Diagram Puzzles

[impossibleroot]

What do these diagrams represent?

1:

[mathgrant]

I'd guess prime numbers for number 1. As for the others. . . I can't see them!

[impossibleroot]

<grin> They're coming, they're coming, slow down. Here's 2:

2:

[Chuck]

2: A Back to The Future script (early draft)

[impossibleroot]

Actually, the trilogy (with 1885). More on the way; you guys are good.

[CzarJ]

*Is reminded of A Beautiful Mind...* Man, I wish that guy was real. He was cool=)

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"Blah blah blah. Blah blah blah. Blah blah blah."
--The Reverend Al Sharpton

[Purgation]

*doesn't get the first one*

[impossibleroot]

1: Starting from the 'center' and spiraling outward (starting to the right, with the one in bold), the circles represent the integers from 1 to 100. The primes tend to fall into these diagonal lines. This pattern looks meaningful but amounts to little, as researched by Stanislaw Ulam: http://yoyo.cc.monash.edu.au/~bunyip/primes/primeSpiral.htm

Of course, leave it to mathgrant to nail it immediately.

[Bicho the Inhaler]

Damn, mathgrant. 2 minutes is pretty good.

[extropalopakettle]

How does that spiral go? Where are the primes 2,3,5 & 7 on there?

[impossibleroot]

[impossibleroot]

3:

[daniel801]

you can count on me not to reveal the answer

[test78]

since daniel chose not to
I'll put it invisible just to see if I was able to solve one of these...

1 2 3 4 5 6 7 8 9 ?

[impossibleroot]

--> The inverse of digital LCD clock numbers



[This message has been edited by impossibleroot (edited 01-13-2002 11:21 AM).]

[Bicho the Inhaler]

I got one. Whee. I'll check test's answer to see if it agrees, but I'm sure it does.

[mith]

i don't understand what the big deal is about the primes forming "mysterious diagonal lines". of course they're on diagonals, it's sorta like a chess board with all the odds on black squares and all the evens on white. since the only even prime is 2, all the rest of the primes appear on the same set of diagonals. with that in mind, there isn't much interesting about the diagram. i'd be much more interested if all the primes were actually connected. they arent.

[mith]

(random rant at people seeing patterns when there isn't really anything there. sorta like the pi thing in vsn)

[impossibleroot]

Don't get me wrong, mith, I'm not really fascinated by the phenomenon either. Like I said, it amounts to little in the end. It's just that people *want* to see order where there may be none -- it would appear that understanding primes is beyond our reach.

[extropalopakettle]

I think this is different. Yes, it's like a checkerboard - the spiral places odd numbers on black squares, and even numbers on white squares. But if I were to randomly place checkers on black squares, I wouldn't expect them to line up. Certain diagonals seem to be very strongly filled with primes, and others not. Furthermore, there are a few that run at angles other than the obvious 45 and -45 degrees. A good pic is here:

[extropalopakettle]

BTW, I think I see a GOD DAMN ALIEN in there.

[impossibleroot]

4:

[Alter Ego]

The Moons of Saturn? Nah.

[Milt]

Invisible spoiler...

M M L J A R C C G E P C T T T T T P H J P P J J J J R

[impossibleroot]

Indeed. Next one soon...

[impossibleroot]

5:

[ronl]

OK ... now you guys got me feeling really stupid. Not only could I not figure out #4 from the diagram, I can also not figure it out from the spoiler (and I don't mean I can't see the hidden message). I would really appreciate an additional, but less cryptic, hint.


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This post is rated NWS: Not Worthy of a Signature.

[Bicho the Inhaler]

Hey, how about a hint on 4? Milt's spoiler wasn't much of one.

[edit: looks like ronl had an I. S. E. (hey, I haven't seen ronl in a while)]

[This message has been edited by Bicho the Inhaler (edited 01-18-2002 12:47 AM).]

[mathgrant]

Cantor's Proof of Rational Number Enumerability!

[This message has been edited by mathgrant (edited 01-18-2002 01:18 AM).]

[Milt]

4.

Matthew Mark Luke John Acts Romans...

[impossibleroot]

Oh, not *you*, mathgrant! <grin>

Care to explain for everyone else?

[impossibleroot]

6:


Larger view

[impossibleroot]

ISE

[This message has been edited by impossibleroot (edited 01-18-2002 10:11 AM).]

[daniel801]

how a bill becomes a law

[Lucky Wizard]

I think 6 looks like a flowchart - possibly the one used by a computer game's manufacturers to keep track of the possibilities in the computer game.

Oh, and for 4, I can't see any connection between these circles and the Bible. Though maybe the connection is blindingly obvious to Christians and not to agnostics like me.

[impossibleroot]

Lucky Wizard, 4 is just a diagram of the books of the New Testament, with circle size representing number of chapters in each book. No discrimination meant, just as I don't mean to leave out people who haven't taken a math course (for 1) or who don't watch movies (for 2).

[Bicho the Inhaler]

Jeepers, I can't believe it...that's what I thought at first, but for the rationals, traditionally you skip the repeated ones. It would work better as a proof that the set of all ordered pairs of naturals is countable...and then I thought that was getting a little obscure. But basically, to show a set is "countable," all you have to do is show that there exists a 1-1 correspondence between that set and the naturals, i.e., that there is a "counting order." (Easy example if this is a little hazy: you can count the set of all integers in the order 0, 1, -1, 2, -2, 3, -3, 4, -4, etc., so the set of all integers is countable.) Now, on the diagram, each little circle is an ordered pair of naturals (or a single rational number, if you want, although you would probably repeat a few (or an infinity)), and the counting order is the order indicated by the arrows. You can see that given any finite ordered pair, you will count up to it in a finite number of steps.

[Sofis]

6: Is this a map of a maze of twisty little passages, all alike?

[Boeuftete]

6 looks like a representation of a finite autotomata. (essentially a finite-state machine). But a representation of what i haven't determined yet.


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[impossibleroot]

Sofis, indeed it is. <grin> I knew someone would be old-school enough...