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Joined 2 years ago
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Cake day: June 12th, 2023

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  • Let f(x) = 1/((x-1)^(2)). Given an integer n, compute the nth derivative of f as f^((n))(x) = (-1)(n)(n+1)!/((x-1)(n+2)), which lets us write f as the Taylor series about x=0 whose nth coefficient is f^((n))(0)/n! = (-1)^(-2)(n+1)!/n! = n+1. We now compute the nth coefficient with a simple recursion. To show this process works, we make an inductive argument: the 0th coefficient is f(0) = 1, and the nth coefficient is (f(x) - (1 + 2x + 3x^(2) + … + nx(n-1)))/x(n) evaluated at x=0. Note that each coefficient appearing in the previous expression is an integer between 0 and n, so by inductive hypothesis we can represent it by incrementing 0 repeatedly. Unfortunately, the expression we’ve written isn’t well-defined at x=0 since we can’t divide by 0, but as we’d expect, the limit as x->0 is defined and equal to n+1 (exercise: prove this). To compute the limit, we can evaluate at a sufficiently small value of x and argue by monotonicity or squeezing that n+1 is the nearest integer. (exercise: determine an upper bound for |x| that makes this argument work and fill in the details). Finally, evaluate our expression at the appropriate value of x for each k from 1 to n, using each result to compute the next, until we are able to write each coefficient. Evaluate one more time and conclude by rounding to the value of n+1. This increments n.


  • I don’t think you need permission to send someone an email directly addressed to and written for them. I don’t have context for the claims about Kagi being disputed, but I’d be frustrated if someone posted a misinformed rant about my work and then refused to talk to me about it. I might even write an email. Doesn’t sound crazy. If there’s more to the “harassment” that I don’t know about, obviously I’m not in favor.





  • I’m a hobbyist speed typer (200wpm+), generally prefer linear switches. I do bottom out almost always. To reduce the impact of bottoming out, if this is an issue for you, you can:

    • use a softer and/or more flexible plate. An aluminum or brass plate is very stiff and will absorb less of the impact compared to an FR4 or polycarbonate plate. The mounting style of the keyboard can also affect this, e.g. a gasket mount has the pcb “floating” on rubber pads that absorb shock, and a plate that is screwed directly into a metal chassis will absorb almost nothing. The plate/pcb can have flex cuts added to improve flexibility and absorb more shock.

    • use switch springs with a higher actuation force. Common choice is 63.5g or 68g, which is a little heavier than the Akko switches’ ~45g. The spring can also have a variable profile such that the resistance increases more as the spring is depressed, so it kind of cushions the impact a tiny bit. I use extra long springs which has the opposite effect, the response curve is more constant.

    • use rubber o-rings on the switches. This will make them feel squishy and I don’t really recommend it, but it’s an option if replacing your keyboard isn’t.

    FWIW I mostly use an Odin75 keyboard with an FR4 plate and stock alpaca switches. This is gasket mount + soft plate with lots of flex cuts, so it’s a reasonably soft typing experience.