Why do I do this to myself? I read Julius Evola's Ride The Tiger recently, because someone enthused about it on a blog I read, and the Amazon reviews were positive. Evola came from a family of minor Sicilian aristocrats. He was well-read and seemed to understand what he read, which means he understood Heidegger, and that's more than most people do.
However, his book is rambling, long on critical exposition, very short on prescription and the text yearns for a return to something called "Tradition" that he never describes and which I can only assume is the way he saw the world when he was about ten. When people pine for the past, that's usually about the past they are pining for. When they were too young to see how complicated and messy the world was.
So let's say something out loud and address his real concern. There are a lot of ugly, dull and mediocre people in the world, and there are a lot of reasonably decent people who work well, love their children, tolerate their spouses and would have me heading for an imagninary appointment in twenty minutes. Some of them make a lot of money and drive nice cars and have trophy wives, and that irritated me at first and then I got over it as I understood what it takes to make that money and live with that kind of woman, and realised that I didn't want to be that guy. I want to have sex with his wife, but I want to hand her back afterwards. Most men are fine as colleagues at work, or for specific purposes and events, but not as someone I would want to spend a whole day with. I am easily bored and my vanity won't let me be seen with ugly people. Call me shallow, superficial and a jerk. I accept that.
The question then is how those of us who feel that way live. Surrounded by people that we would help in an emergency (if we could help at all), and regard as fellow citizens due the politness and consideration they deserve, but who we would actually want as a fixture in our lives, how do we live? How do we deal with the ugliness, triviality and tedium that can suddenly descend on us if we sit in the wrong place or with the wrong people?
The old-school answer involved the phrase "aristocratic detachment", which conveys an idea of formal politeness combined with distance and a visible reluctance to become involved or stay in any group or conversation, with the suggestion that one has an elsewhere to be soon. The catch with aristocratic detachment is that I still have to be aware of the ugliness, medicority and the irritation that always accompanies the discovery that an attractive woman is also an air-head.
That's way too much effect for the world to be having on me. I'm going to go for "Affable detachment”.
Affable detachment is what we do when we realise we cannot go on and on being disappointed and dismayed and disgusted. So we stop hoping for anything from the world and it no longer tires us out with its banality, ugliness and inconvenience. We find our own interests in the huge range of sciences, arts, crafts and participative sports and training, that are available in this post-modern capitalist economy. Those interests are what gives us the value in our lives.
Affable detachment is recognising the awful ("land whale trying to sit next to me on the train") and then carrying on with your life so that you don't think about it because you have something that interests you to occupy you. It is the art of tuning out the world when it does not deserve our attention. We do not ignore it because it is hateful, we ignore it because we are giving our attention to something we like more. That’s the real difference between affable disengagement and aristocratic detachment. We don’t begrudge the "real world” with its “real women” and “real men” and “real relationships” for not interesting us. Affable detachment turns the outside world into a giant art gallery with a lot of very tatty performance and installation pieces. We have to walk through it, but we don't have to buy any of it and take it home.
Noise-cancelling earphones help, as well as something to read or a computer to type on. Also a place of your own, and a gym membership.
One thing we affably disengaged have in common with the aristocratically detached and Rational Males, is that women are an enhancement to a man's life, but not its centre or purpose. I’m not going to expand on that now.
This does not mean we don’t have friends and confidants. We can and often do. We don’t expect any of the next three hundred people we meet to be either. Just as we don’t expect any of the next three hundred females we pass by to be even remotely sexually attractive and available. Just as we don’t expect the next programme on television to be worth watching, or the next single from the next over-produced girl singer to be worth hearing. We do not live in despair at never finding love, or sex, or friendship: we understand that those things are rare, and it is very unlikely that the next person we meet will provide any of them.
Affable detachment is easier to do when I'm employed in a job I find okay, with enough money coming in to pay the bills and some over for fun and savings, working somewhere that's half-way reasonable, having quiet, unobtrusive neighbours, and a daily routine that doesn't force me into lengthy contact with oafs, dummies and fuglies.
There are some circumstance where affable disengagement isn't going to work. Stuck with a shrew for a wife, or a bully for a boss, or with a drink problem, or a lack of employment or money, for instance. There are things that sensitise us to everything else in the world. I've been there, and if you are, you have my sympathy. In the end you have to change your circumstances, or wait for the boss to move on and your shrew to die or divorce you.
It sounds like some utter slob could be affably disengaged. Well, that's not likely. Affable detachment works when you have a justifed sense of self-respect and don't need other people to notice and validate you. (This is different from getting good reviews around annual review time, but if you can't do that without compromising yourself you need to change employer.) So you will be in shape, exercise, eat well, dress becomingly but modestly, and all that good stuff. Slobs know they are, and so they know everyone else knows they are, and shrugging that thought off is not easy. It's a lot easier not to be worried about what other people are thinking when the chances are they are thinking "what a good looking older man" (women) and "He's a boss. You can tell just by looking." (men).
You can seek promotion, play Texas Hold’Em, make art or music, write books, study for a PhD, climb mountains or do whatever else you want to do. In fact, that’s the whole point. That you have something in your life that gives it direction and value to you, and that you don’t get your validation from outside, from the gang, from the admiring glances of other men as you walk in the room with Anna Ewers on your arm, or from Ms Ewers herself. Prizes and recognition follow commitment and achievement. This week’s blonde, and this year’s CEO Of The Year “award”, are not prizes awarded by peers but liabilities.
If I'm spending all day being as little connected to and affected by the world as possible, will I still get aroused when she appears? Yes, because I'm still scanning the world, I'm not ignoring it. When someone appears who does arouse me, I know it immediately. Happened to me recently, and every time it does I feel disappointed in myself that I didn't approach her. There are many women I look at and think "Well, yes, if it was easy" or fit them into a particular fantasy and don't have a moment's regret that I didn't approach. As with women, so with jobs, clothes, music or anything else. If it's what you want, you will feel it when you see it. And you won’t like yourself if you don't go for it. We don’t stop hoping, we just quit bitching and moaning when our hopes are disappointed.
Thursday, 24 March 2016
Monday, 21 March 2016
Wanted: Mainstream-Friendly Nationalism
Nationalists are portrayed as rough, nasty, working-class, with bad taste in tattos, tend to regard flags as clothing, and are just plain lunatic-fringe. Need I say 'Nigel Farage' to make my point? What presently defines Nationalists is a dislike of the foreigners who have taken their jobs and council housing, filled the schools with children who don't speak English and whose parents make demands for special treatment, and generally lowered the native's standard of living towards their own. Nationalism is driven by hate and that's not a look most people want to wear.
Nationalism needs to be mainstream-friendly. Which means it needs to be re-phrased as a positive ideology that loves all people, but gives economic, political and and social preference to native-borns. It needs to spell out policies that explain how a child born to two UK citizens is going to get a useful education, a starter job, and within five years a job that pays enough for them to see some kind of future involving partners, children and home ownership. Because if it doesn’t, then the ordinary people won’t feel as if it is addressing their real needs.
There are two truths about the labour market: a) every migrant or offshored worker takes away a job that a national could have been trained to do, and b) someone decides to hire the migrants and offshores the jobs and it ain’t the working man. Reducing and discouraging the use of migrant or offshore labour is only a third of the solution. Another third is making the national population employable. And the final third is having employers making products and providing services that are valued enough to let them pay a decent wage.
An employer that really can’t make a profit unless they pay under minimum wage is either making a product that no-one much wants, or doesn’t know how to present it so that they can charge a decent price for it and so pay their workers. (The truth is that employers who complain about wage rates are mostly just plain greedy. The bosses see that £1/hour as money they personally could be getting. If adding £1/hour to their workers’ wages really will sink the company, it probably doesn’t deserve to be floating.)
A mainstream-friendly Nationalist would emphasise good business practice, a living wage, be tough on greedy businessmen (who are very often the ones employing migrant and offshore labour), talk about training and work acculturation, and about the life people want to lead. And every now and then throw in the condition that the people who were born here get first-served. They would blame the people who are actually to blame: bad, incompetent, greedy businessmen and the politicians who support them. And they would praise firms that pay well, make products people want to pay for and employ and train nationals.
Try these for size...
When every British citizen who is able to work after suitable training (and in some cases also acculturation) is working, then employers can import Bulgarian builders and Australian programmers. Foreign workers - imported or offshored - are allowed only to companies with training programs that will make the employment of foreign workers un-necessary in two years.
British citizenship is for people born in the UK both of whose parents are British citizens. If one or other of the parents isn’t British, they can sort out the child’s non-British citizenship for themselves. British citizens who marry non-British citizens can bring their spouse to the UK, but nobody can marry into citizenship. When they get divorced, the non-citizen partner has to go home.
Everyone is welcome to come to the UK and enjoy the cultural, scenic, recreational and educational opportunities available. People with huge fortunes who want to buy property and spend their money in the UK are welcome. Paying a £350,000 annual fee (offset against their tax bill) for enjoying the benefits of honest civil servants, policemen and judges, plus the other benefits of the British State, will be no problem for them.
Non-citizens have to go home when they run out of money or can’t find work (after, say, four weeks) after their current employer lets them go. Family go with them: they have a right to a family life, but not to choose the country where they enjoy that right.
Anyone, British citizen or not, who pays their due taxes in the UK gets all the benefits that the UK State provides. Except unemployment.
Any foreign national who commits a crime gets sent home, with their family. They can appeal once they have landed at the other side. The jury says “Guilty” and the accused and her family are going home the same day. This works retrospectively for people who have already settled in the UK. If they are broke, we’ll pay the costs of sending them all back. They don’t get to come back in again. Any assets they have can be seized to pay the fines and costs. Note that since entering a country illegally is a crime, illegal immigrants will be sent home immediately. (And no legal aid for handling immigration issues and appeals. Everyone has a right to legal counsel, just not for free.)
The British Government will place the interests of its citizens first in all policies, negotiations and legislation. (Now there’s a radical idea!). Once the people believe that, the amount of ill-will and all-round cussedness for which the English are noted will decline. Within the decade.
Nationalism needs to be mainstream-friendly. Which means it needs to be re-phrased as a positive ideology that loves all people, but gives economic, political and and social preference to native-borns. It needs to spell out policies that explain how a child born to two UK citizens is going to get a useful education, a starter job, and within five years a job that pays enough for them to see some kind of future involving partners, children and home ownership. Because if it doesn’t, then the ordinary people won’t feel as if it is addressing their real needs.
There are two truths about the labour market: a) every migrant or offshored worker takes away a job that a national could have been trained to do, and b) someone decides to hire the migrants and offshores the jobs and it ain’t the working man. Reducing and discouraging the use of migrant or offshore labour is only a third of the solution. Another third is making the national population employable. And the final third is having employers making products and providing services that are valued enough to let them pay a decent wage.
An employer that really can’t make a profit unless they pay under minimum wage is either making a product that no-one much wants, or doesn’t know how to present it so that they can charge a decent price for it and so pay their workers. (The truth is that employers who complain about wage rates are mostly just plain greedy. The bosses see that £1/hour as money they personally could be getting. If adding £1/hour to their workers’ wages really will sink the company, it probably doesn’t deserve to be floating.)
A mainstream-friendly Nationalist would emphasise good business practice, a living wage, be tough on greedy businessmen (who are very often the ones employing migrant and offshore labour), talk about training and work acculturation, and about the life people want to lead. And every now and then throw in the condition that the people who were born here get first-served. They would blame the people who are actually to blame: bad, incompetent, greedy businessmen and the politicians who support them. And they would praise firms that pay well, make products people want to pay for and employ and train nationals.
Try these for size...
When every British citizen who is able to work after suitable training (and in some cases also acculturation) is working, then employers can import Bulgarian builders and Australian programmers. Foreign workers - imported or offshored - are allowed only to companies with training programs that will make the employment of foreign workers un-necessary in two years.
British citizenship is for people born in the UK both of whose parents are British citizens. If one or other of the parents isn’t British, they can sort out the child’s non-British citizenship for themselves. British citizens who marry non-British citizens can bring their spouse to the UK, but nobody can marry into citizenship. When they get divorced, the non-citizen partner has to go home.
Everyone is welcome to come to the UK and enjoy the cultural, scenic, recreational and educational opportunities available. People with huge fortunes who want to buy property and spend their money in the UK are welcome. Paying a £350,000 annual fee (offset against their tax bill) for enjoying the benefits of honest civil servants, policemen and judges, plus the other benefits of the British State, will be no problem for them.
Non-citizens have to go home when they run out of money or can’t find work (after, say, four weeks) after their current employer lets them go. Family go with them: they have a right to a family life, but not to choose the country where they enjoy that right.
Anyone, British citizen or not, who pays their due taxes in the UK gets all the benefits that the UK State provides. Except unemployment.
Any foreign national who commits a crime gets sent home, with their family. They can appeal once they have landed at the other side. The jury says “Guilty” and the accused and her family are going home the same day. This works retrospectively for people who have already settled in the UK. If they are broke, we’ll pay the costs of sending them all back. They don’t get to come back in again. Any assets they have can be seized to pay the fines and costs. Note that since entering a country illegally is a crime, illegal immigrants will be sent home immediately. (And no legal aid for handling immigration issues and appeals. Everyone has a right to legal counsel, just not for free.)
The British Government will place the interests of its citizens first in all policies, negotiations and legislation. (Now there’s a radical idea!). Once the people believe that, the amount of ill-will and all-round cussedness for which the English are noted will decline. Within the decade.
Labels:
Society/Media
Monday, 14 March 2016
Read Andrew Gelman, He Is Our Master In Everything Statistical
I’m doing this to prove I’m still alive. I’ve been working hard on my Riemann-Roch essay when I haven’t been, you know, doing the day job and hefting iron, and this weekend, giving the ornamental grasses their winter savaging and keeping the lawn from getting out of control.
If you’re remotely interested in the philosophy of science, statistics, or read science articles in the press, or even research in medical, sociological and psychology journals, or you're into business analysis and insight, or are likely to believe “studies” that prove people with more facial hair are likely to be more sexist, then you need to be reading Andrew Gelman’s blog, and especially this paper on the Garden of Forking Paths. A few weeks of doing so, and catching up with the previous posts, will soon set you straight. I would go so far to say that you should not read one more newspaper “science” article until you understand the idea behind the Garden of Forking paths. Also read his contribution to the ASA report on p-values.
Professor Gelman is the only other person I’ve read who references Imre Lakatos, who was a philosopher of science at the LSE in the late 1960’s and early 1970’s. Recently, as with this post Professor Gelman has been hitting his stride on the issue of low-quality and junk research. That particular post is as polemical, prescriptive and on-the-money as anything Lakatos ever wrote.
He has serious technical chops, having co-created a Bayesian inference language called STAN, and co-authored the first textbook on Bayesian statistics I’ve found convincing. He also has serious common sense and if you don’t believe a statistician can demonstrate sprezzatura then read this.
(Now I’m going back to trying to be sure that, just because I can embed a Riemann surface into a complex projective curve, doesn’t mean that it is a projective curve. I think it means that Riemann surfaces are like cross-sections of projective curves.)
PS: The title is a light-hearted reference to what Gauss said about Euler: "Lisez Euler, lisez Euler, c'est notre maître à tous."
If you’re remotely interested in the philosophy of science, statistics, or read science articles in the press, or even research in medical, sociological and psychology journals, or you're into business analysis and insight, or are likely to believe “studies” that prove people with more facial hair are likely to be more sexist, then you need to be reading Andrew Gelman’s blog, and especially this paper on the Garden of Forking Paths. A few weeks of doing so, and catching up with the previous posts, will soon set you straight. I would go so far to say that you should not read one more newspaper “science” article until you understand the idea behind the Garden of Forking paths. Also read his contribution to the ASA report on p-values.
Professor Gelman is the only other person I’ve read who references Imre Lakatos, who was a philosopher of science at the LSE in the late 1960’s and early 1970’s. Recently, as with this post Professor Gelman has been hitting his stride on the issue of low-quality and junk research. That particular post is as polemical, prescriptive and on-the-money as anything Lakatos ever wrote.
He has serious technical chops, having co-created a Bayesian inference language called STAN, and co-authored the first textbook on Bayesian statistics I’ve found convincing. He also has serious common sense and if you don’t believe a statistician can demonstrate sprezzatura then read this.
(Now I’m going back to trying to be sure that, just because I can embed a Riemann surface into a complex projective curve, doesn’t mean that it is a projective curve. I think it means that Riemann surfaces are like cross-sections of projective curves.)
PS: The title is a light-hearted reference to what Gauss said about Euler: "Lisez Euler, lisez Euler, c'est notre maître à tous."
Wednesday, 2 March 2016
I pledged $150 to Mike Cernovich’s Kickstarter for his movie on Free Speech. That speaks louder than any words I’m likely to write.
It’s cold. I can’t enjoy eating because of the braces on my lower jaw. I’m just about over the fever I had a couple of weeks ago. At least I’m working on the R-R essay, which I thought I had given up on entirely. And I started looking through the photographs I’ve been taking over the years because I’d like to print some out and make a couple of collages, and that was totally disheartening. They are terrible. I used to be able to see pictures, but now it seems I can’t and haven’t been able to for years. Unless it’s a snapshot of somewhere utterly wonderful, like Castelejo.
It isn’t that I’ve run out of things to say, it’s that I no longer have the motivation to say them. The political elite seem more and more out of touch with what we-the-people actually believe. The US Presidential election – assuming that Trump doesn’t get assassinated by a “single loan nut” – is going to be won by a populist right-wing businessman who is going to spend at least five years discomforting the political classes (Hillary doesn’t have a hope in hell, since her constituency consists entirely of some black voters and feminist women over about 35). The British people are just likely to vote the UK out of the EU, when the UK political class will throw a huge hissy fit as the populists of both parties elbow their way up to the trough. There is a serious chance that Boris Johnson might be PM. (Yea, go Boris!) Apple and the FBI? It’s a non-debate: no, the US executive branch cannot have the power to compel anyone to do anything, which is what they are after. All those BS gender issues? Tired and bored. Manosphere stuff? I haven’t really changed my position on any of that for a couple of years. Immigration? Let us deport convicted foreign criminals without appeal, forbid the entry of convicted criminals, and train and employ the 7 million or so people born here who need to work. Then you can import Bulgarian builders and Polish council workers. We should be regarding imported labour as a stop-gap while we train British-born people. Immigration at the moment is treason against the native people. But I’ve said this already.
Over the weekend, I pledged $150 to Mike Cernovich’s Kickstarter for his movie on Free Speech. That speaks louder than any words I’m likely to write.
It isn’t that I’ve run out of things to say, it’s that I no longer have the motivation to say them. The political elite seem more and more out of touch with what we-the-people actually believe. The US Presidential election – assuming that Trump doesn’t get assassinated by a “single loan nut” – is going to be won by a populist right-wing businessman who is going to spend at least five years discomforting the political classes (Hillary doesn’t have a hope in hell, since her constituency consists entirely of some black voters and feminist women over about 35). The British people are just likely to vote the UK out of the EU, when the UK political class will throw a huge hissy fit as the populists of both parties elbow their way up to the trough. There is a serious chance that Boris Johnson might be PM. (Yea, go Boris!) Apple and the FBI? It’s a non-debate: no, the US executive branch cannot have the power to compel anyone to do anything, which is what they are after. All those BS gender issues? Tired and bored. Manosphere stuff? I haven’t really changed my position on any of that for a couple of years. Immigration? Let us deport convicted foreign criminals without appeal, forbid the entry of convicted criminals, and train and employ the 7 million or so people born here who need to work. Then you can import Bulgarian builders and Polish council workers. We should be regarding imported labour as a stop-gap while we train British-born people. Immigration at the moment is treason against the native people. But I’ve said this already.
Over the weekend, I pledged $150 to Mike Cernovich’s Kickstarter for his movie on Free Speech. That speaks louder than any words I’m likely to write.
Labels:
Diary
Monday, 22 February 2016
Homotopy Type Theory
I’ve had the Univalent Foundations Program’s book on Homotopy Type Theory on my to-read list for quite a while after reading about the project on Michael Harris’s blog. For some reason, recovering from a nasty fever was the exact right time to skim-read the bits I would know about, viz, the Introduction, and the chapters on Set Theory, Category Theory and real numbers.
Call me a rude mechanical but I’ve always thought that people who go in for type theories have missed a number of points. Yes I do know that Homotopy Type Theory is currently the subject of active research by people who are cleverer in their sleep on a bad day than I am awake on a good day, but as someone once remarked about the "highly motivated individuals" that were popular in recruitment in the 1970’s, the catch is that they can all highly motivate themselves up a gum tree.
Type theory was an ugly kludge invented by Bertrand Russell to get round the fact that, in its unrestricted form, the Axiom of Comprehension leads immediately to inconsistencies of which Russell’s Paradox is the most famous. The "set of all sets that are not members of themselves” looks like a well-formed definition, but now consider that very set. If it does belong to itself, it doesn’t, and if it doesn’t, it does. Russell’s kludge was to stratify logical formulae into “types”, and impose the rule that a set could only belong to a set of higher type than itself. It worked well enough for him to finish the project of showing that mathematics could be developed from “purely logical foundations” that was the aim of his massive Principia Mathematica.
A few years later, however, Zermelo, Fraenkel and Skolem devised the current axioms of mainstream set theory, traditionally called ZFC “Zermelo-Fraenkel with (the Axiom of) Choice” (for some reason Skolem’s name always gets left out). The foundationalist programme became “mathematics is derivable from the axioms of ZFC and mathematical logic” instead of “mathematics is derivable from the Axiom of Comprehension, type theory and mathematical logic”. A lot of people are very happy with that, including me. The point of the foundational programme was to show that such a derivation was possible, not to argue that fractions were really ordered pairs of massively nested copies of the empty set. Once we have ZF, we don’t need the kludge that is types.
And there it should have died. Along with the biplane, the TOG tank, the Sinclair C5, airships and programmable calculators. All may have been wonderful and useful once, but the world has moved on. And the same goes for mathematical theories, which are developed to solve problems. Cantor’s set theory was not an attempt to fabricate a “new language for mathematics” but an attempt to understand the limit points of Fourier Series. It so happened it let other mathematicians re-state other theories in a clearer and more systematic way, which was why it was adopted so quickly. We still use it because it’s still the best way of stating many definitions and theorems. But as a subject on its own?
In its own right, set theory is an interesting for a) large cardinal theory, or b) Cohen forcing constructions for independence proofs and proving the existence of weird objects. These are not going to make your e-mails any safer or your pictures any less fuzzy any time soon. People work on set theory as they work on model theory, both of which John Bell drummed both into me back in the day, but I’m not going to sell you on the commercial benefits of saturated structures (generalisations of the idea of algebraically-closed fields). It’s interesting to some people, but it’s a creek off the main river of mathematics. The same goes for any foundational subject.
Category theory is foundational in that sense. It was devised to formalise proofs and constructions that occurred in multiple branches of mathematics, and to formalise the “X and Y have different fidget groups, but fidget groups are preserved under twiddles, so X and Y are not twiddle-equivalent” arguments that were appearing in algebraic geometry at the time. There’s some quiet satisfaction from the moment when you realise that an SQL inner join is really a pullback in disguise, but that knowledge does not make you a designer of more stylish queries. In the same way that, just because you can show that a folklore Haskell programming trick actually illustrates Kan Extensions, it doesn’t meant that knowing anything about Kan extensions will make you a slicker programmer. Academic computer scientists love their Haskell and their category theory, but if either was a pre-requisite for a job at Google, Business Insider would have run an article called “Here’s the far-out math theory you need for a job at Google" a long time ago.
And there’s one more thing. Type theories have, in general, a non-classical logic! (Except at the “-1” level, where you can do classical logic.) Would you have guessed? I have nothing against the study of multi-valued and modal logics, though again, I’m not sure I want my taxes to pay for it. I get (or did at the time I read about it) why it appears naturally as the “natural logic” of certain categories of sheaves, but that’s no more profound than saying that the “natural logic” of non-complemented lattices is non-classical, and nobody thought to do that. For some reason failure of the law of the excluded middle is seen as some kind of abstract virtue and I can’t help hearing alarm bells when it is so presented. It’s something to do with hair-shirts, I think. Maths goes better with the occasional non-constructive proof by contradiction.
I have no problem with what consenting mathematicians choose to talk about in the privacy of their conferences, though if it was me, I wouldn’t use a lot of taxpayer’s money to fund research into Univalent Foundations. Voevodsky is selling it as a theorem-prover, and that will aways get some attention, but you and I know that it wouldn’t help much even if it did produce an effective theorem-prover. Types can only capture a certain class of errors, not something subtle everyone has so far missed about about (say) Cohen-Macauly rings over finite fields.
So do you read the book and follow the work? Look, some people still swear by the λ-calculus for dealing with functions. I know it works. But anyone who actually used a λ-function in actual production code would find their code re-factored to get rid of it at the first opportunity. Ditto types: I’m sure the maths is impeccable. It’s the project that’s a little pointless.
The whole foundations thing was done in the early twentieth-century. The point of mathematics is to solve problems, and while the majority of those problems mostly still come from physics orgambling probability theory, some now come from cryptography, computing, biology and other sciences. Most are, in the end, to do with solving differential or difference equations. I’m going out on a limb here, but I’m pretty sure no-one is going to improve image-enhancement techniques with higher homotopy types.
Call me a rude mechanical but I’ve always thought that people who go in for type theories have missed a number of points. Yes I do know that Homotopy Type Theory is currently the subject of active research by people who are cleverer in their sleep on a bad day than I am awake on a good day, but as someone once remarked about the "highly motivated individuals" that were popular in recruitment in the 1970’s, the catch is that they can all highly motivate themselves up a gum tree.
Type theory was an ugly kludge invented by Bertrand Russell to get round the fact that, in its unrestricted form, the Axiom of Comprehension leads immediately to inconsistencies of which Russell’s Paradox is the most famous. The "set of all sets that are not members of themselves” looks like a well-formed definition, but now consider that very set. If it does belong to itself, it doesn’t, and if it doesn’t, it does. Russell’s kludge was to stratify logical formulae into “types”, and impose the rule that a set could only belong to a set of higher type than itself. It worked well enough for him to finish the project of showing that mathematics could be developed from “purely logical foundations” that was the aim of his massive Principia Mathematica.
A few years later, however, Zermelo, Fraenkel and Skolem devised the current axioms of mainstream set theory, traditionally called ZFC “Zermelo-Fraenkel with (the Axiom of) Choice” (for some reason Skolem’s name always gets left out). The foundationalist programme became “mathematics is derivable from the axioms of ZFC and mathematical logic” instead of “mathematics is derivable from the Axiom of Comprehension, type theory and mathematical logic”. A lot of people are very happy with that, including me. The point of the foundational programme was to show that such a derivation was possible, not to argue that fractions were really ordered pairs of massively nested copies of the empty set. Once we have ZF, we don’t need the kludge that is types.
And there it should have died. Along with the biplane, the TOG tank, the Sinclair C5, airships and programmable calculators. All may have been wonderful and useful once, but the world has moved on. And the same goes for mathematical theories, which are developed to solve problems. Cantor’s set theory was not an attempt to fabricate a “new language for mathematics” but an attempt to understand the limit points of Fourier Series. It so happened it let other mathematicians re-state other theories in a clearer and more systematic way, which was why it was adopted so quickly. We still use it because it’s still the best way of stating many definitions and theorems. But as a subject on its own?
In its own right, set theory is an interesting for a) large cardinal theory, or b) Cohen forcing constructions for independence proofs and proving the existence of weird objects. These are not going to make your e-mails any safer or your pictures any less fuzzy any time soon. People work on set theory as they work on model theory, both of which John Bell drummed both into me back in the day, but I’m not going to sell you on the commercial benefits of saturated structures (generalisations of the idea of algebraically-closed fields). It’s interesting to some people, but it’s a creek off the main river of mathematics. The same goes for any foundational subject.
Category theory is foundational in that sense. It was devised to formalise proofs and constructions that occurred in multiple branches of mathematics, and to formalise the “X and Y have different fidget groups, but fidget groups are preserved under twiddles, so X and Y are not twiddle-equivalent” arguments that were appearing in algebraic geometry at the time. There’s some quiet satisfaction from the moment when you realise that an SQL inner join is really a pullback in disguise, but that knowledge does not make you a designer of more stylish queries. In the same way that, just because you can show that a folklore Haskell programming trick actually illustrates Kan Extensions, it doesn’t meant that knowing anything about Kan extensions will make you a slicker programmer. Academic computer scientists love their Haskell and their category theory, but if either was a pre-requisite for a job at Google, Business Insider would have run an article called “Here’s the far-out math theory you need for a job at Google" a long time ago.
And there’s one more thing. Type theories have, in general, a non-classical logic! (Except at the “-1” level, where you can do classical logic.) Would you have guessed? I have nothing against the study of multi-valued and modal logics, though again, I’m not sure I want my taxes to pay for it. I get (or did at the time I read about it) why it appears naturally as the “natural logic” of certain categories of sheaves, but that’s no more profound than saying that the “natural logic” of non-complemented lattices is non-classical, and nobody thought to do that. For some reason failure of the law of the excluded middle is seen as some kind of abstract virtue and I can’t help hearing alarm bells when it is so presented. It’s something to do with hair-shirts, I think. Maths goes better with the occasional non-constructive proof by contradiction.
I have no problem with what consenting mathematicians choose to talk about in the privacy of their conferences, though if it was me, I wouldn’t use a lot of taxpayer’s money to fund research into Univalent Foundations. Voevodsky is selling it as a theorem-prover, and that will aways get some attention, but you and I know that it wouldn’t help much even if it did produce an effective theorem-prover. Types can only capture a certain class of errors, not something subtle everyone has so far missed about about (say) Cohen-Macauly rings over finite fields.
So do you read the book and follow the work? Look, some people still swear by the λ-calculus for dealing with functions. I know it works. But anyone who actually used a λ-function in actual production code would find their code re-factored to get rid of it at the first opportunity. Ditto types: I’m sure the maths is impeccable. It’s the project that’s a little pointless.
The whole foundations thing was done in the early twentieth-century. The point of mathematics is to solve problems, and while the majority of those problems mostly still come from physics or
Labels:
Maths,
philosophy
Friday, 19 February 2016
And next up… a health report
I spent eighteen (18) hours asleep on Thursday. My Fitbit said so. I would sleep for maybe seventy or eighty minutes, sit on the side of my bed, get up by leaning against the wall, walk very carefully to the loo where I got rid of some water from one end and took some more on at the other. A very little bit more. I didn’t eat a thing. I had no appetite. I did not even want to get out of bed.
That was after taking Wednesday off because I had a fever and I couldn’t actually walk upstairs, but had to crawl on my hands and feet, and then grasp the balustrade as I got to the top. Still had to do that this morning, but managed to get out to Richmond for some lunch and to stock up on cough syrup and Lemsip. You would be amazed how few cough syrups are actually alcohol- or ethanol-free. I made it back just in time to lay on the couch for a rest. When my blood pressure drops so much that if I sit up too quickly I get very dizzy. I haven’t even eaten any chocolate, though I did have a Cote Creme Caramel.
If I spend an entire day in bed, it’s almost always because I’m recovering from food poisoning, but it wasn’t that. All I was doing on Tuesday afternoon was coughing slightly. I went to the gym and everything. Then at midnight I woke up and, looked at the clock and realised I wasn’t going anywhere for at least a couple of days. Hot, headachy and fever-dreams, you know, obsessional and meaningless.
It’s half-term. There were children on the train. It was also (effing) cold, so my immune system could have been operating at less than 100%. I blame the parents: they should have had the littledarlings back home, eating tea and watching Blue Peter by the time I got anywhere near a train. And the railway companies should spray all their evening trains with some nasty chemical that kills all known germs and viruses before we grown-ups get on. I have no idea what Vladimir Putin has infected your kids with this winter, but it’s a winner. Spray it over NATO forces, wait two days and he can take over Europe before lunch with a couple of divisions of marines.
When Donald Trump is President, there will be no more children on commuter trains. I bet Ivanka didn’t travel by train anywhere, anyday.
That was after taking Wednesday off because I had a fever and I couldn’t actually walk upstairs, but had to crawl on my hands and feet, and then grasp the balustrade as I got to the top. Still had to do that this morning, but managed to get out to Richmond for some lunch and to stock up on cough syrup and Lemsip. You would be amazed how few cough syrups are actually alcohol- or ethanol-free. I made it back just in time to lay on the couch for a rest. When my blood pressure drops so much that if I sit up too quickly I get very dizzy. I haven’t even eaten any chocolate, though I did have a Cote Creme Caramel.
(You don't eat this if your digestion is gippy)
If I spend an entire day in bed, it’s almost always because I’m recovering from food poisoning, but it wasn’t that. All I was doing on Tuesday afternoon was coughing slightly. I went to the gym and everything. Then at midnight I woke up and, looked at the clock and realised I wasn’t going anywhere for at least a couple of days. Hot, headachy and fever-dreams, you know, obsessional and meaningless.
It’s half-term. There were children on the train. It was also (effing) cold, so my immune system could have been operating at less than 100%. I blame the parents: they should have had the little
When Donald Trump is President, there will be no more children on commuter trains. I bet Ivanka didn’t travel by train anywhere, anyday.
Friday, 12 February 2016
Would younger viewers look at Godard and say “Well, I guess you had to be there at the time”?
A friend sent me this link to an edit of early Godard movies.
Godard in Fragments from Criterion Collection on Vimeo.
Inspired by this, and if it wasn’t a school night, I would stay up and watch La Chinoise and Two or Three Things I Know About Her. But it is, and I have the last two episodes of S7 of Sons of Anarchy to watch.
Watching this made me wonder: would younger viewers look at it and say “Well, I guess you had to be there at the time”? Or is the sheer style and innovation still clear today? Or does it come across as “Yeah, they did that avant-garde stuff in the 60’s. Have you seen Cremaster?"
Godard in Fragments from Criterion Collection on Vimeo.
Inspired by this, and if it wasn’t a school night, I would stay up and watch La Chinoise and Two or Three Things I Know About Her. But it is, and I have the last two episodes of S7 of Sons of Anarchy to watch.
Watching this made me wonder: would younger viewers look at it and say “Well, I guess you had to be there at the time”? Or is the sheer style and innovation still clear today? Or does it come across as “Yeah, they did that avant-garde stuff in the 60’s. Have you seen Cremaster?"
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