Extra Dimensions

[Angrboda]

"It was not until some weeks later that I realized there is no need to restrict oneself to 2 by 2 matrices. One could go on to 4 by 4 matrices, and the problem is then easily soluable. In retrospect, it seems strange that one can be so much held up over such an elementary point. The resulting wave equation for the electron turned out to be very successful. It led to correct values for the spin and the magnetic moment. This was quite unexpected. The work all followed from a study of pretty mathematics, without any thought being given to these physical properties of the electron."
P.A.M. Dirac

Ideas generated purely in dreams or imagination that didn't pan out tend to outnumber those that did by about infinity to one. Without something constraining the search, blind searching based on dreams or imagination is pointless.


In a spot during a recent rebroadcast of an episode of the science fiction series Fringe, it was claimed that there was an individual who, after receiving a blow to the head, became able to play and compose music, unlike before the injury. I don't know whether the claim itself is valid or just a viral promo, but they described the individual as experiencing the music synesthetically, that he "saw" a visual representation of the music in front of him (literally), and he simply followed along. Even if true, however, as in the case of the discovery of the benzene molecule, it was prior real world experience which gave rise to the fruitful imaginings. If these things weren't coming from prior real world experience, you might have a parallel, but the 'imaginings' of people without some prior real world experience tend to be universally sterile. (As are imaginings from drug induced experiences. Oddly enough, Dirac tended to eschew practical experiment in favor of his mathematical explorations; however to expect someone with only mathematical knowledge to generate systems relevant to physics by their intuition alone is far fetched. If someone with no prior experience of music suddenly could compose symphonies after a blow to the head, then you would have some interesting questions; however, I suspect that even then, the answer would lie in the person's prior experiences [and evolved traits] rather than sheer imagination.)