Everything is Obvious

I caught a bit of an interview with Duncan Watts on the radio last night. He is a sociological mathematician and the author of the fabulously titled Everything is Obvious Once You Know the Answer.

Since he works as a Yahoo researcher now he knows everything there is to know about social networking. His thesis that our recent riots were mathematically and sociologically predictable was fascinating.

Football and Luck

Those of you who don't like soccer or numbers can look away now. This really don't concern you.

Last season I played the Premiership fixture list using a coin toss. I used a simple system. Heads was a goal; tails wasn't. I tossed a coin for each team until I got tails, then I stopped. Form and home advantage were ignored. So a fixture would have a result:

Villa: heads, heads, heads, tails = 3
Birmingham: tails = 0

Or:

Arsenal: heads, heads, tails = 2
Chelsea: heads, tails = 1

I know it's sad and you think I have too much time on my hands but I get time off and am alone a lot.

What I wanted to find out was the range of points totals produced simply by luck.

The outcome? Well I'm glad you're still with me and interested. It's fascinating isn't it? To win my league required 67 points. The four champions league places were achieved with 67, 65, 61 and 61. The three relegated teams got 31, 37 and 41.

In effect this gives us the monkey mark.

So now we look at the real league table for 2010/11. We discover that the top four, Man Utd, Chelsea, Man City and Arsenal all achieved more than 67 points. They were above average and outperformed the toss of a coin. We probably knew that. Our top four teams were a cut above all the rest.

The three relegated teams all got more than 31 but less than the safety mark of 42 in the, excuse me, tossers league. They were below average and would probably have done better if they had resolved their games on a coin toss.

Everyone else was very average and luck probably played a part in the order teams 5 -17 finished.

In case you are interested Wigan won my league and Man Utd, West Ham and Wolves were relegated. I tired hard not to put any bias into my tossing apart from exercising a deep hatred of Wolves. West Brom finished second. Needing to win their last game to clinch the league they lost 1-0 at home to Man City.

There were far more draws, especially 0-0 draws in my system. It follows, since tails-tails will happen, on average, every fourth time.

Mental Arithmetic

Yesterday we were trying to calculate the salary to offer to someone who was going to work 25 hours or 62.5%.

Person Y
I've got a calculator on my phone.

St's head
That's five eighths.

Person Y
Now where did I put it? I turned it off for the interview. What was the number again?

St's head
Divide by 8, divide by 2, move decimal point.

Person X
It's going to be about £guess.

St
(After scribbling on the back of an envelope) The answer is... ( a precise number a little less than the guess)

Person X
How did you do that? Did you divide by 100 and multiply by 65 that quickly?

Person Z
62.5.

St
It's five eighths.

Person X
Oh, I was doing 65.

Person Y
The answer is... ( a precise number a little less than the guess, same as the previous one)

Does anyone know how to do mental arithmetic anymore? I wonder if some of the brain power that was once utilised doing number work is now side-tracked to dealing with the question, 'Which of my portable devices has a calculator app and where did I put it?'

I realise I am sounding a bit old. I'll be complaining that young people mumble next.

6 Music

Much has been written about BBC Six Music recently. I am like many others; from time to time I dropped in but simply not often enough to register on the audience figures. Like Woolworths - glad it was there but rarely visited. Not good enough.

Phill Jupitus kept me company on the breakfast show over a number of months.

One morning we had a text vote for whether or not to play Curtain Call by the damned in its full 18 minutes of overwrought gothic glory. Hundreds voted yes. Of course, by minute 10, most had changed their mind. That is the beauty of 6 Music. If you don't like what's on now, there's always something good on in a minute.

I love Phill, the populist polymath, but believe he should stick to comedy, poetry, panel games and DJing. Leave well alone the world of maths, there's a love.

Marcus du Soutoy

I enjoyed Marcus last night. Few mathematics professors in my experience wear lime green trousers, pink velour trackie tops and yellow T-shirts with buzz cut, possibly bleached, hair. Weird but cool. Good communicator.

He gave a brilliant, one hour, illustrated lecture which should leave the few children who were there fascinated by numbers for the rest of their lives. Advice on choosing lottery numbers so you don't share the winnings, why footballs spin rapidly as they slow, number series, primes and movie clips.

'Is mathematics creativity or discovery,' someone asked. Good question, said Marcus.

Key message for me, 'Are you sure you're asking the right questions?' When maths gets complicated, mathematicians try to make sure they are asking the right questions. It enabled them to predict how the rarity of prime numbers expands (they get rarer the larger the number). You can say how many there will be without yet knowing a formula for finding the next one. I might not have put that right, not being a mathematician. There are prizes for finding big prime numbers. That's how hard it is, but you can programme your computer to do it during its down time.

I will try to go to more of this festival next year. The ticket cost £6.

Maths Solution

Problem expressed the other day. Use 5, 5, 5 and 1 to get 24.

If you multiply 5 by 5 and subtract 1 to the power 5 you get 24. I can't get this blog to do superscript so I apologise for the clunky expression of the solution.

I Forget

Regular readers will know I am interested in brains, probably never having had a fully functioning one I self-insult before you lot have a go. Pah!

The onset of middle-aged forgetfulness happened quite early. I have always found myself easily distracted from the task in hand and so walking into a room and doing something other than that for which I walked in and then returning only to have to repeat the journey for that which I intended is a regular part of my week. I solve a lot of problems but rarely the one which I intended.

Yesterday was worse because R left a maths problem on my answerphone and it took most of the day and I didn't crack it until I was in the shower this morning.

Can you get the total 24 using all the digits 5, 5, 5 and 1 and all or some of the usual symbols plus, minus, times and divide. If you don't understand the question yet don't bother trying to solve it. It's elegant.

So why did I start this? See what a problem I have. Oh yes. Putting things back. How do you trick your mind to remember to return things? I never remember to readjust my wife's car seat when I have borrowed her vehicle, or the mirrors. Today I discovered that she, using the ensuite shower whereas she normally uses one a bit further away to save disturbing me, had pulled down the head and increased the temperature. Maybe it was the bruise and the scalding that helped solve the maths problem.

Too much information. Laters.

Alternative Advent Calendar

Smaller Than Life is one of my favourite drop-in blogs. Here you will find an advent calendar depicting Christmas songs as mathematical formulae and venn diagrams. Cracking.

Money, technology and death

Here's a conundrum. Probably not one we anticipated. Simply stated it's this; we are getting too good at saving people's lives. I'll qualify that. Lives are valuable and we ought to save them if possible.

A huge amount of money is invested in developing new drugs to cure a large range of illnesses and ailments which have been fatal to previous generations. Once tested, the first formats of such remedies are normally pretty expensive.

Equal, if not greater, sums of money are spent on defence, such that protective equipment is in existence which, for instance, substantially reduces the likelihood of bullets killing soldiers.

What happens? People die who are not administered the drugs. People die if they haven't got the bullet-proof gear. Inquests then suggest that the death was 'preventable' and grieving relatives are seen haranguing ministers to make sure 'this never happens again.' Of course as the devices/drugs get cheaper the likelihood of it happening again reduces, although, of course, new technologies come along to save some and not others and anger a new set of grievers.

Should we ever go to war with any less than the latest technology? Because old helicopters crash more than new ones should we only use new ones? Who would pay?

We are very afraid of mentioning money in a public discussion of this. If a cure for cancer was found tomorrow but its use would require 1p in the pound on income tax and you had a vote would you accept it? What about 5p? 20p?

The value of a life? We live in an age where we have to do such maths but not in an age where we are free to talk about it without an outcry.

Coping using maths

I was doing OK. All was well. Then I tipped. I think it was the 27th, or maybe 270th, person who asked me how I was going to cope during the forthcoming vacancy - my colleague here at Holy Trinity and Trendlewood is leaving in a couple of weeks - and I wondered if psychologically, mentally and emotionally everyone seems to expect the place to crash and burn. It gave me a bit of an adrenalin rush. Last time I had one of those a doctor told me to sort my life out. I did.

So this time I'll be fine. The parish might fall apart (unlikely, but parishes can do this at any time not just during vacancies) but I won't. Trust me. I won't.

This is because, and here's a cunning technique, instead of me working three times as hard (Ken did twice as much as me most days) I'm going to work 1% harder and so are all of us. Volunteers, staff, hangers-on and those not yet aware they are about to belong - all of us will have 1% more to do. For every hour you gave previously give an hour and (get this) 36 seconds.

Another way of thinking about it (allowing for the fact that 36 seconds isn't that useful alone). There are roughly 300 or so of us here. We can find 60 hours a week by all offering 12 minutes extra. Or an hour a month. Or six hours twice during the next year. I'll give my 12 minutes by shouting at people and asking them to do things. I'll do it nicely. OK?

We can manage this. Repeat after me. We can manage this. I can't but we can. None of us is as useful as all of us.

Normal Men?

Genuine conversation held in the cafe at Redwood Leisure Centre today:

What are you thinking about?

Prime numbers?

Why can't you be like normal men?

Why, what do normal men think about?

Things like tits.

Am I missing some tits?

No, but you're not normal.

Will you tell me when there are tits worth looking at if I tell you about the interesting mathematics in the world?

No.

Who Do You Think You Are?

I enjoyed Matthew Pinsent's appearance on this programme very much. Whilst there was the usual interest in relatively recent relatives - great uncles who died in the Great War - Pinsent unearthed a so-called 'golden relative', a knight of the realm who would therefore figure in Burkes' Peerage and whose ancestry would be traceable a long way further back. Indeed Pinsent was able to trace his family tree back through Edward I to Biblical King David and stopping only at God so detailed were the records. I kid you not.

Thing is, whilst this made great tele, there were thirty two generations between today and King Edward I. Coincidentally, if you double the number one, 32 times you get the population of the earth. To put this simply, go back 32 generations and we could all have a common ancestor. Now in my case the records probably don't exist but if I were to follow the right line back, eventually I'd reach a monarch too. Bound to.

Great tele; rubbish maths.

Times Maths

'Did you know', said Peter, 'that 74,000 deer die on the roads of this country every year.'

'That sounds a bit high,' said Mark and I doing some quick maths. 'That's about 200 a day.'

'Said so in the Times,' said Peter.

Peter, very graciously, brought a copy of the Times' article round the next day. The headline is indeed, '74,000 deer die on roads'. Trouble is, this number is calculated by adding the number killed outright (7,000) to the number which die later (10,000).

Maths. It's so hard.

Still too many dead deer though. Drive carefully.

Blue and Green Taxis

I was disappointed that nobody had a go at intuiting the taxi problem. I can only assume that all my readers are mathematicians who had worked it out long before me. Anyway, save embarrassment for those who didn't know the answer and didn't feel like showing themselves up in public, although the witness sounds reliable he will be right only 12 in 29 times and wrong 17 in 29 therefore his likeliness of being correct is about 41% and he should be chased out of the witness box.

Intuition

The psychologists Kahneman and Tversky give this example to demonstrate the unreliablility of intuition.

A cab was involved in a hit and run accident at night. A witness identified the guilty cab as blue. Agreed data:

• Two cab companies, the Green and the Blue, operate in the city.
• 85% of the cabs in the city are green; 15% are blue
• In a scientific test under the same conditions as existed on the night of the accident the witness was found to identify correctly each of the two colours 80% of the time.

What is the probability that the cab involved in the accident was green rather than blue and that the witness was wrong?

Those of you who are mathematic/scientific by background will already be well on the way to working out the correct answer and can probably do it quite quickly. (Your maths has honed your intuition as it were.) For those who are not, and who couldn't imagine how to begin, let me know, intuitively, if you would trust this witness and use his/her evidence to sway a conviction for say, manslaughter, or leaving the scene of an accident, both of which carry custodial sentences.