## The Mathematical Universe

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

### Re: The Mathematical Universe

Hi Dave,
As previously stated (somewhat emphatically), there is no way to Mathematically create True Randomness. You can take that to the bank.
I did. I was quite excited about it – thought at last I have a deposit for a house, but the bank manager was not having any of it. Far from taking that as my 20%, he wouldn’t even give me a dime.
I am really puzzled by your fascination with maths. I had a look at someguy1’s post on March 16th, 2017, 8:53 pm. He's not as emphatic as you, but he pretty much answers all your claims, quite patiently. It is evident he really knows his stuff. Unlike others who evidently don’t. For example, “In math 3 doesn't exist "before 4" or something. (like you keep harping on to me) Everything is a set.”
Anyway I’m done with this thread.
Regards
R
Except for one more thing
vivian maxine » April 6th, 2017, 4:10 pm wrote: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.
What!! Who wrote that book? Wasn't Dave by any chance? :)
rajnz00
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### Re: The Mathematical Universe

Perhaps the excitement surrounding Cellular Automata as being physically motivated is still a kind of grounded excitement. It may be reasonable in a final assessment, but for an entirely different reason than the reasons beaten to death in this 8-page discussion. Maybe Dave_O has discovered chaos theory in cellular automata. That's good progress, I would say.

There does exist the deep topic of platonism in mathematics. It's a topic worthy of book-length expository.

There does exist the topic of determinism in quantum mechanics. Another topic deep enough for book-length expository.

The topic of in-computability in math. Also could fill a whole book. No doubt.

There are (variously) topics of Mathematical Universe Hypothesis, the Simulation Hypothesis, and even Schmidhuber with his metaphysical idea that the universe we inhabit is computable. (The "computable universe hypothesis"?)

Anyways,

Perhaps what Dave_O is discovering about the world is not "World is math" but maybe he has, in his later years, stumbled upon what the rest of us have been calling Chaos Theory. Decades ago, the idea that the world around us operates on Chaos Theory was laughed away as crackpottery. (see the biography of Benoit Mandelbrot). But today, Chaos Theory is now universally understood to be a very accurate depiction of how our universe operates.

Completely deterministic, simple, local rules can give rise to extremely complex dynamics and very intricate temporal and spatial patterns. This happens when there is feedback among them coupled with sensitivity to initial conditions.

We have this idea that the intricacy and complexity of the forest floor ecosystem derives from the inherent noisiness of the real world. This can be countered with chaos theory :: that intricacy and noise could, in principle, arise from deterministic rules that are shockingly simple. So while from the level of macroscopic human scientists and their energy-limited measuring sticks, there could be an apparent randomness. And that apparent randomness could, in principle, be created by deterministic simple processes.

I thought that someone on this forum needed to say this. The principle idea is not bankrupt. Someone should have extended that much to Dave_O. No one yet has.

There is an entirely separate issue regarding determinism in quantum mechanics. The die-hards have been given free reign in this thread to shout that argument down everyone's throats. (forum regulars were variously insulted, told to "look up Bell's Inequalities" , deemed "research-impaired", told that they "don't understand probability" and other social misgraces).

But at the end of the day , quantum mechanics is severely limited in metaphysical scope. QM provides no coherent narrative about the world. The Interpretations of QM run the board. The Formalism of QM is barely more than a calculating device. The universe we inhabit follows the results of that calculating device with extreme precision. Nobody really knows why. Nobel prize winner in physics, Eugene Wigner didn't understand it either. The way in which the fundamental particles obey math , Wigner wrote "..borders on the mystical..." (end-quote). If you believe some guy on this forum understands this topic better than Eugene Wigner, I recommend you to turn the volume up on your skepticism.

But yes, Chaos Theory is a particular branch of mathematics. It should not be used as a synonym for "math" itself. Chaotic systems can give rise to noise that passes all statistical tests of randomness, even when the creator of the algorithm knows it is purely deterministic. One example would be block ciphers in cryptography. They must be deterministic because they must be reversed (decrypted) eventually. But the resulting ciphertext is unreadable noise.

hyksos
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### Re: The Mathematical Universe

vivian maxine » June 20th, 2016, 11:49 am wrote:Perhaps what they are really saying is that the universe came into being with designs that formed patterns which enabled us to explain the designs mathematically. Perhaps, for that reason, they are saying mathematics is the universe. Maybe they simply mean all the patterns were there that enabled the term. Almost everything in the universe seems to have some form of balanced pattern. And perhaps we are saying we can't use the word "mathematics" for that because we already use it after the fact. But, can we use it? If not, then what term can we use?

What confused me at the start was the statement "Mathematics is the Universe". I am probably far off base here but does "The Universe is mathematics (mathematical) fit? Is mathematics always dealing with patterns? If it is, then mathematics came into being at the time the universe came into being. Not before but with - mathematics being the pattern the universe formed as it came into being.

I am not a mathematician. Can someone who is answer one question. Does everything that mathematics deals with fall into patterns? If not, all I've said above is gibberish. It probably is anyway.

Carry on, Ronjanec. Keep us thinking.

In experiments to understand the universe at the time of the big bang, humans have created new elements that last only seconds. I think claiming that something that lasts only a few seconds is an element, is an exaggeration. But the possibility that at the time of the big bang atoms may have combined in ways that don't work, would indicate things happened spontaneously without a plan.

Cicero said, "By them [the Greeks] geometry was held in the very highest honor, and none were more illustrious than mathematicians,. But we [Romans] have limited the practice of this art to its usefulness in measurement and calculation."
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### Re: The Mathematical Universe

I read 'Flatterland' (2000) by Ian Stewart recently. It takes a 2-dimensional young women (a line) through an extra-dimensional math Universe. It's quite enjoyable reading and eventually gets to the Multi-verse, strings, branes etc.

GaryCGibson
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### Re: The Mathematical Universe

GaryCGibson » April 24th, 2017, 2:42 pm wrote:I read 'Flatterland' (2000) by Ian Stewart recently. It takes a 2-dimensional young women (a line) through an extra-dimensional math Universe. It's quite enjoyable reading and eventually gets to the Multi-verse, strings, branes etc.

Haven't read that but wouldn't a line be 1-dimensional? Kind of a boring world, you keep butting heads with people or running into (rhymes with) brass poles. <joke>Not unlike this forum</joke>.
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### Re: The Mathematical Universe

I present the following as strong evidence that the universe is a mathematical structure. (rather than say, a collection of physico-mechanical substances that happen to be describable by math after-the-fact).

Nuclei of atoms are , to some approximation composite objects comprised of protons and neutrons. The nucleons are then known to have sub-structures called quarks.

It is known that nuclei of atoms contain angular momentum. With any other composite physical "object" in our universe, the direction of rotation of the object can be in any direction that you so choose, at any speed that you so choose. The formalism of physics produces a vector called the "angular momentum" of a rotating object. The nuclei of atoms have angular momentum that is quantized. Fundamental particles themselves (say electrons) also have this peculiar angular momentum, also quantized.

The idea that this 'spin' would be quantized did not come from some physicist having a visual model of the nucleus, from whence he then derived its mechanical behavior throughout time. The situation is far worse. The pure mathematical formalism of QM demanded that whenever a system is observed it would only admit stationary states that correspond to eigenstates of a Hilbert space (along with a self-adjoint operator for the observable).

So basically what you do is you set up a matrix that represents rotations in 3D space (cr. Pauli Matrices). Then you "pull the mathematical crank" to obtain the admissible eigenvectors of that matrix. You point at the eigenvectors on your chalkboard and declare that these are the only "states" admissible for the system upon measurement. You declare that this will physically happen.

Yes - this actually works. This is exactly how nuclei act in a laboratory setting. You turn the crank, get a non-commuting observable. Then that's what matter and energy does. Period.

Then (most regular people) demand to know why. Why is this? Why does the universe act like this?

• Why does this happen with nuclei? Nobody knows.
• Okay so what is mechanically going on in there? There is no mechanism.
• Alright but what are you visualizing geometrically? There is no visualization.
There is no picture to draw that would satisfy one's desire for a gears-turns-gears narrative.

In the case of silver nuclei , the admissible states of angular momentum are only two solutions. We call these Spin Up and Spin Down. Even though any regular human being would understand that silver nuclei are quite a complicated bunch of neutrons and protons, their angular momentum (as a nucleus) only takes on two states. This is physically real, and was shown in experiment in the early 1920s.

When the dust clears: whatever matter 'actually is' in some metaphysical sense, the particles that undergird matter and energy act according to mathematics. They do so continually, precisely, and accurately. There is no physico-mechanical explanation for quantized angular momentum. There is barely any geometrical interpretation. However, the mathematics is valid, experimentally, theoretically, and logically.

If you squeeze the equations of spinors enough -- you might come up with some sort of "understanding" of what quantum spin might be suggesting about reality. But on your very best days, you get mystical gobbledegook : There exists a complex space of higher dimensions that seems to know about the negative sign on the square root of negative 1. I.e. that matter and energy "know" that i and -i exist.

But such "insights" do not get one closer to a physico-mechanical gears-on-gears narrative. One finds oneself only getting pulled deeper into mathematical abstractions. Finding one's self saying that those abstractions must be "real" in some way. In a desperate attempt to disengage from the world as a mathematical structure, one gets pulled only more deeply into the arguments for pro-math.

hyksos
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### Re: The Mathematical Universe

Re: The Mathematical Universe
hyksos, et al,

Everything we know today about Earthly human constructs, the forces that appear to surround us, of the biggest things like the universe - to - quarks, it a result of the first human that started basic Arithmetic (addition). But the laws of the universe were in place well before man. Mans merely discovered them.

From the Fibonacci Series (1,1,2,3,5,8,13,21,34,55,89…), the Square Numbers Series (1, 4,9,16,25,36,49…), sequence of triangular numbers (0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ….), and all the plane geometric figures to sequenced with the the basic solid forms up through the dodecahedron; much like the Pentagon Number Series (1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176…) which are all a result of cascade effects. We have al heard of the Magic Square series. And most of us has never heard of the Catalan Number Series (1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862…); and there are even more.

hyksos » April 27th, 2017, 1:35 pm wrote:I present the following as strong evidence that the universe is a mathematical structure. (rather than say, a collection of physico-mechanical substances that happen to be describable by math after-the-fact).

Nuclei ⇔ The nucleons are then known to have sub-structures called quarks.
Angular momentum that is quantized.
Mathematical formalism of QM demanded → set up a matrix that represents rotations in 3D space → eigenvectors (transformation) of that matrix.
Mathematics → experimentally, theoretically, and logically.
etc

But such "insights" do not get one closer to a physico-mechanical gears-on-gears narrative. One finds oneself only getting pulled deeper into mathematical abstractions. Finding one's self saying that those abstractions must be "real" in some way. In a desperate attempt to disengage from the world as a mathematical structure, one gets pulled only more deeply into the arguments for pro-math.

(PARAPHRASING)

Please excuse me if I (in fact) butchered your posting all to very much. (I apologies.) For this once, we can dispense with:

Rules:
Rule 6: Never apologize, mister, it's a sign of weakness. (SSA Gibbs or CPT Brittles)
Rule: 42 Don't ever accept an apology from someone that just sucker-punched you.

INVOKING: Rule 51: "Sometimes you're wrong."

(COMMENT)

We can see, very well, that this very question leads to an inevitable necessity for a dialectical method.

The universe came first, and man invented Mathematics and geometry to describe and resolve abstract issue. And the philosopher Plato and Aristotle were (in the same way as Albert Einstein and Niels Bohr) had opposing views. We still have that same question today.

One thought that complicates the matter is the onset of chaos. There is no greater enemy to a mathematical constructs as chaos. And man must determine how the Second Law of Entropy applies? This idea (the natural order of the universe) is to advance from order to disorder.

But what (may you ask) do I know. I am at that age where you can say I have rapidly approaching entropy. I am a modern day Meno to Socrates.

Most Respectfully,
R

RoccoR
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### Re: The Mathematical Universe

hyksos » April 27th, 2017, 11:35 am wrote:I present the following as strong evidence that the universe is a mathematical structure. (rather than say, a collection of physico-mechanical substances that happen to be describable by math after-the-fact).

Two arguments I just don't get.

One, that just because we have a mathematical formalism whose meaning we don't yet understand, the world must simply "be" that formalism. Isn't it possible instead that someday we'll understand what the formalism means? Just like relativity gave meaning to Newton's formalism of gravitational attraction.

Two, that just because matrices are handy gadgets for computing 3D rotations, matrices have some ontological reality in the world. Couldn't they just be handy gadgets for calculating, the same way the numbers on your grocery receipt aren't actually your vegetables?
someguy1
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### Re: The Mathematical Universe

Hi Folks,

The previous debate got a bit heated and the Mods decided to clip the latter part and move it to feedback.

I asked for permission to put my Summary back here and got no reply.. so I have put it back. Why? I felt the last several pages of debate where not relevant to this concept I've been promoting. The issue is about what it means to Compute. Naturally, most will assume this means like how a typical computer works. How Algorithms operate or even a Turing Machine computes. The arguments presented are perfectly valid if I meant "Compute" in the way a computer machine operates.

But that is not my intended definition for Computing.

My version of "Computing" is via a Logic Network, as is found in Cellular Automatons. Such Computing Networks operate much like how our Brains compute. And yes, our Brains certainly do Compute. They input information, run comparisons and make decisions that affect our every waking moment. Try programming a Computer to drive a car. We can do it so easy, we hardly spend any conscious thought on such. But coding programs for a standard computer to drive a car.. is very difficult.

Anyway, to balance out all the recent noise, I wanted to restate the concepts in a brief Summary as follows:

Given the full embodiment of All Mathematics, One subset is Cellular Automatons.

Given the full embodiment of Cellular Automatons, there are an infinite set of potential rules.

For each possible set of rules, there exists a complete Solution that is fully Deterministic.

Given that Cellular Automatons are internally interactive, they posses the processing equivalence of a Cellular Logic Network.

Given the subset of Expandable Cellular Automatons in Three or more Dimensions and given the Exclusion of all Solutions that produce, in essence, garbage, noise or just pure symmetry.

What remains is still an almost infinite subset of extremely complex multi-dimensional deterministic solutions.

For those within this final subset, some will have enough complexity to manifest the field backbone of Quantum Mechanics of various complexities.

Some of those will have sufficient complexity to manifest Gravity, Chemistry, Life and Self-Aware Life.

Thus, within some Solutions of Fully Deterministic Cellular Automatons, self aware Life can be an emergent property.

It is my belief that.. our Reality is one of those Solutions.

The only way such a Solution can be said to Exist is if it is Fully Deterministic.

Thus, the only reasonable counter argument against such a view is if True Randomness exists.

To support such a counter view, one must accept that an Event can exist without a Cause.

I call this latter view Magic.

I would rather believe in a fully Deterministic Universe than believe in Magic.

This brings into play the age old arguments regarding Freewill, of which I take a Compatibilist stance.

So, in summary, that's my stance until something better comes along.

Now, even though I came to these conclusions independently, I can't lay claim to such being solely mine, as many other, far more astute Experts, were already on this path long before me. And they have done a far better job at defining such than I could ever hope to do.

I did have one unique concept I presented about 5 years ago.. the idea that Quantum Life evolved long before Matter appeared in the Universe. This has lead me to consider the following possibility:

Some might believe I have omitted a God in this viewpoint. Not necessarily True. If the Whole Universe is a Quantum Computer, then it may be possible that such an Intelligent Universe may have Evolved to self-awareness of itself. If that is true, then I can't dismiss the possibility that such a Cosmic Mind may have had some say in how the Universe evolved and perhaps tipped some scales to promote the Genesis of Living Matter.

I might call this the Universe's way of making a few new friends.

Note: I need to come back and address some recent posts.. but it's 4:12 AM here now and I'm too sleepy to proceed until I catch some sleep. Back later...

Best wishes all,
Dave :^)

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### Re: The Mathematical Universe

Dave_Oblad » April 28th, 2017, 6:13 am wrote:To support such a counter view, one must accept that an Event can exist without a Cause.

I call this latter view Magic.

Only, the truth is that magic is typically seeing causes where none exist. ...like saying a magic word makes a rabbit disappear, thinking that the positions of the stars in the sky dictate your personality and fortune, believing that crystals and/or springwater cures cancer, or spilling the blood of people or animals will give you some kind of power.

Dave_Oblad » April 28th, 2017, 6:13 am wrote:I would rather believe in a fully Deterministic Universe than believe in Magic.

I would rather believe what the objective evidence dictates.

Dave_Oblad » April 28th, 2017, 6:13 am wrote:This brings into play the age old arguments regarding Freewill, of which I take a Compatibilist stance.

Whereas I think this makes the characters in novels conscious and alive because all that matters is an appearance of life and will, and our most basic human experience is all just an illusion. Self organization is indeed an important part of what the living process is all about, but while I think consciousness is closely connected with this, I think the subjective experience is also directly connected with the decoherence of a superposition of future possibilities into the singular actualities of the past. This is the only thing in physics which matches our experience of the present as locus of our conscious existence. Thus I see no reason to dispute what the evidence shows, which is that future possibilities are real because they are not determined by pre-existing condition. We are not characters in a book which has already been written. Our story is being written right now in the present moment and this is the substance of our conscious experience. For this reason I take the Incompatibilist stance.

Dave_Oblad » April 28th, 2017, 6:13 am wrote:I did have one unique concept I presented about 5 years ago.. the idea that Quantum Life evolved long before Matter appeared in the Universe. This has lead me to consider the following possibility:

Some might believe I have omitted a God in this viewpoint. Not necessarily True. If the Whole Universe is a Quantum Computer, then it may be possible that such an Intelligent Universe may have Evolved to self-awareness of itself. If that is true, then I can't dismiss the possibility that such a Cosmic Mind may have had some say in how the Universe evolved and perhaps tipped some scales to promote the Genesis of Living Matter.

What I imagine is that quantum computing may bring indeterminacy into computing world. If so then perhaps this will make machine life possible with real conscious intelligence, which rather than being programmed must learn just as a child has to learn.

Nearly the same determinism/indeterminism debate is found among theists... those who believe in a God who controls everything in absolute predestination and those who believe in free will and thus that we choose our own fate. I am one who believes the greater God is one who chooses love and freedom over power and control, and that real omnipotence includes a power over oneself and the ability to take risks, sacrifice power, give privacy, have faith and all the other things which are often associated with the ability to love.

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### Re: The Mathematical Universe

mitchellmckain » April 28th, 2017, 6:01 pm wrote:What I imagine is that quantum computing may bring indeterminacy into computing world. If so then perhaps this will make machine life possible with real conscious intelligence, which rather than being programmed must learn just as a child has to learn.

It's been shown that quantum computers have exactly the same computational power as classical ones.
Although quantum computers may be faster than classical computers for some problem types, those described above can't solve any problem that classical computers can't already solve. A Turing machine can simulate these quantum computers, so such a quantum computer could never solve an undecidable problem like the halting problem. The existence of "standard" quantum computers does not disprove the Church–Turing thesis.

https://en.wikipedia.org/wiki/Quantum_c ... ity_theory

Speaking of the Church-Turing thesis, this also falsifies OP's claim that cellular automata have some kind of different processing abilities than Turing machines. They do not. Period.
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### Re: The Mathematical Universe

Hi mitchellmckain,

Truth be told, I suspect we have a lot more in common than may be evident.

The reason I hold such a strong Deterministic stance has to do with what it means to "Exist". That's a bit hard to explain, but I'll give it a brief try:

I fully accept the Decimal Value of Pi <EXISTS> because it is not something we invented. It has a singular value that can be witnessed by any number of observers, from anywhere in our Universe at any time in the Universe.

That the major difference between the Existence of Pi and the Existence of the Universe is just a matter of complexity. Both get their Existence value from being utterly Deterministic.

But suppose there was some form of bizarre Math that could actually produce Real Randomness. Nothing that can be produced by such Math can be said to have Real value in the form of Existence. Such Math can only produce Random Noise without a continuous evolving building of a foundation or history. Such output would be totally formless and without structure. It can't even evolve.. it's just noise. It lacks the special quality of Sequential Existence.

But on the other hand, I can think of many systems that have the Quality of Pseudo-Randomness (like Pi), but are still built from absolutes in an absolute sequence.

Is there a happy medium?

I can easily see in a fully Deterministic Mathematical Existence, the possibility of Reflections, Echoes and Race conditions. This Fuzzy kind of Reality might work, if the Noise didn't overwhelm the emergent structures building within it. I might call such Fuzzy Determinism a possibility and still not relegate it to the Magic bin. Ultimately, it would still be utterly Deterministic, but the Fuzzy factors don't have to be resolved immediately. This view might seem to be more compatible with observations. I don't have a problem with such.

Best wishes,
Dave :^)

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### Re: The Mathematical Universe

Dave_Oblad » April 28th, 2017, 8:13 pm wrote:Hi mitchellmckain,

Truth be told, I suspect we have a lot more in common than may be evident.

Of course. Just because we are not exactly the same and have one (or even ten) disagreement(s) does not mean we are totally different. We likely have many things in common.

Dave_Oblad » April 28th, 2017, 8:13 pm wrote:The reason I hold such a strong Deterministic stance has to do with what it means to "Exist". That's a bit hard to explain, but I'll give it a brief try:

I fully accept the Decimal Value of Pi <EXISTS> because it is not something we invented. It has a singular value that can be witnessed by any number of observers, from anywhere in our Universe at any time in the Universe.

Pi is a fixed, unchanging abstraction, and certainly not alive. Our existence is different in nearly every way -- dynamic, concrete, and alive. Furthermore, I do not buy into this idea that pi must be distinguished from things which are invented. Were airplanes really invented when the requirements of flight are found in the mathematical laws of nature? I dispute the idea that any of the thinking behind mathematics is any more inevitable than airplanes. Yes pi has a singular value, but living things are very very different. I deny that we (that living things) can be confined to any such singularity of existence because while our past is fixed our future is a superposition of possibilities.

Dave_Oblad » April 28th, 2017, 8:13 pm wrote:That the major difference between the Existence of Pi and the Existence of the Universe is just a matter of complexity. Both get their Existence value from being utterly Deterministic.

And I have refuted this idea already in responses to your previous posts. I deny that life is nothing more than complexity. There is a difference between the nonlinearity in the computational world of computers and the nonlinearity in the real world which has quantum indeterminacy at its roots. A computer simulation of the weather is 100% predictable because the initial conditions are a series of recorded bits. But real weather will never be predictable because the initial conditions simply do not exist to an infinite degree of precision. That is what we learn from quantum physics. When we look closely at the components of our existence, we find they do not have precise values for every measurement/interaction but generally exist in states of superposition of possibilities. The evidence thus tells us that we in fact "get our existence" from a reality which is both deterministic in some areas/parts/regimes and indeterministic in others.

Dave_Oblad » April 28th, 2017, 8:13 pm wrote:But suppose there was some form of bizarre Math that could actually produce Real Randomness. Nothing that can be produced by such Math can be said to have Real value in the form of Existence. Such Math can only produce Random Noise without a continuous evolving building of a foundation or history. Such output would be totally formless and without structure. It can't even evolve.. it's just noise. It lacks the special quality of Sequential Existence.

No I will not suppose any such thing. Math is deterministic. But I deny that mathematics is the summation of our existence. Mathematics is a useful tool and nothing more. It provides a very valuable way of looking at the universe, but it is not the universe -- no more than the universe is red just because it looks red when we look at it through rose colored glasses.

Dave_Oblad » April 28th, 2017, 8:13 pm wrote:But on the other hand, I can think of many systems that have the Quality of Pseudo-Randomness (like Pi), but are still built from absolutes in an absolute sequence.

Is there a happy medium?

No. Pseudo-randomness is all you will ever find in the computational world of mathematics and (today's) computers. But out here in the real world it is different because we find there are no initial conditions (hidden variables) which determine the outcome of quantum decoherence.

Dave_Oblad » April 28th, 2017, 8:13 pm wrote:I can easily see in a fully Deterministic Mathematical Existence, the possibility of Reflections, Echoes and Race conditions. This Fuzzy kind of Reality might work, if the Noise didn't overwhelm the emergent structures building within it. I might call such Fuzzy Determinism a possibility and still not relegate it to the Magic bin. Ultimately, it would still be utterly Deterministic, but the Fuzzy factors don't have to be resolved immediately. This view might seem to be more compatible with observations. I don't have a problem with such.

Computer simulations are like that. The results remain the same no matter how many times you run them and because of this, they are a book which is already written from the start. You may believe that we are no different than the characters in a fancy holographic computer novel which someone can run forward and backwards however they choose, BUT... I do not believe this. I do not believe the characters in such a novel ever have any subjective experience of consciousness, because they are inanimate objects. We are not, and I think it is the quantum indeterminacy by which a superposition of future possibilities decoheres into the actualities of our existence which makes the crucial difference.

mitchellmckain
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### Re: The Mathematical Universe

someguy1 » April 28th, 2017, 8:55 am wrote:
hyksos » April 27th, 2017, 11:35 am wrote:I present the following as strong evidence that the universe is a mathematical structure. (rather than say, a collection of physico-mechanical substances that happen to be describable by math after-the-fact).

Two arguments I just don't get.

One, that just because we have a mathematical formalism whose meaning we don't yet understand, the world must simply "be" that formalism. Isn't it possible instead that someday we'll understand what the formalism means? Just like relativity gave meaning to Newton's formalism of gravitational attraction.

Two, that just because matrices are handy gadgets for computing 3D rotations, matrices have some ontological reality in the world. Couldn't they just be handy gadgets for calculating, the same way the numbers on your grocery receipt aren't actually your vegetables?

The long answer: Nuclear quantization of angular momentum( "spin") is not the only example of this perplexing problem in physics. It is, in my opinion, the most violent and strong example of how the universe works in a way that is contrary to physico-mechanicalism. ("gears-turns-gears narratives").

Holomorphic functions map a complex number into a complex number. `F(z) --> z'.` Performed over the entire complex plane, holomorphic functions map the complex plane into the complex plane. All holomorphic functions will have a mirror image of their shape below the real axis. The reason for this is because complex vectors all have dopplgangers called complex conjugate vectors. Example. `v = 5+7i.` Conjugate vector `v* = 5-7i`

Obviously, any sane human being, regardless of this metaphysical prejudices would recognize that
• Humans invented math.
• Complex numbers are mathematical jargon
• Conjugate vectors are conventions of our 'invented' formalism, and should be discarded.

Paul Dirac was not a normal dude. He was very weird and highly eccentric (consult his biography). Even someone as eccentric as Dirac also understood the three points above. Dirac was willing and ready to toss out complex conjugate vectors, because, after all they "mathematical detritous" to be "discarded" because "Humans invent math". Clearly a complex conjugate vector surely does not correspond to something physical in the world -- that would be "silly".

RIGHT?

Wrong.

Dirac was Ph.d who had grad students working under him. One of his most adept students was named Robert Oppenheimer. (maybe you've heard his name somewhere). Anyways, long story short. Dirac had produced the solution to a relativistic wave corresponding to the electron. The solution admitted two answers: 1) The regular complex vector solution. and 2) the solution corresponding to the complex conjugate vector.

Dirac tossed out the second solution as 'non-physical'. (because ya know, math is "invented by humans" and all that jazz). Young Oppenheimer told Dirac that no --- we left Sane Regular World 20 years ago. That second solution is a real thing. It must represent an actual physical particle.

Indeed it does. It is the positron. Positrons are real physical objects. They are created in labs by the billions at CERN, SLAC, and other particle colliders.

Just as the mathematics predicts, a positron will be identical to an electron in all ways (spin number, mass, strength of charge) but its charge will be the reverse polarity. Whereas the electron is negatively charged, its doppleganger positron will have a positive charge.

When a positron collides with its partner electron, they "cancel out" and produce a single photon. Just like adding a complex conjugate vector cancels out the imaginary component. `v+v* = 5+7i+5-7i = 10`

Do you suppose that you could know what this means? Do you suppose that anyone on this forum knows what this "means"?

Initial opening salvos on the metaphysics front produce some bizarre explanations. The physical world appears to "know" about the existence of the square root of negative 1. And that's silly : Even Paul Dirac thought it was silly. It's absurd.

But it's true. Not only does the universe know about i, it seems to know that -i , when added will cancel out the original i and produce zero. Why should the matter and energy of this universe obey and follow the petty little conventions of "human-invented" chalkboard mathematics?

Indeed, angular momentum of nuclei, and the existence of positrons are not the only examples. The history of the development of the Standard Model is rife with such examples. Decade after decade, the nuclear physicists and mathematicians working on the Standard Model found themselves always having to shed all metaphysical prejudice and simply believe what the equations say.

Eugene Wigner was the winner of the Nobel Prize in physics in 1963. He was well-aware of this crazy procedure. "Shed all metaphysical prejudice. Believe the equations." Time and again, this is exactly how the universe operated. The crazy mantra was wildly successful as a science.

Wigner was scared to his bones by this. Wigner finally broke his silence about physics and wrote a paper where he told the world: "Okay mathematics should be useful for what we are doing, but it should not be this suspiciously effective at predicting how the world behaves.". He then called this effectiveness unreasonable. He also said that this unreasonable effectiveness quote,
"..borders on the mystical."

end-quote.

So you have Dirac discarding secondary solutions as un-physical, and Wigner saying that the universe following math is getting absurd, and bordering on the mystical.

Now we don't have any nobel prize winners on this forum. I ask you to open your ears and hearts to what actual Nobel-prize-winning physicists have said about this topic.

hyksos
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### Re: The Mathematical Universe

hyksos
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### Re: The Mathematical Universe

No I will not suppose any such thing. Math is deterministic. But I deny that mathematics is the summation of our existence. Mathematics is a useful tool and nothing more. It provides a very valuable way of looking at the universe, but it is not the universe -- no more than the universe is red just because it looks red when we look at it through rose colored glasses.

You can't just sit on this forum saying "no" all day. That's an internet troll tactic. You are better than that. (I trust that you are.) You should adopt an actual position that is something more substantial than "OP is wrong".

• Are you adopting the position that the universe is a physico-mechanical substance , which is only then described by mathematics after the fact?
• You seem so confident, that I would almost think that you know the origin of physical laws. Why does your substance-universe obey laws written as mathematical equations?
• Are physical laws physical?
• Vis-a-vis that question, why would a "substance" obey laws?
• What is the ontological status of quantum mechanical laws? Do they float outside the "substance"?
• Are you adopting the position that "laws" are subjective experiences of perceivers wishing up patterns?
• Do you assert that the universe is only pure randomness in some "objective" sense?
• Have you ever considered the possibility that the universe is not a mechanical "substance" at all to begin with?

hyksos
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### Re: The Mathematical Universe

[quote="hyksos]When a positron collides with its partner electron, they "cancel out" and produce a single photon.[/quote]

Hyksos, several days ago, I wanted to ask a question and decided not to do it. Now, I think you said it above. The question I wanted to ask is what happens to the energy that is created when a positron collides with an electron and they mutually annihilate each other? Is what I quoted from you above the answer? Light is energy. Yes?

Thank you.
vivian maxine
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### Re: The Mathematical Universe

hyksos » April 29th, 2017, 3:26 am wrote:When a positron collides with its partner electron, they "cancel out" and produce a single photon. Just like adding a complex conjugate vector cancels out the imaginary component. `v+v* = 5+7i+5-7i = 10`

Do you suppose that you could know what this means? Do you suppose that anyone on this forum knows what this "means"?

Are you joking? You're talking to someone who knows what complex conjugation is. If you want to make a religion out of it that's cool but I'm afraid I can't join your bandwagon. You reflect a plane vector in the x-axis. What of it? It's no surprise that math has a formalism to match a physical theory. Math has formalisms to match everything. It's like a toolbox that's got something to fix everything in your house. That doesn't mean your house is a toolbox.
someguy1
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### Re: The Mathematical Universe

Dirac tossed out the conjugate solution as "non-physical" for exactly the same metaphysical prejudices being voiced in this forum thread. This actually happened in history: And I have linked a modern derivation and it should be examined prior to you responding to my posts here: http://i.imgur.com/1pP9paA.png Dirac was wrong. Oppenheimer was right. Read your history.

someguy1 Did you have anything in response to the actual points I made about Dirac tossing out the "non-physical" conjugate solution ?

hyksos
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### Re: The Mathematical Universe

vivian maxine » April 29th, 2017, 4:08 pm wrote:[quote="hyksos]When a positron collides with its partner electron, they "cancel out" and produce a single photon.[/quote]

Hyksos, several days ago, I wanted to ask a question and decided not to do it. Now, I think you said it above. The question I wanted to ask is what happens to the energy that is created when a positron collides with an electron and they mutually annihilate each other? Is what I quoted from you above the answer? Light is energy. Yes?

Thank you.[/quote][/quote]

By "cancel out" I was talking about the fact that the photon has a neutral charge. The photon is the force-carrying particle of the electromagnetic field. There is an energy associated with it, that is tightly related to the photon's frequency. No energy is created in a positron/electron collision. The total energy of the particles is converted into the energy associated with the photon.

hyksos
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### Re: The Mathematical Universe

Thanks, hyksos. I'm confused but I think that, basically, the answer is yes - despite that I stated your purpose wrong. I still end up that the energy created by annihilation is/becomes the photon. Hope I have that right.
vivian maxine
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### Re: The Mathematical Universe

hyksos » April 29th, 2017, 4:56 am wrote:
No I will not suppose any such thing. Math is deterministic. But I deny that mathematics is the summation of our existence. Mathematics is a useful tool and nothing more. It provides a very valuable way of looking at the universe, but it is not the universe -- no more than the universe is red just because it looks red when we look at it through rose colored glasses.

You can't just sit on this forum saying "no" all day. That's an internet troll tactic. You are better than that. (I trust that you are.) You should adopt an actual position that is something more substantial than "OP is wrong".

• Are you adopting the position that the universe is a physico-mechanical substance , which is only then described by mathematics after the fact?
• You seem so confident, that I would almost think that you know the origin of physical laws. Why does your substance-universe obey laws written as mathematical equations?
• Are physical laws physical?
• Vis-a-vis that question, why would a "substance" obey laws?
• What is the ontological status of quantum mechanical laws? Do they float outside the "substance"?
• Are you adopting the position that "laws" are subjective experiences of perceivers wishing up patterns?
• Do you assert that the universe is only pure randomness in some "objective" sense?
• Have you ever considered the possibility that the universe is not a mechanical "substance" at all to begin with?

Would my answer of no to many of these questions make you throw a fit, as if I dared to know my own mind on the subject? Dictating how others should answer questions seems rather trollish to me. But I shall assume you are actually interested in my answers for now and dive into my mind on the subject of ontology.

It is my position that everything is made of a single substance (much like what we call energy) and the physical universe is a highly mathematical form of that substance but not perfectly so. Which is to say that mathematics is an excellent tool for describing the physical universe, but assuming it to be absolutely perfect is apparently foolish.

Physical laws are physical. Human laws are human. And blue skies are blue. Is any of this surprising?

What we call the "laws of nature" are a way of describing the geometrical space-time structure of the physical universe. Thus its substance "obey" these so called "laws" only because they accurately describe the thing which it composes.

Quantum physics is part of that description and the most accurate of such descriptions so far. All of these descriptions exist as far as we know for sure in the minds of human beings or encoded in various media of human communication. I am a nominalist in that way and opposed to Platonic idealism.

My position is that our primary access to reality is subjective and that the objective is thus a product of abstraction. But we have excellent evidence that there is an objective aspect to reality but not sufficient evidence to claim that reality is exclusively objective.

I do not assert that the universe pure randomness in any sense. The discovery of science is that there are both events which are dictated by initial condition and other events which are not dictated by initial conditions (also known as hidden variables).

I consider that the universe is made of a substance (like energy) which is capable of having a form and structure that is mathematical (i.e. mechanical) but that the physical universe is not an absolutely perfect mathematical and mechanical form of that substance in the sense that some events are not determined by initial conditions.

mitchellmckain
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### Re: The Mathematical Universe

hyksos » April 29th, 2017, 10:07 am wrote:
someguy1 Did you have anything in response to the actual points I made about Dirac tossing out the "non-physical" conjugate solution ?

Clever idea, although he thought the anti-electron was the proton, which could not be because the proton's mass is too big.

I just don't follow this historical fact to your metaphysical conclusion. After all, the existence of Pluto was predicted decades ahead of its discovery on the basis of the mathematics of its orbit. That doesn't prove that the universe is a floppy-eared dog.

hyksos » April 29th, 2017, 3:26 am wrote:Initial opening salvos on the metaphysics front produce some bizarre explanations. The physical world appears to "know" about the existence of the square root of negative 1. And that's silly : Even Paul Dirac thought it was silly. It's absurd.

But it's true. Not only does the universe know about i, it seems to know that -i , when added will cancel out the original i and produce zero. Why should the matter and energy of this universe obey and follow the petty little conventions of "human-invented" chalkboard mathematics?

Yet another misleading argument. Multiplication by i corresponds to a plane rotation through a quarter turn counterclockwise. It's about as mysterious as turning left at an intersection on the way to the grocery store. Two left turns leaves you facing the opposite direction as when you started. $i^2 = -1$. It's really that simple.

You can try this experiment at home. Stand facing east. Make a quarter turn to the left to face north. Another to face west, another to face south, and one more turn brings you to where you started, facing east. $i^4 = 1$. You just proved, in the comfort of your living room, that the mysterious number i is nothing more than a gadget for keeping track of quarter turns in the plane.

You are confusing the poor teaching of complex numbers in school with some metaphysical conclusion that simply doesn't follow.

Note also that the four directions east, north, west, and south, expressed as powers of i, are nothing more than a copy of the group of integers mod 4. A representation, if you will, in the sense of representation theory. Another mathematical tool beloved by physicists. You can represent the complex numbers as certain 2x2 matrices, and of course rotation matrices are also used by physicists.

Now, is it interesting and strange that our formal logical manipulation of symbols corresponds to physical reality? Yes, it's a puzzler. Does it prove that the universe "is" a matrix or some mathematical structure? No, it doesn't. The imagery is suggestive and metaphorical but nothing more, until a better argument or better evidence shows up.

And of course mathematicians understand rotation groups far better today than physicists did in the 1930's.
Last edited by someguy1 on April 29th, 2017, 4:17 pm, edited 4 times in total.
someguy1
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### Re: The Mathematical Universe

Hi mitchellmckain,

mitchellmckain wrote:Pi is a fixed, unchanging abstraction, and certainly not alive. Our existence is different in nearly every way -- dynamic, concrete, and alive. Furthermore, I do not buy into this idea that pi must be distinguished from things which are invented. Were airplanes really invented when the requirements of flight are found in the mathematical laws of nature? I dispute the idea that any of the thinking behind mathematics is any more inevitable than airplanes. Yes pi has a singular value, but living things are very very different. I deny that we (that living things) can be confined to any such singularity of existence because while our past is fixed our future is a superposition of possibilities.

Once again, I'm not talking about how something is computed. I'm specifically trying to describe what it means to EXIST!

Pi is mathematically computed.
The Universe is computed but within a Growing Cellular Logic Network.
Pi is <Not> Dynamic while a Logic Network <Is> Dynamic and is internally interactive.

Don't mix the two definitions of what it means to be COMPUTED.

This has lead my Thread astray for several pages now. A Logic Network can Compute.. but not like any Turing Machine or Instruction Based Procedure Driven Stepped Mechanical Device via Iterations.

In any case, it appears I have failed to communicate my concept of what it means to have a defined "Existence".

Simply restated:
Determinism = Existence. (has structure)
Randomness = Non-Existence. (has no structure)
I really can't express this any more simply.

Best Regards,
Dave :^)

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### Re: The Mathematical Universe

If someone claims to have falsified the Church-Turing thesis by finding a mode of computation that is not a Turing machine, an assertion contrary to the universal opinion of computer scientists, isn't the burden on that individual to supply evidence that they've made such a revolutionary breakthrough? Given the rules of a CA, you can simulate the same behavior with a TM.

Merely repeating the same false claim ad infinitum for six years constitutes neither evidence nor proof of falsifying the Church-Turing thesis. It's also strange that someone making such a radical claim wouldn't have taken the trouble even to read the relevant Wiki pages in all this time to understand the flaw in their own argument. You'd think someone claiming to overthrow 80 years of theory would take the trouble to learn the basics.
someguy1
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### Re: The Mathematical Universe

Hi Someguy1,

Not a debate about how a Turing Machine operates. Not a debate about Numbers.

How many Numbers fly through your Brain when you have to catch a ball thrown near you?

Your Brain is a Logic Network. Your Brain Computes but doesn't use Numbers. There is no Turing Machine between your ears.

I will grant a Turing Machine can process Logic. But each Cell in a Logic Network would have to be its own separate, but interconnected, Turing Machine. Thus.. your Brain may be described as Trillions of interconnected Turing Machines operating on input(s) = output(s) Logic with massively inter-connected neighboring Cells.

Regards,
Dave :^)
Last edited by Dave_Oblad on April 29th, 2017, 5:36 pm, edited 1 time in total.

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### Re: The Mathematical Universe

For someone who said they're no longer addressing me, you sure respond to me a lot. No point in responding to you until you retract your earlier statement that you're not interacting with me. Not to mention the multiple gratuitous insults in violation of forum policy, sadly unaddressed by the forum moderators. Your manners and integrity are as atrocious as your logic.

As usual, you reply to a substantive argument by ignoring it and waving your hands. For someone who claims to be a computer scientist, you clearly haven't taken the trouble in six years to acquaint yourself with even the bare basics of the subject.
someguy1
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### Re: The Mathematical Universe

Hi Someguy1,

http://sciencechatforum.com/viewtopic.php?f=51&t=30776&start=90#p318436

Someguy1 wrote:I will also say that the type of person I am, if I explain the mathematical definition of decimal representations, and they conclude that I do not understand iteration, they may be met with MOCKERY, DERISION, SARCASM, and OBLOQUY. Fair warning given.

I will no longer pay attention to you if you persist in personal attacks against my character rather than my ideas. For seven years I've been on this site and never attacked another posters character until I met you. I called you a Troll.. because of your "MOCKERY, DERISION, SARCASM, and OBLOQUY" tactics.

This site is not the proper place for such behavior. I'll happily respond to your comments.. if you can conform to Forum Guidelines.

Best Regards,
Dave :^)

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### Re: The Mathematical Universe

Everyone here can see when a poster consistently fails to respond to substantive criticism of his arguments, as you have been doing since 2010. You are an obnoxious moron. You started the insults and I don't plan to passively accept them. If you don't want to be insulted, don't address me. You promised you'd stop addressing me. Now be a man of your word and stfu.

And really, just some supportive advice. Take five minutes and read up on the basics of CS so you can stop embarrassing yourself. It's awful to see someone repeatedly claim to be a computer scientist who hasn't even read the basic Wiki pages on the subject, let alone actually studied the theory of computation.
Last edited by someguy1 on April 29th, 2017, 6:26 pm, edited 1 time in total.
someguy1
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### Re: The Mathematical Universe

Hi Someguy1,

Someguy1 wrote:Everyone here can see when a poster consistently fails to respond to substantive criticism of his arguments, as you have been doing since 2010. You are an obnoxious moron. You started the insults and I don't plan to passively accept them. If you don't want to be insulted, don't address me. You promised you'd shut up, now why don't you?

Really?

Best wishes,
Dave :^)

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