Dear Dr. Rickles,

Congratulations on an excellent essay. I am still reading it carefully, but I disagree with the main idea that it is not possible to be nothing. An empty set is a trivial counter example. You may argue that the notion of a set presupposes some mathematical construct and therefore this is not a truly “nothing”, but this is only a semantic argument. If nothingness is...

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Dear Dr. Rickles,

Congratulations on an excellent essay. I am still reading it carefully, but I disagree with the main idea that it is not possible to be nothing. An empty set is a trivial counter example. You may argue that the notion of a set presupposes some mathematical construct and therefore this is not a truly “nothing”, but this is only a semantic argument. If nothingness is impossible/inconsistent, then we should not be able to represented it and use in any proof, (and in particular in proving that there should be something rather than nothing).

But the question remains: why there is something rather than nothing? My take on this is that your 2 ways of answering it (existence is necessary, or bootstrap) are both wrong. The simple answer is that we have something rather than nothing because “something” can be. (You may argue that I am only shifting the discussion towards introducing a first cause, but I am not, and I will address this at the end).

So what is existence? What are its core critical requirements? Those are 3:

1. “universal” logical consistency: meaning the truth value of existence should be universal and not confined to the boundary of an axiomatic system.

2. interaction. Without interaction we are confined to the frozen Platonic word of math

3. infinite complexity. This is necessary to escape a brain in a vat argument.

If you now look carefully at the 3 requirements, we observe that they specify precisely how our physical world is different than the Platonic world of math. But here comes the truly remarkable part: one can extract mathematical consequences from them and prove very important uniqueness results about our universe. (see my essay entry: Heuristic rule for constructing physics axiomatization)

Now it seems that there are 4 classes of “existence”: A. complete nothingness, B. the frozen Platonic world of math, C. an universe nursery satisfying only requirements 2 and 3 and D. our universe satisfying requirements 1,2, and 3. Time does not exists in cases A, B, and C, and while in the D case we have standard quantum mechanics, in case C we have split-complex (or hyperbolic) quantum mechanics. (I ran out or room to describe the cosmological ideas in my essay, but there is no first cause because there is no time in hyperbolic quantum mechanics which violates requirement (1) because it violates the von Neumann’s uniqueness theorem regarding different representations) I strongly believe we can mathematically prove that our universe is unique: it should have 3 spatial and one time dimension, it should have quantum mechanics, the 4 forces, the elementary particles we observe and their properties, etc. But a new question arises: why is our universe happening only once? This is at odds with a Copernican principle which states that we are in no way special. Here the class ( C ) of existence can potentially come to the rescue IF this speculation will turn out to be true and we will be able to work out the math into proving it.

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Thanks for one of the few essays that actually address the ultimate in physics or the ultimate role of it anyways. “Why anything?” seems to be most profound. If physics were to answer this, it will certainly be something ultimate, although you have not much expounded on the role of physics (rather than math) in answering it. Anyways, your discussion of why this is a pseudo-question stops at...

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Thanks for one of the few essays that actually address the ultimate in physics or the ultimate role of it anyways. “Why anything?” seems to be most profound. If physics were to answer this, it will certainly be something ultimate, although you have not much expounded on the role of physics (rather than math) in answering it. Anyways, your discussion of why this is a pseudo-question stops at the surface. Since your essay evidences a serious author behind it, I encourage you to go further, say towards the Robert Nozick or Wittgenstein level and understand so called “category mistakes” [G. Ryle: The Concept of Mind. (1949)]. It is “pseudo” because it only looks like a well formed question. You either split into modalities (possible, existent, necessary) or not. If not, you cannot ask about any of them. If you do, you cannot afterwards mix them up haphazardly like “Either existence is contingent or it is necessary” [page 6]. It is muddleheaded use of terminology.

A few miscellaneous remarks since I am at it (please take my blunt criticisms as a compliment: I will not comment if I do not consider an essay quite reasonable):

1) “Reality is mathematical (as evidenced by the effectiveness of mathematics in the sciences). Therefore, there is existence.” [page 6]

The “effectiveness” is simply due to the co-evolution of our thinking along with our problems; basically, we keep the useful and toss the useless, the most abstract and thus widely applicable we then call “math”. It is also mere PR (Look how effective our stuff is). One could just as well point out how ineffective math is. A completely arbitrary attribution does not evidence anything. The “there is existence”, i.e. existence exists constitutes again a category mistake.

2) “We do not have the same kind of problem with the existence of mathematics. Mathematical statements are necessarily true in the sense that if they are true in one world (in the sense of modal logic) then they are true in all worlds” [page 9]. The axiom of choice does not have to be true in all worlds, except in case the statement is to be understood as an empty tautology (all is everything and includes all cases where it is either true or not but not both at once …). The bare validity of math would be just the same even if no worlds were possible and nobody existed to appreciate it. Everything else is a redefinition of “existence” into something it is not meant to distinguish.

3) The “theory has overtaken experiment in very recent years” [page 2] is over appreciating what happens to be in vogue. Apart from that much of the “overtaking” is speeding in useless directions, it is also not a phenomenon of “very recent years”. Just a few examples: Riemann geometry (turned out useful), GRT of black holes (maybe no experiment possible that probes inside the horizon), quaternions/octonions (counter example to your general position, beautiful math probably never finding any widely accepted use in physics).

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Sascha. These are excellent comments. Thanks.

I'm sure you appreciate that it's very hard to do more than scratch the surface of this question in 10 pages and was intent on keeping it as close to math/physics as possible. There was an awful lot I wanted to put it, and I'm not happy with the actual argument itself. Also, however, this essay was for fun rather than part of my serious...

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Sascha. These are excellent comments. Thanks.

I'm sure you appreciate that it's very hard to do more than scratch the surface of this question in 10 pages and was intent on keeping it as close to math/physics as possible. There was an awful lot I wanted to put it, and I'm not happy with the actual argument itself. Also, however, this essay was for fun rather than part of my serious research: I am only a hyper-Pythagorean in my spare time!

On to your comments:

You are perfectly correct that it is mathematics doing the work here rather than physics, but that is why I included the merger between physics and mathematics. Physics would then amount to the probing of those parts of the mathematical universe that interest us humans.

On the category mistake issue. My original conclusion had Wittgenstein's stuff about letting the fly out of the bottle, essentially by dissolving the "big questions" into such simple category errors. I disagree with such objections. I didn't split into possible, necessary, existent. Existence was descried as something that can be possible or necessary. When I say existence is necessary I always mean *some kind of existing 'thing'*. We are rather constrained by language here. Of course Wittgenstein and the ordinary language brigade focused squarely on how concepts are used in practice. I thought we'd gotten beyond that straightjacketed form of philosophizing?

By the way, Nozick does not fall into this category. He expresses genuine perplexity over the problem, noting that it is compounded by the fact that anything we might use as explanatory ammunition is part of what needs to be explained, so we end up with circularity (this is the incompleteness problem I mentioned in my essay). I have a copy of his Philosophical Explanations, and what he says is:

"The question appears impossible to answer. Any factor introduced to explain why there is something will itself be part of the something to be explained, so it (or anything utilizing it) could not explain all of the something - it could not explain why there is *anything* at all." [Phil. Exp. p. 115]

Nozick views the problem as forming the absolute limit of our understanding. The point beyond which we cannot go. Incidentally, my title is based on a section title from his book! I also like his claim that: "The question cuts so deep...that any approach that stands a chance of yielding an answer will look extremely weird". That is, of course, a necessary rather than sufficient condition.

(1) On the effectiveness of math issue. It's true that there is selection bias going on here: we ignore the unsuccessful. But the successful still needs explaining. How is it that the mathematical representations we construct enable us to make often surprising successful predictions? It doesn't matter that sometimes we get unsuccessful predictions. Of course we do. Consider the prediction of the white spot in the center of the shadow cast by an opaque disc onto which light is shone, predicted by Poisson (on the basis of Fresnel's theory). The unsuccessful cases do not mitigate against cases such as this. There is a sense here in which our mathematical representation and parts of reality are isomorphic. One easy (but hard to stomach, no doubt) way is to assume that reality is itself mathematical.

The "there is existence" was supposed to be elliptical for there is the existence of *something*, but something sounded to hard and concrete. The section this comes from was certainly the worst bit. But I'd run out of space by this point and didn't really have time to revise - have a conference talk to write as well!

(2) You say: "The bare validity of math would be just the same even if no worlds were possible and nobody existed to appreciate it." That is the root of my point.

(3) When I say theory has overtaken experiment, I am referring (as you can probably tell) to quantum gravity and 'beyond the standard model'. When I say very recent, I mean within the last 100 years (I'm a historian of physics: this is recent for historians)! Riemannian geometry was not devised as a physical theory (though Riemann was aware of physical aspects). True, it was then applied in GR (which was not ahead of experiment, but based on anomalous extant data: Mercury perihelion). This seems like a case in my favour. Not sure what the black hole case is supposed to be proving here. But again, you admit that there are physical/experimental limits imposed by the scales of the new physics. That is precisely my point. If you still want to continue doing physics in the same way, then the recourse to more mathematical explorations seems inevitable.

On the quaternions/octonions as a counterexample to applicability. Certainly not true. Both find plenty of applications in physics (whether they are 'widely applicable' or not seems to be irrelevant). Two nice books are:

http://www.amazon.com/Division-Algebras-Quaternions-Math
ematics-Applications/dp/0792328906/ref=sr_1_1?ie=UTF8&s=book
s&qid=1253180087&sr=8-1

and

http://www.amazon.com/Introduction-Octonion-Non-Associative-
Algebras-Mathematical/dp/0521017920/ref=sr_1_3?ie=UTF8&s=boo
ks&qid=1253180087&sr=8-3

Also, my point was meant to be more general: even if there happen now to be structures that happen not to be applied to physics; it is hard to believe that one could not find some representational link between them and some aspect of the world - but this is, of course, impossible to prove: it's a plausibility argument.

Thank you again. These were thoughtful, intelligent questions.

Cheers,

Dean

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"The question appears impossible to answer. Any factor introduced to explain why there is something will itself be part of the something to be explained, so it (or anything utilizing it) could not explain all of the something - it could not explain why there is *anything* at all." [Phil. Exp. p. 115]

Very interesting arguments about this issue here!

The problem is indeed...

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"The question appears impossible to answer. Any factor introduced to explain why there is something will itself be part of the something to be explained, so it (or anything utilizing it) could not explain all of the something - it could not explain why there is *anything* at all." [Phil. Exp. p. 115]

Very interesting arguments about this issue here!

The problem is indeed circularity/tautology.

If one assumes that we have something rather than nothing because “something” can be, one simply states that "something rather than nothing is possible because it is possible".

If one assumes that something rather than nothing is necessary, one simply states that "something rather than nothing is necessary because it is necessary" (without answering *why* it is necessary).

That something rather than nothing is possible, is evident.

That something rather than nothing is necessary, is only "evident" if one assumes that boolean logics is the one-and-only everlasting truth, eternal and the source of all relations that can be built.

If one assumes that the question about something rather than nothing has no rational answer via logics (human intelligence/mind), the necessity-argument vanishes, but the possibility-argument survives.

If one assumes via logics that logics is limited in the sense that mutually exclusive polarities aren't really mutually exclusive at a deeper level, then both arguments could count, necessity as well as possibility. The melting of these polarities could be done by realizing via logics that each side of the polarities *defines* its counterpart in an entanglement-like fashion. This seems to be logic for me. Now one can conclude out of this line of reasoning that there must be a deeper level that isn't concerned with definitions, its realm is an *undefined* area on which one can project definitions. For me, it seems that such an area could best fit with - vaguely spoken - an area of imagination-like abilities including intentions and emotions. But even this argument has its circularity-problem, because it presupposes the one thing it wants to explain, namely existence of consciousness (to be able to evidently state at all that there is rather something than nothing and "something" is at least possible).

With observers which would live forever and some properties of "observing something" would be an in-built-feature of all particles/matter/fields, the whole problem wouldn't be existent. There would be only transformations from possibilities to actualities (and maybe backwards). There would be only creativity by transforming a problem into its solution. If in this case the problem of "something rather than nothing" doesn't really exist, therefore another "thing" must exist "a priori", namely consciousness and its transformatory power. But this could only be possible if consciousness itself would be self-evident to itself and would realize that itself has created the polarities of something and nothing. So consciousness at its core level must be something that goes deeply beyond "something" and "nothing". It would deal *mainly* with values, not with quantitative proportions like maths.

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Hi Dean-

You are stating the interesting issue of existence and suggest that there are two ways to go about answering the questions that you bring up:

But now what if we are puzzled about existence itself? Why is there anything at all? This is really the ultimate question: why is there something when, presumably, there might not have been? There are two ways to go about answering...

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Hi Dean-

You are stating the interesting issue of existence and suggest that there are two ways to go about answering the questions that you bring up:

But now what if we are puzzled about existence itself? Why is there anything at all? This is really the ultimate question: why is there something when, presumably, there might not have been? There are two ways to go about answering this kind of question:

1. Show that existence is in fact necessary, so that there couldn't possibly have been nothing-in other words, we deny that there might have been nothing, so that the presumption above is seen to be mistaken.

2. We somehow give a 'bootstrap' explanation showing how consistency alone brings reality into being, perhaps via some kind of (non-vicious) explanatory loop.

The questions are answered in the context of Quantum Field Mechanics (QFM), which is described in my essay "Ultimate Possibilities of Physics". QFM originates from A.P. Kirilyuk. I have extended QFM in some areas and provided it with tutorial style explanations on my website.

The issue of existence issues boils down to the existence of two pre-space pre-time physically motivated fields (aka protofields) and their mutual attraction. This configuration is mathematically described as a state equation, also called existence equation.

Refering to your item 1: Existence is a necessary (unavoidable) consequence of the mutually attractive protofield interaction.

Refering to your item 2: Bootstrapping occurs, again, a consequence of attractive protofield interaction, which causes uncessing pulsations, rotation, and random motion of the interacting protofields.

In the essay, protofield attraction is postulated, but its physical need is motivated as follows. Without interaction, any perturbation in a protofield will 'spread out' and thus be unstable. Protofield attraction could potentially ensure that protofield perturbations are 'self-stabilizing'. As shown by the mathematical analysis of the state equation (existence equation), under the assumption of protofield attraction, protofield stabilized pulsating entities can indeed occur and be identified with particles.

Sincerely,

Ben Baten

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Your essay contains important questions but I don't see the responses and real results. What are the limits of physics 'explanatory power? Can physics explain existence itself? These questions do not have responses in your essay. 'Reality is mathematical. Therefore, there is existence.'

It explains nothing. If reality is mathematical then please transform a formula into a material body. Or...

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Your essay contains important questions but I don't see the responses and real results. What are the limits of physics 'explanatory power? Can physics explain existence itself? These questions do not have responses in your essay. 'Reality is mathematical. Therefore, there is existence.'

It explains nothing. If reality is mathematical then please transform a formula into a material body. Or try to transform a body into a formula. Therefore your approach to EXISTENCE is erroneous. You cannot explain the EXISTENCE using simple logical discussions like 'the only way one can explain existence is to demonstrate that non-existence is a logical impossibility'. The answer for EXISTENCE lies in a deep physics. 'Why is there being?' The answer for this fundamental question lies in the region of nature of space-time: all bodies EXIST IN SPACE. All bodies EXIST IN TIME. To find a sense of EXISTENCE you must explain why a body occupies space and why a body exists in time. The discussions about 'Reality is mathematical' do nothing here.

'why does something exist (rather than nothing)? Please see in my essay the explanation of nothing.

http://www.fqxi.org/data/essay-contest-files/Leshan_Leshan.p
df

It is a hole in space-time without extension and duration properties. It is the primal void, it is the fundament of universe and 'being'. Thus a hole in space-time is an example of the non-existence. To explain the existence, please explain first the non-existence (a hole in space-time). After that you can explain why a body have extension and duration properties and it will be the explanation of existence (why is there being?). You cannot explain EXISTENCE without explanation of extension and duration properties. The explanation of EXISTENCE means explanations of extension and duration: why a body exists in space and time?

All discussions about EXISTENCE using mathematical reasons are senseless. Bodies exist in space and time but not in imaginary mathematics.

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Dean wrote:

'Formulae are 'representations' of mathematical structures, not the structures themselves'

What is the difference? Can you transform a mathematical structure into a material object? Please understand - really exists only physical (material) structures only. The Earth is a physical object, not mathematical. The mathematical model of Earth exists in heads (imagination) of...

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Dean wrote:

'Formulae are 'representations' of mathematical structures, not the structures themselves'

What is the difference? Can you transform a mathematical structure into a material object? Please understand - really exists only physical (material) structures only. The Earth is a physical object, not mathematical. The mathematical model of Earth exists in heads (imagination) of mathematicians only. Can you show me the (material) mathematical abstraction that really exist?

'But spacetime is not nothing'

You are right. Space-time is a physical (real) object. To create NOTHING we must destroy (remove) space-time from the chamber. Since the space-time disappears, the walls of chamber must come into a proximity (because extension disappears). Also time dilation effect must appear because time disappears. This NOTHING exists a very short time only because it is filled quickly by environment. (Please read my essay for more information).

'To say nothing is a 'hole' in space-time as you do depends on there being some boundary'

Yes, a hole in space-time has a boundary, it is the wall of the chamber. You cannot create a hole without a boundary. But we speak about a hole inside of chamber, it is a true nothingness, it is an absolute void without extension and duration properties. The absolute void collapses quickly into a dimensionless point.

Let us explain the EXISTENCE now. The existence is the property of body to have EXTENSION and DURATION properties. Without extension and duration a body cannot exist.

Do you see the difference between existence and non-existence? All objects must have extension and duration properties in order to exist. The absolute vacuum is nothingness which does not possess the extension and duration properties. There is no EXISTENCE inside of a hole in space-time. Thus we defined non-existence. Then let's define existence.

Bodies exist really in space-time because they have extension and duration properties. Why they have extension and duration? The modern physics do not know the answer.

If you'll write another essay about existence then try to use extension and duration instead of mathematical reality.

Constantin

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Dear Dean,

I have finally had the time to read carefully your essay in its entirety.

Let me start by saying that I do agree 100% with your conclusion, and my own essay shows how you unify math and physics. What I do disagree however, are your arguments for this conclusion.

The arguments are a bit convoluted in taking the pro and against positions and I need to sketch them to...

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Dear Dean,

I have finally had the time to read carefully your essay in its entirety.

Let me start by saying that I do agree 100% with your conclusion, and my own essay shows how you unify math and physics. What I do disagree however, are your arguments for this conclusion.

The arguments are a bit convoluted in taking the pro and against positions and I need to sketch them to frame the arguments:

you present [MN] vs. [C] and present [S] as an argument for [MN] and against [C]. Then you present some weaknesses of [S] and this should weaken [MN]. Your ultimate position is completely against [MN] and you take this as proof of existence.

Finally you say:

“Either existence is contingent or it is necessary. If it is contingent

then there is no complete coherent account of existence. If it is necessary then we need a necessary structure to ground this fact. Mathematical tructures are of this kind. If reality is mathematical then it must exist. Reality is mathematical (as evidenced by the effectiveness of mathematics in the sciences). Therefore, there is existence.”

So here are my comments regarding this discussion.

MN and S are all wrong to some degree.

Instead of MN, we should have MD (metaphysical democracy) where existence and non-existence can coexist peacefully. The world of math is not only timeless, it is also made of incompatible axiomatic systems coexisting side by side and if math and reality are unified, then existence and non-existence should be able to coexist as well in the same fashion. [S] is a rather naïve mechanicist argument at odds with quantum field theory. I do not know enough of [C] to comment on it.

Now your statement: “If it is contingent then there is no complete coherent account of existence.” is reminiscent of Einstein’s position in his debate with Bohr, and from this perspective, it is wrong especially after Aspect’s experiments proved Born right and not Einstein.

“If it is necessary then we need a necessary structure to ground this fact.” Yes

“Mathematical structures are of this kind.” Yes.

“If reality is mathematical then it must exist.” No, only that it can exist.

“Reality is mathematical (as evidenced by the effectiveness of mathematics in the sciences).” Yes (see also my essay on how to reality is unified with mathematics)

“Therefore, there is existence.” No, because existence is contingent.

Your obvious counter argument will be that you are talking about existence in general, and not only our universe in particular. To that I say that existence is only defined in time; time is one of its core requirements. To argue about existence from a timeless point of view outside our universe is impossible because the very notion of existence is not defined there; it is like talking about notions of distance and neighborhood in formal logic. By Goedel, there is not comprehensive axiomatization of mathematics, and your discourse domain about existence in general is ill defined precisely because of that. Suppose for the sake of argument, that Goedel’s incompleteness theorem is false, and there is such a thing as mathematical axiomatization. Then your analysis will be valid. This is a different argument that what you argue in your discussion of Goedel.

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Dear Mr. Rickles,

I have read your essay. For me it is an absolutely exemplary case for why metaphysics found little applause among scientists. But that does not mean, that I believe such investigations to be meaningless. On the contrary: They are enormously important, because only they can heal the break between philosophy and physics.

In the past metaphysical propositions were not...

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Dear Mr. Rickles,

I have read your essay. For me it is an absolutely exemplary case for why metaphysics found little applause among scientists. But that does not mean, that I believe such investigations to be meaningless. On the contrary: They are enormously important, because only they can heal the break between philosophy and physics.

In the past metaphysical propositions were not wrongly suspected of being meaningless, because often it was not clear what they actually meant.

I think the question why is there something rather than nothing belongs to this category. Usually something and nothing are regarded as opposites. But I doubt whether this is indeed the case.

If the word something is used the simple fact is evocated that there is a world which can be perceived by us. In other words: Something relates to the fact that there are visible things. Visibility here is not meant in a purely visual sense, but in a more general sense as something which can be perceived at all. This includes the usage of all kinds of technical tools, like a telescope.

If we look deeper we can find that distingushibality is the most elementary precondition of perception. A thing can only be seen if there is any difference towards other things. If there would be no difference, such a thing would be, in principle, invisible.

If we follow this way of reasoning then the opposite of SOMETHING would be something, which is by its very nature invisible and indistinguishable.

Or in brief:

Something .. Visibility .. Distinguishability

Something .. Invisibility (Non-Visibility) .. Indistingishability

This philosophical setting was never investigated in detail, because not only nothingness was an unclear physical concept invisibility was an physical unclear concept as well. But we can precise the concept of invisibility. We can give it a well-defined physical meaning. In my paper Taming of the One I have tried to explain invisibility as the natural result of a certain kind of radical non-dual conception of the Universe.

If this explanation would really hold, then Leibniz question appears as a classical case, which the philosopher Ludwig Wittgenstein would have called as the bewitchment of our intelligence by means of language.

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Though I agree that ‘physics and mathematics have a common basis’, there is a fundamental difference. If in a self-creating universe the sum of everything inside, including spacetime itself somehow must stay zero (conservation law), then the physicist cannot treat physical quantities and phenomena like a mathematician does his numbers and symbols. Where his numbers and symbols exist only in...

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Though I agree that ‘physics and mathematics have a common basis’, there is a fundamental difference. If in a self-creating universe the sum of everything inside, including spacetime itself somehow must stay zero (conservation law), then the physicist cannot treat physical quantities and phenomena like a mathematician does his numbers and symbols. Where his numbers and symbols exist only in the mind of the mathematician, the physicist is part of the sum he studies, so he is not allowed, for example, to imagine how the universe looks from the outside as any physical observation requires a at least a specification of his position with respect to what he observes, his distance and the conditions at the place he looks from, which by definition is impossible outside the universe. If he nevertheless imagines to see galaxies of about the same age (since he believes their particles to be created at the same time) receding from each other faster than light, then this is only possible by seeing their spacedistance, but ignoring their corresponding timedistance: by thinking like a mathematician.

‘… The mathematical universe is safe from Godel’s theorem …’

I’m afraid this is not the case. If to explain some phenomenon or prove some theorem we start our reasoning from assumptions and axioms which contain preconceptions, if the truth of our allegations depends on the truth of unprovable assumptions and axioms, then we can never prove them in an absolute sense, however valid they may be within the set of axioms and rules of reasoning they are formulated. The problem is that though our assumptions and axioms may seem self-evident, they aren’t necessarily true as they only reflect our view of our world and express a logic which may differ from nature’s logic. Richard Powers (in The Gold Bug Variations) ‘Why is the last line of a proof surprising, if its truth is already hiding tautologically in the lines above?’ suggests as much: that we put as much information in our choice and formulation of axioms and rules of reasoning as we can get out of them. If the proof of a theorem to some extent also involves the proof of the implicit assumptions which are built into our axioms and rules of reasoning, then the formulation of a theorem can be thought of as an effort to formulate this implicit information explicitly, its proof being incorporated in the theorem as it is formulated. If in that case we don’t so much prove something but rather adapt our thinking to the way our observation evolves, then the impossibility to (dis)prove statements which can be made within a consistent set of rules and axioms (Gödel) might originate in the incompleteness or indefiniteness of our definitions and axioms, in the lack of information or restrictions we’ve put into our rules, axioms and assumptions, so statements can inherently be too ambiguous to prove or disprove. The problem is that much of the information we put in them appears too obvious for us to consider as being information, as if it reflects a truth that needs no inspection: as it is almost impossible to be aware of this implicit information, we indeed are surprised at the last line of the proof, as if we got some information for free that we didn’t put in ourselves in the first place. As our reasoning and the tools we think with are rather the product, the expression of our relation to our world than something which is open to inspection (by itself), it is difficult to detect the implicit information present in our assumptions, in the preconceptions they may contain. This might mean that if we could explicitely formulate all implicit information in a set of axioms and rules so there would be no ambiguity, nor in the theorems we can formulate within that set, Gödel’s theorem would no longer apply, any statement or theorem being a tautology. If we have more confidence in a theory as it is more consistent and it is more consistent as it relates more phenomena, makes more facts explain each other and needs less additional axioms, less more or less arbitrary assumptions, then any good theory has a tautological character though a tautological theory of course isn’t necessarily true nor useful.

In an uncaused, causeless universe which creates itself (see Mechanics of a Self-Creating Universe), where things and events create each other, they explain each other in a circular way, are each other’s ‘cause’. Though a circular reasoning at first sight may seem ridiculous, here we can take any statement, any link of the chain of reasoning without proof, use it to explain the next link and so on, to follow the circle back to the statement we started with, which this time is explained, proved by the foregoing reasoning. Though in a self-creating, noncausal universe a proof seems to be less convincing than a proof which follows a causal reasoning, a causal assertion or explanation ultimately is invalidated as the primordeal cause it is built upon by definition cannot be understood nor proved. The point is that if our logic originates in nature’s logic and not the other way around, that our logic is but a reflection of our relation to our world and not a reflection of some absolute, platonic kind of truth which precedes, exists outside that world, an objective reality as there’s no such thing, mathematics and its development follow physics, and not the other way around, so we cannot blindly rely on its conclusions that explain the why and how of our universe, its laws. Though dreaming up mathematics without bothering too much about the nature of the quantities its equations refer to sometimes can help decide whether ideas in physics make sense, mathematics itself cannot dream up really new physical approaches or ideas. An excessive emphasis on mathematics tends to create its own reality and confuse our view on physical issues. Though many models in physics may mathematically be consistent, I’m still waiting for the one model which obviously, compellingly and necessarily excludes any other model and explains why the universe needs the particular particles we find, why the ratio between their masses is as it is etcetera.

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