The Mathematical Universe

Discussions on the nature of being, existence, reality and knowledge. What is? How do we know?

Re: The Mathematical Universe

Postby Dave_Oblad on April 6th, 2017, 5:38 pm 

Hi Raj,

If said Triangle existed on a curved surface.

Do you disagree with the concept that given Infinite Complexity and Infinite Depth of a CA, that you might Exist there in one of them?

What does it mean to Exist?

Regards,
Dave :^)
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Re: The Mathematical Universe

Postby Positor on April 6th, 2017, 7:31 pm 

Dave_Oblad » April 6th, 2017, 3:11 pm wrote:Look at 10/3 as a question (yes I know that involves numbers but bear with me).
You don't have to be very astute to see (in decimal) the answer is 3.333333333333 etc.

If I asked what the 1,000,000th digit to the right of the decimal point.. you would say "3" with complete confidence. Why? Because it can't be anything else, given the method of deduction used.

But if you asked: "What is the square root of 4?", I would reply "+2 or -2". It could be either; there is no uniquely correct answer. The two answers are not equivalent, since +2 is not equal to -2. It has to be one or the other. Does this introduce indeterminacy into math and/or logic — at least in the context of a mathematical universe, which would have to "choose" one of the two values?
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Re: The Mathematical Universe

Postby someguy1 on April 6th, 2017, 9:34 pm 

Positor » April 6th, 2017, 5:31 pm wrote:But if you asked: "What is the square root of 4?", I would reply "+2 or -2". It could be either; there is no uniquely correct answer. The two answers are not equivalent, since +2 is not equal to -2. It has to be one or the other. Does this introduce indeterminacy into math and/or logic — at least in the context of a mathematical universe, which would have to "choose" one of the two values?


Mathematically that's not a problem. The convention that the square root of a real number is the positive one is just that, a convention.

In complex variable theory the complex square root function is multivalued. In fact there's a mathematical structure that packages this up very nicely. It's called a Riemann surface.

Some functions such as the complex logarithm are infinitely valued. A Riemann surface lets you consider all the possible outputs at once, as a topological structure.

If one is a Platonist and asks what mathematical structures God (or the great computer in the sky, same evidence-free metaphysical belief) would make, my answer (to the extent I'm wearing my Platonist hat for sake of discussion) is that God made the Riemann surfaces. They're very natural. Limiting the square root function to only real numbers and beating into students the convention that "the square root is the positive one of the two," I would say is historically contingent human-created math. It's the full Riemann surface that is the Platonic mathematical object. Humans found the real numbers first because we're so limited. The complex numbers are the more natural setting for the mathematics of the universe. If I believed in such a thing, which I sometimes do and sometimes don't.

ps -- Here's a picture of the Riemann surface for the complex square root function. You can see that each vertical line intersects the surface at two points, which are the two square roots. Many things that are clunky in the real numbers make much more sense in the complex numbers.

Image
Last edited by someguy1 on April 6th, 2017, 9:51 pm, edited 1 time in total.
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Re: The Mathematical Universe

Postby rajnz00 on April 6th, 2017, 9:48 pm 

Dave, I see you have been unable to prove that in any triangle, two angles taken together, in any manner, are less than two right angles.

OK here's another problem - you are to measure the height of the Great Pyramid of Cheops. Your only instrument, a stick 1 metre long. You also know, (have measured), the square base of the pyramid and its sides measure 230 m. And one face is due north. How will you get the height of the pyramid to the nearest metre?

I disagree.

To exist is to be present in a certain space over a certain period of time.
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Re: The Mathematical Universe

Postby mitchellmckain on April 7th, 2017, 4:30 am 

Positor » April 6th, 2017, 6:31 pm wrote:
But if you asked: "What is the square root of 4?", I would reply "+2 or -2". It could be either; there is no uniquely correct answer. The two answers are not equivalent, since +2 is not equal to -2. It has to be one or the other. Does this introduce indeterminacy into math and/or logic — at least in the context of a mathematical universe, which would have to "choose" one of the two values?


That is not correct according to proper mathematical procedure. The square root of 4 is 2 -- just 2. You are confusing this with the solution to the equation "x squared equals 4." In that case the answer is +2 or -2, two solutions to the equation. Proper procedure solves the equation as follows.

x^2 = 4
you take the square root of both sides to get
x = +/- square root of 4.
See? here and everywhere else in mathematical procedure the square root is taken as a positive number. But you have rules which come into play when you do things to both sides of an equation like take a square root in order to give you all of the solutions.*

You have the same thing in the quadratic formula.
a x^2 + b x + c = 0
gives
x = [- b +/- sqrt(b^2 - 4 a c)]/(2 a)
Again the square root is taken as positive and you need that +/- in the formula to give you the two solutions.

*Another example is when you divide both sides by an expression in common like (x-3). In that case you have to add x=3 to the solution set. (i.e. whenever you divide both sides by an expression you have to add all the solutions which makes that expression zero)
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Re: The Mathematical Universe

Postby Dave_Oblad on April 7th, 2017, 1:17 pm 

Raj,

First, I did answer your question. You are wrong. If I map a triangle on a sphere, all three angles can be 90'. But I thought you were past testing me. If you want to test people, start a thread in Science Fun and let everyone participate.

Everyone else:

I am avoiding a God reference here. Most Gods come with Intelligence. My approach requires no Intelligence. It is the simple recognition that for every possible Rule Set for a CA, a Solution will Exist and being too Complex isn't Relevant.

I tried to show that your confidence in knowing that 10/3 will be a determined 3.33333.. etc.. is that the same level of confidence can then be applied to the idea that given an Infinite set of Possible CA's with the potential for Infinite Complexity, that every possible Reality can be expressed.

My reference to William Blake's "Grain of Sand" is relevant to what I see in the Power of a CA. I see infinite potential for defining Universes with enough complexity for Chemistry and Life (and all else) to be emergent.

If you don't want to believe you Exist inside the Solution of a CA, then that's your prerogative. I suppose you must have a better Model with less issues, such as the origin of Time, Space and Energy.. etc.. Most people can't grasp the concept that physically solid stuff isn't necessary for stuff to Exist that is merely Relational in nature but without a truly solid aspect.

Ok, gotta run.. work calls.

Best wishes,
Dave :^)
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Re: The Mathematical Universe

Postby rajnz00 on April 8th, 2017, 1:51 am 

Dave,
How can I be wrong, I only asked a question. A 2-D triangle in a plane. I need to ask you because you are fascinated by very elementary, primary school arithmetic, and from that extrapolate to some deep insight about the nature of the Universe.
"Most people can't grasp the concept that physically solid stuff isn't necessary for stuff to Exist that is merely Relational in nature but without a truly solid aspect."
You are confused by your own words. What do you mean by "stuff"? Admitted that solid "stuff" originates out of "unsolid" energy, but you need to get your head around the possibility that just because it does, that doesn't mean that solid stuff is an illusion. Max Tegmark is mistaken. I'll go with Carlo Rovelli. Mathematics is invented and developed by humans and does not exist of and by itself.
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Re: The Mathematical Universe

Postby Dave_Oblad on April 8th, 2017, 4:26 pm 

Hi Raj,

You, like some others, take what I say and translate it to what you think I said. Then you may even debate against what you thought I said. This is very common for many of us. For example: I am not fascinated by Elementary Primary School Arithmetic.

Most of the posters on the last several pages are very highly educated and very intelligent people in Mathematics etc. But if I use the word Compute, they automatically assume I mean Numerical Mathematics using Numerical Operators when in fact I'm using Logical Operators and Boolean Algebra.

I hope I put that to bed when I refer to the way a Human Brain computes. It uses Logic not Number Mathematics.

I used the term Stuff to cover all forms of Matter. That all Matter is a composite of Smaller Stuff, down to the Scale that Matter is no longer any form of Solid Stuff, but is just a disturbance or knot in a Field. At that point, Quantum Mechanics picks up the proverbial ball and runs with it. And Stuff can get pretty weird. Or.. at least weird when one's mind is locked into Macro Descriptions and Solids. But when perceived in the form of Waves and Fields, the weirdness becomes comprehensible. Except for those that can't release the concept of solidness.

I'm not impressed with Rovelli. His papers tend to be loaded with weak arguments and lots of strawman arguments. I think (but am not sure) it was one of his lectures where he dismissed the Block Model because it is a Static Device, and by waving his hand, proved that Motion is valid and thus not part of a Static Model. To me, that lecturer had no grasp of what a Block Model really is.

I also accept that Mathematics is pretty much a Universal Language, once we agree on the Symbology being used. So I would agree that we invented the Symbols to represent Concepts, but we didn't invent the Math Concepts themselves. We discovered such Concepts because they are in fact.. Universal and Timeless.

Best Wishes,
Dave :^)
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Re: The Mathematical Universe

Postby rajnz00 on April 8th, 2017, 7:51 pm 

Hi Dave,
But if I use the word Compute, they automatically assume I mean Numerical Mathematics using Numerical Operators when in fact I'm using Logical Operators and Boolean Algebra.

You sound like Peter denying Christ, when confronted about knowing him, after being his most avid disciple.
I have never discussed “compute” with you, whereas several times you have asked me to look closely at the millionth numerical figure (in our decimal system) of 10/3 or the 6th of Pi etc., as though they held some deep philosophical secrets, which lead me to hypothesise that you hold some deep sub-conscious fascination with numbers, while at the same time publicly disavowing it. A kind of numerical Stockholm Syndrome disorder.
Logical Operators and Boolean Algebra, ultimately operate upon numbers.
Stuff can get pretty weird. Or.. at least weird when one's mind is locked into Macro Descriptions and Solids. But when perceived in the form of Waves and Fields, the weirdness becomes comprehensible. Except for those that can't release the concept of solidness.

Again, you sound like someone who has firmly grasped the bull by the tail, or hit the hammer smack on the point of the nail.
There is no weirdness about “stuff” to a child, or the ordinary guy in the street, or your cat or dog, or a lion or its prey in the Serengeti. It is weird to a nuclear scientist or a theoretical physicist. You, on the other hand, perhaps uniquely, seem to consider your ham sandwich utterly weird, but electromagnetic “waves”, “permeating” through “empty space” perfectly unremarkable.
Cellular Automatons, which you also seem to be fixated upon, are just a mathematical, computational explanation of how evolution (including biological evolution) is possible.
Evolution, to my mind, is what is the fundamental property of nature. The universe has evolved from simplicity to complexity. That “solid matter”, stars, galaxies, microbes, grass, trees, animals and humans have evolved and are composed of atoms, which in turn are composed of protons, electrons and neutrons, which in turn are composed of “massless particles”, does not make them unreal. The universe is dynamic. It is moving, evolving. Only your mind is stuck in your deterministic, block universe.
Regards
R
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Re: The Mathematical Universe

Postby Dave_Oblad on April 9th, 2017, 4:24 pm 

Hi Raj,

Raj wrote:I have never discussed “compute” with you, whereas several times you have asked me to look closely at the millionth numerical figure (in our decimal system) of 10/3 or the 6th of Pi etc., as though they held some deep philosophical secrets, which lead me to hypothesise that you hold some deep sub-conscious fascination with numbers, while at the same time publicly disavowing it. A kind of numerical Stockholm Syndrome disorder.

The point you seem to be missing is Determinism.

Raj wrote:Logical Operators and Boolean Algebra, ultimately operate upon numbers.

Wrong. They can.. but generally, such depicts True & False or Yes & No status. They can have numerical weight assigned, such as 0 & 1 when used for Math Calculations.
IE: 0101 = 5.

Raj wrote:That “solid matter”, stars, galaxies, microbes, grass, trees, animals and humans have evolved and are composed of atoms, which in turn are composed of protons, electrons and neutrons, which in turn are composed of “massless particles”, does not make them unreal.

I never said the Universe was Unreal. I said it is totally Informational. Meaning its composition is pure relational Information.. there is nothing that is a true solid.

Yes, I am fixated on CA's as they have the power to define a working Universe. A Deterministic Universe. A Universe that starts with a first Iteration.. which would be the Beginning of "Time".

Do you have a better description for how "Time" began?

Or.. perhaps how to get Something (Information) from Nothing?

Raj wrote:The universe is dynamic. It is moving, evolving.

So is a CA.. obviously. Why can't you see or understand that?

To be specific, the Model I embrace is an Expanding 4D Block Model (CA).

The tell tale aspects would be a minimum indivisible discrete Scale (Planck Units) and a stepped facet to all relations at the smallest Scales. That "Time" has Thickness and "Momentum" is directly connected to History in a Geometrical Sense. You can see all these things in the image I presented called "Gospher's Gun".

The real question I want to ask is "Do you have a Point?". It feels like you simply like to argue about a subject you barely are grasping. That gets tedious real fast.

Best wishes,
Dave :^)
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Re: The Mathematical Universe

Postby rajnz00 on April 9th, 2017, 6:46 pm 

The point you seem to be missing is Determinism.

Dave alas you have displayed ignorance of the most basic maths, which I suspect is the source of your propensity to give examples from elementary school arithmetic, and worship algebra, for which you have shown to have, at best, a tenuous grasp of. The millionth numerical figure of 10/3 is determined because it is set by predetermined rules. From that you cannot deduce the Universe is deterministic. If it were so, the Nobel committee would be hammering at your door, to bestow you their prize for your brilliant discovery.
Have you heard of Heisenberg's Uncertainty Principle? Non-deterministic algorithms?
Wrong. They can.. but generally, such depicts True & False or Yes & No status.

It is amazing that being a computer programmer, and one that argues against the reality of solid stuff based on its ultimate composition, you seem to be unaware that ultimately computers respond to a series of 0’s and 1’s.
Yes, I am fixated on CA's

Yep. It follows
they have the power to define a working Universe. A Deterministic Universe.

You seem to be unaware that CA's, aside from possibly class 1 CA's, are not deterministic. https://en.wikipedia.org/wiki/Cellular_ ... sification
I dont know if they have the power to define a working universe, but the operative word here is "define" not be.
A Universe that starts with a first Iteration.. which would be the Beginning of "Time".
Do you have a better description for how "Time" began?

What kind of explanation have you given? The universe started with the first iteration -great. What not the first egg, explosion, Big bang etc? Where did the first whatever come from?
As it happens I do have a better explanation. The universe always existed. It changes but is never created nor destroyed.
So is a CA.. obviously. Why can't you see or understand that?

Obviously not. CA is a construct of humans. It can do nothing on its own, The idol you worship is unfortunately powerless on its own.
"Do you have a Point?" Just pointing out the pointlessness of yours.
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R
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Re: The Mathematical Universe

Postby hyksos on April 9th, 2017, 10:40 pm 

mitchellmckain » March 30th, 2017, 11:22 am wrote:Look up Bell's inequality.

His entire answer was "Look up Bell's inequality." Literally. Like this is not quote-snipped or anything.

Well mitchellmckain, I have looked it up. But also, I heard a lot about it years before this thread even started on this forum. Bell's Inequality issues are related to naysayers who do not believe that entanglement happens in the way that the equations of Quantum Mechanics suggest it does (naively).

(For those of you entering into this conversation between me and m.mckain) Entanglement is a spooky correlation between two quantum system's state separated by a distance. It is a not a randomness between them, but an inexplicable correlation between their states. (correlation is, of course, the opposite of randomness)

At the formal level, QM says that if separated particles are in a superposition with each other, they should be treated as a "single" quantum system, rather than two different systems, even if the constituents move very far away from each other. (As far as I understand) The naysayers against entanglement are not adopting a computable universe hypothesis. Rather for years the naysayers were saying that entanglement was due to a yet-unmeasured invisible signal being sent between the systems -- an invisible signal supposed to move at a speed less than the speed of light ("sub-luminal").

For emphasis, loophole-free Bell's Inequality experiments have lain this issue to rest firmly in my own mind and heart. I do not believe there is an unmeasured "signal" correlating the systems separated by miles. But the existence of Entanglement in our universe suggests higher incidences of correlation between systems, not more randomness amongst them.

In the forked thread I created for the benefit of m.mckain, I even differentiated non-locality from non-contextuality. (roughly superluminal signalling versus no objective quantum states). This issue of "hidden variable theories" is not as straightforward as he pretends it is within this thread. One can adopt non-local physics to "explain" entanglement, without making any concessions to the objective states of systems prior to measurement. m.mckain thinks these two things are the "same issue", yet no one else on the internet nor in academia does.

As far as I can see, not a single person on this forum has espoused Local Realism. Local Realism is the "same thing" as hidden variable theory? It certainly isn't. It is likely the case that Local Realism vanished from physics by the time of James Clerk Maxwell. It is also difficult to see how we could have objective states of systems, when Alice and Bob cannot agree on whether events took place simultaneously or not, and that thought has existed in physics at least as early as 1905.
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Re: The Mathematical Universe

Postby hyksos on April 9th, 2017, 11:30 pm 

When I say the Universe is made from Math, everyone jumps into Math Mode. I don't deal that much with Add, Subtract, Multiply and Divide. I deal more with And, Or, Nor and Exclusive Or. Still a form of Math in the Field of Logic.

Funny, "read some philosophy" has come up.. yet I can find no reference regarding Cellular Automatons going back very far in History. A couple of decades perhaps. This Idea of the Universe being a Cellular Automaton is pretty New.. in fact.. it may be an original Idea.. as Max Tegmark has not embraced the concept yet, even though he beat me to the concept that the Universe may be composed of Math.

Generally, the constituency of this forum has completely lost track of the metaphysical issues that are resolved by a Mathematical Universe. So far only viviane maxine has realized that this topic is really about the origins of the laws of physics.

Tegmark is suggesting that the world is not substance, and the world is definitely not "substance suspended in space". Nor is Tegmark saying "The universe is a thing X, and that stuff X can be described by mathematics". That is something a bright educated 20 year old might conclude. Tegmark is claiming something far more profound. He is claiming that when we view or measure the universe, we are literally viewing a mathematical structure.

What is the essential metaphysical situation we find ourselves in here?
  • The universe is composed of something? And that something is likened unto a "substance"?
  • The "substance" obeys laws which themselves are not existing with the same kind of metaphysical existence of "substance". So why does the substance obey the laws?
  • Are the law imposed upon substance from without? Who imposes?
  • Are physical laws physical?
  • Where did the laws "come from"? And how do they interact with the "substance"?
Or is it the case that every one of these questions is wrong-headed? Perhaps this medieval notion of "substance" and "existence of the lawful substance" is bankrupt from the get-go. It's detritous of our psychology as upright walking animals on African savannah.

Maybe the universe is not composed of a substance at all, in any sense. In this view of things, we now longer have to "explain" the origin of physical laws. This is where Max Tegmark comes in. The reason the "substance" obeys "laws" is because there is no substance -- the universe we see is laws itself ... it is pure math.

And where did these laws "come from"? They don't "come from" at all. Mathematical truth is eternal. It does not originate.

Cellular Automata has some pluses that are being obscured in this endless digression into Chaitin's constant. CA has the benefit of avoiding thorny philosophical issues related to continuous motion. The entire development of Quantum Mechanics from Planck to DeBroglie was basically men coming to understand that infinitesimal wavelengths makes no physical sense (read your history). CA has the benefit of explaining why all information is conserved. It can even "explain" why physics is reversible in time. If a CA is reversible, it is necessarily also information-preserving. Some people might slough that off as a coincidence -- I think the connection goes deeper.
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Re: The Mathematical Universe

Postby rajnz00 on April 10th, 2017, 7:23 am 

Bell's Inequality issues are related to naysayers who do not believe that entanglement happens in the way that the equations of Quantum Mechanics suggest it does (naively).

As I understand it Einstein, along with a couple of others came up with the Hidden variable theory because he was unhappy with the "the fundamentally probabilistic nature of quantum mechanics".
Einstein stated, "I admit, of course, that there is a considerable amount of validity in the statistical approach which you were the first to recognize clearly as necessary given the framework of the existing formalism. I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance [In other words be totally deterministic like GR].... I am quite convinced that someone will eventually come up with a theory whose objects, connected by laws, are not probabilities but considered facts, as used to be taken for granted until quite recently"

Bell proved him wrong, as did Von Neumann before him.

Bell's theorem states - "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics." and that phenomena that are both deterministic and local must satisfy Bell Inequality. Quantum mechanics violates Bell inequality, thus local phenomena cannot be deterministic.
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Re: The Mathematical Universe

Postby hyksos on April 10th, 2017, 12:20 pm 

rajnz00,

Prepare a quantum system such that it has two discrete eigenstates upon measurement. For example, prepare silver nuclei as ions and shoot them through a powerful magnetic field (a Stern-Gerlach device). Silver nuclei have two quantized states of angular momentum, which we can call spin Up and spin Down. We know that during flight, the nuclei will evolve deterministically as a unitary wave. But upon colliding at the collection plate, the nucleus will "snap" into one of those eigenstates. The act of colliding with the collection plate is a "measurement". Because only eigenstates are admissible upon measurement, we find that either the nuclei goes all the way to the left, or all the way to the right, and never appears in the center. Spin Up nuclei deflected left, and Spin Down nuclei deflected right.

This physically happens. Check.

m.mckain and yourself may be adopting a position that says : the leftness or rightness of the nuclei is a totally random coin flip, in some grand metaphysical sense. Anyone who denies Grand Metaphysical Coin Flip of the nuclei upon measurement must be a crackpot who is espousing a hidden variable theory!

Not only is what you are doing a strawman : but your errors in understanding the literature run deeper. The reality of this situation is thus, the raw formalism of Quantum Mechanics is totally silent on the issue.

Let me repeat that in boldface, so everyone on this forum can see I'm being serious. During measurement, a specific eigenstate must be selected out a discrete collection of them, and which one is selected? The formalism of Quantum Mechanics is silent on this issue.

If a person claims then : "The selection of the eigenstate is not random or uncaused" that person is definitely not also claiming that "The quantum system was in an objective state prior to measurement" and then somehow denying Copenhagen. Those are two distinct and separate claims.

If m.mckain is really a "grad student in theoretical physics", as he claims, he must also admit that his discipline has numerous colleagues on the inside of academia who adopt all sorts of zany opinions about how a specific eigenstate is selected upon measurement. The opinions run the board, many are contradictory to each other, and in general, there is no consensus in academia. He must admit such, or he is a liar.

There are people in the inner sanctum of disciplined academic physics, who adopt the opinion that we experience the eigenstate that, and I quote: "with which we are entangled". That particular eigenstate, (the one with which we are entangled) is definitely not a random one.

When the dust clears, this statement is definitely wrong :
Bell's inequalities proves that the selection of an eigenstate upon measurement must be a totally random coin flip.


We might have people on this forum who adopt the claim "I personally think the selection of an eigenstate is a metaphysically random coin flip." And that would be their opinion. To elevate such an opinion to scientific fact would constitute willful deception.
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Re: The Mathematical Universe

Postby Braininvat on April 10th, 2017, 4:09 pm 

Thank universe for Bayesian analysis! ;-)
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Re: The Mathematical Universe

Postby mitchellmckain on April 10th, 2017, 4:37 pm 

hyksos » April 9th, 2017, 9:40 pm wrote:
mitchellmckain » March 30th, 2017, 11:22 am wrote:Look up Bell's inequality.

His entire answer was "Look up Bell's inequality." Literally. Like this is not quote-snipped or anything.

Well mitchellmckain, I have looked it up. But also, I heard a lot about it years before this thread even started on this forum. Bell's Inequality issues are related to naysayers who do not believe that entanglement happens in the way that the equations of Quantum Mechanics suggest it does (naively).

(For those of you entering into this conversation between me and m.mckain)

Only... it was not a conversion between me and hyskos, but hyskos inserting himself in a discussion between myself and someguy1. Well now I consider myself properly warned NOT to treat any of hyskos' questions with any sincere help to point him in the right direction. I will simply assume that any questions he asked are for the purpose of rhetoric only and without the authentic interest shown by making any effort to look things up! I will no longer expect discussion from him but only some absurd debate competition for which I have no interest whatsoever!

Oh and by the way... I am NOT a graduate student. I am completely graduated with a B.S. in mathematics and a Masters degree in theoretical physics. But yeah the research impaired are free to doubt whatever they want because the prejudices in their head are more important than information publicly available to everyone.
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Re: The Mathematical Universe

Postby Dave_Oblad on April 10th, 2017, 6:37 pm 

Hi Raj,

Raj wrote:Dave alas you have displayed ignorance of the most basic maths, which I suspect is the source of your propensity to give examples from elementary school arithmetic, and worship algebra, for which you have shown to have, at best, a tenuous grasp of. The millionth numerical figure of 10/3 is determined because it is set by predetermined rules. From that you cannot deduce the Universe is deterministic. If it were so, the Nobel committee would be hammering at your door, to bestow you their prize for your brilliant discovery. Have you heard of Heisenberg's Uncertainty Principle? Non-deterministic algorithms?

As shown in Red.. you seem incapable of communicating without the use of denigrating commentary.

And in Blue.. you have simply confirmed my point that Math can only produce a deterministic solution based on a set of Rules.

And in Green.. You come to my Hypothesis that the Universe is a Cellular Automaton and thus must be fully deterministic.

Heisenberg's Uncertainty Principle simply states there exists a limit in how much we can know about a system under measurement. This says absolutely nothing about Determinism.

Non-deterministic algorithms rely on external inputs, such as a Random Number Generator. If you exclude external inputs to such an algorithm then you will only have Deterministic Algorithms.

You can't create True Randomness using Math alone.
You can't create True Randomness using Math alone.
You can't create True Randomness using Math alone.

Do I really need to repeat this any more times?

Raj wrote:It is amazing that being a computer programmer, and one that argues against the reality of solid stuff based on its ultimate composition, you seem to be unaware that ultimately computers respond to a series of 0’s and 1’s.

Firstly, I am intimately aware how computers work. 1's and 0's is simply a convention for binary expression. It is equally valid to state they operate on (True and False) or (On and Off) inputs.

If you play a 3D computer Game and are faced with a Door that won't let you pass.. Just how Solid do you believe that Door to be?

Raj wrote:As it happens I do have a better explanation. The universe always existed. It changes but is never created nor destroyed.

This is a cop-out answer. You are hiding inside infinite regressions, which BTW, do not agree with observables. The Universe constantly loses energy in a non-recoverable form. It is expanding and shows no sign of reversing, in fact, just the opposite, the expansion is accelerating.

My point is quite simple and it is unfortunate you can't see it.. or you refuse to see it.

Here is a simple cartoon that may help you:
https://xkcd.com/505/

Explanation of a "Bunch of Rocks":
https://www.explainxkcd.com/wiki/index.php/505:_A_Bunch_of_Rocks

The concept most don't get is the students in the classroom (in the last frame) owe their Existence to some fella moving a bunch of rocks about, following a set of rules.

How Solid is the Desk of such a Student (last frame)?
If you replace that Fella with a CA.. does that make the students Desks More or Less solid?

Regards,
Dave :^)
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Re: The Mathematical Universe

Postby rajnz00 on April 10th, 2017, 9:35 pm 

Hi Dave,

My apologies for appearing denigrating. You are a likeable chap. I like you, but you talk so much rubbish. And you go on repeating the values of 10/3, drawing squiggly lines and referring me to cartoons. Wouldn’t anyone find that exasperating?

And I was merely stating my observations, don’t you remember your horrible attempt at algebra while trying to prove Time = Distance?
Dave: 1's and 0's is simply a convention for binary expression. It is equally valid to state they operate on (True and False) or (On and Off) inputs.


No, they actually operate on, on and off switches, but mathematically they correspond to 1’s and 0’s. (Binary NUMBERS). I might remind you, this is in response to: Me “Logical Operators and Boolean Algebra, ultimately operate upon numbers.” And You “Wrong. They can.. but generally, such depicts True & False or Yes & No status.” I am not wrong, you are.

Then you go on and on with utter rubbish like:
Dave: ”Non-deterministic algorithms rely on external inputs, such as a Random Number Generator. If you exclude external inputs to such an algorithm then you will only have Deterministic Algorithms”.

An algorithm is just a set of instructions, like a recipe. A Non-deterministic algorithm is like a deterministic algorithm except that its outputs are novel, unpredictable, non-deterministic. And:
Dave: “The Universe constantly loses energy in a non-recoverable form.”

It violates the law of conservation of energy? What does it lose energy to? Where does the energy go?

I tell you what – let’s call it a draw. I have free will, my future is open and you are totally deterministic. Yesterday you computed the value of 10/3, today you have, and you will tomorrow. And the universe was, is, and forever will be, a cellular automaton for you.

Mathematically, using your favourite Boolean Algebra:

IF,
f(x)=a_0+∑[/sub](n=1)^∞▒(a_n cos⁡〖nπx/L〗+b_n sin⁡〖nπx/L〗 )
OR,
√(n&a^n )={Int(a,@|a|,&)┤
AND, a= Odd
THEN,
∃x("Person" (x(Dave))∧∀y("aTime" (y)→"Deterministic - Blocked" (x,y)))
ELSE, a= Even
THEN,
∃x("Person" (x(Raj))∧∀y("aTime" (y)→Free- "Happy" (x,y)))

How about that?
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Re: The Mathematical Universe

Postby Dave_Oblad on April 11th, 2017, 5:41 am 

Hi Raj,

Agreed.. with a few final statements that reflect on your opinions:

Raj wrote:And you go on repeating the values of 10/3, drawing squiggly lines and referring me to cartoons. Wouldn’t anyone find that exasperating?

That would depend on what you take from them. I am hoping to project deeper insights aimed at intelligent minds, yours included. I believe it is worth my effort, even if you don't.

Anyway..

I had never heard of a Non-deterministic Algorithm and had to look it up. Sure enough, it only exists if one pumps an external randomness into it or two (or more) are run simultaneously and allowed to interact and create Race conditions.
https://en.wikipedia.org/wiki/Nondeterministic_algorithm

Funny sidebar: I had actually used such without knowing what it was called. I did so while creating a Chess playing program. It searched future possible game paths and scored them. In cases of a tied score, it had to accept input from a clock source to decide on a path choice. The use of Pseudo-Random number generators didn't cut the mustard and made a program that was too predictable.. meaning.. if the program played itself, the results where always utterly repeatable. So my external random input was a Clock.. because Time never repeats itself. Or, to be more precise, it's nearly impossible to sync a Game to a Clock by accident.

And Entropy does indicate the Universe will finish with a Heat Death and thus is not Eternal.
https://en.wikipedia.org/wiki/Heat_death_of_the_universe

Put simply, some forms of Energy can't be recovered and are spent forever, Heat being a big one. So, if we Exist in the last Universe Cycle, assuming Cyclic Regression as a valid argument, then there must have been a First Universe and thus raises the question: How did the First Universe come into Existence?

This is why I choose a Universe composed of Information Only. Math has the unique property to generate new information from old information and old information can be expressed as a "What If?" preset.

Thus, from an Infinite set of "What If?" presets, an Infinite set of Universes can be resultant.

And if such a Preset defines a CA, such that "John the Farmer" Exists deep within the solution then "John the Farmer" can be said to Exist in the same sense as the 1000th digit of 10/3 Exists. The only honest difference is complexity and the Algorithms employed.

While True Randomness is still prevalent within Science, I'm quite confident that it is being handed its proverbial hat and being shown to the door (on its way out).

True Randomness hides behind the Facade of Measurement issues, which someday should be resolved. It's what we humans do. We find a way.

Another sidebar: <IF> the Universe is a Quantum Computer and is Self-Aware.. then a fringe topic might include the possibility that the Universe is sensitive to our desires and may adjust itself accordingly.

Isn't that a fun concept?

Best wishes,
Dave :^)
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Re: The Mathematical Universe

Postby vivian maxine on April 11th, 2017, 7:04 am 

Dave_Oblad) "Firstly, I am intimately aware how computers work. 1's and 0's is simply a convention for binary expression. It is equally valid to state they operate on (True and False) or (On and Off) inputs."

And Base 2? :-)
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Re: The Mathematical Universe

Postby rajnz00 on April 11th, 2017, 1:13 pm 

Hi Dave,
I had never heard of a Non-deterministic Algorithm

From your Link "a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs" Or in my simple language gives novel, unpredictable, non-deterministic outputs.
Sure enough, it only exists if ..

Some human writes it and runs it, just like any other algorithm, recipe, CA, mathematical formula, theory, you can think of. Amazing huh?
You are greater than Macavity, he only broke every human law and the law of gravity, but you have the most sacred law of all - the law of conservation of energy, made it vanish into "thin air" or thinner space. You say you don't believe in magic, but no magician could hold a candle to you. You are a true magician. :)
Another sidebar: <IF> the Universe is a Quantum Computer and is Self-Aware.. then a fringe topic might include the possibility that the Universe is sensitive to our desires and may adjust itself accordingly.
Isn't that a fun concept?

It is indeed. Why not ask it for free will, or even time travel, instead of just being sealed into a block?
I am hoping to project deeper insights aimed at intelligent minds, yours included.

You have, and made me think. Thanks for that.
Regards
R
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Re: The Mathematical Universe

Postby Dave_Oblad on April 11th, 2017, 1:19 pm 

Hi Vivian,

(And anyone else that's interested but not familiar with Binary)

If one intends to do standard Math, then today, most modern computers use Base 16. You would think they would use Base 10 as we humans do, but Base 10 is not efficient at storing data or variables in the form of On-Off switches.

Here is a sample of Base 16:

8421 = Binary Weight of respective column below it.
-----------
0000 = 0
0001 = 1
0010 = 2
0011 = 3
0100 = 4
0101 = 5
0110 = 6
0111 = 7
1000 = 8
1001 = 9
----------------
1010 = A
1011 = B
1100 = C
1101 = D
1110 = E
1111 = F

See number "5" above?
See it is "0101" in Base 2?
See the column Weight above at top?
It says that 8 and 2 are switched OFF (0) while 4 and 1 are switched ON (1).
Thus (4 & 1) switched on = 5.

Note: All the number combinations (A,B,C,D,E,F) beyond 9 that Decimal (Base 10) misses.

Yes.. A,B,C,D,E,F are actually Numbers in Hexadecimal.
They are not Letters (symbolically speaking).

Click here to see how "Letters" are actually represented in the various systems:
http://www.asciitable.com/

I think Vivian already knew all the above.. but for some others that didn't.. some added value.. lol.

Best wishes,
Dave :^)
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Re: The Mathematical Universe

Postby hyksos on April 11th, 2017, 1:33 pm 

mitchellmckain » April 11th, 2017, 12:37 am wrote:Oh and by the way... I am NOT a graduate student. I am completely graduated with a B.S. in mathematics and a Masters degree in theoretical physics. But yeah the research impaired are free to doubt whatever they want because the prejudices in their head are more important than information publicly available to everyone.

mitchellmckain , are you adopting the position that Bell's Inequality experiments firmly prove that the universe is incomputably random?

Second question: Are you further claiming that anyone could look up this "plain fact", if they are not "research imparied"??
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Re: The Mathematical Universe

Postby rajnz00 on April 11th, 2017, 1:36 pm 

If one intends to do standard Math, then today, most modern computers use Base 16.
Just a silly question - is that what computers use or programmers?
I ask because all I see are 0's and 1's and computers still run on On-Off switches?
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Re: The Mathematical Universe

Postby someguy1 on April 11th, 2017, 2:12 pm 

rajnz00 » April 11th, 2017, 11:36 am wrote:
I ask because all I see are 0's and 1's and computers still run on On-Off switches?


You know, this is an interesting point. There aren't any actual "on-off" switches in a computer. There are circuits whose voltage cycles between low and high states, forming a square wave. But since this is a physical mechanism, there can never be a perfect square wave. Rather, there is a transition interval during which the high/low state of the circuit is indeterminate.

If we were to measure the circuit during the transition period, we would not be able to determine if it represents 1 or 0. Instead what we do is use the system clock to make sure that we measure only in the middle of each wave period, so that we get a distinct high/low reading.

In other words, the "one/zero" property is only an artifact of when we choose to observe the voltage in the circuit. The impression of definiteness is due to our choice in when to take the measurement.

As with everything in computing, it's all about layers of illusion.
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Re: The Mathematical Universe

Postby mitchellmckain on April 11th, 2017, 5:34 pm 

hyksos » April 11th, 2017, 12:33 pm wrote:mitchellmckain , are you adopting the position that Bell's Inequality experiments firmly prove that the universe is incomputably random?

Second question: Are you further claiming that anyone could look up this "plain fact", if they are not "research imparied"??


Why should I answer your questions when I have no confidence that you are sincerely interested in any answers to them?

However, I will go out on a limb this time to remind you of the conclusion of our other discussion. The universe is computable to a very large degree but the Bell's inequality establish that, given the premises which have been accepted for the scientific world view for the last century, SOME events are not computable because the idea there are hidden variables to make such a computation possible conflict with the fact that Bell's inequality is violated. Thus either local realism or physical determinism has to be discarded. Yes there are very few such as David Bohm who are willing to discard local realism in order to stubbornly cling to physical determinism, but the vast majority choose interpretations such as Copenhagen, Everett and Bayesian which accept the verdict of scientific experiments that physical determinism must be discarded.
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Re: The Mathematical Universe

Postby rajnz00 on April 11th, 2017, 5:45 pm 

Hi someguy1, thanks for that info. It seems we no longer live in the age of the telegraph, with someguys tapping an on/off switch.
The impression of definiteness is due to our choice in when to take the measurement.
It seems to me that the choice creates more than an impression, rather it makes it definite for the computer to act upon
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Re: The Mathematical Universe

Postby Dave_Oblad on April 11th, 2017, 6:27 pm 

Hi Raj,

Wiki wrote:a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs" Or in my simple language gives novel, unpredictable, non-deterministic outputs.

The writer wishes this were true and it should be challenged as it is badly worded.

Race Conditions:

For the expression above, they are running the same algorithm on two or more multitasking fronts. The program literally switches locally between programs (A,B,C) etc.
If program (A) selects a Path via a Pseudo-Random Generator, than that option is closed. The next version of the program (B) can't choose that option (already taken) so it must pick an alternate. This is what is defined as a race condition. When run on different computers simultaneously, you can get an unpredictable behavior.

This has proven to be a major obstacle for Gamers playing over the Internet. You and another player shoot each other simultaneously:

The program has to resolve a conflict for:
A: Both are killed.
B: Both missed their shot.
C: Who had the most accurate shot.
D: Use a Time Stamp from a shared server to decide who shot first.

As in real life, choice (A) is usually the preferred choice.

Other than a Race condition, all such Non-deterministic Algorithms must resort to external inputs for Randomness.

As previously stated (somewhat emphatically), there is no way to Mathematically create True Randomness. You can take that to the bank. This is not a personal opinion.. it is an obvious Fact.

Best wishes,
Dave :^)
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Re: The Mathematical Universe

Postby hyksos on April 11th, 2017, 9:13 pm 

Yes there are very few such as David Bohm who are willing to discard local realism in order to stubbornly cling to physical determinism, but the vast majority choose interpretations such as Copenhagen, Everett and Bayesian which accept the verdict of scientific experiments that physical determinism must be discarded.

In my opinion, Bohm, Everett, and Bayesians are all stubbornly clinging. Everett in particular. He simply declares that the eigenstate which appears upon measurement is just the one which "happened" in our particular universe/reality. There is another universe/reality where the silver nuclei was spin Down. Many-Worlds H is, in some sense, a kind of pluralistic determinism. We dodge problem of selection of an eigenstate by saying "Well, all the eigenstates are realized somewhere. Problem solved".

I do not believe that lack of determinism entails incomputable randomness. (In another thread) I used the example of indetermined pear color which upon roll out of the trees fruiting, does not give a random distribution of colors. Those Indetermined Pear Trees would follow the mathematics of Copenhagen, but not necessarily produce incomputable randomness.

More generally speaking, the formalism of Quantum Mechanics is silent on these issues. We can simplify our chalkboard math and simplify our lives by just "assume a random sampling distribution", and then get on with applying the Born Rule. The math works out, but that's kind of a self-fulfilling prophecy.
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