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 March 27th, 2017, 7:46 pm 

Hi all,

I don't know why we humans always attribute something we don't understand to Magic. Just because we don't know why a particle decayed when it did, is that grounds for embracing Randomness (magic)?

If some people are satisfied with the Magic of Randomness.. then so be it. I personally think we have a lot further to go in our investigations and at sometime (hopefully not too long from now), the concept of True Randomness will be obsoleted. Every Event will have a Cause.. IMHO.

When Science started to explore the world of smallness, we found that each smaller thing we could find was made of still smaller things. From Molecules to Quarks.. are Quarks the bottom or are they made of still smaller structures.. perhaps called Preons? And if so, are Preons the bottom or are they made of still smaller structures?

Some hypothesis regarding Preons:
https://arxiv.org/abs/0908.4070

What I am suggesting is that there exists structures all the way to the bottom of Scale. That someday, CA's may replace String Theory. I don't hold that CA's must compute, even if they can. What I'm looking for is the ability to transfer and regulate information flow over a Network, in much the same way a Neural Network behaves.

If I must decide between Syrup or Jam on my Pancakes, did I use floating point Math to make that decision? How did my mind compute my desire and come to a decision? Did it use Math in the traditional sense?

I believe the Universe has a minimum Scale, sometimes referred as the Planck Length. Without a minimum indivisible Scale then distance becomes meaningless. That such a minimum indivisible Scale would appear to be discreetly Cellular. That this would manifest itself into discrete steps from Energy Levels to Sub-Atomic Spins.. etc.

So is Space-Time a Cellular Structure? Is it just 3D or 4D as Quantum Mechanics seems to have adopted? Are particles real or just knots in a Field? What is such a Field really made of? What Medium does Entanglement employ that allows it to exceed Light Speed?

Hi Vivian,
I'm not sure I can communicate an answer to your question, and it's not about your intelligence.

My belief is that the Universe is purely Informational. Information that can have an effect on other forms of information. That the basic underlying mover is just a set of rules. This is the only way I found to get around the aspect of Something from Nothing.. when trying to fathom how it all came about.

The simplest form of an Entity (Universe) that is strictly Rule Based is a Cellular Automaton or CA as we have been calling it. It's about how information flows through such a Network and can influence the Geometry of Paths for the flow of other information.

It has nothing to do with computable numbers.

Ok, gotta get back to work.

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

Postby hyksos on March 27th, 2017, 10:30 pm 

It has nothing to do with computable numbers.

I saw that.
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Re: The Mathematical Universe

Postby someguy1 on March 27th, 2017, 10:37 pm 

hyksos » March 27th, 2017, 8:30 pm wrote:
It has nothing to do with computable numbers.

I saw that.


OP is correct. OP expressed his opinion, to which he is entitled. He didn't make an argument or provide evidence, but these are old complaints (at least six years old) and if he wishes to express his personal opinion here it's ok by me.

And he is correct. It has nothing to do with computable numbers!

Why? Because OP has conveniently omitted his previous claims to have banished randomness. In other words OP has quietly dropped the premise that has been shown contradictory with his other one.

Perhaps someone will ask the OP if they still claim to have "banished randomness" from their CA universe after six years, having now understood that to banish randomness, they must address the issue of the computational strength of the CA they propose, and they are not prepared to do that.

If they still claim to have banished randomness, then noncomputable numbers are very on point, since they contradict that assumption unless the CA in question is far weaker than a TM. In which case the universe is a trivial and boring place. Interesting worlds entail undecidability.

I would add that some people express opinions; and others analyze arguments; and that analyzing an argument has nothing to do with contradicting or opposing anyone's opinion. On the contrary, when you analyze someone's argument, you do them a service by helping them make their own case stronger. OP seems unclear on that point and often gives the impression of being uninterested in the strength of their argument, as long as they can simply repeat their unsupported opinions as they have been doing for six years. It's as if OP is under the impression that stating an unsupported opinion is the same as making a substantive logical and evidentiary argument.
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Re: The Mathematical Universe

Postby NoShips on March 27th, 2017, 11:07 pm 

Look out! There's gonna be a nerdy donnybrook!

Beware of flying functor shrapnel.
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Re: The Mathematical Universe

Postby Dave_Oblad on March 28th, 2017, 5:34 am 

Hi all,

I have always claimed to be an Absolute Determinist. This auto excludes the concept of True Randomness.

My very first (bit sloppy) post on this subject was about 7 years ago and was my 2nd posting to this site:
http://sciencechatforum.com/viewtopic.php?f=39&t=16607

Neuro claimed my hypothesis invalid because I ignored the Indeterminacy Principle.

Literally, such a principle means if one can not predict an outcome or see a pattern, then it must be Truly Random. I have a problem with those that can't see the fallacy in this concept. Just because we lack the tools to measure something with absolute precision is no justification to call something Truly Random.

There is no arbitrary limit on the complexity of a CA. I can easily define one with 20 dimensions and a broad array of rules in the relationships between each Dimension. It would still be a fully deterministic system but completely unpredictable of what emergent patterns might come about 10-25 iterations into the solution.

This simple fact means it is utterly impossible to exclude all potential CA's from having the complexity to represent a Universe. With some rule sets, no CA ever settles down to a static ending. Many start with total chaos for a very long period before some Geometry of interactions begins to emerge and stable Patterns become dominant. In other words, every attempt at something this complex plays out with an initial Big Bang.

I believe Science has painted itself into a corner by adopting the stance that Energy can not be created. They are forced to reconcile such a stance by suggesting all the Energy in today's Universe existed at the very beginning or very first moment of Time. Or they may hide behind Big-Bang.. Big-Crunch.. regression scenarios.. all to avoid the Something from Nothing issues.

My stance is that our Big Bang was the literal Creation of all (or most of) the Energy we see today.

So why do I maintain my stance? I have not seen any explanation for the Existence of our Universe that is better than a CA. On the other hand, a CA has certain characteristics that appear evident in our Universe in regards to being Stepped and Scaled. A CA that grows new Cells on an exposed surface can look just like our Expanding Universe.

An interesting sidebar is that New Cells are grown on Previous Cells (in a type of CA) and thus maintain Scale.. but.. this doesn't preclude that all Cells are the same size when separated by some arbitrary distance. Translated, this means that the Planck Length is a constant in Regards to Growth (Time) and Speed of Light.. but the Planck Length real size is a variable dependent on History. That Cell density can be much higher near a Black Hole and less dense (larger Scale) in a deep Void. This density (Scale) Gradient is what Science calls the Curvature of Space-Time. It's not actually curved but is rather a Scale Gradient (IMHO).

This Scale Gradient is the underlying architecture that creates Gravity. That the Geometry of Matter changes when under acceleration. That exposing Matter to this same Scaled Gradient forces it to adopt a Geometry of Acceleration (and it accelerates towards Greater Density as smaller Scale).

But anyway, I'm getting rather off track here.

Bottom line is I will continue my hard stance until something better comes along. I doubt this will ever happen. Perhaps some new body of Mathematics will be discovered that is superior to a CA Universe.. you never know.. lol.

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

Postby vivian maxine on March 28th, 2017, 6:02 am 

Dave, thank you for your response. I'll not reply to it - although I do have some thoughts - because it would pull this thread off topic. My fault for my random - but sincere - comment. Another time? Another place?
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Re: The Mathematical Universe

Postby Dave_Oblad on March 28th, 2017, 6:31 am 

Hi Vivian,

Please add your thoughts or questions.

Remember, I actually created this particular Thread to answer a question from you to begin with.

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

Postby Dave_Oblad on March 28th, 2017, 1:30 pm 

Hi all,

In my post 3/28 I said:
"completely unpredictable of what emergent patterns might come about 10-25 iterations into the solution."

I meant to say:
"completely unpredictable of what emergent patterns might come about 1025 iterations into the solution."

Sorry, every day that passes I get more prone to Typos and Errors. One shouldn't proof their own work either.. lol.

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

Postby mitchellmckain on March 28th, 2017, 1:38 pm 

someguy1 » March 27th, 2017, 12:26 pm wrote:
mitchellmckain » March 27th, 2017, 1:24 am wrote:Quantum physics establishes that true randomness exists and therefore the world is not a computation.


So you would be disagreeing with the OP on physical grounds. Something that was already done in 2010 to no avail.

For my part I never make arguments based on physics, because I don't know enough physics. But people who do know physics tend to argue against the OP's point of view using exactly that argument.

After reading this I went back and read the OP to see for myself what I saw claimed there. I will address this below.

The conclusions of quantum physics is a long standing disagreement between me and Dave. I have told him before that his arguments in opposition to the conclusions of science sound just like the "god of the gaps" type arguments we hear from creationists. It is perfect nonsense to hope for a rescue of physical determinism in the unmeasurability in the Plank scale for science has already demonstrated that hidden variables simply do not exist.

someguy1 » March 27th, 2017, 12:26 pm wrote:
mitchellmckain » March 27th, 2017, 1:24 am wrote:But then right above you claim that "(1) the world is a computation; and (2) there is no randomness in the world" are inconsistent. But that would only be the case if randomness can be computed. Is there a typo somewhere in this?


The OP claims the universe is computational (a CA rather than a Turing machine but I'm not sure how much of a difference this makes to the discussion); and that he claims to "banish," his word, randomness. But even in a computable universe, you can't solve the halting problem, thus there is randomness/noncomputability anyway. That argument makes perfect sense to me, no typos. Can you help me to see why you are finding fault with it?
...

The issue seems to be with how we are understanding the words " there is no randomness in the world." You seem to interpret this as including noncomputable reals as part of the world, where I do not. For me to say that randomness is in the world would mean that there were truly random events in the world. Because of quantum physics I agree this is the case and conclude the world is not computable.

In fact you could say that this is where I take issue with the OP and all its argumentation that math is a discovery of something "out there." I think this is questionable because it ultimately eradicates the difference between discovery and invention completely. No matter what the invention, if aliens follow the same thought process then they will come up with the same things so does that make it a discovery? I am not convinced that all aliens will follow the same thought processes that give us mathematics to make it a universal language like so many sci-fi movies claim. I would have thought that one thing we can learn from the example of Ramanujan is that there is great role for creativity in mathematics than can lead in many different directions and there is no guarantee that aliens will adopt the same premises for the same mathematical system that we do.


someguy1 » March 27th, 2017, 12:26 pm wrote:
mitchellmckain » March 27th, 2017, 1:24 am wrote:The halting problem does not provide a mathematical procedure for generating true randomness.


Perhaps we have different definitions of randomness. I'm using random as a synonym for noncomputable, meaning "not the output of an algorithm." The digits of Chaitin's Omega are not computable. If they were the output of an algorithm we could use that algorithm to solve the halting problem, falsifying an established result. You agree?
...
Correct. Not computable = random in my usage. Are we using the same definition?

Yes we are on the same page here. It is how I understood you originally and why I decided that Dave was asking you for an inconsistency like demanding that you count an uncountable.

someguy1 » March 27th, 2017, 12:26 pm wrote:
mitchellmckain » March 27th, 2017, 1:24 am wrote:But if the universe is computable then you are excluding such things from having any impact on events and thus it is right to conclude there is no real randomness in the universe.

But you raise an interesting point. Are you saying that in a computable universe, Chaitin's Omega would be noncomputable/random but have no "impact on events?" I don't think I know what that means. It's certainly not an argument the OP is giving. "Yes, noncomputable real numbers fall directly out of computability theory, but they have no impact on events." Is that your interpretation of something the OP said? Is that an argument for a computational universe?

The randomness of a noncomputable has no way of impacting events. If such a means did exist then it would also be a means of computation, which would mean it is computable. This is proof by contradiction of the first statement.

This is certainly NOT an argument for this universe being a computable universe which should be obvious because I have already given my dispute with such an idea. However, I can imagine a different universe to be computable and draw conclusions about such a universe. I personally don't think that such a universe is capable of supporting anything I would call life because unlike Dave I do not see anything alive in the automatons of the so called "game of life."

someguy1 » March 27th, 2017, 12:26 pm wrote:Of course the universe might well turn out to be computational.

No the universe cannot turn out to be computational any more that the Star Trek fantasy of FTL space ships can become a reality. The findings of science make both of these quite unreasonable, and I am not willing to set the discoveries of science aside for the sake of the lovely nature of our fantasies in books and films.

someguy1 » March 27th, 2017, 12:26 pm wrote:But the OP has stated that "randomness is banished" from the universe, and I believe the halting problem falsifies that statement. Can you explain what you mean to the contrary?

No we agree on this point (disagreeing with the OP) for different reasons.

someguy1 » March 27th, 2017, 12:26 pm wrote:The serious CUH people spend a lot of time trying to deal with the halting problem. How do you account for that if it has no "impact on events?" And how you know noncomputable phenomena have no impact on events? Perhaps that's how you get free will in a computable universe. It seems like a rhetorical trick to say, "Well yes there is noncomputability even in a computable universe, but I claim it's not really there or has no impact on events." What can that mean?

Yes the existence of noncomputables can have an impact on events, but the actual noncomputables themselves -- their particular stream of random digits -- can have no effect on events even in our non-computable universe full of quantum randomness.
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Re: The Mathematical Universe

Postby hyksos on March 28th, 2017, 3:34 pm 

I would add that some people express opinions; and others analyze arguments; and that analyzing an argument has nothing to do with contradicting or opposing anyone's opinion. On the contrary, when you analyze someone's argument, you do them a service by helping them make their own case stronger. OP seems unclear on that point and often gives the impression of being uninterested in the strength of their argument, as long as they can simply repeat their unsupported opinions as they have been doing for six years. It's as if OP is under the impression that stating an unsupported opinion is the same as making a substantive logical and evidentiary argument.

I was actually going to say that we are dealing now with a situation where Dave_O is being presented with the concise predictions of his own theory, and when he does not find those predictions convenient, he simply waves his hands and dismisses them. I mean, I posted "necessarily computable," and I even underlined the word "necessarily" Two posts later, and we're all "It has nothing to do with computable numbers." Which in turn motivated my, "I saw that."

This is doubly ironic after I had told him that he cannot escape these mathematical consequences as easily as he pretends to. Let me give an analogy. OP says that K is the product of a bunch of integers K = a1*a2*a3*...an. An innocent bystander arrives in the thread and claims, "K cannot be prime". The OP attempts to deny this by saying : "This has nothing to do with prime numbers".
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Re: The Mathematical Universe

Postby vivian maxine on March 29th, 2017, 8:22 am 

Dave, I promised to get back to you with what I understand of your theory. Let's see how much I remember that I wanted to say.

Firstoff, a general feeling whenever I read it: If I may borrow (steal) a word you used about randomness, what I sense is "Magic". I get a feeling of vague magic,''

That's enough of that. On to trying to understand with a question: Are you saying the universe is "mathematics" or "mathematical"? Did you ever say the universe is "mathematics" or did I just misquote? In the OP of this thread, you are saying it is "mathematical". I thought that, elsewhere, you said it was mathematics. No, that is not quibbling. There is a vast different between being mathematics (a noun, a name word) and being mathematical (an adjective, a descriptive word).

In the OP of this thread, you call it mathematical. I'm not sure exactly how you mean that word. To me, it only describes a universe that can be measured, its parts counted, and has patterns. I want to say has designs but that word seems to always bring out accusations of thinking there is a divine creator out there and that is not what I mean. Anyone who does not see design/patterns in the universe has never examined a rose bush, a pine cone or a maple tree twig; has never looked into the sky and seen Orion's belt, the Big Dipper, the Pleiades.

But, all that said, I have a strong feeling that this is not what you mean by mathematical. I have a very strong feeling that you are saying the universe is not "concrete" but some magical form of emptiness that is called "mathematics". Making more involved, complicated equations using simple numbers and symbols to solve more major problems is mathematics. It is also "concrete" in that it can be put on paper for all to see but it is not this sphere I and you are standing on.

So, no, I do not understand what you are saying. I cannot turn the concept of mathematics into all these spiraling spheres and near spheres with their surrounding gases into an intellectual concept called mathematics.

As for the question of 'is mathematics a discovery or invention, if mathematics is an invention, the next question is who invented it and I fear that will get you accused of believing in that divine creator. If it is a discovery, you may get the same accusation of having a divine creator create mathematics for us to discover.

My thoughts? We do not know what started the universe. I personally do not take sides on the issue. On one side, we can't prove or disprove a divine creator. On the other side, I'm still trying to figure out how some previously non-existing elements managed to burst forth into one big bang that ended up with Earth as my home. No, that's not quite what I am doing. I am not trying to figure it out because I am not a physicist. I am just constantly asking how and listening to everyone who writes about it - even David_Oblad. :-)

If you are right and I fail to understand only because I know what I see and I cannot see your universe, I can only quote:

Who has seen the wind?
Neither I nor you
But when the leaves hang trembling
The wind is passing through.

Who has seen the wind?'
Neither you nor I
But when the trees bow down their heads
The wind is passing by.
-----Christina Rossetti

Maybe you are right and I just don't see it. And now I must go pay my rent. Have a good day.
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Re: The Mathematical Universe

Postby NoShips on March 29th, 2017, 8:33 am 

Dang! No One reads a post that long, Viv
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Re: The Mathematical Universe

Postby vivian maxine on March 29th, 2017, 8:42 am 

Thank you, NoShips. I know. I'm verbose. A gene I inherited from my grandmother, rest her soul. :-)
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Re: The Mathematical Universe

Postby hyksos on March 29th, 2017, 12:47 pm 

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Re: The Mathematical Universe

Postby mitchellmckain on March 29th, 2017, 1:38 pm 



I saw the link.

However without more explanation which tells me wny this is relevant to me personally I see little reason to follow it. With a masters degree in theoretical physics, I am well versed on the topic of the non-commutability of quantum observables.



Oh...!!! But I did not notice the new thread. I will read your OP.
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Re: The Mathematical Universe

Postby vivian maxine on March 29th, 2017, 2:02 pm 

ronjanec » June 20th, 2016, 8:04 pm wrote:vm,

Any "design" in the beginning...and any subsequent further "design" anywhere else in the the rest of the universe before man himself existed and any intelligent extraterrestrials, would have to represent a supreme being actually being involved here in the "design" Vivian, because all "design" requires an intelligence behind it. This particular theory is actually based on a religious belief, and is also known as "Intelligent Design"

I am not sure who "they" are that you are referring to in your post Vivian, but I doubt "they" meant what you are thinking here: Again, because of the religious connotation of the word "design" in this particular context.



I think you are saying that there cannot be a design unless a divine creator created it. Lay a bar magnet down into a field of iron filings. Designs appear in the filings. Move a U magnet among same filings. Designs appear. All right. You might say a divine creator enabled those to happen by creating magnetism but is that the same as creating the designs? If we go back to the beginning (the beginning that we know as Big Bang) and if we say there was no divine creator, would that magnetism still have existed and caused designs when it was attracted by iron filings?

Those may sound like dumb questions to the better informed. But what I am really saying is two things: (1) I think we are simply applying different definitions to the word "design". To me it is simply a synonym for "pattern". Perhaps you do not see it as a synonym. That's fine. I'll use "patterns" hereafter.

(2) Until you can prove how the big bang happened, can you really say that anything we find in the universe has to indicate a divine creator? I don't think so.

P.S. I just checked my little dictionary. Amazing what it calls design. Even calls it "mental planning". Also calls it "art of making patterns". Of course, all these may not fit into how scientists use the word. That would make a difference.
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Re: The Mathematical Universe

Postby Braininvat on March 29th, 2017, 3:10 pm 



The "tag" brackets in the full editor are what you need to ping someone. E.g.

hyksos

I don't know what happens if you put a made up name in the brackets....probably just produce a dead link. Let me try....

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Re: The Mathematical Universe

Postby someguy1 on March 29th, 2017, 8:22 pm 

mitchellmckain » March 28th, 2017, 11:38 am wrote:

I have told him before that his arguments in opposition to the conclusions of science sound just like the "god of the gaps" type arguments we hear from creationists.


Agreed. OP was told he was doing metaphysics in 2010. I observed earlier in this thread that his use of sequences to make a cosmological point struck me as identical to an argument of William Lane Craig, a Christian apologist. The great computer in the sky is essentially a theological claim.

mitchellmckain » March 28th, 2017, 11:38 am wrote:It is perfect nonsense to hope for a rescue of physical determinism in the unmeasurability in the Plank scale for science has already demonstrated that hidden variables simply do not exist.


That's the bit I never learned. Is a simple explanation possible?


mitchellmckain » March 28th, 2017, 11:38 am wrote:The issue seems to be with how we are understanding the words " there is no randomness in the world." You seem to interpret this as including noncomputable reals as part of the world, where I do not. For me to say that randomness is in the world would mean that there were truly random events in the world. Because of quantum physics I agree this is the case and conclude the world is not computable.


You believe physics precludes a computational world, therefore you refuse to even consider the premise. I can't respond because you deny my premises, restate your conclusion, and don't bother to address the point I made.

"You seem to interpret this as including noncomputable reals as part of the world," -- Where in this entire thread have I ever made such a claim? I categorically deny ever writing such a thing.

What is said is that IF the world is a computer and it's Turing-complete, THEN the halting problem entails some degree of randomness in the world.

Are you under the impression that I am claiming there are noncomputable things in the world? I have no idea what's in the world. Am I misunderstanding you here?

I am not talking about the world at all. I have no idea what is the ultimate nature of the world. I'm talking about the argument that says the world is computable and it contain no randomness. That argument is flawed and it's flawed in a very interesting way.

Do you understand that I have not made and do not make the claim you think I made?





mitchellmckain » March 28th, 2017, 11:38 am wrote:I am not convinced that all aliens will follow the same thought processes that give us mathematics to make it a universal language like so many sci-fi movies claim.


I am in full agreement with that. I am a mathematical anti-Platonist. I do not believe 1 + 1 = 2 would necessarily be obvious to alien mathematicians. I ran across a fantastic essay by physicist Carlo Rovelli. It's called Michelangelo’s Stone: an Argument against Platonism in Mathematics.


mitchellmckain » March 28th, 2017, 11:38 am wrote:The randomness of a noncomputable has no way of impacting events.


I wonder what that means. Say the universe is computable. [I know, you disagree with the premise on physical grounds but put that aside for the moment]. What does the halting problem mean? It's studied in computer science. But if one's metaphysics says that the universe is a computer, then what do you make of the existence of noncomputability? You can't just sweep it under the rug. How do you know noncomputable quantities don't impact events?

I'm slightly reminded of the Pope telling Galileo that he can discuss heliocentrism as long as Galileo explains it as a convenient way of doing computations, but it's not really true. You and OP seem to regard undecidability the same way. It's inherent in computation but you don't think it's meaningful in the world. How do you know?

mitchellmckain » March 28th, 2017, 11:38 am wrote:This is certainly NOT an argument for this universe being a computable universe which should be obvious because I have already given my dispute with such an idea.


I'm stipulating the premise and examining the logical consequences. You reject the premise on physical grounds. Can you explain your physical point in terms I can understand? Otherwise I say, "CUH implies such and so," and you respond, "CUH is false on physical grounds," and no conversation is taking place.


mitchellmckain » March 28th, 2017, 11:38 am wrote:However, I can imagine a different universe to be computable and draw conclusions about such a universe. I personally don't think that such a universe is capable of supporting anything I would call life because unlike Dave I do not see anything alive in the automatons of the so called "game of life."


I certainly agree with you there. The CA animations look like video games from 1975. I truly fail to understand how anyone thinks they prove anything about the world, other than that simple algorithms can make cool animations. Disney made Mickey Mouse cartoons out of thousands of individual still drawings. Maybe the universe is a flip book.

OP's argument that "Cool animations exist therefore the universe is a cool animation" certainly has no logical force in my view.

mitchellmckain » March 28th, 2017, 11:38 am wrote:
someguy1 » March 27th, 2017, 12:26 pm wrote:Of course the universe might well turn out to be computational.

No the universe cannot turn out to be computational any more that the Star Trek fantasy of FTL space ships can become a reality. The findings of science make both of these quite unreasonable, and I am not willing to set the discoveries of science aside for the sake of the lovely nature of our fantasies in books and films.


You and OP are true believers! OP says, "The world is X." You say, "The world can not possibly be X." I say I have no idea how or what the world is. Only that you can't fully banish randomness from a sufficiently interesting (= Turing complete) computational world.

Once again your response to me involves simply denying my premise. You are making a point about quantum physics without explaining it. I can't be the only reader not up on the theory of why quantum physics entails randomness. My understanding is that that is an interpretation of physics not shared by everyone. Can you say more?



mitchellmckain » March 28th, 2017, 11:38 am wrote:Yes the existence of noncomputables can have an impact on events, but the actual noncomputables themselves -- their particular stream of random digits -- can have no effect on events


I'm pretty confused by that.


mitchellmckain » March 28th, 2017, 11:38 am wrote:even in our non-computable universe full of quantum randomness.


I've read that quantum randomness is just an interpretation. Hoping you can give me a simplified explanation of this point, which is key to your own point of view.

Consider the thought experiment of tossing infinitely many fair coins to generate a bitstring. The odds are zero that the bitstring is computable. What do you and the OP make of that? Where does that fit in your own theory of the world?

And if you have an ultimate theory of the world ("Contemporary physics = Truth with a capital T") aren't you doing metaphysics too?
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Re: The Mathematical Universe

Postby someguy1 on March 29th, 2017, 8:49 pm 

mitchellmckain, Apologies if any of the previous post came out ranty. I think I figured out where you're coming from and why your post frustrated me a little. I take this to be your thesis:

* Physics entails randomness.

* Current physics is the ultimate physics of the universe. It's True, not just a historically contingent approximation to a truth that may not even exist.

* Therefore the OP's thesis is wrong.

* And therefore I'm wasting my time analyzing the logical consequences of CUH because CUH is wrong anyway.

* Not only that, but if I am open-minded enough to allow that the universe MIGHT be computational, you think I'm absolutely wrong about even the possibility.

Is that where you are coming from?
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Re: The Mathematical Universe

Postby Braininvat on March 30th, 2017, 12:42 am 

I am in full agreement with that. I am a mathematical anti-Platonist. I do not believe 1 + 1 = 2 would necessarily be obvious to alien mathematicians. I ran across a fantastic essay by physicist Carlo Rovelli. It's called Michelangelo’s Stone: an Argument against Platonism in Mathematics.

- SGuy

Neuro, Marshall (may he RIP), and I have all posted the link to this wonderful article by Rovelli, in several related threads. I think I may have posted it a ways up this thread, actually. I was fascinated by his example of aliens on a much smaller planet not developing Euclidean geometry and using spherical geometry instead, being more aware of the curvature of the surface they lived on. I hope everyone here reads the essay, which can be found on arXiv.
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Re: The Mathematical Universe

Postby someguy1 on March 30th, 2017, 1:35 am 

Braininvat » March 29th, 2017, 10:42 pm wrote:
Neuro, Marshall (may he RIP), and I have all posted the link to this wonderful article by Rovelli, in several related threads. I think I may have posted it a ways up this thread, actually. I was fascinated by his example of aliens on a much smaller planet not developing Euclidean geometry and using spherical geometry instead, being more aware of the curvature of the surface they lived on. I hope everyone here reads the essay, which can be found on arXiv.


Before I read that article I thought I was the only person in the world who did not think 1 + 1 = 2 would be automatically obvious to any conscious mind; let alone something that's "true" in the absence of minds at all. [These are two different flavors of Platonism, I wonder if that distinction is made by Platonists -- True for all minds as opposed to true without any minds at all].

Maybe I found the article by seeing it in this thread then forgot that's where I saw it. Great article though.
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Re: The Mathematical Universe

Postby mitchellmckain on March 30th, 2017, 3:22 am 

someguy1 » March 29th, 2017, 7:22 pm wrote:
mitchellmckain » March 28th, 2017, 11:38 am wrote:It is perfect nonsense to hope for a rescue of physical determinism in the unmeasurability in the Plank scale for science has already demonstrated that hidden variables simply do not exist.


That's the bit I never learned. Is a simple explanation possible?

Look up Bell's inequality.

someguy1 » March 29th, 2017, 7:22 pm wrote:
mitchellmckain » March 28th, 2017, 11:38 am wrote:The issue seems to be with how we are understanding the words " there is no randomness in the world." You seem to interpret this as including noncomputable reals as part of the world, where I do not. For me to say that randomness is in the world would mean that there were truly random events in the world. Because of quantum physics I agree this is the case and conclude the world is not computable.


You believe physics precludes a computational world, therefore you refuse to even consider the premise.

Incorrect. Yes I believe physics precludes a computation world, but no I do not refuse to even consider the premise. I bring up my position on this preclusion only when you ask about my motives for disagreeing with you when considering the premise.

someguy1 » March 29th, 2017, 7:22 pm wrote:"You seem to interpret this as including noncomputable reals as part of the world," -- Where in this entire thread have I ever made such a claim? I categorically deny ever writing such a thing.

I never said you did. This is only my attempt at understanding why we disagree regarding a conflict between "(1) the world is a computation; and (2) there is no randomness in the world." Since we agree that computation and randomness are incompatable, it seemed that our disagreement must be about what we mean by no randomness in the world.

someguy1 » March 29th, 2017, 7:22 pm wrote:What is said is that IF the world is a computer and it's Turing-complete, THEN the halting problem entails some degree of randomness in the world.

And I do not agree. You would only get randomness that way by inserting randomness in your choice of program. But for a fixed program the result is not random at all.

someguy1 » March 29th, 2017, 7:22 pm wrote:Do you understand that I have not made and do not make the claim you think I made?

Do you understand that I have not made and do not make the claim (about what you claim) you think I made?

someguy1 » March 29th, 2017, 7:22 pm wrote:
mitchellmckain » March 28th, 2017, 11:38 am wrote:I am not convinced that all aliens will follow the same thought processes that give us mathematics to make it a universal language like so many sci-fi movies claim.


I am in full agreement with that. I am a mathematical anti-Platonist. I do not believe 1 + 1 = 2 would necessarily be obvious to alien mathematicians. I ran across a fantastic essay by physicist Carlo Rovelli. It's called Michelangelo’s Stone: an Argument against Platonism in Mathematics.

Indeed. I am an anti-Platonist as well.

someguy1 » March 29th, 2017, 7:22 pm wrote:
mitchellmckain » March 28th, 2017, 11:38 am wrote:The randomness of a noncomputable has no way of impacting events.

How do you know noncomputable quantities don't impact events?

I supplied you with a proof by contradiction of this.

someguy1 » March 29th, 2017, 7:22 pm wrote:
mitchellmckain » March 28th, 2017, 11:38 am wrote:Yes the existence of noncomputables can have an impact on events, but the actual noncomputables themselves -- their particular stream of random digits -- can have no effect on events

I'm pretty confused by that.

Why? You cannot compute them. So how could their particular stream of random digits have any impact on you when you could never know what they are, for example?

someguy1 » March 29th, 2017, 7:22 pm wrote:And if you have an ultimate theory of the world ("Contemporary physics = Truth with a capital T") aren't you doing metaphysics too?

Why shouldn't I do metaphysics. And by the way, NO, I do not equate Contemporary physics with Truth... But I certainly do take the conclusions of science seriously and I guess I do not share some of the aversions you apparently have...
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Re: The Mathematical Universe

Postby Positor on March 30th, 2017, 9:56 am 

In a computable universe, does Chaitin's Omega count as part of the world? If so, does this imply that randomness would still actually exist, i.e. that no universe can be fully computable?

Also, I would be interested if anyone could address the following point by hyksos:
hyksos » March 26th, 2017, 1:35 am wrote:"Yes, Hyksos, but what Turing means is that there exists no algorithm which can produce the digits and this is the blah blah blah". Nope. That's the concept of compressibility, not computability. An algorithm A, which produces a stream of digits d, could itself be stored as a string of bits. Those bits of A would constitute a "compression" of the bits of d. In in a situation in which A must be at least as larger or larger than d -- we simply write the digits of d instead, and declare it un-compressible. .
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Re: The Mathematical Universe

Postby mitchellmckain on March 30th, 2017, 6:15 pm 

Positor » March 30th, 2017, 8:56 am wrote:In a computable universe, does Chaitin's Omega count as part of the world? If so, does this imply that randomness would still actually exist, i.e. that no universe can be fully computable?

No.

Positor » March 30th, 2017, 8:56 amAlso, I would be interested if anyone could address the following point by hyksos:
[quote="hyksos » March 26th, 2017, 1:35 am wrote:
"Yes, Hyksos, but what Turing means is that there exists no algorithm which can produce the digits and this is the blah blah blah". Nope. That's the concept of compressibility, not computability. An algorithm A, which produces a stream of digits d, could itself be stored as a string of bits. Those bits of A would constitute a "compression" of the bits of d. In in a situation in which A must be at least as larger or larger than d -- we simply write the digits of d instead, and declare it un-compressible. .

This applies to numbers like pi but not to the uncountable majority of reals which are not computable. Most of these differ from Chaitin's Omega in that they are not even defined and may not be definable. We only know that they exist, but a means to define one of them without stating an algorithm by which to compute them is not so easy to come by. One way to get a countable subset is to start with a defined non-computable like Chaitin's Omega and make some mathematical alteration of it and we would have a defined non-computable.
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Re: The Mathematical Universe

Postby someguy1 on March 30th, 2017, 10:08 pm 

Positor » March 30th, 2017, 7:56 am wrote:In a computable universe, does Chaitin's Omega count as part of the world? If so, does this imply that randomness would still actually exist, i.e. that no universe can be fully computable?


Good question. What does halting randomness mean? It's equivalent to Gödel's incompleteness theorem. It can be understood as the limitations of formal systems. If we programmed the rules of number theory into a computer and then had it crank out every possible theorem that it could, there would still be syntactically valid propositions that can neither be proved or disproved. And there would be facts about the natural numbers that have no proofs. They're true but there's no reason they're true. They're random truths. I believe this is Chaitin's point of view.

Gregory Chaitin wrote:... some mathematical facts are true for no reason, they are true by accident, or at random. In other words, God not only plays dice in physics, but even in pure mathematics, in logic, in the world of pure reason. Sometimes mathematical truth is completely random ...


I mention this to provide another way to think about the randomness entailed by the halting problem. If the world is a computer, there will be facts that are true about the world but that weren't generated by the computer. They're random truths.
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Re: The Mathematical Universe

Postby Dave_Oblad on April 4th, 2017, 2:41 am 

Hi Guys,

I'm back. Was a very busy and intense last week. I am a bit settled now. So, where were we?

In trying to prove that Math can't be used in a simulation of the world, I think you guys have done a great job in proving that no one can trust the many thousands of Computer Simulations employed on a daily basis in practically every possible field.. from Cosmology to Biology to Medicine to Geology to Physics... etc.

I'm equally confident that the Halting Problem has cause no end of issues for every Programmer on the Planet in trying to produce Sims of our Reality. The fact we can't produce Mathematical Randomness has also been of equal concern. Even Pseudo Randomness Algorithms have proven nearly worthless in tying to reproduce our Reality in a a complex Sim. I know I can't use Pseudo Randomness in creation of a Chess playing program.. as it's too predictable. Us programmers have to resort to using inputs from the Real World, such as Static Noise Amplification hardware, because it's literally impossible to create True Randomness Mathematically.

We should also scrap the Internet as it can't possibly work in a Universe filled with non-computable number systems. Computers must be utterly worthless in a Real World.

Note: If you guys can employ strawman arguments then so can I.

Science knows everything! No hidden variables. We know exactly why a point particle can spin and must spin twice to present the same face. We know exactly how the same particle can be in multiple locations simultaneously. There is only one valid interpretation of Quantum mechanics and it's complete.
https://en.wikipedia.org/wiki/Hidden_variable_theory

Science absolutely knows the Universe began with all the Energy we see today.. because Energy can't be Created. Science knows how, and why, the Universe & Time began. There are no unknowns in Science.

All that being said.. Not one single person has offered any proof that our Universe can't be a Cellular Automaton.

Instead, there seems to be a great deal of confusion on the term "Compute". For me, this is just a description of a Causal Event Chain. It doesn't require Floating Point Math or introduction of non-computable numbers or their systems. I believe the Human Brain is a Computer but it sure doesn't employ any form of Numbering System or Floating Point Mathematics. It's not limited by the existence of non-computables.

I do draw a strong correlation between a Neural Network and a Cellular Automation, in the way both work in processing information through Connectivity and Gated structure.

Remember William Blake's Quote: "To see a world in a grain of sand and..". Well, I was asked to provide some evidence to my Hypothesis and posted the following CA Gif:

GospersGun.gif
Gosper's Gun from Conway's Life CA

I believe it was Someguy1 that thought the image irrelevant and called it a "Silly Picture". Where as I see that "Grain of Sand" that William Blake spoke of.

I wrote my first CA on an Atari-800 and published it through Bulletin Boards (early precursor to today's web sites). I've have been studying them for decades, fascinated by their power. Simple 2D versions have already demonstrated remarkable abilities ranging from full on computing (Turing Machines) to Big Bang Scenarios. They fully fall within the scope of Mathematics as Boolean Algebra etc.

I am fully within the scope of Science to suggest the Universe is not just described by Math but is rather Composed solely of Math, in the realm of CA's and all that they can be:



The above samples are heavily limited in respects that it only employs 2 layers of Time and connectivity to just a few local neighbors. When expanded to 3D and 4D with connectivity to deeper layers of Time and greater number of neighbors, they can become outrageous in their power and complexity. And also nearly impossible to view the Emergent Geometries. If one avoids perfect symmetry within the Rule sets, then no Human design is needed to produce highly complex Big Bang scenarios.

Since it is all purely Mathematical and utterly Deterministic.. I see an obvious solution to the question of "Something From Nothing", the starting of "Time", and a whole host of issues resolved. Since there exists no arbitrary limit on the complexity of the rule sets, there is no limit on the complexity that can exist in CA's as a whole.

Unlike my example of how many Images your Computer Monitor can Display, there is no limit on the Number of Universe's that can be defined within CA's. Again, most will be trash, but many will be functional Universe's, like the one we Exist inside of.

At some point some one will ask: "Ok, so where is this Super Computer that is Computing our Universe?"

The obvious answer is that the Whole Universe <IS> the Computer. Each Planck Sized Cell is doing its individual share of processing the information it's being presented with and propagating the results to the next layer of Time and newly created surface Cells (the Expansion of the Universe).

I fully endorse the concept that all aspects of Quantum Mechanics can be manifested within a complex CA.. that is.. everything except True Randomness. It is fully predictable that given the complexity of systems and the limitations regarding the tools of Measurements of the Ultra Small, that we must resort to Probability Mathematics. I just disagree that such limitations should be interpreted as True Randomness existing within the Quantum Universe.

I simply don't believe in Magic.

So.. take another look at Gospers Gun above and tell me it's a silly picture.. that you don't see a Universe in a "Grain of Sand".. as I do.

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

Postby rajnz00 on April 6th, 2017, 8:27 am 

someguy1 on March 27th, 2017, 12:57 am wrote: Rajnz00, How on earth could I ever expect to push the OP around. OP operates in write-only mode and has done so for six and a half years. The argument never changed and no effort was ever made to address substantive arguments to the contrary; the main one being that the OP would be well advised to read some philosophy and find out just how old these kinds of ideas are.

That was just tongue in cheek. You are giving as good as you get. Dave gets a bee in his bonnet and that's where it stays poor fellow.

Braininvat on March 30th, 2017, 12:42 am wrote: I was fascinated by his example of aliens on a much smaller planet not developing Euclidean geometry and using spherical geometry instead, being more aware of the curvature of the surface they lived on.

Highly unlikely. No planetary creature would be aware of the spherical nature of his planet to start with. Carlo Rovelli himself argues against Platonism in mathematics by essentially arguing mathematics develops from humble beginnings, counting and flat shape geometry
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Re: The Mathematical Universe

Postby Dave_Oblad on April 6th, 2017, 10:11 am 

Hi Raj,

I am a very inquisitive person. I want answers.. Science has failed to provide said answers. I found an answer, and until something better comes along, why should I budge?

I hear "No Hidden Variables". How much of our Universe is made of Dark Matter? Did the Standard Model predict "Dark Matter"? Can we see this "Hidden" Matter? Seems like a pretty large Hidden Variable to me.

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.

Here is perhaps the hardest concept for anyone to grasp:

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.

If I keep upping the complexity of the Question, most will agree there exists a solution, even if the complexity goes beyond our ability to work the problem in our heads.

If I switch to 2D or 3D or 4D tables.. it's still just an increase in complexity.. but still fully deterministic.

If I switch from Math Functions to Logic Functions.. still.. complex but deterministic.

If I switch to interactive values taken from previously established values, same thing again.

With interactivity and no limit set on a growing table size, how complex can we get?

If you can see the 1,000,000th digit of 10/3 Exists as a specific value, then the Question defines the fixed Solution.

If I see the Existence of You in the solution at a dramatically increased level of complexity, then your Existence is just as justified as the 1,000,000th digit of 10/3.

Basically, an increase in complexity doesn't devalue the concept of Existence within a deterministic Solution.

So.. how many folks really understand or grasp that concept? It's a hard one to communicate.

This is how I define Existence. There is no arbitrary limit on the complexity and setup of an unlimited number of Cellular Automatons. Deep inside any solution, if a Person is found to Exist within a society, why is that Person more or less Real.. than you?

I see many parallels between an Automaton and our Universe.. except one. True Randomness (Magic). So yes, I believe the Universe is Computing its own existence, but not using Math in the sense of Numbers, but rather Logical Operators. This is why I keep rejecting all the arguments presented recently that revolve around Number Theory.

Perhaps that is my fault for using the term "Compute".

When I say "Compute".. I mean like how a Neuron Network Computes.. not an Adding Machine. How you Navigate a Car, or Catch a Ball, or even Dream. Do we use Real Numbers (etc) when we Dream? Is Dreaming a facet of Computing? Do we Dream using floating point Math or by Switched Logic Circuits using massive inter-connectivity?

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

Postby rajnz00 on April 6th, 2017, 4:01 pm 

I am a very inquisitive person. I want answers.

I'd be happy to provide you with the answers of the nth value of 10/3. It's 3, Now come back tomorrow for the (n+1)th value. You will be astonished by the answer.
Come unto me, for you seem to be heavy laden, if you could drag yourself away from the endless loop of trying to figure out the millionth value of 10/3, or you legions of mindless automatons, posted haphazardly about the universe, in random motion.

I'll give you a new sum every day to keep your mind occupied, such as 1/3 =?
Here's one for your inquisitive mind: Prove that in any triangle, two angles taken together, in any manner, are less than two right angles.
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Re: The Mathematical Universe

Postby vivian maxine on April 6th, 2017, 4:10 pm 

10/2=3.3333333333333333333 + :-)

10 degree angle plus 10 degree angle?

I've been into the "New Math". It has absolutely fogged my brain. 4/5 is smaller than 5/8. Says so right here in this Math Made Easy book.

OK. I'll leave. A bit of jocularity is good for the soul - if one has a soul. Nos dawch. (Good night)
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