Hacker News: bustermellotron

New comment by bustermellotron in "I let AI build a tool to help me figure out what was waking me up at night"

bustermellotron — Tue, 12 May 2026 05:10:57 +0000

You could use air scrubbers https://en.wikipedia.org/wiki/Soda_lime

New comment by bustermellotron in "A recent experience with ChatGPT 5.5 Pro"

bustermellotron — Sat, 09 May 2026 05:12:28 +0000

I saw Tim Gowers give a talk at the AMS-MAA joint meeting in Seattle about ten years ago where he predicted that in 100 years humans would no longer be doing research mathematics. I wonder if he’s adjusted his timeline.

At the time I thought the key missing tool was a natural language search that acted like mathoverflow, where you could explain your problem or ideas as you understood them and get references to relevant literature (possibly outside your experience or vocabulary).

New comment by bustermellotron in "After a 40-year wait, technology enables three-sided zipper design"

bustermellotron — Wed, 06 May 2026 05:39:52 +0000

Go go Gadget arms!

New comment by bustermellotron in "A beginner's guide to split keyboards"

bustermellotron — Fri, 20 Feb 2026 06:25:22 +0000

I found it easy to adapt to the x-bows keyboard (column staggered and splayed). The thumb buttons and large ctrl, alt, space are great for emacs. My only complaint is that the braces are a bit far away.

New comment by bustermellotron in "The manager's unbearable lack of endorphins"

bustermellotron — Sun, 23 Jun 2024 09:23:22 +0000

I think the book "The Now Habit" discusses this well. (Could be another book though...)

I once completed a 3000 mile cycling tour across the US (and didn't take ADHD meds while on the trip) and was I was basically disappointed to reach the west coast.

New comment by bustermellotron in "The Case for Bash (2021)"

bustermellotron — Fri, 19 May 2023 09:18:53 +0000

This covers most of what you need for "housekeeping" scripts in Python: https://automatetheboringstuff.com

New comment by bustermellotron in "Only one pair of distinct positive integers satisfy the equation m^n = n^m"

bustermellotron — Thu, 20 Apr 2023 19:53:30 +0000

On the other hand, your proof really only needs the binomial theorem and geometric series.

New comment by bustermellotron in "Only one pair of distinct positive integers satisfy the equation m^n = n^m"

bustermellotron — Thu, 20 Apr 2023 19:45:22 +0000

The “claim” more or less proves that k-1 th root of k is less than 2 if k is larger than 2. So I think your argument is equivalent.

New comment by bustermellotron in "Only one pair of distinct positive integers satisfy the equation m^n = n^m"

bustermellotron — Thu, 20 Apr 2023 10:06:22 +0000

Here is an elementary proof:

Since m and n are distinct, we may assume that m > n >= 2. From the equation and unique factorization, we know that n divides m, so write m = nd.

Then (nd)^n = n^(nd). Hence d^n = n^{n(d-1)}, which yields d = n^{d-1} >= 2^{d-1}.

Claim: if k is an integer greater than or equal to 3, then k < 2^{k - 1}.

Proof: the base case is clear: 3 < 4. Suppose k > 3 and k - 1 < 2^{k - 2}. Then k < 2^{k-2} + 1 <= 2^{k-1}, where the last inequality holds because 2^{k-1} - 2^{k-2} = 2^{k-2} >= 1. QED

So, d must be less than 3. Since m = nd and m and n are distinct, d is not 1, so d = 2. Since d = n^{d-1} and d - 1 = 1, we have n = d, so m = 4.