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FQXi FORUM

January 27, 2021

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

TOPIC: Does division of extension mean the same in mathematics as it does in physics? by Akinbo Ojo [refresh]

TOPIC: Does division of extension mean the same in mathematics as it does in physics? by Akinbo Ojo [refresh]

In this essay, I attempt to raise and address some questions concerning the procedure of dividing extension mathematically, which is mental and the actual act of doing so, which is physical. By extension is implied a length, whether of matter or of a distance. And by dividing is implied the procedure of creating parts. Inevitably, such a discussion would touch on the continuity or otherwise of extended parts. I end the essay by moving the motion that we exorcise the lingering millennia old Parmenidean spell cast on our mathematics and physics and allow that whatever exists can perish.

I am a practising physician with keen interest in foundational physics topics. I have authored a published paper and other unpublishable ones. I also enjoys 'dialectic' with physicists over the internet.

A little grammatical correction and a small question arising from what discuss in my essay...

CORRECTION: The last sentence in my Bio should have read: I also enjoy 'dialectic' with physicists over the internet.

A LITTLE QUESTION: I had posed a question to Pentcho Valev on Feb. 4, 2015 @ 19:51 GMT on FQXi forum topic: The limits of mathematics, which I am also interested in discussing here.

When we write 2 + 3 = 5,

is it a very, very, very high probability that when we add 2 and 3 we get 5 or is it a certainty?

Thanks for reading and commenting.

CORRECTION: The last sentence in my Bio should have read: I also enjoy 'dialectic' with physicists over the internet.

A LITTLE QUESTION: I had posed a question to Pentcho Valev on Feb. 4, 2015 @ 19:51 GMT on FQXi forum topic: The limits of mathematics, which I am also interested in discussing here.

When we write 2 + 3 = 5,

is it a very, very, very high probability that when we add 2 and 3 we get 5 or is it a certainty?

Thanks for reading and commenting.

Depends on how you have defined the operation + and what you mean with the question. Provided that you mean the normal addition law in the natural numbers, it's a certainty, if you ask for mathematical proof. If you ask for the physical/observational truth, you will ever only get a high probability.

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Sophia,

Thanks for your comment. In other words, I get from your comment that Mathematical truth is not necessarily the same as Physical/Experimental truth, even though they may be close.

As I mention in y essay, even for Mathematical truth there is an unstated, underlying assumption that things that are being added cannot perish during the addition process. Is this a certainty even for mathematical truth?

As I commented elsewhere, I speculate that it is not a certainty that 2 + 3 = 5 but a very, very, very high probability, with the probability increasing with the size of the object being counted and reducing with the size of the object. In other words, 2 house + 3 houses = 5 houses is more likely to be correct than 2 electron + 3 electrons = 5 electrons. Not necessarily because of the experimental difficulty in identifying an electron but as I discuss in my essay, it is more likely for an electron to perish than for a whole house during the process of counting to determine the sum total.

Regards,

Akinbo

Thanks for your comment. In other words, I get from your comment that Mathematical truth is not necessarily the same as Physical/Experimental truth, even though they may be close.

As I mention in y essay, even for Mathematical truth there is an unstated, underlying assumption that things that are being added cannot perish during the addition process. Is this a certainty even for mathematical truth?

As I commented elsewhere, I speculate that it is not a certainty that 2 + 3 = 5 but a very, very, very high probability, with the probability increasing with the size of the object being counted and reducing with the size of the object. In other words, 2 house + 3 houses = 5 houses is more likely to be correct than 2 electron + 3 electrons = 5 electrons. Not necessarily because of the experimental difficulty in identifying an electron but as I discuss in my essay, it is more likely for an electron to perish than for a whole house during the process of counting to determine the sum total.

Regards,

Akinbo

Hello Akinbo,

I was thinking about your idea of minimum physical length and whether probabilities of 2+3=5 exist depending of the length of the object. It could be useful to put objects into perspective to see if there is consistency.

Maybe you can create a single log scale going from the maximum size object we know (universe) to the minimum size object we known. On this scale, you can highlight from what size we are starting to have issues with standard mathematics. Maybe it has already been done?

Regards,

Christophe

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I was thinking about your idea of minimum physical length and whether probabilities of 2+3=5 exist depending of the length of the object. It could be useful to put objects into perspective to see if there is consistency.

Maybe you can create a single log scale going from the maximum size object we know (universe) to the minimum size object we known. On this scale, you can highlight from what size we are starting to have issues with standard mathematics. Maybe it has already been done?

Regards,

Christophe

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Dear Akinbo,

You have certainly taken an elemental notion and worried it to death. But as you point out "Till this day the issues raised here have not been fully settled in physics and philosophy…" A few observations. On page 7 you mention that cutting of matter results in "the creation of space between the divided parts". But was the space already there, simply filled by the matter? Is what you create "empty space"?

Your point about curvature implying composite is interesting. I don't quite understand your discussion of extension as starting to exist and ceasing to exist and the discrete nature of otherwise syrupy space becoming manifest. I tend to view the field or continuum as the fundamental reality, which I guess is your "syrupy space". I found your essay on comparison of the 'math versus physics' meaning of division well-written and fascinating. You discuss Zeno's Dichotomy Argument. My essay concerns a dichotomy, that of whether spin only exists as the dichotomy of 'up' and 'down' (or a superposition thereof) or whether this is simply a characteristic of the state of the "measured" spin based on alignment or anti-alignment with the measuring field.

You say "current mathematical doctrine does not appear to have allowance for what is to perish." Similarly current physics does not like the idea of information perishing. But if a "non-aligned spin" enters the magnetic field and becomes aligned, either the information associated with its original orientation vanishes or it is transformed into a positional deflection, which as I note implies QM is incomplete.

Judging by my downward trending score this not a popular argument, but as it should be experimentally testable, low scores will not change the fact that quantum mechanics may be proved to be incomplete. I invite you to read my essay and comment.

Good to see you back!

Edwin Eugene Klingman

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You have certainly taken an elemental notion and worried it to death. But as you point out "Till this day the issues raised here have not been fully settled in physics and philosophy…" A few observations. On page 7 you mention that cutting of matter results in "the creation of space between the divided parts". But was the space already there, simply filled by the matter? Is what you create "empty space"?

Your point about curvature implying composite is interesting. I don't quite understand your discussion of extension as starting to exist and ceasing to exist and the discrete nature of otherwise syrupy space becoming manifest. I tend to view the field or continuum as the fundamental reality, which I guess is your "syrupy space". I found your essay on comparison of the 'math versus physics' meaning of division well-written and fascinating. You discuss Zeno's Dichotomy Argument. My essay concerns a dichotomy, that of whether spin only exists as the dichotomy of 'up' and 'down' (or a superposition thereof) or whether this is simply a characteristic of the state of the "measured" spin based on alignment or anti-alignment with the measuring field.

You say "current mathematical doctrine does not appear to have allowance for what is to perish." Similarly current physics does not like the idea of information perishing. But if a "non-aligned spin" enters the magnetic field and becomes aligned, either the information associated with its original orientation vanishes or it is transformed into a positional deflection, which as I note implies QM is incomplete.

Judging by my downward trending score this not a popular argument, but as it should be experimentally testable, low scores will not change the fact that quantum mechanics may be proved to be incomplete. I invite you to read my essay and comment.

Good to see you back!

Edwin Eugene Klingman

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Dear Sir,

Should we be concerned about scoring points or finding the truth? We go for the later. Scoring points is harming progress of science, as often papers are presented by incrementally building on 'accepted theories', even when such theories have been known to be untrue or non-existent like dark energy and extra dimensions, as pointed out in our essay. There is a need for reviewing and rewriting science.

Regards,

basudeba

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Should we be concerned about scoring points or finding the truth? We go for the later. Scoring points is harming progress of science, as often papers are presented by incrementally building on 'accepted theories', even when such theories have been known to be untrue or non-existent like dark energy and extra dimensions, as pointed out in our essay. There is a need for reviewing and rewriting science.

Regards,

basudeba

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Thanks very much Edwin Klingman for stopping by and more importantly for pointing to areas that need clarification.

On your question,*"But was the space already there, simply filled by the matter? Is what you create "empty space"?"*

Thanks for raising this, as it is something that may similarly agitate others. So let me explain by first asking: Going by Euclid's definition and...

view entire post

On your question,

Thanks for raising this, as it is something that may similarly agitate others. So let me explain by first asking: Going by Euclid's definition and...

view entire post

Hi Akinbo,

I still don't quite get the "two points, one relating to matter and the other to 'empty space', occupying the same point." I see points as conceptual overlays on reality. The coordinate system is defined to consist of these conceptual points, which identify location. What is*actually* at that location, whether matter or 'empty space' is irrelevant. I don't see the "two...

view entire post

I still don't quite get the "two points, one relating to matter and the other to 'empty space', occupying the same point." I see points as conceptual overlays on reality. The coordinate system is defined to consist of these conceptual points, which identify location. What is

view entire post

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Dear Sir,

Your definition of division is too restricted. You can universalize it by following the definition of number in our essay. There is a limit (call it the Planck scale if you want) up to which a number can be divided. Physically, it is the quarks. Zero is not nothingness (no magnitude), but something that does not exist at here-now. One is without similars, where the dimensions are...

view entire post

Your definition of division is too restricted. You can universalize it by following the definition of number in our essay. There is a limit (call it the Planck scale if you want) up to which a number can be divided. Physically, it is the quarks. Zero is not nothingness (no magnitude), but something that does not exist at here-now. One is without similars, where the dimensions are...

view entire post

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Dear Basudeba,

Thanks for reading my essay and the lengthy reply. It makes one happy when fellow seekers after truth take from their precious time to do this. In replying, I will be using parts of your response to interrogate the issues in contention, while not claiming to understand all the statements in your post.

You say my definition of division is too restricted. That may be so,...

view entire post

Thanks for reading my essay and the lengthy reply. It makes one happy when fellow seekers after truth take from their precious time to do this. In replying, I will be using parts of your response to interrogate the issues in contention, while not claiming to understand all the statements in your post.

You say my definition of division is too restricted. That may be so,...

view entire post

Dear Sir,

Mathematics is the science of numbers that describes quantitative aspects of Nature. Nature is what exists, is intelligible (knowable) and communicable (describable). Numbers are properties of all substances by which we differentiate between similars. If there are no similars, it is one; otherwise it is many, which is successive perceptions of ‘one’s at high speed. Below Planck scale, you cannot perceive anything. Thus, number stops there.

Separation of points by space would not be points, as space is the interval between objects that exist. Point has existence, though no dimensions. Thus, space is the interval between points also.

Since everything is three dimensional only, there cannot be a multitude of discrete points at the same point, as point has no extended dimension, but the intersection of three of its components.

The distance between Atlanta and his destination is neither infinite nor changing, whereas his own position has been replaced by momentum, which is ever approaching destination covering fixed positions. The paradox would have been valid, had the space also expanded or his velocity reduced proportionately.

Regarding whether one can perish, please read in our other comment.

Regards,

basudeba

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Mathematics is the science of numbers that describes quantitative aspects of Nature. Nature is what exists, is intelligible (knowable) and communicable (describable). Numbers are properties of all substances by which we differentiate between similars. If there are no similars, it is one; otherwise it is many, which is successive perceptions of ‘one’s at high speed. Below Planck scale, you cannot perceive anything. Thus, number stops there.

Separation of points by space would not be points, as space is the interval between objects that exist. Point has existence, though no dimensions. Thus, space is the interval between points also.

Since everything is three dimensional only, there cannot be a multitude of discrete points at the same point, as point has no extended dimension, but the intersection of three of its components.

The distance between Atlanta and his destination is neither infinite nor changing, whereas his own position has been replaced by momentum, which is ever approaching destination covering fixed positions. The paradox would have been valid, had the space also expanded or his velocity reduced proportionately.

Regarding whether one can perish, please read in our other comment.

Regards,

basudeba

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Dear Sir,

This is in addition to our earlier post. We will reply to the points raised by you separately.

When you look at the various colors in the strip, you could distinguish the different wave lengths of radiation emanating from out of it. When you reach “fundamental extended lengths which being indivisible” is not distinguishable from others, you are looking at the radiation...

view entire post

This is in addition to our earlier post. We will reply to the points raised by you separately.

When you look at the various colors in the strip, you could distinguish the different wave lengths of radiation emanating from out of it. When you reach “fundamental extended lengths which being indivisible” is not distinguishable from others, you are looking at the radiation...

view entire post

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Akinbo,

A pretty good read. Thank you.

I will say that there is another way to think about division. That is as the inverse operation of multiplication. This effectively sidesteps many of your concerns since the act of division simply returns the thing that is divided to its pre-multiplication state.

Obviously, that ignores situations such as those that are the subject of your essay ... namely things that cannot clearly divided, or whose division is ambiguous.

Something that I have never understood regarding the concept of a Planck length ... I understand that it is intended to introduce a certain graininess to the universe, but the electron is considered to be a point particle in the truest sense. Therefore, why does the universe need to be grainy? Surely the electron is part of the universe.

Oddly enough, I have thought of the possibility of motion being a creator and destroyer of space. I have also thought of the possibility that a particle is created in the direction in which it is moving and destroyed in the direction from which it moves. The two general ideas seem to be pretty complimentary.

Best Regards,

Gary Simpson

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A pretty good read. Thank you.

I will say that there is another way to think about division. That is as the inverse operation of multiplication. This effectively sidesteps many of your concerns since the act of division simply returns the thing that is divided to its pre-multiplication state.

Obviously, that ignores situations such as those that are the subject of your essay ... namely things that cannot clearly divided, or whose division is ambiguous.

Something that I have never understood regarding the concept of a Planck length ... I understand that it is intended to introduce a certain graininess to the universe, but the electron is considered to be a point particle in the truest sense. Therefore, why does the universe need to be grainy? Surely the electron is part of the universe.

Oddly enough, I have thought of the possibility of motion being a creator and destroyer of space. I have also thought of the possibility that a particle is created in the direction in which it is moving and destroyed in the direction from which it moves. The two general ideas seem to be pretty complimentary.

Best Regards,

Gary Simpson

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Gary,

Thanks for offering me this fresh insight and new way to think about division. From this perspective, it would appear clear that that which is to be divided or multiplied must therefore have some finite NON-ZERO value. If that is the case, are you then of the opinion that there is no limit to division?

The Planck length is suggested to be in some sense that limit to division, a fundamental sort of length.

What do you understand by point particle? Is it a particle that has mass and is of zero dimension and thus infinite density? Or does your point have a dimension? Many mathematicians postulate that the point is of zero dimension. In my 2013 essay I discussed the history behind this idea.

I am happy you have yourself contemplated these ideas about motion. The two ideas are complimentary as you said. Indeed, the second is the way motion is depicted on a computer and TV screen. I similarly thought about the possibility before opting for what I discuss in my essay, which also resolves the other Arrow paradox by Zeno, which you can view here and here.

Regards,

Akinbo

Thanks for offering me this fresh insight and new way to think about division. From this perspective, it would appear clear that that which is to be divided or multiplied must therefore have some finite NON-ZERO value. If that is the case, are you then of the opinion that there is no limit to division?

The Planck length is suggested to be in some sense that limit to division, a fundamental sort of length.

What do you understand by point particle? Is it a particle that has mass and is of zero dimension and thus infinite density? Or does your point have a dimension? Many mathematicians postulate that the point is of zero dimension. In my 2013 essay I discussed the history behind this idea.

I am happy you have yourself contemplated these ideas about motion. The two ideas are complimentary as you said. Indeed, the second is the way motion is depicted on a computer and TV screen. I similarly thought about the possibility before opting for what I discuss in my essay, which also resolves the other Arrow paradox by Zeno, which you can view here and here.

Regards,

Akinbo

Akinbo,

To me, it is possible in mathematical abstraction to divide something as many times as desired. In practice, this is not true. So, it seems that you have identified a difference between mathematics and physics. Namely the concept of divisibility (or non-divisibility).

So perhaps the Planck Length has meaning for empty space but not for particles such as protons or neutrons.

It is easier to multiply numbers than it is to divide them. I was taught multiplication before I was taught division. So, division is thought of as the inverse operation of multiplication. That makes it easy to divide something if that something is the result of a multiplication. This is perhaps not useful if something can not easily be divided ... for example half of a proton. Of course, a distance could be half of the diameter of a proton.

Best Regards,

Gary Simpson

Regarding the electron, my understanding is that it has no physical dimension and that it has mass. Therefore, it has infinite density. My inference from this is that we do not have a correct understanding of the electron. I have presented some speculation regarding the electron in two papers that are posted to viXra.org. In the first post in my forum, I list the web address of those papers.

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To me, it is possible in mathematical abstraction to divide something as many times as desired. In practice, this is not true. So, it seems that you have identified a difference between mathematics and physics. Namely the concept of divisibility (or non-divisibility).

So perhaps the Planck Length has meaning for empty space but not for particles such as protons or neutrons.

It is easier to multiply numbers than it is to divide them. I was taught multiplication before I was taught division. So, division is thought of as the inverse operation of multiplication. That makes it easy to divide something if that something is the result of a multiplication. This is perhaps not useful if something can not easily be divided ... for example half of a proton. Of course, a distance could be half of the diameter of a proton.

Best Regards,

Gary Simpson

Regarding the electron, my understanding is that it has no physical dimension and that it has mass. Therefore, it has infinite density. My inference from this is that we do not have a correct understanding of the electron. I have presented some speculation regarding the electron in two papers that are posted to viXra.org. In the first post in my forum, I list the web address of those papers.

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Thank you for reading my essay.

I am thinking - now - that many physical laws, describing a mathematical world, does not have access to the real world (if describing material objects); there is ever a minimum dimension where the divisibility ad infinitum is not applicable. So that a mathematical object (the physical law) have a limit of applicability in the real world.

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I am thinking - now - that many physical laws, describing a mathematical world, does not have access to the real world (if describing material objects); there is ever a minimum dimension where the divisibility ad infinitum is not applicable. So that a mathematical object (the physical law) have a limit of applicability in the real world.

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Dear Akinbo,

Thank you for the comment you made about my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL My essay explains how the real Universe is occurring. Reality does not have an abstract uncommon, but abstract interesting perspective. I did not mistake an abstract image of an abstract object for the abstract object itself. You did that. Abstract images may be abstractly conveyed by abstract traveling abstract light, however, real light can only appear provided it is seen as adhering to a real surface that is traveling at the constant speed of surface.

Only an abstract universe could come from an abstract nothing.

Regards,

Joe Fisher

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Thank you for the comment you made about my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL My essay explains how the real Universe is occurring. Reality does not have an abstract uncommon, but abstract interesting perspective. I did not mistake an abstract image of an abstract object for the abstract object itself. You did that. Abstract images may be abstractly conveyed by abstract traveling abstract light, however, real light can only appear provided it is seen as adhering to a real surface that is traveling at the constant speed of surface.

Only an abstract universe could come from an abstract nothing.

Regards,

Joe Fisher

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Hi Joe,

I am of the view that the question, "Where did the universe come from?" is not stupid and is worth contemplating.

By the way, the theory surrounding this predates Stephen Hawking. Among the earlier thinkers was the Belgian priest and mathematician Lemaitre and the Russian George Gamow. It was however Hubble's finding of the redshift-distance relation that let the horse out of...

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I am of the view that the question, "Where did the universe come from?" is not stupid and is worth contemplating.

By the way, the theory surrounding this predates Stephen Hawking. Among the earlier thinkers was the Belgian priest and mathematician Lemaitre and the Russian George Gamow. It was however Hubble's finding of the redshift-distance relation that let the horse out of...

view entire post

Dear Akinbo Ojo,

Wow. You obviously put a lot of thought into this essay and I congratulate you on your effort. I found it very challenging to read partly because I couldn’t see the “point” (no disrespect, but pun intended). I realize that it is typical of philosophers to pick a detail such as you did and obsess over it until they have pulled every possible string to its limit, but as...

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Wow. You obviously put a lot of thought into this essay and I congratulate you on your effort. I found it very challenging to read partly because I couldn’t see the “point” (no disrespect, but pun intended). I realize that it is typical of philosophers to pick a detail such as you did and obsess over it until they have pulled every possible string to its limit, but as...

view entire post

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Ted,

Thanks for your comments. We seem not to be in the same boat on a number of issues, viz. eternally existing universe vs. my finitely existing universe; preference for space-time vs. my space; timeless existence vs. my finite duration of existence. But no matter.

I rushed superficially through your paper, 'The space-time-motion diagram: a relational model'. I can see that you are like me interested in knowing what "continuum" means. It is a frequently used but in my opinion a poorly defined term. Your ideas make use of Lorentz transformation and you like other 'relational' physicists consider space a 'non-entity', unlike some of us who like Newton consider space an 'entity'. But before concluding about whether space or space-time is a non-entity ponder what entity vibrates as gravitational waves travelling at*c*, i.e. if GR is correct, and also check what entity is compressed or extended in the Alcubierre drive, a model based on space-time like yours.

I will request more clarification on your thread how you resolve Zeno's paradox with your model.

Regards,

Akinbo

Thanks for your comments. We seem not to be in the same boat on a number of issues, viz. eternally existing universe vs. my finitely existing universe; preference for space-time vs. my space; timeless existence vs. my finite duration of existence. But no matter.

I rushed superficially through your paper, 'The space-time-motion diagram: a relational model'. I can see that you are like me interested in knowing what "continuum" means. It is a frequently used but in my opinion a poorly defined term. Your ideas make use of Lorentz transformation and you like other 'relational' physicists consider space a 'non-entity', unlike some of us who like Newton consider space an 'entity'. But before concluding about whether space or space-time is a non-entity ponder what entity vibrates as gravitational waves travelling at

I will request more clarification on your thread how you resolve Zeno's paradox with your model.

Regards,

Akinbo

Your work convincingly relates that mathematics and physics are more artful.

Sincerely,

Miss. Sujatha Jagannathan

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Sincerely,

Miss. Sujatha Jagannathan

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I liked the simplicity of the essay. I completely agree with your postulate to imagine points coming into and going out of existence exactly when needed. I call this the emergence of space from the actions of objects in time as opposed to the a priori existence of space as an infinity of points coming and going as a place for action and objects.

You further argue that dividing an object with neural action does not involve energy, but obviously any thought of dividing does take energy; the energy needed to sustain that neural packet of a moment of thought. In fact, it would in principle take an infinite energy for the infinite thoughts of dividing infinitely...thank goodness most minds are not prone to this neurosis.

There are two universes; math and physics, and math divides an object of our mind into an infinity of smaller objects with a neural action of our mind. Physics divides an object external to our mind into some physical limit of smaller objects with actions using other objects and of course using energy as well. Math represents objects as we imagine them to be and physics represents objects as they actually are outside of our mind. But our mind does use energy for all thought.

The irony is that it is by the neural action of our mind that we imagine both the infinity of smaller objects in an imaginary reality as well as the finite atoms of real objects. In other words, math equally well describes both the infinite as well as the finite. In particular, can infinitesimal points exist in the lonely nothing of empty space? Or is it only objects, time, and action that exist? It is not only our science that makes an object out of empty space, something out of nothing, space seems to emerge from our neural reality as well.

1.5, entertaining

1.0, well written

2.1, understandable

2.0, relevance to theme

6.6 total

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You further argue that dividing an object with neural action does not involve energy, but obviously any thought of dividing does take energy; the energy needed to sustain that neural packet of a moment of thought. In fact, it would in principle take an infinite energy for the infinite thoughts of dividing infinitely...thank goodness most minds are not prone to this neurosis.

There are two universes; math and physics, and math divides an object of our mind into an infinity of smaller objects with a neural action of our mind. Physics divides an object external to our mind into some physical limit of smaller objects with actions using other objects and of course using energy as well. Math represents objects as we imagine them to be and physics represents objects as they actually are outside of our mind. But our mind does use energy for all thought.

The irony is that it is by the neural action of our mind that we imagine both the infinity of smaller objects in an imaginary reality as well as the finite atoms of real objects. In other words, math equally well describes both the infinite as well as the finite. In particular, can infinitesimal points exist in the lonely nothing of empty space? Or is it only objects, time, and action that exist? It is not only our science that makes an object out of empty space, something out of nothing, space seems to emerge from our neural reality as well.

1.5, entertaining

1.0, well written

2.1, understandable

2.0, relevance to theme

6.6 total

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Thank you Steve for your comments. I think you make some sense that mathematical division requires energy of some sort ("But our mind does use energy for all thought").

On your statement, "I call this the emergence of space from the actions of objects in time as opposed to the a priori existence of space as an infinity of points coming and going as a place for action and objects", which partly supports my hypothesis, I cannot help wondering whether if in your theory, objects should stop acting for a moment, whether space would then disappear? I think not.

We will continue our dialectic where we usually "meet" on this website.

Thanks and best regards,

Akinbo

On your statement, "I call this the emergence of space from the actions of objects in time as opposed to the a priori existence of space as an infinity of points coming and going as a place for action and objects", which partly supports my hypothesis, I cannot help wondering whether if in your theory, objects should stop acting for a moment, whether space would then disappear? I think not.

We will continue our dialectic where we usually "meet" on this website.

Thanks and best regards,

Akinbo

Andrew,

Since I trust in the only compelling definitions of an ideal mathematical point as having no extension and of an ideal mathematical continuum as never losing its property to have three, two, or just one dimension/extension no matter how often it is cut into 3D, 2D, or 1D, respectively parts, I consider your "infinitesimal points" entertaining.

An infinitesimal length dx is still a length, an infinitesimal area dA is still two-dimensional, etc. Okinbo's splittable point was certainly not C. S. Peirce's best idea. I am claiming a better understanding in 2342.

Eckard Blumschein

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Since I trust in the only compelling definitions of an ideal mathematical point as having no extension and of an ideal mathematical continuum as never losing its property to have three, two, or just one dimension/extension no matter how often it is cut into 3D, 2D, or 1D, respectively parts, I consider your "infinitesimal points" entertaining.

An infinitesimal length dx is still a length, an infinitesimal area dA is still two-dimensional, etc. Okinbo's splittable point was certainly not C. S. Peirce's best idea. I am claiming a better understanding in 2342.

Eckard Blumschein

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I’ve replied to your comments of my essay in my essay comment section. I comment on your essay in the interest of dialectic discourse.

Your essay raises many conceptual issues that should be addressed by current physics. A new physics model of the universe is needed. The new model should take decisions about the issues you raise.

I ask a different question of my physics. I think...

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Your essay raises many conceptual issues that should be addressed by current physics. A new physics model of the universe is needed. The new model should take decisions about the issues you raise.

I ask a different question of my physics. I think...

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Akinbo,

There is something that I wanted to mention to you regarding the .pdf file that I posted for you in my forum. For the function f(x) = ax^2, the value for (deltay/deltax) = 0 for x = -(deltax/2). Isn't it curious that there is a zero root at the midpoint of a segment that cannot be divided? How do you interpret this?

Best Regards and Good Luck,

Gary Simpson

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There is something that I wanted to mention to you regarding the .pdf file that I posted for you in my forum. For the function f(x) = ax^2, the value for (deltay/deltax) = 0 for x = -(deltax/2). Isn't it curious that there is a zero root at the midpoint of a segment that cannot be divided? How do you interpret this?

Best Regards and Good Luck,

Gary Simpson

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Thanks Gary.

Among the different alibis given in response by other contestants in order to bypass the issues I have raised is that zero should be removed from considerations of physical reality. The logic being that what is zero does not exist.

My exchange made me to check up on C. S. Peirce's view on the subject and I found this in the Stanford Encyclopedia:*"...Peirce says that if a line is cut into two portions, ***the point at which the cut takes place** actually **becomes two points**..."..

Whether this would mean that 'the point at which the cut takes place' has two parts? And if so, contradict the original geometric definition is an outstanding issue.

So, in answer to your question, I think I will leave the interpretation to you. It is sufficient I think that I have pointed out a difficulty in my opinion and suggested a hypothesis which may be wrong.

Regards,

Akinbo

Among the different alibis given in response by other contestants in order to bypass the issues I have raised is that zero should be removed from considerations of physical reality. The logic being that what is zero does not exist.

My exchange made me to check up on C. S. Peirce's view on the subject and I found this in the Stanford Encyclopedia:

Whether this would mean that 'the point at which the cut takes place' has two parts? And if so, contradict the original geometric definition is an outstanding issue.

So, in answer to your question, I think I will leave the interpretation to you. It is sufficient I think that I have pointed out a difficulty in my opinion and suggested a hypothesis which may be wrong.

Regards,

Akinbo

``Redefinition of things that are already defined is one way to resolve paradoxes and absurdities. But then such redefinitions must stand up to scrutiny and should be verifiable or falsified.’’

That is they must be useful. Zeno and Penrose suggest a definition of division that is not useful in general.

``I like your definition of Multiplication and Division. It can resolve paradoxes of motion like Zeno's, if "Real numbers do not apply to distance" as you say.’’

Division and therefore the real numbers such as 1/3, pi, etc. is a transformation that is not physical. Hence, my definition of the inverse of multiplication. There may be some argument about whether irrational, transcendental, etc. numbers are real because all distances along a line are either greater than or less than the irrational number. That is there is no distance along a line that equals the irrational number. This also suggests the problem with Penrose where again we have the ``divide’’ definition issue. I suggest this as a way to avoid the things like Zeno’s paradox, which are not consistent with observation (physical). After all we can go through a door.

My own contention is that the plenum is discrete and also continuous in some sense. Thus displaying a duality. Continuous because there is no distance between its lengths, but discrete because those lengths can perish or be created from Nothing. The fundamental unit of my plenum is the extended (not zero-dimensional) point.

Can this concept be reduced to a hypothesis and measurement? Mine, at least, has been applied to cosmology and the double-slit observations.

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That is they must be useful. Zeno and Penrose suggest a definition of division that is not useful in general.

``I like your definition of Multiplication and Division. It can resolve paradoxes of motion like Zeno's, if "Real numbers do not apply to distance" as you say.’’

Division and therefore the real numbers such as 1/3, pi, etc. is a transformation that is not physical. Hence, my definition of the inverse of multiplication. There may be some argument about whether irrational, transcendental, etc. numbers are real because all distances along a line are either greater than or less than the irrational number. That is there is no distance along a line that equals the irrational number. This also suggests the problem with Penrose where again we have the ``divide’’ definition issue. I suggest this as a way to avoid the things like Zeno’s paradox, which are not consistent with observation (physical). After all we can go through a door.

My own contention is that the plenum is discrete and also continuous in some sense. Thus displaying a duality. Continuous because there is no distance between its lengths, but discrete because those lengths can perish or be created from Nothing. The fundamental unit of my plenum is the extended (not zero-dimensional) point.

Can this concept be reduced to a hypothesis and measurement? Mine, at least, has been applied to cosmology and the double-slit observations.

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Dear Dr. Ojo! For a practising physician, syntropy is a very vital concept, because life is all 'we have'. In my opinion, Dr.Ulisse di Corpo very well speaks about: The Law of Syntropy' in his latestst e-book, based on Schrödinger, Szent-Györgyi and Fantappie. Retro-causality is a key concept of this medical approach which looks at conditioning and conditions. Best wishes and cordially: stephen (www.lifeenergyscience.it)

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Hi Akinbo,

Thank you for your comment on my blog.

I think I see where you are coming from with your essay and where you are trying to get to.

I have a clear idea about the subject.

I believe that the Universe is made of what I call Universal Bits (Existence/non-existence). They are the smallest of everything and cannot be subdivided. They are just bits of potential information, they are not material and they do not have a shape as such, but their apparent size, in any directions, is one Planck Length and they flick between existence and non-existence every Planck Time.

In order for a coherent world to develop, these Universal Bits must group into Coherent Basic Units (made of synchronised Universal Bits). Particles are simply a temporal pattern created by these Coherent Basic Units. But that’s only my point of view …

All in all, I thought that your essay was spot on track. I just rated it accordingly.

All the best,

Patrick

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Thank you for your comment on my blog.

I think I see where you are coming from with your essay and where you are trying to get to.

I have a clear idea about the subject.

I believe that the Universe is made of what I call Universal Bits (Existence/non-existence). They are the smallest of everything and cannot be subdivided. They are just bits of potential information, they are not material and they do not have a shape as such, but their apparent size, in any directions, is one Planck Length and they flick between existence and non-existence every Planck Time.

In order for a coherent world to develop, these Universal Bits must group into Coherent Basic Units (made of synchronised Universal Bits). Particles are simply a temporal pattern created by these Coherent Basic Units. But that’s only my point of view …

All in all, I thought that your essay was spot on track. I just rated it accordingly.

All the best,

Patrick

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Dear Akinbo,

I am glad to be at contest again with you, as in 2013.

Simple but deep.’Yes' and 'No' in (v) is crucial for me.

More about: „How should we think of infinity?“ You can see at Ruđer Bošković [1, paragraph 391]. “Now, although I do not hold with infinite divisibility, yet I do admit infinite componibility“. More you can see in paragraphs 391 to 396. Therefore I say: the mass, radius and any other fenomenon is finite but the number of their combination is infinite.

[1] Boscovich J. R.: (a) "Theoria philosophia naturalis redacta ad unicam legem virium in naturaexistentium", first (Wien, 1758) and second (Venetiis, 1763) edition in Latin language; (b) "A Theory of Natural Philosophy", in English, The M.I.T. Press, Massachusetts Institute of Technology, Cambridge, Massachusetts and London, England, first edition 1922, second edition 1966

Best Regards,

Branko Zivlak

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I am glad to be at contest again with you, as in 2013.

Simple but deep.’Yes' and 'No' in (v) is crucial for me.

More about: „How should we think of infinity?“ You can see at Ruđer Bošković [1, paragraph 391]. “Now, although I do not hold with infinite divisibility, yet I do admit infinite componibility“. More you can see in paragraphs 391 to 396. Therefore I say: the mass, radius and any other fenomenon is finite but the number of their combination is infinite.

[1] Boscovich J. R.: (a) "Theoria philosophia naturalis redacta ad unicam legem virium in naturaexistentium", first (Wien, 1758) and second (Venetiis, 1763) edition in Latin language; (b) "A Theory of Natural Philosophy", in English, The M.I.T. Press, Massachusetts Institute of Technology, Cambridge, Massachusetts and London, England, first edition 1922, second edition 1966

Best Regards,

Branko Zivlak

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Dear Branko,

Thanks for your comment. I don't think I agree that if divisibility is finite, the number of possible combinations can be infinite. With finite number of constituents and finite number of compartments, the number of combinations, even if astronomical, must be finite also. However, if the number of compartments and constituents is increasing, as would be the case for an expanding universe, the number of different possible arrangements in the system will also be increasing. This is illustrated by the second law of thermodynamics. Entropy of the universe is finite, but increasing with time.

Regards,

Akinbo

Thanks for your comment. I don't think I agree that if divisibility is finite, the number of possible combinations can be infinite. With finite number of constituents and finite number of compartments, the number of combinations, even if astronomical, must be finite also. However, if the number of compartments and constituents is increasing, as would be the case for an expanding universe, the number of different possible arrangements in the system will also be increasing. This is illustrated by the second law of thermodynamics. Entropy of the universe is finite, but increasing with time.

Regards,

Akinbo

Dear Akinbo,

I enjoyed your essay and I think it was nicely written. As far as extension in physics, things become a little more complicated if it involves also a temporal dimension, as in relativity theory. Zeno's paradoxes are resolved in special relativity because there is no motion in space but in spacetime. However, we all do not have to agree with the ramifications of this approach but it represents a solution.

Actually, Zeno's paradox of dichotomy is about motion being impossible. It cannot even commence since there will be always a point closer to the start than any other point ad infinitum. If we have to preserve the autonomy of this world, or to be more exact, its quasi-autonomy, then this paradox can be resolved only in the context of a tensless theory of time and existence. Another solution is the one given by Descartes that I also speak in my 2011 essay involving a continuous recreation of the world (at discrete time and space, i.e. a virtual reality). Obviously, the subject is more involved than that.

All the best.

Efthimios

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I enjoyed your essay and I think it was nicely written. As far as extension in physics, things become a little more complicated if it involves also a temporal dimension, as in relativity theory. Zeno's paradoxes are resolved in special relativity because there is no motion in space but in spacetime. However, we all do not have to agree with the ramifications of this approach but it represents a solution.

Actually, Zeno's paradox of dichotomy is about motion being impossible. It cannot even commence since there will be always a point closer to the start than any other point ad infinitum. If we have to preserve the autonomy of this world, or to be more exact, its quasi-autonomy, then this paradox can be resolved only in the context of a tensless theory of time and existence. Another solution is the one given by Descartes that I also speak in my 2011 essay involving a continuous recreation of the world (at discrete time and space, i.e. a virtual reality). Obviously, the subject is more involved than that.

All the best.

Efthimios

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Thanks Efthimios,

I will reply more in your blog as I just read your 2011 Essay.

Regarding motion in special relativity, I am not sure the mechanism you describe fits. Check the mechanism for the Alcubierre drive in Wikipedia, to see how spacetime in front of the moving object is compressed and spacetime behind the object expands.

I will also be asking on your blog whether the 4-dimensional block universe you propose as reflecting the correct situation exists and if it exists, whether it can perish or it is an eternally existing universe?

Regards,

Akinbo

I will reply more in your blog as I just read your 2011 Essay.

Regarding motion in special relativity, I am not sure the mechanism you describe fits. Check the mechanism for the Alcubierre drive in Wikipedia, to see how spacetime in front of the moving object is compressed and spacetime behind the object expands.

I will also be asking on your blog whether the 4-dimensional block universe you propose as reflecting the correct situation exists and if it exists, whether it can perish or it is an eternally existing universe?

Regards,

Akinbo

Dear Akinfo,

You raised fundamental issues on point, space and time. I enjoyed reading your argument. You raised a solution, you wrote: I next propose a hypothesis of time as the separator of minimum lengths, enabling the physical manifestation of discreteness in otherwise 'syrupy' space." I would say if I may point it out that KQID states that space or extended line or matter is indeed 3D time, or time extension. That is why I made a slogan that space is the fetus of time and time is pregnant with space. Therefore, our Multiverse is the fetus of time and time is pregnant with our Multiverse. Crazy statement but logical? yes. Simple idea? Yes. Common sense and "of course" simple idea so obvious in Wheeler's sense? I would say, definitely yes.

You are the warrior of the truth, I comment you and keep on marching no matter what. I admire and share your spirit, I am with you marching no matter what they say and do,

Leo KoGuan

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You raised fundamental issues on point, space and time. I enjoyed reading your argument. You raised a solution, you wrote: I next propose a hypothesis of time as the separator of minimum lengths, enabling the physical manifestation of discreteness in otherwise 'syrupy' space." I would say if I may point it out that KQID states that space or extended line or matter is indeed 3D time, or time extension. That is why I made a slogan that space is the fetus of time and time is pregnant with space. Therefore, our Multiverse is the fetus of time and time is pregnant with our Multiverse. Crazy statement but logical? yes. Simple idea? Yes. Common sense and "of course" simple idea so obvious in Wheeler's sense? I would say, definitely yes.

You are the warrior of the truth, I comment you and keep on marching no matter what. I admire and share your spirit, I am with you marching no matter what they say and do,

Leo KoGuan

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Akinbo,

Clever presentation. Does your last statement indicate your affirmation of Parmenides or of consciousness being the key to what is real? My "Connection: Mind, Math and Physics is comparatively mundane.

Jim

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Clever presentation. Does your last statement indicate your affirmation of Parmenides or of consciousness being the key to what is real? My "Connection: Mind, Math and Physics is comparatively mundane.

Jim

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Thanks James for looking in. The essence of my essay is a refutation of Parmenides proposal that things do not change. I then try to illustrate what implication this has for physics. I will read and comment on your perspective this weekend.

Akinbo

Akinbo

Akinbo,

As time grows short, I am revisiting those I have read to see if I have rated yet. Yours I have not so I am doing so today.

Thank you for reading mine.

Jim

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As time grows short, I am revisiting those I have read to see if I have rated yet. Yours I have not so I am doing so today.

Thank you for reading mine.

Jim

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I really loved your well thought out essay. I was impressed by your quote * "Ultimately, if extension cannot be its own separator into discreteness, the hypothesis proposed introduces 'time' as the separator of extension into discrete. By 'time', I mean duration of existence, i.e.extension can start to exist and cease to exist and as all minimum lengths do not have the same life span, the discrete nature of otherwise syrupy space becomes manifest.* And the idea of perishing distance and how extension works when we walk about the room is intriguing. Well done it really makes me think.

John C. Hodge mentioned in his post on my essay that your essay would be very interesting and he was correct! My essay is about Sorites Paradox; it explores discrete time units (where Plank's constant is made a cyclic-measuring-device or a Hamiltonian for duration)in contrast to your essay about discrete lengths (and Zeno's Paradox). I think there might be some overlap between our two points of view. I hope you get a chance to read my essay. I gave your essay a good mark. Yours Harri

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John C. Hodge mentioned in his post on my essay that your essay would be very interesting and he was correct! My essay is about Sorites Paradox; it explores discrete time units (where Plank's constant is made a cyclic-measuring-device or a Hamiltonian for duration)in contrast to your essay about discrete lengths (and Zeno's Paradox). I think there might be some overlap between our two points of view. I hope you get a chance to read my essay. I gave your essay a good mark. Yours Harri

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Thanks Harri for looking in. I also just read your essay. Yes, I think there is room to link our two essays, as you say 'discrete lengths' and 'discrete time units'. Note however that I suggest that what separates length or extension into discreteness is 'time'.

I will rate your essay towards the end of competition to give it a lift when needed most.

Regards,

Akinbo

I will rate your essay towards the end of competition to give it a lift when needed most.

Regards,

Akinbo

Dear Akinbo,

1. FIRST, answering your title-question (Essay, p.1): No.

2. SECOND, a request: Please define/explain in greater detail the Akinbo point** (this strange new point on p.5 of your essay), based on this preliminary attempt to clarify your text (p.5):

"I [Akinbo Ojo] prefer to call that fundamental unit (which is extended, in contrast to the zero-dimensional point of some mathematicians), the [impure per Leibniz]*** "Akinbo point". The Akinbo point, my fundamental unit of length, is [somehow] featureless, save that it is a [somehow] extended thing."

Please explain, for example: the connection between the original point and your identified extension. (PS: Was this extension discovered or created; by the gods; etc?) Perhaps compare this extension with extension by colour, or life-time, or its god(s); etc. And since it is NOT zero-dimensional: of what dimension is it?

* reserving "the Ojo point" for a proposed gift to the mighty Ojo clan!

** here named; seeking to eliminate misunderstandings already wildly breeding.

*** Though the immediate case I bring is against you (and not (YET) against the ancients or the gods), I and Leibniz (via his 1714b, para #2) seem to be as one

Regards; Gordon

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Dear Gordon,

Thanks for the feedback and the opportunity to shed more light on possible grey areas on this topic.

1. Good to see a No answer. So in your opinion what's the difference?

2. FIRSTLY, there is no strangeness or originality in the extended point. As I discussed in my first essay, it dates back to the Pythagoreans and was a bone of contention between The...

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Thanks for the feedback and the opportunity to shed more light on possible grey areas on this topic.

1. Good to see a No answer. So in your opinion what's the difference?

2. FIRSTLY, there is no strangeness or originality in the extended point. As I discussed in my first essay, it dates back to the Pythagoreans and was a bone of contention between The...

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Dear Akinbo:

To assist with my reply to your nice details above, could you help here please.

1. Regarding those who take "the reals" to be continuous, how do they write/represent/denote the last real before 2 and the first real after it?

2. Do you take "the reals" to be continuous?

With best regards from this local realist; Gordon Watson: Essay Forum. Essay Only.

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To assist with my reply to your nice details above, could you help here please.

1. Regarding those who take "the reals" to be continuous, how do they write/represent/denote the last real before 2 and the first real after it?

2. Do you take "the reals" to be continuous?

With best regards from this local realist; Gordon Watson: Essay Forum. Essay Only.

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Dear Gordon,

As far as I know the answers I can give to your two questions are:

1. There is no definite real before 2 nor any defined real after 2.

2. I take 'the reals' to be continuous as do most, if not all mathematicians. I think the important question is how the real number line applies to physical reality. In this regard, I have a favourite quote from Roger Penrose's...

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As far as I know the answers I can give to your two questions are:

1. There is no definite real before 2 nor any defined real after 2.

2. I take 'the reals' to be continuous as do most, if not all mathematicians. I think the important question is how the real number line applies to physical reality. In this regard, I have a favourite quote from Roger Penrose's...

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I have considered your questions Akinbo, and copied the answers below...

1st - the Mandelbrot's cusp at (.25,0i) is the minimum extent and highest energy represented in the Mandelbrot figure. But the theory would indicate that this translates into a minimum time step. However; for anything to persist longer than the Planck time, in this theory, it must have a non-zero size.

2nd - particles act as probes of the properties of a given space, retaining and conveying information about separability and separation. I would say that once forms exist as self-contained independent units, which can move relative to each other, this defines or helps determine the dimensionality of space as well.

3rd - I think part of the meaning of Math is that it preserves some features of natural law that are persistent, from cosmological era to era, from inception to its demise or the beginning of a new cycle, or from universe to universe in a multiverse scenario (more below).

As for atoms of space, however; that concept speaks mainly to how the fabric of spacetime emerges, and one can't discern individual unit cells after that. If space and time are relativistically indistinguishable; then there is a lower limit of around 10^-13 cm - where particle separability is possible - in which Relativity is defined. And item 2 answers this.

The Cosmology based on the Mandelbrot Set does not tell us whether a cold dark end is the universe's ultimate fate, or whether a new cycle would begin, as I can show you the graphical representation of both scenarios. Likewise; it supports the idea that the universe is singular and allows for the possibility of multiple universes. This suggests these possibilities coexist equivalently.

All the Best,

Jonathan

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1st - the Mandelbrot's cusp at (.25,0i) is the minimum extent and highest energy represented in the Mandelbrot figure. But the theory would indicate that this translates into a minimum time step. However; for anything to persist longer than the Planck time, in this theory, it must have a non-zero size.

2nd - particles act as probes of the properties of a given space, retaining and conveying information about separability and separation. I would say that once forms exist as self-contained independent units, which can move relative to each other, this defines or helps determine the dimensionality of space as well.

3rd - I think part of the meaning of Math is that it preserves some features of natural law that are persistent, from cosmological era to era, from inception to its demise or the beginning of a new cycle, or from universe to universe in a multiverse scenario (more below).

As for atoms of space, however; that concept speaks mainly to how the fabric of spacetime emerges, and one can't discern individual unit cells after that. If space and time are relativistically indistinguishable; then there is a lower limit of around 10^-13 cm - where particle separability is possible - in which Relativity is defined. And item 2 answers this.

The Cosmology based on the Mandelbrot Set does not tell us whether a cold dark end is the universe's ultimate fate, or whether a new cycle would begin, as I can show you the graphical representation of both scenarios. Likewise; it supports the idea that the universe is singular and allows for the possibility of multiple universes. This suggests these possibilities coexist equivalently.

All the Best,

Jonathan

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Hi Akinbo,

I liked your essay but I am still not fully convinced that a discrete physical model cannot be possible… although some of your ideas really made me think!

I must admit, I was almost ready to give up trying to make sense of some of your points because I wasn’t really following exactly what you were getting at. But then I think I got a better understanding… Please...

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I liked your essay but I am still not fully convinced that a discrete physical model cannot be possible… although some of your ideas really made me think!

I must admit, I was almost ready to give up trying to make sense of some of your points because I wasn’t really following exactly what you were getting at. But then I think I got a better understanding… Please...

view entire post

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Thanks Jon for finding time to read my essay.

It may be that I have to improve and make clearer the points I was trying to put across. Especially as you ask, "I believe your view is that in order for space/distance/point to exist in this universe, it must be constructed of something", "too many people will find it hard to abandon the notion of a background space that exists independent...

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It may be that I have to improve and make clearer the points I was trying to put across. Especially as you ask, "I believe your view is that in order for space/distance/point to exist in this universe, it must be constructed of something", "too many people will find it hard to abandon the notion of a background space that exists independent...

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Dear Akinbo,

It took me a while, but I'm finally getting back to you with my comments on your essay.

Many authors in this contest have stated that mathematics is necessarily unchanging ("timeless"), and they conclude from this that the fundamental nature of the physical world cannot be mathematical. I think your point of view of "perishable" mathematics is very interesting, and I agree with you that it is possible to conceive of mathematical structures that can be "born" and "perish". As I said in my reply to your post on my forum, I think it is possible to define a mathematical structure that is related to another structure that acts as a time-counter, and relative to that time-counter, the first structure can evolve, even appear and disappear. That's why I have no problem in believing that a physical universe that is born, evolves and ultimately perish can be thought as nothing more than a mathematical structure.

What you propose is original and ambitious, and as you say in your conclusion, it will be interesting to see if your hypothesis is falsifiable by real or thought experiments.

Good luck in the contest and in your future research!

Marc

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It took me a while, but I'm finally getting back to you with my comments on your essay.

Many authors in this contest have stated that mathematics is necessarily unchanging ("timeless"), and they conclude from this that the fundamental nature of the physical world cannot be mathematical. I think your point of view of "perishable" mathematics is very interesting, and I agree with you that it is possible to conceive of mathematical structures that can be "born" and "perish". As I said in my reply to your post on my forum, I think it is possible to define a mathematical structure that is related to another structure that acts as a time-counter, and relative to that time-counter, the first structure can evolve, even appear and disappear. That's why I have no problem in believing that a physical universe that is born, evolves and ultimately perish can be thought as nothing more than a mathematical structure.

What you propose is original and ambitious, and as you say in your conclusion, it will be interesting to see if your hypothesis is falsifiable by real or thought experiments.

Good luck in the contest and in your future research!

Marc

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Thanks for your comments Marc. Ultimately, what I have argued and tried put across is that whatever is given the attribute of existence must have the capability of the opposite, i.e. non-existence. If our universe perishes, nothing whether physical or mathematical will outlive it and the ball is in the court who propose the opposite to show the place and the manner how such timeless existence is exhibited.

Regards,

Akinbo

Regards,

Akinbo

Dear Akinbo,

Thank you for writing such an interesting essay.

What I get from it is that the real numbers are not a good model for physical space and physics in general. This leads to an interesting question: why does physics work so well with a bad model of it? Because of all the discrepancies you bring up between R and physics, why is it that R nevertheless works so well?

Another question. Much of physics can be rewritten with finite approximations. Is there some result in physics which demands the real numbers and would not work with a finite approximation?

Thank you again for a great essay.

All the best,

Noson

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Thank you for writing such an interesting essay.

What I get from it is that the real numbers are not a good model for physical space and physics in general. This leads to an interesting question: why does physics work so well with a bad model of it? Because of all the discrepancies you bring up between R and physics, why is it that R nevertheless works so well?

Another question. Much of physics can be rewritten with finite approximations. Is there some result in physics which demands the real numbers and would not work with a finite approximation?

Thank you again for a great essay.

All the best,

Noson

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Dear Noson,

Thanks for finding the time to comment on my essay.

As regards, your first query why the real number system works so well in spite of all the discrepancies highlighted in my essay. My initial answer would be that most models would work well, if adhoc entities are invented to fill the loop holes in the modelling, even though paradoxes, counter-intuitive notions and...

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Thanks for finding the time to comment on my essay.

As regards, your first query why the real number system works so well in spite of all the discrepancies highlighted in my essay. My initial answer would be that most models would work well, if adhoc entities are invented to fill the loop holes in the modelling, even though paradoxes, counter-intuitive notions and...

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Akinbo,

To answer your question about points there are discrete concepts of distance. A meter stick has discrete set of centimeter marks, and a discrete set of millimeter marks and so forth. We have no particular problem with integer distances or rational numbers that are distances. The subtle issue is with irranional numbers. An isosceles triangle with two lengths 1 and 45 degree angles has hypotenuse of sqrt{2}. You will not find this in a rational way. This gets one into the question of the continuum and how there are an uncountably infinite number of points between any two points. Dedekind made a point that one can find this point with an infinitely sharp “knife” that cuts perfectly.

The problem is that we are dealing with infinities and are not directly computable. To compute something means one can run this on a machine and find a numeric expression. However, numbers such as sqrt{2} have no such representation. We can only at best express them numerically with a numerical approximation.

This gets into my idea of mathematics having a body and soul, where the body involves things that can be physically computed, while the soul involves abstractions that can be infinite or infinitesimal. I am not committed to any existential properties of the “soul,” but the body of mathematics is what is transduced into physical quantities. There are some funny elements to this, such as whether the fine structure constant really has this property, or is it after so many decimal points uncertain.

LC

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To answer your question about points there are discrete concepts of distance. A meter stick has discrete set of centimeter marks, and a discrete set of millimeter marks and so forth. We have no particular problem with integer distances or rational numbers that are distances. The subtle issue is with irranional numbers. An isosceles triangle with two lengths 1 and 45 degree angles has hypotenuse of sqrt{2}. You will not find this in a rational way. This gets one into the question of the continuum and how there are an uncountably infinite number of points between any two points. Dedekind made a point that one can find this point with an infinitely sharp “knife” that cuts perfectly.

The problem is that we are dealing with infinities and are not directly computable. To compute something means one can run this on a machine and find a numeric expression. However, numbers such as sqrt{2} have no such representation. We can only at best express them numerically with a numerical approximation.

This gets into my idea of mathematics having a body and soul, where the body involves things that can be physically computed, while the soul involves abstractions that can be infinite or infinitesimal. I am not committed to any existential properties of the “soul,” but the body of mathematics is what is transduced into physical quantities. There are some funny elements to this, such as whether the fine structure constant really has this property, or is it after so many decimal points uncertain.

LC

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Thanks for looking in Lawrence. I left some questions on your forum, which you have answered in part here.

When you say here that*"A meter stick has discrete set of* 10^{-2}m *marks, and a discrete set of* 10^{-3}m *marks and so forth..."*

Thus this*and so forth* extend beyond the 10^{-35}m (Planck length limit)?

In our universe, we know from experience that there can be a line AB, along which for example Newton's first law tells us an object can move if not subjected to force. We also know that a sharp knife can be swung and cut through this line despite not being infinitely sharp and despite Calculus suggesting that the line contains an infinite number of points. Following from these, i.e. the observation that cutting of a line can take place in our universe without an infinitely sharp knife, and in spite of the supposed presence of an infinite number of points between A and B, would it be unreasonable to look at other ways that this cutting can be logically achieved without the sort of absurdities that Dedekind tried to avoid?

On the question of the continuum, would the fact that there can be no other point between two points not be sufficient to establish the continuum? I suggest if the points are "discrete concepts of distance" as you said, but there can be no other distance between two of these discrete concepts, then the continuum is established without appealing to an infinity of points. The remaining piece of the puzzle is, if distance cannot separate points, what can? It is here that we need to question whether points are eternally existing entities, and if not whether they have the same lifespan.

Best regards,

Akinbo

When you say here that

Thus this

In our universe, we know from experience that there can be a line AB, along which for example Newton's first law tells us an object can move if not subjected to force. We also know that a sharp knife can be swung and cut through this line despite not being infinitely sharp and despite Calculus suggesting that the line contains an infinite number of points. Following from these, i.e. the observation that cutting of a line can take place in our universe without an infinitely sharp knife, and in spite of the supposed presence of an infinite number of points between A and B, would it be unreasonable to look at other ways that this cutting can be logically achieved without the sort of absurdities that Dedekind tried to avoid?

On the question of the continuum, would the fact that there can be no other point between two points not be sufficient to establish the continuum? I suggest if the points are "discrete concepts of distance" as you said, but there can be no other distance between two of these discrete concepts, then the continuum is established without appealing to an infinity of points. The remaining piece of the puzzle is, if distance cannot separate points, what can? It is here that we need to question whether points are eternally existing entities, and if not whether they have the same lifespan.

Best regards,

Akinbo

Akinbo,

A good well presented essay on an important topic where poor or limited understanding has always prevailed. I think this situation did need 'flagging up' to help remove creeping complacency. You well identify those present limits of descriptive powers and identify the flaws.

I second your postulate, but with the proviso we are not ruling out 'disappear' from the...

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A good well presented essay on an important topic where poor or limited understanding has always prevailed. I think this situation did need 'flagging up' to help remove creeping complacency. You well identify those present limits of descriptive powers and identify the flaws.

I second your postulate, but with the proviso we are not ruling out 'disappear' from the...

view entire post

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Hi Peter,

Thanks for looking in. I appreciate your comments and consider them. When you talk of 'disappearing' possibly being implemented by 'dimensional orders', this is possible for a universe or for physicists who believe that there can be any number of dimensions ranging from 0 to even 10 in our universe. I for now believe that ALL that exists does so in 3 dimensions. A line with length, but without breadth or depth cannot exist in my model. Likewise, a surface, which is usually referred to as 2-dimensional for ease of analysis, but in reality if its thickness is zero, that surface cannot exist. You may want to show me one such surface which has no thickness yet exists :-)

I will check your essay this weekend. I had browsed through before but all this Bell's stuff getting me dizzy so I have left it to others. I however asked Gordon Watson to have a look at your essay and that of Edwin Klingmann because he seems to have a good grasp of what is involved. However, it appears you two have been in touch before and each has decided to stick only with his own model without compromise. Will look at your essay as I said and will rate appropriately.

Best regards,

Akinbo

Thanks for looking in. I appreciate your comments and consider them. When you talk of 'disappearing' possibly being implemented by 'dimensional orders', this is possible for a universe or for physicists who believe that there can be any number of dimensions ranging from 0 to even 10 in our universe. I for now believe that ALL that exists does so in 3 dimensions. A line with length, but without breadth or depth cannot exist in my model. Likewise, a surface, which is usually referred to as 2-dimensional for ease of analysis, but in reality if its thickness is zero, that surface cannot exist. You may want to show me one such surface which has no thickness yet exists :-)

I will check your essay this weekend. I had browsed through before but all this Bell's stuff getting me dizzy so I have left it to others. I however asked Gordon Watson to have a look at your essay and that of Edwin Klingmann because he seems to have a good grasp of what is involved. However, it appears you two have been in touch before and each has decided to stick only with his own model without compromise. Will look at your essay as I said and will rate appropriately.

Best regards,

Akinbo

Akinbo,

You seem to infer my hypothesis of 'smaller' states of motion than the limit for electromagnetic harmonic coupling may mean something other than "ALL that exists does so in 3 dimensions." Far from it. THAT is the big difference, and so consistent with just about all findings with no mysteries (i.e. the 'hyperfine' spin found in neutron interferometry).

It just needs thinking beyond current doctrinal assumptions; So called 'quantum spin' is then just the rotation of the charge which orbits in the 'spin-orbit coupling' of light. In a way it's perhaps rather arrogant of us to assume we can 'detect' all that can exist, so I say you're right with "disappear", but that may not imply other things 'beyond' that! In the same way can't assume the current observable limits of the universe are all there is. We know well that's untrue!

I must read Gordon's essay. We were in very close agreement about 'QM' previously. I suggest there's no mystery, it's all 3D and OAM, and show the it's the 'sock-switch' maths 'con trick' that confounds current doctrine.

Have you seen the video? Do you have 9 mins to spare yet?

Peter

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You seem to infer my hypothesis of 'smaller' states of motion than the limit for electromagnetic harmonic coupling may mean something other than "ALL that exists does so in 3 dimensions." Far from it. THAT is the big difference, and so consistent with just about all findings with no mysteries (i.e. the 'hyperfine' spin found in neutron interferometry).

It just needs thinking beyond current doctrinal assumptions; So called 'quantum spin' is then just the rotation of the charge which orbits in the 'spin-orbit coupling' of light. In a way it's perhaps rather arrogant of us to assume we can 'detect' all that can exist, so I say you're right with "disappear", but that may not imply other things 'beyond' that! In the same way can't assume the current observable limits of the universe are all there is. We know well that's untrue!

I must read Gordon's essay. We were in very close agreement about 'QM' previously. I suggest there's no mystery, it's all 3D and OAM, and show the it's the 'sock-switch' maths 'con trick' that confounds current doctrine.

Have you seen the video? Do you have 9 mins to spare yet?

Peter

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Hi Akinbo,

I enjoyed your thought provoking essay. Your proposed physics without conservation laws is I believe even more of an extreme revolution than the Instantaneous Action At A Distance principle that I am advocating. However it is indeed worthy of further thought.

My feeling that the measurable fundamental quantities (mass and charge) that we can detect and measure with Newtonian mutual interaction force laws are real and are conserved. The historical problem came with the development of the concept of Energy. I believe that energy is not fundamental but is rather a human engineering invention which acts a very convenient book keeping method of accounting for force and motion. It also displays a property which implies conservation of this quantity and this tool undoubtedly hastened the industrial revolution and got physicists interested in this industrial quantity. However even by the time of Einstein and Dirac, energy became conflated with mass and required an interpretation of what was meant by negative and disappearing energy. While retaining the dimensions of energy, new concepts entered into the conservation of what was always a man made quantity. Now logically you seem to make a case that if we continue to use the current definitions of all of the supposedly conserved quantities we run into contradictions implying the failure of current theories.

I have not had time to really study your argument, but would it be true that if energy conservation was not as fundamental as the conservation of Newtonian mass and charge (ie no Special and General Relativity) then maybe we could retain conservation as a bedrock of physics?

Your essay demonstrates that there is much to discuss further in this area where physics meets philosophy. Well Done.

Regards

Neal Graneau

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I enjoyed your thought provoking essay. Your proposed physics without conservation laws is I believe even more of an extreme revolution than the Instantaneous Action At A Distance principle that I am advocating. However it is indeed worthy of further thought.

My feeling that the measurable fundamental quantities (mass and charge) that we can detect and measure with Newtonian mutual interaction force laws are real and are conserved. The historical problem came with the development of the concept of Energy. I believe that energy is not fundamental but is rather a human engineering invention which acts a very convenient book keeping method of accounting for force and motion. It also displays a property which implies conservation of this quantity and this tool undoubtedly hastened the industrial revolution and got physicists interested in this industrial quantity. However even by the time of Einstein and Dirac, energy became conflated with mass and required an interpretation of what was meant by negative and disappearing energy. While retaining the dimensions of energy, new concepts entered into the conservation of what was always a man made quantity. Now logically you seem to make a case that if we continue to use the current definitions of all of the supposedly conserved quantities we run into contradictions implying the failure of current theories.

I have not had time to really study your argument, but would it be true that if energy conservation was not as fundamental as the conservation of Newtonian mass and charge (ie no Special and General Relativity) then maybe we could retain conservation as a bedrock of physics?

Your essay demonstrates that there is much to discuss further in this area where physics meets philosophy. Well Done.

Regards

Neal Graneau

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Thanks Neal for your comments. Actually, there is obedience to the most fundamental conservation in what I describe. Perhaps, you will agree that displacement as an entity is more fundamental than energy, momentum, mass, charge, etc or you may not agree. But in motion and in Action at a distance, displacement is conserved. That is, in attraction or repulsion between bodies, the amount of displacement created or destroyed between bodies for repulsion or attraction respectively IS EQUAL TO the amount of displacement destroyed or created respectively outside the bodies in the line of interaction.

From my cosmological perspective, nothing is ultimately conserved or stated in an alternative way, the sum of all being sought to be conserved is zero. That is why the universe can emerge from Nothing and expand, which Universe, when you add all the plus and minus side still sums to zero. Trying not to digress outside the topic here but can give a link to my tentative model, if you are interested. If the Universe starts from zero, is currently zero and will end up zero, then no mathematical laws are broken. In my model, Mass is + and Radius is -, both summing to zero. As the universe starts from zero mass and zero radius, both M and R increase in tandem. The thermal history of the Big bang model of the Universe bears this out. Mass increases with radius. No point containing all the mass now in the universe from Day one - an absurdity, if I may call it so.

Regards,

Akinbo

From my cosmological perspective, nothing is ultimately conserved or stated in an alternative way, the sum of all being sought to be conserved is zero. That is why the universe can emerge from Nothing and expand, which Universe, when you add all the plus and minus side still sums to zero. Trying not to digress outside the topic here but can give a link to my tentative model, if you are interested. If the Universe starts from zero, is currently zero and will end up zero, then no mathematical laws are broken. In my model, Mass is + and Radius is -, both summing to zero. As the universe starts from zero mass and zero radius, both M and R increase in tandem. The thermal history of the Big bang model of the Universe bears this out. Mass increases with radius. No point containing all the mass now in the universe from Day one - an absurdity, if I may call it so.

Regards,

Akinbo

Dear Akinbo,

This is true:

"The non-zero dimensional point does not have an eternal existence, but can

appear and disappear spontaneously, or when induced to do so "

Previously produced many questions, such as:

What is the distribution of the duration of the non-zero-dimensional points (particles)?

Why proton has a very long duration?

Why there are fermions and bosons?

What kind of divisions is allowed in physics? ...

You explained it, to a large extent, and you'll get a high rating. I invite you to comment my essay.

Regards,

Branko

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This is true:

"The non-zero dimensional point does not have an eternal existence, but can

appear and disappear spontaneously, or when induced to do so "

Previously produced many questions, such as:

What is the distribution of the duration of the non-zero-dimensional points (particles)?

Why proton has a very long duration?

Why there are fermions and bosons?

What kind of divisions is allowed in physics? ...

You explained it, to a large extent, and you'll get a high rating. I invite you to comment my essay.

Regards,

Branko

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Dear Akinbo,

After reading your essay for me there is one key take away, namely that to quantize something (in this case space) it would make sense to have something acting like a separator. In my opinion, the experiments showing that the spacetime is smooth and not discrete are very convincing, but it is a completely different matter to see this principle formulated in terms of sufficient reason. It is very surprising and nice to understand it from this point of view. I hope you do carry on with your research, for which I am rating your essay accordingly.

Warm regards,

Alma

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After reading your essay for me there is one key take away, namely that to quantize something (in this case space) it would make sense to have something acting like a separator. In my opinion, the experiments showing that the spacetime is smooth and not discrete are very convincing, but it is a completely different matter to see this principle formulated in terms of sufficient reason. It is very surprising and nice to understand it from this point of view. I hope you do carry on with your research, for which I am rating your essay accordingly.

Warm regards,

Alma

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Dear Akinbo,

thanks for reading my essay and the comment. In principle, I agree with you that there is no real infinity. As you I see it as a concept to an value which can be arbitrarily large (but not fixed).

Certainly, if there is a conflict between physics and math I would prefer physics (if it is experimentally confirmed). But I think it is unlikely.

I also read your essay and rate them higher (8 points) but with no real effect on the number.

Good look for the contest

Torsten

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thanks for reading my essay and the comment. In principle, I agree with you that there is no real infinity. As you I see it as a concept to an value which can be arbitrarily large (but not fixed).

Certainly, if there is a conflict between physics and math I would prefer physics (if it is experimentally confirmed). But I think it is unlikely.

I also read your essay and rate them higher (8 points) but with no real effect on the number.

Good look for the contest

Torsten

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Akinbo,

You referred to Gordon Watson's essay in discussing mine. I did indeed find it consistent, if the maths slightly too complex for me! Gordon has also now made very generous comments supporting mine and we're discussing others.

I see I have my 'minute of fame' at the top, which is far too early for the tape and last minute bun fight so all scores welcomed! I still think yours is under rated and see it's near the cusp. (I checked and yes I did rate it).

Very best of luck in the run in.

Peter

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You referred to Gordon Watson's essay in discussing mine. I did indeed find it consistent, if the maths slightly too complex for me! Gordon has also now made very generous comments supporting mine and we're discussing others.

I see I have my 'minute of fame' at the top, which is far too early for the tape and last minute bun fight so all scores welcomed! I still think yours is under rated and see it's near the cusp. (I checked and yes I did rate it).

Very best of luck in the run in.

Peter

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Dear Akinbo,

Contests FQXi - is primarily a competition for new ideas. You give such ideas. Your ideas are close to me in spirit, to overcome the split basis of fundamental science and the the "LifeWorld" (E.Husserl). My high score. It is always interesting to discuss with you on the forum.

I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld", as a picture of the world poets and philosophers. Today, more than ever, are relevant philosophical covenants of A. Einstein and J. Wheeler:

"Presently the physicist is compelled to deal with philosophical problems in much bigger degree, than it had to be done to physics of the previous generations. To it physicists are compelled by difficulties of their own science." "Philosophy is too important to be left to the philosophers."

Kind regards,

Vladimir

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Contests FQXi - is primarily a competition for new ideas. You give such ideas. Your ideas are close to me in spirit, to overcome the split basis of fundamental science and the the "LifeWorld" (E.Husserl). My high score. It is always interesting to discuss with you on the forum.

I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld", as a picture of the world poets and philosophers. Today, more than ever, are relevant philosophical covenants of A. Einstein and J. Wheeler:

"Presently the physicist is compelled to deal with philosophical problems in much bigger degree, than it had to be done to physics of the previous generations. To it physicists are compelled by difficulties of their own science." "Philosophy is too important to be left to the philosophers."

Kind regards,

Vladimir

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Hi Akinbo,

Thanks for kindly commenting in my forum, and for voting me up. The bottom line on our disagreement about mathematics and philosophy is also the bottom line of your essay: "I ... move the motion that we exorcise the lingering millennia old Parmenidean spell on our mathematics and physics and allow that what exists can perish. Nothing is ultimately conserved."

I draw the line at "existence exists" as the necessary and sufficient foundation of logic -- I'll concede Aristotle and even Parmenides that much. :-)

Even though I regard your philosophy as nihilistic, I'll give you as much credit as I give Aristotle for being entertaining as well as provocative!

Best,

Tom

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Thanks for kindly commenting in my forum, and for voting me up. The bottom line on our disagreement about mathematics and philosophy is also the bottom line of your essay: "I ... move the motion that we exorcise the lingering millennia old Parmenidean spell on our mathematics and physics and allow that what exists can perish. Nothing is ultimately conserved."

I draw the line at "existence exists" as the necessary and sufficient foundation of logic -- I'll concede Aristotle and even Parmenides that much. :-)

Even though I regard your philosophy as nihilistic, I'll give you as much credit as I give Aristotle for being entertaining as well as provocative!

Best,

Tom

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Dear Akinbo,

I finally got to read your essay. Since it deals with a subject matter on which I am not expert, I can not make definitive assertions, but I may be able to help direct you towards potentially fruitful directions.

1) I have the impression that subject matter of your essay is most directly covered by measure theory. Indeed there are "pathological" measures which may be useful in considering these sorts of problems. One is the Cantor set, which has measure zero but contains an uncountable number of points. There are others, and they may inform your view on this matter.

2) Until I took set theory I had no appreciation (and I think this is also true for almost everyone else, including physicists) that any real number, say, 1, is a completely different animal from its natural number counterpart. Learning how to represent these numbers by sets teaches one to appreciate the difference. In short while each natural number can be considered as a single object, each real number is an infinity unto itself. Our notation helps bring about the failure to appreciate this: if we wanted to properly notate, say, the real number 1, we would have to write 1.0000000000000000000000000000000000000000000000000... stretching over an infinite distance. I think this distinction may have some bearing on your arguments.

3) Your example involving Lagos and New York reminded me of the Alcubierre metric.

4) You may also want to consider how your arguments turn out in other kinds of geometries, like the projective geometry, for example.

Again, I regret that I could not say anything definitive about your ideas, but I hope that you found my pointers useful.

Best wishes,

Armin

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I finally got to read your essay. Since it deals with a subject matter on which I am not expert, I can not make definitive assertions, but I may be able to help direct you towards potentially fruitful directions.

1) I have the impression that subject matter of your essay is most directly covered by measure theory. Indeed there are "pathological" measures which may be useful in considering these sorts of problems. One is the Cantor set, which has measure zero but contains an uncountable number of points. There are others, and they may inform your view on this matter.

2) Until I took set theory I had no appreciation (and I think this is also true for almost everyone else, including physicists) that any real number, say, 1, is a completely different animal from its natural number counterpart. Learning how to represent these numbers by sets teaches one to appreciate the difference. In short while each natural number can be considered as a single object, each real number is an infinity unto itself. Our notation helps bring about the failure to appreciate this: if we wanted to properly notate, say, the real number 1, we would have to write 1.0000000000000000000000000000000000000000000000000... stretching over an infinite distance. I think this distinction may have some bearing on your arguments.

3) Your example involving Lagos and New York reminded me of the Alcubierre metric.

4) You may also want to consider how your arguments turn out in other kinds of geometries, like the projective geometry, for example.

Again, I regret that I could not say anything definitive about your ideas, but I hope that you found my pointers useful.

Best wishes,

Armin

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Dear Akinbo,

You have presented a very interesting essay. I like how you take special care in distinguish the context of mathematics and physics in order to discuss your ideas. Moreover, you are able to analyse this different context and arrive to the conclusion that the meaning in both areas is different. I think that is a very good philosophical work.

As a matter of speculation, is your essay supporting the idea that space and time must be discrete?

Kind Regards,

Yafet

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You have presented a very interesting essay. I like how you take special care in distinguish the context of mathematics and physics in order to discuss your ideas. Moreover, you are able to analyse this different context and arrive to the conclusion that the meaning in both areas is different. I think that is a very good philosophical work.

As a matter of speculation, is your essay supporting the idea that space and time must be discrete?

Kind Regards,

Yafet

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An enjoyable read Akinbo..

I thought your reasoning was very tight, until some point near the end where an unwarranted conclusion or two slip in. But I'd have to read again for detail, to point out any error or false claim, and I must instead move on to a few more essays.

All the Best,

Jonathan

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I thought your reasoning was very tight, until some point near the end where an unwarranted conclusion or two slip in. But I'd have to read again for detail, to point out any error or false claim, and I must instead move on to a few more essays.

All the Best,

Jonathan

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About the finite divisibility of physical objects: rather than the need of a distance interval to insert in a division, mentioning atoms as roughly indivisible parts of material objects, would be more directly clear, wouldn't it ?

"there is a limit to the number of extended points or fundamental lengths, but there is also no distance between those points, since that distance will also...

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"there is a limit to the number of extended points or fundamental lengths, but there is also no distance between those points, since that distance will also...

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Akinbo,

I have been thinking more about your question. It seems to me that the problem reduces to whether or not integer numbers are a subset of real numbers. Here is what I mean by this ... integer numbers are treated as though they have an infinite amount of precision ... i.e., 1 is equal to 1.0000000000 ad infinitum. Most measurements are real numbers of some sort and they have a fixed amount of precision ... such as 1 inch = 2.54 centimeter or something similar. So, if it is possible for a real number to have an infinite amount of precision, then space can be infinitely divided. If integers are a subset of reals and integers have infinite precision, then reals should also have infinite precision. I was taught that integers are a subset of the reals ... but perhaps that is not actually true.

Best Regards and Good Luck,

Gary Simpson

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I have been thinking more about your question. It seems to me that the problem reduces to whether or not integer numbers are a subset of real numbers. Here is what I mean by this ... integer numbers are treated as though they have an infinite amount of precision ... i.e., 1 is equal to 1.0000000000 ad infinitum. Most measurements are real numbers of some sort and they have a fixed amount of precision ... such as 1 inch = 2.54 centimeter or something similar. So, if it is possible for a real number to have an infinite amount of precision, then space can be infinitely divided. If integers are a subset of reals and integers have infinite precision, then reals should also have infinite precision. I was taught that integers are a subset of the reals ... but perhaps that is not actually true.

Best Regards and Good Luck,

Gary Simpson

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Dear Gary,

Thanks for your interest and comment. You are likely a better mathematician than myself but let me answer as best as I can.

By the statement, "if it is possible for a real number to have an infinite amount of precision, then space can be infinitely divided", I take it that if a real number CANNOT have an infinite amount of precision, then space cannot be infinitely...

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Thanks for your interest and comment. You are likely a better mathematician than myself but let me answer as best as I can.

By the statement, "if it is possible for a real number to have an infinite amount of precision, then space can be infinitely divided", I take it that if a real number CANNOT have an infinite amount of precision, then space cannot be infinitely...

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Akinbo,

First, let me offer congratulations. It looks like you will make the finals. It is odd that no announcement has been made.

Regarding my statement ... "If it is possible for a real number to have an infinite amount of precision, then space can be infinitely divided" ... The logical contrapositive is ... "If space cannot be infinitely divided then real numbers cannot have...

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First, let me offer congratulations. It looks like you will make the finals. It is odd that no announcement has been made.

Regarding my statement ... "If it is possible for a real number to have an infinite amount of precision, then space can be infinitely divided" ... The logical contrapositive is ... "If space cannot be infinitely divided then real numbers cannot have...

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Akinbo,

As requested, I've read the text of the SR essay that you provided. Firstly, let me state that I do not consider myself to be very knowledgeable regarding SR. I am aware of the paradoxes and I studied the subject very briefly in a Physics class in college. People who take a degree in Physics dedicate an entire semester or more to the subject. My background includes only a few...

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As requested, I've read the text of the SR essay that you provided. Firstly, let me state that I do not consider myself to be very knowledgeable regarding SR. I am aware of the paradoxes and I studied the subject very briefly in a Physics class in college. People who take a degree in Physics dedicate an entire semester or more to the subject. My background includes only a few...

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Gary,

I will incorporate some of your advice into any possible paper that may develop. Many thanks for your very useful comments.

Generally speaking, and based on my understanding Galilean relativity predict that the two photons will return in 2 years, but Special relativity does not permit the addition of velocities to be above c, and so in that case the photons will return in 3 years. All in all I am satisfied with your comment.

Regards,

Akinbo

I will incorporate some of your advice into any possible paper that may develop. Many thanks for your very useful comments.

Generally speaking, and based on my understanding Galilean relativity predict that the two photons will return in 2 years, but Special relativity does not permit the addition of velocities to be above c, and so in that case the photons will return in 3 years. All in all I am satisfied with your comment.

Regards,

Akinbo

Akinbo,

The value of two years is based upon reference frame O. The three year value that you use mixes reference frame O on the trip to the mirrors and the reference frame of the photons on the trip back. You must use the same reference frame for both parts of the journey.

Good Luck,

g

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The value of two years is based upon reference frame O. The three year value that you use mixes reference frame O on the trip to the mirrors and the reference frame of the photons on the trip back. You must use the same reference frame for both parts of the journey.

Good Luck,

g

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Greetings Akinbo -

Are you close to Lagos? I passed through to catch a cheap flight to New York and then my home in Louisville KY on returning from Peace Corps service building fish ponds in Cameroon in 1992. Hope the maniacal Boko Haram menace poses no direct threat to your life and work.

Pardon my long delay in replying to your comment (repeated below) on my Trick or Truth essay,...

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Are you close to Lagos? I passed through to catch a cheap flight to New York and then my home in Louisville KY on returning from Peace Corps service building fish ponds in Cameroon in 1992. Hope the maniacal Boko Haram menace poses no direct threat to your life and work.

Pardon my long delay in replying to your comment (repeated below) on my Trick or Truth essay,...

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