Sunday, November 8, 2009

Count On It

Blog post # 12:

First, another whimsical picture, so as to continue the theme (whimsy) from the last blog post:

This picture seems unoriginal to me, in that I swear I have seen rainbow-ladybugs somewhere sometime before I made the picture.

And though the picture is whimsical, I do not feel like joking today. (Or more accurately, I can't remember any of my jokes right now.)

Hmmm. Okay, here are two dumb jokes that I think most people who know me have already heard:

Why was the cigarette smoking-mad????

Because it was the butt of this joke!...


What happened to the square-shaped car when it got in an accident?

It became a wreck-tangle!....


Okay, something of more substance:


When I think of truth, I do not think of what people usually refer to by the word "Truth": something that is believed to be true just because someone else said it was true. (As in, ""THE Truth"", thunderclap!)

I instead define the truth as that which is real, whatever that is, whether I believe in it or not.
I think that was the original definition of truth. So, you could say I am a Platonist -- where Platonism is a mathematical philosophy that states that mathematical objects (shapes, numbers, theorems, etc) exist outside of the human perception of them. (They are REAL, even if we are not.)

So, I think that 'what is' exists outside of human understanding.

But... quantum physics states that the observer is an important element in the nature of what is observed. But even then, quantum physics itself exists outside of our understanding of it. Or does it?

And in any case, the observer only has miniscule affect on what is observed. Yet, in some situations (Schrodinger's Cat, for example [Google it]), the observer is indeed very important to the observation and to the REALITY of what is observed.

*(Hmmmm... Maybe liberals observe Schodinger's Cat as dead, and conservatives see it as alive... or vice versa, or versa vice.)


Okay, I swore I would not post math ever on this blog, but I want to post this "guess the number sequence puzzle" here anyway.

(Really simple math.)

Here are the starting terms of a number sequence:

1, 1, 2, 4, 2, 6, 2, 12, 2, 10, 2, 34, 2, 14, 2, 20, 2, 24, 2, 54, 2, 22, 2, 70, 2, 26, 2, 46, 2, 46, 2, 36, 2, 68, 2, 94, 2, 38, 2, 74, 2, 62, 2, 70, 2, 138,....

Now, as with all these "guess the sequence" IQ-test-style questions, there are an INFINITE number of descriptions for the sequence (of a finite number of terms) that are valid.
But, try anyway to find the rule that generates this sequence.

If you discover a rule that pops out the sequence I gave, whether it is what I intended or not, then you still win.

Here are some clues:

*All odd-numbered (odd-indexed) terms, not including the first, are equal to 2.
*All terms, except the first two (which are both 1), are even.
*The intended rule uses only addition and involves division somehow.
*The n-th term is computed using terms that occur earlier in the sequence, and uses the value of n somehow.

I have given too many clues. I will post the answer in a few days in the comments to this post. I doubt anyone will try to solve this, but maybe YOU will try to solve this and succeed!


Leroy Quet


Anonymous said...

This is Leroy (me) posting anonymously.

The answer is that the first term is 1 (obviously), and after that the nth term is the sum of the previous terms that divide n.

For example:
Among the first 7 terms, the terms which divide 8 are 1, 1, 2, 4, 2 and 2.
So the 8th term = 1+1+2+4+2+2 = 12.

Did anybody try to solve this?

Anonymous said...

I think that Platonic concept came from Pythagorus, don't quote me on that