. Cantor's theory
would have us believe simultaneously that the world of computation is
countable and that there "exist" uncountable sets, from which we are
supposed to be able to conclude that there "exist" mathematical
objects that are not part of the world of computation. But that last
conclusion does not inform us about the reality underlying mathematics
(i.e. the world of computation). So it can't be considered true. It's
meaningless. So if we insist that mathematics should be meaningful,
that last conclusion must not be part of mathematics, and hence,
Cantor's theory cannot be accepted as part of mathematics; a
mathematical object exists if and only if it can be observed within
the world of computation.
It should be noted that formal systems are objects that live in the
world of computation, and hence a formalization of Cantor's theory
(e.g. ZFC) is an object to be studied within mathematics. But formal
theorems within such a formal system do not correspond to mathematical
truths if they have no interpretation as making predictions about the
outcome of computational experiments.
IS INFINITY PART OF MATHEMATICS?
Infinity is not part of the underlying reality of mathematics. It is
not essential to mathematics. Infinity is an abstraction, or a useful
fiction, and when we develop a theory of the infinite, we must be able
to say exactly how it is useful. What we actually observe are finitary
approximations to infinitary objects, and we can extend the notion of
"existence" to infinitary objects by associating them with
meaningfully defined converging sequences of finitary objects (recall
that the "meaning" of a statement may be equated with its observable
implications). Then, to ensure that mathematical statements are about
truth, we must require that for any statement about an infinitary
object, there is a corresponding meaningful statement about the
objects in the underlying converging sequence of finitary
approximations. What Gauss said about infinity really was right on the
mark: infinity is merely a figure of speech we find useful when
talking about limits.
We can create a mathematically useful theory of infinite sets meeting
the requirements of the previous paragraph, but that theory won't be
Cantor's theory.
WHAT ABOUT THE DIAGONAL ARGUMENT?
If we are given a well defined list of well defined real numbers, so
that every digit of every real number on the list can be computed,
then the diagonal argument gives us a new well defined real number not
on that list. But that certainly doesn't justify the Cantorian
conclusion that there must exist mathematical objects not living
within the world of computation.
WHY IS IT IMPORTANT TO DEBUNK CANTOR'S THEORY?
Mathematics - the science of phenomena observable within the world of
computation - truly is scientific in nature. It makes testable,
falsifiable predictions. It deals with an observable reality. In
contrast, Cantor's theory is a story about a world beyond what we can
observe. It's not about reality. Cantor's theory is pseudo-scientific,
and just about any good reason we can imagine for debunking
pseudoscience in general is also a good reason for debunking Cantor's
theory; when people pursue pseudoscience, they lose touch with
reality, and when people make decisions based on pseudoscience, they
are setting themselves up for a collision with reality.
The Cantorians have taken over the mathematics community, and they've
chased out non-believers. And among those non-believers are people
with great potential as mathematicians. So the Cantorians are
depriving society of what those people have to offer, not to mention
the injustice done to those people who are excluded. There is a great
social injustice there.
Although it may sound slightly hokey, the mathematicians are setting a
bad example. People in other disciplines do look upon mathematics as a
paragon of truth and reason, and when they see that the mathematicians
are creating clever, precise and "beautiful" theories with no
connection to reality, and achieving consensus within their community
by chasing out dissenters, those people often either copy that
behavior, or become cynical about academia altogether.
The Cantorian dominance within the mathematics community is
interfering with potentially important scientific and technological
research. Or at least, it is plausible to believe that. Let's consider
the field of artificial intelligence.
The purpose of mathematics, when viewed as a science, is provide tools
that help us understand the world in which we live. So if we want
computers to understand the world in which we live, we should probably
teach them mathematics. And mathematics as the science of phenomena
observable within the world of computation, is precisely what we
should be teaching them. Since an artificial intelligence lives in a
computer, it has access to the world of computation. It can make
observations and perform experiments in the world of computation. It
can explore that world. They key to applying mathematics is to
understand what predictions it makes about computational experiments.
So if we require that mathematical statements make predictions about
the outcomes of computational experiments, then the artificial
intelligence will easily understand how to apply those statements.
>From this point of view, it is plausible to equate the foundations of
mathematics with the foundations of artificial intelligence. But
researchers in the field of artificial intelligence almost never even
consider that route to A.I. simply because the appropriate
mathematical research has not been done, and the research that has
been done in the foundations of mathematics, based on Cantor's theory
of infinite sets, is worse than useless for the field of A.I. It's
the "meaning" of mathematics (the connection between mathematics and
reality) that is especially important to an A.I. and that's what's
missing from Cantorian mathematics.
Given the enormous benefits to humanity expected to come from
artificial intelligence, it is plausible to believe that Cantor's
theory has already had a huge negative impact on society.
WHY DOES CANTOR'S THEORY PERSIST?
Almost everyone who criticizes Cantor's theory eventually points out
the similarities between Cantor's theory and religion (or mysticism).
Cantor's theory is a mythology about a more perfect world lying beyond
the world we observe. It's an escape from reality. The Cantorians even
sometimes refer to it as a paradise. It's not about truth. It's not
an agreement by all observers about the nature of reality, but rather
it's agreement among the elites about a world view to be imposed upon
a gullible community for reasons other than to benefit society as a
whole. Cantor's theory persists for the same reasons that religion and
mysticism persist.
The big lie of Cantor's theory is that mathematicians gain freedom by
giving up the requirement that mathematics be connected to reality;
the mathematicians have become slaves to a mythology.
WHERE DO WE GO FROM HERE?
If the mathematicians were to change their beliefs in response to
reason, it would probably be the first time in human history that a
religion has reformed in response to reason alone. Mathematicians will
see the need for change when people quit paying attention to them.
Throughout history, almost all of the really important ideas in
mathematics have come from outside the field, typically from
physicists and engineers. It's likely that the ideas that will reform
mathematics will also come from outside the mathematics community.
Maybe the researchers in the field of artificial intelligence will
provide the ideas that will reform the foundations of mathematics.
QUOTES
There have been lots of critics of the Cantorian world view, and there
are many prominent mathematicians among those critics. Here's what
they have to say.
"those of us who work in probability theory or any other area of
applied mathematics have a right to demand that this disease
[Cantorian set theory] be quarantined and kept out of our field" (From
"Probability Theory: The Logic of Science" by E. T. Jaynes)
"I am convinced that the platonism which underlies Cantorian set
theory is utterly unsatisfactory as a philosophy of our subject,
despite the apparent coherence of current set-theoretical conceptions
and methods ... platonism is the medieval metaphysics of mathematics;
surely we can do better" (From "Infinity in Mathematics: Is Cantor
Necessary?" by Soloman Feferman)
"Set theory is based on polite lies, things we agree on even though we
know they're not true. In some ways, the foundations of mathematics
has an air of unreality." (William P. Thurston)
"[Cantor's paradise] is a paradise of fools, and besides feels more
like hell" (Doron Zeilberger)
"...classical logic was abstracted from the mathematics of finite sets
and their subsets...Forgetful of this limited origin, one afterwards
mistook that logic for something above and prior to all mathematics,
and finally applied it, without justification, to the mathematics of
infinite sets. This is the Fall and original sin of [Cantor's] set
theory ..." (Hermann Weyl, 1946)
"I don't know what predominates in Cantor's theory - philosophy or
theology, but I am sure that there is no mathematics there" (Kronecker)
Rupert
wrote:
Which formal systems do have the property that their theorems
correspond to mathematical truths?
What problems might arise from believing that Cantor's theory
corresponds to reality?
Newberry
No, it does not. If each number is well defined then its definition is
finite. The diagonal argument will fail.
Newberry
I have desribed one here
http://xnewberry.tripod.com/Presuppositions_2007_05_19.html
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Jesse F. Hughes
> On Jun 4, 7:12 pm, Rupert <rupertmccal...@yahoo.com> wrote:
>> Which formal systems do have the property that their theorems
>> correspond to mathematical truths?
>
> I have desribed one here
> http://xnewberry.tripod.com/Presuppositions_2007_05_19.html
Right. In that system, we see that there are situations in which P is
meaningful, Q is meaningful but P v Q is literally nonsense.
How precisely is that relevant to anything in this thread? Is this
merely a preemptive strike to ensure that you get to be the reigning
sci.logic crank for another couple of weeks?
--
"Now I realize that he got away with all of that because sci.math is
not important, and the rest of the world doesn't pay attention.
Like, no one is worried about football players reading sci.math
postings!" -- James S. Harris on jock reading habits
Jesse F. Hughes
> WHAT ABOUT THE DIAGONAL ARGUMENT?
>
>
> If we are given a well defined list of well defined real numbers, so
> that every digit of every real number on the list can be computed,
> then the diagonal argument gives us a new well defined real number not
> on that list. But that certainly doesn't justify the Cantorian
> conclusion that there must exist mathematical objects not living
> within the world of computation.
Wow. Who knew that *that* was the Cantorian conclusion? Gosh, it
does seem implausible, when you put it that way. Wait, not
implausible... that other one... oh yeah, incoherent.
Freakin' incoherent Cantorians. No wonder you're always going on
about them mystical Jewish freaks.
Anyway, this latest salvo will sink that ship of fools for sure.
Congrats!
--
Jesse F. Hughes
"Maybe I screwed up on one of my assumptions [...]. Otherwise, um,
it's very easy to factor, and things are about to get really, really
weird." -- James S. Harris
Virgil
david petry <david_lawr...@yahoo.com> wrote:
> In this article, "Cantor's theory" refers to the ideas about infinity
> and infinite sets introduced into mathematics by Cantor. The claim
> here is that Cantor introduced an element of make-believe into
> mathematics, and we'd all be better off without it.
>
>
> PHILOSOPHICAL PRINCIPLES
>
>
> Our technologically advanced society needs mathematics. Ultimately,
> the purpose of mathematics is to meet the needs of society.
Such a "Big Brother" view is anathema.
> When
> thinking about the foundations of mathematics, we should ask the
> question of just why it is that mathematics is so useful
The question has often been asked and no completely satisfactory answers
have been found.
More to the point is to give thanks to whatever gods there be for
producing such concrete usefulness out of such abstract ideation, and
pray it continues.
> and then we
> can define mathematics in terms of the answer to that question.
Mathematics does not need to be "defined" by non-mathematicians, and
particularly not by anti-mathematicians.
Glen Wheeler
Please, everybody who doesn't, learn how to snip.
--
Glen
Newberry
> Newberry <newberr...@gmail.com> writes:
> > On Jun 4, 7:12 pm, Rupert <rupertmccal...@yahoo.com> wrote:
> >> Which formal systems do have the property that their theorems
> >> correspond to mathematical truths?
>
> > I have desribed one here
> >http://xnewberry.tripod.com/Presuppositions_2007_05_19.html
>
> Right. In that system, we see that there are situations in which P is
> meaningful, Q is meaningful but P v Q is literally nonsense.
>
> How precisely is that relevant to anything in this thread?
Let's make it explicit. The question was "Which formal systems do have
the property that their theorems correspond to mathematical truths?"
The system I have described does have the property that their theorems
correspond to mathematical truths. I think the relevance could not be
clearer.
Rupert
> No, it does not. If each number is well defined then its definition is
> finite. The diagonal argument will fail.
>
There does not exist a countable language such that all real numbers
have a finite definition in that language.
The World Wide Wade
david petry <david_lawr...@yahoo.com> wrote:
> Our technologically advanced society needs mathematics.
True. So what?
> Ultimately,
> the purpose of mathematics is to meet the needs of society.
Present day society depends on mathematics. Therefore the the purpose of
mathematics is to meet the needs of society. You know, there's a reason
there are two f's in iff. Think about it some time.
> The reality underlying mathematics is computation.
Stop being so ignorant.
> It's useful to
> think of the computer as the mathematicians' laboratory instrument.
You really have no idea what mathematics is, do you?
Tonico
> In this article, "Cantor's theory" refers to the ideas about infinity
> and infinite sets introduced into mathematics by Cantor. The claim
> here is that Cantor introduced an element of make-believe into
> mathematics, and we'd all be better off without it.
>
> PHILOSOPHICAL PRINCIPLES
>
> Our technologically advanced society needs mathematics. Ultimately,
> the purpose of mathematics is to meet the needs of society.
*******************************************************************
Uh??? Says who?? You?? Either you're just kidding, or else you've some
urge to forward your dogmas....a propo what you wrote later about
religion. :>)
*******************************************************************
When
> thinking about the foundations of mathematics, we should ask the
> question of just why it is that mathematics is so useful, and then we
> can define mathematics in terms of the answer to that question.
>
> Mathematics is part of mankind's quest for truth. Truth informs us
> about reality. Reality is what we observe and interact with. We all
> observe and interact with the same reality, and we can come to an
> agreement about what we observe and about the nature of our
> interactions with reality, and that agreement is what we call "truth".
> Truth necessarily has observable and testable implications. Truth is
> unique. The meaning of a statement may be equated with its observable
> and testable implications, and statements having no such implications
> are meaningless.
*******************************************************************
I bet that you, as most other anticantorian cranks, aren't even a
mathematician...:P
*******************************************************************
Mathematics is not meaningless.
>
> DEFINITION OF MATHEMATICS
>
> The reality underlying mathematics is computation.
*******************************************************************
LOOOOOL!...Yes! You are kidding!! Ok, I didn't get that straight at
first...good one!
Regards
Tonio
David L. Wilson
> david petry <david_lawr...@yahoo.com> wrote:
>> Present day society depends on mathematics. Therefore the the purpose of
> mathematics is to meet the needs of society.
Flawed logic. Rain depencs on water...so the purpose of water is rain?
Bob Kolker
>
> In this article, "Cantor's theory" refers to the ideas about infinity
> and infinite sets introduced into mathematics by Cantor. The claim
> here is that Cantor introduced an element of make-believe into
> mathematics, and we'd all be better off without it.
If we had it your way math would be only good for toting up grocery
bills and balancing our bank accounts.
Without "ideal" elements we could not show whether solutions to
differential equations existed or not (for example). Without "ideal"
elements we could not give essential topological characterization to
verious spaces used in physics. And kill differentiable manifolds
goodbye, which means no General Relativity.
Bob Kolker
Jesse F. Hughes
> On Jun 4, 8:10 pm, "Jesse F. Hughes" <j...@phiwumbda.org> wrote:
>> Newberry <newberr...@gmail.com> writes:
>> > On Jun 4, 7:12 pm, Rupert <rupertmccal...@yahoo.com> wrote:
>> >> Which formal systems do have the property that their theorems
>> >> correspond to mathematical truths?
>>
>> > I have desribed one here
>> >http://xnewberry.tripod.com/Presuppositions_2007_05_19.html
>>
>> Right. In that system, we see that there are situations in which P is
>> meaningful, Q is meaningful but P v Q is literally nonsense.
>>
>> How precisely is that relevant to anything in this thread?
>
> Let's make it explicit. The question was "Which formal systems do have
> the property that their theorems correspond to mathematical truths?"
> The system I have described does have the property that their theorems
> correspond to mathematical truths. I think the relevance could not be
> clearer.
Hey, I have a question. Can you tell me if you agree with the
following statements? Thanks.
(1) I can imagine a round triangle.
(2) I cannot imagine an equilateral round triangle.
(3) I cannot imagine a non-equilateral round triangle.
I'm sure you can see what I'm getting at. Imagining a round triangle
amounts to imagining something satisfying P & ~P, right? And you can
do that, but you have this strange incapacity to imagine P & ~P & Q.
Well, never mind. I think it's super-keen that your system's theorems
exactly correspond to logical proofs. Except, of course, you haven't
stated any axioms or rules of inference. But otherwise, kudos!
--
Jesse F. Hughes
"I, like, cry, when I listen to it, it's so good."
-- Paris Hilton on her new album
Jesse F. Hughes
> Well, never mind. I think it's super-keen that your system's
> theorems exactly correspond to logical proofs. Except, of course,
^^^^^^^^^^^^^^ mathematical truths
> you haven't stated any axioms or rules of inference. But otherwise,
> kudos!
Argh.
--
"Sure, maybe I have a tiresome task that is nearly impossible, but
part of who I am is an endless amount of energy as long as there is
hope. Without hope, I find that I start to lose focus, and feel, just,
well, hopeless." -- James S. Harris
Daryl McCullough
>
>In article <1181008495.4...@w5g2000hsg.googlegroups.com>,
> david petry <david_lawr...@yahoo.com> wrote:
>
>> In this article, "Cantor's theory" refers to the ideas about infinity
>> and infinite sets introduced into mathematics by Cantor. The claim
>> here is that Cantor introduced an element of make-believe into
>> mathematics, and we'd all be better off without it.
>>
>>
>> PHILOSOPHICAL PRINCIPLES
>>
>>
>> Our technologically advanced society needs mathematics. Ultimately,
>> the purpose of mathematics is to meet the needs of society.
>
>Such a "Big Brother" view is anathema.
I just want to point out that David Petry is a nut, even by
USENET standards. He is deeply disturbed. It's hard to know
if he is actually dangerous, but he certainly has shown sympathy
for violence and he has a bizarre animus against
liberals, modern mathematics, secular humanism:
http://tinyurl.com/2skg88
http://tinyurl.com/3c2ut6
http://tinyurl.com/2ecesc
http://tinyurl.com/yovz8x
Daryl McCullough
Ithaca, NY
The World Wide Wade
Herman Jurjus
[snip]
> I just want to point out that David Petry is a nut, even by
> USENET standards.
Hm. Then i'd say you have very limited experience with usenet? Anyways.
Since i see a fox being haunted by a bunch of barking hounds in this
thread, i feel forced to speak up. For what it's worth: i think mr.
Petry is basically right.
Only: he has been repeating his mantra for more than 10 years now, and
he doesn't seem to make much progress in a mathematical direction. Why
didn't he spend some of all that time in producing some mathematics to
/show/ concretely to what /mathematics/ his ideas can lead?
I, for one, would be very interested if he did.
--
Cheers,
Herman Jurjus
tommy1729
GOOD QUOTES :-)
good text in general !
you have a friend in me concerning the debunking of cantor's theory.
well kind of.
people should read the entire text, since DAVID is NOT agianst infinity !
indeed cantor is wrong but infinity is still important.
cantors theory can be replaced bye a handfull "correct" ones.
1) there are 2 kinds of infinity : countable and uncountable
2) the famous wheel paradox ( piont to point correspondence does not imply equal length, surface or volume.
...
bye the way im skeptical about the halting problem too.
but thats another thing.
i might seem a crankpot now.
and david too.
but then kronecker would be one too ????
i was about to write a similar text.
so , david , im not jealous you where first.
im actually happy you saved me the typing work.
greets
tommy1729
Daryl McCullough
>
>Daryl McCullough wrote:
>[snip]
>
>> I just want to point out that David Petry is a nut, even by
>> USENET standards.
>
>Hm. Then i'd say you have very limited experience with usenet?
No, that's based on many years experience with usenet. My
experience is limited in the sense that I don't hang out at
the kook newsgroups such as misc.activism.militia, and the
people who hang out there don't usually post to sci.logic.
David Petry is pretty unusual in that respect.
There is a difference between having eccentric ideas and claiming that
violence and concentration camps may be necessary against your opponents,
which is what David Petry has said.
>Since i see a fox being haunted by a bunch of barking hounds in this
>thread, i feel forced to speak up. For what it's worth: i think mr.
Petry is basically right.
http://tinyurl.com/yovz8x
David Petry says Hitler was right to view liberals as evil:
>Hitler did in fact see the evil reality lurking behind liberal
>propaganda. Recall that as Hitler was rising to power, Stalin,
>the darling of the liberals, was slaughtering and starving and
>enslaving millions upon millions of people in the name of creating
>a workers' paradise where everyone gives according to his ability,
>and receives according to his needs. Hitler saw through the
>propaganda.
>So we (e.g. Patriots, militia types) have to admit that we do have
>something in common with Hitler; we see the evil lurking behind
>the liberal propaganda.
http://tinyurl.com/2ecesc
David Petry loathes anything smacking of "humanities"...
>I have never passed a humanities course (at the college level). I have
>been told by humanities instructors that I am simple minded, closed minded,
>superficial, anti-thinking, afraid to face the important issues, playing
>games, and a few more things that aren't very nice. I despise Humanism.
>I loathe Humanism. I hate Humanism with every ounce of hate I can muster.
>If I could pass a humanities course, I could have a college degree and be
>one of the intellectual elites such as yourself.
http://tinyurl.com/3c2ut6
David Petry says that Humanists must be killed, if that's the
only way to stop their influence...
>The Humanism problem is the most outstanding problem facing America
>today. If we have a revolution, but fail to solve the Humanism
>problem, the revolution will have been for naught.
>Humanism is a disease which has corrupted the soul of our society. We
>simply must be willing to do anything and everything necessary to wipe
>Humanism off the face of the earth. If it means killing Humanists, so
>be it. If it means building gas chambers, so be it. If it leads to the
>death of two or three innocent people for every Humanist killed, well,
>that's not too high a price to pay for freedom.
http://tinyurl.com/2skg88
David Petry says that Humanists are bullies, that can only be
stopped with violence:
>The Humanists can be thought of as people who were beaten up by
>playground bullies when they were children, so they retaliated by
>learning how to beat people up with words. The Humanists will try
>to laugh that off, but the psychological damage the Humanists do with
>their words can be far more destructive in the long run than the few
>easily healed bruises that the playground bully inflicts.
>The Humanists are intellectual bullies. Like any bullies, they gain
>their power through membership in an exclusive social group (gang)...
>One way or another, we need to solve the Humanism problem. I don't
>foresee it being solved without violence. Every bit of evidence
>I see suggests that it will prove to be impossible to solve it
>through rational discussion with the Humanists, and our government
>and legal system have been too corrupted by Humanism to deal with
>the problem.
--
Daryl McCullough
Ithaca, NY
MoeBlee
> I just want to point out that David Petry is a nut, even by
> USENET standards. He is deeply disturbed. It's hard to know
> if he is actually dangerous, but he certainly has shown sympathy
> for violence and he has a bizarre animus against
> liberals, modern mathematics, secular humanism:
>
> http://tinyurl.com/2skg88http://tinyurl.com/3c2ut6http://tinyurl.com/2eceschttp://tinyurl.com/yovz8x
>
Did you include his thread about "Jewish mathematics"?
Petry is a kook who advocates mass executions, claims that
"Cantorists" are "evil" (or whatever, actually stronger, wording he
uses), describes "Jewish mathematics" as the problem, and whose
motivation for his over twenty(?) year long grudge about set theory is
his having been, as an undergraduate, intellectually snubbed by some
professor or another. Of course, such reminders as to the character of
Petry himself are not responses themselves to his philosophical
diatribes, but such reminders do, hopefully, contribute to an
enjoyment of the comedy that is the posting career of David Petry.
MoeBlee
david petry
> Since i see a fox being haunted by a bunch of barking hounds in this
> thread, i feel forced to speak up. For what it's worth: i think mr.
> Petry is basically right.
>
> Only: he has been repeating his mantra for more than 10 years now, and
> he doesn't seem to make much progress in a mathematical direction. Why
> didn't he spend some of all that time in producing some mathematics to
> /show/ concretely to what /mathematics/ his ideas can lead?
>
> I, for one, would be very interested if he did.
When I developed these ideas, about 15-20 years ago, the question on
my mind was how I could teach an artificial intelligence to understand
mathematics. The purpose was not to do mathematics per se. Anyway, I
do believe that anyone who thinks about the same questions I was
thinking about will come to the same conclusion: modern mathematics
has taken a detour away from truth and reality.
I have to admit that it's not entirely clear to myself why I bother
writing these USENET articles.
WM
> In this article, "Cantor's theory" refers to the ideas about infinity
> and infinite sets introduced into mathematics by Cantor. The claim
> here is that Cantor introduced an element of make-believe into
> mathematics, and we'd all be better off without it.>
> "Set theory is based on polite lies, things we agree on even though we
> know they're not true. In some ways, the foundations of mathematics
> has an air of unreality." (William P. Thurston)
>
> "[Cantor's paradise] is a paradise of fools, and besides feels more
> like hell" (Doron Zeilberger)
Thank you, David, for this profound contribution. Let me add: The
information contents of the accessible universe is limited and will
forever remain so. There are no infinite sets. Therefore, a
mathematician living in the 21st century and teaching, by belief or by
axiom, the existence of completed infinite sets has the same degree of
intellectual capacity or honesty as a theologian living in the 21st
century and teaching, by belief or by dogma, the physical existence of
hell and devil.
Regards, WM
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
He whose Universe is restricted to only the physical world and cannot
enter the many worlds of the imagination has a life hardly worth living.
Mathematics exists only in those worlds of the imagination, and has
nothing to do directly with that physical world.
And it is a matter of considerable wonder that what exists only in the
imagination has such important effects in that physical world.
WM
> david petry wrote:
>
> > In this article, "Cantor's theory" refers to the ideas about infinity
> > and infinite sets introduced into mathematics by Cantor. The claim
> > here is that Cantor introduced an element of make-believe into
> > mathematics, and we'd all be better off without it.
>
> If we had it your way math would be only good for toting up grocery
> bills and balancing our bank accounts.
Would always be better than the present fruitless mess good for
nothing but the idle occupation of some intellectual clowns (in order
to avoid the overstressed trem "crank").
>
> Without "ideal" elements we could not show whether solutions to
> differential equations existed or not (for example). Without "ideal"
> elements we could not give essential topological characterization to
> verious spaces used in physics. And kill differentiable manifolds
> goodbye, which means no General Relativity.
>
The information contents of the accessible universe is limited and
will forever remain so. Therefore there are no infinite sets, never
and nowhere. There is only the imagination or autosuggestion that
infinite sets could be imagined or handled. Nevertheless theory of
relativity exists independent of your axioms.
Well, what is here the meaning of "to exist"? It means that the theory
when applied to reality yields results which can be tested without
autosuggestions and beliefs in dogmas or axioms. That means "to
exist"!
Regards, WM
Aatu Koskensilta
> Thank you, David, for this profound contribution. Let me add: The
> information contents of the accessible universe is limited and will
> forever remain so. There are no infinite sets.
It is certainly possible, perhaps even plausible or probable, that there are
no infinite sets of physical stuff. What does that have to do with set
theory, which, after all, is not a branch of physics?
--
Aatu Koskensilta (aatu.kos...@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
Brian Chandler
There's a curious asymmetry in your analogy. Shouldn't it be:
... a mathematician living in the 21st century and teaching, by belief
or by
axiom, the *physical* existence of completed infinite sets has the
same degree of
intellectual capacity or honesty as a theologian living in the 21st
century and teaching, by belief or by dogma, the physical existence of
hell and devil.
If the "physical" attribute is applied correspondingly, I don't
suppose anyone would disagree, though they would normally state it in
a less hysterical fashion.
Brian Chandler
http://imaginatorium.org
>
> Regards, WM
MoeBlee
> When I developed these ideas, about 15-20 years ago, the question on
> my mind was how I could teach an artificial intelligence to understand
> mathematics. The purpose was not to do mathematics per se. Anyway, I
> do believe that anyone who thinks about the same questions I was
> thinking about will come to the same conclusion: modern mathematics
> has taken a detour away from truth and reality.
Nevermind all that. Please just tell us more of your thoughts on
"Jewish mathematics". Please expound on what you think is the special
role of Jews in all this humanism, liberalism, and Cantorism that you
so revile. I mean, nothing puts the ideation of a kook into such sharp
relief as when it's mixed with a good strong measure of anti-Semitism.
Don't hold back, David, tell us what you think!
MoeBlee
Justin
: When I developed these ideas, about 15-20 years ago, the question on
: my mind was how I could teach an artificial intelligence to understand
: mathematics. The purpose was not to do mathematics per se.
No worries there; I didn't see any mathematics in your post anyway.
Justin
WM
A number does not exist other than by a representation in the physical
universe, be it in the ind of a mathematician or in a computer or
elsewhere. If it is known that a number, even a natural number, can
never be known by any mind or computer or elsewhere, then it is known
that this number does not exist.
It can be proved that between 10^10^10^10 and 10^10^10^20 there are
more than 10^10^10^10 places where natural numbers should be, but are
not. No mathematician can ever talk about one of these "numbers" or
identify it as an individual, i.e., distinguish it from other
"numbers" of this kind. Therefore, my statement is correct without
mentioning "physical".
Regards, WM
>
Hagen
> mess good for
> nothing but the idle occupation of some intellectual
> clowns (in order
> to avoid the overstressed trem "crank").
Hallo Herr Mueckenheim,
I am a member of a Fraunhofer-Institute, where approximately
200 intellectual clowns are earning their money using what
you call completed infinite sets (curently about 7 000 000 €
per year, 4 000 000 paid by enterprises of the free market).
They use it in models for problems in fluid dynamics,
aerodynamics, statistics etc. and it works quite well: they solve
problems posed by enterprises in the automotive area, airplane
factories, pharmaceutical industries etc. They use it to communicate
with the members of these enterprises, and although these
members are often not even mathematicians, no problems but the
usual ones when communicating about mathematics occur.
It is clear and trivial that at the end of the story these people use
or create an algorithm or a computer program. So they do some-
thing finite. But if if they had to develop ideas for solutions using
only finite techniques - THAT would really be a mess. And it
would be almost impossible to communicate these solutions
or ideas. It would be like looking at a computer monitor and
saying: I currently see a cloud of 123456 pixels at the
coordinates .... using the RGB codes ... instead of saying I
currently see an image of Mr. Gorbatchov.
H
H
WM
> > Would always be better than the present fruitless
> > mess good for
> > nothing but the idle occupation of some intellectual
> > clowns (in order
> > to avoid the overstressed trem "crank").
>
> Hallo Herr Mueckenheim,
>
> I am a member of a Fraunhofer-Institute, where approximately
> 200 intellectual clowns are earning their money using what
> you call completed infinite sets (curently about 7 000 000 €
> per year, 4 000 000 paid by enterprises of the free market).
> They use it in models for problems in fluid dynamics,
> aerodynamics, statistics etc. and it works quite well:
No, Herr Hagen, they and you don't use it (completed infinite sets of
numbers) and cannot use it, simply because it does not exist. What you
may be using is the impression you would use it. (Only the fact that
you cannot really handle sets of 10^30 and more numbers allows this
impression.) And you may even successfully continue to do so, but a
real mathematician should be aware of the fact that this only can be
maintained as long as one is not looking too closely.
Most engineers are not using relativity theory or quantum mechanics,
when developing a new engine for a car or for a ship. But every
engineer is aware of the fact that position and moment of a physical
body are not available and *do not exist* with unlimited precision.
The same degree of knowledge should become common among
mathematicians, in particular as far as they claim to observe highest
precision among all arts and sciences.
Therefore: Continue to use infinite sets, but be aware that they are
an idealisation which vanishes if you look more closely. There are not
more than 10^100 numbers available. But that is by far more than ever
will be needed.
Regards, WM
Franziska Neugebauer
> A number does not exist other than by a representation in the physical
> universe,
"To represent" (likewise "to approximate") necessitates compulsively
some kind of existence of the representee (likewise the approximee).
If this existence is denied it is senseless to talk about
representation (likewise approximation).
F. N.
--
xyz
Daryl McCullough
>Petry is a kook who advocates mass executions, claims that
>"Cantorists" are "evil" (or whatever, actually stronger, wording he
>uses), describes "Jewish mathematics" as the problem, and whose
>motivation for his over twenty(?) year long grudge about set theory is
>his having been, as an undergraduate, intellectually snubbed by some
>professor or another. Of course, such reminders as to the character of
>Petry himself are not responses themselves to his philosophical
>diatribes, but such reminders do, hopefully, contribute to an
>enjoyment of the comedy that is the posting career of David Petry.
I don't consider fantasizing about killing and death camps to
be comedy. Well, I suppose it could be black comedy...
Newberry
wrote:
> On 2007-06-06, in sci.logic, WM wrote:
>
> > Thank you, David, for this profound contribution. Let me add: The
> > information contents of the accessible universe is limited and will
> > forever remain so. There are no infinite sets.
>
> It is certainly possible, perhaps even plausible or probable, that there are
> no infinite sets of physical stuff.
What about constellations, galaxies, constellations of constellations
of galxies, constellations, constellations of constellations of
galxies? I think that is physical stuff. Potential infinity certainly
does exist.
What does that have to do with set
> theory, which, after all, is not a branch of physics?
But it is a branch of logic, which makes inferences about perceptible
affairs. Actual infinity is a contradiction in terms.
>
> --
> Aatu Koskensilta (aatu.koskensi...@xortec.fi)
Wolf
>> What does that have to do with set
>> theory, which, after all, is not a branch of physics?
>
> But it is a branch of logic, which makes inferences about perceptible
> affairs. Actual infinity is a contradiction in terms.
No, logic is about patterns of argument. You may apply a given pattern
of argument to some given "perceptible affair", but that's not part of
logic (some people call that 'applied logic.') Another person may apply
a different pattern of argument to the same "perceptible affair," in
which case you will have to justify your assumption that the pattern you
chose is the correct model and the person's choice is incorrect.
"My argument is logical,
yours is merely plausible,
his is nonsensical."
[...]
--
Wolf
"Don't believe everything you think." (Maxine)
Aatu Koskensilta
> On Jun 6, 12:46 am, Aatu Koskensilta <aatu.kos...@xortec.fi>
> wrote:
>
>> It is certainly possible, perhaps even plausible or probable, that there are
>> no infinite sets of physical stuff.
>
> What about constellations, galaxies, constellations of constellations
> of galxies, constellations, constellations of constellations of
> galxies? I think that is physical stuff. Potential infinity certainly
> does exist.
Whether there's a finite or infinite number of physical things, whatever
they might be, is a question I'm happy to leave to the physicists. It has
nothing to do with mathematics.
>> What does that have to do with set theory, which, after all, is not a
>> branch of physics?
>
> But it is a branch of logic, which makes inferences about perceptible
> affairs.
Set theory is a branch of mathematics, elements of which are extremely
useful in a wide variety of mathematical contexts.
> Actual infinity is a contradiction in terms.
That's just a silly way of saying you don't like set theory. Fine -- don't
do set theory, or use set theoretic notions and principles in your
mathematical reasoning. Do finitistic mathematics or whatever tickles you
the right way; who knows, perhaps you'll discover something as interesting,
useful and powerful as modern abstract mathematics.
--
Aatu Koskensilta (aatu.kos...@xortec.fi)
Marshall
>
> It can be proved that between 10^10^10^10 and 10^10^10^20 there are
> more than 10^10^10^10 places where natural numbers should be, but are
> not. No mathematician can ever talk about one of these "numbers" or
> identify it as an individual, i.e., distinguish it from other
> "numbers" of this kind.
But you just did. You just mentioned 10^10^10^20. You talked
about it, identified it as an individual, and distinguished
it from 10^10^10^10. And you said no one could. Oh, no, wait,
I see; you said no *mathematician* could, so I didn't spot an
inconsistency in what you said after all.
Marshall
lui...@yahoo.com
>
> Infinity is not part of the underlying reality of mathematics. It is
> not essential to mathematics. Infinity is an abstraction, or a useful
> fiction, and when we develop a theory of the infinite, we must be able
> to say exactly how it is useful.
> Mathematics is the science of the phenomena observable within the
> world of computation. Mathematical statements must make falsifiable
> predictions about the outcomes of possible computational experiments.
> If we want to assert that some object exists within the world of
> computation, we must be able to say how to observe the object. All of
> the mathematics that has the potential to help us understand the world
>in which we live fits within the scope of that definition.
Those ideas are the death of Mathematics.
The Goldbach conjecture is a mathematical phenomenon but cannot be
falsifiable by any computational experiment.
There is no way how to observe the prime where pi(x) > Li(x)
but Littlewood showed that after some x it will occur.
Mathematics is not a natural science for helping us to understand
the world.
Mathematics is a game as chess, only that its pieces
are spaces, points, numbers and formal propositions.
Being a game it is also an art.
As Oscar Wilde said:
"Art is completely useless"
Ludovicus
lui...@yahoo.com
Moreover, Androcles in the thread 'Matrices' expressed:
In a sense, all mathematics is a "plaything", mathematicians know
this.
Mathematics is art. If you use it as a tool for science and
engineering,
it's a useful tool, but first and foremost it is still art.
Mathematicians happily delve into the impossible with the single rule
that they must be consistent. An example is the Klein bottle. It
doesn't
physically exist, yet it is mathematically consistent with four
spatial
dimensions. Physically, there are only three.
There is no requirement for mathematics to apply to physics or
engineering,
math is art. If a subset of math does apply then you have a bonus.
There is no "physical" origin to matrices, but they are useful to
those
that know how to use them. In these days of computers they are really
the equivalent of a slide rule or book of log tables, not really
needed.
Ludovicus
Eric Gisse View profile
More options Apr 26, 9:01 pm
Newsgroups: sci.math, sci.physics, alt.folklore.science,
alt.folklore.computers
From: Eric Gisse <jowr...@gmail.com>
Date: 26 Apr 2007 18:01:29 -0700
Local: Thurs, Apr 26 2007 9:01 pm
Subject: Re: physical origins of matrix algebra?
Reply | Reply to author | Forward | Print | Individual message | Show
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On Apr 26, 5:55 am, dances_with_barka...@yahoo.com wrote:
> matrices, and their algebra, were invented
WM
> In article <1181114803.207678.302...@q75g2000hsh.googlegroups.com>,
No, that is no wonder. Good mathematics is physics. For instance, the
geometrical division of a line leads to two halves, which are really
equal to each other. Small wonder. Only transfinite set theory and
things alike lead to results which are completely inapplicable and
self contradicting like sum n = 0.
Regards, WM
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
> The information contents of the accessible universe is limited and
> will forever remain so.
But there is no need for such busybodies as WM to try to limit it
further.
Such forms of thought policing are anathema to those of us who cherish
our freedoms.
> Therefore there are no infinite sets, never
> and nowhere.
At least not in the miserable world of WM's MathUnrealism.
> There is only the imagination or autosuggestion that
> infinite sets
All of mathematics is of the imagination. None of it actually exists
except as ideas. Often powerful ideas, but nevertheless only ideas.
WM's efforts to impose thought policing on those ideas is evil.
MoeBlee
> I don't consider fantasizing about killing and death camps to
> be comedy. Well, I suppose it could be black comedy...
Black comedy is one form. And there is humor in the bluster and
irrationality of advocates of evil ideologies (obvious e.g. such as
Chaplin's 'The Great Dictator'; though it does not mention the
Holocaust directly, it is a lampoon of Hitler himself). And humor is
found in lack of sensitivity to evil and other human foibles in its
context (obvious e.g., Brooks's 'The Producers'). This is not to
trivialize evil but still to find an ironic pathos in peoples's
character and mentality - the character and mentatlity of the kook,
the bigot, and even the executioner. Moreover, not that I wish to get
on the subject at too great length, but there is Jewish humor about
the Holocaust, and some of it pretty grim. If I recall correctly,
Fraenkel (not the mathematican and set theorist) in his book mentions
that camp inmates devised skits among themselves that satirized their
own circumstances. And I don't even have to go to references to know
that Jewish humor about the Holocaust exists, since I know it (the
humor, not the Holocaust, thankfully) from personal experience, even
in one particular example as performed in a synagogue. It seems to me
that EMOTIONAL response to evil is subjective. Emotions are not as a
logic circuit board such that certain inputs must always arrive at
certain solemn outputs. Compassionate and principled people may find
humor, and understandably so, even regarding evil so vast as to be
incomprehensible.
MoeBlee
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
Then what WM means by "exist" and what mathematicians mean, are quite
different. There are al sorts of things existing in mathematicians'
worlds which are absent from WM's world. That WM does not choose see
them, does not mean that others should be forcibly constrained to his
deficiency
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
> On 6 Jun., 12:25, Hagen <k...@itwm.fhg.de> wrote:
> > > Would always be better than the present fruitless
> > > mess good for
> > > nothing but the idle occupation of some intellectual
> > > clowns (in order
> > > to avoid the overstressed trem "crank").
> >
> > Hallo Herr Mueckenheim,
> >
> > I am a member of a Fraunhofer-Institute, where approximately
> > 200 intellectual clowns are earning their money using what
> > you call completed infinite sets (curently about 7 000 000 ?
> > per year, 4 000 000 paid by enterprises of the free market).
> > They use it in models for problems in fluid dynamics,
> > aerodynamics, statistics etc. and it works quite well:
>
> No, Herr Hagen, they and you don't use it (completed infinite sets of
> numbers) and cannot use it, simply because it does not exist.
If one uses those properties of such systems which require completed
infinite sets and would not hold if WM were right, then WM is wrong!
Can WM prove that all the theorems, models, etc., that are being used by
the institute will hold without sets?
Unless WM can prove that, he is claiming what he cannot justify.
As WM has been doing all along.
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
Einstein disagrees with you.
> Good mathematics is physics.
That is a delusion may physicists and their worshippers have.
But there is more to mathematics than mere physics.
G. Frege
wrote:
(A) "Good mathematics is physics."
(Wolfgang Mückenheim)
(B) "The empirical interpretation of mathematics, that is,
the view that mathematical facts are a special kind of
physical [...] facts, is too absurd to be seriously
maintained."
(Kurt Gödel)
Quiz:
~~~~~
Which of the two claims sounds more reasonable?
[ ] (A)
[ ] (B)
-----------------------
F.
--
E-mail: info<at>simple-line<dot>de
WM
> On 2007-06-06, in sci.logic, WM wrote:
>
> > Thank you, David, for this profound contribution. Let me add: The
> > information contents of the accessible universe is limited and will
> > forever remain so. There are no infinite sets.
>
> It is certainly possible, perhaps even plausible or probable, that there are
> no infinite sets of physical stuff. What does that have to do with set
> theory, which, after all, is not a branch of physics?
Adhere to Wittgenstein. Do you understand what he is saying below.
>
> --
> Aatu Koskensilta (aatu.koskensi...@xortec.fi)
>
> "Wovon man nicht sprechen kann, daruber muss man schweigen"
> - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
If there are "numbers" which cannot be identified and individually
addressed, like most natural numbers between the natural numbers
10^10^10^10 and 10^10^10^20, then these numbers cannot be spoken of.
What we cannot talk about, that has to be covered with silence (and no
ballyhoo about infinite sets will change this situation.) And there is
another quote by Wittgenstein: If one person can see it [Hilbert's
paradise] as a paradise for mathematicians, why should not another see
it as a joke?
Regards, WM
WM
A mathematician would have read my text and probably would have
understood it.
Please read again what I wrote, or read this: 10^10^10^10 and
10^10^10^20 and even 10^10^10^10^10^10^20 are natural numbers. They
can be identified and addressed by means of few bits. iIdid it, as
you correctly recognized. *Between* these numbers there should be
about 10^10^10^10^10^10^20 other natural numbers. But most of them
cannot be addressed.
Regards, WM
WM
but only such numbers which can be addressed individually. Certainly
we can address a number at which pi(x) > Li(x) and other numbers
where the reverse occurs. But most probably we cannot address exactly
that position where it happens first. What is the problem? We cannot
identify the smallest positive fraction either. Both do not exist.
Well, for prime numbers the nonexistence appears somewhat unfamiliar.
Forget your feeling. Face reality. That would be mathematical
thinking.
Regards, WM
WM
>
> Moreover, Androcles in the thread 'Matrices' expressed:
> In a sense, all mathematics is a "plaything", mathematicians know
> this.
> Mathematics is art. If you use it as a tool for science and
> engineering,
> it's a useful tool, but first and foremost it is still art.
But it should not be mythology. The assumption of numbers which cannot
be addressed or named other than by naming a bunch of 10^10^120 or
more, is not fine and not art but foolish nonsense.
Regards, WM
WM
> In article <1181130535.712370.105...@q75g2000hsh.googlegroups.com>,
>
>
>
>
>
> WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 6 Jun., 12:25, Hagen <k...@itwm.fhg.de> wrote:
> > > > Would always be better than the present fruitless
> > > > mess good for
> > > > nothing but the idle occupation of some intellectual
> > > > clowns (in order
> > > > to avoid the overstressed trem "crank").
>
> > > Hallo Herr Mueckenheim,
>
> > > I am a member of a Fraunhofer-Institute, where approximately
> > > 200 intellectual clowns are earning their money using what
> > > you call completed infinite sets (curently about 7 000 000 ?
> > > per year, 4 000 000 paid by enterprises of the free market).
> > > They use it in models for problems in fluid dynamics,
> > > aerodynamics, statistics etc. and it works quite well:
>
> > No, Herr Hagen, they and you don't use it (completed infinite sets of
> > numbers) and cannot use it, simply because it does not exist.
>
> If one uses those properties of such systems which require completed
> infinite sets and would not hold if WM were right, then WM is wrong!
>
> Can WM prove that all the theorems, models, etc., that are being used by
> the institute will hold without sets?
I expect that the sets used in the Fraunhofer-institutes to be simply
infinite sets like all natural numbers or the complete real line or
space. That are just approximations. What I understand by intellectual
clownery is the mathematics of aleph_(omega + 17) and related jokes or
the summation of all natural numbers with the result 0.
Regards, WM
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
We can certainly see WM's MathUnRealism as a joke, but not a very good
one.
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
But if any of them fail to exist, so would the numbers you claim do
exist. That is the nature of naturals, none can exist unless all their
predecessors down to the very first also exist.
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
> On 6 Jun., 18:00, luir...@yahoo.com wrote:
> > The Goldbach conjecture is a mathematical phenomenon but cannot be
> > falsifiable by any computational experiment.
> >
> > There is no way how to observe the prime where pi(x) > Li(x)
> > but Littlewood showed that after some x it will occur.
> >
> > Mathematics is not a natural science for helping us to understand
> > the world.
> >
> > Mathematics is a game as chess, only that its pieces
> > are spaces, points, numbers
>
> but only such numbers which can be addressed individually.
If WM claims that any natural numbewr can exist without all of its
predecessors down to the first one also existing, he does not understand
what natural numbers are all about.
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
> On 6 Jun., 18:24, luir...@yahoo.com wrote:
> > On Jun 6, 12:00 pm, luir...@yahoo.com wrote:
> >
> >
>
> >
> > Moreover, Androcles in the thread 'Matrices' expressed:
> > In a sense, all mathematics is a "plaything", mathematicians know
> > this.
> > Mathematics is art. If you use it as a tool for science and
> > engineering,
> > it's a useful tool, but first and foremost it is still art.
>
> But it should not be mythology.
Whyever not?
Mathematics is entirely about things which have no physical existence.
If those things have any existence at all it is as ideas, just like
myths are ideas without physical reality.
It is those, Like WM, who would subjugate mathematics to the whims and
vagaries of non-mathematicians, who are causing all the problems.
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
Can WM prove that all the theorems and other results that the
Fraunhofer-Institute "clowns" depend on, remain true when all those
infinite sets are replaced by WM's non-sets?
Unless he can PROVE this, he is claiming what he does not know.
But that is his SOP.
> What I understand by intellectual
> clownery
WM's postings are the best example since JSH of intellectual clownery.
Franziska Neugebauer
> I expect that the sets used in the Fraunhofer-institutes to be simply
> infinite sets like all natural numbers or the complete real line or
> space. That are just approximations.
Approximation to/of what?
,----[ <4666a2dd$0$97217$892e...@authen.yellow.readfreenews.net> ]
| "To represent" (likewise "to approximate") necessitates compulsively
| some kind of existence of the representee (likewise the approximee).
| If this existence is denied it is senseless to talk about
| representation (likewise approximation).
`----
F. N.
--
xyz
Ralf Bader
>> Would always be better than the present fruitless
>> mess good for
>> nothing but the idle occupation of some intellectual
>> clowns (in order
>> to avoid the overstressed trem "crank").
>
> Hallo Herr Mueckenheim,
>
> I am a member of a Fraunhofer-Institute, where approximately
> 200 intellectual clowns are earning their money using what
> you call completed infinite sets (curently about 7 000 000 €
> per year, 4 000 000 paid by enterprises of the free market).
> They use it in models for problems in fluid dynamics,
> aerodynamics, statistics etc. and it works quite well: they solve
> problems posed by enterprises in the automotive area, airplane
> factories, pharmaceutical industries etc. They use it to communicate
> with the members of these enterprises, and although these
> members are often not even mathematicians, no problems but the
> usual ones when communicating about mathematics occur.
>
> It is clear and trivial that at the end of the story these people use
> or create an algorithm or a computer program. So they do some-
> thing finite. But if if they had to develop ideas for solutions using
> only finite techniques - THAT would really be a mess. And it
> would be almost impossible to communicate these solutions
> or ideas. It would be like looking at a computer monitor and
> saying: I currently see a cloud of 123456 pixels at the
> coordinates .... using the RGB codes ... instead of saying I
> currently see an image of Mr. Gorbatchov.
That reminds me of the philospher Hartry Field, He, AFAIR, was it who called
mathematics "an intellectual juice extractor". In his view, physics doesn't
depend on mathematics in a logical sense but nevertheless it does depend in
a practical sense.
Probably for your colleagues it is part of the task to give estimates how
far the numerical solutions obtained by their algorithms might be off the
true values. It is difficult to talk about these errors, let alone
determine bounds for them if one doesn't have an ideal of absolute
precision as a kind of background. We don't know precisely why the
application of mathematics to the real world is working, but it surely is,
and I am convinced that the reason is that mathematics is something
different from the world. If it were a replica of the world, as Mr
Mückenheim wants it to be, it would be superfluous - the world is already
there and we do not need a copy of it. How should we be able to just think
about determining the "size" of the universe (the bound for Mückenheim's
antimathematics) without a /theory/ which could handle /any/ size, even an
actually infinite one? Mr Mückenhim's "Matherealism" is in this sense a
position of maximal stupidity. Moreover it is just ideological crap. There
is nothing of any mathematical substance and value Mückenheim can present.
He is just waisting taxpayers' money.
R.B.
Ralf Bader
To "name numbers" is no more the business of mathematics as "naming
molecules" (real molecules, not the types of them) is the business of
chemistry.
Aatu Koskensilta
> The Goldbach conjecture is a mathematical phenomenon but cannot be
> falsifiable by any computational experiment.
Really? How about finding an even natural n > 2 and verifying, by brute
force computation, that it is not the sum of two primes?
--
Aatu Koskensilta (aatu.kos...@xortec.fi)
lui...@yahoo.com
> > WM wrote:
> A number does not exist other than by a representation in the physical
> elsewhere. If it is known that a number, even a natural number, can
> never be known by any mind or computer or elsewhere, then it is known
> that this number does not exist.
>
mathematics.
For example: There is an interval of integers X,X+Y that have more
primes than
the interval 0,Y. The value of X never will be known, but it exists.
Ludovicus
Marshall
> A mathematician would have read my text and probably would have
> understood it.
>
> Please read again what I wrote, or read this: 10^10^10^10 and
> 10^10^10^20 and even 10^10^10^10^10^10^20 are natural numbers. They
> can be identified and addressed by means of few bits. iIdid it, as
> you correctly recognized. *Between* these numbers there should be
> about 10^10^10^10^10^10^20 other natural numbers. But most of them
> cannot be addressed.
You did it again! You addressed them. You described a property
they should have, but don't. You were speaking explicitly about
the set of all natural numbers > 10^10^10^10 and < 10^10^10^20
that "should be" but "cannot be." I don't see how you can say
they can't be addressed when you keep addressing them.
But perhaps I'm simply misunderstanding you. Can you give
me a formal definition that a mathematician would understand
of what it means to say a number "should be" and a definition
of what it means to say a number "cannot be addressed?"
I would be very interested to discover the largest natural number
that can be addressed such that all other numbers below it
can be addressed.
Marshall
Jack Campin - bogus address
> more primes than the interval 0,Y. The value of X never will
> be known, but it exists.
Boggle.
Got a reference for that one? (Number theory is not my thing,
nonconstructive number theory even less so).
============== j-c ====== @ ====== purr . demon . co . uk ==============
Jack Campin: 11 Third St, Newtongrange EH22 4PU, Scotland | tel 0131 660 4760
<http://www.purr.demon.co.uk/jack/> for CD-ROMs and free | fax 0870 0554 975
stuff: Scottish music, food intolerance, & Mac logic fonts | mob 07800 739 557
Subluxian
How about Y = 1, X = 2?
Cheers - Chas
Newberry
wrote:
> On 2007-06-06, in sci.logic, Newberry wrote:
>
> > On Jun 6, 12:46 am, Aatu Koskensilta <aatu.koskensi...@xortec.fi>
> > wrote:
>
> >> It is certainly possible, perhaps even plausible or probable, that there are
> >> no infinite sets of physical stuff.
>
> > of galxies, constellations, constellations of constellations of
> > galxies? I think that is physical stuff. Potential infinity certainly
> > does exist.
>
> Whether there's a finite or infinite number of physical things, whatever
> they might be, is a question I'm happy to leave to the physicists. It has
> nothing to do with mathematics.
It has nothing to do with physics. When you have finite set of natural
numbers you can create infinitely many sets from them e.g. {1,2}, {1,
{{{1,2}}} etc. If you assign a natural number to each star in the
universe you can conceive infinitely many constellations. Whether
there are infinitely many things is not an empirical question.
>
> >> What does that have to do with set theory, which, after all, is not a
> >> branch of physics?
>
> > But it is a branch of logic, which makes inferences about perceptible
> > affairs.
>
> Set theory is a branch of mathematics, elements of which are extremely
> useful in a wide variety of mathematical contexts.
>
> > Actual infinity is a contradiction in terms.
>
> That's just a silly way of saying you don't like set theory. Fine -- don't
> do set theory, or use set theoretic notions and principles in your
> mathematical reasoning. Do finitistic mathematics or whatever tickles you
> the right way; who knows, perhaps you'll discover something as interesting,
> useful and powerful as modern abstract mathematics.
>
> --
> Aatu Koskensilta (aatu.koskensi...@xortec.fi)
Wolf
> On 2007-06-06, in sci.logic, lui...@yahoo.com wrote:
>> The Goldbach conjecture is a mathematical phenomenon but cannot be
>> falsifiable by any computational experiment.
>
> Really? How about finding an even natural n > 2 and verifying, by brute
> force computation, that it is not the sum of two primes?
>
OK, write the program, and enlist the aid of all those people who've
grown tired of donating cycles to SETI or the protein folding problem.
--
Wolf
"Don't believe everything you think." (Maxine)
Wolf
IMO, it's obvious. there has to be such an interval. It just can't be
specified. WM would argue that therefore it doesn't exist.
"(Non)existence proofs are the bugaboo of small intellects", to
paraphrase somebody or other (I think it was Emerson.)
Wolf
It seems to me that ludovicus had Y>X in mind.
The proposition is trivially true for all X,Y and X>Y, for then interval
/0,Y/ < /0,X/, and therefore etc.
It is not trivially true for X,Y and X<Y, for then /0,Y/ and /X, X+Y/
overlap, and /0,Y/ > /X, X+Y/.
Now that I think about it more, the proposition is not obvious. The
obvious conclusion is that the proposition is false. How can the smaller
interval contain more primes than the larger?
So what am I missing?
Gerry Myerson
Wolf <ElLob...@ruddy.moss> wrote:
> Jack Campin - bogus address wrote:
> >> For example: There is an interval of integers X,X+Y that have
> >> more primes than the interval 0,Y. The value of X never will
> >> be known, but it exists.
> >
> > Boggle.
> >
> > Got a reference for that one? (Number theory is not my thing,
> > nonconstructive number theory even less so).
> >
> > ============== j-c ====== @ ====== purr . demon . co . uk
> > ==============
> > Jack Campin: 11 Third St, Newtongrange EH22 4PU, Scotland | tel 0131 660
> > 4760
> > <http://www.purr.demon.co.uk/jack/> for CD-ROMs and free | fax 0870 0554
> > 975
> > stuff: Scottish music, food intolerance, & Mac logic fonts | mob 07800 739
> > 557
>
>
> IMO, it's obvious. there has to be such an interval. It just can't be
> specified. WM would argue that therefore it doesn't exist.
If it's obvious to you, then you have a better insight into these things
than Hardy & Littlewood, who conjectured the opposite.
It still isn't known for sure that such X and Y exist, but it's known
that the Hardy-Littlewood conjecture and the prime k-tuples
conjecture can't both be true, and the consensus of informed
opinion is that prime k-tuples is true.
A reference is Hensley, Douglas; Richards, Ian On the incompatibility
of two conjectures concerning primes. Analytic number theory (Proc.
Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972),
pp. 123--127. Amer. Math. Soc., Providence, R.I., 1973.
If that reference is not available to you then probably asking Google
for some of the keywords therein will get you something.
--
Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)
kunzmilan
> To "name numbers" is no more the business of mathematics as "naming
> molecules" (real molecules, not the types of them) is the business of
> chemistry.
"Naming molecules" (real molecules, not the types of them) is the
business of chemistry. Reading DNA is determining the sequence of
aminoacids in strings, similarly as we read sequences of digits in
long numbers.
The natural numbers have their names in the natural languages.
Problems exist with too great natural numbers not allowing to
pronounce them properly ([10^10^...] is not a word of any natural
language).
We have only ten signs for natural numbers n (0, 1, 2...9), eventually
we must use alphabet for larger systems than decadic. But we do not
define yet, how to write such larger numbers.
Square root from 2 is not a natural number, since it is not included
in their list.
We construct rational numbers r as
r = n/ sum of all defined natural numbers.
We get the list 0.1, 0.2,...0.9.
Square root from 2/10 is not included in this list. Therefore, it is
not a rational number.
Now we can enlarge our lists of natural numbers and rational numbers
till infinity.
kunzmilan
G. Frege
wrote:
>
> Now we can enlarge our lists of natural numbers and rational numbers
> till infinity.
>
Mr. Mückeheim thinks otherwise. (And in a certain sense he's right,
of course, since we can't _really_ do that. On the other hand, who
cares? That might have been what the other guy was referring to
when claiming: "'name numbers' is not the business of
mathematics".)
Wolf
> In article <46676599$0$16951$9a6e...@news.newshosting.com>,
> Wolf <ElLob...@ruddy.moss> wrote:
>
>> Jack Campin - bogus address wrote:
>>>> For example: There is an interval of integers X,X+Y that have
>>>> more primes than the interval 0,Y. The value of X never will
>>>> be known, but it exists.
>>> Boggle.
>>>
>>> Got a reference for that one? (Number theory is not my thing,
>>> nonconstructive number theory even less so).
>>>
[...]
>> IMO, it's obvious. there has to be such an interval. It just can't be
>> specified. WM would argue that therefore it doesn't exist.
>
> If it's obvious to you, then you have a better insight into these things
> than Hardy & Littlewood, who conjectured the opposite.
[...]
See my subsequent post.
Aatu Koskensilta
> OK, write the program, and enlist the aid of all those people who've
> grown tired of donating cycles to SETI or the protein folding problem.
I have no real interest in efforts to find a counter-example to Goldbach's
conjecture. The point was simply that it is possible, in some idealised
sense, to falsify Goldbach's conjecture, curiously called a "phenomenon" by
luiroto, by a "computational experiment".
WM
> In article <1181163489.600343.280...@z28g2000prd.googlegroups.com>,
representation were the unary system.
The existence of IIII implies the existence of III.
But these times have passed away - and with them the foundation of
Peano's axioms.
Let me explain: Suppose you have only 7 symbols available and you have
to use the decimal system. Then you could use these 7 symbols to
address all numbers with seven digits up to 9999999.
You could also address a number with 11 digits like
12333333333 = 123(9*)
But you could not address the number
p = 31415926
which has 8 digits.
You could only say that it lies in the interval between
31000000 and 32000000
310(6*) and 320(6*)
or, slightly better, between
31333333 and 31444444, namely,
313[6*] < p < 314[6*].
Regards, WM
WM
Neugeba...@neugeb.dnsalias.net> wrote:
> WM wrote:
> > I expect that the sets used in the Fraunhofer-institutes to be simply
> > infinite sets like all natural numbers or the complete real line or
> > space. That are just approximations.
>
> Approximation to/of what?
>
That are approximations to sets of many coordinates. If a picture is
supposed to consist of infinitely many pixels, if a body is supposed
to consist of infinitely many atoms and if the real plane is supposed
to consist of infinitely many points, then these suppositions are
approximations of reality.
Of course we physicists calculate with fluid or gaseous continua, even
in the interior f nuclei. That simplifies computing. But we know that
these models are approximations. And we would highly suspect results
yielding alephs and beths.
Regards, WM
WM
> On Jun 6, 7:51 am, Aatu Koskensilta <aatu.koskensi...@xortec.fi>
> wrote:
>
>
>
>
>
> > On 2007-06-06, in sci.logic, Newberry wrote:
>
> > > On Jun 6, 12:46 am, Aatu Koskensilta <aatu.koskensi...@xortec.fi>
> > > wrote:
>
> > >> It is certainly possible, perhaps even plausible or probable, that there are
> > >> no infinite sets of physical stuff.
>
> > > What about constellations, galaxies, constellations of constellations
> > > of galxies, constellations, constellations of constellations of
> > > galxies? I think that is physical stuff. Potential infinity certainly
> > > does exist.
>
> > Whether there's a finite or infinite number of physical things, whatever
> > they might be, is a question I'm happy to leave to the physicists. It has
> > nothing to do with mathematics.
>
> It has nothing to do with physics. When you have finite set of natural
> numbers you can create infinitely many sets from them e.g. {1,2}, {1,
> {{{1,2}}} etc. If you assign a natural number to each star in the
> universe you can conceive infinitely many constellations. Whether
> there are infinitely many things is not an empirical question.
Sorry, you are wrong. If you have three bits, you can make of them 2^3
numbers, but only one (or at most three single-bit numbers) at a time.
Regards, WM
Wolf
> On 2007-06-07, in sci.logic, Wolf wrote:
>> OK, write the program, and enlist the aid of all those people who've
>> grown tired of donating cycles to SETI or the protein folding problem.
>
> I have no real interest in efforts to find a counter-example to Goldbach's
> conjecture. The point was simply that it is possible, in some idealised
> sense, to falsify Goldbach's conjecture, curiously called a "phenomenon" by
> luiroto, by a "computational experiment".
>
Quite so, which is why WM's (and possibly luiroto's) stance is IMO
inconsistent. He wants to limit mathematics to physically realisable
proofs, with "proof" being some kind of physical listing of all the
elements in the proof set. He seems to require listability in real time.
It's the unlistability in real time that leads him to reject infinite
sets. IE, as I understand WM's stance, he demands that given theorem
T(n), list all the elements of {n} for which T is true. That notion of
proof includes your idealised computation of a counter example for
Goldbach, of course: if such a number were computed, it would form a
list of one element - no problem for WM there.
But formulas that describe the elements of infinite sets are a problem.
If WM is "konsequent", to use the German word for it, he would have to
reject any formula describing a set with no upper bound, for such sets
obviously cannot be completely listed (=enumerated) in real time. What's
more, most of the elements of such sets are so large that they are
individually unlistable (=unwritable) in real time. The subset of
listable numbers is in fact a vanishingly small subset of the set as
described. Yet nothing that WM has said suggests that he would reject a
formula such as F(x)=x^2, which describes a set with no upper bound. So
his stance is inconsistent: It appears that he would accept a formula
that describes an infinite set, yet rejects the notion of infinite sets.
Or so it seems to me.
Wolf
> On 6 Jun., 23:36, Virgil <vir...@comcast.net> wrote:
>> In article <1181163489.600343.280...@z28g2000prd.googlegroups.com>,
>>
>> WM <mueck...@rz.fh-augsburg.de> wrote:
>>> On 6 Jun., 18:00, luir...@yahoo.com wrote:
>>>> The Goldbach conjecture is a mathematical phenomenon but cannot be
>>>> falsifiable by any computational experiment.
>>>> There is no way how to observe the prime where pi(x) > Li(x)
>>>> but Littlewood showed that after some x it will occur.
>>>> Mathematics is not a natural science for helping us to understand
>>>> the world.
>>>> Mathematics is a game as chess, only that its pieces
>>>> are spaces, points, numbers
>>> but only such numbers which can be addressed individually.
>> predecessors down to the first one also existing, he does not understand
>> what natural numbers are all about.
> Old-fashioned stuff! You were right, if the only form of
> representation were the unary system.
> The existence of IIII implies the existence of III.
> But these times have passed away - and with them the foundation of
> Peano's axioms.
>
> Let me explain: Suppose you have only 7 symbols available and you have
> to use the decimal system. Then you could use these 7 symbols to
> address all numbers with seven digits up to 9999999.
With 7 distinct symbols, you can address 7^7 numbers of seven digits in
length. That's 823543 numbers, or about 8% of 9999999. IOW, your scheme
leaves out over 90% of the 7 didgit numbers between 0000000 and 9999999.
That is, if "address" you mean "use a unique combination of symbols to
label a number." If you mean something else, kindly demonstrate.
[snip]
Marshall
> On 6 Jun., 23:49, Franziska Neugebauer <Franziska-
>
>
> That are approximations to sets of many coordinates. If a picture is
> supposed to consist of infinitely many pixels, if a body is supposed
> to consist of infinitely many atoms and if the real plane is supposed
> to consist of infinitely many points, then these suppositions are
> approximations of reality.
Okay, I buy those first two, but I'm not as sure about the third
one. To tell for sure, what's an experiment we could run on the
real plane to verify what you say? Do you have one in your
lab we could observe? We're talking about reality here; we
have to check what we say against empirical observations.
Otherwise it's not physics. At that point we'd just be talking
about some kind of *abstract* systematic treatment of
magnitude, relationships between figures and forms, and
relations between quantities expressed symbolically.
Marshall
Franziska Neugebauer
> On 6 Jun., 23:49, Franziska Neugebauer <Franziska-
> Neugeba...@neugeb.dnsalias.net> wrote:
>> WM wrote:
>> > I expect that the sets used in the Fraunhofer-institutes to be
>> > simply infinite sets like all natural numbers or the complete real
>> > line or space. That are just approximations.
>>
>> Approximation to/of what?
>
> That are approximations to sets of many coordinates.
What does "that" refer to?
,----[ <4666a2dd$0$97217$892e...@authen.yellow.readfreenews.net> ]
| "To represent" (likewise "to approximate") necessitates compulsively
| some kind of existence of the representee (likewise the approximee).
| If this existence is denied it is senseless to talk about
| representation (likewise approximation).
`----
Do you agree to that statement?
When we (informally) say
x is an approximation of y.
we usually mean that the (necessarily assumed as existent) value of y
lies in the neighbourhood of x. Do you agree?
Simple questions:
1. Assume mass was defined in terms of a mass-prototype. Assume you
steal that Kilogram-Prototype (defined mass is 1 kg) and put it on a
scale. The scale says: "1.00002 kg". Do you agree that the value
1.00002 kg is an approximation to the real mass of 1 kg?
2. Assume the square root of two defined by x > 0 having x * x = 2.
Now you steal some pocket calculator and calculate according to some
formular sqrt(2) = 1.4142. Do you agree that the value 1.4142 is an
approximation to the real value of square root of two?
> If a picture is supposed to consist of infinitely many pixels, if a
> body is supposed to consist of infinitely many atoms and
Pictures and bodies are physical entities. Math is not about physical
models.
> [I]f the real plane is supposed to consist of infinitely many points,
> then these suppositions are approximations of reality.
You put the cart before the horse by claiming that maths is about
physical entities. It is futile to rise up against the the fact that it
is not.
F. N.
--
xyz
victor_me...@yahoo.co.uk
>
> I just want to point out that David Petry is a nut, even by
> USENET standards. He is deeply disturbed.
Thanks Daryl for some very revealing insights into
Mr Petry's personality. How would you say he compared with
Hatto von Aquitanien?
Victor Meldrew
"I don't believe it!"
WM
> Aatu Koskensilta wrote:
> > On 2007-06-07, in sci.logic, Wolf wrote:
> >> OK, write the program, and enlist the aid of all those people who've
> >> grown tired of donating cycles to SETI or the protein folding problem.
>
> > I have no real interest in efforts to find a counter-example to Goldbach's
> > conjecture. The point was simply that it is possible, in some idealised
> > sense, to falsify Goldbach's conjecture, curiously called a "phenomenon" by
> > luiroto, by a "computational experiment".
>
> Quite so, which is why WM's (and possibly luiroto's) stance is IMO
> inconsistent. He wants to limit mathematics to physically realisable
> proofs, with "proof" being some kind of physical listing of all the
> elements in the proof set. He seems to require listability in real time.
> It's the unlistability in real time that leads him to reject infinite
> sets. IE, as I understand WM's stance, he demands that given theorem
> T(n), list all the elements of {n} for which T is true. That notion of
> proof includes your idealised computation of a counter example for
> Goldbach, of course: if such a number were computed, it would form a
> list of one element - no problem for WM there.
>
> But formulas that describe the elements of infinite sets are a problem.
> If WM is "konsequent", to use the German word for it, he would have to
> reject any formula describing a set with no upper bound, for such sets
> obviously cannot be completely listed (=enumerated) in real time.
It is not the time which is the problem (although it could become a
problem) but the lacking memory space.
I would not reject a formula like, e.g.,
forall n in N : n is positive.
All natural numbers which can be addressed will turn out positive.
>What's
> more, most of the elements of such sets are so large that they are
> individually unlistable (=unwritable) in real time.
It is not the time, which is the problem. There is not enough "ink" in
the universe.
> The subset of
> listable numbers is in fact a vanishingly small subset of the set as
> described. Yet nothing that WM has said suggests that he would reject a
> formula such as F(x)=x^2, which describes a set with no upper bound. So
> his stance is inconsistent: It appears that he would accept a formula
> that describes an infinite set, yet rejects the notion of infinite sets.
Look: For all practical purposes (FAPP as the late John Bell would
have said) we can apply the axiom
FAPP: E n ==> E n+1.
Students of mathematics should be told that this axiom is only FAPP
true, but FAPP they can go on as they did hitherto, except those who
work in set theory. That is like in physics. People should know about
the existence of atoms, but need not bother further - except those who
work with very small portions of matter.
Regards, WM
tommy1729
> >,
> >
> >
> >
> >
> >
> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > On 5 Jun., 03:54, david petry
> <david_lawrence_pe...@yahoo.com> wrote:
> > > > In this article, "Cantor's theory" refers to
> the ideas about infinity
> > > > and infinite sets introduced into mathematics
> by Cantor. The claim
> > > > here is that Cantor introduced an element of
> make-believe into
> > > > mathematics, and we'd all be better off without
> it.>
> >
> > > > "Set theory is based on polite lies, things we
> agree on even though we
> > > > know they're not true. In some ways, the
> foundations of mathematics
> > > > has an air of unreality." (William P. Thurston)
> >
> > > > "[Cantor's paradise] is a paradise of fools,
> and besides feels more
> > > > like hell" (Doron Zeilberger)
> >
> > > Thank you, David, for this profound contribution.
> Let me add: The
> > > information contents of the accessible universe
> is limited and will
> > > forever remain so. There are no infinite sets.
> Therefore, a
> > > mathematician living in the 21st century and
> teaching, by belief or by
> > > axiom, the existence of completed infinite sets
> has the same degree of
> > > intellectual capacity or honesty as a theologian
> living in the 21st
> > > century and teaching, by belief or by dogma, the
> physical existence of
> > > hell and devil.
> >
> > He whose Universe is restricted to only the
> physical world and cannot
> > enter the many worlds of the imagination has a life
> hardly worth living.
> >
> > Mathematics exists only in those worlds of the
> imagination, and has
> > nothing to do directly with that physical world.
> >
> > And it is a matter of considerable wonder that what
> exists only in the
> > imagination has such important effects in that
> physical world.-
>
> No, that is no wonder. Good mathematics is physics.
> For instance, the
> geometrical division of a line leads to two halves,
> which are really
> equal to each other. Small wonder. Only transfinite
> set theory and
> things alike lead to results which are completely
> inapplicable and
> self contradicting like sum n = 0.
>
> Regards, WM
>
i totally agree :-)
WM
Sorry, I see the short coming of my explanation. What I meant is: You
may use any symbol available on your keyboard, but the sheet of paper
where the symbols are printed cannot cover more than seven.
So, if you have to use the decimal system, you may use all 10 numerals
and parentheses and what may appear useful, but not more than seven
per number. In order to abbreviate sequences of same numerals like
777777 you may write 7(6*).
>
> That is, if "address" you mean "use a unique combination of symbols to
> label a number." If you mean something else, kindly demonstrate.
Exactly. But the number of (copies of) symbols is limited in the
example and in the universe.
Regards, WM
WM
In order to express ideas symbolically, we need at least one symbol
per idea. But there are not more than 10^100 symbols available.
>
Regards, WM
tommy1729
> <vir...@comcast.net>
> wrote:
>
>
> (A) "Good mathematics is physics."
>
> (Wolfgang Mückenheim)
>
>
> (B) "The empirical interpretation of mathematics,
> that is,
> the view that mathematical facts are a special kind
> nd of
> physical [...] facts, is too absurd to be seriously
> maintained."
>
> (Kurt Gödel)
>
>
> Quiz:
> ~~~~~
>
> Which of the two claims sounds more reasonable?
>
> [ ] (A)
> [ ] (B)
>
>
> -----------------------
>
>
> F.
>
> --
>
> E-mail: info<at>simple-line<dot>de
(c) "mathematics is potentially good theoretical physics.
cantor is useless in theoretical physics.
mathematics is older than physics.
bye occams razor cantor is wrong."
(tommy1729)
Alan Smaill
WM
Neugeba...@neugeb.dnsalias.net> wrote:
> WM wrote:
> > On 6 Jun., 23:49, Franziska Neugebauer <Franziska-
> > Neugeba...@neugeb.dnsalias.net> wrote:
> >> WM wrote:
> >> > I expect that the sets used in the Fraunhofer-institutes to be
> >> > simply infinite sets like all natural numbers or the complete real
> >> > line or space. That are just approximations.
>
> >> Approximation to/of what?
>
> > That are approximations to sets of many coordinates.
>
> What does "that" refer to?
the sets used in the Fraunhofer-institutes
>
> ,----[ <4666a2dd$0$97217$892e7...@authen.yellow.readfreenews.net> ]
> | "To represent" (likewise "to approximate") necessitates compulsively
> | some kind of existence of the representee (likewise the approximee).
> | If this existence is denied it is senseless to talk about
> | representation (likewise approximation).
> `----
>
> Do you agree to that statement?
>
> When we (informally) say
>
> x is an approximation of y.
>
> we usually mean that the (necessarily assumed as existent) value of y
> lies in the neighbourhood of x. Do you agree?
No. Growth of a tree is an approximation to its final height. The tree
can be cut before it reaches its final heigth. So there is no final
height.
Life is an approximation to the paradise. Paradise ???
3.14 is an approximation to pi. pi???
>
> Simple questions:
>
> 1. Assume mass was defined in terms of a mass-prototype. Assume you
> steal that Kilogram-Prototype (defined mass is 1 kg) and put it on a
> scale. The scale says: "1.00002 kg". Do you agree that the value
> 1.00002 kg is an approximation to the real mass of 1 kg?
In fact the original kilogram in Paris, which I did not steal, has
changed its mass. Now there is the question, what is the
approximation?
>
> 2. Assume the square root of two defined by x > 0 having x * x = 2.
> Now you steal some pocket calculator and calculate according to some
> formular sqrt(2) = 1.4142. Do you agree that the value 1.4142 is an
> approximation to the real value of square root of two?
It is an approximation to the best fraction which can be found for
this purpose. The real value exists as little as the real product of
momentum and coordinate of a particle.
>
> > If a picture is supposed to consist of infinitely many pixels, if a
> > body is supposed to consist of infinitely many atoms and
>
> Pictures and bodies are physical entities. Math is not about physical
> models.
But it is nothing without such models.
>
> > [I]f the real plane is supposed to consist of infinitely many points,
> > then these suppositions are approximations of reality.
>
> You put the cart before the horse by claiming that maths is about
> physical entities. It is futile to rise up against the the fact that it
> is not.
Contrary to the objects of physics which exist on their own, math is
what you have in your head. What you have in your head is created by
atoms, neurons, electrical currents, hormones, enzyms, etc. Whithout
these constituents you cannot think and there is no math in your
brain. Therefore math is constrained by these ingredients. By
implanting some electrodes or inhaling some drugs your abilities and
your thinking can be completely changed. (Already by inhaling too much
set theory there is usually a significant reduction of cognitive
capabilities.) Therefore math is nothing without your thought and your
thought is impossible without the physical basis. You cannot think of
more than 10^100 different numbers. Therefore more cannot exist for
you. The same holds for every other mathematician.
Remember: While an atom's existence is independent of anybody who is
knowing it, a thought does not exist unless at least one brain thinks
it or one memory stores it.
Regards, WM
G. Frege
wrote:
>
> It is not the time which is the problem (although it could become a
> problem) but the lacking memory space.
>
A fair description of your problems, I guess.
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
> On 6 Jun., 23:36, Virgil <vir...@comcast.net> wrote:
> > In article <1181163489.600343.280...@z28g2000prd.googlegroups.com>,
> >
> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > On 6 Jun., 18:00, luir...@yahoo.com wrote:
> > > > The Goldbach conjecture is a mathematical phenomenon but cannot be
> > > > falsifiable by any computational experiment.
> >
> > > > There is no way how to observe the prime where pi(x) > Li(x)
> > > > but Littlewood showed that after some x it will occur.
> >
> > > > Mathematics is not a natural science for helping us to understand
> > > > the world.
> >
> > > > Mathematics is a game as chess, only that its pieces
> > > > are spaces, points, numbers
> >
> > > but only such numbers which can be addressed individually.
> >
> > If WM claims that any natural numbewr can exist without all of its
> > predecessors down to the first one also existing, he does not understand
> > what natural numbers are all about.
> Old-fashioned stuff! You were right, if the only form of
> representation were the unary system.
The binary, trinary, octal, decimal, etc., systems for naturals work the
same, each natural in any of them, except the first must be a successor
of another.
> The existence of IIII implies the existence of III.
> But these times have passed away - and with them the foundation of
> Peano's axioms.
WM claims that the naturals as based on the Peano properties are passe,
but would discard that sound foundation for no foundation at all.
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
So that WM will restrict his own capacity to that of a highly limited
calculator while mathematicians will not.
Gerry Myerson
Wolf <ElLob...@ruddy.moss> wrote:
I only see one subsequent post of yours (appended),
and I don't see how it responds to what's above.
> Quite so, which is why WM's (and possibly luiroto's) stance is IMO
> inconsistent. He wants to limit mathematics to physically realisable
> proofs, with "proof" being some kind of physical listing of all the
> elements in the proof set. He seems to require listability in real time.
> It's the unlistability in real time that leads him to reject infinite
> sets. IE, as I understand WM's stance, he demands that given theorem
> T(n), list all the elements of {n} for which T is true. That notion of
> proof includes your idealised computation of a counter example for
> Goldbach, of course: if such a number were computed, it would form a
> list of one element - no problem for WM there.
>
> But formulas that describe the elements of infinite sets are a problem.
> If WM is "konsequent", to use the German word for it, he would have to
> reject any formula describing a set with no upper bound, for such sets
> obviously cannot be completely listed (=enumerated) in real time. What's
> more, most of the elements of such sets are so large that they are
> individually unlistable (=unwritable) in real time. The subset of
> listable numbers is in fact a vanishingly small subset of the set as
> described. Yet nothing that WM has said suggests that he would reject a
> formula such as F(x)=x^2, which describes a set with no upper bound. So
> his stance is inconsistent: It appears that he would accept a formula
> that describes an infinite set, yet rejects the notion of infinite sets.
>
> Or so it seems to me.
--
Wolf
> On 7 Jun., 17:26, Wolf <ElLoboVi...@ruddy.moss> wrote:
>> WM wrote:
>>> On 6 Jun., 23:36, Virgil <vir...@comcast.net> wrote:
>>>> In article <1181163489.600343.280...@z28g2000prd.googlegroups.com>,
>>>> WM <mueck...@rz.fh-augsburg.de> wrote:
>>> Let me explain: Suppose you have only 7 symbols available and you have
>>> to use the decimal system. Then you could use these 7 symbols to
>>> address all numbers with seven digits up to 9999999.
>> With 7 distinct symbols, you can address 7^7 numbers of seven digits in
>> length. That's 823543 numbers, or about 8% of 9999999. IOW, your scheme
>> leaves out over 90% of the 7 didgit numbers between 0000000 and 9999999.
>
>
> Sorry, I see the short coming of my explanation. What I meant is: You
> may use any symbol available on your keyboard, but the sheet of paper
> where the symbols are printed cannot cover more than seven.
OK.
> So, if you have to use the decimal system, you may use all 10 numerals
> and parentheses and what may appear useful, but not more than seven
> per number. In order to abbreviate sequences of same numerals like
> 777777 you may write 7(6*).
>> That is, if "address" you mean "use a unique combination of symbols to
>> label a number." If you mean something else, kindly demonstrate.
>
> Exactly. But the number of (copies of) symbols is limited in the
> example and in the universe.
>
> Regards, WM
>
So IIUYC you claim that if you can't write the address or label of the
number, then the number doesn't exist. Why not?
Wolf
> On 7 Jun., 17:11, Wolf <ElLoboVi...@ruddy.moss> wrote:
>> But formulas that describe the elements of infinite sets are a problem [for WM].
>> If WM is "konsequent", to use the German word for it, he would have to
>> reject any formula describing a set with no upper bound, for such sets
>> obviously cannot be completely listed (=enumerated) in real time.
>
> It is not the time which is the problem (although it could become a
> problem) but the lacking memory space.
>
> I would not reject a formula like, e.g.,
> All natural numbers which can be addressed will turn out positive.
>
>> What's
>> more, most of the elements of such sets are so large that they are
>> individually unlistable (=unwritable) in real time.
>
> It is not the time, which is the problem. There is not enough "ink" in
> the universe.
Time or 'ink', makes no difference. Nor does the scale that you choose
for 'ink' or for time. If the universe is of finite size, then,
expanding or not, there will be a smallest number that you cannot write
down in the available space. If time must have a stop, then there will
be a smallest number whose address you cannot write down between now and
then. Whether you have written down other numbers or not, makes no
difference.
Quite an interesting state of affairs, that. As the universe draws to an
end, the available pool of addressable numbers will shrink, and at the
last point of space-time, just before the universe winks out of
existence, you will have space and time enough to write down only one
address: 0.
OTOH, if time is unending, then you will be stuck with an infinitely
long address. For then there is number such that for every 'tick' you
will be writing the next symbol. For ever and ever.
A conception worthy of Douglas Adams, WM. You're in good company. ;-)
[...]
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
Mathematics in independent of physics, which some supporters of physics
as sole parent of mathematics, in their arrogance, ignore.
Those, like WM, who would put mathematics in chains would effectively
emasculate it.
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
> Sorry, you are wrong.
Says someone who knows no math.
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
> It is not the time, which is the problem. There is not enough "ink" in
> the universe.
That is mere supposition. The finiteness of the universe is still mere
hypothesis, and is likely to remain so.
Virgil
WM <muec...@rz.fh-augsburg.de> wrote:
> In order to express ideas symbolically, we need at least one symbol
> per idea. But there are not more than 10^100 symbols available.
That presumes a finite universe, which is mere presumption.