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the new math: old battle of the lovees was: PDP1 3598


the new math: old battle of the lovees was: PDP1 3599
Sure. I've got no problems with their compiler thinking. One does not apply it to OS. I have rabid problems with people who advocate one size (one OS or one...

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the new math: old battle of the lovees was: PDP1 3600
We agree on that. It's the structure of natural languages. One will always find exceptions. During the OS wars for Unix in the 80s I had another personal thread. John Backus...

take for example the problem of calculating the gravitational field of a sphere. i know immediately that doing the calculation in cartesian co-ordinates (x,y,z) is a waste of time ...the 'best' choice is a co-ordinate system that embodies the symmetry of the problem; in this case a spherical polar (r, theta, phi) system that allows me to ignore the irrelevant co-ordinates (theta, phi) in the solution. if i were to work out the solution for a spinning fluid mbutt, the 'correct' choice might naively be the oblate spherical system (in reality we do no such horrible thing, rather we work out the higher order perturbations of a spherical solution...)

or examine the simple harmonic oscillator: here the restoring force is linear in the displacement, so the potential is quadratic in the displacement. immediately we know that the ground state wavefunction is symmetric about the origin. further, we know also that if we impose a perturbation linear in x (or in fact, varying as any odd power of x) upon the potential, the ground state energy will not change (since the integral of the product of an odd function and an even function vanishes due to reflection symmetry)

there is a very powerful theorem called Noether's theorem that relates continuous symmetries to conservation laws. discrete symmetries like reflection are a different kettle of fish, but yeild similar insights.

one may clbuttify systems based on their symmetry groups, and if one is clever enough, one can extract all manner of information about the particle content and conserved quanbreasties of the system without actually working out very much detail.

one of my favorite examples is the hydrogen atom and the O(4) symmetry thereof, which after some minor manipulation gives the conserved Runge-Lenz vector without ever solving a differential equation...

sidd

the new math: old battle of the lovees was: PDP1 3601
There is something in people's minds that react to functional languages. I have tried to push collegues in the direction of more functional programming in several programming projects. This is...


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the new math: old battle of the lovees was: PDP1 3597