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February 20, 2018

CATEGORY:
Trick or Truth Essay Contest (2015)
[back]

TOPIC: Mathematics is the Link Between Physics and Metaphysics by Efthimios Harokopos [refresh]

TOPIC: Mathematics is the Link Between Physics and Metaphysics by Efthimios Harokopos [refresh]

Mathematics allows us to develop physical theories that make accurate predictions. These theories relate a primitive ontology to nomological variables. All of our physical theories make metaphysical commitments that are directly or indirectly related to mathematical models. After a brief introduction to some of the fundamental issues associated with the use of mathematics in developing physical theories, I discuss how the link between physics and metaphysics was achieved in classical mechanics, special relativity and quantum theory. I argue that mathematics may not be sufficient for developing a theory of everything due to incompleteness of formal systems or the existence of unknowable truths.

Efthimios Harokopos received Bachelor’s and Master’s degrees from State University of New York at Buffalo, a Master’s degree from Columbia University and completed the necessary coursework for a PhD while working for AT&T and Bell Labs. He is an independent researcher in the field of philosophy of science.

Thanks Sujatha!

Good to be back with another essay after 4 years from last one. This is a great community a an abundant source of interesting ideas. I see that some other authors also claim that math may not be enough. Let me be clear because this may get tricky: math is more than enough if what we are after is some accurate predictions about everyday life phenomena. Math may not be enough if what we are after is a theory of everything because of unknowable truths or incompleteness or formal systems. Thanks to the pioneers that "lifted all the intellectual weight", we already know enough but not nearly enough for a theory of everything. Math is a great tool and it is neither trick nor a panacea.

My best regards to all participants.

Good to be back with another essay after 4 years from last one. This is a great community a an abundant source of interesting ideas. I see that some other authors also claim that math may not be enough. Let me be clear because this may get tricky: math is more than enough if what we are after is some accurate predictions about everyday life phenomena. Math may not be enough if what we are after is a theory of everything because of unknowable truths or incompleteness or formal systems. Thanks to the pioneers that "lifted all the intellectual weight", we already know enough but not nearly enough for a theory of everything. Math is a great tool and it is neither trick nor a panacea.

My best regards to all participants.

Dear Efthimios,

Your comment elsewhere talking about the need to identify the most appropriate out of the different varieties of space or spacetime drew my attention to the fact that here was someone knowledgable about some of the fundamental issues in contention.

I enjoyed your essay very much and the reasoning was impeccable in many places. You however seemed to place too much...

view entire post

Your comment elsewhere talking about the need to identify the most appropriate out of the different varieties of space or spacetime drew my attention to the fact that here was someone knowledgable about some of the fundamental issues in contention.

I enjoyed your essay very much and the reasoning was impeccable in many places. You however seemed to place too much...

view entire post

report post as inappropriate

Dear Akinbo,

Thank you for your good words. I don't pretend to know everything but I'm not aware of any experiment that falsifies special relativity. If you are ware of one I would be very interested in knowing that.

About Zeno's paradox I talked in detail in my 2011 essay.

I will read your essay and comment soon.

All the best.

Thank you for your good words. I don't pretend to know everything but I'm not aware of any experiment that falsifies special relativity. If you are ware of one I would be very interested in knowing that.

About Zeno's paradox I talked in detail in my 2011 essay.

I will read your essay and comment soon.

All the best.

Dear Efthimios,

I just replied you on my blog. Also I just read your 2011 Essay and your discussion of Zeno's Dichotomy paradox. I see that you desire to make spacetime as the foundation of your proposed solutions. Please be careful about this.

When you say, "I'm not aware of any experiment that falsifies special relativity", are you aware of observations and experiments that falsify...

view entire post

I just replied you on my blog. Also I just read your 2011 Essay and your discussion of Zeno's Dichotomy paradox. I see that you desire to make spacetime as the foundation of your proposed solutions. Please be careful about this.

When you say, "I'm not aware of any experiment that falsifies special relativity", are you aware of observations and experiments that falsify...

view entire post

report post as inappropriate

Dear Akinbo,

I agree with you that if any of the two main postulates of SR are falsified the theory will be falsified. However, I am not aware of conclusive evidence that falsifies either. As I said I do not know every little detail. Please note that regarding SR and QM I have not expressed personal views but those that are accepted. However, my objective was not to promote any theory but...

view entire post

I agree with you that if any of the two main postulates of SR are falsified the theory will be falsified. However, I am not aware of conclusive evidence that falsifies either. As I said I do not know every little detail. Please note that regarding SR and QM I have not expressed personal views but those that are accepted. However, my objective was not to promote any theory but...

view entire post

Efthimios Gia sou, Ciao,

very interesting essay. Do you think that meta-math will still be expressed in some new math?

Good work and right on the subject.

Antonio

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very interesting essay. Do you think that meta-math will still be expressed in some new math?

Good work and right on the subject.

Antonio

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Ciao Antonio,

I have no idea as I wrote in the essay whether it is possible to have a meta-mathematical framework in physics and I cannot speculate of its form. Possibly some sort of new math but I don't know what. Thank you.

I have no idea as I wrote in the essay whether it is possible to have a meta-mathematical framework in physics and I cannot speculate of its form. Possibly some sort of new math but I don't know what. Thank you.

Today after this was posted I show a 9 public rating and now I see a 5.5. Quick calculation shows that someone gave me 2 points. I would appreciate if he can state the reason for that. Then we can all learn something.

Your essay touches on something that I have pondered. Newton’s second law of motion

F = ma,

has a vector quantity that is physical equal to a physical scalar times a vector that is purely geometric. The acceleration a = d^2r/dt^2 is a derivative of one geometric object, a vector in space with respect to another geometric parameter called time. In some funny sense we might think of the geometric quantity as converting the physical scalar into a physical vector. The physical vector is a dynamical quantity that results from the multiplication of a physical scalar (kinematic in nature) with the geometric object.

LC

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F = ma,

has a vector quantity that is physical equal to a physical scalar times a vector that is purely geometric. The acceleration a = d^2r/dt^2 is a derivative of one geometric object, a vector in space with respect to another geometric parameter called time. In some funny sense we might think of the geometric quantity as converting the physical scalar into a physical vector. The physical vector is a dynamical quantity that results from the multiplication of a physical scalar (kinematic in nature) with the geometric object.

LC

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Note that F = ma is referred to as Newton's second law but it is not, according to the statements in Principia. I think Euler stated that law and it happens to correspond to Newton's law when the mass is constant, F = dp/dt

I am not sure time is a geometric parameter. Actually, I have no idea what it means other that it is a reading of a clock. Thus, there is some physics in both sides of the equation but also metaphysics. I see nothing wrong about that as long as it works and it does in weak-field limit. After that one must use general relativity or equivalent and maybe there are no forces, i.e., the metaphysical commitments may change.

Thanks LC

I am not sure time is a geometric parameter. Actually, I have no idea what it means other that it is a reading of a clock. Thus, there is some physics in both sides of the equation but also metaphysics. I see nothing wrong about that as long as it works and it does in weak-field limit. After that one must use general relativity or equivalent and maybe there are no forces, i.e., the metaphysical commitments may change.

Thanks LC

Dear Efthimios Harokopos,

I very much enjoyed your well-written essay. Unless I have forgotten someone, I do not believe any other essays maintain such a clear focus on linking physics and metaphysics through math, and it seems quite an appropriate undertaking. What is most interesting is that you managed to do so using the most basic concepts and beginning with Newton. The math is...

view entire post

I very much enjoyed your well-written essay. Unless I have forgotten someone, I do not believe any other essays maintain such a clear focus on linking physics and metaphysics through math, and it seems quite an appropriate undertaking. What is most interesting is that you managed to do so using the most basic concepts and beginning with Newton. The math is...

view entire post

report post as inappropriate

Dear Edwin Eugene Klingman,

I truly appreciate your good words about my essay. However, I have a problem with your invitation to read your essay as follows:

Before your comments my community rating was at 6.0 based on two votes. Afterwards, it dropped to 5.0 based on a single vote. This means that someone rate it at 3. There are two possibilities then

(1) Either you rated my...

view entire post

I truly appreciate your good words about my essay. However, I have a problem with your invitation to read your essay as follows:

Before your comments my community rating was at 6.0 based on two votes. Afterwards, it dropped to 5.0 based on a single vote. This means that someone rate it at 3. There are two possibilities then

(1) Either you rated my...

view entire post

Dear Efthimios Harokopos,

I saw your complaint about scoring on your thread before I commented on your essay, so I knew that you were already upset about scoring. What I had not realized was that you think you can, in general, correlate comments with voting behavior. It is upsetting when low scores are received for no apparent reason. During the first weeks of this contest I was the top...

view entire post

I saw your complaint about scoring on your thread before I commented on your essay, so I knew that you were already upset about scoring. What I had not realized was that you think you can, in general, correlate comments with voting behavior. It is upsetting when low scores are received for no apparent reason. During the first weeks of this contest I was the top...

view entire post

report post as inappropriate

Efthimios,

I think something has happened to your .pdf file. I have attempted to download your essay several times and it is blank. Obviously from comments above, your essay was present in the system. I have downloaded other essays, so I am not sure what has changed. Perhaps the file has become corrupted or perhaps my Adobe Reader has become corrupted. Also, I have Windows 8. It is...

view entire post

I think something has happened to your .pdf file. I have attempted to download your essay several times and it is blank. Obviously from comments above, your essay was present in the system. I have downloaded other essays, so I am not sure what has changed. Perhaps the file has become corrupted or perhaps my Adobe Reader has become corrupted. Also, I have Windows 8. It is...

view entire post

report post as inappropriate

Efthimios,

False alarm on my part. It appears that somehow my Adobe Acrobat .pdf reader became corrupt.

In your statement of Newton's 2'nd Law, you implicitly assume that the force and the resulting change in motion are collinear. This is the standard understanding. What would you do if they were not collinear? The reason for my question is that I can use Hamilton to produce an...

view entire post

False alarm on my part. It appears that somehow my Adobe Acrobat .pdf reader became corrupt.

In your statement of Newton's 2'nd Law, you implicitly assume that the force and the resulting change in motion are collinear. This is the standard understanding. What would you do if they were not collinear? The reason for my question is that I can use Hamilton to produce an...

view entire post

report post as inappropriate

Hi Gary,

By "change in motion" it is meant change in momentum vector mv. This is the meaning of "motion" in Newton's law. In circular motion the change in momentum dp/dt is along the direction of the center of the path. Thus, a centripetal acceleration is generated and a centripetal force. By definition, these are collinear.

You said:

"The reason for my question is that I can...

view entire post

By "change in motion" it is meant change in momentum vector mv. This is the meaning of "motion" in Newton's law. In circular motion the change in momentum dp/dt is along the direction of the center of the path. Thus, a centripetal acceleration is generated and a centripetal force. By definition, these are collinear.

You said:

"The reason for my question is that I can...

view entire post

I do not understand the part about power and cause-free motion but the rest is an honest attempt to answer the essay questions. First time I read a concise explanation of relativity theory. Good essay.

report post as inappropriate

report post as inappropriate

Thanks. The explanation of relativity is not mine. See related reference in the essay that gives credit where it is due.

Thank you Joe. If I said anything else, i.e., about accurate predictions, I would be wrong given that Newton's law applied to free fall was tested to be accurate to about 1 part in a trillion and Einstein's equivalence was tested to even better accuracy. But as I write, there is a lot of metaphysics behind the math. I sense you did not read the whole essay, just the abstract.

Dear Dr. Harokopos,

You sense wrong. I read all of your essay. Newton's abstract law applied to abstract free fall of what? All real surfaces must travel at the same constant speed. You apparently only understand codswallop abstractions.

Warm regards,

Joe Fisher

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You sense wrong. I read all of your essay. Newton's abstract law applied to abstract free fall of what? All real surfaces must travel at the same constant speed. You apparently only understand codswallop abstractions.

Warm regards,

Joe Fisher

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If I am correct about only surface having the ability to travel at a constant speed, it means that scientists attempting to build a spaceship that would have a physical surface that could travel “faster” than that of a surface of a garbage can are engaged in an act of utter futility.

Warm Regards,

Joe Fisher

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Warm Regards,

Joe Fisher

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Dear Efthimios Harokopos,

Thank you for a very readable essay touching on some basic concepts.

If I understand you correctly, the primary evidence of physics (experimental results) coupled with mathematical expressions (or equations) constitute the primitive ontological basis of physics. The nomological variables are more the interpretation of the experimental results and need to...

view entire post

Thank you for a very readable essay touching on some basic concepts.

If I understand you correctly, the primary evidence of physics (experimental results) coupled with mathematical expressions (or equations) constitute the primitive ontological basis of physics. The nomological variables are more the interpretation of the experimental results and need to...

view entire post

report post as inappropriate

Dear Donald,

Thank you very much for an interesting comment. I admit I have not thought of things this way. Your thinking is quite original. I talked about the accuracy of special relativity and quantum mechanics. Apparently, I paid for this mistake and have received low marks because this contest is flooded with cranks of all kinds that have no connection to math and physics whatsoever but...

view entire post

Thank you very much for an interesting comment. I admit I have not thought of things this way. Your thinking is quite original. I talked about the accuracy of special relativity and quantum mechanics. Apparently, I paid for this mistake and have received low marks because this contest is flooded with cranks of all kinds that have no connection to math and physics whatsoever but...

view entire post

Dear Efthimios,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

report post as inappropriate

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

report post as inappropriate

Dear Efthimios,

It was refreshing to read a paper on the connection between physics and mathematics that made explicit that the manifestation of this connection in different domains involves metaphysical commitments that are often not sufficiently acknowledged.

I think you are right the choice of a particular mathematical formalism to represent an aspect of reality entails a...

view entire post

It was refreshing to read a paper on the connection between physics and mathematics that made explicit that the manifestation of this connection in different domains involves metaphysical commitments that are often not sufficiently acknowledged.

I think you are right the choice of a particular mathematical formalism to represent an aspect of reality entails a...

view entire post

report post as inappropriate

Hello Armin,

I appreciate your comments and they are indeed useful.

Here are my comments:

"Concerning your axiom of motion, I must say, as metaphysical as "Force" is, it seems in some sense more concrete than Power. I don't know if this is an artifact of my education,"

It may be more concrete because it has already become common sense through education. But the notion...

view entire post

I appreciate your comments and they are indeed useful.

Here are my comments:

"Concerning your axiom of motion, I must say, as metaphysical as "Force" is, it seems in some sense more concrete than Power. I don't know if this is an artifact of my education,"

It may be more concrete because it has already become common sense through education. But the notion...

view entire post

Efthimios,

Excellent paper indeed! A real understanding touching the crux of the problem; the lack of substance. The bridge that mathematics provide between our reality and the metaphysical one.

A theory of everything will be a symbiosis between physics and metaphysics with a mathematical bridge. Natural Metaphysics runs on a logical engine with the rule of non-contradiction as starting impossibility, evolving/exploding time at a certain rate as substance, any differential in the time rate as a cause. Yep! Good old substance and cause. Physics can always say how it happens, metaphysics will tell why. They are complementary but mutually exclusive components of knowledge.

Bests,

Marcel,

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Excellent paper indeed! A real understanding touching the crux of the problem; the lack of substance. The bridge that mathematics provide between our reality and the metaphysical one.

A theory of everything will be a symbiosis between physics and metaphysics with a mathematical bridge. Natural Metaphysics runs on a logical engine with the rule of non-contradiction as starting impossibility, evolving/exploding time at a certain rate as substance, any differential in the time rate as a cause. Yep! Good old substance and cause. Physics can always say how it happens, metaphysics will tell why. They are complementary but mutually exclusive components of knowledge.

Bests,

Marcel,

report post as inappropriate

Thanks.

However, "mainstream" physics may not agree. They are immersed in "math games". Billions have been spent in string theory math research although it does not produce a single unique prediction. After all, one task of modern physics has been obscuring issues and a focusing on epistemology. Fitch's paradox is a slap on science face. The price for mentioning it in my paper is the low "community" grade. Most scientists are naive enough to believe that a theory of everything will be obtained through math alone without requiring omniscience, i.e., man becoming God.

However, "mainstream" physics may not agree. They are immersed in "math games". Billions have been spent in string theory math research although it does not produce a single unique prediction. After all, one task of modern physics has been obscuring issues and a focusing on epistemology. Fitch's paradox is a slap on science face. The price for mentioning it in my paper is the low "community" grade. Most scientists are naive enough to believe that a theory of everything will be obtained through math alone without requiring omniscience, i.e., man becoming God.

Efthimios,

Calculus allowed us to remove time so that we could write equation on paper which is not the passing time background we live in. All our notions of physics are over integrated in time by one order. What concerns us on paper is energy. But what concerns the universe is power. Energy is a dimension of knowing the final result or a form of accounting. Power is a dimension of happening, what it is like out there.

Marcel,

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Calculus allowed us to remove time so that we could write equation on paper which is not the passing time background we live in. All our notions of physics are over integrated in time by one order. What concerns us on paper is energy. But what concerns the universe is power. Energy is a dimension of knowing the final result or a form of accounting. Power is a dimension of happening, what it is like out there.

Marcel,

report post as inappropriate

Thanks.

However, "mainstream" physics may not agree. They are immersed in "math games". Billions have been spent in string theory math research although it does not produce a single unique prediction. After all, one task of modern physics has been obscuring issues and a focusing on epistemology. Fitch's paradox is a slap on science face. The price for mentioning it in my paper is the low "community" grade. Most scientists are naive enough to believe that a theory of everything will be obtained through math alone without requiring omniscience, i.e., man becoming God.

Yes, or put it in math language, power is the rate of change of energy, i.e. the flow of energy in time. In your house you get power and you pay for its integral, energy. No one cares how much work was done. You may as well dissipate all energy back in space. Power is the single most important concept in physics. When I published my paper on the laws on motion based on power in 2005, I received many emails from physicists around the world that were excited but ask me not to mention them because they were possibly afraid of consequences. There has been no rebuttal since but mainstream journals have refused publishing articles on it, considering the case closed in favor of force. There is a fundamental reason for that struggle, it will be explained ion my soon to be published book. In a nutshell, behind any theory in since, even math, a certain ideology hides, often of sociopolitical nature. Science nowadays is indistinguishable from politics. Physics is becoming like economics: there are many truths but no one knows which one applies at a given moment or the choice is based on ideology. If you believe in locality, you adhere to that one QM theory and if you believe in non-locality you adhere to the other theory but surprise! They all generate the same predictions. Isn't that funny?

Thanks and all the best.

However, "mainstream" physics may not agree. They are immersed in "math games". Billions have been spent in string theory math research although it does not produce a single unique prediction. After all, one task of modern physics has been obscuring issues and a focusing on epistemology. Fitch's paradox is a slap on science face. The price for mentioning it in my paper is the low "community" grade. Most scientists are naive enough to believe that a theory of everything will be obtained through math alone without requiring omniscience, i.e., man becoming God.

Yes, or put it in math language, power is the rate of change of energy, i.e. the flow of energy in time. In your house you get power and you pay for its integral, energy. No one cares how much work was done. You may as well dissipate all energy back in space. Power is the single most important concept in physics. When I published my paper on the laws on motion based on power in 2005, I received many emails from physicists around the world that were excited but ask me not to mention them because they were possibly afraid of consequences. There has been no rebuttal since but mainstream journals have refused publishing articles on it, considering the case closed in favor of force. There is a fundamental reason for that struggle, it will be explained ion my soon to be published book. In a nutshell, behind any theory in since, even math, a certain ideology hides, often of sociopolitical nature. Science nowadays is indistinguishable from politics. Physics is becoming like economics: there are many truths but no one knows which one applies at a given moment or the choice is based on ideology. If you believe in locality, you adhere to that one QM theory and if you believe in non-locality you adhere to the other theory but surprise! They all generate the same predictions. Isn't that funny?

Thanks and all the best.

This is a fascinating paper. This is the first time I read that power could take the place of force in mechanics and yield laws of motion.

Jason

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Jason

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Efthimios,

That's a big oups! The word "God" is out of context! Anyone seeing that may think that there are other words or concepts out of context and dismiss the whole paper. My opinion is that this extension of "omniscience to God" opens up a whole can of worms which is not your first intent, which is physics and mathematics. Give yourself a chance and leave that one out. It is like pulling down your shirt and asking for flogging.

Just my opinion.

Thanks,

Marcel,

report post as inappropriate

That's a big oups! The word "God" is out of context! Anyone seeing that may think that there are other words or concepts out of context and dismiss the whole paper. My opinion is that this extension of "omniscience to God" opens up a whole can of worms which is not your first intent, which is physics and mathematics. Give yourself a chance and leave that one out. It is like pulling down your shirt and asking for flogging.

Just my opinion.

Thanks,

Marcel,

report post as inappropriate

I give you a chance and keep it in., You deserve a chance.

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