March 2020 was barely over when people started talking about the `Before Times’ when, so it was rumoured, people were allowed to leave their houses or flats for more than thirty minutes a day, and could invite as many people as they liked into said flats and houses, and furthermore could gather together in public spaces, public transport, offices, cinemas, theatres and other such places for the purpose of, well, anything. The propaganda at the time was intense: this was going to change everything for ever, and we were never going to have family Christmas dinners again. Let alone picking up attractive women in crowded bars for the purposes of… oh no, none of that. There were months in 2020 when the British Government made sex illegal unless you were already in a relationship. Seriously. And everyone went along with it - which either meant they were ignoring it, or all the rumours about nobody getting laid these days were true. Or both.
Most people agree that something has changed since then, but cannot say exactly what, except that it is for the worse.
I’ll take a shot at it.
Part the First. Transferring To The Internet.
At the start of 2008, the world and its Old Ways was still out there. Just over 11 years later most of the Internet had migrated to dedicated apps on our phones, connected by 5G wireless, which brought speeds some broadband services could not provide in 2010. By 2020 many broadband providers were offering FTTH. Everything we really needed to do, from reading a newspaper to renewing a driving license, from paying bills and ordinary shopping, to presenting airline and train tickets, and all our non-IRL communications were done on the phone. Or maybe a laptop or tablet. Nobody read a newspaper in public, or used an A-Z (ask your grandfather) to navigate anywhere. Nobody sat at home hangin’ on the telephone
and everybody turned up for social events because there was no way to flake out in the last hour, when everyone was travelling to the meeting-point. Dating apps replaced going out on the pull, or taking a chance on the Personals in the papers and Private Eye.
This happened over a period of time. The applications mostly appeared in the mid-late 2000’s. The iPhone with 3G and apps appeared in late 2008. 3G was not the experience people needed, which came with 4G in 2013 (in the UK) and 5G in 2019. We had got used to the apps, and after 2013 could swipe left and right real fast. By 2019, a lot of people had migrated a lot of their transactions onto the Mobile Internet. But not everything and not everyone. And the Old Ways were still there. Banks still had branches. Pret A Manger still took cash. Amazon deliveries during the working week could be tricky. The big companies would have waited a couple more years to make sure that the Mobile Internet was not a fad that we would tire of, before they started cutting back the Old Ways over a period of maybe five years.
The Lockdowns did that for them. In. An. Instant.
The Old Ways were closed and banned and could kill you if you stood too close to someone in a queue, and the transfer of our lives to the Internet and our phones was complete by the end of March 2020. We got used to it, and the Old Ways could be and were shut down much faster.
That’s part of why March 2020 is the dividing line.
Part The Second. What You Didn’t Know You Learned From The Lockdowns
Before March 2020, you thought you knew about yourself and the people around you. By March 2022 you knew it was all an illusion.
You now know things about the people around you that you kinda wish you didn’t. They are curtain-twitching grasses. They are irresponsible killers because they did not believe masks are effective, nor stood six feet away, took walks that lasted more than thirty minutes, and ignored The Rule of Six. They are super-gullible people who understand nothing about how to identify a deadly killer virus, and how a Government should report its effects. They are fools who think they know better than the Government Experts and the BBC. And worse, you know you fell for it, at least for a while. Unless you didn’t, and snuck round to your girlfriend’s place at night, because to hell with it. You know that the Experts are not, that your Government thinks nothing of hiring Behavioural so-called Scientists to scare you with lies and exaggeration. You know the BBC is not an independent news service, but a stooge of the State. You know that nearly all the academics, journalists and other assorted intellectuals will say whatever the Government tells them to say, because they cannot afford to stop sucking on the teat of Government grants. All those psychotherapists, psychologists and online content creators telling you that human contact and presence and relationships are so important, and how bad for us isolation is? Where were they? Not a peep. You know that no-one stands between you and the arbitrary power of the State, because you have felt that power exercised and seen millions go along with it. You have no idea if there will be a next time, and if there is, if you will fold like a cheap suit, or call it out for the BS that it is. You know that it does not matter what you believe or try to do, because the State will close the shops, the libraries, the churches, the cafes and restaurants, or whatever it is they need to close to make our beliefs and actions pointless. There were more restrictions put on the British public between March 2020 and March 2022 than in the Second World War, and nobody protested for a moment.
These are not things we are supposed to know about ourselves and others. Which is why a lot of people have stuffed the Lockdowns down a memory-hole. It was an emergency, the NHS was at risk, and every country was doing it. It will never happen again. There is nothing to see here. Let’s move on. The unconscious never forgets, and the people around us don’t either.
That’s why there are the Before Times. We were innocents in the Before Times, and now we are not.
Friday, 16 October 2026
Friday, 9 October 2026
Twelve Albums To Listen To
There was a time when, according to the Rock Press, the Best Albums Ever were Revolver and Pet Sounds, in either order of your choosing.
Not even the journalists who said that believed it. It’s just what they have to say so they keep their Rock Journalist Cred Card. For one thing, the best Beatles album is either Rubber Soul or The White Album. For another thing, Pet Sounds is not the best Beachboys album: that would be some Greatest Hits compilation, because the Beachboys were a pop-singles band. And their best song is Heroes and Villains, closely followed by Good Vibrations. In case you were wondering.
In the 1960’s all the pop bands were trying to do the same thing: entertain the public, sell records and get into the Top Ten, but even then there were tribes - Surfers, Mods, Rockers, Hippies - for whom music was part of a lifestyle. By the 1970’s The Sex Pistols were not trying to do the same thing as Yes, who were not trying to do the same thing as Blue Oyster Cult, who were not trying to be America. From the 1970’s onwards the audience for `music’ was so large and cosmopolitan that bands could make a living writing for niche markets. The idea of a `best album’ had become silly.
Given the sheer output of some artists, it barely makes sense to ask what is their `best’ album? One’s `favourite’, sure, but best? Which of Miles’ output is the `best’? Or Neil Young? Joni Mitchell? Madonna? Eric Clapton? Frank Zappa? John Digweed? As opposed to, which one will blow your head off with its experiments? Some artists do have a `best’ that also sold a container-load, and go on to produce a steady output that is bought by a core of die-hard fans, see for example Suzanne Vega. Some artists have a `period’, usually of not more than five years or so. If they don’t break up, they carry on afterwards, but the magic has passed. Jefferson Airplane, The Who, The Beat, Prince, Spandau Ballet, and others.
Some bands just can’t make an album that has no clunkers. They are basically singles artists, and their Greatest Hits album is usually almost too much too take.
Here’s my list of Twelve Albums That You Must Listen To:
After Bathing At Baxters - Jefferson Airplane (1967)
Everyone Knows This is Nowhere - Neil Young and Crazy Horse (1969)
Blue - Joni Mitchell (1971)
Bod Dylan’s Greatest Hits Vol 2 - Bob Dylan (1971)
Bremen / Lausanne - Keith Jarrett (1973)
Get Up With It - Miles Davis (1974)
Press Colour - Lizzie Mercier Descloux (1979)
Timeless - Goldie (1995)
Endtroducing - DJ Shadow (1996)
Bedrock, Complied and Mixed by - John Digweed (1999)
Broken Social Scene - Broken Social Scene (2005)
These are all older, because by the 1990’s all the genres had become settled and refined. There’s no Metal and no Rap, because neither speak to me, and both genres were settled more or less the first time they were played. There’s no Stadium Rock, Folk or post-Coltrane jazz because it isn’t experimental, it’s settled.
The Good Stuff is always at the start, when the rules aren’t set, the limits aren’t known, the A&R people don’t understand what they are dealing with, and there isn’t a huge technical hurdle for newcomers to jump. Every new technology has to be learned by everyone from scratch, and that takes away the advantage of older musicians, if only for a couple of years. Every new movement in pop music starts with a new technology or the rejection of something from the past: punk explicitly rejected the techno-flash of early 70’s bands; 80’s music has the sound it does because of all those early synthesisers and drum machines; Britpop was a deliberate rejection of the slick production of the 80’s; nuMetal was a fusion of Metal and rap that dropped the need for shredding; Grunge was Punk v2. Rejecting the techniques and the slickness means that the bands have to focus on songs, and pop music has always been about songs.
It may be no kind of co-incidence that the two most creative bands - The Beatles and Miles Davis - both worked with classically-trained musicians - George Martin and Teo Macero - who had gone into music production when it was a suit-and-tie salaried job for classically-trained people who didn’t quite fit in to the orchestral performance world. Both Martin and Macero not only knew all the usual classical composition technique, they also knew about the avant-garde composers. They knew about electronic music, sound effects, musique concret, and the like, and they knew about what the avant-garde jazz musicians were doing. These were possibly the most musically well-informed guys who ever graced a recording studio. Miles was no slouch either, and Paul McCartney spent the months before recording Revolver listening his way round London’s `Underground Music’ scene. (Revolution No 9 was the Beatles saying Yeah, we are so freaking good we can even do musique concret.) They had to look back on the history of other genres of music, because rock / pop had no history of its own. By the mid-1970’s there was enough history for the whole enterprise to have its own history, and it became more consistent and stable.
Not even the journalists who said that believed it. It’s just what they have to say so they keep their Rock Journalist Cred Card. For one thing, the best Beatles album is either Rubber Soul or The White Album. For another thing, Pet Sounds is not the best Beachboys album: that would be some Greatest Hits compilation, because the Beachboys were a pop-singles band. And their best song is Heroes and Villains, closely followed by Good Vibrations. In case you were wondering.
In the 1960’s all the pop bands were trying to do the same thing: entertain the public, sell records and get into the Top Ten, but even then there were tribes - Surfers, Mods, Rockers, Hippies - for whom music was part of a lifestyle. By the 1970’s The Sex Pistols were not trying to do the same thing as Yes, who were not trying to do the same thing as Blue Oyster Cult, who were not trying to be America. From the 1970’s onwards the audience for `music’ was so large and cosmopolitan that bands could make a living writing for niche markets. The idea of a `best album’ had become silly.
Given the sheer output of some artists, it barely makes sense to ask what is their `best’ album? One’s `favourite’, sure, but best? Which of Miles’ output is the `best’? Or Neil Young? Joni Mitchell? Madonna? Eric Clapton? Frank Zappa? John Digweed? As opposed to, which one will blow your head off with its experiments? Some artists do have a `best’ that also sold a container-load, and go on to produce a steady output that is bought by a core of die-hard fans, see for example Suzanne Vega. Some artists have a `period’, usually of not more than five years or so. If they don’t break up, they carry on afterwards, but the magic has passed. Jefferson Airplane, The Who, The Beat, Prince, Spandau Ballet, and others.
Some bands just can’t make an album that has no clunkers. They are basically singles artists, and their Greatest Hits album is usually almost too much too take.
Here’s my list of Twelve Albums That You Must Listen To:
After Bathing At Baxters - Jefferson Airplane (1967)
Everyone Knows This is Nowhere - Neil Young and Crazy Horse (1969)
Blue - Joni Mitchell (1971)
Bod Dylan’s Greatest Hits Vol 2 - Bob Dylan (1971)
Bremen / Lausanne - Keith Jarrett (1973)
Get Up With It - Miles Davis (1974)
Press Colour - Lizzie Mercier Descloux (1979)
Timeless - Goldie (1995)
Endtroducing - DJ Shadow (1996)
Bedrock, Complied and Mixed by - John Digweed (1999)
Broken Social Scene - Broken Social Scene (2005)
These are all older, because by the 1990’s all the genres had become settled and refined. There’s no Metal and no Rap, because neither speak to me, and both genres were settled more or less the first time they were played. There’s no Stadium Rock, Folk or post-Coltrane jazz because it isn’t experimental, it’s settled.
The Good Stuff is always at the start, when the rules aren’t set, the limits aren’t known, the A&R people don’t understand what they are dealing with, and there isn’t a huge technical hurdle for newcomers to jump. Every new technology has to be learned by everyone from scratch, and that takes away the advantage of older musicians, if only for a couple of years. Every new movement in pop music starts with a new technology or the rejection of something from the past: punk explicitly rejected the techno-flash of early 70’s bands; 80’s music has the sound it does because of all those early synthesisers and drum machines; Britpop was a deliberate rejection of the slick production of the 80’s; nuMetal was a fusion of Metal and rap that dropped the need for shredding; Grunge was Punk v2. Rejecting the techniques and the slickness means that the bands have to focus on songs, and pop music has always been about songs.
It may be no kind of co-incidence that the two most creative bands - The Beatles and Miles Davis - both worked with classically-trained musicians - George Martin and Teo Macero - who had gone into music production when it was a suit-and-tie salaried job for classically-trained people who didn’t quite fit in to the orchestral performance world. Both Martin and Macero not only knew all the usual classical composition technique, they also knew about the avant-garde composers. They knew about electronic music, sound effects, musique concret, and the like, and they knew about what the avant-garde jazz musicians were doing. These were possibly the most musically well-informed guys who ever graced a recording studio. Miles was no slouch either, and Paul McCartney spent the months before recording Revolver listening his way round London’s `Underground Music’ scene. (Revolution No 9 was the Beatles saying Yeah, we are so freaking good we can even do musique concret.) They had to look back on the history of other genres of music, because rock / pop had no history of its own. By the mid-1970’s there was enough history for the whole enterprise to have its own history, and it became more consistent and stable.
Friday, 2 October 2026
The Guitars of Woodstock…. Were Not Strats
There’s a neat little video about this.
The notes have the following list:
John Fogerty - 1969 Rickenbacker 325
Jerry Garcia - 1967 Gibson SG Standard
Jorma Kaukonen - 1964 Gibson ES‑345
Alvin Lee - 1959 Gibson ES‑335 “Big Red”
Johnny Winter - 1968 Fender XII
Buzzy Feiten - 1960s Gibson ES‑335
Leslie West - Gibson Les Paul Junior
Pete Townshend - 1968 69 Gibson SG Special
Carlos Santana - 1960s Gibson SG Special
and finally….
Jimi Hendrix - 1968 Fender Stratocaster
Gibson 7, Fender 2, Rickenbacker 1. Gibsons evenly split between SG’s and ES’s. The sound of Woodstock was the sound of the humbucker. Legendary session guitarist Tim Pierce said that the standard advice on the West Coast when he was getting started was get an ES335 and a Fender Princeton.
How? Why? After all, Hank B Marvin was a big deal in the UK, and this guy called Buddy Holly was apparently a thing in the States, and they played Strats in the 1960’s (and that was good enough for Dave Gilmour). Well, it was the days before pedals, when any effects had to be obtained by some kind of abuse of studio equipment. Anyone who wanted a `sound’ had to get it from the guitar and the amp, and maybe refine it with some EQ in the studio board.
It was two things. One is an effect often seen in the early history of a technology, the other was gain pedals.
The largest amount of whacky, creative weirdness in any technology is always just after its invention, while it is all still being made in garages and small factories, and no-one has invested serious money on production lines and staff training. Take a look at some of the early desktop and laptop computers in the 1970’s and 1980’s. Or mobile phones in the 1990’s and 2000’s, before the iPhone. Or MP3 players before the iPod. Once IBM waded in with a desktop design, everyone else followed suit, because, you know, IBM. Once Apple waded in with its massive production and superior marketing, all MP3 players looked the same, as did smart phones a bit later. Someone `gets it right’ and does so at the right time with the right business muscle behind it. Leo Fender might have got it right with the Tele and the Strat, but the business heft wasn’t there. Sit through this to spot when someone got behind Fender / Squire.
There were all sorts of guitar weirdness in the 1960’s, often tied with a genre. Surfers used offsets, bluesmen used humbuckers, jazz players used archtops with humbuckers or P90’s, country musicians used Gretch and anything else that would twang. Rock musicians wanted a big fat sound, and back then, that meant humbuckers. Later on, metal shredders would adopt Ibanez.
Once the gain pedals appeared in the mid-1970’s, a Strat+pedal could drive the amps as hard as a humbucker, and the more gain and effects in the signal chain, the less difference the guitar makes to the sound. The Strat can be easily modified, and is more comfortable to play. The more the guitar becomes a tone generator for the effects in the signal chain, the less it matters what the actual instrument is, so you may as well play something comfortable and easy to repair.
Or something along those lines.
The notes have the following list:
John Fogerty - 1969 Rickenbacker 325
Jerry Garcia - 1967 Gibson SG Standard
Jorma Kaukonen - 1964 Gibson ES‑345
Alvin Lee - 1959 Gibson ES‑335 “Big Red”
Johnny Winter - 1968 Fender XII
Buzzy Feiten - 1960s Gibson ES‑335
Leslie West - Gibson Les Paul Junior
Pete Townshend - 1968 69 Gibson SG Special
Carlos Santana - 1960s Gibson SG Special
and finally….
Jimi Hendrix - 1968 Fender Stratocaster
Gibson 7, Fender 2, Rickenbacker 1. Gibsons evenly split between SG’s and ES’s. The sound of Woodstock was the sound of the humbucker. Legendary session guitarist Tim Pierce said that the standard advice on the West Coast when he was getting started was get an ES335 and a Fender Princeton.
How? Why? After all, Hank B Marvin was a big deal in the UK, and this guy called Buddy Holly was apparently a thing in the States, and they played Strats in the 1960’s (and that was good enough for Dave Gilmour). Well, it was the days before pedals, when any effects had to be obtained by some kind of abuse of studio equipment. Anyone who wanted a `sound’ had to get it from the guitar and the amp, and maybe refine it with some EQ in the studio board.
It was two things. One is an effect often seen in the early history of a technology, the other was gain pedals.
The largest amount of whacky, creative weirdness in any technology is always just after its invention, while it is all still being made in garages and small factories, and no-one has invested serious money on production lines and staff training. Take a look at some of the early desktop and laptop computers in the 1970’s and 1980’s. Or mobile phones in the 1990’s and 2000’s, before the iPhone. Or MP3 players before the iPod. Once IBM waded in with a desktop design, everyone else followed suit, because, you know, IBM. Once Apple waded in with its massive production and superior marketing, all MP3 players looked the same, as did smart phones a bit later. Someone `gets it right’ and does so at the right time with the right business muscle behind it. Leo Fender might have got it right with the Tele and the Strat, but the business heft wasn’t there. Sit through this to spot when someone got behind Fender / Squire.
There were all sorts of guitar weirdness in the 1960’s, often tied with a genre. Surfers used offsets, bluesmen used humbuckers, jazz players used archtops with humbuckers or P90’s, country musicians used Gretch and anything else that would twang. Rock musicians wanted a big fat sound, and back then, that meant humbuckers. Later on, metal shredders would adopt Ibanez.
Once the gain pedals appeared in the mid-1970’s, a Strat+pedal could drive the amps as hard as a humbucker, and the more gain and effects in the signal chain, the less difference the guitar makes to the sound. The Strat can be easily modified, and is more comfortable to play. The more the guitar becomes a tone generator for the effects in the signal chain, the less it matters what the actual instrument is, so you may as well play something comfortable and easy to repair.
Or something along those lines.
Friday, 25 September 2026
Tony - Not A Film About Anthony Bourdain
I saw Matt Johnson’s Tony recently. It is supposed to be about the young Anthony Bourdain, and specifically, his first year working in a restaurant kitchen in 1970’s Provincetown, on Cape Cod, Massachusetts. The older chef who kicks his butt and mentors him is played by Antonio Banderas, so you know he has to be a Good Guy At Heart. That’s what you cast Banderas for. The chef who actually kicked Bourdain’s butt was an omni-competent, all-knowing, slave-driving, underpaying, and probably over-exaggerated in the telling, monster called Bigfoot. Who appeared in Bourdain’s life after he had gone through the Culinary Institute of America (yep, the CIA) and done another year in P-town.
Dominic Sessa was cast as Bourdain. What you need to know about Bourdain is that he was 6’4”, skinny and had a malice-free mischievousness in his face. Being 6’4” for a man is like having a nice smile and 36D’s for a woman: the world is going to cut you a lot of slack. Sessa is not 6’4” - he’s about the same height as Banderas - and so we do not feel the sheer presence Bourdain would have exerted.
Next problem. Bourdain was a Boomer, and Matt Johnson has Sessa play him like a Gen Z, because that’s going to be the audience and Sessa was born slap in the middle of Gen Z. And this was when I realised why films made about twenty or so years ago feel very different to the current crop. They don’t have Gen Z’s, and precious few Millennials (the oldest of whom would have been 25 in 2006). They have real people who grew up before the Internet, and have only ever used the word `problematic’ with irony quotes. Films today, even nice little art movies, are made for Gen Z and later Millennials, who are a bunch of prissy nebbishes, who will never, let’s face it, be able to afford a two-star dinner. It’s as if the writers pulled the punches so as not to shock the fragile souls of their young audience.
Bourdain was a self-confessed Chaos Monkey and professional Asshole of a Manager. Read his best-selling Kitchen Confidential (I re-read it after the movie) and it is clear that: a) he loved food from an early age, partly because it could be used to shock (aka `gross out’) regular people, b) he was consciously dedicated and put the work in to become a professional line chef, in the same way that young men and women put in the work to compete in the Leeds Piano Competition at age 20 (the youngest allowable in 2027); c) he was prepared to live the life. None of that comes through in the film, possibly because it is utterly antithetical to the attitudes of Gen Z, and we would not want to alienate the audience, would we?
There isn’t one moment when Sessa’s Bourdain was seen to actively enjoy the food. We have no idea at all why at the end of the movie he is seen interviewing for the CIA (insert CIA joke here).
Leo Woodall’s ‘Sal’ is far closer to the spirit of the original than Sessa. I’d call his performance relaxed and seemingly spontaneous, but that might not do justice to the amount of work he put into creating that character.
There have been other Chef Movies. Jon Favreau’s 2014 Chef, John Wells’ 2015 Burnt, Campbell Scott and Stanley Tucci’s 1996 Big Night, and Bob Giraldi’s definitive 2000 Dinner Rush. Bradley Cooper starred as `Jack Bourdain’ in a 2005-6 TV series that ended too quickly. I may try to find that.
Dominic Sessa was cast as Bourdain. What you need to know about Bourdain is that he was 6’4”, skinny and had a malice-free mischievousness in his face. Being 6’4” for a man is like having a nice smile and 36D’s for a woman: the world is going to cut you a lot of slack. Sessa is not 6’4” - he’s about the same height as Banderas - and so we do not feel the sheer presence Bourdain would have exerted.
Next problem. Bourdain was a Boomer, and Matt Johnson has Sessa play him like a Gen Z, because that’s going to be the audience and Sessa was born slap in the middle of Gen Z. And this was when I realised why films made about twenty or so years ago feel very different to the current crop. They don’t have Gen Z’s, and precious few Millennials (the oldest of whom would have been 25 in 2006). They have real people who grew up before the Internet, and have only ever used the word `problematic’ with irony quotes. Films today, even nice little art movies, are made for Gen Z and later Millennials, who are a bunch of prissy nebbishes, who will never, let’s face it, be able to afford a two-star dinner. It’s as if the writers pulled the punches so as not to shock the fragile souls of their young audience.
Bourdain was a self-confessed Chaos Monkey and professional Asshole of a Manager. Read his best-selling Kitchen Confidential (I re-read it after the movie) and it is clear that: a) he loved food from an early age, partly because it could be used to shock (aka `gross out’) regular people, b) he was consciously dedicated and put the work in to become a professional line chef, in the same way that young men and women put in the work to compete in the Leeds Piano Competition at age 20 (the youngest allowable in 2027); c) he was prepared to live the life. None of that comes through in the film, possibly because it is utterly antithetical to the attitudes of Gen Z, and we would not want to alienate the audience, would we?
There isn’t one moment when Sessa’s Bourdain was seen to actively enjoy the food. We have no idea at all why at the end of the movie he is seen interviewing for the CIA (insert CIA joke here).
Leo Woodall’s ‘Sal’ is far closer to the spirit of the original than Sessa. I’d call his performance relaxed and seemingly spontaneous, but that might not do justice to the amount of work he put into creating that character.
There have been other Chef Movies. Jon Favreau’s 2014 Chef, John Wells’ 2015 Burnt, Campbell Scott and Stanley Tucci’s 1996 Big Night, and Bob Giraldi’s definitive 2000 Dinner Rush. Bradley Cooper starred as `Jack Bourdain’ in a 2005-6 TV series that ended too quickly. I may try to find that.
Friday, 18 September 2026
Brocherds, Flu, and Vertex Algebras
I’m still recovering from the flu. About 90% there, but this blog is written using the final 10%. Plus I have foresworn commenting on wast we used to call Current Affairs, or you would have got something about the Lindsay Clancy trial and the continuing farce of Age Verification. Not to mention the unanswered question of our time: WTF was the American Military doing when it told its Commander-in-Chief that a war against the Iranians and their best mates the Houthis could be won this side of a cold hell? The Middle East never did make sense, and it makes even less sense now. I might have weighed in about the protests against illegal immigration as well. But I have said I won’t do any of that, so I won’t.
So in the meantime, I’m half-way down this rabbit-hole. If you want to know what actual mathematics sounds like, try this. Don’t try to understand the maths, at least the first time through, but aim for the biographical remarks Borcherds drops from time to time. When I heard Borcherds saying that the entire subject arose from someone’s study of a super-obscure lattice, I had to reach for Rule 14 of the methodology of mathematics: no progressive research programme ever came of Lattice Theory.
The utter incomprehensibility of this talk - again on the first time through - is an example of why philosophers of mathematics are, with a handful of exceptions, confined to marginal comments and subjects. It takes some serious effort to understand this stuff, and even more to understand why it might have the slightest value to anyone.
See you next week.
So in the meantime, I’m half-way down this rabbit-hole. If you want to know what actual mathematics sounds like, try this. Don’t try to understand the maths, at least the first time through, but aim for the biographical remarks Borcherds drops from time to time. When I heard Borcherds saying that the entire subject arose from someone’s study of a super-obscure lattice, I had to reach for Rule 14 of the methodology of mathematics: no progressive research programme ever came of Lattice Theory.
The utter incomprehensibility of this talk - again on the first time through - is an example of why philosophers of mathematics are, with a handful of exceptions, confined to marginal comments and subjects. It takes some serious effort to understand this stuff, and even more to understand why it might have the slightest value to anyone.
See you next week.
Friday, 11 September 2026
The Group of Constant-Value Matrices
Now this one is really cool.
I would have bet your life on the fact that in any group of matrices, the identity is always a matrix with a 1 along the diagonal and 0 everywhere else. Nothing else is contemplated in an undergraduate maths course, and we were never confused by counter-examples. But here is one.
(This is a catch-up post.)
I would have bet your life on the fact that in any group of matrices, the identity is always a matrix with a 1 along the diagonal and 0 everywhere else. Nothing else is contemplated in an undergraduate maths course, and we were never confused by counter-examples. But here is one.
(This is a catch-up post.)
Friday, 4 September 2026
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