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Cristinel Stoica: on 10/6/12 at 16:10pm UTC, wrote Hi Frederico, Please check this link and find how five essays, including...

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December 13, 2019

CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: The Final Theory and the Language of Physics by Frederico Pfrimer [refresh]

Author Frederico Pfrimer wrote on Sep. 5, 2012 @ 11:32 GMT
Essay Abstract

Which of our basic physical assumptions are wrong? The precise meaning of this question, and so its answer, depends on several other questions creating a dependency chain: Which are our basic physical assumptions? What is a wrong physical assumption? What is a physical assumption? What is each of our physical theories? What is a physical theory? None of these questions has a precise answer, the reason is that, the concept of physical theory, and our main physical theories, are like open concepts: you cannot give them a precise definition. Our theories are still open theories. Most, if not all, of our fundamental concepts are open and imprecise concepts. We discuss how these and other aspects of language impose limits on science, and how can physics overcome it. But foundational physics has been guided by the wrong principles. The interpretation of a physical theory should provide the precise and clear language to talk about the theory, not a philosophical discussion relying over imprecise concepts. Foundational physical theories should provide a precise meaning to our fundamental concepts and the worldview that makes our theories understandable. We argue that these questions have a precise answer only for closed theories, and then we discuss on the nature of, and how these questions can be answered for a closed theory. We clarify the notion of a final theory of physics, the fundamental closed theory that serves as the foundation for all physics. We show how to use this notion to clarify and also distinguish the concepts of postulate and physical assumption. We claim that the main wrong assumption of physics is actually a logical assumption: the principle of excluded middle.

Author Bio

I received my B.S. in Physics from UFG, a Brazilian university, in 2010. Now I’m a M.Sc. student working on a new axiomatic formulation of the formalism of quantum mechanics and the FTP. My interests have always been about foundations, and I just proposed a new interpretation and formulation for the foundations of quantum theory.

Anton Lorenz Vrba wrote on Sep. 5, 2012 @ 22:13 GMT
Hi Frederico,

Thank you for your contribution, your essay is a timely reminder of what a physics theory is.

What I am missing in your essay is a discussion on "are our fundamental theories cast in stone?". The reason for saying this is, should a fundamental assumption be wrong then everything that follows is wrong too. A scenario not particularly appealing, resulting in the over protection of the fundamental assumptions.

This cast in stone philosophy I challenge in my essay by showing that a model (or theory) of an alternate reality is possible.

Regards

Anton @ (  ../topic/1458  )

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Author Frederico Pfrimer replied on Sep. 6, 2012 @ 16:59 GMT
Dear Anton,

Thanks for your comments. I believe when we have a consistent physical theory, and so a consistent mathematical formalism, a wrong assumption does not destroy all the results and application of the theory. Actually, when you find that an assumption you were using is wrong, the only thing that changes is the domain of validity of you theory. All the results are still valid, but with a smaller domain.

This is precisely what happened with classical mechanics when relativity appeared. Classical mechanics is still valid, and the proof is that engineering works! All our buildings are based in this theory, and we can’t say that it is completely wrong, but only that it is not valid when objects are moving close to the speed of light.

In a sense, I think our fundamental theories are somehow permanent, well the most established ones. But only in a sense. The interpretation we give to our theories will change in the future, and the way they are formulated, but their essence will remain the same.

The reason of that is the core of my essay. Closed theories are precisely the ones that are a permanent achievement. They cannot be modified. Any modification will probably give rise to a whole new theory. However, I argue that our theories are not yet closed theories. That’s the point. Once they get to a point where there formulation is just like the formulation of what is ring in mathematics, then they are permanent and cast in stone.

The examples of mathematics are perfect. If you change a single axiom from the definition o a ring, then it is not a ring anymore and deserves a new name. The same holds for closed theories

Best Regards,

Frederico

Anonymous wrote on Sep. 5, 2012 @ 23:36 GMT
Dear Frederico

Very nice to see a fellow brazilian in the FQXI contest (I´m from Fortaleza). Your essay is impressive, clearly written and I think it touches on points frequently overlooked by physicists.

You have emphasized the relation between physics and language which is often tacitly understood . This is something I see with interest as well. There a paragraphs that are true...

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Author Frederico Pfrimer replied on Sep. 6, 2012 @ 18:00 GMT
Dear Daniel,

I thought I was the only Brazilian here; it is good to know I’m not alone! I wish you “boa sorte”! And thanks for your comments. We have very similar ideas, and your comments really got into the point.

Natural language is our first tool, and it is necessary in every beginning of a whole new theory. First you have to do something handmade, just then you can build a...

view entire post

Pentcho Valev wrote on Sep. 6, 2012 @ 20:25 GMT
Frederico asked: "What is a wrong physical assumption?"

Here is one:

http://www.fourmilab.ch/etexts/einstein/specrel/www/

"...
light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."

REDUCTIO AD ABSURDUM: If the speed of light is independent of the state of motion of the emitting body,...

view entire post

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Frederico Pfrimer replied on Sep. 13, 2012 @ 18:54 GMT
Well, this is really a great paradox. I was not aware of this, and so is great to know another idea that blows our mind. However, I'm not an specialist on relativity so I cannot really discuss this paradox.

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Helmut Hansen wrote on Sep. 14, 2012 @ 10:40 GMT
Dear Frederico,

I read your paper with great interest. I think you are right with respect to your final conclusion, that the principle of excluded middle is - in a way - the main wrong assumption of physics.

I am working on a Modern Metaphysics - in the belief, that it is the key to a final theory, because it is based on a truly foundational ground like the ONE.

In introducing the ONE as a physical entity I have defined it explicitly of being INVISIBLE (= NON-VISIBILITY), whereas the UNIVERSE is explicitly defined of being VISIBLE.

I found, that in a reality, that follows this dual conception, the ONE represents with respect to the UNIVERSE logically the Excluded Middle. But this logical status of the ONE does not disturb the universe in any way because the ONE being INVISIBLE is physically excluded from the VISIBLE universe!

The ontological meaning of this self-referential conception of reality is actually astonishing: By the physical exclusion of the logical Principle of the Excluded Middle as it is represented by the ONE, the visible universe can make an unrestricted use of ALL possibilities that logic allows. It can indeed go to the outmost limits of logic - to a point, where a violation of logic cannot be avoided any longer, because its boundary conditions (at infinity) are becoming contradictory.

I was quite surprised when I read Wittgenstein's tractus logico-philosophicus, in which he also described contradiction as the outer limit of propositions (5.143)

In a previous contest I've sketched this Modern Metaphysics.

see:The Taming of the ONE

http://www.fqxi.org/community/forum/topic/502

Kind Regards

Helmut

P.S. I've seen you are also inspired by the work of C.F.v.Weizsäcker. His works were (and still are) a great source of inspiration for me.

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Author Frederico Pfrimer replied on Sep. 14, 2012 @ 15:36 GMT
Dear Helmut

Thanks for your reply. We might not agree in every aspects, but our deep motivations and inspirations are the same. Weizsäcker is someone who deeply inspired me, and there are times I feel like I was trying to continue his work. Wittgenstein also inspires me, I’ve read his Tracttatu several times, and the sentence you cite made me think for a while.

I’ve also been...

view entire post

Helmut Hansen wrote on Sep. 17, 2012 @ 06:01 GMT
Dear Frederico,

I agree mathematics is necessary to give a physical concept a precise meaning, but I am not sure whether it is an ultimate guide to a fundamental theory of reality, because mathematics itself is intrinsically limited. It has its own blind spots.

Gödel's incompleteness theorem is certainly the most important one. It has shown that mathematics cannot be both consistent and complete. There are always some basic propositions that may be true but that are intrinsically not provable.

You do not relate to this inner limitations of mathematics neither in your current paper nor in your paper "The Nature of Reality".

Referring to this incompleteness theorem the physicist Roger Penrose has claimed, that there could be certain aspects of reality (i.e. consciousness) for which no mathematical resp. computational algorithm can be created.

I am convinced that a modern metaphycis can meet this mathematical incompleteness by being a self-referential system of thought.

Kind Regards

Helmut

P.S. I like to point to my current paper: Is the Speed of Light of Dual Nature? which might be an important piece of a complete quantummechanical description of reality you are looking for.

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Author Frederico Pfrimer replied on Sep. 18, 2012 @ 02:32 GMT
Dear Helmut,

I also wouldn’t say that math is the ultimate guide for a fundamental theory of reality, but only that it is the language we should use. And I do agree that math has its own blind spots and most of them are precisely on the foundations of mathematics. A also believe math must be improved for being used in such a fundamental theory.

About Gödel's incompleteness theorem, I think the point is about completeness. I do not want to make a theory that is complete in this sense, but consistent, useful and insightful. And this theorem may also affect any other formal language, every language has some limitations.

A theory is complete when every formula in its language either is provable or its negation is provable. In other words “if it is consistent, and none of its proper extensions is consistent.” But, a fundamental theory of reality must have proper extensions because every theory that describes an aspect of reality is an extension of it.

Self-referential system can be very powerful, but they are also very dangerous. Well, you may find a consistent one, but most of the paradoxes of logic and mathematics were found in self-referential systems. So we need extra care when dealing with these systems. But I believe Gödel's incompleteness theorem represents no danger for metaphysics because of what I mentioned before. I think you don’t need to worry about this theorem. Make your theory and if someone says it is impossible then simply show you have already done it!

P.S. I’m taking a look on your paper. I’ll rate it as an author; please rate mine.

Helmut Hansen wrote on Sep. 18, 2012 @ 08:50 GMT
Dear Frederico,

I am not quite sure whether we agree with respect to the role that mathematics is playing in physics.

To discuss the case of metaphysics: In my view of a modern metaphysics all formulas without any exception have to fail, otherwise the metaphysical concept of TRANSCENDENCE does not have any physical meaning. This demand implies that we have to extend our theories to infinite values, f.e. to an infinite velocity, but just these values are usually regarded as a sign that the underlying concept is physically meaningless.

What do you think about this? Are there infinite values involved in a truly fundamental theory of the universe?

Kind Regards

Helmut

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Author Frederico Pfrimer replied on Sep. 19, 2012 @ 19:53 GMT
Dear Helmut

My point is that math is a precise language, and any theory, when it gets enough precise and clear, it can be formulated in a mathematical language. Therefore, even a metaphysical theory can at some moment be, in principle, formulated in mathematical language. Can you already talk about transcendence using math? That’s the question. However, not everything that can be described by a mathematical equation is a physical observable. In the theory I propose in “On the Nature of Reality”, everything is described mathematically but there are many elements that are not physical observables. But can you explain what you think of transcendence?

Well, I see no problem of infinities on physics. The problem is only with math which cannot hand infinities very well. Once our math could handle them properly and elegantly they will begin to appear on our physical theories.

Best Regards

Frederico

Hoang cao Hai wrote on Sep. 19, 2012 @ 14:02 GMT
Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regard !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Author Frederico Pfrimer wrote on Sep. 19, 2012 @ 20:20 GMT
Dear Hải.Caohoàng,

Thanks for your encouraging comments. Definitely, to find a clearly defined basis for foundations physics is the greatest of all intellectual challenges; and we should work together to accomplish it.

However I have to admit that I don’t have much knowledge about the standard model and Higg’s bosons. I have yet no opinion about these things and so I cannot answer your questions. I hope we could find something else to discuss. I’m reading and I will rate you essay as an author. Please rate mine.

I believe no theory is simply correct or incorrect. Its correctness depends on where it is being applied, that is, if its assumptions holds in a specific domain, then the theory is correct on that domain, if the assumptions does not holds on that domain, then it is incorrect in that domain.

Best Regards!

Frederico

Hoang cao Hai replied on Sep. 27, 2012 @ 03:46 GMT

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Helmut Hansen wrote on Sep. 20, 2012 @ 09:12 GMT
Dear Frederico,

transcendence is, of course, an epistemological term indicating that the most fundamental branch of reality (i.e. the ONE) cannot be described and observed in any way. Transcendence is the common feature of all religious systems.

But to fill this purely epistemological term with a physical resp. metaphysical content you have to choose an ontological one. The most...

view entire post

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Member George F. R. Ellis wrote on Sep. 24, 2012 @ 19:21 GMT
Dear Frederico

your essay and associated paper are thought provoking and deep. It will take time to assimilate it. My main comment for the present refers to this statement of yours:

"I have means to say that the main wrong assumption of physics is not

a physical assumption, but a millenary logical assumption: the principle of excluded middle .. This principle says that a proposition is either true or false, in other words, either the proposition or its negation is true" I think that you might be saying that the truth or falsity of a proposition may depend on its context. That is very close to the concept of contextual effects that I discuss in my essay.

George Ellis

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Author Frederico Pfrimer replied on Sep. 27, 2012 @ 05:23 GMT
Dear George,

Thanks for your comments and sorry for the late reply. Actually, what I mean by the violation of the principle of excluded middle can be understood when we think of a system in a superposed state. For example, when a cat is not in a superposed state, we can say that it is dead when the state is
$|D\rangle$
or it is alive when the state is
$|A\rangle$
. But then, when it is in a superposition
$|D\rangle + |A\rangle$
, it is not dead but it is also not alive! It is in a superposition of dead and alive! But according to that principle, if it is not dead, then it is alive. Therefore, superposition means precisely violation of the principle of excluded middle! In the classical world there is no superposition, therefore the principle holds in a particular case. I hope it could make the idea clearer.

Best Regards,

Frederico

Hoang cao Hai wrote on Sep. 27, 2012 @ 03:58 GMT
Dear Frederico Pfrimer

Suggest you look at and comment on my introduction for the "absolute theory" (topic 1417- out side of my essay)

Regards.

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Author Frederico Pfrimer replied on Sep. 28, 2012 @ 02:51 GMT
Dear Hoang Cao Hai,

Best Regards

Frederico

Hoang cao Hai replied on Sep. 28, 2012 @ 14:56 GMT
Dear Frederico Pfrimer

Always be "10" for allies.

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Stefan Weckbach wrote on Sep. 27, 2012 @ 19:02 GMT
Dear Frederico,

i read your essay and you did a good job in examining the suspicious premises that are widly held high. Especially what you write about Commensurability is of interest for me, but i have to think about it some more time and also read your arxiv-paper. Nonetheless you struck me with your statement

"There, reality becomes a closed and completely precise notion. Therefore, I have means to say that the main wrong assumption of physics is not a physical assumption, but a millenary logical assumption: the principle of excluded middle. It is the source of most of the paradoxes and misunderstandings about quantum theory and is precisely the assumption that gives rise to the classical world."

For this statement alone you deserved - in my humble opinion - a positive score, nonetheless that my own usage of some exceptions to the principle of the excluded middle are more than epistemological in nature. My own interpretation is that there are ontological states that aren't anymore driven by this principle and i tried to explain this in my own essay. Especially i explain why the "collapse of the wave function" occurs, namely because at the point this does "happen", the causal structure of the system has consistently changed and the mathematical description of the former - unmeasured dynamics - isn't valid anymore. Indeed - as i believe - the schroedinger equation is just an illusion that mimics causality. It is no more than a mathematical tool, misinterpreted as an ontological dynamic process! I call that whole process of quantum mechanical mimics "physical retrodiction". If you like, i would be happy you could have the time to visit my essay and leave a comment.

Its very easy to read, informative as well as entertaining (i guess) and you don't have to dive into some complex mathematics.

Best wishes,

Stefan

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Author Frederico Pfrimer wrote on Sep. 27, 2012 @ 21:59 GMT
Dear Stefan,

Thanks for your encouraging comments. My arXic paper might be very interesting because it shows how the ideas proposed in the essay can be implemented. Well the principle of excluded middle is a hidden assumption that is part of the language we use. It is almost impossible to understand how it can be violated using only ordinary language, specially English. Try to say something...

view entire post

Stefan Weckbach replied on Sep. 28, 2012 @ 03:44 GMT
Dear Frederico,

thanks for replying to my comment.

I read George Ellis' comment and yours and i agree with both comments.

George states that classical information depends on the context. He uses the term "proposition" to indicate the premises we have built in to come to a certain conclusion about truth/false values. From the reference frame of a classical observer the opposite...

view entire post

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Stefan Weckbach replied on Sep. 28, 2012 @ 14:01 GMT
Minor corrections to my latest post:

"by assuming an extended pure state for every mixed state by assuming the mixed state"

"by assuming an extended pure state for every mixed state"

i wrote

"Extrapolating the Schroedingers' wave function to be universally valid only leads to many-worlds; they may be complete in a certain sense and...

view entire post

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Stefan Weckbach replied on Sep. 28, 2012 @ 19:08 GMT
Dear Frederico,

i now read your arXiv-paper. Although i must confess that i did not check every part of your statements to be reasonable or not, my main interest was to look at what you have to say in your plain text.

You wrote

"The importance of the distinction between pure and mixed states, and the fact that only pure states can be associated with a vector (ket) is...

view entire post

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Thomas Howard Ray wrote on Sep. 28, 2012 @ 11:45 GMT
Frederico,

I think it's a rather bold conjecture that "The quest for giving a precise meaning to our fundamental concepts cannot be accomplished using natural language" ... without giving an example of a mathematical statement that cannot in principle be translated to natural language.

So I'm in the uncomfortable position of agreeing with your conclusions while disagreeing with the...

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Author Frederico Pfrimer wrote on Sep. 28, 2012 @ 19:12 GMT
Dear Thomas

Thanks for your comments. Well, the problem is that we need to translate math to natural language and natural language to math, we need both, and what I call an interpretation is what allows it. Try to read the equation F=ma. In the context of classical mechanics you would say the total force equals to the product of the mass and the acceleration. But out of context, or better,...

view entire post

Author Frederico Pfrimer replied on Sep. 28, 2012 @ 20:42 GMT
Dear Thomas,

Just to make sure, I understood that your view on a complete theory is not the one that can leat to a contradiction with Godel's theorem. I just wanted to say that other people may understand it the wrong way and criticize because of the incompletness theorem.

Thomas Howard Ray replied on Sep. 29, 2012 @ 14:13 GMT
Hi Frederico,

You write, "Try to read the equation F=ma. In the context of classical mechanics you would say the total force equals to the product of the mass and the acceleration. But out of context, or better, without any interpretation, you cannot say it."

If you mean only that I have to expand the shorthand symbols to natural language, such that I should write, "Force equals mass...

view entire post

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James Putnam replied on Sep. 29, 2012 @ 15:18 GMT
Hi Tom,

You wrote:

"Hi Frederico,

You write, "Try to read the equation F=ma. In the context of classical mechanics you would say the total force equals to the product of the mass and the acceleration. But out of context, or better, without any interpretation, you cannot say it."

If you mean only that I have to expand the shorthand symbols to natural language, such that...

view entire post

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Yuri Danoyan wrote on Sep. 29, 2012 @ 00:54 GMT
Frederico Pfrimer wrote:

"I have means to say that the main wrong assumption of physics is not

a physical assumption, but a millenary logical assumption: the principle of excluded middle1."

"There are trivial truths and the great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true."

u2LwwTk8pFUyOzeb.99

Few peoples understand it unfortunately.

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Author Frederico Pfrimer replied on Sep. 30, 2012 @ 17:56 GMT
Dear Yuri,

Great point. It fits perfectly at this situation. Also it shows something very deep: it is very simple to know what the opposite of a trivial truth represents, but to know what the opposite of a great truth represents is a great challenge. In this case, for example, we could say that quantum logic is non-classical or maybe non-boolean, but then what it really means? To answer it we must perfectly understand how is the logic of the quantum world…

Best Regards,

Frederico

Yuri Danoyan replied on Sep. 30, 2012 @ 18:45 GMT
I do not understand why my cоmmunity rating becomes lower....

Yuri

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Amanda Gefter wrote on Sep. 29, 2012 @ 08:29 GMT
Hi Frederico,

I enjoyed reading your interesting essay. I agree that the non-Boolean logic inherent to quantum mechanics is precisely what gives rise to all the weirdness that conflicts with our classical intuitions. Personally, however, I'm not sure it's enough to say that quantum logic is non-Boolean and leave it at that - that's merely a description, not an explanation. I think it remains important to ask, in Wheeler's famous phrase, why the quantum? Why non-Boolean logic?

I take a speculative stab at that question in my essay, suggesting that non-Boolean quantum logic expresses a radical frame-dependence in the nature of reality, one most strongly argued for by holography and Lenny Susskind's notion of "horizon complementarity".

Great work.

Regards,

Amanda

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Author Frederico Pfrimer replied on Sep. 30, 2012 @ 17:47 GMT
Dear Amanda,

Thanks for reading and commenting on my essay. I also think to say that the logic is non-Boolean is not enough. I have an arXiv paper, “On the Nature of Reality” where I develop a new interpretation and formulation of QT. Most of it is related to the logic of quantum world. There I think it is clear why the logic is non-Boolean and how it actually is. There, I extend QT for having a logic about truth, knowledge, necessity and possibility, what is much more that pure propositional logic. This is how quantum logic becomes no classical: it becomes a kind of modal logic where truth is a modality, that is, a proposition can be true, false, known to be true, known to be false, necessarily true, necessarily false, possibly true… I suggest you reading it but outside the scope of this contest. I’ll read your essay and rate it without judging from my own viewpoints. Please rate mine too!

Well, I try to answer why the quantum and why non Boolean logic from the following approach: it is the simplest closed theory possible for describing reality. In my paper what I develop is a closed theory in the sense of this essay, and you will see how simple all the axioms and the definitions are. It is almost impossible to make them simpler.

Best Regards,

Frederico

Author Frederico Pfrimer wrote on Sep. 29, 2012 @ 18:38 GMT

While I’m trying to answer your posts, a propose a challenge: try to read unambiguously the following equation:

$\frac{5\big((a^2+3 b + 5)^{12} + 1\big) + x}{3+a}$

This exercise shows some limitations of natural language. It is very hard if not impossible to read this equation unambiguously.

However, the real focus is not translating mathematical language to natural language, but the opposite, translating natural language to math. This can only be done when you have a theory and an interpretation. For example, everybody can talk about money and finances in natural language, but you can only say the same thing in mathematical language when there is a theory that allows you modeling the situation. This the great challenge of all sciences. At the time of Aristotle they could talk about the movement of particles, interactions and other physical notions, but they couldn’t say the same things in math; classical mechanics was what allowed us to do so.

The great challenges are for example what it means mathematically to say that QM is realist? What are the equations that must be satisfied for this to happen? What it means mathematically to say that QM violates classical logic? What it means mathematically to say that QM is complete or incomplete?

One we can find a consensual answer to all these question, the philosophical problems vanish. Then all you have to do is to prove that QM satisfies or not an equation. The philosophical problem is finding the equation, the rest is simply theorem proving.

Best Regards

Frederico

Thomas Howard Ray replied on Sep. 30, 2012 @ 11:13 GMT
Hi Frederico,

Okay, I understand better what you're saying now. Really, though, what does "ambiguous" mean in terms of mathematics? After all, by the fundamental theorem of algebra, a polynomial equation has as many solutions as the equation has degrees. Does that mean the solutions are ambiguous? -- to say so would imply that there is one "real," or true, solution to the equation, yet such is not the case. All solutions are true for the given degree.

Your approach may shed light on something very important, however, about the form of mathematics we use to model physical reality. If the fundamentally algebraic rules of quantum mechanics leave us with the questions you ask: -- ... what it means mathematically to say that QM is realist? ... equations that must be satisfied for this to happen? ... QM violates classical logic? ... QM is complete or incomplete? -- then just maybe algebra (i.e., the mathematics of discrete functions) can't tell us what lies at the foundation of reality.

Problem is, that our thinking equipment *is* designed for discrete decisions, not continuous functions. How the quantum-mechanical brain connects with the stately motion of the cosmos will be as science-changing a model as Newton's explanation of why the moon falls toward the Earth without hitting it.

You might be interested in this powerpoint I did for ICCS 2007 that takes advantage of Gregory Chaitin's research into the uncertainty of arithmetic that we talked about earlier.

Best,

Tom

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Author Frederico Pfrimer replied on Sep. 30, 2012 @ 16:20 GMT
Hi Tom,

It is is very hard to find ambiguities in mathematics because good mathematics is always unambiguous. But I found some examples in Ambiguities in Mathematics. A simple example extracted from there:

“Certain functions, particularly trigonometric functions like sin and cos, are often written without parentheses: “sin x” instead of “sin(x)”. So what does the expression “sin ab” mean? It can mean either “sin(ab)” or “(sin a)b”. Generally, it’ll mean the former. However, it can sometimes mean the latter! For example, I’m looking at some lecture notes right now which uses implicit differentiation to find the derivative of arcsine: you let y=arcsin x, which means that sin y=x, then you differentiate both sides and get: “cos y dy/dx = 1″. In this context, “cos y dy/dx” means “(cos y)dy/dx”!”

Well, the solutions of a polynomial are not ambiguous, they are a set of number. For example, a more rigorous way of expressing the solutions of x^2-3 is

$\{x \in \mathbb{R}:\; x^2-3 = 0 \} = \{\sqrt{3}, - \sqrt{3} \}$
.

Now you can see that there is no ambiguity.

Well, but that’s it. In the end we depend heavily on mathematics. I’m not sure that the mathematics of today is already capable of providing us with all the tools. The problems are foundations of math itself are not really established. Math is the best language we have, but we are always limited by our language. Math allow us advancing further than natural language, but it still have limitations.

About the continuous, a large part of quantum theory (i.e. information and computation theory) is done with discrete quantities. I think we should first solve the foundational problems for the discrete, then we extend it to the continuous. But I agree with what you said, but we must find ways to overcome it.

Best regards

Frederico

P.S.: I’m taking a look on your presentation.

Thomas Howard Ray replied on Oct. 1, 2012 @ 10:21 GMT
Hi Frederico,

I make a distinction between abuse of notation and ambiguous results. Bad notation, as your examples show, can lead to misinterpretation. The same is true of bad grammar in natural language, as well as ambiguities of syntax and semantics and other linguistic failings (such as Chomsky's well known example, "Colorless green ideas sleep furiously").

Unlike natural language, though, mathematics gets its meaning from logical judgments which are never purposely ambiguous -- if they are, one charges the result with an error. Internal consistency of the language is independent of the correspondent meaning.

"Time flies like an arrow; fruit flies like a banana" shows the dependence of natural language on context, where concrete terms (flies) and abstract terms (time) relate in entirely different ways to an object corresponding to the meaning.

Mathematical symbols are limited in the same way. The Greek letter pi can stand for the transcendental number that describes the relation between the radius and circumference of a circle; pi can also represent a discrete prime integer. Results from use of these terms, however, cannot be confused by one who speaks the language -- just as in the natural language above.

You write, " ... a large part of quantum theory (i.e. information and computation theory) is done with discrete quantities."

Actually, all of it is done with discrete quantities. That's where "quantum" gets its meaning.

"I think we should first solve the foundational problems for the discrete, then we extend it to the continuous. But I agree with what you said, but we must find ways to overcome it."

We have, actually. Topological quantum field theory -- among other topological methods -- incorporates the global meaning of quantum events. We can't get a non-arbitrary continuum from discrete quantities; we can, however, derive discrete events from the continuum.

All best,

Tom

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Member Benjamin F. Dribus wrote on Sep. 30, 2012 @ 00:27 GMT
Dear Frederico,

I greatly admire your essay. You ambitiously tackle issues that some of history’s greatest scientists, from Liebniz to the founders of quantum theory, have wrestled with. Your general approach is relevant to the whole practice of science. For mathematical reasons (principally Godel’s incompleteness theorem), I think that the achievement of a “perfectly closed...

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Steve Dufourny Jedi replied on Sep. 30, 2012 @ 12:25 GMT
:) in all humility of course,This theory has been found by a young belgian of 37 years old.

Of course it is irritating for a lot of scientists. Just due to the potential of this theory of spherization. Indeed I have found dear sciences community. Of course there are a lot of jealousy and envy. Just due I am repeating to this potential at shot middle and long term. Of course several...

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Daniel Wagner Fonteles Alves replied on Sep. 30, 2012 @ 14:34 GMT
Ben

You see the common point between my essay and Frederico´s? A ''closed theory'' for Frederico is something very close to what I called semantically complete in our discussions. And just to remember, by trying to produce a closed classical theory, the outcome is Machian philosophy which gives rise to GR almost uniquely via Barbour´s arguments. But the classical theory is not yet completely closed. I feel this could be made rigourous.

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Author Frederico Pfrimer wrote on Sep. 30, 2012 @ 19:11 GMT
Dear Benjamin

Thanks for your comments. For sure mathematics is our upper bound. We can go just as far as math allow us, and there will be times we’ll need to first extend math; but that’s not new in physics.

Well, you talked about the incompleteness theorem. Some days ago I found something very interesting about it, and I was willing to discuss about it. A theory is complete in...

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Member Benjamin F. Dribus replied on Oct. 1, 2012 @ 21:35 GMT
Dear Frederico,

I am interested to see your "closed formulation" of part of quantum theory. I take it that is your reference 1?

Regarding Godel, I'm not an expert on undecidability, but I think that Godel's result applied to systems like the natural numbers is rather clear intuitively. The following isn't a proof, but it shows intuitively what an absolute miracle it would be if...

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Peter Jackson wrote on Oct. 1, 2012 @ 12:07 GMT
Frederico

A brilliant theory of theory, and a helpful eye opener for me. I agree translation and interpretation between words and maths is crucial and that we're very short of 'words' to discern meanings. This seems equivalent to mathematical abstraction being very limited in 'bits' compared to nature. But do you agree the brain can work best and find important results without either, then...

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Author Frederico Pfrimer replied on Oct. 1, 2012 @ 19:59 GMT
Dear Peter,

Thanks for your comments. It looks like you could understand a bit deeper the content of my essay. That’s really a theory of theory, and curiously the only possible theory of theory is a theory about closed theories, because you cannot be more explicit giving the form of an open theory. Almost anything can be an open theory.

As you like quantum and other logics you might like my arXiv paper. There you’ll see three logics unified and applied to quantum theory: propositional, modal, and epistemic. You can talk about truth, knowledge, necessity and possibility in quantum theory! I’ll read and rate your essay, and if you haven’t, please rate mine! I would like to keep discussing beyond the scope of this essay! We have close interests, and you might improve my ideas…

Wish you all the best!

Frederico

Sergey G Fedosin wrote on Oct. 4, 2012 @ 04:30 GMT
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is
$R_1$
and
$N_1$
was the quantity of people which gave you ratings. Then you have
$S_1=R_1 N_1$
of points. After it anyone give you
$dS$
of points so you have
$S_2=S_1+ dS$
of points and
$N_2=N_1+1$
is the common quantity of the people which gave you ratings. At the same time you will have
$S_2=R_2 N_2$
of points. From here, if you want to be R2 > R1 there must be:
$S_2/ N_2>S_1/ N_1$
or
$(S_1+ dS) / (N_1+1) >S_1/ N_1$
or
$dS >S_1/ N_1 =R_1$
In other words if you want to increase rating of anyone you must give him more points
$dS$
then the participant`s rating
$R_1$
was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process.

Sergey Fedosin

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Jeff Baugher wrote on Oct. 6, 2012 @ 00:18 GMT
Frederico,

Great essay! Voted. I do agree very much with your essay. I just put up a Powerpoint for my essay, and am curious how you would use FTP to describe the Poisson equation. Specifically slide 18. (Let me know if you catch any goofs on my part, I put it together for hopefully before voting ends.)

Thanks

Jeff

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Concerned Public wrote on Oct. 6, 2012 @ 09:25 GMT
Sergey G Fedosin is bombing entrants' boards with the same "why your rating has dropped" message. They are all dated Oct. 4... same message.

WTH? I've seen one fine essay drop 89 (eighty-nine) positions, in "Community Rating" in the past 24 hours, and “Sergey’s note” came BEFORE it plummeted. Hmm.

The vote/scaling of this contest is quite nebulous.

"Hackers Rule!", I suppose!

Well??? What else is one to think? The General Public is... Watching…

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Cristinel Stoica wrote on Oct. 6, 2012 @ 16:10 GMT
Hi Frederico,

Please check this link and find how five essays, including yours, were removed from the 35 finalists. I posted some messages with attachments containing the page and screenshots at 0:01.

Good luck,

Cristi Stoica

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