Utterly fascinating to see how very simple mechanical devices, like differing gear ratios, can be used to calculate things like logarithms.
Utterly fascinating to see how very simple mechanical devices, like differing gear ratios, can be used to calculate things like logarithms.
For example, could an electrical analog system be a way of carrying out large-time molecular dynamics simulations? With proper tuning of the material, might you be able to create arbitrary potentials between the electrons within it so that they would interact roughly like atoms in an MD simulation? Or, perhaps you could create an analog chip where the electrons would 'naturally' solve various NP-hard problems, effectively by brute force?
http://www.worldscientific.com/doi/suppl/10.1142/p650/suppl_...
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For a completely different portrayal of futuristic mechanical computers, check out Neal Stephenson's story The Diamond Age. It's set in an era of nanotech, and the computers are nanoscale clockwork computers.
Musicians are still using them. Modular synthesizers are the bomb.
This is cool, because the Hubbard model is a simple and displays interesting phenomena, but understanding it is a hard problem. The Hamiltonian (that is to say, the energy) consists only of a kinetic energy plus an interaction between the spin up and spin down particles on the same site (e.g. if I have two spin up bosons and four spin down bosons, the interaction contribution to the energy is 8 U, where U is a constant parameter---the strength of the interaction.) Depending on this interaction strength U, the system might behave either like a conductor or an insulator.
The problem is hard to deal with analytically (for reasons I can't say I understand) and, as I understand it, the space of possible states is so huge that the numerics become computationally intractible at about a lattice 5 sites x 5 sites x 5 sites. So being able to see the phase transition happen is very neat, and exactly what you expect from an "analog quantum computer": simulating with cold atoms a system that we can't really simulate with ordinary computers.
Guns, not missiles. At 0:50, the narrator refers to "initial shell velocity."
They were last used in combat in the 1990s, when the Iowa-class battleships fired their 16-inch guns at Iraqi positions in Kuwait. The Navy never bothered to replace them with digital computers, because they were already accurate enough for the guns they controlled.
This 1937 video about differentials is also enlightening:
http://www.youtube.com/watch?v=yYAw79386WI
Why is it that old tutorial videos are so thorough and informative?
http://www.nps.gov/goga/nike-missile-site.htm
Highly worth a visit if you're interested in this sort of mechanical computing stuff…
[1] So far I saw : analog target computations, wheel differentials, wave diffusion
Thanks!