Des·erts·edge (dez ûrts ej′), n. 1. the transition between dry, barren wilderness and lush, forested land. 2. the frontier between my ignorance and my understanding.
Contact me: mark@desertsedge.com
Des·erts·edge (dez ûrts ej′), n. 1. the transition between dry, barren wilderness and lush, forested land. 2. the frontier between my ignorance and my understanding.
Contact me: mark@desertsedge.com
Recent Books:
Meta Math, The Quest for Omega, Gregory Chaitin. This book provides another way of looking at incompleteness in mathematics. The author develops the idea of randomness and constructs a maximally random, completely unknowable and incompressible number, Ω. The idea is that the digits of this number can never be described by an algorithm. There is no way to compress this number into a smaller data set. Numbers like π and e, although transcendental, and infinite decimals, can still be described concisely with small formulas; therefore they are not truly random. The idea of compressing data into smaller sets is carried over to formal axiomatic systems. The only reason to have systems of axioms is so that the set of theorems represents a smaller data set than the results derived from those theorems.
The Road to Reality, Roger Penrose. Reviews the mathematics used in theoretical physics.
Purple Cow, Seth Godin
Latest favorite web sites:
The math site that has it all http://mathworld.wolfram.com/. I use it as an encyclopedia or as a starting point for any mathematical inquiry.
I like to use Unicode characters in my math equations; here's the reference site I use: http://unicode.org/
Latest math forays:
My recent investigation of truth tables between 2 independent Boolean variables.
The coat problem:
A large number of people enter a room and check their coat at the door. Later, upon exiting, everyone is given a coat at random.
Question: What is the probability that everyone gets the wrong coat? Answer: 1/e
The Counterfeit Penny Problem: There are ten stacks of pennies, each with ten pennies. One of the stacks is known to contain counterfeit pennies, which weigh slightly different than the other pennies in the other stacks. Assume all good pennies weigh the same. Also assume that the pennies in the counterfeit stack weigh the same as each other in that stack. Now suppose you're allowed to use a conventional scale that reads out an exact weight (like a bathroom scale) and that you're only allowed to use it once.
Question: How can you determine which stack is the counterfeit stack and how much each counterfeit penny weighs ?
The Thread Problem: You have two threads. Each of them will burn for exactly one hour if one of its sides is set on fire.
Question: How can one measure 45 minutes exactly, using only these threads and a lighter ?
Answer: