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Update: Mathematics Education

Standard mathematics has recently been rendered obsolete by the discovery that for years we have been writing the numeral five backward. This has led to reevaluation of counting as a method of getting from one to ten. Students are taught advanced concepts of Boolean algebra, and formerly unsolvable equations are dealt with by threats of reprisals.

–Woody Allen
In Howard Eves’ Return to Mathematical Circles, Boston: Prindle, Weber, and Schmidt, 1988.

Mark Woodard, Furman University

Well what are you?

I’m third tier. Oddly enough I don’t fit any of the criteria, really. “Culturally apathetic”. Well, when the Manchester Camarata got the loan of a Strad I had my wife on the phone quicker than Jackie Robinson. What did I get from my mother for my birthday? A very nice set of the Lord of the Rings. I had a single volume paperback since I was 10 (I am now 42) and read it to death. That ook died from love, not hate. How very dare Prof. Mike Savage call me a barbarian. Oddly enough he ranks the Elite, the top tier as having been to Oxbridge or the LSE. He is a professor at the LSE. Odd that isn’t it. Well, I’m a Nottingham and Queen Mary College graduate. I was taught QMech by a guy who won the Nobel (Physiology and Medicine – he essentially invented the MRI scanner) so Prof Savage can profoundly fuck off. My personal tutor at Queen Mary had been a PhD student of Hawking and you will probs have seen Carl Murray on the TV who taught solar system dynamics there. Now, he had a strong interest in Gaelic poetry (he was Irish).

I hate this. The idea that a facility at maths and science makes you uncultured is outrageous. The fact I can code-up some HTML5 don’t mean I don’t do it listening to Bach or Sibelius. I once shared a house with a Bellendius maximus. He was a history student. He was also a twat. He was of the opinion that whilst science and engineering might be difficult (right, Mr Wix, you’ve studied ergodic theory?) it wasn’t creative. He wrote a thesis on “Domestic Service in C19th Nottingham) like anyone gives a toss. I am not criticising arts grads but I am criticising the arts and social science graduates who routinely mock the grads of the physical sciences. Why? Because they assume (a lot of them do) we is all dull. I go to the theatre and art galleries and stuff. I am well-read and I take these nasturiums badly. Frankly, I don’t care. But Chris Wix really was a twat and almost certainly still is a twat. If you can’t see science as creative (and it is) then you are a twat. Stick this in your pipe and smoke it…

Let G be a compact abelian group, μ the normalized Haar measure, and T a group automorphism of G. Let G* be the Pontryagin dual group, consisting of the continuous characters of G, and T* be the corresponding adjoint automorphism of G*. The automorphism T is ergodic if and only if the equality (T*)n(χ)=χ is possible only when n = 0 or χ is the trivial character of G. In particular, if G is the n-dimensional torus and the automorphism T is represented by a unimodular matrix A then T is ergodic if and only if no eigenvalue of A is a root of unity.

… from Wikipedia.

If I can follow that (and I can) I think Shakespeare is easy. God help me! The greatest playwright ever wrote for people who were drinking and whoring and indulging in “country pleasures”. I am not saying the Arts are easy. They are not but the likes of Wix slagging science for just being learning a load of facts is risible. By my third year at Nottingham I entered the exam hall bearing only a pencil. A Rotring. That was it. Me against the universe with only a mechanical pencil. There are few better feelings.

So, allegedly, I’m not into high culture because I can do sums. Ye\h, right Mr Wix. I might not know as much as you about domestic servants in C19th Nottingham but baby I don’t care…


What happens when a Turing Machine meets a Blackhole?

A while back I promised to write this. It has taken some time.

Well the short answer is nobody knows. In principle. Let me explain…

But seeing as this is not QI and I am not the curly haired loon Alan Davis I’d best try to explain why…

There are questions that are unanswered and there are the unanswerable.

Magic don’t exist. Science does and it is a kinda magic (or is that Queen?). Robert Oppenheimer certainly proved that. Well, with his pencil he certainly wielded more power than Dumbledore did with a twig. Real science is magic and it is magic beyond anything these sort of numpties could dream of.

In 1995 at Nottingham University a geezer dressed in a manner that would make Arch-Chancellor Ridcully look under-dressed handed me a piece of paper that was the official recognition of my getting the keys to the Universe. It was emotional, I can tell you. It was a BSc in Physics.

So what I am getting at in this preamble is that magic is real and it’s magic because it doesn’t always make “common sense”.

So, to the point!

Black-holes are essentially collapsed stars that have all their mass within their Schwarzchild radius. This is the radius which even classically, light can’t escape from because as you know Neil, Buzz and Mike had to go rather fast to get off this rock but seeing as the speed of light is a cosmic speed limit once the gravity of a collapsed star gets to that having an escape velocity above that of light then you are in it for the duration. By the way I’m sticking with the non-charged, non-rotational solutions here. Hence Schwarzchild will suffice.

If you really want to muck about with Kerr-Newman metric then knock yourselves out. We’ll keep it without angular velocity (or charge). Now I appreciate the revolutions of Beyonce’s twerking her fundamental singularity as much as the next person but for the current porpoise the entertainer on the stage might as well be Noel Coward in a dinner-suit singing some old nonsense that the late Queen Ma would like.

Because the simple truth is black holes have a property which is awesome. It brings information theory (one of the grandest achievements of C20 maths) into a kind of conflict with one of the grandest achievements of C20th physics. And it’s dead simple. By which I mean it lacks complexity. Now, modeling weather is complicated because modeling multiple processes is. This is a different kind of hard. It does not involve the kind of recursive computation that gets a Julia Set on screen. It is conceptually hard rather than computationally so. Hold that thought – it will matter. There are incredible complicated things that are hard and there are simple things that are hard. Things can be hard in qualitatively different ways.

Now, in the 1930s Alan Turing came up with a theoretical model for computers. I’m typing on one now. Now Turing proved (as did Alonzo Church) by a different route (and Kurt Gödel had a look in too) proved this. Now some of this was purely formal such as the disproof of Peano Arithmetic which set out to prove essentially that the mathematics of integers can be based on a single finite and logically consistent axiom-set. That this was a bit of an embuggeration (especially to David Hilbert) is to say the least. Hilbert had proposed a program in which he hoped all mathematics could be reduced to a single axiom set. Peano Arithmetic was a jolly good punt at that. Essentially he’d proposed an idea to develop something much like the characteristica universalis of Leibniz. Essentially an attempt to reduce everything to rule-following. The idea was this…

When the Peano axioms were first proposed, Bertrand Russell and others agreed that these axioms implicitly defined what we mean by a “natural number”. Henri Poincaré was more cautious, saying they only defined natural numbers if they were consistent; if there is a proof that starts from just these axioms and derives a contradiction such as 0 = 1, then the axioms are inconsistent, and don’t define anything. In 1900, David Hilbert posed the problem of proving their consistency using only finitistic methods as the second of his twenty-three problems. In 1931, Kurt Gödel proved his second incompleteness theorem, which shows that such a consistency proof cannot be formalized within Peano arithmetic itself

That’s from wikipedia

So it is entirely a bust flush. Or is it?

Anyway, I realized I’m hundreds of words in and haven’t answered the question! Sorry, but I had to foreground and the essential problem is to do with words like “definable”, “consistent” and especially “infinite”. Now the final one is the impenetrable. Now way back when Galileo realized infinity was a tough nut to crack when he put as an aside the idea (which is true) that the set of Naturals had exactly the same cardinality as the set of Perfect Squares. Now the first set is {1,2,3…} and the second starts {1,4,9…} but both have the same number of members. Huh? You might be thinking there are more of the first because of the gaps in the second? But as Galileo argued and Cantor proved the cardinality (the size of the sets – sort of) can be proven to be the identical for both because both can be put in an exact 1-1 bijection – essentially for each member of the first set there is a one on the other side – kinda like the perfect tea-dance – with integers He (Cantor) called this number Aleph-null. The first of the transfinite cardinals (there are many more cardinals – more than they have in Rome – and some are fucking enormous – a technical term I owe to a Leeds University number theorist). I am getting a bit OT here but I must mention a collection known (and I know this sounds rather “Father Ted” but there are, amongst many others, ineffable cardinals. Please read this because it conveys the total Woo-Woo.

Yes, there are numbers that are infinite in ways that can’t be uttered but must exist, logically. Yes this sounds mystic and it is but it is provable. This is not homeopathy. This is reality.

What was that paragraph about? Well it was really about trying to say (and this is relevant) that there. In an arguably similar way General Relativity contains solutions (such as those due to Kurt Gödel which include the possibility of time-travel but whilst mathematically impeccable do not pertain to our Universe, but could in principle, just don’t). Now that is interesting. So interesting I wrote an MSc thesis on it. What was dear old Gödel up to? Fuck knows! I don’t know fuck so I don’t. It is all a piggy-rotten mystery and no mistake. It’s like Windows 8. No bastard groks that one.

Anyway Blackholes are simpler. Once you cross the event horizon you is doomed and I mean proper Frazer doomed. Not only are you not getting out but you can’t really communicate out either. Because nothing can get out of an event horizon. It’s kinda like dropping car keys down a toilet. Now I’m on my uppers here (but promised to write this piece) but my understanding is that in the vicinity of an event horizon time slows as seen by an external observer but seems the same for the subject falling in. They also get gravitationally red-shifted and dim into the IR. So if you chuck your mate into a blackhole and they wave back at you it seems ever slower and ever redder until you can see nothing of them. Now this time dilation is kinda like working a 36hr day and then a 48hr day and then a 72hr day so you get more done. Essentially any computable problem accelerates (i.e. breaking a code and not whether Miley Cyrus ought to wear pants) because the effective time the Turing machine’s rate of knots has becomes asymptotic because time has slowed for it – though not for the observer at a safe distance. So it can actually solve or get round the likes of the Entsheidungsproblem

Except. As the Turing machine (and if you are reading this – you have one – just not a local blackhole – I hope) hits max and goes infinite it is going beyond the event horizon so you never get to know the results. I know. It sucks. Of course you could leap in after it but you’d never be able to get the data out so what is the point?

Now I have no idea whatsoever where my trash goes. But if it were to be chucked in a blackhole then nothing of it would remain to the external observer other than mass, electric charge and angular momentum. This applies to anything. This applies to pork bellies, gold ingots, the works of Shakespeare and your Aunty Gladys. All meaningful information is lost to the Universe. In a very real sense that is why blackholes are something else. And that is why a Turing machine can achieve infinite speed (even that dreadful Acer you bought five years ago) but anyone outside the hole can do nothing with it. And if you are past the event horizon neither can you.

And for my next trick I have this cat and this box ;-)


For after all what is man in nature? A nothing in relation to infinity, all in relation to nothing, a central point between nothing and all and infinitely far from understanding either. The ends of things and their beginnings are impregnably concealed from him in an impenetrable secret. He is equally incapable of seeing the nothingness out of which he was drawn and the infinite in which he is engulfed.
- Blaise Pascal, Pensées #72

All I have to say M. Pascal is this..

The first transfinite.

Sowell: “Studies Prove…”

Often we hear that “all the experts agree” that A is better than B or that “studies prove” A to be better than B. ….

A fascinating discussion of the fact that statistical studies can be interpreted and presented in various ways…with varying degrees of rigor and of intellectual honesty…for various reasons. Dr. Sowell provides some excellent examples in this three-part article.

Part 1:

Part 2:

Part 3:

That Dashing Young Man and His — WHAT Machine??

Over at Samizdata, Natalie has posted something on the mewlings of a certain Public Intellectual. One thing led to another with the result that Nick (nice-guy) Gray brought up what he calls “mental pollution.” Through the magic of YrsTrly’s wetware, the same found this, which might provide some entertainment for those Kitties who are loafing around rather than occupying themselves properly with Kounting….

There is a short video of this technological miracle in operation at

While there, visitors might wish to consult the Site Map.

Apocalypse postponed – again.

We all know it was finito on the 21st. Due to the end of the Mayan Long Count.

Except it like wasn’t… Mind fair play to the Mayans – they still exist and still have their language and culture – shorn of human sacrifice – that does happen in Mexico mind mainly as a result of the deathly tango between “The War on Drugs” and the gangs… But that’s another matter…

But quite a few of them made a few quids out of new-age twats. And if a hippie and his or her money is parted due to ancient and brilliant mathematics and astronomy then Nick is happy.

Over at the “Christian Science Monitor” they have a round-up of their top-five failed (obviously) prognostications of global doom. They are all corkers…


The Millerites* – serial prognosticators of doom – kinda like religious Alan Hansens – but there was a “Great Disappointment” for them when the world didn’t end in 1844. They split and we got the Seventh Day Adventists and ultimately the Branch Davidians.


December 21st (again) 1954. This is a cracker…

Martin’s followers, many of whom quit their jobs and gave away their possessions, gathered in her home to await the aliens. (Martin’s husband, a nonbeliever, slept upstairs through the whole thing.) To avoid being burned by the flying saucer, her followers removed all metal from their persons, including zippers and bra straps. Midnight came and went and the group became increasingly agitated. Finally, at 4:45am, Martin said that she received another message from Clarions informing her that God was so impressed by her groups actions that He changed His mind and decided to spare the earth.

I love the fact hubby slept through the End of the World and what sounds like some sort of deranged Dianetics orgy. I mean why worry about the clap if it is the End of Days? Or maybe it was like the Heaven’s Gate “Away Team” who watched Star-Trek videos before they drank the Kool-Aid (or whatever). Some of those even castrated themselves so they didn’t get a stiffy when Lt Uhuru fiddled with the Crimble dec in her lug. Me, I lugged the ‘scope and Pentax out the back and got some pretty decent photos of Hale-Bopp. With my girlf and a cable release. Mentalists. I mean I knew my Solar System Dynamics lecturer Carl Murry had a year’s sabbatical in Florida to work on his book so why worry? Prof Murry is still with us and so is Florida. The book is available from Amazon. The paperback is fifty quid. There is a used hardback for nigh on nineteen hundred quid. I assume it is a mint signed first edition or similar. Very bright chap Prof Murray. Looked to the future. I have a copy of the earlier ring-bound photocopied version with my own spider-crawl marginalia.


Hal Lindsey. Bog standard apocalyptica though repeated – often. He now claims (after his predictions for 2000AD didn’t come to pass) that Prez Obama is setting the stage for the antichrist. If the antichrist is Joe Biden I think we can all sleep safely for he is a moron.


Pat Robertson, who in a 1980 broadcast of “The 700 Club” said “I guarantee you by the end of 1982 there is going to be a judgment on the world.”

The world didn’t end in 1982, but “WKRP in Cincinnati,” did.

So why was Mr Robertson running in several desultory attempts for the presidency when it’s all effed anyway?


And finally my personal fave. The Prophet Hen of Leeds. This one is instructive for utterly contra to millennial or apocalyptic visions this shows that the good folk of Yorkshire then, as now, have a warped, nay, fowl, sense of humour. And in these final days it is good to have a certain sense of continuity.


Now we only have the enforced jollity of Crimble. Ho, ho, ho! to look forward to.

Something I saw in the Telegraph darkly amused me. The Crimble Special of the execrable “Call the Midwife” on BBC1 (which has displaced the “Who” spesh – Dear Gods!) said it would, “Have you crying into your Christmas pud”. True, in a sense. In the sense of outraged boredom and terminal tedium.

Merry Christmas everyone!

(Bah, humbug!)

*Not to be confused with the Miller Lites which is only the end of beer (as if that wasn’t bad enough).

Two bad cases of the DTs

From The Telegraph on the subject of the predecessor to the Bloodhound SSC project…

Thrust SSC was, at 4m wide and 10 tonnes – powered by twin Rolls-Royce Spey turbofan engines, more commonly found beneath the wings of an F-4 Phantom II jet aircraft – an unwieldy beast. Rather than simply tweak its design, Noble and Green opted to begin from scratch. A slimmer, lighter car could, they reckoned, significantly outstrip Thrust. But first they needed jets.

This is what an F-4 Phantom looks like:

Do you see any engines under the wings? Now obviously I knew this already but finding that (and many more) images took 5s with Google. And it’s not like it’s an obscure ‘plane so anyone writing on this sort of stuff ought to know anyway.

If I were editor of the DT I’d carpet Mr Ross for such sloppy idleness. Now I’m a fair man so I’d give him a start before I released the hounds and wouldn’t spray his genitals with aniseed first. I reserve that as a unique punishment.

The second is this gem of bollocks reporting and woo-woo headlining.

Look, you numpty, this is what the USA thought of doing… They were going to detonate a kT range-yield nuke (I hate the term “atomic bomb” which is used in the article) to show the Soviets that the USA could hit the Moon or even in principle weaponize it. Bear in mind this was the ’50s when serious popular science journals were considering the (stupid and unworkable) idea of missile batteries on the moon. Unworkable because it took an entire Saturn V rocket to get three men there and stupid because it took three days to get there (or back). Who wants to launch a nuclear strike giving the other side that much notice? Of course in those days small (and not so small) boys were reading action comics in which the USMC (Space Division) and the Spetznaz (Space Division) would be slugging it out (with ray-guns, natch) over Copernicus Crater.

It all goes back perhaps to Arthur C Clarke (and maybe John Wyndam) and the concept of orbital weapons. Again a militarily ridiculous concept if you think about it*. Ultimately technical, military and economic logic won though against SF dreams and the sub-orbital ballistic missile was born. Couple that with a nuclear powered submarine and you have a far more potent weapon at orders of magnitude less money. You think a Vanguard or Ohio class submarine is expensive? Compare with the cost of building nuclear silos on the Moon…

I guess it hit a popular Zeitgeist based, perhaps, on the feeling that we’d gone from the Wright brother’s stick and string to Sputnik in half a century and from lobbing hand-grenades from primitive biplanes to Little Boy in even less time.

“Everyday it’s a-gettin’ closer
Goin’ faster than a roller coaster”

-Buddy Holly.

Perhaps it’s also down to other little boys fantasizing about using their ray-guns to waste some tentacled horror and win the heart of the alien princess who might be green but that’s OK because she has unfeasibly large breasts (that’s Zero-G for you!). Seriously, the interaction between popular culture, fashion, trends in aerospace and governmental policy can’t be underestimated. Perhaps whoever wrote this Telegraph schlock was one of those little boys but of course this persisted long after the ’50s. Consider two films from about 1980. There was a sort of proto-”Deep Impact” movie (I forget the name) which featured pre-existing Soviet and US nukes being turned against an incoming meteor or some such and also of course “Moonraker” with the USMC in space-combat with Drax’s mob. Drax also has deadly weapons in space. Of course he does! And he wears a Mao suit.

Instead we had Apollo. You know they left medals commemorating lost cosmonauts as well as the astronauts who died in the Apollo oxygen fire?

Back to Earth! The wider problem I see with this hopelessly sloppy reporting on aerospace related issues by the dear old DT is that this is a subject I know a lot about. And it isn’t just the DT. They are all at it. The contempt the MSM scribblers show for basic fact checks and employing anyone competent** in the first place is staggering. And this is something I know about so I can chortle but what about the huge numbers of things I don’t really know about? That’s a worry. I don’t have the internal knowledge to appraise immediately nor the time to acquire it. They can’t sell me a load of pony on certain things but on others… And the same dear reader applies to you. None of us are polymaths anymore.

But as to the aerospace specifically, suspect deep-down it is a symptom of an ingrained belief amongst the “serious” papers (the ones without unfeasibly large breasts – more honest – you know where you are with a tit) that the really important stuff only happens between Whitehall and Wapping and getting actual facts – easy, non-controversial, non-debatable facts correct about all that nasty, complicated stuff with “like sums with letters in them” doesn’t really matter to their journalism trained minds. Something Michael Gove said is ever so much more important. No. It. Isn’t. When the Govester and his EBacc are mere footnotes in Hansard (some other wanker will be re-arranging the deckchairs by then anyway) studied only by the dullest of graduate students people will remember Armstrong, Aldrin and Collins.

Well, that tech-stuff does matter and I’d much rather read something written by someone with no qualifications in journalism but an understanding of the area they are reporting on anyway. As I said, in many areas I don’t know what to think because I don’t trust what I read not just because it is propaganda or lies or deranged opinion but because I can’t accept the basic, verifiable, “truths” they use within the piece as real or otherwise because I know how sloppy they are on things I do know because I know they don’t even care to find out an F-4 Phantom has fuselage mounted engines rather than under-wing ones. I’ll leave the penultimate words to a quote from Bertrand Russell (I think this is about right),

I’d rather be reported by my worst enemy in philosophy than someone ignorant of it.

Quite, Bert.

Without facts to argue from analysis and opinions are devoid of meaning. Without a respect for facts analysis and opinions range from doubtful to disingenuous to out-right “Noble Lies” (in the Platonic sense).

I want to know truth and not an unreality built upon a lack of genuine, objective facts. Every ignoring of reality (whether deliberate or through idleness or stupidity) contributes towards an “invented reality” so let’s ultimately hear from Jorge Luis Borges.

Ten years ago, any symmetrical system whatsoever which gave the appearance of order — dialectical materialism, anti-Semitism, Nazism—was enough to fascinate men. Why not fall under the spell of Tlön and submit to the minute and vast evidence of an ordered planet? Useless to reply that reality, too is ordered.

- Tlön, Uqbar, Orbis Tertius

PS. I know this rambles. I’ve spent too long on it.
PPS. I know (see PS) this is posted after Levenson introduced (BBC – “His long-awaited enquiry results”. Not by me it wasn’t. I wasn’t calling for the DT to be taken to task by the “Regulators” (think Western movies) over these inexcusably bad pieces of journalism. No. I was calling for the likes of us to point out and laugh because, like a small boy who sees a potentate in the nip.

*Either geostationary over Moscow and DC or in predictable orbits or burning lots of fuel to vary orbit which would mean a very limited life-span or some form of space refueling.
**In the first article there is some wibbling about “Computational Fluid Dynamics”. Clearly the author hasn’t a clue what he is on about.

How to get to the stars…

The Alcubierre drive (or Alcubierre metric see: Metric tensor) is a speculative idea based on a valid solution of the Einstein field equations as proposed by Miguel Alcubierre by which a spacecraft might achieve faster-than-light travel, making travel to other stars a possibility. However, it should be understood that this is different from a ship actually exceeding the speed of light within its local frame of reference. Rather, the ship would traverse distances due to the expansion and contraction of space behind and before the ship, respectively, as indicated in the diagram to the right.

Don’t look at the diagram – it only confuses matters. Basically it contracts space ahead and elongate it behind. Basically it works like this (there shall be some maths a-coming) but this is in principle the guts. The key word is “metric”. Relativity forbids travel faster than light which is a pain if you really want to go anywhere fast. But it doesn’t ban spacetime itself moving faster than light. Now if you can do that you can have a weekend trip to Proxima Centauri. Now that is much more fun than Southend.

And this is how it works… This is the metric…

It gets better. I actually understand this which shocks me…

That is gorgeous. And BTW tanh is pronounced “than”. It is the hyperbolic tangent.

If we can harvest enough “exotic matter” it can be done. Windmills obviously won’t do it. Now the maths is tricky but did you really think tricking the light barrier was “simples” as the Meerkat said?

Oh, there is a problem. And it is potentially a biggie. The fact that the Alcubierre metric is a valid solution of the Einstein Field Equations means it is merely mathematically valid. It does not mean it applies to our universe. For example the Goedelian solutions to the EFEs are mathematically correct but almost certainly don’t apply here. Interesting but not correct.

Alan Turing

Today would be Alan Turing’s 100th birthday. Alas it never transpired. He died in still debatable circumstances when he was in his prime. Was he a great pure mathematician? Yes, I’d put him almost as high as Gödel and that is like comparing a footballer to Pele. Both of course were not normal men. Turing had some fairly odd ideas and Kurt Gödel starved to death. Gödel was paranoid and refused to eat any food not prepared by his wife, then his wife died. Now Gödel was a nutter. Perhaps everyone who scales such (literally) infinite heights is going to be a bit unusual. It is hard to say what killed Turing. It has entered the popular consciousness that he was a sort of gay martyr (the statue of him in Manchester is in the gay village and not where it ought to be – in front of the University) and this is possibly true. He was convicted of “gross indecency” for having sex with another man. If there is a great villain here it is the law. My understanding is Turing had sex with Arnold Murray in his own home in Wilmslow and it all came out when he reported a burglary by his shagging partner. I fail to see how anyone can be “indecent” in their own home.

But it is possible the cyanide coated apple was a mere mistake. It has been mooted. Certainly Turing (a pure mathematician not schooled in lab discipline) was new to the game. And trust me as a physicist I have worked with lethal things and I wouldn’t trust a mathematician in my lab. Mainly those lethalities were in the sense of serious voltages and radioactive stuff and not any biohazard or poison*. So maybe? Who knows! Who cares! I am typing this on a Lenovo S205. That is what matters. It is certainly possible that the female hormones Turing was ordered to take after his conviction that caused him to grow breasts outraged him because he was also verging on being a world-class long-distance runner or following his conviction (not unrelated to the Cambridge spies) he lost his security clearance (for being gay – unlike the Cambridge spies he was not a KGB agent, just gay) or even the fact he was only a reader at Manchester because the security about Enigma/Lorenz had left a “black-hole” in his career. A fundamental thing here is that we were moving from Empire at the time and gave as a parting gift Enigma machines we’d snicked from the Germans but we didn’t want them to know we could break the code. Sneaky? Brilliant! But it meant nobody involved with Station X or Ultra got the credit. You can compare and contrast with Manhattan. Of course that was for obvious reasons much harder to keep on the QT.

There are people who define centuries. Roughly the Stephensons defined the C19. The C20th was invented by Nikola Tesla. Our time belongs to Turing. If you are reading this you are reading this on a Turing Machine. Much the same as the Turing machine I am writing this on. I got my first Turing machine (a 48K Speccie) in 1984. I felt like a king – I had a computer and they had been huge things maintained by fit librarian-type birds in lab-coats with clip-boards and owned by Bond villains in Mao suits and cats. I wrote a game even – it was very poor – but hell’s buggery – I wrote a game! I learned maths and drew fractals from outlines of programs from Scientific American my Dad nabbed from work. Alan Turing made it so. The game BTW was called “Orc Fighter” and was truly dreadful.

So fill your cups for Alan Turing. He made us. We have a category here called “Transformative Technologies”. Turing is certainly up there. He is up there with George Stephenson and the Wright Brothers. He is there in the pantheon with Tesla and Newton. And I don’t say that about many folks.

*My final university experimental project was… Well I built a magnetometer out of bits. It worked down to very few fractions of a Tesla. Nano Tesla I think. It annoyed some profs because I had proven data of car movements in the car park… Not everyone was actually clocking in or out at time. But that was not my original scheme. Oh, no I wanted to play with magnetotactic bacteria as a model for certain solid state systems. Three problems. A budget of GBP35, the fact these buggers come from New England swamps and thirdly nobody in the physics department having the slightest idea on the H&S issues. The magnetometer was built in the end with scavenged parts for about a tenner. God knows what happened to it.

In Praise of Islam.

After the “Joseph” post, a post on Islam.

Not in praise of Islam in today’s context (although some people may see some relevant point), but in the context of the world in which it became important and powerful.

This was not the Classical World – the world of Ancient Greece and the Roman Republic. Where people (in many places – although far from all) were either free or slaves.

Slavery certainly existed in the world in which the Muslims went forth on the path of conquest (just as it existed among the Muslims themselves) – but the world they faced was a world where the vast majority of people were semi serfs. Tied to the land, or tied to their urban occupations (tied from birth).

The first thing to go had been the right to keep and bear arms (the classical mark of a free man – in both Ancient Greece and Republican Rome, just as with the Celtic and Germanic tribes). Octavian (“Augustus”) had got rid of most private ownership of, and training in, arms. Useing the argument that he was saving Rome from the dangers of civil war (the repeated civil wars of the Imperial period – where different factions of the army backed different Emperors somehow do not count as civil wars I suppose).

So the Ancient World abandoned the central principle of that great work of classical literature “Starship Troopers” – “everyone fights” (meaning everyone who is to be considered a citizen must be prepared to fight).n And I am not being, entirely, sarcastic – after all Robert Heinlein (the author of Star Ship Troopers) got the idea from Aristotle. In the “Politics”, Aristotle explains how the idea of the armed citizen is not just Greek, how (for example) the men of Carthage are allowed to vote or stand for public office unless they have first accepted military service (of course this rule was later abandoned by Carthage – with tragic results).

Most “citizens” of the new Rome (which now meant the entire Classical world) had no military weapons and were not trained in their use.

Later more and more regulations and restrictions (and higher and higer taxes) were imposed on these “free citizens” – till, in the time of the Emperor Diocletian, they basically became cattle. Tied to the land (if they were peasants) or to their urban occupations (sometimes in state owned factories).

And it even became acceptable to keep these “free citizens” in chains (physcial chains) if it was expected they were going to run away (i.e. no longer farm the land – but run off to the barbarians, or whatever).

And, of course, flogging and all forms of torture (under the Republic only to be applied to slaves) gradually (over the years and centuries of decay) became accepted ways of relating to most ranks of “free citizens”.

Nor were things fundementally different with Rome’s great enemy – the Persians.

The Pathians seem to have tolerated the Greek and other civilizations they became overlords of. But the new (or restored – depending on one’s point of view) regime of the Persians established a new civilization.

With (yes you guessed it) hereditory castes determining a person’s fate in life from birth (much as in Hindu India – accept under the banner of Zorastrianism).

Under the Persians there was also a de facto religous monopoly (how could there not be – the Magi of Zorastrianism were also the magistrates and officials), apart from in the “land of the King” (basically Babylonia – where the King of the Persians ruled directly) where a wide measure of religious tolerance (for Jews and others) was practiced.

The Romans, after the conversion to Christianity, also moved towards a defacto religious monopoly with the persecution of all other forms of belief.

Some Christian Emperors (such as Valentarian) believed this was unChristian. But Emperors eventually adopted the position that it was their role to discriminate against nonChristians – indeed to persecute even fellow Christians over differences in theology.

Of couse in the 7th century the hatred this persecution of Christians by other Christians produced was to have fatal consequences for the Byzantines in the Holy Land – for many Christians (of persecuted types) went over to the Muslims in the middle of the key battle (the fact that these Christians were ethincally Arab was also a factor of course – but Pagan Rome, and Christian Emperors who did not practice persecution NEVER faced defection in the middle of a battle – not even to barbarians of the same ethnic group as troops on their own side).

Augustine, amongst other theologians, provided useful arguments about how using violence, including torture, in matters of religion was not really anti Christian. How did Augustine refute the Hebrew, Amoraic and Greek texts? Well he could not really read any of these languages, so he did not have to.

Ah dear Augustine – it was, of course, him who was one of the leading theologians to ridicule ancient science. And to mock the idea that people could choose to behave decently, none of this “Pelagian” free will for Augustine (that was as bad as being able to read Greek or Hebrew or Amoraic – you know the langugage that that Jesus bloke spoke, why someone interested in the Amoraic words of the Jesus bloke [or the Greek writings of the people who knew him] might be so absurd as to actually visit the land he lived in, which, of course, the wise Augustine never did ). Predestination, and human efforts are doomed, all the way – that is Augustine (he was a true father of the Dark Age).

To me it is no accident that the first theologian in England in the Middle Ages to stress the study of Greek and Hebrew, Roger Bacon, was also interested in submarines, aircraft (and so on) – contray to what is often thought there is no contradiction between a love of ancient learning and hopes for a better future. On the contrary it is the book burners (those who wish to destroy the learning of the past) who tend to be the people who strangle the future.

Of course the Western Roman Empire had collapsed by the time of the comming of Islam (although the Byzantines ruled in most of what had been Roman Africa – as well as in Sicily and other parts of Italy). However, the Germanic regimes that had taken over the rest of the Roman Empire in the West had kept the Roman sytem.

Most of the population reduced to de facto serfdom – a population where the “everyone fights” rule (of free citizens of the Classical World, or of the Germanic world itself) was ignored. Is it really any wonder that the Muslims found it fairly easy to conquer vast populations – even thought their own numbers (at first) were small?

The populations the Muslims took over had been treated as cattle for centuries – both in the East and the West, so conquest just meant a change of masters (not a loss of the freedom they did not have anyway).

And the Persians?

With them it was even worse. Insane social/religious experiments (for example trying to share out “all goods and women”) had almost destroyed the Persian Empire (torn it apart into chaos and civil war) long before the Muslims arrived.

The followers of Muhammed (a member of family of traders) might plunder the goods of other people – but they had no truck with denying the rights of private property amongst themselves.

At least where it came to goods – Islamic law as concerning LAND is more contested, which was to prove a major weakness in Islamic civilization, in comparision to that of the emerging “Feudal” law of the West. Such as the Edict of Quierzy of 877 which restated that even a King of France could not take a fief of land from the children of the person who held it, and give it to someone else – which meant that a Western King was a different sort of thing than a Roman Emperor or an Islamic ruler.

Western Kings might rob. rape and murder people – but these remained CRIMES even if the King did them (as King John was to discover), just as a Western King might have mistresses, but not a “harem” and his heir was expected to be from a marriage (not a slave girl).

A Western King might be a terrible hypocrite and criminal – but there was an objective standard to judge them by (unlike a Roman Emperor) and (again unlike a Roman Emperor) independent land holders with large numbers of armed (and trained) men, to hold them to account. “The Emperor’s will is law” would be an outrage to a mind of the Middle Ages.

And as for the powers of the “barons” themselves – a lord who overstepped the mark with free peasants might well get a longbow arrow in his face, at least in later period England (but other forms of death in other places). Remember even in England at the hight of the “Norman Yoke” only half the population were serfs (which means the other half were not). And the Kings of England (and the various lords) were desperate for armed (i.e. free) men to increase their own power, at home and overseas (that is the whole point of “bastard feudalism” – but it goes back a lot further). As early as the time of Henry the first (son of William the Bastard) the King was already desperatly reaching out to Englishmen to fight his Norman brothers (litterally his brothers) and marrying a direct decendent of Alfred the Great to bolster his claim to the throne.

So indeed “everyone fights”. And the Black Death meant the de facto end of what serfdom there was in England – whatever the demented statutes of Parliament said.

But Islam in the 7th century did not face the Kingdoms of the Middle Ages.

It faced the Persian despotism (desperatly trying to recover from its own madness), the despotism of the Byzantines (really the late Roman Empire – although after their defeat by Islam, what survived of Byzantine civilization was to change…) and the recently (well a century or so) arrived Germanic overlords of places like Spain – where the old Roman system (i.e. most people are cattle – unarmed) remained basically in force.

The Muslims were in a way a throw back to the Classical World – “everyone fights” (indeed believers had a religous duty to train and fight). And, amongst themselves, believers (at least in the early stages of Islam) had rights – they could not be treated as cattle (as the “free citizens” of the late Roman world, or of the Persian world, were).

There was even, again in the early stages, an intense Islamic interest in Classical learning and science – and scholars (Christan, Jewish and Muslim) made progress in these areas (although progress rather over stressed by BBC programmes) that was unmatched (at that time) in the Byzantine Empire or the Western Kingdoms.

For the Muslims (at least at first – and for the most part, there were nasty exceptions such as the ruler who burnt what was left of the library of Alexandria) did not know they were supposed to reject the learning of the ancient world (not build upon it), whereas too many of the Christians and too many of the Magi did reject it – because they thought it represented the civilization they had replaced.

Of course, within a few generations the Islamic world started to reject Classical learning and science more than the folk of the Western Kingdoms did.

However, the story of how that came to pass will have to wait for another time – or another person to tell it.

Shafted Through Five Ringpieces.

I have for quite some time wanted to post about the epic insanity that is the London Olympics. Then just today I found an epic take-down of the whole nonsense in The Guardian by Larry Elliot. He is spot on. His central point is that the 1948 games made a profit and this will cost a fortune. To be honest Mr Elliot (and I like his schtick overall here – never read him before but he is no Keynesian which is surprising for The Graun) doesn’t make a point I would have done so I shall make it now. Hey, not blaming the fella. He makes an awful lot of good points.

Various cities have gone to extreme lengths and much expense to host the Olympics in order to attract tourists or “put themselves on the map”. Can this honestly be said about London? It is and has been for over a millennium one of the truly great cities of the Universe. I adore it with an unrequited passion. Indeed a couple of months back I saw on the front of the Indy a story that the Games will harm tourism to London this Summer. This chimed with me. Hotels are putting prices up, there will be ZiL-lanes for corrupt IOC wonks and a security lockdown that will make North Korea look like Key West during Fantasy Fest. Yes, it was a Burt Bacchanalian alright and the birds I saw wearing nothing but body-paint and flip-flops were fitter than those. Either that or I had had rather too many mojitos. Now when we booked the honeymoon neither me nor my bride to be knew what Fantasy Fest was. I roughly assumed it would be more JRRT than DD (the latter doesn’t involve rolling a 3D6). I was fruitfully wrong. I expected to see computer science grads wearing elf ears and reciting Icelandic sagas. Instead I saw hordes of folks having fun in bars whilst wearing virtually nothing, drunk as skunks and a generally jovial atmosphere. I got a piccy somewhere of a gay male couple painted as lizards. I was struck (not for the first time in the USA) about how genuinely liberal the USA is. Last time I was in Blackpool for example (how dare I compare the Keys to that epic shit-hole!) it was full of Scousers pissed on Carling having fights – sometimes with themselves.

But anyway, all those fun and frolics is self financed. The Olympics this year in London will cost the tax-payer a staggering GBP 11 billion. That is 11,000,000,000 quids. That is almost a respectable defence budget. Well, for Belgium anyway.

Anyway, the reason for that excursion was to tell a story worth telling. Just read the whole thing because I could get away with that excursion because he says it all really. It says everything that has gone wrong with our polity since the war.

And this is the really bizarre twist. We keep hearing about how this is the greatest show on Earth. Now if that really is the case it ought to be profitable as it was in 1948. I mean PT Barnum even earlier had the greatest show on Earth and made a mint. Hell’s teeth the likes of Camerons Mackintosh and James aren’t exactly dropping their pants for food are they? What the fuck is up with us? On the other hand Cameron iDave (and Gideon) and Broon and Blair before that are just gang-raping us. And they are only doing this because we let them.

That 11 billion isn’t just an epic sum (though it is). I mean we are building a handball court in East London. Who the fuck gives a toss about handball? What is handball anyway? I mean Attlee’s mob inherited a buggered economy but hey there was a bloody good excuse for debt at 250% of GDP after fighting and winning the most epic war in history (by the way 11 billion quids is just a shade under Britain’s entire GDP for 1948). What have we got for serially pissing monies up the wall?

No it isn’t just an epic sum it is four times over what we told the IOC it would cost. Look at it this way. If quoted you 500 quid for a computer (and you can build a pretty cool machine for that) and then delivered it and said, actually it’s two grand I believe I would leave your home or business wearing it.

In 1948 the Ollies cost a bit over 700,000 (under projection) and made an operating profit of 30,000. Bloody Hell! But of course this is all unpatriotic moaning. I mean expecting professional sportspeople to you know be like professional and you know make money by be entertaining enough to make a living and all. I might as well kick the Churchill dog to death. Oooh No!

And if they aren’t why do we owe them a living? It don’t happen with footie. Or bands. I mean the Stones never extracted money from me by threat of force. Nobody forced me as a point of patriotism with a gun to have to pay for the Lion King on the London Stage. The computer games industry doesn’t extort money from me. Why is athletics allowed to?

Because it involves bizarre national pride in a vaguely sinister tomorrow belongs to way… Well whoever we have collectively put our knackers on the anvil for this jamboree. Now what is the last refuge of a scoundrel again?

The Dead Budgie Sketch

I’ve just been down the road for a Coke and a packet of crisps. In the queue I glanced over the newspaper front pages. Paul has been proven 100% correct (see this and any number of other posts or comments by Paul here or Samizdata or elsewhere in which Paul regarded this budget as a test of the government’s political sanity). Gideon is being hauled over the coals in almost all the press over the epic 50% to 45% “giveaway” that isn’t. Now I have a feory. I don’t think Gideon is that smart. Anyone who has even vaguely followed British politics over roughly my lifetime (and probably before) must realise a terrible truth about how people perceive tax. And it is this simple. If you say “tax” to almost anyone their first reaction is to think income tax. It’s the headline grabber. It’s silly but that’s it. And a tax (by which I mean income tax – of course – people tend to ignore all the other forms) cut for the rich provokes ire. Gideon should have known this. Even if he isn’t the sharpest pencil in the tin you at least expect someone who rose to his exalted status to display low animal cunning. I think they politely call that “political ability”.

If I were chancellor I’d be sore tempted to scrap the fiction of NI in order to simplify the system and reduce bureaucracy. Let’s say I did that and left everything else the same but raised income tax to compensate in what would analytically be a neutral budget there would still be weeping, wailing, gnashing of teeth and rending of garments throughout the land because the “headline rate” (why do you think it gets called that) of “tax” as perceived by way too many people would of course have gone up quite a lot.

Or it’s like the VAT hike from 17.5% to 20%. That really hit everyone but there was only mild grumbling. I don’t recall even the greatest champions of progressive taxation bitchin’ and pukin’ over what was essentially an increase in a flat tax in the sense that the duke and the dustman pay the same rate. I hazard a guess that if shops and restaurants displayed prices ex-VAT (as they do with sales taxes in the USA) people would have noticed more. I only really think of it when buying computer kit because my usual supplier quotes prices ex-VAT them dealing with trade and all.

Anyway, it’s all OK because the Duchess of Cambridge borrowed a frock from her mother. Now I leave as an exercise for the reader to work out how many daughters for how many years will have to borrow dresses from their mother (rather than buy a new one from say Monsoon) to pay for such fluorescent idiocy as HS2. Of course if you work in clothing retail you’re going to have to retrain (boom, boom!) as an engine driver but I’m sure Gideon has a magic money tree (a Fiscus fantasia I am led to believe) down Threadneedle Street to pay for that.

PS I have done my back of an envelope calculation earlier on HS2 here.

You couldn’t add it up.

I have a physics degree. My definition of “bad at math” is struggling with the derivative of a function of a function. Or let’s put it more bluntly – as an undergrad I never used a calculator in exams. It was all letters – mostly Greek but in some cases Hebrew. But apparently I am unusual. 49% of UK apparently adults can’t do sums. I wouldn’t even call it mathematics. Sums is not math. This is maths. Adding-up is not. Hell! When I was 16 I got a summer job in a sweet shop and people looked at me funny because I was quicker than the till. Still am and they still look at me funny and now I know why.

I mean for fuck’s sake! What sort of arseholes are we? The nation of Newton and Wren can’t hack this:

Hasran has planned a new TV cupboard. A TV is 40cm wide and will sit in the middle of a shelf that is 900mm wide. How wide is the gap on each side of the TV?

A: 10cm; B. 25cm; C. 43cm; D. 50cm

God fuck us all! Although what I’d like to know is why Hasran has built a 900mm TV cupboard for a 400mm TV? Why has he built a cupboard in the first anyway? My TV hangs on the wall. It’s hardly a secret passion is it? I mean when the Sky man came to upgrade our box to HD and all it wasn’t like I asked him to park round the back like an illegal abortionist was it?

Now here’s the real rub. Can they see through the Monty Hall veridical paradox? Because it took me two seconds. There were pure maths post-docs in the pub that evening tearing apart beer-mats to scribble on but I clocked it in the noggin in a witch-space second. A mere astrophysics student. And keen amateur poker player. BTW if you want a really good explanation of Monty Hall then this is the best I’ve read. Not a great book overall but that bit is gold. There is also a bit on bifurcation chaos theory and period-doubling which I can’t make my mind up about. It is either a brilliant portrayal of the longs and shorts of Asperger’s Syndrome or it is utterly wrong. And if the latter then it is possibly a satire. I have considered a post about it. Paul Marks would like what I had to say.

Anyway, I guess I just wrote the last paragraph because I wear my mathematical ability with pride. Apparently a lot of my country-folk are proud of their lack in that respect. Well, various people are proud of that. Lots apparently. I do not, as various researchers do, feel for the general economy. No! I just think they have missed out on the ravishing exceptional beauty of the very Queen of Science herself. As someone who has poked under her petticoats I can tell you they are missing a right treat. Now of course you could do “Modern Studies” at the “University” of Wolverhampton. You could do that but you could also rip the Universe apart and see how it ticks. I did. Your choice.

PS. I’m not sure Wolverhampton still does “Modern Studies” but a quick Google reveals it no longer does modern European languages. That is piss-poor.

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