I was listening to Mark Cuban say that there is no way that most of these AI companies will ever pay back the hundreds of billions of dollars they’re borrowing to spend on datacenters. His opinion was that it’s a winner-take-all situation and the only way to win is to spend more than your competitors. But in the end, the investors are going to be left holding the bag.
ChatGPT is weird. It’s so smart, and yet it’s capable of being incredibly dumb. It’s also perfectly willing to completely make things up. And when it does, it sounds just as confident as when it’s not. None of this is fundamentally different than humans. Smart humans can be surprisingly dumb at times. People make stuff up. People can even make stuff up without realizing that they’re doing so. But…
At the start of each year, Ron Minsky (from Jane Street) runs a friendly competition where participants are invited to make some predictions about the next year. More specifically, there are 10 events which may or may not happen in the next year and, for each event, participants are asked to give a probability that they will happen. Then, at the end of the year, the predictions are scored. Here’s…
Parenting book #2! I’m on a roll.
In my 7 year old’s math class, they’re learning about time. In particular, they’re learning how to figure out how many hours and minutes are between two times. For example: If it’s 1:45, how long until it’s 5:18? They way they are taught is by counting up by hours until you get within one hour, and then count up by minutes. Something like this: This seems like a totally great way to explain it.…
So I finally read a parenting book! I know, not my usual topic choice, but I want to write down what I learned so I don’t forget.
This post is attempting to answer one of the questions at the end of Let’s build an operator which introduces the idea of hyperoperations. It’s not strictly necessary to read that post first, but I’d recommend it. \[\newcommand{\tetration}[2]{ {}^{#2}#1 }\] Repeated addition turns into multiplication. Repeated multiplication turns into exponentiation. What does repeated exponentiation turn into?…
In this post we’re going to build an operator together. Actually, not just one operator, but a whole family of operators. What do I mean by “an operator”? I mean something like \(+\), \(\cdot\), or \(-\). Also, all the operators we’re going to build are “binary” operators meaning they take 2 numbers as inputs and produce 1 number as an output (again, like plus, minus, etc). Actually the first one…
Let’s play a game. I’m going to draw two points on an x-y plane and give you a rule which you can use to generate new points. You can generate as many new points as you want using my rule. If you connect all the points, you get a function. Your goal is to guess the function. Ok? Let’s go. Ok, I’ve drawn two points, \(a\) and \(b\). From these two points, you can generate a new third point \(c\),…
I believe pretty strongly in evolution. I’m quite skeptical of people who argue against it. But if you asked me to lay out the strongest case for evolution, until recently… I’d be pretty hard-pressed? I’d probably mumble something about fossils and then get kind of embarrassed. If I can’t make the case, then why do I believe it so strongly? I think the honest answer is that I find the people who…