Being truly independent is nowadays extremely difficult, if not impossible as I hinted in my introduction. I have scientist colleagues who try to be independent, and I know the problems they face. Tony Smith was one example.
He received a summa cum laude A.B. degree in mathematics from Princeton University in 1963. He enrolled in graduate studies at Georgia Tech, and worked there under the guidance of a somewhat eccentric and original theoretical physicist, David Finkelstein, but failed his exams:
He was working full time as a lawyer and pursuing his original research in theoretical physics and mathematics at the same time. Probably that would go unnoticed, but Tony dared to create an original and popular website, where he was presenting his ideas. That was too much! He was blacklisted from the physics archive - “arxiv.org” - and he was regularly attacked by the “guardians of science” whenever an opportunity arises. To quote from one discussion blog in the past:
The anonymous comment left yesterday on the guest post by Tony Smith annoyed me quite a bit. The visitor, instead of discussing the topic presented in the post, decided to produce a personal attack on Tony, guilty of having a web site of his own, containing personal theories and ideas. At the heart of the comment was a question directed to me: why do you give credit to this person, who is evidently a crackpot?”
On January 23, 20202 Peter Woit commented as follows:
"I was sorry to hear of the death a few months ago of Tony Smith, who had been a frequent commenter on this blog and others. Unfortunately my interactions with him mainly involved trying to discourage him from hijacking the discussion in some other (often unusual) direction. Geoffrey Dixon did get to know him well, and has written a wonderful long blog entry about Tony, which I highly recommend (Dixon’s newish blog also has other things you might find interesting)."
You can find the full list of Tony's publications on vixra.org here.
As an example of his extraordinary wide interests and knowledge, let me point out here to just two of his papers:
1. Overture to Beethoven’s Grosse Fugue (Opus 133) is an
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" As the distinguished mathematician Arnold opined [1]: “Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap. In the middle of the twentieth century it was attempted to divide physics and mathematics. The consequences turned out to be catastrophic. Whole generations of mathematicians grew up without knowing half of their science and, of course in total ignorance of other sciences.”Physics was traditionally a required minor for math students until it was dropped after World War II. Consequently, ninety percent of math professors today have studied no physics at all! They remain ignorant of advances in mathematics outside their narrow specialties."
David Finkelstein could have helped Tony more if he had wanted to but Finkelstein claimed to not understand what Tony was doing and actually discouraged some visitors to Georgia Tech who were interested in Tony's Wyler-like calculations. It can't be that the math was what Finkelstein didn't understand so it had to be like with Wyler the physical basis.
ReplyDeleteFrom Tony: "Note that I normalize the size of CP2 so that its volume equals the volume of a unit 4-sphere S4. My reasoning is that: the high-energy physical 8-dim spacetime breaks into two 4-dimensional structures, one a 4-dim Physical Spacetime and the other a 4-dim Internal Symmetry Space; if the 4-dim Physical Spacetime were Eulidean with S4 structure, it would inherit unit radius normalization from the parent 8-dim spacetime; the 4-dim Physical Spacetime regarded as Euclidean S4 should have volume equal to the CP2 4-dim Internal Symmetry Space, which is the other half of 8-dim spacetime; and I am effectively regarding CP2 as an S4 everywhere except for structure at infinity, which for CP2 = C2 u CP1 = C2 u C1 u {point} is CP1 = C1 u {point} and for S4 = R4 u {point} is {point}, and I am identifying C2 with R4 in the obvious way and saying that the structure at infinity only affects topological structure, not 4-dim volume".
Back to me: It might have seemed physically weird to treat the internal symmetry space as having the same volume as the large dimensions of spacetime but your twistor/dual lightcone idea makes that OK. Tony even mentioned the structure at infinity only to ignore it for volume purposes. Elsewhere Tony says: "Why can't we perceive all eight dimensions like Buckaroo Banzai? Because when we move along a mini-dimension, we are moving around the perimeter of the cylinder, which instantaneously leads us back to where we started. In other words, we move through eight dimensions all the time, but we just don't know we've made the trip because it was so short! Therefore, we don't have time to perceive it." Tony is kind of having the extra dimensions large and small at the same time, kind of hovering over your twistor/dual lightcone but not quite there enough as a physical basis.
Funny thing is that in the first four versions of a personality paper I was treating conformal gravity as an analogy for the Enneagram personality model only to give up in the 5th version and realize the Enneagram is leaving out the time-like parts (Extraversion-Introversion) and conformal gravity obviously has timelike parts. Your 6-dim twistor has conformal group symmetry and leaves out the timelike parts of the 8-dim spacetime so seems quite Enneagram of personality-like. Now if only category theory could handle all these Tonyish analogies.
Perhaps not all composers are aware of this.... Nevertheless, some of them compose music that is isomorphic to a certain mathematical description. When they discover this they are probably madly entranced and decide to become mathematicians.
ReplyDeleteBeethoven is in fact one of my favourite composers (what flowed from his depths is translated into some interesting structures). There are many mathematical structures hidden in his works, but it is only today that I see someone confirming my specific observations.
It is all not a mere coincidence. It is all essentially the same thing. It flows from the same source. This is an exceptionally pleasant observation.
What you do professionally is less important than the essence of what you create. It could be paintings, it could be music, it could be philosophy, theology, biology, physics, your life experiences and your psyche. In essence - it's all the same thing, as long as you create with passion and the works arise from your depths, rather than being mere forms imposed by the system.
ReplyDeleteIf one day you see what connects all these things and you see some meta-level, a meta-language that you can use to describe it - then you know the way forward. This 'truth' we seek is a very deep abstraction. It can manifest itself through our works in different spheres of science and art.