The gist of it seems to be as follows. The Riemann zeta function, defined on some complex numbers, is the function f(x) = 1/1^x + 1/2^x + 1/3^x + ..., which is the limit, if it exists, of the sequence 1/1^x, 1/1^x + 1/2^x, 1/1^x + 1/2^x + 1/3^x, ... . The function is defined on all complex numbers whose real part is greater than 1. If it were defined on -1, then f(-1) would be 1 + 2 + 3 + ..., but it isn't defined on -1, because the sequence 1, 3, 6, ... has no limit. However, there does exist a unique analytic function g such that, for all complex numbers x, if f(x) is defined then so is g(x), and f(x) = g(x), and g is defined on -1. For reasons I don't understand, g(-1) = -1/12, and that somehow entitles one to say that 1 + 2 + 3 + ... = -1/12.

Come to think of it, I don't understand why the Riemann zeta function can't just be considered as a function on the reals, or even the rationals, and then proceed from there. Is it because in that context it does not extend to an analytic function that is defined on -1? Is that why it is necessary to invoke the complex numbers?

The "proof" I've seen is predicated not on the zeta function (which I don't really understand) but on other "proofs" that involve shady manoeuvres like

S1 = 1 - 1 + 1 - 1 + ... = 1/2 (because it yields partial sums 1 and 0 of which 1/2 is the mean lol)

Eliminate the impossible...

It's the not knowing whether a solution even exists. A problem is easier to solve if you know in advance that a solution exists. I keep hoping it's there, a hidden Faberge egg staring at me like the Cheshire cat, but the evidence to the contrary is accumulating. Failure is damaging to one's faith.

Accentuate the positive!

Wow. A kindred spirit. I stop off in the local for a pint, and meet a woman who knows more than me about the A6 murder case, thinks Hangover Square is one of the greatest books ever written, and that Fall Out is the greatest work of art ever. She's called Denis, like in the Blondie song.

It's funny to look back and remember Blondie as being (rightly) adored by the year zero set when quite a few of their hits, like Denis, were covers (very much frowned upon at the time).

What a great band though.

Blondie was part of the canon.

I had to finish early today. Quickest way from Mayfair to Victoria was via Waterloo Bridge. Unless you want to go via Kensington LOL. Some demonstration. I check every Friday whether there is one planned in support of Palestine, which there has been every other Saturday for the past six months, so I'm not sure what this one was. Mexicans in the back. At first they don't get it, but when they see the mayhem everywhere it's "you treated us like a friend", which was a nice thing to say. The aforementioned pub near me is some rare spacetime conjunction of people I like. By coincidence, some hippy gets in at Victoria yesterday, "just a short journey, man", and it turns out he's a friend and neighbour of one the regs. Of course I don't charge him. Gay Pride next Saturday. Legalize it and they start acting like they own the place. Just kidding. Nothing is happening.

Hippies still exist!. What a time warp. I haven’t seen a real original hippie in at least 20 years, possibly more. And he didn’t realize what planet he was on which is just as well. He just faded away into a wisp of sweet smelling weed smoke. Just a faded memory on the jagged edge of history.

It's the Magic Taxi, man. Free rides for hippies, sick children and Chelsea Pensioners.

I must go and visit Benedict Arnold's resting place sometime. I live not far away. Happy Independence Day!

https://www.changesinlongitude.com/b...old-in-london/

Freedom is Slavery

Making money is addictive. One sees it in some of the wealthy, and in the lie that people choose to be impoverished. My innate sense of survival again facilitates my annual pilgrimage up the North. I shall be visiting York Minster, Hadrian's Wall, and the Durham Miners Gala, among other things, and have purchased copies of the magazines Viz and Philosophy Now for the train journey up, to get me in the mood.

People are always leaving stuff in the cab. Umbrellas, hats, gloves, sunglasses, wallets full of money and drugs, but most of all it's the phone. It's such a nuisance that I am working on acquiring the habit of checking the back after each journey, but this time they contrive to leave it in one one of the fold-down seats, so I couldn't see it in any case. The Lost Property office used to be central, but TFL, in their wisdom, have moved it to the back of West Ham bus garage, which is the most out of the way, difficult, and completely un-signposted place to find, and where all the parking places are currently chained off. Entry is via garbled intercom, local government flunkeys are always the most officious, and collection of lost property is strictly by appointment only. Good. Stop leaving your goddam phone in the cab, man.

Aren’t they usually drunk and don’t notice it sliding out of their pocket?

Anything left in the cab is yours: drugs, babies, contraband, used condoms, newspapers, etc. Stop sobbing about it. Take what is useful and throw the rest into the Thames.

Lastcard, piss on Hadrian’s wall for me. It’s the American thing to do. Thanks. I owe you a few pints.

The American thing to do would be to dump his car battery on it.

The wallet people were drunk, but usually they're either old, or disoriented tourists, or those people who go through life not caring. You see them stepping out in the road all the time, blissfully unaware of oncoming traffic, normally dragging a toddler behind them. I almost envy them, sometimes.

I did briefly consider throwing this one in the Thames. But I have this pesky conscience, like Pinocchio.

I never meant to be some boy about town. Knightsbridge, Chelsea, St. James. It must be something within me. Or rather, some sick conjunction of random events. To Homerton. E9. I went to Seaham Wetherspoons on holiday, Seaham being a defunct mining town on the Durham coast, where Uncle Wilf came from, but Hackney Wetherspoons is just as rock bottom. £2 a pint LOL. Cutting edge, Scott of the Antarctic hipster frontier. Check out A Path Through Haze radio show. Totally authentic. Maybe more on that later. An excellent meal. You can tell where the bombs fell in Hackney.

how much does a pint cost elsewhere?

Wetherspoons in Victoria is £4.90, and in Enfield is £2.70. My local, which is just off Sloane Square, is £6.70.

How common is it for you to get fares going across a huge segment of London?

For no good reason, the idea popped into my head of you rolling up at Heathrow, somebody jumping in, and giving an address in the East End.

I’ve taken a few taxis in London; I paid them off with large sacks of Gold Coin; Tip included.

If I ended up in the wrong saloon, I would have to find a job just to get a buzz on.

Had one from Paddington to Tooting Broadway a couple of weeks ago, and maybe on the same day, Nine Elms to Golders Green, both about £50. Maybe a couple of those a month. Although I have dropped off at Heathrow many times, the examiner who gave the talk on the day I got my badge said she'd never picked up from there because that's a too complicated other world, and what happens to them is they lose their Knowledge.

Yeah, also went in The Gun in Homerton (£6.30). I prefer my 1860s pubs not to have large, neon signs in them, and to retain something original: the bar, the windows, the ceiling... something. But that's perhaps not the hipsters' fault and at least they're keeping it alive. It's David Lynchian inside; wrong, but yet not wrong. A pile of free CRACK magazines on one of the tables, and terrific music, suggestive of a whole ocean of great music I've never heard, namely the A Path Through Haze radio show. What the cool kids are up to.

Make sure you have enough cash to get a blow job from some crack whore in the East End to top off the evenings frivolities!