Chris Purcell

Mathematician, computer scientist, bassist, knitter?

ORCID: https://orcid.org/0000-0001-9869-1097

Last Notes

2026-08-05 13:51:44 CEST

- reply

I'm undecided. In fact I think maybe it should be done on a case by case basis. I can't think of an example off hand but I bet there's a generating function result or something of that nature where the base case is the empty graph. See the discussion here: https://link.springer.com/chapter/10.1007/BFb0066433 (also a fun title "is the null graph a pointless concept?")

2026-08-05 09:15:24 CEST

- reply

one of the reasons to define the set of vertices of a graph to be non-empty is that otherwise you mess with the equivalent definitions of a tree. The (supposed) null graph has no cycles and is vacuously connected, yet it has as many vertices and edges.

2026-04-12 23:23:29 CEST

- reply

there was an astonishing headline along the lines of "Vance complains about Europe interfering with Hungarian election while campaigning for Orban"

2025-08-13 20:42:14 CEST

- reply

do you (or any reader) think there's a reason for the east to west effect? Just chance or is it something to do with the way the image is generated. Long chats with chatgpt tend to degenerate in quality in my subjective experience. I could believe that something like that is at play here.

2025-08-05 15:40:26 CEST

- reply

one way to dispense with this unspoken assumption is by observing that 2/4 = 1/2 (or similar).

2025-04-17 10:23:59 CEST

- reply

sorry should have just read to the end before commenting!! thanks.

2025-04-17 10:20:00 CEST

- reply

I suppose that was too much to hope for... thanks for the link I will check it out! It's still a little odd to me that there are no obvious cones here, nor in @greganSF 's list of proofs. Am I just thinking about it in the wrong way? Can we extract some cone from the calculations or are all "fitting" cones sort of equivalent here? Perhaps there's some obvious correspondence between circles in 4d and cones in 3d I'm not getting.

2025-04-17 10:14:48 CEST

- reply

wow thanks. Interestingly, this thought was planted in my head at our local science museum-type-thing-for-kids (Techmania in Plzen), where they have a big cone full of blue liquid you can rotate to see the conic sections. Right next to it they have an ellipse-shaped pool table to demonstrate the "whispering gallery" property. And they have multiple real "whispering galleries" achieved by parabolic dishes etc.

2025-04-17 09:03:02 CEST

Here's a stupid #geometry / #astronomy question. Planetary orbits are ellipses (under the obvious simplifying assumptions) which are conic sections. So what's the cone? There are infinitely many cones that fit of course. But is there one that best explains? To put it another way, is there a neat geometric argument that an orbit should be an ellipse, that doesn't require too much physics? #mathematics

2025-03-20 11:03:29 CET

- reply

it's an extreme case, and macabre, but the Warsaw Ghetto Hunger Study comes to mind. I hope (and believe) conditions in America will not get that bad, but it's an example of hunkering down for sure. They also managed to overcome a typhus epidemic, which is rather topical. The wikipedia page has references, but I haven't read them to be honest.

2025-02-01 08:37:15 CET

My usual test of #chatgpt is to give it a huge number and ask if it's even or odd. It recently passed the test.
Inspired by a hacker news post about doing fizzbuzz by converting to base 15, I gave it a number in base 15 and asked it to check divisibility by 3. It failed miserably and doubled down on its wrong answer. Even when I coached it, it initially made a mistake in even reading the last symbol.
It finally summarised the method as: *either* add up the digits *or* check the last one.