Ainan on a Theory of Everything.
A couple of days ago, I was talking to Ainan, ten, about Einstein's efforts to create a Unified Field Theory...which in modern parlance, would be termed a "Theory of Everything". This would be a single physical theory that would unite and explain all physical forces and phenomena.
As I spoke of Einstein's purpose, an understanding entered Ainan's eyes with such certainty that I could almost read it, there, before he spoke:
"In Physics," Ainan began, quietly, but with a force of conviction that was unmistakeable, "if your equation isn't simple, there is something wrong with your Universe."
Ainan had, it seemed, come upon the belief, for himself, that in Physics, truth and simplicity are one: that which is true, is also that which is simple. Of course, what Ainan means by simplicity might not be what most people mean...but I think the intention is clear: a Unified Field Theory, or a Theory of Everything, would not, in Ainan's view, be complex to express, even if it is was difficult to derive.
What I find most interesting about this little observation of his is not the observation itself, whatever anyone might think of it - but the certainty with which he conceived it. There is, in him, an inner barometer of scientific truth, that tells him what the world is like, and what science should be. This barometer is vital, I believe, to the essence of a true scientist for, without it, it is easy to flounder in misconceptions, that, with it, one would never be tempted by. Ainan has developed, it seems, an inner guide as to what science should be. That, to me, is a very hopeful sign. I look forward to where it might lead him and to what. I only know this: that whatever he finds, he will try to express it as simply as he can. Thus, he would try to make known, even his most masterful thoughts, in the clearest manner possible - for that is how he believes science should be.
Happy hunting Ainan.
(If you would like to learn more of Ainan Celeste Cawley, 10, or his gifted brothers, Fintan, 6 and Tiarnan, 4, this month, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html
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Labels: Ainan Celeste Cawley, Albert Einstein, scientific intuition, simplicity and complexity, the future of science, Theory Of Everything, truth in science, Unified Field Theory
3 Comments:
For making things short it's hard to beat Geometric Algebra (GA, real-valued Clifford Algebra). Maxwell's Equations, which take about 50 characters in four equations to specify in vector form (counting multiplications and equation separators) requires only 8 characters in one equation in GA, and that equation has several advantages over the traditional form: being boost (Lorentz) invariant, coordinate-free, unifying the E and B components into a four-dimensional current, not requiring cross-products which are misleading in their geometric content (doesn't work except in 3 or 7 dimensions; looks like a vector, but really is the dual representation of a directed planar area "bivector"), and without cross products, there is thus no "right-hand rule". In natural units, it's even shorter, 4 or 5 characters, stating that the gradient of the force equals the four-current. (BTW, Ainan should take a look at the "natural units" page on Wikipedia and see what new relations he can find)
Of course understanding and unpacking any form of Maxwell's equations takes a semester or three. In fully unpacked form specifying all the components with signs, constants, subscripts, superscripts, formatting, counting implicit multiplications, etc, that innocent-looking four-character equation can sprawl out to around 350 characters.
GA has similar advantages in computer simulation, optics, mechanics, relativity and quantum mechanics, and provides a much more uniform and intuitively understandable system of notation and representation than the native mathematical dialects of those fields.
Thank you, E. Harris, for directing my attention to GA. I will, in turn, direct Ainan's attention to it, since he is charmed by elegance of thought and expression and would, no doubt, find it, therefore, of interest.
Thanks also for the Wikipedia tip.
Are you a physicist yourself? Or a mathematician?
Kind regards
No, I'm not a physicist or mathematician - or at least I don't have a degree or a paycheck in those fields - but I've been interested in physics for a long time and GA has been an interest of mine for several years. I have read many different presentations of GA so I can recommend a few:
I highly recommend the free GAViewer software to build visual intuition. The tutorial that goes with GAViewer is also quite helpful. This would be the best place to start. Professor Dorst also has some other links and tutorials worth looking at.
Cambridge GA group works:
The paper: "A unified mathematical language for physics and engineering in the 21st century" by J. Lasenby, A.N. Lasenby and C.J.L. Doran is a good introduction to the history and applications of GA. It is for a general audience and has few equations.
"Imaginary Numbers are not Real - the Geometric Algebra of Spacetime" by the same authors is one of the best mathematical introductions, especially to the 4-D spacetime case. (the quote from William Kingdon Clifford, of Clifford algebra fame, above the introduction is worth repeating: "...for geometry, you know, is the gate of science, and the gate is so low and small that one can only enter it as a little child.")
The Cambridge GA group's "Part III" course "Physical Applications of Geometric Algebra" is more lengthy and rigorous and assumes the student is a final-year Cambridge physics major, but it does have the advantages of college course materials such as worked problems.
For an overall reference, Ian Bell's site is comprehensive and gets into advanced computer applications not found elsewhere. Unfortunately his HTML-math encoding is archaic and requires an old browser to view properly - but he does have a link on his site to an archive of such browsers. Ian Bell also wrote the first 3D microcomputer game: "Elite".
All these are easy to google, using "geometric algebra" together with the names, so I won't add links.
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