The following problem can be solved the easy way or the hard way:
"Two trains 200 miles apart are moving toward each other; each one is going at a speed of 50 miles per hour. A fly starting on the front of one of the trains flies back and forth between them at a rate of 75 miles per hour. It does this until the trains collide and crush the fly to death. What is the total distance the fly has flown?"
In a strict mathematical sense the fly actually hits each train an infinite number of times before it gets crushed, and one could solve the problem the hard way with pencil and paper by summing an infinite series of distances. This is they way that most trained mathematicians will solve the problem. Conversely a mathematical novice will most likely solve the problem the easy way - since the trains are 200 miles apart
and each train is going 50 miles an hour, it takes 2 hours for the trains to collide, therefore the fly was flying for two hours, at a rate of 75 miles per hour, and so the fly must have flown 150 miles. Easy.
When this problem was posed to John von Neumann, he immediately replied, "150 miles."
"Ah, I see you've heard this one before, Professor von Neumann. Nearly everyone tries to sum the infinite series."
"What do you mean?" asked von Neumann. "That's how I did it!"
An MIT student cornered the famous professor in a hallway:
Student: "Er, excuse me, Professor von Neumann, could you please help me with a calculus problem?"
John von Neumann: "Okay, sonny, if it's real quick -- I'm a busy man."
S: "I'm having trouble with this integral."
JvN: "Let's have a look." (a brief pause) "Alright, sonny, the answer's two-pi over 5."
S: "I know that, sir, the answer's in the back - I'm having trouble deriving it, though."
JvN: "Okay, let me see it again." (another pause) "Yep, the answer's two-pi over 5."
S (frustrated): "Uh, sir, I know the answer, I just don't see how to derive it."
JvN: "Whaddya want, sonny, I worked it out in two different ways!"
"Johnny was the only student I was ever afraid of," the mathematician George Pólya once recalled. "If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me as soon as the lecture was over, with the complete solution in a few scribbles on a slip of paper."
Von Neumann was the subject of many dotty professor stories. He supposedly had the habit of simply writing answers to homework assignments on the board (the method of solution being, of course, obvious). One time one of his students tried to get more helpful information by asking if there was another way to solve the problem. Von Neumann looked blank for a moment, thought, and then answered, "Yes".
In the 1950s, von Neumann was employed as a consultant to IBM to review proposed and ongoing dvanced technology projects. One day a week, von Neumann "held court" at 590 Madison Avenue, New York. On one of these occasions in 1954 he was confronted with the FORTRAN concept (the first 'high level' computer programming language); its developer, John Backus, remembered von Neumann being unimpressed and that he asked "why would you want more than machine language?"
"The spectacular thing about Johnny was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didn't bother to remember things. He computed them. You asked him a question, and if he didn't know the answer, he thought for three seconds and would produce an answer." - Paul Halmos, Mathematician.
Perhaps unsurprisingly, John von Neumann was strictly logical in his thinking. One afternoon his assistant, Paul Halmos, dropped von Neumann off at home. "Since there was to be a party there later, and since I didn't trust myself to remember exactly how I got there," Halmos recalled, "I asked how I'd be able to know his house when I came again. 'That's easy,' he said. 'It's the one with that pigeon sitting by the curb.'"
Henry Ford had ordered a dynamo for one of his plants. The dynamo didn't work, and not even the manufacturers could figure out why. A Ford employee told his boss that von Neumann was "the smartest man in America," so Ford called von Neumann and asked him to come out and take a look at the dynamo.
Von Neumann came, looked at the schematics, walked around the dynamo, then took out a pencil. He marked a line on the outside casing and said, "If you'll go in and cut the coil here, the dynamo will work fine."
They cut the coil, and the dynamo did work fine. Ford then told von Neumann to send him a bill for the work. Von Neumann sent Ford a bill for $5,000. Ford was astounded - $5,000 was a lot in the 1950s - and
asked von Neumann for an itemised account. Here's what he submitted:
Drawing a line with the pencil: $ 1
Knowing where to draw the line with the pencil: $4,999
Ford paid the bill.
30 July 2010
19 July 2010
Saint Philby
Think famous spies and you think James Bond. Think harder and you hopefully think of Kim Philby He was an English spy who turned double-agent and spied for the Russians through the Cold War. He was a very naughty boy, but he's not half as interesting as his dad, Harry St. John Bridger Philby, usually known as 'Saint.'.
Saint was the your archetypal man of the British Empire. He was born in
1885 in Sri Lanka, he went to school at Westminster and then Cambridge,
where he was friends and classmates with Nehru - later prime minister of
India. He was a clever little bugger who got into the Indian Civil Service (no mean feat, a sample question on the entrance exam read: "State the arguments for and against Utility, considered as (1) the actual, and (2) the proper, basis of morals.") and learnt to speak 5 languages.
Anyway, during WWI he and some other gung-ho chaps went over to what is
now Saudi Arabia with the aim of a) helping the Arabs rebel against the Ottoman Empire (which was allied with Germany with which Britain was
fighting), and b) protect the oil-fields at Basra in modern day Iraq so the Royal Navy could continue getting oil.
That was all well and good, but if you wanted an Arab revolt, you had to have a "King of the Arabs" - Britain wanted a guy called Sheriff Hussein, who was leader of the Hashemites, an Arab dynasty. Lawrence of
Arabia and an archaeologist and explorer, Gertrude Bell (who taught Saint the finer points of espionage), had been building up the Hashemites for years, primarily as a group who could rule Iraq - but Saint was friendly with Hussein's bitter rival, Ibn Saud, and thought he was the man for the job.
That all ended up going nowhere in the end, because at the end of WWI Britain reneged on her promise to hand the Middle East over to a King of the Arabs, and instead parcelled the remains of the Ottoman Empire up between herself and France, with nominal free governments, but really run as British and French colonies.
Saint did well out of this - being appointed Internal Security Minister of the newly formed Iraq (or British Mandate of Iraq - their new name for a colony). He whipped the Iraqis up a constitution and other democratic accoutrements, but was pretty embarrassed that Britain had gone back on its word. He then moved over and ran the secret service for the British Mandate of Palestine, but he was still keen for a "King of the Arabs," and thought his mate Ibn Saud was still a contender. Eventually the British, who still supported the Hashemites, got sick of him and chucked him out of the Foreign Office, but old Saint still had lots of friends in high places, and so could advise Ibn on exactly how far he could go in conquering Hashemite territory before the British Empire would get pissed off enough to intervene. In this way Ibn created Saudi Arabia, and Saint handled the coronation.
Saint was sitting pretty now, he was best mates with the king of Saudi Arabia, the king's advisor on all matters British, and could spend time pootling about Saudi Arabia mapping things, exploring, and bird-watching (he liked to name the birds he discovered after women he admired). To get into the swing of things he converted to Islam in 1930.
Oil was growing in popularity, and in 1933 Saint helped negotiate an exclusive contract between Saudi Arabia and America's Standard Oil to drill for oil along the Persian Gulf. Britain won't listen to your opinions and continue backing those fucking Hashemites and bloody Lawrence of Arabia? Well, let's see how they like missing out on massive oil reserves in favour of their successors to the rule of the world, America. He continued in this vein for the next few years, undermining Britain's interests in Aden, and then facilitating a merger of Standard Oil, Texaco and the Saudi Government to form ARAMCO, today the world's largest oil company with revenues of more than US$200 billion/year.
This anti-British stuff all got a bit out of hand when before the start of WWII Saint had meetings with the Nazi Adolf Eichmann and put forward a plan for neutral Saudi Arabia to sell oil to pretending-to-be-neutral Spain who could then sell it to definitely-not-neutral Germany. While supporting the Nazis on one hand, he also came up with the "Philby Plan," which included unlimited Jewish migration into Palestine, as long as the Jews supported Ibn's son, Faisal, as the heir to the throne of Saudi Arabia. In return Saudi Arabia would also chip in to resettle the Palestinians.
Strangely, Saint then returned to Britain, which he must have found bloody freezing, and ran for election to the House of Commons on a peace platform. He lost that, went to India, and was arrested as a Nazi Sympathiser. His mate (and most influential economist of the 20th century) John Maynard Keynes spoke up for him though, and he was released.
Back in Saudi Arabia things started to go downhill. When Ibn heard about the "Philby Plan" he was less than impressed, as Saint hadn't consulted him on all the details, and began to suspect Saint was perhaps more
interested in Britain's, or possibly the Jews' interests, rather than Saudi Arabia's. They started having massive arguments, largely provoked by Saint, who thought that all that oil money had turned his old mate Ibn into a wanker. To keep himself happy Saint went and got himself a second wife, a 16 year old slave he bought at a market near Mecca.
Ibn Saud died in 1953 and Saint's choice for successor, Faisal, was pipped by his brother, Saud, who Saint had openly criticised. Saint was exiled to Lebanon where he lived with his son Kim, whom he introduced to
many of his contacts in Arab politics. Eventually he was reconciled with the Saudi royal family, but in 1960, while he was back in Beirut visiting Kim, he died in bed, with Kim at his side. His last words were "God, I'm bored."
Saint was the your archetypal man of the British Empire. He was born in
1885 in Sri Lanka, he went to school at Westminster and then Cambridge,
where he was friends and classmates with Nehru - later prime minister of
India. He was a clever little bugger who got into the Indian Civil Service (no mean feat, a sample question on the entrance exam read: "State the arguments for and against Utility, considered as (1) the actual, and (2) the proper, basis of morals.") and learnt to speak 5 languages.
Anyway, during WWI he and some other gung-ho chaps went over to what is
now Saudi Arabia with the aim of a) helping the Arabs rebel against the Ottoman Empire (which was allied with Germany with which Britain was
fighting), and b) protect the oil-fields at Basra in modern day Iraq so the Royal Navy could continue getting oil.
That was all well and good, but if you wanted an Arab revolt, you had to have a "King of the Arabs" - Britain wanted a guy called Sheriff Hussein, who was leader of the Hashemites, an Arab dynasty. Lawrence of
Arabia and an archaeologist and explorer, Gertrude Bell (who taught Saint the finer points of espionage), had been building up the Hashemites for years, primarily as a group who could rule Iraq - but Saint was friendly with Hussein's bitter rival, Ibn Saud, and thought he was the man for the job.
That all ended up going nowhere in the end, because at the end of WWI Britain reneged on her promise to hand the Middle East over to a King of the Arabs, and instead parcelled the remains of the Ottoman Empire up between herself and France, with nominal free governments, but really run as British and French colonies.
Saint did well out of this - being appointed Internal Security Minister of the newly formed Iraq (or British Mandate of Iraq - their new name for a colony). He whipped the Iraqis up a constitution and other democratic accoutrements, but was pretty embarrassed that Britain had gone back on its word. He then moved over and ran the secret service for the British Mandate of Palestine, but he was still keen for a "King of the Arabs," and thought his mate Ibn Saud was still a contender. Eventually the British, who still supported the Hashemites, got sick of him and chucked him out of the Foreign Office, but old Saint still had lots of friends in high places, and so could advise Ibn on exactly how far he could go in conquering Hashemite territory before the British Empire would get pissed off enough to intervene. In this way Ibn created Saudi Arabia, and Saint handled the coronation.
Saint was sitting pretty now, he was best mates with the king of Saudi Arabia, the king's advisor on all matters British, and could spend time pootling about Saudi Arabia mapping things, exploring, and bird-watching (he liked to name the birds he discovered after women he admired). To get into the swing of things he converted to Islam in 1930.
Oil was growing in popularity, and in 1933 Saint helped negotiate an exclusive contract between Saudi Arabia and America's Standard Oil to drill for oil along the Persian Gulf. Britain won't listen to your opinions and continue backing those fucking Hashemites and bloody Lawrence of Arabia? Well, let's see how they like missing out on massive oil reserves in favour of their successors to the rule of the world, America. He continued in this vein for the next few years, undermining Britain's interests in Aden, and then facilitating a merger of Standard Oil, Texaco and the Saudi Government to form ARAMCO, today the world's largest oil company with revenues of more than US$200 billion/year.
This anti-British stuff all got a bit out of hand when before the start of WWII Saint had meetings with the Nazi Adolf Eichmann and put forward a plan for neutral Saudi Arabia to sell oil to pretending-to-be-neutral Spain who could then sell it to definitely-not-neutral Germany. While supporting the Nazis on one hand, he also came up with the "Philby Plan," which included unlimited Jewish migration into Palestine, as long as the Jews supported Ibn's son, Faisal, as the heir to the throne of Saudi Arabia. In return Saudi Arabia would also chip in to resettle the Palestinians.
Strangely, Saint then returned to Britain, which he must have found bloody freezing, and ran for election to the House of Commons on a peace platform. He lost that, went to India, and was arrested as a Nazi Sympathiser. His mate (and most influential economist of the 20th century) John Maynard Keynes spoke up for him though, and he was released.
Back in Saudi Arabia things started to go downhill. When Ibn heard about the "Philby Plan" he was less than impressed, as Saint hadn't consulted him on all the details, and began to suspect Saint was perhaps more
interested in Britain's, or possibly the Jews' interests, rather than Saudi Arabia's. They started having massive arguments, largely provoked by Saint, who thought that all that oil money had turned his old mate Ibn into a wanker. To keep himself happy Saint went and got himself a second wife, a 16 year old slave he bought at a market near Mecca.
Ibn Saud died in 1953 and Saint's choice for successor, Faisal, was pipped by his brother, Saud, who Saint had openly criticised. Saint was exiled to Lebanon where he lived with his son Kim, whom he introduced to
many of his contacts in Arab politics. Eventually he was reconciled with the Saudi royal family, but in 1960, while he was back in Beirut visiting Kim, he died in bed, with Kim at his side. His last words were "God, I'm bored."
8 July 2010
The L&N Don't Stop Here Anymore
Carryl and I are heading to Dunkeld for a quiet weekend away soon. Playing around on Google Earth I noticed there was a rail line passing nearby. I started investigating and soon found that Victoria formerly had an amazing amount of rail lines to all corners of the state. This is the network in 1947:
These lines were used less and less as Victorian agriculture became more centralised; freight was moved more by truck; and people tended to drive rather than catch public transport. With the downturn in profitability, and the rise of a more right wing take on political economics, corporatisation, and then privatisation, has led to this:
It's more profitable, and patronage has increased, but I can't catch a train to Dunkeld any more.
6 July 2010
Trimming de fat from de DoD
Earlier this year the former Chief of the Australian Army, Lieutenant
General Peter Leahy, suggested that the Department of Defence's annual
budget of $27 billion should be cut and the money directed to diplomacy
and foreign aid. This amazingly sensible proposal takes into account the
fact that the current role of our defence force is not to prepare for
some sort of invasion from China or Indonesia, but to stabilise
countries such as Afghanistan and Iraq, where militant factions and
political instability currently serves as both an indictment of the
West's wars in these regions, and a base for terrorism. When it comes to
stabilising a country, erecting a fortified structure in an area like
Tarin Kowt, running daily patrols, finding the odd 'Improvised Explosive
Device' and shooting a few goat-herds turned Taliban guerrillas will
probably cost more, and achieve less, than putting diplomatic pressure
on Afghanistan to adhere to transparent political practices while giving
them concrete aid to do so.
Leahy's proposal was picked up and run with by exactly no-one, despite
the fact that in the preceding months a number of negative reports about
DoD spending had hit the news. These included:
- The National Auditor, following up on a 2006 audit, found that the
Defence Materiel Organisation (the bit of the DoD that buys the bullets)
had failed to tighten its procurement process, despite promises in 2006
that it would. The audit also found $1.2 billion worth of munitions were
not ready for battle, being either broken, in need of maintenance, or
past their use-by-dates.
- The fact that the DoD has replaced its fleet of Leopard-class tanks
(which had never seen battle, Australia never having been invaded by
land) with a fleet of 59 second-hand Abrams-class tanks at a cost of
$550 million, despite the fact that these tanks were prone to engine fires.
- The revelation that, in line with the DoD having to publish all
private sector contracts worth more than $10,000 to the internet:
a) $37,000 had been spent on horse transport. The private
contractor named had no record of said contract.
b) $30,000 had been spent on "stuff" from a marketing and
promotions company.
c) $33,000 had been spent on hiring a Lear jet. The private
contractor named had no record of said contract.
d) $250,000 had been spent for one night at the Hyatt Regency Hotel
in Adelaide. The Hyatt had no record of this contract.
Such waste and lack of concern for public accountability is more
important than the non-issue of Asylum-Seekers which is currently the
focus of public debate. The DoD obviously has money to burn. The
Australian people need to take back $7 billion or so and direct it in a
smarter and more productive direction.
General Peter Leahy, suggested that the Department of Defence's annual
budget of $27 billion should be cut and the money directed to diplomacy
and foreign aid. This amazingly sensible proposal takes into account the
fact that the current role of our defence force is not to prepare for
some sort of invasion from China or Indonesia, but to stabilise
countries such as Afghanistan and Iraq, where militant factions and
political instability currently serves as both an indictment of the
West's wars in these regions, and a base for terrorism. When it comes to
stabilising a country, erecting a fortified structure in an area like
Tarin Kowt, running daily patrols, finding the odd 'Improvised Explosive
Device' and shooting a few goat-herds turned Taliban guerrillas will
probably cost more, and achieve less, than putting diplomatic pressure
on Afghanistan to adhere to transparent political practices while giving
them concrete aid to do so.
Leahy's proposal was picked up and run with by exactly no-one, despite
the fact that in the preceding months a number of negative reports about
DoD spending had hit the news. These included:
- The National Auditor, following up on a 2006 audit, found that the
Defence Materiel Organisation (the bit of the DoD that buys the bullets)
had failed to tighten its procurement process, despite promises in 2006
that it would. The audit also found $1.2 billion worth of munitions were
not ready for battle, being either broken, in need of maintenance, or
past their use-by-dates.
- The fact that the DoD has replaced its fleet of Leopard-class tanks
(which had never seen battle, Australia never having been invaded by
land) with a fleet of 59 second-hand Abrams-class tanks at a cost of
$550 million, despite the fact that these tanks were prone to engine fires.
- The revelation that, in line with the DoD having to publish all
private sector contracts worth more than $10,000 to the internet:
a) $37,000 had been spent on horse transport. The private
contractor named had no record of said contract.
b) $30,000 had been spent on "stuff" from a marketing and
promotions company.
c) $33,000 had been spent on hiring a Lear jet. The private
contractor named had no record of said contract.
d) $250,000 had been spent for one night at the Hyatt Regency Hotel
in Adelaide. The Hyatt had no record of this contract.
Such waste and lack of concern for public accountability is more
important than the non-issue of Asylum-Seekers which is currently the
focus of public debate. The DoD obviously has money to burn. The
Australian people need to take back $7 billion or so and direct it in a
smarter and more productive direction.
1 July 2010
Fluorescent Girl Dream
I usually walk. Today I had driven; parked in a steep, grassy vacant block that I knew from my walk.
Afterwards, making my way to where I had parked, one of my students, Quoc, ran up to me and asked if he could get a lift. He had run hard to catch me, and when I asked him where he was going I saw a look of alarm cross his face between the ragged breaths he was taking.
“You usually go through town don’t you, sir?”
“Always.”
“Well, into town then. Just drop me somewhere convenient.”
I told him that was fine and we picked our way down the slippery hillside to where I had parked. Nearing the car I saw him glance back up the hill; once again a look of alarm crossed his face. Following his gaze I saw a teenager with a bright purple bob coming towards us quite quickly.
“We should get in the car, sir.”
Something in his tone made me do as he said, almost thoughtlessly. As soon as I let him in he locked his door and, finding the car had no central locking, nearly shouted at me, “Lock your door!”
As I pushed the lock down I saw a flash of bright purple in the side mirror and suddenly the teenager had her faced pressed against my driver’s window. She was pale and quite pretty, but in an abstract way, like a china plate can be pretty. Her eyes were completely abnormal, flat and dull, and her head moved back and forth as if she were a snake about to strike. She tried to open the door, found it locked, and tried again, yanking the handle back and forth with such force that the car rocked.
I knew I had to drive. To start the car, put it in gear, and get away from this strange, fluorescent haired girl-thing as soon as possible, but then she put her face to the glass and said a nonsense word. It was cold but the word made no mist on the glass.
“Shibbeth.”
With the word, I knew that I had to unlock the door and let her into the car. I reached for the lock but Quoc grabbed my hands and held them firmly in his own. Outside the car I saw that Quoc’s brothers and, even more bizarrely, his father, were arranged on his side of my car – outside, but seemingly unafraid of the girl-thing. His brother Truoc, fat and almost painfully shy, was licking the bonnet.
“Say ‘Bethish,’ sir. Say it quickly.”
CUT TO:
A kitchen. Quoc’s brothers and his father are at the table sitting on mismatched chairs. On the table are two houseplants. The one on the left is brown and withered, the water it is sitting in is black like oil. The brothers and the father are staring intently at the plants. Truoc is licking half an onion.
CUT TO:
“Say it, sir. Say it. Bethish. Say it. Bethish.”
It seems unimportant, not nearly as important as opening the car door, but to please him I say the word. He was always a good student.
“Bethish.”
CUT TO:
The black water that one of the house plants is sitting suddenly turns clear. Immediately the plant begins to look healthier, green flushing its leaves.
WAKE.
Afterwards, making my way to where I had parked, one of my students, Quoc, ran up to me and asked if he could get a lift. He had run hard to catch me, and when I asked him where he was going I saw a look of alarm cross his face between the ragged breaths he was taking.
“You usually go through town don’t you, sir?”
“Always.”
“Well, into town then. Just drop me somewhere convenient.”
I told him that was fine and we picked our way down the slippery hillside to where I had parked. Nearing the car I saw him glance back up the hill; once again a look of alarm crossed his face. Following his gaze I saw a teenager with a bright purple bob coming towards us quite quickly.
“We should get in the car, sir.”
Something in his tone made me do as he said, almost thoughtlessly. As soon as I let him in he locked his door and, finding the car had no central locking, nearly shouted at me, “Lock your door!”
As I pushed the lock down I saw a flash of bright purple in the side mirror and suddenly the teenager had her faced pressed against my driver’s window. She was pale and quite pretty, but in an abstract way, like a china plate can be pretty. Her eyes were completely abnormal, flat and dull, and her head moved back and forth as if she were a snake about to strike. She tried to open the door, found it locked, and tried again, yanking the handle back and forth with such force that the car rocked.
I knew I had to drive. To start the car, put it in gear, and get away from this strange, fluorescent haired girl-thing as soon as possible, but then she put her face to the glass and said a nonsense word. It was cold but the word made no mist on the glass.
“Shibbeth.”
With the word, I knew that I had to unlock the door and let her into the car. I reached for the lock but Quoc grabbed my hands and held them firmly in his own. Outside the car I saw that Quoc’s brothers and, even more bizarrely, his father, were arranged on his side of my car – outside, but seemingly unafraid of the girl-thing. His brother Truoc, fat and almost painfully shy, was licking the bonnet.
“Say ‘Bethish,’ sir. Say it quickly.”
CUT TO:
A kitchen. Quoc’s brothers and his father are at the table sitting on mismatched chairs. On the table are two houseplants. The one on the left is brown and withered, the water it is sitting in is black like oil. The brothers and the father are staring intently at the plants. Truoc is licking half an onion.
CUT TO:
“Say it, sir. Say it. Bethish. Say it. Bethish.”
It seems unimportant, not nearly as important as opening the car door, but to please him I say the word. He was always a good student.
“Bethish.”
CUT TO:
The black water that one of the house plants is sitting suddenly turns clear. Immediately the plant begins to look healthier, green flushing its leaves.
WAKE.
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