Hi,
Dr. Dick has given an amazingly clear summary of his work in his post below re: math theorem in his paper.
In my reply I realised it appears there is a simple way to test his claim.
Here I give the test:
Require: sheet(s) of paper; pencil or biro etc.
Instructions:
Draw a straight line of dots.
(Strictly speaking; you could I guess draw a wiggly line of dots; even a scattering of dots over the page).
Using the simple line of dots method: make the dots gradually bunch closer together and gradually space further apart; as if the dots were cars in a deceleration/acceleration traffic jam.
(Strictly speaking; you could have dots in a wiggly line with arbitrary bunchings and arbitrary bigger spacings. Strictly: I guess you could have the dots scattered about, with arbitrarily more densely populated areas of the page.)
Using the simple line of "decelerating/accelerating" dots:
Draw a similar such line of dots at right angles to the first line, so it crosses the first line at a dot on the first line.
(Strictly speaking, you could perhaps join a sequence of arbitrarily scattered dots on a page, such that some parts of the resulting wiggly line have closer bunchings of dots, and others have wider spacings).
Using the simple version: choose one dot from each, of your two at-right-angles dot-lines.
Now choose a direction to travel in along each of your lines. Take the next position of your two dots. Arange the page so one line is horizontal, one is vertical.
Plot the next-dot on the horizontal line on the paper for where that dot would be if that line passed through (at right angles) your next-dot
position on your vertical line.
The idea is; keep plotting the next-dot positions that result from superposing one line on the other, as if the dot were a car tavelling through two traffic-jams at right angles, simultaneously.
You should get a symmetrical curve like a math function graph of new dots.
Imagine what you need to do to this curved line to make it appear straight: you have to rotate (spin) and twist it. (These two spin operations may represent 2 of the quantum numbers in physics).
Having got a straight perspective on the line, its dots have become differently bunched together.
The test:
Is it posible; no matter what two dots you chose from your two starting lines; no matter what order you add the lines in if you added more lines after the straightening operation on curved lines prior to adding new lines; is it possible to always place invented intervening lines of dots SUCH THAT the addition of these arbitrary invented lines of dots and invented chosen dots would allow ANY PARTICULAR SEQUENCE OF REAL LINES OF DOTS AND REAL CHOICES OF DOTS TO BE DEFINED BY
the constraints imposed by mixing in invented lines of dots and invented choices of dots?
In other words: can you start with any "random" arrangement of dots on a sheet of paper;
and with any arbitrary joining of these dots into a wiggly line where dots have various spacing-density;
then, can you get that arbitrary starting pattern, from any other such arbitrary pattern; if you include enough additions of invented patterns to get combined patterns combined with further patterns etc. ?
Are all "random" patterns thus connected in this way? By these laws of comparing and matching patterns? These laws of combining; taking the result and spinning it in two dimensions so as to get the result as seen from one of its constituent dimensions; then adding another pattern; spinning again so it looks like it does from one of the two perspectives making it up; and adding another; and so on?
And so; like the double helix of DNA? Everything in physics comes from this?
It's about seeing things from another's perspective?
Regards,
Alan |