ark said:
Proofs of the theorems are checked using our ordinary logic...
He also wrote serious articles about "Interaction of the Past of parallel universes" - http://arxiv.org/abs/physics/9910037
and "Time machine as four-dimensional wormhole" - http://arxiv.org/abs/gr-qc/9612064
If you throw in future effects past causality and parallel universes (many worlds) then quantum logic actually does make sense using ordinary logic. This press release really is like someone trying to solve a problem that doesn't exist by admiring the tools in his tool box without having any idea what to do with the tools. More fundamental than mathematics is much better PR though.
One promising use of topoi so far in a physics sense not just pure math sense seems to be Grothendieck's use of topoi to help himself and others find deep relationships between numerical equations and geometry. I think this may actually be more the use of ideas that lead to topoi rather than actual topoi.
http://www.valdostamuseum.org/hamsmith/Mar2006Update.html#awls
Miss Isness said:
It seems like such a fascinating subject. How I wish I had more of a background in math and science so I could really delve into it. It's not at all surprising that this article for public consumption is misleading. It would sure be great if people like me had access to real cutting edge information that was presented in a way that simple minds could understand.
Physics does seem to have the same problems as the world at large. The link I gave above mentions the sheep-like behavior of physicists. This link also mentions Bott's periodicity which is actually a concept that can be explained in lay person terms. By the way, you being here means you have much more than a simple mind. The only skill I found useful for delving into this stuff at my lay person level was some high school trigonometry (my college calculus was zero help) but I was relating sacred geometry to real geometry which isn't a physics thing directly anyways.
Back to Bott periodicity. If you take the view than ultimately physics comes from patterns in numbers then if every new number produced a totally new pattern aka totally new physics then physics research would be in huge trouble cause then you would need a computer the size of the universe to see what's going on (Ark has enough problems with computers not being fast enough as it is). Bott periodicity kind of says that patterns seen using the numbers 1 through 8 are like patterns for 9 through 16 and 17 through 24, etc. So to understand physics you just need to understand the 1 through 8 patterns. If only that was as easy as it sounds, though it is actually easy to see one aspect of the pattern:
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
This is Pascal's triangle showing a row for each of the 8 patterns. Let's say you want to know the tenth row. You could make this by using the 8th and the 2nd rows (have to always use as many 8ths as you can, 7 and 3 would not work). To get the 37th row you would need four 8ths and one of the 5th rows. The notation is Cl(8) x Cl(8) x Cl(8) x Cl(8) x Cl(5) = Cl(37).
To describe what a row is look at the 8th row, the beginning 1 is the number of ways to take zero things from 8 things, the 8 is the number of ways to take 1 thing from 8 things, the 28 is the number of ways to take 2 things from 8 things, etc. up to the last 1 which is the number of ways to take 8 things from 8 things.
Now to actually get the 10th row from the 8th and 2nd row you take that 8th row and form multiples of it using the 2nd row and add the multiples together like this:
1 8 28 56 70 56 28 8 1 (1 times 8th row via first 1 of 2nd row)
2 16 56 112 140 112 56 16 2 (2 times 8th row via the 2 in 2nd row)
1 8 28 56 70 56 28 8 1 (1 times 8th row via the last 1 of 2nd row)
Adding the above gives the 10th row:
1 10 45 120 210 252 210 120 45 10 1
Perhaps all of everything kind of comes from this.
