Tags: Optimize Everything Personal Branding Mathematics
you might have noticed the ∇ everywhere. in front of my name here, as the prompt on my website, as the favicon.
so why ∇?
what it is
∇ is called nabla (or del). in math and physics it is an operator: the vector of partial derivatives in every direction
∇ = (∂/∂x, ∂/∂y, ∂/∂z)
it measures how something changes across space. you can use it in 4 ways:
- gradient ∇f: the direction in which a function increases the fastest, and how steep it is. a temperature gradient points to where it gets hotter the fastest
- divergence ∇·F: how much a field flows out of a point. is it a source or a sink?
- curl ∇×F: how much a field swirls around a point
- laplacian ∇²f: how a point compares to the average of its neighbours. shows up in the heat equation, the wave equation and schrödinger
it is basically the language physics uses to talk about fields. maxwell’s equations are full of it.
why i picked it
the gradient is the one i care about. ∇f points in the direction of greatest improvement.
and that is pretty much how i want to live: know which direction makes things better, take a step, re-evaluate, take the next step. → Optimize Everything
it is also exactly how machines learn. gradient descent follows −∇f step by step until the model gets good. pretty much every neural network you use was trained like that.
you don’t need to be at the optimum. you just need to know which way to go.