Not a riddle but a warning against 'gut feeling'

[Wyndon]

Imagine you have a ball of string that just reaches around the equator. Now add 3 feet. What is the approximate clearance above the ground? Apologies for imperial measures, but use 1 metre if you feel more comfortable with that. When I work this out, I can't believe the answer - rather I can, but it's totally contrary to my 'gut feeling'. I've met many people who pride themselves on their gut feeling and use it as a reason for ignoring the facts. It's a mistake to do so.

[gazuty]

Circumference is 2 pi r

So c = 2 p r

C+ 1 = 2 p r

R =(c+1)/2p

Given the circumference of the earth is massive. Adding 1m to something like 40,000,000 m ain't going to move dial on r.

This fits with my intuition? Was not expecting a different result.

If on the other hand the question had been how much extra rope do you need to move 1 m above the earth, the gut feel may play greater havoc.

[LinusP]

15cm?

I was expecting a much smaller number tbh.

[LinusP]

And 6.3m longer on the rope to get 1m above the ground...

[Wyndon]

Correct Linusp. gazuty, you have the correct answer, but haven't taken on board the implications. (c+1)/2pi = c/2pi + 1/2pi = radius of the earth + 1/pi. If you add 1 yard, the extra height above ground level would be roughly 6 inches (using a rough approximation of pi as 3). The increase in radius is independent of the size of the original circle. It could be 1 inch or a light year. This is what my mind can't grasp.

[gazuty]

Understood.

Can't believe I write out the formula and still get the implications wrong. Just proves your point.

If I have a circle with a circumference of one metre and you add another metre to make the circumference two meters the distance between the two circles (outwards from the radius) is a constant 1/2pi. Crudely 16 cm.

And no matter how big the starting circle, adding one metre of circumference always increases the radius by 16 cm.

[gutuami]

if you add something to diameter of a circle you would always get that 3.14 times on its lengh

[gutuami]

but the fact that it does not matter the size of the circle seems weird indeed when you take big sizes:
__C________________Pi__________D______
40000000.00********3.14159*******12732406.20
40000003.14********3.14159*******12732407.20

4000.00 3.14159 1273.24
4003.14 3.14159 1274.24

the added 3.14 to C gets you 1 to D

[gazuty]

If you want to take away some real life implications of using pi I found this really interesting.

http://www.r-bloggers.com/betting-on-pi/

Euler has made similar posts before on points in randomness where one may feel like a genius only to go on a run of losses that wipes out ones bank.

[Wyndon]

Yes. And it works both ways. When do you give up on a strategy that may be merely going through a random bad patch? The best book I've ever read on randomness and which shows how many 'brilliant' careers are often based on the inevitable workings of chance is 'The Drunkard's Walk' by Leonard Mlodinow.

[gazuty]

And for me it is Malcolm Gladwell's - Outliers.

There are a whole lot of conditions needed for any person to be successful and flourish.

[Wyndon]

I probably shouldn't have said 'many brilliant careers' - the book looked at the chances of at least 1 baseball player having an outstandingly successful season over a number of years and a film executive who picked 5 or 6 winners in a row and the lost his/her touch. However there is a lot more in the book than just this aspect of randomness.

[gazuty]

Trying to buy Drunkards Walk on kindle. So frustrating (I changed my country to USA to get some books) but that book is not available in the USA.

Legilsation needs to be passed to stop the BS on digital rights management by jurisdiction. For goodness sake.

[Will Sharpe]

Trying to buy Drunkards Walk on kindle. So frustrating (I changed my country to USA to get some books) but that book is not available in the USA.

Legilsation needs to be passed to stop the BS on digital rights management by jurisdiction. For goodness sake.

Yeah, it's sometimes very frustrating when you can't get hold of something that is readily available in the US. And often at a much more attractive price. As if a download would cost the vendor more depending on distance

[LinusP]

If you want to take away some real life implications of using pi I found this really interesting.

http://www.r-bloggers.com/betting-on-pi/

Euler has made similar posts before on points in randomness where one may feel like a genius only to go on a run of losses that wipes out ones bank.

Very interesting, cheers for the link.

Off to make my millions 'late number gambling' the horses this afternoon...