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Menger sponge.

Infinite surface area, yet no actual volume.

Fractal geometry is cool.

stewie wrote:Benford's Law

Take a big pile of really random numbers.

If they are truly random, the first digit in each number will NOT be randomly distributed from 1-9. In fact, about 30% of the time, the first digit will be 1.

The number 2 will be the first digit a little over 17% of the time, and the probability drops and drops until you get to 9, which is the first digit only about 4.5% of the time.

This is used by the IRS in forensic accounting and fraud detection.

Truly random data showing extremely predictable behaviour? Fucking awesome.

What is a random number? I mean, if these are truly random numbers, some of them never end, and if you limit the number of digits, it's not longer purely random.

Is this a "random" number taken from the real world? If so, it is not really random. If this random number is generated by a machine, and this is still true, then I don't get it.

Yes! Nine is a strange number, odd even. This nine, she is on the cusp, you could say.

For some reason my hungover brain is craving mathematical proofs, so...

Mandroid2.0 wrote:Add any single digit number to the number 9 and the the resulting digits in the sum added to each another are the same as the original single digit number.

X+9 = 10+(X-1)

Combining the digits: 1+X-1=X

Mandroid2.0 wrote:The same holds true with double digit numbers, though they have to be reduced to a single digit number first.

10X+Y+9 = 10X+10+(Y-1) = 10(X+1)+(Y-1)

Combining the digits: X+1+Y-1=X+Y

Mandroid2.0 wrote:If you do the same thing with multiplication, the end result will always be 9.

9X=10(X-1)+(10-X)

Combining the digits: X-1+10-X=9



To these, I shall add a trick that chartered accountants are taught early on to cope with the joys of adding up lots of numbers: if, when summing a list of numbers, you make a transposition error in one of the numbers (e.g. 39 instead of 93), the difference between the "correct answer" (the sum without the transposition error) and the "incorrect answer" (the sum with the transposition error) is divisible by 9.

E.g.

5+42+39=86 (i.)
5+42+93=140 (ii.)

(ii.)-(i.)=54
54/9=6

Proof:

a+b+c....+10X+Y (i.)
a+b+c....+10Y+X (ii.)

(i.)-(ii.)=10X+Y-10Y-X=9X-9Y

Looking back, I am baffled why this is of any use, but there you go.

I wish that I had studied more maths after university. Then I would be able to remember and describe some of the awesome facts that a friend who did told me. I remember there being one relativity proof that involved something magnificent involving a man running into a cupboard at the speed of light, but sadly I forget the detail.

Hm. I should have a nap before I spunk more time on pointless minor nerdery.

emmanuelle cunt wrote:

stewie wrote:Benford's Law

What is a random number? I mean, if these are truly random numbers, some of them never end, and if you limit the number of digits, it's not longer purely random.

Is this a "random" number taken from the real world? If so, it is not really random. If this random number is generated by a machine, and this is still true, then I don't get it.

If you are smarter than me, the wikipedia articlemight help.

It is all to do with logs, apparently.

EC, I shall be visiting your city on the weekend of 11-13 July! A cheeky drink might be in order!

allllright... logs and stuff.
log(1)=0
log(2)=0.301... (like the 3db point... kinda. all the same thing. I really prefer natural logs)
log(10)=1
log(20)=1.301
log(100)=2
log(200)=2.301
etc etc etc

so, if we have data that is largely distributed logarithmically, it should have first digit 1 about 0.301 of the time... as relative size/values are usually more important than "absolute," data will often be logarithmic... like our sense of pitch distinction, or volume level (decibels!). Or something like that.

sparky wrote:

emmanuelle cunt wrote:

stewie wrote:Benford's Law

What is a random number? I mean, if these are truly random numbers, some of them never end, and if you limit the number of digits, it's not longer purely random.

Is this a "random" number taken from the real world? If so, it is not really random. If this random number is generated by a machine, and this is still true, then I don't get it.

If you are smarter than me, the wikipedia articlemight help.

It is all to do with logs, apparently.

EC, I shall be visiting your city on the weekend of 11-13 July! A cheeky drink might be in order!

Yay! I'll be out of the city till 9-10 of July! So that's perfect!

I will check wiki page later. Work.

edit: I looked at it.

wiki wrote:Benford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is distributed in a specific, non-uniform way.

So I think it makes sense. I also think I won't be thinking so after I read the entire page. But for now, it makes sense.

This animation is cool, especially when they get into the hyperbolic geomoery.

Not Knot:

Part 1: http://www.youtube.com/watch?v=AGLPbSMxSUM

Part 2: http://www.youtube.com/watch?v=MKwAS5omW_w


More hypergeometry:

http://www.youtube.com/watch?v=lEiNsrtuGcc

http://www.youtube.com/watch?v=FXKe0SiATwQ

http://www.youtube.com/watch?v=beZANvAu7Rs

http://www.youtube.com/watch?v=s27n3QzuE4E

http://www.youtube.com/watch?v=E8rifKlq5hc

Hosoi wrote:primes

Another subtle but engaging theorem concerning primes is Bertrand's postulate, simply stated: for n > 1, there is always a prime number between n and 2n. Why should that be?

This was proved most elegantly by amphetamine poppin' badass Paul Erdős whose extraordinary life is worth a moment of your time.

I once spend a week trying to figure out Cantor's theorem, I think lightning struck me on a saturday night but I've been at a loss ever since.