David Terr's Website

 

Publications

“Fibonacci Expansions and ‘F-adic’ integers,” The Fibonacci Quarterly, v. 34, 1996

“On the Sums of Digits of Fibonacci Numbers,” The Fibonacci Quarterly, v. 35, 1996..

A Modification of Shanks’ Baby-Step Giant-Step Algorithm,” Mathematics of Computation, v. 69, 2000

Here's a copy of my resume

Black Holes and Information Theory

Black holes are very strange objects! It is well-known that a black hole is a region in space so densely-packed with matter that nothing, not even light, can escape. Actually, as Steven Hawking showed in 1974, this is not entirely true. Quantum mechanics predicts that black holes in fact "evaporate", emitting blackbody radiation with temperature inversely proportional to their Schwarzschild radius. For ordinary black holes, i.e. formed from collapsing stars, this evaporation is extremely slow and the radiation temperature extremely low (the order of a ten-millionth of a degree Kelvin). Before black hole evaporation was discovered, it seemed that one could destroy information by tossing it into a black hole. If one threw a book into a black hole for instance, all information in the book would be forever lost except for its mass, angular momentum, and electric charge. (This is a result of the "black holes have no hair" theorem). However, in light of Hawking radiation, we see that information does emerge from a black hole. Now it is believed that information is not destroyed by sending it into a black hole - instead it re-emerges in the form of blackbody radiation. Black holes have in fact been compared to computers in this regard.

The Holographic Principle
The holographic principle is a strange new idea proposed by physicist Gerald t' Hooft in 1993. The principle states that all the information in a three-dimensional region can be modeled by a theory which only considers the boundary of that region. The principle gets its name because holograms act much the same way, i.e. a two-dimensional surface records all visual information of a three-dimensional object. The holographic principle arose by considering black holes. A black hole is a region of space with maximal entropy, and this entropy is proportional to the surface area of the event horizon. Since entropy is really just information, what this says is that the maximal amount of information it is possible to contain in a region is proportional to the surface area, not the volume, of that region.

Wormholes and Time Travel
A wormhole is a theoretical tunnel through spacetime in which two otherwise distant regions of spacetime (widely separated in distance, time, or both) are connected by a short tunnel. By passing through one mouth of the tunnel, one would then re-emerge very far away and/or at a different time. If stable wormholes exist, then they could be used as time machines. The idea is to first create a wormhole, then to accelerate one mouth of the wormhole to nearly the speed of light, and finally return it to its starting position. Because of relativistic time dilation, the accelerated mouth now lies in the past of the stationary mouth. Now by going from the stationary mouth to the mouth that has been accelerated, one travels back in time.