Why eliminate trusted third parties?

Many are voicing concern that the world is running out of data and that this will be a blocker to progress toward smarter AI models. One paper in fact projects timelines for when we will run out. AI researchers are looking for ways to adapt.  Nvidia has trained a specific model to generate synthetic data for […] The post Can AI Models Reason: Is...

Sometimes it’s useful to apply dimensional analysis where it doesn’t belong, to imagine things having physical dimension when they don’t. This post will look at artificially injecting dimensions into equations involving factorials and related functions. Factorials The factorial of n is defined as the product of n terms. If each of these terms had...

Yesterday I wrote about how the right notation could make Newton’s interpolation theorem much easier to remember, revealing it as an analog of Taylor series. This post will do something similar for the binomial theorem. Let’s start with the following identity. It’s not clear that this is true, or how one might generalize it. But […] The post...

Newton’s interpolation formula looks awfully complicated until you introduce the right notation. With the right notation, it looks like a Taylor series. Not only is this notation simpler and more memorable, it also suggests extensions. The notation we need comes in two parts. First, we need the forward difference operator Δ defined by and its […]...

The previous post was an AI-generated podcast that I friend made by crawling my web site. I decided to create an actual podcast for posting occasional audio files. I expect to post very sporadically. I’ve posted two audio files, and I have one more in mind to post some day. Maybe that’ll be the end […] The post Podcast feed first appeared on John...