awanderingmind
Joined 5 years ago
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429
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95
Member since
Nov 22
https://www.awanderingmind.blog/
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Comment · 9 months ago
My personal site where I post essays about various things - generated using hakyll: https://www.awanderingmind.blog/
Comment · 10 months ago
I found the writing, and the descriptions of the types of trisectors, strangely poignant. Most of us do not attempt to trisect an angle with straightedge and compass; but surely many of us have other irrational obsessions with which we waste our time (I have certainly been guilty of this). I hope people can find time to look up from their interactions with social media and LLMs for enough healthy introspection to avoid these traps.
Comment · 1 year ago
This is a strange analogy. The policy saves people money on their power bill. The backyward furnaces are considered a disaster because, among other things, they produced low quality steel, and diverted labour from agriculture and other things, none of which is the case here - people pay for solar panels and install them once, and then achieve savings.
Comment · 1 year ago
I incorrectly had a ≤ instead of =, my apologies.
Comment · 1 year ago
There is a lot of focus in the comments on the authors' credentials and, apparently, their writing style. It is a pity, because I think their discussion of scaling is interesting, even if comparing LLMs to grid-based differential equation solvers might be unconventional (I haven't convinced myself whether the analogy is entirely apt/valid yet, but it could conceivably be).
Comment · 1 year ago
According to the actual paper (https://arxiv.org/pdf/2506.24088), it has been an open conjecture since at least 1977. The quote:
> Unknotting number has long been conjectured to be additive under connected sum; this conjecture is implicit in the work of Wendt, in one of the first systematic studies of unknotting number [37]. It is unclear when and where this was first explicitly stated; most references to it call it an ‘old conjecture’. It can be found in the problem list of Gordon [13] from 1977 and in Kirby’s list [16].
'Additive' here means that if u(K1) is defined as the unknotting number of the knot K1, and u(K1#K2) the unknotting number of the knots K1 and K2 joined together, then u(K1#K2) = u(K1) + u(K2). It is this that has (assuming the paper is correct) been proven false. A deceptively simple property!
edit: I initially incorrectly had a ≤ sign instead of =
Comment · 1 year ago
Cool example in that link, thanks!
Comment · 1 year ago
Cool study. I really want to believe the results, but the effect on life extension is so large (see figure 2B) that I find it hard to. Maybe there was some uncontrolled confounding factor? It is noted in the 'Methods' section that 'Researchers were not blinded to group allocation [...]', which is unfortunate.
Comment · 1 year ago
This perspective is addressed in the article... TLDR; that doesn't seem to be where this is going.
Comment · 1 year ago
This is a rare type of article - a concrete analysis of different approaches to programming (that are arguably themselves reflections of different cognitive styles), that outlines the shortcomings of one approach in a specific domain, without generalising too much.
Comment · 1 year ago
You mean something like this https://en.wikipedia.org/wiki/Bremermann%27s_limit or this https://en.wikipedia.org/wiki/Quantum_speed_limit?