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Slow

michaelnotebook.com

141–150 of 238 posts

Re: Slow

#141
nitpick:

> That's an accuracy comparable to measuring the distance to the Sun to an accuracy of one atom.

This does not exist, because "the location of the Sun" cannot be defined to the precision of one atom, as the Sun is constantly changing shape and size on a much, much larger scale (easily half the orders of magnitude of the distance to be measured).

Re: Slow

#144

I'm reminded of the famous story of (I think) the central beam in a building at Oxford. The story goes something like: The central beam was beginning to fail and the Oxford administration knew they needed to replace it. When they went around for quotes, no one could replace the beam because it was 100 ft in length and sourced from an old growth tree. Such logs were simply unavailable to buy. To solve the issue, the s…

What is a "growth tree"?

You have the real answer, but I suppose it is contrasted with a "value tree."

Re: Slow

#146

Earlier quoted context omitted.

Interesting new contender for simplest to state unsolved problem: The Antihydra Does this program halt? a = 8 b = 0 while b != -1: if a % 2 == 0: b += 2 else: b -= 1 a += a//2 (// being integer division, equivalently a binary shift one to the right: >> 1) https://www.sligocki.com/2024/07/06/bb-6-2-is-hard.html https://bbchallenge.org/antihydra

Fwiw, ChatGPT is able to say that it doesn't. I wonder what other classes of programs it's able to state if it halts?

The math community surely expects a proof of that, and ChatGPT surely doesn't (yet) have one. (Maybe some day it will, as Kevin Buzzard and others are experimenting with asking language models to produce formal proofs.)

You could get LLMs to opine on many unresolved math conjectures, but I doubt much credence should be given to their responses, when not accompanied by a proof.

Re: Slow

#147
post #117
post #63

Earlier quoted context omitted.

This is an urban legend. The college archivist covered it: http://web.archive.org/web/20020816065622/http://www.new.ox.... > In 1859, the JCR told the SCR that the roof in Hall needed repairing, which was true. > In 1862, the senior fellow was visiting College estates on `progress', i.e., an annual review of College property, which goes on to this day (performed by the Warden). Visiting forests in Akeley and Great Ho…

Ah yes, "exacting young man debunks charming tale with touching moral, to the benefit of nobody". A tale as old as time.

I think it still works fine as a parable, and it doesn't hurt to know a little bit more about how the trees are Oxford are really kept.

Re: Slow

#149

Here's another good example of a series of slow experiments: the cosmic distance ladder. https://www.youtube.com/watch?v=YdOXS_9_P4U https://en.wikipedia.org/wiki/Cosmic_distance_ladder You can compute the distance to the moon if you know the radius of the earth by looking at how long lunar eclipses take, data gathered over years of observations. Eratosthenes computed the radius of the earth by clever trigonometry in…

Looking forward to Tao’s book on the subject. This is worthy of its own post, thanks for sharing.

Re: Slow

#150

I'm reminded of the famous story of (I think) the central beam in a building at Oxford. The story goes something like: The central beam was beginning to fail and the Oxford administration knew they needed to replace it. When they went around for quotes, no one could replace the beam because it was 100 ft in length and sourced from an old growth tree. Such logs were simply unavailable to buy. To solve the issue, the s…

There's a better version of this sort of story that I first heard also set at Oxford.

The stone steps in front of one of the college buildings have been worn down by centuries of people walking up them. The college decides to replace it, but it turns out that the stone used comes from a specific quarry in Wales that in the hundreds of year that have elapsed has been finished when it comes to this sort of rock.

Nobody is sure what to do. They want matching stone but the only other source is in South Africa and it would cost a fortune to ship the stone from there.

A young architect suddenly has a brilliant idea. "We could just extract the stone, turn it over and get a brand new edge". Everyone is very excited, and contractors and tools arrive to carry out the simultaneously tricky yet simple procedure.

It was at that point they discovered this had already been done.

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