Nice Sequences

By -
I like sequences that grow fast. Like this: 0, 1!, 2!!, 3!!!, 4!!!!, ...
That's 0, 1, 2, 720!, ... Really jump off the board.

But did you know that there are sequences that grow faster than any computable sequence? They are, of course, incomputable.

Comments

  1. Andy3:10 PM

    I'm fond of 1, 2^2, 3^3^3, ...

    How about f(n) = (2 / (n-2))^2, for n=0, 1, 2...

    f(n) = 1, 4, Infinity...

    ReplyDelete
  2. gcallah3:49 PM

    Incomputable
    That's what you are
    Incomputable
    With pointers near or far
    Like some code from above that clings to me
    Making my CPU just run on infinitely
    Never before has someone been more
    Incomputable

    ReplyDelete
  3. Andy3:58 PM

    Also, 3!!! is not 720. That's 3!!. 3!!! is much larger (1747 digits.)

    ReplyDelete
    Replies
    1. gcallah4:32 PM

      Andy, you're not paying attention: Wabulon Did not say that 3!!! = 720. He said it equals 720!

      Delete
    2. Andy5:37 PM

      Doh!

      Delete

Post a Comment

Popular posts from this blog

Libertarians, My Libertarians!

By -
Cruel to be kind means that I love you . Because, while I think you are mistaken, your hearts are in the right place -- yes, even you, Silas --  unlike some people . This Breitbart fellow (discussed in the link above), by all appearances, deliberately doctored a video of Shirley Sherrod to make her remarks appear virulently racist, when they had, in fact, the opposite import. I heard that at a recent Austrian conference, some folks were talking about "Callahan's conservative turn." While that description is not entirely inaccurate, I must say that a lot of these people who today call themselves conservative give me the heebie-jeebies.
Read more

"Pre-Galilean" Foolishness

By -
 I am currently reading The Master and His Emissary , which appears to be an excellent book. ("Appears" because I don't know the neuroscience literature well enough to say for sure, yet.) But then on page 186 I find: "Asking cognition, however, to give a perspective on the relationship between cognition and affect is like asking astronomer in the pre-Galilean geocentric world, whether, in his opinion, the sun moves round the earth of the earth around the sun. To ask a question alone would be enough to label one as mad." OK, this is garbage. First of all, it should be pre-Copernican, not pre-Galilean. But much worse is that people have seriously been considering heliocentrism for many centuries before Copernicus. Aristarchus had proposed a heliocentric model in the 4th-century BC. It had generally been considered wrong, but not "mad." (And wrong for scientific reasons: Why, for instance, did we not observe stellar parallax?) And when Copernicus propose
Read more