Modeling the Physical World with Common Sense and Mathematics by David Hestenes

David Hestenes

Thanks for your probing queries, Tejinder.

I will not repeat them in my answers, but you can correlate them by paragraph.

You have identified my basic claim about the common ground for physics and mathematics in intuition. Beyond that there are many details, and one should look at specific cases. I suggest you look at my reply to rukhsan ul haq wani for examples. There is more about Grassmann in my reference [29].

Lakoff is a major figure in cognitive linguistics, especially for his work on metaphors.

He demonstrates how metaphors play a crucial role in cognition. Unfortunately, I had to eliminate comments on that to meet the character limit on my essay. But many details are given in my reference [3].

GA is a tool -- deliberately designed to integrate algebra and geometry, and thereby facilitate geometric intuition. The published literature on GA testifies to its effectiveness in this domain.

Evidently you have not looked deeply enough at my papers to see that I make strong and unique claims about the relevance of GA to the foundations of quantum mechanics. Look at my ref. [22], which has the same web address as [21]. I demonstrate that GA reveals hidden geometric structure in the Dirac equation that relates electron spin to complex numbers in quantum mechanics in an essential way. I believe this shows you will never get to the bottom of quantum mechanics from the Schroedinger equation. You might also like to look at my essay "Electron time, mass and zitter," which got second prize in a previous FQXi contest.

Now I must take a look at your essay.

.........David H.

David Hestenes

Thanks for your probing queries, Tejinder.

I will not repeat them in my answers, but you can correlate them by paragraph.

Lakoff is a major figure in cognitive linguistics, especially for his work on metaphors.

GA is a tool -- deliberately designed to integrate algebra and geometry, and thereby facilitate geometric intuition. The published literature on GA testifies to its effectiveness in this domain.

Now I must take a look at your essay.

.........David H.

David Hestenes

Good to hear about your work, Al.

From your note, it looks to be in complete accord with Modeling Theory,

and I believe it can be a boon to teaching that is enlightening as well as entertaining.

As you know there is a huge psychology literature on how our expectations shape what we see. As you know, there is no psychology in the K-12 curriculum, and I have long been wondering how to squeeze it in. Maybe magic is the way to go!.

Modeling Theory has generated what is arguably to most effective and widely used approach to STEM education. To learn more about it, check out: modelinginstruction.org

Actually, I don't agree that physicists are forced by opinion leaders to "use only mathematical models and avoid models depending on imagery." I suppose you are referring to opinions that "the mechanisms of quantum mechanics cannot be visualized." While many competent physicists take that point of view, I assure you that visualization plays a crucial role in their practice of physics. The debate on the foundations of quantum mechanics is by no means settled.

..........David H.

David Hestenes

Dear Panjak,

I agree with your assertion that "Mathematical structures have no independent existence without physical reality."

Your assertion that "Everything in Universe including mathematical structures and physical reality is Vibration" may be an interesting hypothesis, but it lacks adequate scientific support.

David Hestenes

I do not see any inconsistency in your relations among physical constants.

But I am reminded of Arthur Eddington's comment:

"I won't believe the experiment until it is confirmed by theory."

Pankaj Mani

Dear David,

Let me quote scientifically the role of Vibration.That which we call matter and mind are one and the same substance. The only difference is in the degree of vibration. Mind at a very low rate of vibration is what is known as matter. Matter at a high rate of vibration is what is known as mind. Both are the same substance; and therefore, as matter is bound by time and space and causation, mind which is matter at a high rate of vibration is bound by the same law. Mind becomes matter, and matter in its turn becomes mind, it is simply a question of vibration.

It's the hypothesis that requires to be explored further more scientifically.

Regards,

Pankaj Mani

Jose Koshy

Dear Prof. David Hestenes,

Your essay is factual, and educative. From 'commonsense' to 'thinking' to 'modeling' it portrays a clear path of evolution. Quoting from your essay, "CS concepts should be regarded as alternative hypotheses about the physical world that, when clearly formulated, can be tested empirically." "Thinking is a hardwired human ability to freely create mental models and use them for planning and controlling interactions with the physical world." "the transition from common sense to scientific thinking is not a replacement of CS concepts with scientific concepts, but rather a realignment of intuition with experience."

I completely agree with your view, "Likewise the tools of mathematics were invented, not discovered; though it may be said that theorems derived from structures built with those tools are discovered." In my opinion, there indeed need be just one law in mathematics, the law of addition; it is eternal. The structures are based on this fundamental law and are invented; the theorems derived from the structures follow the fundamental law, and are discovered.

You ask the question, "What accounts for the ubiquitous applicability of mathematics to science? You suggest co-evolution of physics and mathematics as the possible reason." I think it is more fundamental than mere co-evolution: A static world does not have any 'laws'. The only role of law is governing changes. Changes can happen by way of 'motion' only. Motion follows mathematical laws. Thus, all the changes in the physical world follow mathematical laws. That is why mathematics is applicable to science, the study of the physical world. The co-evolution is thus predetermined.

I would like to draw your attention to my essay: A physicalist interpretation of the relation between Physics and Mathematics, and my site: finitenesstheory.com.

David Hestenes

Hello Jose,

Here are a few comments on your essay from the point of view of mine.

"Any explanation of the physical world should start from the description of the background . . . The background description is based entirely on direct observation"

There is no such thing as direct observation, only indirect perception.

"So the fact that the physical world changes with time indicates that motion is a property of the physical world."

I agree that motion is fundamental. For more see my "Modeling Games" reference [5] and compare it with what you say about Newton.

"Thus, in explaining the physical world, there should be a clear distinction between properties and laws: properties should be physical

and laws should be mathematical."

I agree with this, but think you slip up when you say:

'Mathematics governs the changes in the physical world'.

Rather, mathematics can be applied to model changes in the physical world.

The relation of properties to laws is an analogy. The laws change as we learn more, but the physical properties remain what they are.

Jose Koshy

Dear Prof. David Hestenes,

Quoting You, "There is no such thing as direct observation, only indirect perception". This indicates our difference in approach or perception regarding the nature of the physical world. I think the physical world is real and we are also real, and our sensory organs are designed to observe this reality to the extent required, and so the physical structures we observe directly are real and not merely a perception.

Given the basic properties, it is mathematical laws that decide the emergent structures. The emergent properties of the structures depend both on the structure and the basic properties. Mathematical laws again decide the next level structures and so on. All these can happen only if motion is one of the basic properties; otherwise there will not be any changes, and hence no laws. This is what I mean by saying, 'Mathematics governs the changes in the physical world'. And, that is the reason why "mathematics can be applied to model changes in the physical world".

"The laws change as we learn more". Do you mean that laws 'actually' change? Or, is it that you meant the changes happen in our 'perception' regarding the law?

Tejinder Singh

Dear Professor Hestenes,

Many thanks for your detailed response. We will study your Refs. [22], [29] as also your 2008 FQXi essay.

Tejinder

Joe Fisher

Dear Professor Hestenes,

Could you please explain to me why you thought that my comment about the real Universe was inappropriate?

You are I hope aware that suppression of the truth is unethical.

Eagerly awaiting your answer,

Joe Fisher

David Hestenes

Sorry Joe,

It was my post that was inappropriate, because it was intended for someone else and I pasted it in the wrong box. When I tried to remove it, your post was expunged and I lost your contact.

When I get your original post back I will reply.

.......David

Joe Fisher

Dear Professor Hestenes,

You wrote: "As we grow and learn through everyday experience, each of us develops a system of common sense (CS) concepts about how the world works."

This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING. Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies he has observed is unique as to its structure and its perceived distance from all other real galaxies. Each real star is unique as to its structure and its perceived distance apart from all other real stars. Every real scientist who has peered at real snowflakes through a real microscope has concluded that each real snowflake is unique as to its structure. Real structure is unique, once. Unique, once does not consist of abstract amounts of abstract quanta. Based on one's normal observation, one must conclude that all of the stars, all of the planets, all of the asteroids, all of the comets, all of the meteors, all of the specks of astral dust and all real objects have only one real thing in common. Each real object has a real material surface that seems to be attached to a material sub-surface. All surfaces, no matter the apparent degree of separation, must travel at the same constant speed. No matter in which direction one looks, one will only ever see a plethora of real surfaces and those surfaces must all be traveling at the same constant speed or else it would be physically impossible for one to observe them instantly and simultaneously. Real surfaces are easy to spot because they are well lighted. Real light does not travel far from its source as can be confirmed by looking at the real stars, or a real lightning bolt. Reflected light needs to adhere to a surface in order for it to be observed, which means that real light cannot have a surface of its own. Real light must be the only stationary substance in the real Universe. The stars remain in place due to astral radiation. The planets orbit because of atmospheric accumulation. There is no space.

Warm regards,

Joe Fisher

David Hestenes

You do indeed nicely articulate a coherent common sense view of how the world works.

I part company with you when you say:

"Each real object has a real material surface that seems to be attached to a material sub-surface."

I would say "perceived object" instead of "real object." The rest of your account is coherent from a CS point of view, but it is inconsistent with the science of light and vision.

Respectfully......David H.

Joe Fisher

Dear Professor Hestenes,

FQXi.org has labeled my work "OBNOXIOUS SPAM," and removed it from several sites where I had posted it.

Sir, do you have a real complete skin surface? Does every animal, insect, and can of soda have a real complete surface? It is physically impossible to perceive a single real surface. No matter in which direction one looks, one will only ever see a plethora of real surfaces. At each point where surfaces touch, a real sub-surface forms. All surface travels at the same constant speed. Each sub-surface travels at a unique speed that remains less than the constant speed of surface. That is why although everything is traveling at the same speed, each object remains in its own unique position.

Grateful that you read my comment and at least made an answer to it.

Joe Fisher

Jayakar Joseph

Dear David,

In a biological system the signal transduction is causal for sensing, processing and retaining the knowledge acquired from its environment; in that, the electro chemical units that is causal for the formation of Mind with sensible Phenomena and the non-sensible Noumena coined by Kant, are the mathematical units only.

In relevant to this science behind Epistemology, I think, whatever the mathematical or physical model we inspire, there is a link between Physics and Mathematics by nature.

With best wishes,

Jayakar

David Hestenes

Dear Jayakar,

If I understand you correctly, I agree. The Brain is the Noumena from which the Phenomena of Mind emerges. In other words, the Mind (conscious or unconscious) is a state of matter, the Brain. To explain how is, perhaps, the ultimate challenge of science.

I believe that will require some version of statistical mechanics, to explain how "macro" states of Mind emerge from "micro" Brain states. It is clear that there are many more degrees of freedom in Brain states than in Mind states, so Mind states must emerge as some sort of cooperative phenomena. The ultimate objective of my Modeling Theory of Mind is to describe the structure of Mind (states) with sufficient precision so we know what we are trying to explain with models of Brain states.

The link between physics and mathematics in nature boils down to the fact that there are regularities (patterns) in nature discovered by physics, and mathematics has been developed as a science of patterns.

Thanks for your comment......David

Rick Lockyer

Thanks so much for responding.

I have a difficult time seeing how a non-associative algebra could ever be a subalgebra of an associative algebra, since selective zero valued coefficients applied within the associative algebra clearing out all but the chosen subalgebra basis elements would necessarily still need to be associative. Certainly one may go the other way where there are 7 associative quaternion subalgebras within the non-associative octonion algebra.

You might find my 2012 FQXi essay The Algebra of Everything interesting. The algebraic structure of octonion algebra gives us clues on how the equations describing nature must look and actually do conform to the idea that there is no preferred definition for octonion algebra. This means observables are invariant to all possible chiral changes after singularly enumerating the quaternion associative triplets. I have demonstrated the the divergence of the stress-energy-momentum forms for electrodynamics are but a subset of the full octonion (non-tensor) representation, mandated to be what they must be by enforcing octonion algebraic invariance, as it must in a more inclusive approach. The Lorentz transformation falls out of restricting the two portions of each field component to transform in kind. Look at the essay, and if you are interested, drop me an email and I will send you a PDF of my in progress book that goes well beyond the limited essay. It is not and can't be your GA since you seem to insist on associative product structure. I think it is superior since it is a successful representational structure that is mandated by the octonion algebra itself and not by hand inserted. I think octonion algebra itself could be considered a "geometric algebra", just not yours.

Thanks and with much respect,

Rick

Edwin Klingman

Dear David Hestenes,

Thank you for your kind words on my essay. I do not expect to convince many people that Bell is wrong with my essay. My hope is that I will convince a number of people that Bell may be wrong, based on my analysis. This would represent a very significant change from today's situation, in which Bell's conclusions are stated as fact. I believe that time and effort spent on understanding my theory will call Bell's physical assumptions into question, and I have faith that once the questioning begins, the right answer will be forthcoming.

Thank you for introducing ET Jaynes Probability Theory: the Logic of Science. Like you I regard his as one of the greatest books of the 20th century, and I treat him in my 2013 FQXi essay, Gravity and the Nature of Information, which you might also find interesting. It is a little more "blue sky" than my current essay but one Jaynes quote from that essay is well suited to my current essay on Bell, to wit:

"... a false premise built into a model which is never questioned cannot be removed by any amount of data."

In closing, I thank you yet again for Geometric Algebra, Space-Time Algebra, and all the rest of your work. You have contributed well to mankind.

Edwin Eugene Klingman

Mohammed Khalil

Dear Prof. Hestenes,

Wonderful essay! I agree with your arguments, and enjoyed reading them. I share some of your views in my essay. I would be honored to have your opinion.

Best regards,

Mohammed

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