How Math Explains the World.pdf
that comprise our universe, the photons and quarks and gluons and elec- trons and neutrinos of the Standard Model, the particles ...
Edward Witten. Witten is a Fields Medalist and a leading exponent of string theory. The lecture was attended by many leading sci ...
is multiplied by c^2. In order to produce a particle of mass m, one must look at the equivalent equation mE/c^2 ; and it takes ...
Einstein did not simply tinker with Newton’s theory; he devised a differ- ent way of looking at the universe. Nonetheless, both ...
He may not have framed them, at least for publication, but it is hard to believe that he did not at least speculate about them. ...
the force) on the surface of the larger sphere is^1 / 9 ^1 / 32 , the photon den- sity on the surface of the smaller sphere. Ju ...
proach caught lightning in a bottle—literally. Not only did this assump- tion result in Einstein’s equations of general relativi ...
changing allows particles to assume other forms, and species changing among neutrinos accounts for the solar neutrino deficit. B ...
tum mechanics to produce their extraordinarily accurate results. Relativity, the best theory we have on gravitation, is a classi ...
seen, this is a frequently occurring situation—one possibility is to solve the exact equations approximately, but another is to ...
a monumental gap, so this is an ultra long shot—more so if the extra spa- tial dimensions are smaller than 10^18 meter. The Sha ...
See http:// en .wikipedia .org/ wiki/ Theory _of _relativity. This site is an excellent primer on relativity, and has reference ...
iSect on III Information: The Goldilocks Dilemma ...
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9 Murphy’s Law Nobody knows who Murphy is, but virtually everyone knows Murphy’s Law, which sums up much of life’s frustrations ...
are some problems that are so intrinsically difficult that it may not be pos- sible to get them right; at least not in a reasona ...
There’s a lot of idle time here, but that’s to be expected. The important point is that all tasks are finished after twelve hour ...
used. There’s a major problem with that: there could be an awful lot of schedules, especially if there are a lot of tasks. How H ...
instance, suppose the top four cards on the old stack, in order, are Betty- Al-Don-Carla. We keep track of the old stack, the ne ...
Let’s start by looking at the number of different possible routes we could take. Suppose there are three cities other than home, ...
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