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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...

Suppose one company would like to buy another company’s client list, but only if the lists don’t overlap too much. Neither company wants to hand over their list to the other before a sale takes place. What can they do? A low-tech solution would be for both parties to provide their client lists to a […] The post Why eliminate trusted third...

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 […]...