“The winner gets $X + ($1,000,000/submission)”

I imagine the submission median would rise without bound (after first having slowly approached, then departed from 1,000,000/X). I think Rayo would have walked away with the $20. :)

Also, for smaller groups of, lets say N acquaintances, I wonder how the group’s “submission median” would respond to the following tweak in the rules:

“The winner gets $1,000,000/submission, but each loser must provide 1/Nth of the prize money to the winner”

Just food for thought.

]]>Sure, we expected (and hoped for) a few cynics to wreck things— but plenty of people tried for a real prize!

I think the outcome would be about the same when played with any large group. Smaller groups, especially small groups of acquaintances, have a very different dynamic.

]]>

Euro Millions Lottery SPE.,

2011 Zaventem , Belgium .

Euro Millions are Affiliate of Belgium National Lottery (BNL).

Sir/Madam,

CONGRATULATIONS: YOU WON â‚¬1,000,000.00

We are pleased to inform you of the result of Euro Millions Lottery SPE, which was held on the 9th June. 2007. You were entered unaware as an independent email participant with: Ticket Number: 657-954-2509 with Serial Number-1413-09. Your email address attached to Lucky Draw number: 4-11-17-23-30 with Bonus number 25 which consequently won the Euro Millions Lottery SPE lottery in the 3rd category. This lucky draw came first in the 1st Category of the Sweepstake. You will receive the sum of â‚¬1,000,000.00 (One Million Euros) only from our authorized bank.

* Because of some mix-up with sweepstake prizes, including the time limited placed on the payment of your prize:, *

etc etc etc

Just as lucrative as our give-away, I’m sure.

]]>In the discussion of Graham’s Number we talk about Knuth’s “arrow notation”. In this notation, A(n) is written n^^n, and one Nikiplex is 100^^100. A Nakiplex is (100^^100)^^(100^100)

This is way smaller than 100^^100^^100^^100 (the order of operations is read right to left) which is just 100^^^4 in the arrow notation. That arrow notation is hard to beat!!

But then ** Graham’s number** trounces that hugely, by iterating arrows, much like you were iterating exponentiation, over and over again.

The REALLY STAGGERING THING though, was Rayo’s number, which is so frighteningly immense as to defy description. In fact, that is its definition. It is the smallest number bigger than any number that can be described in fewer than a googol’s worth of symbols, in any mathematical manner. To put that in perspective, a Nakiplex took fewer about 20 symbols in the Knuth notation; Graham’s number can be described in fewer than 100. If we list out EVERYTHING that can be mathematically described in fewer than a googol’s symbols, and then top that, we get Rayo’s number.

(Of course I just described Rayo’s number in about a paragraph, but the notion of “mathematically describing” has a very precise meaning.)

YOW!

]]>A(1)=1, A(2)=2^2, A(3)=3^3^3, A(4)=4^4^4^4, A(5)=5^5^5^5^5, A(6)=6^6^6^6^6^6, A(7)=7^7^7^7^7^7^7, etc. My first number, which I call a “Nikiplex” (inspired by the name of my girlfriend) = A(100). My second number, the one I was going to submit, which I called a “Nakiplex” = A(1 Nikiplex). This is substantially larger than “the number of possible states of the universe” ^ “the number of possible states of the universe.” Perhaps one day there’ll be another large number contest and I will become the winner of the smallest monitary prize ever. Until then, great job to these participants! ]]>

WOW. There is software that can recognize faces and some other objects.Imagine if they could build a quantum computer that is capable of firstly generating these images and secondly analyzing them to see if they are faces.

That would be pretty cool and hard to get your head around.

Of course I don’t think even quantum computers would be able to carry out all these operations within a single lifetime. ]]>

Lessee, very very roughly (everything is only to within a few dozen orders of magnitude) The number of possible positions in the universe is, well, now wait a minute. I guess let’s be generous and say that two positions are different if they are at least 10^{-33} m apart. That’s a lot smaller than any particle, but is apparently considered the smallest meaningful scale. And let’s just suppose the universe is a box 10^{10} light years on a side, which comes to about 10^{78}m^{3} in volume. So there are, say 10^{177} different positions possible.

This is totally ridiculous, so please don’t jump all over any inaccuracies!

Now there are something like 10^{ 80 } particles in the universe, according to something I saw someplace. Somewhere else I think I might have heard there are 10^{125}; since we are just aiming for a rough sense of things:

Let’s then suppose there are 10^{200} positions and 10^{100} particles. This gives a whopping (10^100)^(10^200) possible states for the universe:

10^10^202. Let’s just call it an even 10^10^200, shall we.

This is one big number.

]]>