Mersenne's Miscelleny

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Re: Mersenne's Miscelleny

Post by Mersenne »

"If we could see all of ourselves, what would be doing the seeing?"- Ian Watson, Miracle Visitors.

I'll have to disagree with respect to Penrose, so the question of whether one can programme oneself is moot. How can a digital computer even handle an irrrational number, or a genuinely random process? However, it may be possible to manfacture an alternative expression of your horoscope, and hence of your "self". An artist conveys more of him than an autobigrapher; in a sense, the artist recreates himself in his work. Why not the informed atrologer?
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Re: Mersenne's Miscelleny

Post by James Strom »

What if there were no such things as irrational numbers? If it takes an infinite number of digits to write the square root of two, for instance, then that number cannot be expressed by any entity in the universe. If something is inexpressable then it cannot be said to exist even in the abstract.
Genuine randomness only can exist in the subjective world as it requires a lack of knowledge from the viewer of the randomness. Anything that seems random must necessarily involve the input of something outside the realm of our knowledge. Since it is possible to know anything except yourself then all truly random events are subjective in nature. Subatomic particles only seem to move randomly because, in order to observe them, we must get so close that they become a part of us. The Universe can, and must, be both deterministic and unpredictable.

The quantum physics of Art

1) To measure something is to change it.
2) To do Art is to express yourself.
3) To express yourself you must know yourself.
4) To know yourself is to change yourself.
5) Therefore you only know your old self; not your present one. Go to 1)
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Re: Mersenne's Miscelleny

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What if there were no such things as irrational numbers? If it takes an infinite number of digits to write the square root of two, for instance, then that number cannot be expressed by any entity in the universe. If something is inexpressable then it cannot be said to exist even in the abstract.
But there are! Some equations need irrationals for their solutions. The digital (or rather discrete) method does use infinite runs of symbols to express an irrational number, but irrational numbers are easily expressed in a finite way by other methods- so this is a weakness of the discrete (digital) method and of any machine based on it.

Example; x^2=2 has solution sqrt(2). So this is a finite expression of the irrational number.
Genuine randomness only can exist in the subjective world as it requires a lack of knowledge from the viewer of the randomness. Anything that seems random must necessarily involve the input of something outside the realm of our knowledge. Since it is possible to know anything except yourself then all truly random events are subjective in nature.
Surely this is the "hidden variables" argument, Enstein/Rosen/Podolsky's objection to randomness in quantum mechanics? Bell/Aspect showed this reasoning to be incorrect; randomness is plumbed into the objective universe.

Might be a weakness in my understanding here- if you're equating randomness with consciousness, then the whole universe may be considered subjective (Chalmer's position, though he expresses it in terms of information rather than randomness). Is this your position?
Subatomic particles only seem to move randomly because, in order to observe them, we must get so close that they become a part of us. The Universe can, and must, be both deterministic and unpredictable.[\quote]

It's not just that the mechanics of the act of observation involve randomness, since any interaction on the subatomic scale, consciously directed or not, entails a probablistic outcome.
The quantum physics of Art

1) To measure something is to change it.
2) To do Art is to express yourself.
3) To express yourself you must know yourself.
4) To know yourself is to change yourself.
5) Therefore you only know your old self; not your present one. Go to 1)
[/quote]

I like this idea. Hofstadter argues for regression as the basis of consciousness, this would express it well.
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Re: Mersenne's Miscelleny

Post by James Strom »

"Some equations need irrationals for their solutions."

I disagree. Everything eventually boils down to a finite amount of information. As such, all math can be expressed with integers and functions. The way I visualize it, in order to get a square root something must first be squared. If that number itself is a root repeat the process until we arrive at a finite, rational number. The confusion arises from how we define 'two.' Two what? Two pairs? Then the root is plainly rational. When I mentally picture doing a square root I first visualize squaring something and then just running it in reverse.
In this sense even fractions do not exist. In order to divide you must first have something multiplied. 3/5 may be seen as 3 parts of a quintet. Everything comes down to integers in the end.

"Bell/Aspect showed this reasoning to be incorrect; randomness is plumbed into the objective universe."

Any definition of randomness you can come up with will involve some subjective element. Thus in a completely objective realm randomness cannot exist by definition. It would be like an unstoppable force in a universe with an immovable object.

"It's not just that the mechanics of the act of observation involve randomness, since any interaction on the subatomic scale, consciously directed or not, entails a probablistic outcome."

True. Visualize a universe much like a very large checkerboard with the checkers moving according to set of rules (such as one square at a time in the direction of the last movement unless encountering... ). Everything in this universe is deterministic. The smallest quantums are squares and a checkers. There is even a form of relativity as nothing can move faster than one square at a time. Movement slower than that is only the illusion generated when an object goes back and forth many times before moving to the next square.
Even though this universe is Newtonian in its predictability we run into a problem when looking at the smallest of things. To find out where a checker is necessarily involves moving it. It becomes impossible to know for certain where something is. Things begin to look 'fuzzy' on the smallest scale. Yet there is no randomness whatsoever involved.
Such a universe is in fact inevitable if we are limited to using a finite amount of information, no matter how large, to describe it.
In other words, quantum weirdness and relativity are a must in any conceivable universe that can be designed or created by any entity whatsoever.
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Re: Mersenne's Miscelleny

Post by James Strom »

I came up with this last night.

Day rulership

Sign Planet Quantity

Leo Sol Mass
Vir Mer Length
Lib Ven Area
Sco Mar Volume
Sgr Jup Time
Cap Sat Frequency
Aqr Ura Velocity
Psc Nep Acceleration
Ari Jun Momentum
Tau Pal Force
Gem Cer Action
Cnc Ves Energy

Night rulership

Sign Planet Quantity

Cnc Lun Current
Gem Mer Charge
Tau Ven Flux
Ari Mar Potential
Psc Jup Conductance
Aqr Sat Capacitance
Cap Ura Inductance
Sgr Nep Resistance
Sco Jun Strength
Lib Pal Intensity
Vir Cer Temperature
Leo Ves Luminosity
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Re: Mersenne's Miscelleny

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"Some equations need irrationals for their solutions."
I disagree... Everything comes down to integers in the end...
This isn't a matter of opinion! Georg FLP Cantor proved it in 1891. Gist of proof; there are more numbers than are needed to account for the natural numbers.

If it turns out that all matter, space and time in the universe is absolutely discrete and consists of countably many "thingies", there will still be the non-material to account for.
Any definition of randomness you can come up with will involve some subjective element... Thus in a completely objective realm randomness cannot exist by definition.
Well, any definition has a subjective element, because some person has made it. But there are objectively random processes, radioactive decay being the exemplar. Are you refering to the deterministic evolution of the wave function prior to observation? This is true only of an isolated system- as long as there's an outside to interact with a series of probablistic outcomes must occur. Given an infinite unverse/multiverse, every finite thing has an outside.
"It's not just that the mechanics of the act of observation involve randomness, since any interaction on the subatomic scale, consciously directed or not, entails a probablistic outcome."

True. Visualize a universe much like a very large checkerboard with the checkers moving according to set of rules...
In other words, quantum weirdness and relativity are a must in any conceivable universe that can be designed or created by any entity whatsoever.
This is certainly the Einstein/Rosen?podolsky "hidden variables" approach. This just isn't the case.

Did creationism just sneak in?
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Re: Mersenne's Miscelleny

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James Strom wrote:I came up with this last night... Luminosity

Oscar Wilde: "I wish I had said that"
JM Whistler: "You will, Oscar, you will."
From L.C. Ingleby, Oscar Wilde (1907)
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Re: Mersenne's Miscelleny

Post by James Strom »

"This isn't a matter of opinion! Georg FLP Cantor proved it in 1891. Gist of proof; there are more numbers than are needed to account for the natural numbers."

I do not believe that Cantor proved anything. Since no infinity can be defined exactly then infinity is invalid as a mathematical concept. Therefore any sort of proof that uses some version of an infinity is a spurious proof, no better than one that uses division by zero.
I will go further. The very concept of infinity has no value in the discussion of anything objective. If one does not permit the use of of it in our own thinking many seemingly intractable problems can be resolved. Take the Achilles Paradox, for instance. It relies upon a infinitely divisible continuum of length. If it insisted that there can only be a finite number of divisions then the problem is resolved.
What is the first digit of ten? 1, right? But 9.999999...(infinite number of 9's) is also equal to ten. So is the first digit then 9? Not if we disallow the use of infinity.
I can't think of any paradox out there that doesn't contain an infinity somewhere.
A lot of things become clearer when thinking this way. How many natural numbers are there? As many as you wish to count up to, but no more. The definition of the number of natural numbers then is plainly a subjective one.
There can never be a real proof if an infinity is involved because the question can never be answered by the "manual" method. That is, rather than following the reasoning of the argument we simply check every possibility by hand. This can be done with any argument that has objective definitions, even if it were not practically feasible.

"If it turns out that all matter, space and time in the universe is absolutely discrete and consists of countably many "thingies", there will still be the non-material to account for."

The non-material is the subjective. It exists objectively only to those outside of yourself. That isn't to say that you're not real!
Since no being can truly know itself it must exclude its own form from what it perceives to be objective reality. The spiritual realm is our own selves projected onto the world around us.

"But there are objectively random processes, radioactive decay being the exemplar."

Anything in the objective universe is finite and can therefore be modeled precisely. A fast enough digital computer with sufficient memory should be programmable to recreate any thing or event. But no programmer, regardless of even god-like abilities, could generate a true random number. Therefore radioactive decay occurs at least in part in a subjective manner or it is not random.
I do not think that the "hidden variable" is in the particle we're observing but rather in what we're measuring it with.

"Given an infinite universe/multiverse, every finite thing has an outside."

But if you give it an infinite universe to work with it is no longer finite

"Did creationism just sneak in?"

Maybe. I believe in the law of the conservation of information. You can't create something from nothing. That information came from somewhere.
In a checkerboard universe such a law holds. You could look at any situation and be able to determine exactly what happened at any time in the past and even predict the future with certainty. But this is prevented by the impossibility of any being living in such a universe to determine exactly where the "checkers" are, analogous to quantum physics. Of course, if information can be neither created or destroyed then the second law of thermodynamics isn't quite valid. Who says entropy must always increase?

When I draw a divide between the objective universe and the subjective one it isn't meant to be in black or white. There is a lot of gray area in between. Everything has some of both.
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Re: Mersenne's Miscelleny

Post by Mersenne »

Hi James,

A thought-provoking post as usual.
I do not believe that Cantor proved anything. Since no infinity can be defined exactly then infinity is invalid as a mathematical concept. Therefore any sort of proof that uses some version of an infinity is a spurious proof, no better than one that uses division by zero.
Infinity is well defined- indeed different types of infinity are well defined.
I will go further. The very concept of infinity has no value in the discussion of anything objective.


It's used daily to resolve practical problems, as are infinitesimals.
If one does not permit the use of of it in our own thinking many seemingly intractable problems can be resolved. Take the Achilles Paradox, for instance. It relies upon a infinitely divisible continuum of length. If it insisted that there can only be a finite number of divisions then the problem is resolved.


An infinite number of infinitesimal components comprise a finite quantity- this is the basis of integral calculus, which resolves the AP.
What is the first digit of ten? 1, right? But 9.999999...(infinite number of 9's) is also equal to ten. So is the first digit then 9? Not if we disallow the use of infinity.


Both are just conventions. The first digit of any representation of the number ten depends on the system used. In Roman numerals it's X. In base 4 it's 2 (22).
I can't think of any paradox out there that doesn't contain an infinity somewhere.


Apparent paradox, such as the AP, is resolved with a proper understanding of infinities.
A lot of things become clearer when thinking this way.
Clearer does not entail true. This way of thinking fails to address the difficulties inherent in understanding infnities- which exist!- by refusing to recognise them. By doing so we achieve deeper and indeed practical understanding.
How many natural numbers are there? As many as you wish to count up to, but no more. The definition of the number of natural numbers then is plainly a subjective one.


Well, your definition is! The Peano axioms are a little firmer.
There can never be a real proof if an infinity is involved because the question can never be answered by the "manual" method. That is, rather than following the reasoning of the argument we simply check every possibility by hand. This can be done with any argument that has objective definitions, even if it were not practically feasible.


Real proofs use infinities all the time. Penrose (Emperor's New Mind) argues that the mind is non-algorithmic because it addresses infinities (strictly, because it can draw information from utside any finite system); if this weren't the case, machines could do proofs. They can't, because information external to the system employed is required.
The non-material is the subjective. It exists objectively only to those outside of yourself. That isn't to say that you're not real! Since no being can truly know itself it must exclude its own form from what it perceives to be objective reality. The spiritual realm is our own selves projected onto the world around us.


I think you're wrong to identify the nonmaterial with the subjective, but this statement does puzzle me. Perhaps you cold enlarge on it?
Anything in the objective universe is finite and can therefore be modeled precisely. A fast enough digital computer with sufficient memory should be programmable to recreate any thing or event.


No, the majority of processes can in the universe can only be modelled approximately by a computer, using finite numerical calculus. Exact models use ininitesimal calculus and so admit the use of infinities.
But no programmer, regardless of even god-like abilities, could generate a true random number.
The programmer could, but the machine he/she programs couldn't. The programmer has god-like abilities, i.e. spirit.
Therefore radioactive decay occurs at least in part in a subjective manner or it is not random.
I do not think that the "hidden variable" is in the particle we're observing but rather in what we're measuring it with.
There are no hidden variables, is what aspect/Bel proved experimentally. Radiocative decay is indeed random. A Geiger counter is a very good analogue random number generator.
ME: "Given an infinite universe/multiverse, every finite thing has an outside."

JS: But if you give it an infinite universe to work with it is no longer finite
An infinite number of finite systems comprises an infinity.
(Re. Creationism) Maybe. I believe in the law of the conservation of information. You can't create something from nothing. That information came from somewhere.
In a checkerboard universe such a law holds. You could look at any situation and be able to determine exactly what happened at any time in the past and even predict the future with certainty. But this is prevented by the impossibility of any being living in such a universe to determine exactly where the "checkers" are, analogous to quantum physics. Of course, if information can be neither created or destroyed then the second law of thermodynamics isn't quite valid. Who says entropy must always increase?
I sympathise with the concept of conservation of information- there's strong evidence for it from the behaviour of black holes and the "hologrphic universe" theory. But if it's true it doesn't require a checkerboard universe. Claude Shannon explored continuous information sources as well as discrete, and his findings hold for both.
When I draw a divide between the objective universe and the subjective one it isn't meant to be in black or white. There is a lot of gray area in between. Everything has some of both.
This makes sense, but doesn't fit in with your "checkerboard". That's black and white, and a piece is either in one or the other.

Regards,

Mersenne.
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Re: Mersenne's Miscelleny

Post by James Strom »

Sorry for taking so long to reply but I guess I don't know how to use a computer. I have forgotten my password so I did the "forgot password?" thing. Of course it doesn't email me the forgotten password. That would make sense. Instead it gives me a new one that I'm guaranteed to forget even if I were "Rainman." So I composed a long reply to this thread only to have it deleted because I apparantly wasn't logged in. This is the second time. I'll try again. Meanwhile I'll try and stay away from sharp objects for my own and the public's safety.
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