## Posts Tagged ‘geometric derivatives’

### Singularity Summit Talk

May 7, 2013

As readers of this blog are probably aware, I’m a rather big fan of multiplicative calculus, an obscure mathematical tool that is very useful in reasoning about quasi-exponential trends. And I’m rather sad that I get few occasions to apply it. So, it should come as no surprise that when I was given an opportunity to speak at Singularity Summit last fall, a conference largely concerned with exponential trends in technology, I decided to try to persuade people of the utility of multiplicative calculus and the value of mathematical abstractions.

Now, there was a bit of confusion because a lot of people thought that I was going to be speaking about my work — that’s what all the other Thiel Fellows did — but I think this was much more valuable. The things I do are generally of very domain specific interest and don’t have super deep implications world-changing for the future of technology, just some minor, incremental improvements. In any case, you can watch me and the other fellows talk.

My public speaking skills aren’t the greatest, and it wasn’t the best talk I’ve given… but it was pretty cool when Vernor Vinge came up to me and told me that he liked my talk! (And I think Ray Kurzweil may have said so as well, but I wasn’t sure if it was him.) And then I and the other fellows had dinner with Eliezer Yudkowsky (and lots of other awesome people, but he sat beside us). So it was a crazy awesome experience in general!

### Function Approximation by Geometric Derivatives

December 9, 2010

If the idea behind a normal derivative might be describe as the amount one needs to ad to move forward. If so, then the idea behind a geometric derivative is the amount one needs to multiply by.

The definition of a geometric derivative is $D^* f(x) = \lim _{h\to 0} \left(\frac{f(x+h}{f(x)}\right)^\frac{1}{h}$

One thing one might wonder is whether we can use them to approximate functions, like we can use derivatives to approximate functions with Taylor series. A quick Google search didn’t reveal anything, but it isn’t too hard to figure out.