Connotation Counting

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Re: Connotation Counting

Postby Vytron » Sat Nov 29, 2014 2:36 am UTC

71 - Conway's Constant's Algebraic Degree.

Okay, first, let's talk about algebraic degrees and polynomial.

A polynomial can be represented by constants or variables that form them, and they just need to have an end point. These are all polynomials:

1
x
x2+y3

The first two are monomials, that is, polynomials of one term.

The degree of a (nonzero) monomial is the sum of the exponents of its variables (all monomials are degree 0 because x0=1)

The degree of a polynomial is the maximum of the degrees of its terms after the polynomial has been expanded. For example, the polynomial (1+ square root of 2)⁢x2⁢y3+12⁢x2⁢y2 has degree 5.

And that's all we need.

Let's look at the sequence:

-6 (degree 0)
3x-6 (degree 1)
-6x2+3x-6 (degree 2)
+12⁢x3-6x2+3x-6 (degree 3)
...

Once you expand it, you get to this monster:

x71-x69-2⁢x68-x67+2⁢x66+2⁢x65+x64-x63-x62-x61-x60-x59+2⁢x58+5⁢x57
+3⁢x56-2⁢x55-10⁢x54-3⁢x53-2⁢x52+6⁢x51+6⁢x50+x49+9⁢x48-3⁢x47-7⁢x46-8⁢x45
-8⁢x44+10⁢x43+6⁢x42+8⁢x41-5⁢x40-12⁢x39+7⁢x38-7⁢x37+7⁢x36+x35-3⁢x34+10⁢x33
+x32-6⁢x31-2⁢x30-10⁢x29-3⁢x28+2⁢x27+9⁢x26-3⁢x25+14⁢x24-8⁢x23-7⁢x21+9⁢x20
+3⁢x19-4⁢x18-10⁢x17-7⁢x16+12⁢x15+7⁢x14+2⁢x13-12⁢x12-4⁢x11-2⁢x10+5⁢x9+x7
-7⁢x6+7⁢x5-4⁢x4+12⁢x3-6⁢x2+3⁢x-6

Which is degree 71 and gives this number its connotation.

The result is Conway's Constant:

λ≈1.303577296

But, from where do these numbers come from?

From the Look and Say Sequence.

The look an say sequence is an infinitely growing sequence where, to define the next number, you look and say what you saw in the previous member.

Starting with:

1

What do you see?

A one.

Or, one one. Thus, the next member is:

11.

What do you see?

Two ones.

So the next member is 21.

What do you see?

One two and one one.

So the next member is 1211.

And it goes 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211...

And it never has a number higher than 3.

When you start with number d, where d is an integer different from 1, you get:

d, 1d, 111d, 311d, 13211d, 111312211d, 31131122211d...

As the sequence.

All starting values will keep growing infinitely except for the degenerate (lol, they do have a term for this!) sequence 22, 22, 22...

Anyway, the terms eventually grow in length by about 30% per generation, or, 30.3577296...% per generation (multiply by λ≈1.303577296...)

In other words, if Ln is the number of digits of the nth member of the sequence, then the limit of the ratio Ln+1/Ln (i.e. how bigger the next number of the sequence can be) is:

Conway's Constant (λ≈1.303577296...)

As n approaches infinity.

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Re: Connotation Counting

Postby ramblinjd » Mon Dec 01, 2014 1:16 pm UTC

Room temperature (for imperial system thermostats) = 72

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Re: Connotation Counting

Postby Vytron » Mon Dec 01, 2014 1:23 pm UTC

Arecibo's message length (73)

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Re: Connotation Counting

Postby 12obin » Mon Dec 01, 2014 10:34 pm UTC

74: the worldwide average life span of a female* human, rounded to the nearest year.

*
Spoiler:
I don't accept any statistic that divides all human into two sexes, because that is simply not how human bodies work. There are absolutely a statistically significant number of intersex people (who are likely counted as female), let alone how trans people would affect these stats (e.g. I imagine a trans man is about as likely as a cis man to get involved in the sort of violent/risky behavior that tends to skew male life expectencies lower, but he'd also likely be counted as female). But for the purposes of this game...whatever, it's fine.
Robin, she.

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Re: Connotation Counting

Postby Vytron » Tue Dec 02, 2014 12:12 am UTC

So, I guess we've reached the uninteresting numbers, I didn't expect we'd do it this soon, but I really had to struggle to find something for this one (considering things like "rhenium's number" or "year in which the Temple of Peace was built" or even "3/4 in percentage" very boring.)

75. Diamond Wedding' Year.

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Re: Connotation Counting

Postby azule » Tue Dec 02, 2014 6:30 am UTC

Years are going to come up a lot. I'm thinking "birthday year (within a century) of the U.S." for '76. I haven't looked anything up.
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Re: Connotation Counting

Postby Vytron » Tue Dec 02, 2014 6:59 am UTC

I thought that'd be cheating (it's one thing to look at what happened in year 76 and report some event, but '76 basically gives you access to any century.)

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Re: Connotation Counting

Postby azule » Tue Dec 02, 2014 7:57 am UTC

I didn't say my thought was valid. Yep, maybe better as 1776.
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Re: Connotation Counting

Postby Vytron » Tue Dec 02, 2014 7:59 am UTC

It'd probably be valid (thread does not forbid cheating.)

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Re: Connotation Counting

Postby azule » Tue Dec 02, 2014 9:40 am UTC

Maybe but research is encouraged. First search result is an iconic gas station.

Further research says it's the same 76 I said up there. I get my cake and eat it too.

A few contenders for 77 but I'll leave that for the next poster.
Last edited by azule on Tue Dec 02, 2014 9:53 am UTC, edited 1 time in total.
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Re: Connotation Counting

Postby Vytron » Tue Dec 02, 2014 9:42 am UTC

I hope next poster actually does address 76.

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Re: Connotation Counting

Postby azule » Tue Dec 02, 2014 9:54 am UTC

Oh. I meant....:

76. gas station.
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Re: Connotation Counting

Postby Vytron » Tue Dec 02, 2014 10:48 am UTC

77. Interestate.

I don't like where this is going, but oh well.

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Re: Connotation Counting

Postby azule » Tue Dec 02, 2014 12:00 pm UTC

what about 66? what's special about 77 as interstate? if you don't like it then don't go there. :P
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Re: Connotation Counting

Postby Vytron » Tue Dec 02, 2014 12:03 pm UTC

I didn't like 66 either, but, as I said, numbers seem harder at this level, and I'm looking forward to someone giving a spin for 78.

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Re: Connotation Counting

Postby Yablo » Tue Dec 02, 2014 6:10 pm UTC

78. Tarot (Number of cards in a standard deck)
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Re: Connotation Counting

Postby Vytron » Tue Dec 02, 2014 11:08 pm UTC

See? That was very cool! I wish there was something like that for 79.

Alas, I'll have to go with...

79. Gold's atomic number.

Because, Gold is cool, or something.

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Re: Connotation Counting

Postby Knee Jerk » Sun Dec 07, 2014 2:20 pm UTC

Vytron wrote:
Knee Jerk wrote: These two threads appear to be different. Am I missing an important aspect?


Agreed, to me both threads were unique and fun in their own way, despite this one playing as 12obin hoped h to play like.

I also had a similar idea, but I think 3 similar threads would be too much so I dropped it.
Glad to have you appreciate and join my thread, 12obin. Too bad to hear of the loss of your thread, Vytron. What was it going to be? Maybe we're ready to move onto yours.

12obin wrote:Allow me to throw myself on the grenade that is 69.

edit: I don't think I formulated my post properly for how this thread works. I don't know what the word would be, though. I do not want to be graphic.
I appreciate your attempt anyway. How about the phrase "fifth grader's favorite sex position"? (US, and maybe other, school year naming system.)

Vytron wrote:I didn't like 66 either, but, as I said, numbers seem harder at this level.
You're free to contest any you don't think should count, hopefully also by providing a more valid alternative.

I agreed from the start that it will become more difficult. Sometimes games can be challenging. ;)

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Re: Connotation Counting

Postby Vytron » Mon Dec 08, 2014 5:54 am UTC

Knee Jerk wrote:What was it going to be? Maybe we're ready to move onto yours.


Mine is based on the proof that all numbers are interesting, which I want to disprove :)

Anyway, here it is, it has arbitrary significance out from the OP, so I think it'll be the most hard version of this game.

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Re: Connotation Counting

Postby ramblinjd » Mon Dec 08, 2014 2:22 pm UTC

Inaugural games of the Flavian Amphitheatre

Spoiler:
AD 80 - The Colosseum opens


http://en.wikipedia.org/wiki/Inaugural_games_of_the_Flavian_Amphitheatre

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Re: Connotation Counting

Postby Vytron » Mon Dec 08, 2014 4:09 pm UTC

81 - Shogi Playing Board Squares.

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Re: Connotation Counting

Postby ramblinjd » Mon Dec 08, 2014 5:48 pm UTC

MLB Winning Season

Spoiler:
"In Major League Baseball, the number of games a team must win to secure a winning season is 82."

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Re: Connotation Counting

Postby Yablo » Mon Dec 08, 2014 6:17 pm UTC

83. Second Bar Mitzvah

Apparently, in Judaism, the normal lifespan is considered to be 70 years, so if a man makes it to 83, he gets to be 13 again.
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Re: Connotation Counting

Postby azule » Mon Dec 08, 2014 10:01 pm UTC

Thanks. Now I know that!
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Re: Connotation Counting

Postby Vytron » Tue Dec 09, 2014 5:45 am UTC

On MLB: Or tie it if some other team also has 82 wins?

84 - How many years it takes Uranus to orbit the sun once.

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Re: Connotation Counting

Postby ramblinjd » Mon Dec 15, 2014 2:39 pm UTC

Vytron wrote:On MLB: Or tie it if some other team also has 82 wins?


No - a winning season just implies the team has more wins than losses - 82 is one more than half the total games in a standard season (162).

85 is the smallest nonzero repetitive digit number in base 4 (1111).

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Re: Connotation Counting

Postby Vytron » Mon Dec 15, 2014 2:52 pm UTC

Get Smart's number.

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Re: Connotation Counting

Postby Yablo » Mon Dec 15, 2014 10:55 pm UTC

87. Gettysburg Address

"Four score and seven years ago ..." The number of years between the Declaration of Independence and the Battle of Gettysburg.
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Re: Connotation Counting

Postby Vytron » Mon Dec 15, 2014 11:39 pm UTC

88. The number of Constellations visible from Earth.

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Re: Connotation Counting

Postby azule » Tue Dec 16, 2014 1:06 am UTC

Yablo wrote:87. Gettysburg Address

"Four score and seven years ago ..." The number of years between the Declaration of Independence and the Battle of Gettysburg.
Well, thanks. I never could figure out that math. I hope that I will now forever remember this. ^_^
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Re: Connotation Counting

Postby Yablo » Tue Dec 16, 2014 11:57 pm UTC

azule wrote:Well, thanks. I never could figure out that math. I hope that I will now forever remember this. ^_^

Seriously. We come here to have fun, and Knee Jerk tricks us into learning things.
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Re: Connotation Counting

Postby azule » Wed Dec 17, 2014 1:04 am UTC

Remember being a kid? Fun WAS learning. I learn at every opportunity, whether it's facts, social, whatever.

I mean, blecch! Learning is like broccoli. Let's get back to the sticks of sugar.
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Re: Connotation Counting

Postby Vytron » Wed Dec 17, 2014 2:33 am UTC

One never stops learning, and it never stops being fun.

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Re: Connotation Counting

Postby Yablo » Wed Dec 17, 2014 6:12 pm UTC

89. Ditka

As much as it pains me, having been born in Green Bay, Wisconsin, I've gotta go with Mike Ditka. The Chicago Bears retired his jersey number, 89.
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Re: Connotation Counting

Postby Vytron » Wed Dec 17, 2014 10:20 pm UTC

90. Right Angle.

That's correct, apparently all other possible angles are wrong.

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Re: Connotation Counting

Postby Yablo » Wed Dec 17, 2014 11:41 pm UTC

91. American Coins

If you have one of each denomination of American coin less than a dollar (half-dollar, quarter, dime, nickel, penny), you have 91 cents.
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Re: Connotation Counting

Postby Vytron » Wed Dec 17, 2014 11:54 pm UTC

92. Uranium's Atomic Number.

I normally don't do elements, but, come on! It's goddamn Uranium!

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Re: Connotation Counting

Postby Yablo » Thu Jan 01, 2015 12:28 am UTC

93. Victor Hugo

His last novel was "Quatrevingt-treize", or "Ninety-Three". It specifically concerns the year 1793, during the French Revolution.
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Re: Connotation Counting

Postby Vytron » Thu Jan 01, 2015 1:31 am UTC

94. ASCII.

Its character set contains exactly 94 graphic non-whitespace characters.

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Re: Connotation Counting

Postby Yablo » Fri Jan 02, 2015 5:38 pm UTC

(I was going to go with Windows 95, but then I remembered ...)

95. Theses

Martin Luther kicked off the Protestant Reformation on Halloween by nailing the Ninety-Five Theses to the door of the All Saints' Church in Wittenburg, Germany. If he'd thought of just five more ways the Catholic Church pissed him off, this would have been an easier number to remember.
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