Calculus - Revision 2.0 by Gary D. Simpson

Dear Garry D Simpson,

Thank you for having read my essay. I downloaded your essay weeks before (based on the abstract), but found it be just mathematics. Verifying your arguments require some effort, and so I took the easiest route - avoiding any comments.

My opinion is that any theory in physics should be verbally explainable, and treating mathematics as the most appropriate language for explaining the physical world is incorrect. Any concept that 'has physical meaning' and that 'does not go against commonsense' will be verbally explainable.

However, any physical model should be mathematically viable. The simplest and the most suitable mathematical form should be used for this. Even then, venturing into new mathematical ideas, even if complex, is something that has a beauty of its own. You have stated that some original work has been done by you in the field of quaternion functions. I will try to follow your papers in vixra.

Hi Gary,

Do you think it is possible that we may be living in a finite and discrete universe that could be described in an informational way? Do you think we could make more progress in our understanding of physics if we looked towards computer programs/simulations, instead of new sets of math equations, for explaining phenomenon? How much complexity do you think is in the universe, and how much of it is compressible?

Please check out my Digital Physics movie essay if you get the chance.

Thanks,

Jon

Dear Gary,

I've replied to your nice post in my Essay Forum. Points that are relevant to your work here are reproduced below:

4. Geometric Algebra is peeking its head out regarding the beables and their local values.

I am so glad that you see that! Please be the first to help that shy, beautiful (and sometimes tricky) GA out of the closet and work with her in the unified "BT" context proposed in my essay. For I'd love to see elementary GA taught in primary schools: with GA on its way to becoming Nature's local realistic Mathematics.

5. Re GA.

How is your work received within the GA community? Have you any rejections from journals? If so, what do they say? (Write to me privately if you wish.)

Are you familiar with Elio Conte's efforts? For example: Conte, E. (2001). Biquaternion Quantum Mechanics. Bologna, Pitagora Editrice? (Alas, he supports nonlocality!)

How about this Caves, Fuchs, Schack essay [arxiv.org/pdf/quant-ph/0104088v1.pdf] and the view that amplitudes should be complex numbers rather than reals or quaternions?

With best regards, and looking forward to spending time with your important ideas.

Gordon Watson: Essay Forum. Essay Only.

Dear Gary,

I enjoyed reading your derivation and very much agree that Newton was very close to the framework of SR, had it not been for his intuition that space needs to be fixed. I noticed you worked during Christmas (given the date on the document), therefore around Newton's birthday. I am sure he would have been proud to know that people have something to say about his work after four hundred years since it was finished.

Wish you best of luck in the contest!

Alma

Hi Gary,

Thanks for your response on my post. You said, "I think the universe is finite. I cannot say anything about whether or not it is discrete. I'm not even sure how the word "discrete" would be applied to the universe. Is the universe a discrete solution to a massive system of wave equations? Some people argue that the wave equation for a Bose-Einstein condensate at 2.7 K describes the universe."

Here are my thoughts:

I'm not sure if you could actually have a continuous universe that was finite. I assume you are imaging a continuous universe that is bounded by something, say the observable universe or something like that. Here's a math analogy that might illustrate my point: You might say that the interval of real numbers between 0 and 1 is continuous and finite, but I would say that you have the infinite in the form of the infinitesimal because you implicitly believe in infinite precision non-computable real numbers when you believe in the continuum. Infinite precision non-computable real numbers are what make up the continuum in a mathematical sense. Computable reals which include numbers like pi and e (as well as fractions) have a measure 0.

A discrete universe would rule out a continuous wave, just like a computer couldn't actually contain the infinite amount of information needed to represent every point on a curve, although a computer could contain a finite algorithm (e.g. a wave equation) to generate the wave to any desired level of accuracy... It just can't contain the non-compuable, which is what makes the continuum the continuum.

I'm interest to hear your thoughts on this perspective. If you could post a notice in my forum when you respond so I know when to check back that would be helpful.

Jon

Dear Gary,

The math was not very easy for me since I don't have the right background, but I was able to understand it and your work actually helped my understanding very much. It took me maybe three hours to go through it and make sure I really feel the argument. There were some things that I didn't know about the framework and that I was able to guess because of the clarity of your presentation. You should at least consider to publish it in a pedagogical journal because there are many people out there who would benefit from reading it, especially students.

My sincerest appreciation! :-)

Alma

Dear Gary,

Thank you for your post on my thread.

I posted a reply.

Cheers,

Patrick

Dear Gary,

My belief is that your excellent essay is worthy of more attention than it has received. I still have not had the free time to work through your derivations to convince myself, but I see nothing to suggest you made any mistakes. I hope that you continue to develop your ideas and I wish to reiterate that I think you will find David Hestenes' Geometric Algebra papers (and books) quite relevant to your interest.

My best regards and appreciation for your comments and kicking the Hornets nest.

Edwin Eugene Klingman

Gary Simpson,

Studying your paper makes me realize just how much dedication you have. You are so determined to learn and apply Quaternions. Even your many thoughtful comments on other essays show what a [u]Scholar and a Gentleman[/u] you truly are. I catch myself thinking: "Heh! When I grow up -- I'd like to be like this Gary Simpson guy!"

You have succeeded in taking a rather intimidating subject and putting it within the grasp of many others, including myself - for which I'm sincerely grateful.

Perhaps I'm a slower learner than others, for it has taken me more time to evaluate your essay. My personal bent is the find pieces to the Great Cosmic Puzzle and to find tools with which to assemble those pieces into a model. In the timeframe of reading essays in this contest I'm finding that Quaternions is just one of a dozen mathematical toolsets used in physics and quantum mechanics -- most of which I have yet to learn. So I read on...

You say, "Geometric Algebra describes three dimensional space and that Physics occurs within three dimensional space" which I think is the perspective that most of the scientific community shares. In my paper I emphasize that physical reality exists in a 4D Space~Time context, so my model needs 4D Geometry where the 4th dimension is the radius of an ever-expanding Now-manifold inside the context of 4D Spherical standing-waves. While studying your paper I'm asking myself "How to I apply these Quaternions to my 4D context?" Do I have to model each Time-Space point as a Planck-time, Planck-lengths as three Quaternions: (t, X, Y, Z) where X, Y & Z are each Quaternions? Or am I better off using a coordinate system based on plain complex numbers: (t, X, Y, Z) where X,Y,Z are complex? In my mind the real portions of complex/quaternion numbers are positions in space or time and the imaginary parts are the stress-energy tensors of how stretched/compressed the Space~Time Medium is at a particular instant. I think the answer is somewhere around Equation 7 to 10 but at this time I'm still undecided.

In your equations is there something that says time-slows as speed approaches c? Like, your quaternion T: do the complex components represent a rotation of the direction of motion "rotating" towards negative-time - meaning local time slows as the object approaches c?

(Ditto, on the recommendation on David Hestenes' Geometric Algebra.)

Gary,

Time grows short, so I am revisiting essays I've read (3/1/2015) to assure I've rated them. I find that I did not rate yours, though I usually do for those I can relate to. I am rectifying that. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345.

Jim

Hi Gary,

Thanks for the intellectual exchange during the contest. Hope to engage more on the non-contest blogs after the competition if you are interested. I hadn't rated your essay but now got you within firing range hopefully to make the final list despite the 1-bombings. Hope I make it too but I may not really care that much.

Regards,

Akinbo