> This article is bullshit. It fails to mention the many limitations of analog hardware. Right. The actual paper cited: [1] That's an unrelated result. It co

> This article is bullshit. It fails to mention the many limitations of analog hardware. Right. The actual paper cited: [1] That's an unrelated result. It comes from the observation that some functions are not usefully differentiable by sampling and differencing. If the function has fractal-like infinite detail, two samples taken close together have somewhat arbitrary differences. Some people who get wound up about the halting problem have latched onto this idea and try to make a big deal out of it. Any analog system with non-zero noise, which is all of them, effectively has the same problem. You get a very noisy derivative if you try to generate a high-frequency derivative, because you're amplifying noise. This is why differentiators need a low-pass filter in front of them. This introduces some lag in a real time system. Aircraft vertical speed indicators are a classic analog device with this problem. A VSI is a barometric altimeter feeding a differentiator. They lag by several seconds. There are "instantaneous vertical speed indicators" with an accelerometer to provide some short-term correction.[2] Same problem, with a time constant of seconds, and in an analog device. I ran into this problem in the motion interpolation of a virtual world, and fixed it.[3] A low-pass filter on velocity computed from position needed to be added. Completely different domain, same problem. [1] https://arxiv.org/pdf/2205.12626 https://arxiv.org/pdf/2205.12626 [2] https://www.mcico.com/resource-center/articles/instantaneous-vertical-speed-indicators-combat-lag-time https://www.mcico.com/resource-center/articles/instantaneous... [2] https://community.secondlife.com/forums/topic/451190-merrily-we-bump-along/ https://community.secondlife.com/forums/topic/451190-merrily...