Comments on: CD. Alas, Up To A Million Dollars Might Have Been Given Away. http://mathfactor.uark.edu/2007/03/cd-alas-up-to-a-million-dollars-might-have-been-given-away/ The Math Factor Podcast Site Fri, 08 Aug 2014 12:52:06 +0000 hourly 1 https://wordpress.org/?v=4.9.25 By: contactm3 http://mathfactor.uark.edu/2007/03/cd-alas-up-to-a-million-dollars-might-have-been-given-away/comment-page-1/#comment-106 Fri, 03 Aug 2007 00:02:14 +0000 http://mathfactor.uark.edu/2007/03/19/cd-alas-up-to-a-million-dollars-might-have-been-given-away/#comment-106 I’m curious how a group’s “submission median” would respond to a small tweak in the rules:

“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.

]]> By: strauss http://mathfactor.uark.edu/2007/03/cd-alas-up-to-a-million-dollars-might-have-been-given-away/comment-page-1/#comment-104 Wed, 01 Aug 2007 03:42:18 +0000 http://mathfactor.uark.edu/2007/03/19/cd-alas-up-to-a-million-dollars-might-have-been-given-away/#comment-104 Interestingly, a wide majority of the entries were less than 20,000; the median was roughly 1000.

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.

]]> By: dfollett76 http://mathfactor.uark.edu/2007/03/cd-alas-up-to-a-million-dollars-might-have-been-given-away/comment-page-1/#comment-103 Wed, 01 Aug 2007 02:49:24 +0000 http://mathfactor.uark.edu/2007/03/19/cd-alas-up-to-a-million-dollars-might-have-been-given-away/#comment-103 I think the problem with this contest was we all really knew the point before we submitted numbers, and we didn’t really believe there was $1 million dollars available. I’d like to see this experiment on a non-math-enthused audience where $1 million dollars is really available. Perhaps on the audience at a game or talk show.

]]> By: strauss http://mathfactor.uark.edu/2007/03/cd-alas-up-to-a-million-dollars-might-have-been-given-away/comment-page-1/#comment-98 Tue, 26 Jun 2007 13:05:37 +0000 http://mathfactor.uark.edu/2007/03/19/cd-alas-up-to-a-million-dollars-might-have-been-given-away/#comment-98 This email arrived this morning, to the mathfactor address. I can only assume it is related to our own fabulous million dollar give-away!


Euro Millions Lottery SPE.,
2011 Zaventem , Belgium .
Euro Millions are Affiliate of Belgium National Lottery (BNL).
Sir/Madam,

CONGRATULATIONS: YOU WON €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 €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.

]]> By: contactm3 http://mathfactor.uark.edu/2007/03/cd-alas-up-to-a-million-dollars-might-have-been-given-away/comment-page-1/#comment-91 Tue, 12 Jun 2007 20:47:06 +0000 http://mathfactor.uark.edu/2007/03/19/cd-alas-up-to-a-million-dollars-might-have-been-given-away/#comment-91 s “arrow notation”. I mistook 10^^10 as meaning 10^10^10, when it really means 10^10^10^10^10^10^10^10^10^10. Wow! That Knuth guy had big things on his mind. Then to iterate arrows... whoa. Good job Rayo! (I don't know how I'm going to break it to my girlfriend).]]> WOW! I withdraw my earlier statement! I grossly misunderstood Knuth’s “arrow notation”. I mistook 10^^10 as meaning 10^10^10, when it really means 10^10^10^10^10^10^10^10^10^10. Wow! That Knuth guy had big things on his mind. Then to iterate arrows… whoa. Good job Rayo! (I don’t know how I’m going to break it to my girlfriend).

]]> By: strauss http://mathfactor.uark.edu/2007/03/cd-alas-up-to-a-million-dollars-might-have-been-given-away/comment-page-1/#comment-86 Thu, 07 Jun 2007 21:31:49 +0000 http://mathfactor.uark.edu/2007/03/19/cd-alas-up-to-a-million-dollars-might-have-been-given-away/#comment-86 Ah, very nice indeed; in fact, though, as truly immense as they are, these numbers are STILL kind of small compared to some of the entries we had!!

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!

]]> By: contactm3 http://mathfactor.uark.edu/2007/03/cd-alas-up-to-a-million-dollars-might-have-been-given-away/comment-page-1/#comment-85 Thu, 07 Jun 2007 21:16:21 +0000 http://mathfactor.uark.edu/2007/03/19/cd-alas-up-to-a-million-dollars-might-have-been-given-away/#comment-85 I know it’s a bit late, but I came with a huge number which I never submitted. It comes from a sequence I put together, A(x), where:
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!

]]> By: Sye Heinlein http://mathfactor.uark.edu/2007/03/cd-alas-up-to-a-million-dollars-might-have-been-given-away/comment-page-1/#comment-38 Fri, 30 Mar 2007 06:29:11 +0000 http://mathfactor.uark.edu/2007/03/19/cd-alas-up-to-a-million-dollars-might-have-been-given-away/#comment-38 In reply to the first post.
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.

]]> By: strauss http://mathfactor.uark.edu/2007/03/cd-alas-up-to-a-million-dollars-might-have-been-given-away/comment-page-1/#comment-37 Thu, 29 Mar 2007 20:27:39 +0000 http://mathfactor.uark.edu/2007/03/19/cd-alas-up-to-a-million-dollars-might-have-been-given-away/#comment-37 It’s kind of amusing to consider how many possible states the universe could be in! That comes in much bigger than a googolplex, but not so big at all compared to some of the numbers we’ll be discussing soon!

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 1010 light years on a side, which comes to about 1078m3 in volume. So there are, say 10177 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 10125; since we are just aiming for a rough sense of things:

Let’s then suppose there are 10200 positions and 10100 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.

]]> By: strauss http://mathfactor.uark.edu/2007/03/cd-alas-up-to-a-million-dollars-might-have-been-given-away/comment-page-1/#comment-36 Thu, 29 Mar 2007 20:09:15 +0000 http://mathfactor.uark.edu/2007/03/19/cd-alas-up-to-a-million-dollars-might-have-been-given-away/#comment-36 I don’t know— seems a little cheap to me! At least he specified that his number should be larger than any other student’s! (It’d be sad to see him disappear down a logical rabbit hole!)

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