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Author
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Topic: What information is not.
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Melvin H. Fox
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Member # 1684
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posted 30. December 2006 16:00
Matt,
Any system of mathematics takes for granted the context of a universal objective set of truths called axioms. I am not the culprit. These are necessary footers upon which the system is built. By the way, the axioms are arbitrary yet once they are set they are rigid for that system. The system may or may not be usful for making predictions in our physical world.
Yes, the natives can learn our number system but which number system is correct?
You wrote:
quote:
We should have been able to figure out who voted for whom (i.e. known the objective truth) but we couldn’t.
The ideal would be to know or determine the real number of votes for each candidate but just like finding a real, physical, circle determining the true winner of that election was and is impossible; the margin of error being larger than the margin of victory. We agree that an objective truth exists in the matter. The fact is that all of the mathematics in the world can’t help us determine that truth and therefore the final count could not be considered objective.
What of the ducks, there are only three of them? Why is that count not objective? Well it is reasonably objective. As long as everyone we canvass uses our number system and rules for adding, has good eye sight, the ducks are distinguishable and not swimming too fast, no sudden dives are taken by any of them, a muskellunge does not come up and snatch one mid-count, and nobody has money riding on how many swimming ducks there are, then we can be reasonably sure we will all get the same count. However, error can still ruin the score.
I played basketball as a boy growing up, six seasons in all, roughly 150 games. As part of the preparation for each game I had to make sure I packed my game sneakers. Easy enough, one, two, got’em. Well wouldn’t you know it, in the locker room before one of the games I looked in the bag and found one shoe? How could that have happened? I was as confident of that count as any of the other 149 successful counts. Were the others objective and that one not? I submit that none of them were truly objective because the error could have taken place before any of the games.
If you count three ducks and I count two and later we both testify under oath as to our respective tallies and there were no other witnesses to the ducks swimming, then one of us is lying or wrong (maybe both of us). What is the objective judge to do? What information does he have? Most likely there were some ducks swimming but not “much”?
I say again, the mathematics is not the information.
JT75, I will answer you in another post.
-Mel
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Zarathustra
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Member # 3407
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posted 30. December 2006 23:59
JT75 has made a lucid contribution at the bottom of page 6 with respect to the number ducks in the pond, which sums the situation up perfectly. The ducks exist in the physical (i.e. extra-mental) world. Two different observers will usually see the same ducks, and both will report the number "3". This is a description of the number of ducks, and has nothing to do with the ducks themselves. It can be said that the number is "objective", since the observation can be made by any number of people who will agree on the number. [Daniel has already twigged the "description" angle, btw.]
It would be wrong, however, to suggest the the number "3" itself has any physical existence, and in this, Matt's thesis is wholly correct: it is immaterial. Information, being a description of things, is always abstract, which is to say that it lies entirely in the realm of the mind. [There are many who maintain that mental representations and thinking are entirely physical, since there is no reason to believe it is not so, but that is a different debate altogether.]
It is salient to mention that the speed of a cheetah running on the Savannah is not available until it is synthesized from raw observations. Only physical phenomena can be observed, and "speed" is not one of them. It is an abstract quantity based on the observations of an object's position at two different times. I grant that one is not at liberty to fabricate such data; the physical world has proved itself to be remarkably impervious to our attempts to change it simply by asserting that it be different.
The problem of an infinite amount of possible information is solved at a single stroke with the notion that "information" is simply a human description that we choose to agree on; the ducks will always be there, but the "number of ducks" is only manifested when someone bothers to count them.
[Congrats on your new sleeping schedule, btw, Matt. There is more than one way of replicating information, and some of them are more rewarding than using a photocopier.]
Minor points:
Matt: "Einstein showed that space-time is curved, but curved in relation to what?"
Curved with respect to the standard mathematical notion of a straight line.
JT75: "(since science is in the business of deriving necessary laws about natural phenomena)."
Too strong. Not "necessary", just "generally applicable".
Stephen: "But prior to its data being measured by the agent - its information exists - completely independent. Information in this formal sense is not dependent on a "knower" who can have mutual information configured in its mind."
Zarathustra is not entirely unfamiliar with information-theoretic formalisms, having had the dubious pleasure of working in a telecoms research establishment for a number of years in the mid-eighties. I'm fairly certain the discussion on this thread is concerned with "semantic" information, though. Nevertheless, I, for one, would be most pleased were you to start a new topic on a subject involving a more formal treatment. How much information is there in the universe?
Melvin: "Any system of mathematics takes for granted the context of a universal objective set of truths called axioms."
For this statement to be accurate, the words "universal objective" need to be removed, and the word "truths" has to be replaced by "rules". It's fine otherwise.
Z
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Bruce Fast
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Member # 924
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posted 31. December 2006 12:14
Melvin H. Fox, I would love to see you demonstrate an alternative number system that has some level of complexity. I would like to see something that does not represent integer math as we do with a complexity that demonstrates that it is sufficiently different that a simple conversion table cannot convert to the numbering system that we have. The roman numeral system, for instance, does not seem to me to be a new math to me, its just a complex based system (as time is, base 60 seconds to minutes, base 60 minutes to hours, base 24 hours to days ... )
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Zarathustra
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posted 31. December 2006 23:02
quote:
Bruce Fast: Melvin H. Fox, I would love to see you demonstrate an alternative number system that has some level of complexity.
Modular arithmetic. Consider the 360-degree system we use for rotations. The value 412 can be considered equivalent to 52 (i.e. "congruent"). One could misguidedly count 50 ducks using this system, but multiplying the number by ten could make the result equivalent to 140 (or even -220, were one ever to need a negative number of ducks).
quote:
Bruce: The rules of mathematics are fixed. If you attempt to generate different rules, you end up with a mathematical form that is internally inconsistent -- that is useless.
The rules of a particular mathematical system are chosen because they are applicable to a given problem domain, and this applies whether that domain has a physical analogue or not. Gödel put the last nail into the coffin of "completeness" for all sufficiently expressive systems, and mathematics is one of them. You'll just have to get used to the idea, I'm afraid, Bruce.
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Bruce: There is only one mathematics, and it predated me and you. It probably predated the big bang, and therefore time, itself.
It is always a special treat to be told about the state of the universe prior to the instant indicated by the BB extrapolation. We hear too little about that period nowadays. Since "to predate" something means that it occurred prior (in the temporal sense), one does have to ask how anything can "predate" time. Is such a statement meaningful, or has Bruce simply become overheated?
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Martin
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Member # 2001
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posted 01. January 2007 04:36
Matt wrote
quote:
Long before the meaning of these mathematical patterns had been translated into the patterns of the morphemes and symbols of a human language, the patterns still existed in nature, did they not?
Integer numbers as such seems to our reason exist in nature. Might be that all numbers can be expressed using only integer numbers (using series). Yet numbers are only symbols as all words are. They are not reality they only represents somehow reality. Anyway I doubt that Ludolfs number pi=3,14... exists as such in nature - at least you cannot observe it directly, you need use your reason. The same with Euler number.
Kant notion was that it is human reason that put rules into the Nature. And not that we draw rules from Nature (discovery them).
At least reading many years ago Ernest Cassirer I was convinced that words are only symbols that only humans can underestand - that behind them some meaning is.
Btw is not this discussion about "reality" of information old dispute between nominalism vs. realism?
[ 01. January 2007, 05:05: Message edited by: Martin ]
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Martin
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posted 01. January 2007 04:55
JT75 wrote:
quote:
But we live in day that is dominated by Einsteinian physics and some elements of non-Euclidean geometry. Either the laws of the understanding have changed (the very thing that grounded necessity for Kant) or they are not the only thing that enables us to make scientific discoveries (that is it is possible that revolutions in science are based on new information from the extra-mental world), either way Kant is wrong.
I would say that we use quantum physics more than theory of relativity. At least nuclear reactors etc seem to me to be the outcome of modern quantum physics. I do not know where Einstein physics have now use in technic - even in rocket sent to the Moon or the Mars we did not consider it to compute where and when they arrive, did we? Or I am wrong. Now it has come to my mind that it is used to explain some phenomenons in physics of semiconductors because of great numbers of electrons in a material makes its effects substantional.
Euklidian geometry - we still learn it on primary and secondary school same as it was taught 2000 years ago.
My point is that maybe Kants philosophy should not be dismissed completely because it still describes great part of our experience as Euklidean geometry and Newtonian physics do.
[ 01. January 2007, 05:26: Message edited by: Martin ]
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Matt Connally
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posted 01. January 2007 07:47
Melvin:
quote:
Yes, the natives can learn our number system but which number system is correct?
Zarathustra:
quote:
The rules of a particular mathematical system are chosen because they are applicable to a given problem domain, and this applies whether that domain has a physical analogue or not. Gödel put the last nail into the coffin of "completeness" for all sufficiently expressive systems, and mathematics is one of them.
Are they not all different translations of various portions of the same system? The natives translated only a small part; Euclid translated more; Gödel observed that no matter how much we translate we will never be able to wrap our minds around it. For all practical purposes it might be safe to assume that math is infinitely complex, but we can never now—again, as per Gödel’s theorem. It would be erroneous to say that different portions of the system contradict each other. That would be like saying that English and Chinese contradict one another. It all translates.
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Matt Connally
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posted 01. January 2007 07:49
Zarathustra to Bruce:
quote:
It is always a special treat to be told about the state of the universe prior to the instant indicated by the BB extrapolation. We hear too little about that period nowadays.
Actually Zarathustra, all of cosmology rests on the faith that there are physical laws that governed the BB. Unifying/reconciling relativity with quantum mechanics is the search for an objective sentence (an equation is simply any sentence whose main verb is a form of equal) that preceded it all. As Hawking put it, if we discover the Theory of Everything, “We would then all be able to have some understanding of the laws that govern the universe and which are responsible for our existence.” (The Theory of Everything, pp.164)
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Matt Connally
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posted 01. January 2007 08:01
Melvin:
quote:
I say again, the mathematics is not the information.
Zarathustra:
quote:
The problem of an infinite amount of possible information is solved at a single stroke with the notion that "information" is simply a human description that we choose to agree on; the ducks will always be there, but the "number of ducks" is only manifested when someone bothers to count them.
There are an infinite variety of ways that, for example, the meaning of the word three can be represented:
- Fingers (three of them)
- Beads on an abacus (three of them)
- Knots in a rope (three of them)
- 3
- III
- “Three” (English morpheme)
- “San” (Chinese morpheme)
- Eggs (three of them)
- Ducks (three of them)
- Waves (three of them)
- Pebbles (three of them)
- Seashells (three of them)
It would seem you guys are arbitrarily declaring that the first 7 representations “exist” and that the next 5 do not “exist”?
Translating my observation of 3 ducks in a pond simply communicates my view of the (objective) world at that particular time and place. But of course the world (including all the objective information) is always changing—like the images on a movie screen or the notes in a musical piece.
Now, looking at that list of 12 representations in light of my opening post, I am not asking what source they all have in common. I am simply asking what physical property they have in common. Objectively, none. Information is undeniably immaterial, and an immaterial, creative rationality (as coherent and as infinite as arithmetic) pervades every quanta of the cosmos.
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Melvin H. Fox
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Member # 1684
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posted 01. January 2007 10:16
Bruce,
Consider the set A of mathematical objects [numbers] where a, b, c are elements of A and a < b < c < x where x is any element of A not equal to a, b, or c. Define the operation # in the following way; x # y = y # x = y, for y > [or equal to] x and x and y elements of A. Define the operation * in the following way; x*y = xy < y*x = yx for any x and y elements of A with x < y. We construct A from its least elements {a, b, c} in order using the operation * as so:
A = a, b, c, aa, ab, ac, ba, bb, bc, ca, cb, cc, aaa, aab, aac, aba, abb, abc, aca, acb, acc, …
I believe that set A qualifies as a number system with some level of complexity sufficiently different so as no simple conversion table can be used to convert to the numbering system we have.
But what on earth would we measure with it? Perhaps nothing, as I said no physical application need exist. However, suppose it is found that of two agents x and y, when acting as combatants, the more potent agent of the two destroys the less potent agent suffering no ill effects itself [x # y = y]. Further suppose that when two agents [x and y] compose x into y a new agent xy is formed but if they compose y into x a different agent is formed yx and the relative potencies are as follows: x < y < xy < yx. The number system constructed above is a perfect match to measure all possible agents of this sort built from successive compositions of three basic agents.
I agree the agent composition is contrived but we do not know, there might exist some profound application to this fledgling number system.
-Me
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Melvin H. Fox
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posted 01. January 2007 10:32
Zarathustra,
You have taken exception to my statement: Any system of mathematics takes for granted the context of a universal objective set of truths called axioms.
The axioms are universal to the system, they apply every where and always. The axioms are objective, rigid and exact adherence is required so that the same result always appears every time identical trials are performed.
Is it a rule that addition over the set of real numbers is commutative or is it accepted as true without proof?
-Mel
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Melvin H. Fox
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Member # 1684
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posted 01. January 2007 10:58
JT75,
Point #1: I never said there were no applications to mathematics in the physical world. I maintain that mathematics has no physical existence.
Point #2: Yes, I stand corrected. Physical and real are two different qualities and I will try not to confuse them in the future. The point I am trying to make is that while the mathematics hold as objective the application of the maths can never be objective.
Math is not information. Likewise, Spanish is not information and Aramaic is not information.
I don’t know what information is but I do know that math is not information. Math is a tool used to discover and convey the information. It is the vehicle not the content.
-Mel
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Melvin H. Fox
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posted 01. January 2007 11:21
Bruce,
Is there only one geometry? Given a line and an external point, how many lines exist in the same plane that pass through the given point and are parallel to the given line?
Note: I understand that I am not supposed to make more than three [san, III, 3] posts per day on this forum. Perhaps I miscounted?
-Mel
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IF
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Member # 1904
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posted 01. January 2007 12:31
IMHO, information is only useful to any organism if and only if its meaning can be extracted such that a "proper" response is the most likely result if no organisms are available then information is only the existence of discreet objects.
Happy New Year!
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JT75
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posted 01. January 2007 17:06
Martin wrote:
quote:
Kant notion was that it is human reason that put rules into the Nature. And not that we draw rules from Nature (discovery them).
and
quote:
My point is that maybe Kants philosophy should not be dismissed completely because it still describes great part of our experience as Euklidean geometry and Newtonian physics do.
Martin, I never said we should dismiss all of Kant's philosophy, I actually enjoy some of what he says in aesthetics (and this is not to give the impression that I am thoroughly well versed in Kant's entire corpus). Having said this, however, I think it is misguided to place less emphasis on a particular point than the original author did in order to save his system. Kant's transcendental argument for the nature of natural laws being derived from the necessity found in the intellect (or more specifically its intuitions and categories)implies that it would be impossible for their to be a scientific revolution that proves Newtonian physics false (or limited) or Euclidean geometry false (or limited). The fact that such revolutions have occured is an indication that Kant's system is either wrong or in need of significant revision. If you like what he says you must think about the implications when aspects of his system fail. That is, if his conclusions about epistemology follow from his ideas about intuitions and categories, and these ideas have been shown to be questionable, then honesty demands that one re-evaluate his epistemological conclusions. I think one thing that Kant has done is to press home the implications of both Humean skepticism and realism in the form of naive realism (which leads to the antinomies). I hold to a form of Thomistic realism that does not fall prey to Kant's antinomies but these antinomies do help show what type of realism we should avoid (because it leads to contradictions).
It is not the degree to which Einstein is used today that calls Kant into question, but rather the existence of any other system of physics that is not Newtonian. I think if Kant were alive and knew of the present situation in physics he would head in a different direction. As I said, the features of his system that make him a brilliant revolutionary in his own time also make him untenable in our own.
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