Calculus - Revision 2.0 by Gary D. Simpson

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

Author En Passant replied on Apr. 24, 2015 @ 01:24 GMT unstub

Gary,

I don't want to insult Sujatha Jagannathan in case she is not an automaton.

Your perception of the "fluency" of her language is right. Her talk seems to me to be "canned" (and I mean that in more ways than one).

But if you are right, then its creators are cheating. They intersperse regular (machine) dialogue with their human intervention whenever the situation gets too complex for AI (and purposely introduce human errors).

Have no fear of AI. Below, I copy some text that I saw on the Internet just now. Strong AI is simply preposterous.

It would mean that we can lift ourselves by our own bootstraps.

En

May 15, 2013 | Luke Muehlhauser | Analysis

Strong AI appears to be the topic of the week. Kevin Drum at Mother Jones thinks AIs will be as smart as humans by 2040. Karl Smith at Forbes and "M.S." at The Economist seem to roughly concur with Drum on this timeline. Moshe Vardi, the editor-in-chief of the world's most-read computer science magazine, predicts that "by 2045 machines will be able to do if not any work that humans can do, then a very significant fraction of the work that humans can do."

But predicting AI is more difficult than many people think.

To explore these difficulties, let's start with a 2009 bloggingheads.tv conversation between MIRI researcher Eliezer Yudkowsky and MIT computer scientist Scott Aaronson, author of the excellent Quantum Computing Since Democritus. Early in that dialogue, Yudkowsky asked:

It seems pretty obvious to me that at some point in [one to ten decades] we're going to build an AI smart enough to improve itself, and [it will] "foom" upward in intelligence, and by the time it exhausts available avenues for improvement it will be a "superintelligence" [relative] to us. Do you feel this is obvious?

Aaronson replied:

The idea that we could build computers that are smarter than us... and that those computers could build still smarter computers... until we reach the physical limits of what kind of intelligence is possible... that we could build things that are to us as we are to ants -- all of this is compatible with the laws of physics... and I can't find a reason of principle that it couldn't eventually come to pass...

The main thing we disagree about is the time scale... a few thousand years [before AI] seems more reasonable to me.

Those two estimates -- several decades vs. "a few thousand years" -- have wildly different policy implications.

If there's a good chance that AI will replace humans at the steering wheel of history in the next several decades, then we'd better put our gloves on and get to work making sure that this event has a positive rather than negative impact. But if we can be pretty confident that AI is thousands of years away, then we needn't worry about AI for now, and we should focus on other global priorities. Thus it appears that "When will AI be created?" is a question with high value of information for our species.

Let's take a moment to review the forecasting work that has been done, and see what conclusions we might draw about when AI will likely be created.

Thanks Gary. I just posted a reply to your well reasoned comment.

All the best,

Akinbo

Sorry, in addition seeing your interest in the wave equation, what is your assessment/ comment on the correctness of Thomas Erwin Phipps?

Hello Gary,

Would you mind if I tapped your brain a little? I have a draft of a paper (attachment) and post the abstract below.

Regards and thanks,

Akinbo

*You may reply me here or on my essay blog or better still to: taojo@hotmail.com

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Abstract: Absurdities arising from Einstein's velocity-addition law have been discussed since the theory's formulation. Most of these have been dismissed as being philosophical arguments and supporters of Special relativity theory are of the opinion that if the math is not faulted they are ready to live with the paradoxes. Here, we now demonstrate a mathematical contradiction internal to the theory itself. We show that when applied to light there is no way to mathematically reconcile the Einstein velocity-addition law with the second postulate of the theory which may have a fatal consequence.

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