How not to be late for work
See Chapter 1. Graham thinks he may have missed the bus, but can’t be sure. Option 1: He can stay where he is and hope both the bus and its usual passengers are late. (He calls this Bus Not Been.) He’ll be first in the queue (if one materialises) and can jump on board and grab the best seat available. But if the situation is actually Bus Been he could be standing here at the stop for ten minutes and will definitely be late for work. However (Option 2) he can set off up the road and past the trees at the end and stride on another couple of hundred yards to the traffic lights near the shops. This allows him a choice of an additional bus (the number 19 which converges at that point with his usual 13). The two buses alternate in their arrivals. So if he has indeed missed the bus (Bus Been) then he will almost certainly catch a 19 before the next 13 appears. And if it’s Option 2/Bus Not Been then he may in fact catch the tardy 13 at the shops. The choice seems clear. Ish… As this table should show.
Graham’s analytical brain tells him that Option 2 (Walk) gives him more choices of bus and a decent chance that he’ll only be four or five minutes late. Whereas Option 1 (Stay) is a gamble. It’s his only chance of arriving on time – but the downside is greater too. Graham opts to give up ‘possible best’ for ‘least worst’. He decides to minimise his lateness by walking, but by doing so he gives up his only chance of arriving on time. Pathetic. Now get back to where you were in Chapter 1.
We see it, we feel it, we know what it does. So how come it doesn’t exist?
In Chapter 24 Pate’s hair is full of froth from his pint. Don’t ask why. Read the book if you’re bothered. Don’t just turn to the back hoping you’ll find the answers.
“You could do a pirouette,” says Graham. “Then the froth might spray outwards, by centrifugal force.”
“No such thing,” says Pate. “Centrifugal force doesn’t exist.”
“Wha!” explodes Graham. “Now you’re really talking bollocks. I may not be an Einstein, but even I know what centrifugal force is. And where did Chapter 24 go? What are we doing in an Appendix? If it was up to me I’d remove all Appendices.”
“That’s because you know as soon as we hit the Appendix you’re about to lose an argument. So what is Centrifugal Force when it’s at home?”
“It’s the force which when you spin an object round and round it makes it try to fly off into space.”
Pate looks quizzical. “So what exerts this force?”
“Umm. Erm. Well, like, if you sit on one of those roundabout thingies in a playground you start to slide off towards the edge. That’s centrifugal force.”
“No it isn’t.”
“For flip’s sake Pate! You’re arguing that black is white. It is beyond all reasonable doubt. Something’s pushing you outwards. You can test it. It works every time. Whiz whiz whiz, round round round, whee - fly off sideways, land on your arse on the ground. You cannot tell me that’s not true.”
“It’s not centrifugal force.”
“Well it’s not elves and fairies pulling on invisible silken threads. So what the hell else could it be?”
“It’s not centrifugal force.”
“You can’t win this one Pate. You fly in the face of reason. You slap the cheeks of sanity with your ethnic knitted mitts.”
“Right, think it through. You’re going round on a roundabout, OK? Like the gyrating funster you are.”
“Correct. I’m having fun going round in circles. Like your pathetic argument.”
“And suddenly a new force says ‘Hey, there’s someone going round in circles. I think I’ll head outwards from the centre and push him off.”
“Gonads, Mr Paint.”
“You can feel it! It pushes you outwards!!”
“If it’s any consolation, many generations of rotating numbskulls thought just the same as you. They were convinced there was a force. So they called it centrifugal force. From the Latin. To flee the centre.”
“That doesn’t mean they were right. They also thought fire was a substance called phlogiston.”
“But I can wave a bucket of water round my head until it’s horizontal and the water will stay in.”
“You can set your underpants on fire and cycle up and down waving them around on the end of a golf club singing Land of Hope and Glory. You, not the golf club. It still doesn’t make centrifugal force real.”
Graham is irritated beyond even the generous measures which Pate has inspired in the past. “So what the bloody hell pushes you off the roundabout?”
“It’s very simple,” says Pate. “Newton’s Second Law. An object set in motion will continue in a straight line until a force is exerted upon it.”
“Not aha! at all. At every moment of your rotation your body is trying to fly off in a straight line. That’s not centrifugal force. That’s just you cruising along and trying to keep going. Like sparks off a catherine wheel. It’s friction between the roundabout on the seat of your pants which keeps pulling you off course and constraining your motion to a circle. So the force you feel pulling you outwards is just the combination of all the straight lines your body really wants to take. But think of where those sparks go…”
“They fly outwards,” says Graham, but more hesitantly.
“Not in a straight line from the centre of the wheel.”
“No. They fly off at a tangent.”
“Correct. Like your thoughts. The sparks fly off in a straight line from the edge of the spinning wheel - in exactly the direction they were going when they were released. Not like some imaginary centrifugal force which you seem to believe is pushing you out in a straight line from the centre. You’ve seen it with your own eyes.”
“I’ve seen Spiderman swinging from skyscrapers. Doesn’t mean I have to believe it.”
“Suit yourself, guano brains.”
There’s a long and not particularly companionable pause. Needless to say Graham interrupts it. “See the water in the bucket flying round your head on a string? Is it suffering from an illusion? Does it just think centrifugal force is keeping it in the bucket?”
“You think about it, denier of reason.”
Pate actually says this like Graham’s denying something. He hasn’t invented a new, more logical measure of thickness for tights and stockings.
Now accept defeat, and get back to Chapter 24!
How to visit all the towns by the shortest route
See Chapter 38. This is the Travelling Salesman problem. Take for instance:
ABCDEFGA is 148 miles. ABDCEFGA is 138 miles. ABCEDFGA is a massive 180 miles. There are ten roads, but each solution only uses seven of them. Seems trivially simple, but the mathematics of finding a formula for optimal solutions defeated even massive computers, and even bigger mathematicians, for a long time. Instead, you had to use heuristics, which basically means guessing, then trying loads more guesses (iterations) until you think you’re getting warm.
You could also try to use the quickest route rather than the shortest one, or the one which uses least fuel. All equally tricky. There’s still no simple formula for the best answer, although mathematicians now have a process which can get them there. But the delivery guy isn’t a mathematician, which is why he always has an excuse.
Back to where you were in Chapter 38