Tuesday, December 20, 2011

saucer thinking anticipation

Posted by Picasa This flying saucer is hovering just over the fence beside the pub. I have not tinkered with the photograph, but I had drunk  a couple of pints before taking it.

In his book Thinking Fast and Slow Daniel Kahneman illustrates the difference between the two modes of thinking in which we engage, with the following: "Do not, " he says, "try to solve it but listen to your intuition".
   A bat and ball costs $1.10.
   The bat costs one dollar more than the ball.
   How much does the ball cost?
"A number came to your mind," he writes. The number is of course 10: 10c. The distinctive mark of  this easy puzzle is that it is intuitive, appealing and wrong.  Do the math and you will see. If the ball costs 10c then the total cost will be $1.20 c. (10 c for the ball and $1. 10 for the bat). The correct answer is 5 c." I confess I puzzled over this longer than I should have done.
This is just a taste of an intriguing book which is far from being one of those cure-all recipes for how to live. Rather it is serious science presented in a way which we can all understand, and which explains much about our thought processes, decision-making and how we often manage  I speak for myself) to be wrong as often as I am right, if not more often.
I have often thought that I am not very intelligent, yet intelligent enough to know the limits of my intelligence. This book helps me here.

This afternoon I pass a Jack Russell on its way to The Grove. It trots eagerly ahead of its man. In its mouth is a tennis ball. I know Jack Russells' amazing capacity to catch balls in the air on the first or second bounce, and admire them for their speed and enthusiasm. This one reminds me of  how I used to feel when on my way, racket in hand, to the tennis courts, hardly able wait for the feel of the grass or tarmac beneath my feet, and the the thought of a backhand drive or low volley in the game to come.


Lucy said...

That flying saucer has me baffled.

For a very clever Jack Russell, have a look at http://clivehicksjenkins.wordpress.com/2011/10/04/jacks-trick/

The Crow said...

At first glance, I thouht the photo was of a dog looking through an opening in the fence. Consequently, for a split second, I mistook the garbage can lid for a Frisbee.

Of course, now I see that it is indeed a flying saucer, peeking above the fence top.

Lucas said...

That puzzle is quite scary really. It took me ten minutes to work it out, and I've stuck to two units tonight. Well now let me see....I think it came to two.

The Crow said...

Okay...now I'm really confused. Came back for another look (good photo puzzle, btw) and now I have no idea what this is.

Except that there is no dog...of that, I am positive.


Unknown said...

The flying saucer is in fact the top of a one one those heaters used to keep people - usually smokers - warm when they are sitting outside a pub in chilly weather.

Tom said...

Yes, the mathematical observation shows a clear need for the solution of two simultaneous equations:-

x - y = 100 (1)
x + y = 110 (2)

(1) - (2) gives y = 5 cents.
and x = $1.05

where y is the cost of the ball,
and x is the cost of the bat.

Sorry for being such a clever clogs, but I don't often get the chance, (especially with St. Lucy around).

Unknown said...

Tom Thank you. The purpose of the exercise was to demonstrate the difference between quick, intuitive thinking and slow, careful, monitoring processes of thought. However having realised that 10 cents was not the answer, I tried to work out how it came to be 5 cents. I thought that an equation was involved but had forgotten how to go about it. For this relief much thanks.

Lucas said...

Tom's equation is very helpful and adds a maths dimension which at first seemed a problem of wrestling with logic.
The flying saucer is very strange as at first I thought I was seeing it from above, but it is one of those images you can see two ways. Now I can also see it as if i was looking at it from underneath i.e. it is climbing with its bottom rim (nearest us) up, and will soon clear the fence.