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We've spent more than a few Sunday Function features discussing the properties of the prime numbers. They're just so important and interesting in number theory that they're an irresistible target. Let's set some scenery before getting to the actual function this week.
Anybody heard of the idea of The Singularity? Roughly, it goes like this: technological progress builds on itself, and this self-reinforcing feedback loop is eventually going to come to a head where humanity makes a quantum leap into an unknowable and godlike transhuman technological future - possibly as early as the middle of this century. The name of the idea comes from mathematics, where approximately speaking a singularity is a place where a function rockets off to infinity.
Happy Easter, everyone! This Sunday Function is going to be short and sweet, since unfortunately I've got a lot to do before Monday. Let's get down to business! Here's a function I've made up out of thin air. It's pretty arbitrary - in fact, it's discontinuous at x = -1/2 and not differentiable at x = 0:
Yes, it's Tuesday. Busy weekend, including a Relay for Life (you should find your local one and donate!). Today we'll get back on schedule a bit and make this one a rather more utilitarian than usual Sunday Function, playing into the last step we'll need in order to complete the Bose-Einstein condensation discussion. In the course of our journey we will meet this somewhat alarming creature:
This Sunday I was at an event that involved a number of drawings for door prizes. There were perhaps 30 couples there - it was, not to beat around the bush, a wedding registry shindig at Bed, Bath, & Beyond. (Did I mention I'm recently engaged? I am. It's the main reason for the endemic light posting, as I'm afraid the wedding bumps the blog down the priority list a bit. ;) )