Too many Sunday cyclists on the River Lea towpath. You are interrupting my chain of thought!

The conjecture lives! I thought I had found a counter-example, in five dimensions, but I was mistaken. Say that a quadruple (A, B, C, D) of subsets of a (finite) set X is a rectangle if A + B = C + D, and AC = BD, where the sum of two subsets is their symmetric difference, and their product is intersection. Totally standard:

https://en.wikipedia.org/wiki/Symmetric_difference

Say that a set T of subsets of X is a tope if, for any rectangle (A, B, C, D) in X, if both A and C are in T, then at least one of B, D is.

Say that a measure on X is an assignment of an integer m(x) to each element x of X, and then that for a subset A = {x_1, …, x_k}, m(A) = m(x_1) + … + m(x_k).

(I’m aware that measures are supposed to be non-negative. It doesn’t matter here.)

Conjecture For every tope T there exists a measure m such that, if A is in T and B is not in T, then m(A) > m(B).

It might be false; or worse, it might an be unprovable cul de sac. I gave up thinking about it a few months ago because I wasn’t getting anywhere, but now I am thinking about it again. I am a monk.

Capitalize “monk”.

The conjecture is geometric. If X is a set containing n elements, its subsets may be considered as the vertices of an n-dimensional cube. For example, if X has three elements, choose any ordering of them, say (a, b, c), and then consider a subset A of X as the coordinates (x, y, z), where:

x = 1 if a is in A, x = -1 if a is not in A,
y = 1 if b is in A, y = -1 if b is not in A,
z = 1 if c is in A, z = -1 if c is not in A.

So e.g. {b, c} = (-1, 1, 1), {b} = (-1, 1, -1), empty set = (-1, -1, -1), X = (1, 1, 1). Totally standard:



Then (A, B, C, D) is a rectangle, as defined above, if and only if the corresponding coordinates are the vertices of a rectangle. The point of the conjecture, if true, is that for any tope T there would exist a hyperplane separating sets in T from sets not in T, thus providing a description of the geometry of the n-cube independent of infinite Euclidean space.

https://en.wikipedia.org/wiki/Hyperplane

and you ended up a cab driver. what happened. brain damage.

A few factors. A big research theme is that standard mathematics is infinite, computers are finite, so how to upload math? Hit the x^2 button on a calculator enough times and you get an error message. My teachers and peers think that you accept math as it is, and set up a theory of approximation of it. My view, finally, was that you reject infinite math altogether, and try to replace it. Reject it as the nonsense that it is.

I don't get along with the right people. I don't fit in.

i dont either . invent fun ways to make big money slowly. its easy.

The colours of Spring are light colours. Pale greens and yellows. I hadn’t noticed that before, although I have long been of the opinion that the good moments cannot be pre-booked or arranged, and certainly not in loadsamoney Essex. My prejudices are telling me I don’t like it here. But here is a pub old school enough to still have a seafood kiosk outside, and cockles are the best sushi on the planet. They have enough malt vinegar and white pepper too, no problem, and serve up a Guinness without a load of Covid-19 bullshit to accompany it. It’s a beautiful afternoon. That’s a Shelby Cobra, a couple of the locals remark casually, and I catch a glimpse of it burning into Epping Forest. A Shelby Cobra? I’m beginning to feel it.

Until today, you could have shown me this image and I wouldn’t have known what it was:



Even though I’ve seen it hundreds of times before, and now think it’s quite good. Today I started to catalogue the tile murals on the Victoria line platforms. No longer an insider passing through, I am now an outsider looking in. This person seems to know what they’re talking about:

https://thebeautyoftransport.com/201...ine-london-uk/

although Pimlico is the best one, and I knew that already.

Scrap the above, I knew there must have been an anomaly. The reason it didn't register is that for 25 years it wasn't there. I have tried to find a picture of the other design.

It’s Satanic. Enough said.

What do you like about Pimlico?

I like that it's yellow, fills its space, and is of its time, but that's no kind of an answer. It has quality. I mean, is it not obviously the best one?

Although it is clearly of the same epoch as the station, I like that it's slightly at odds with it, which makes you notice it.

and the next big race will be there.

Yeah, I like yellow too, but did you notice that one had a picture of a horsey?

I'm not sure if you think I was being sarcastic, Phat, but I wasn't.

The Q-bert one is clearly the best.

Hot Rod Charlie came in third in the Kentucky Derby just run. Did you have a bet down Charlie? I did not.

I had a bet on Hot Rod Charlie!

Well how come Hot Rod Charlie isn't running in the Preakness, at Pimlico? He'd be a cinch to win it.

What's the cost of a good pint in London Town these days in the COVID Age? Pulled the correct cast way of course.


https://www.bing.com/videos/search?

Some prophesies come true:

he isnt for 3 reasons.

he lost the derby so cant get the triple. its all about fame for breeding

horses need rest between big events. and these are young horses

probably will like the longer belmont than the short pimlico track.

Rendlesham railway viaduct is known locally as the 14 arches. It’s out of the way, and I saw it two or three times during childhood. One time I was about to run a cross country race at nearby Hilly Fields, and somebody said there’s the 14 arches, and you could see it in the distance. It’s not simple to find a good vantage point, even if you were born nearby and know what you’re looking for. But when you see it, there it was all along.

Aha, a cricket match at North Enfield CC. Civilization.

E. A. Bowles was a leading horticulturist of his day, and his garden at Myddelton house is a testament to that.

A slight eeriness to the recently defunct Whitewebbs municipal golf course. Weeds on the fairways. I played it a few times.

A pint and a half of McMullen’s Country bitter at the Wonder costs £5.85. I think you’re up to date.

https://en.wikipedia.org/wiki/Edward_Augustus_Bowles

You ******s.

Addendum to a previous post. Jimmy Moody was shot dead in the Royal Inn on the Park, next to Victoria park, in 1993. The hipsters have moved in since then, and I don't blame them. Victoria park is ultra London.

I once happened to walk past fellow Richardson gang member Mad Frankie Fraser in the back streets of Islington. A tiny individual, out walking his tiny dog, looking utterly at peace with the world. An extremely violent and dangerous person.

https://en.wikipedia.org/wiki/Jimmy_Moody