## A mathematical proof of the existence of the universe (version 2)

• 455
I propose a mathematical construction able to prove the existence of the physical universe indubitably, thereby resolving the primary problem of metaphysics.

To achieve the goal, I adapt and modernize the 'cogito, ergo sum' of Descartes, as only completely satisfactory proof of existence in the corpus of philosophy, for the purpose of proving the existence of the universe. Specifically, I transpose the context of the ”I think” as well as that of the ”I am”, to a new context conductive to the goal whilst retaining the desideratum of indubitable existence. As can be anticipated, the ”I am” is transposed to the ”body of reality” in the form of the physical universe, and the ”I think” will be transposed to a generic indubitable representation of reality in terms of what I introduce as the countable set of universal facts. Finally, a necessary implication between facts and body will be identified which transmit the indubitability of the first to the second.

The paper executes the above-stated strategy in a completely rigorous manner, and yields as the culmination of the process, a near-theory of everything in physics able to explain why the universe exists. Finally, I show that the recovered theory exceeds the explanatory power of current physical theory, by a significant margin.

I am seeking feedback.
• 2.6k
What is D[f] in 2.1? Feynman's path integral has this issue if the measure used is not discussed.

Good luck getting this crowd to read this long, compact print paper. :cool:
• 4.4k

Can you explain briefly in this thread why you think the world exists?

You might want to give your paper to some philosophy professors instead of posting it here. Most of us read the shorter threads and discuss ideas with no more than a few paragraphs
• 12.2k
Is the "experiment" Turing computable and even halting?
• 19.2k
I wonder, who doubts the existence of the universe?
• 2.6k
I wonder, who doubts the existence of the universe?

Someone who is convinced they are a Boltzmann brain.

The Boltzmann brain argument suggests that it is more likely for a single brain to spontaneously and briefly form in a void (complete with a false memory of having existed in our universe) than it is for the universe to have come about in the way modern science thinks it actually did.

https://en.wikipedia.org/wiki/Boltzmann_brain

What's fascinating about this argument is that if you think the universe arose spontaneously by chance, it is far FAR more likely that only a single Boltzmann brain did.
• 19.2k
...and in what did said brain appear?

...if not in the universe?
• 2.6k
...and in what did said brain appear?

I take your point that the atoms had to be there already, so I suppose it depends on whether universe means an ordered universe or if you count a big formless collection. I'll retreat to saying that one who believes they are a Boltzmann brain denies the existence of a universe outside themselves other than a formless collection of atoms. But ok.
• 19.2k

Well, no; the point is more abstract than that. The universe is all that exists. Hence, if there is a Boltzmann Brain (or anything else, for that matter), then the universe exists.

Taking this back to the OP, if an attempted proof that the universe exists, exists... then the universe exists.

So @Alexandre Harvey-Tremblay is on a winner, since even if he is wrong, he is right.
• 4.4k
Anaxarchus, a philosopher who traveled with Alexander the great, has many sayings attributed to him. He may have been the first in the West to deny that anything existed, although they also say he told Alexander that there were infinite worlds, to which Alexander responded with tears because he hadn't even conquered one of them
• 2.6k
Still wondering about the details of D[f] in section 2.1
• 455
@jgill I suppose that is a fair question. The physics really starts at section 2.2. Section 2.1 is more of a mock-up of a theory. In section 2.1 D[f] is just a product of integrals between minus infinity to infinity over a continuous range x, where we assume can be parametrized over x. Similar definition as can be found here https://en.wikipedia.org/wiki/Functional_integration , except it contains the exponential term which make it in fact the same as this definition https://en.wikipedia.org/wiki/Partition_function_(mathematics) (fourth equation down in the definition section).

Please note that my functional integral does not sum over the complexes, but instead over the reals, and thus does not necessarily have the problems of the path integral of quantum mechanics in regards to it being an acceptable measure. My functional integral is the product of statistical physics, not quantum mechanics.

To construct an exact formulation of D[f], I would start with a specific sub-theory (for instance from section 2.2) then utilize the result of geometric interference (equation 46) but instead of as a mere two-state system I would sum over an infinite quantity of such state, capturing all possible linear and reversible transformation and yielding a functional integral. This, along with the partition function baring the exponent and the determinant would coalesce to a formulation of D[f] for this sub-theory.
• 2.6k
I am familiar with summing over a space of functions, and in order to do so you need a measure that assigns numbers to certain subsets of that space. And the integrand is a functional that assigns a number to a function. But there are other "kinds" of functional integrals. Thanks for your reply.
• 455
I wonder, who doubts the existence of the universe?

Any rational person ought to doubt of everything he or she cannot prove.
• 8.4k
Any rational person ought to doubt of everything he or she cannot prove.
Don't you mean prove to their own satisfaction?

I am not planning on reading your OP. If the math is any good I won't understand it entirely. If it isn't either I won't know it or I'll be annoyed at the waste of my time.

But here's a question I think fair even if I don't read your OP - and if the answer is in it, then you can just point me back to it. How does mathematics prove anything about anything that is not mathematics? Key word being prove.
• 455
But here's a question I think fair even if I don't read your OP - and if the answer is in it, then you can just point me back to it. How does mathematics prove anything about anything that is not mathematics? Key word being prove.

You are basically asking me to copy-paste the paper as an answer. But, here is the gist:

• Define universal facts.
• Show that universal facts are true for all possible world.
• Show that universal facts are computationally universal.
• Define reality as a subset of universal facts.
• Define a transformation of reality as bijection of the powerset of universal facts onto itself.
• Show that the maximally informative (e.g. entropy maximization of a probability measure) interpretation of a transformation of reality, is bounded to a mathematical structure isomorphic to the universe.

How does mathematics prove anything about anything that is not mathematics? Key word being prove.

Easy; The existence of such a proof precludes the possibility that the universe is not.
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Maybe you don't doubt hard enough, considering you think doubt is good. I don't see how your bulletpoints prove the world if I persist in doubting it's existence. But then again, Descartes found a way to believe in the world which is highly controversial, so whatever works for you. (In fact, he doubted mathematics a priori)
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(In fact, he doubted mathematics a priori)

By definition, universal facts are the set of mathematical statements that the Cartesian universal doubt method fails to rule out. I'm still in business my friend.
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Any rational person ought to doubt everything he or she cannot prove.

The only thing you can prove is that man's intelligence is incapable of accessing Reality in any substantial way.
• 455
The only thing you can prove is that man's intelligence is incapable of accessing Reality in any substantial way.

I fact, I have shown that man's intelligence is incapable of [departing] reality (necessary coupling to the universe). The exact opposite of what you claim.
• 935
I fact, I have shown that man's intelligence is incapable of [departing] reality (necessary coupling to the universe). The exact opposite of what you claim.

Is it possible for you to encapsulate your mathematical proof into an verbal abstract (for those who have been out of school for several decades)?
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Your thesis seems very impressive. I've just never been a math guy
• 8.4k
Thank you for your reply. If only everyone undertook to reply in the same spirit. My attack shall be on the basis of your "gist."

Define universal facts.
1. Show that universal facts are true for all possible world.
2. Show that universal facts are computationally universal.
3. Define reality as a subset of universal facts.
4. Define a transformation of reality as bijection of the powerset of universal facts onto itself.
5. Show that the maximally informative (e.g. entropy maximization of a probability measure) interpretation of a transformation of reality, is bounded to a mathematical structure isomorphic to the universe.

How does mathematics prove anything about anything that is not mathematics? Key word being prove.
— tim wood

6. Easy; The existence of such a proof precludes the possibility that the universe is not.

I leave the math to you. But for its utility in 6), one might say that for all and any X, if X exists then the universe (i.e., that which contains X) exists - exactly as @Banno noted above.

1) A fact is a proposition, as such never in itself true. Or, to say that a fact is true is a syntactical statement which in itself says nothing about the world. Of course this is not ordinary usage, but then the context is not ordinary.

2) in light of 1) this is either trivial or nonsensical.

3) "Define"? With this you can have what you want. This guts your proof.

4) Again "define"?

5) "Bounded" or "bound"? And I think if you unwind this into plain English you'll see some of the problems - which of course your definitions obscure. Let's try this: An interpretation of an image of X is bounded by a description of that which contains X. Or, an interpretation is bounded by a description. A proposition that is at least debatable.
• 455
I'll start with a response to your point 1 and wait for your response), otherwise if I reply to all points each time, the replies will be just too long. Once we agree on 1), we can move to the next points.

I leave the math to you. But for its utility in 6), one might say that for all and any X, if X exists then the universe (i.e., that which contains X) exists

That may be, but said universe follows the laws of physics only if you do it my way.

1) A fact is a proposition, as such never in itself true. Or, to say that a fact is true is a syntactical statement which in itself says nothing about the world. Of course this is not ordinary usage, but then the context is not ordinary.

fact
/fakt/
noun
noun: fact; plural noun: facts
a thing that is known or proved to be true.
"he ignores some historical and economic facts"

Quoted from my paper (introduction).

If we use the tools of algorithmic information theory, we can write definitions that have no exploits whatsoever: A universal Turing machine which takes a Turing machine $TM$ and a sentence $p$ as inputs, will halt iff $p$ halts on $TM$. Thus the fact that $p$ halts on $TM$ is indeed a fact because it is verifiable on all universal Turing machine. Note the improvement provided by algorithmic information theory in terms of elegance, clarity, loop-hole elimination and language-dependance elimination (no need for any specific symbols such as $\vdash,\implies, etc$... just a sentence $p$ that may in principle use any symbol). The possible facts of reality are then simply the set of all pairs $(TM,p)$ which halts on all universal Turing machines... yielding a completely indubitable definition of reality consistent with the original intent of the philosophical definition of reality in terms of facts, but now formally defined.

Formal definition of an experiment

Let $(\operatorname{TM},p)$ be a pair comprising two sentences of a language $\mathbb{L}$. The first sentence, $\operatorname{TM}$, is called the protocol. The second sentence, $p$, is called the hypothesis. Let $\operatorname{UTM}$ be a universal Turing machine. If $\operatorname{UTM}(\operatorname{TM},p)$ halts then the pair $(\operatorname{TM},p)$ is a (successful) experiment. In this case, we say that the protocol verifies the hypothesis.

An experiment, so defined, is formally reproducible. I can transmit, via fax or other telecommunication medium, the pair $(\operatorname{TM},p)$ to another experimentalist, and I would know with absolute certainty that he or she has everything required to reproduce the experiment to perfection. Indeed, for the protocol $\operatorname{TM}$ to be a Turing machine, the protocol must specify all steps of the experiment including the complete inner workings of any instrumentation used for the experiment. The protocol must be described as an effective method equivalent to an abstract computer program. Should the protocol fail to verify the hypothesis, the entire experiment (that is the group comprising the hypothesis, the protocol and including its complete description of all instrumentation) is rejected.

Then an equivalence between experiment and universal fact:

The set of all experiments are the programs that halt. The set includes all provable mathematical statements and it is universal in the computer theoretic sense. The set of all experiments is the same as the set of all universal facts, and thus, necessarily, can be used to constitute a complete description of reality for the same reasons as those described in the first perspective.

Universal fact are known to be true only by experimentation (they must be run an a universal Turing machine to see if they ever halt) and thus constitute a purely mathematical experimental system... that references *nothing physical*. Can you intuit how this construction can be *useful* to one who might want to prove the universe from first principle?
• 19.2k
Any rational person ought to doubt of everything he or she cannot prove.

I doubt that.
• 2.6k
(9) in section 2.1 is a most peculiar quaisi-mathematical object. I assume you mean to write
$Z=\int{{{e}^{-\beta H(f)}}}D[f]$, and the H is the Hamiltonian operator. But the D[f] remains vague. This makes me question if you understand the math you are using. Also, at the beginning of the section you seem to designate both entropy and action as capital s: S. Although if one looks very closely it appears you use two different fonts. I'm an old math guy, but I don't understand what all the physics math really says. fishfry or fdrake or someone else here might be able to sort this stuff out. If they think its worth the effort. The whole thing seems really strange. :roll:
• 8.4k
That may be, but said universe follows the laws of physics only if you do it my way.
a thing that is known or proved to be true.

You're not paying attention to the language. And while that is not a problem when it does not matter, it is when it does. The universe, nor anything in the universe, follows any laws at all. Laws are after the fact descriptive stories told from a particular viewpoint. And to call or define a fact as any kind of thing is an invitation to the kind of trouble you're caught in.

And, true? We all have good working understandings of "true" based in their respective contexts. But you will be hard pressed to define "true" with particularity and context free. The best I have found is that true just is what is true in some given context - the difficulty being that that quality does not hold over differeing contexts.

The possible facts of reality are then simply the set of all pairs $(TM,p)$ which halts on all universal Turing machines... yielding a completely indubitable definition of reality consistent with the original intent of the philosophical definition of reality in terms of facts, but now formally defined.

It seems to me that reality must in all cases exceed and exhaust all possible representations it. So much for that.
• 19.2k
I think, although this is a fine web site, we can be pretty confident that any novel thinking that will fundamentally change the way we see the universe will not be published to Philosophy Forums first.
• 443
Agree. Although it is a source of amusement when these folks come out here and have "solved" problems that some of the smartest people who ever lived cannot figure out.

And just occasionally I learn something new.
• 455
You have at least 10 people in here arguing against my paper each admitting not to have read the paper.

Who here as read the paper?
• 455

What do you say we cut straight to the meat.

Instead of arguing against each other's metaphors, can you have a look at definition 1 to 7 of my paper and tell me what you think is wrong with them.

This is the axiomatic foundation of my theory.
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