I claimed Sir Roger Penrose refers to noncommutative cubic time. I didn't double check this claim.
To figure out velocity, we divide distance by time. But if we can swap position and momentum interchangeably that means that each may be given their own unique dimension of time. In this way, the universe may be hiding an extra dimension of time from us.
So the "swapping" is noncommutative due to time-frequency uncertainty.
Sir Roger Penrose:
In an open universe, there is, in effect, an imaginary time, which is i times the time scale, which is also a fundamental time.
https://www.aip.org/history-programs/niels-bohr-library/oral-histories/34322
So by "imaginary" we really mean cubic time.
There are four properties of cube root of unity. 1)One imaginary cube root of unity is the square of the other. Hence it is clear that one cube root of unity is the square of the other. 2) Product of three cube roots of unity is equal to 1. 3) Each complex cube root of unity is reciprocal of the other.
So I was "shooting from the hip" based on listening to Penrose and reading him.... I didn't provide a quote. I was just summarizing in my own words...
So my personal pet peeve re: physics is the inability to incorporate the ecological crisis into the actual mathematical structure of science itself. So I captured this in a quote in my old blog - about how "biological life" can only perceive entropy as the direction of time - and so if time reverses itself due to say the collapse of the Universe - then we could not PERCEIVE it. This is, of course, a big "modern human" left-brain dominant anthropocentric blunder on the part of physicists. This is why Nobel Physicist Brian Josesphson says biology is primary to physics.
So there are fascinating "gaps" between the disciplines in science. I started out in International Relations with an environmental option (sustainability). It was a brand new major - and I had to personally integrate Economics and Political Science and Biology. I discovered all three disciplines lied about each other in other to prop up their own claims. Pretty funny.
Of course that Undergraduate Major was just a cover - as I had also been accepted into the Music Composition Degree at University of Wisconsin-Madison. They had a self-directed option and I chose a "global blues" as my personal focus. I then spoke out against the main director of the professors there - so they kind of kicked me out by claiming I had to redo my past assignments that I had already gotten good grades on. haha. That was Orchestration - the claim was my Schoenberg transcription was Communist. Kind of hilarious.
OK... So deep in the back of my mind I was expanding my integration of music theory with quantum physics - from my very first year of college at Hampshire - studying from Professor Herbert J. Bernstein.
However, nothing forbids that the noncommutativity of spacetime might occur at a bigger scale.
https://arxiv.org/pdf/1901.01613.pdf
So only Eddie Oshins working at SLAC and teaching Neigong - made this same realization. I developed this theory on my own from music theory. First I tested it doing the training - and realized YES it is true (and this was a permanent transformation called an "enlightenment experience.") And then I read one scholarly book a day - and discovered Alain Connes using noncommutative music theory. It took his lecture posted on youtube - to realize - YES he is talking about the SAME concept I had realized in music theory as the truth of PreSocratic philosophy (from my high school private music training). When I was at Hampshire College I had tested into the Third Year music theory level - in my first year. I realized I could have graduated with a College Degree in a year and half. So I transferred out of Hampshire. haha.
Toulmin - the importance of dissent vid
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