« on: December 09, 2007, 02:11:06 PM » First post

Tangents

Perhaps this is true in most forums, but within MG a lot of the forum topics take some wicked tangents.  I.e. I posted a topic on Affective Philosophy (corruption of the mind) and folks start talking about their music tastes.  Not that I mind much, I'm just curious and a little entertained by the process.

« on: December 09, 2007, 04:57:03 PM » Reply #1

Re: Tangents

I often find myself a bit upset over some of them :-( .

Not much we can do about them though.


Khalsa

« on: December 09, 2007, 05:20:08 PM » Reply #2

Re: Tangents

Split the thread?

« on: December 09, 2007, 05:34:20 PM » Reply #3

Re: Tangents

That's always an option.  Though some of the more interesting discussions have come from evolution of the original topic, it might help the original topic to remain focused (or just bury it in the "recent posts" list).

« on: December 11, 2007, 06:21:24 AM » Reply #4

Re: Tangents

* tuple searches fruitlessly for a tangential subject and finds no literary branch to hang such a construct on.

« on: December 11, 2007, 06:26:22 AM » Reply #5

Re: Tangents

Quote from: Rocinante on December 09, 2007, 05:34:20 PM

Though some of the more interesting discussions have come from evolution of the original topic

Bollocks.  The threads change because there is a great overseer who is intelligently designing them.  Do you really think all these threads could have gotten so screwed up by pure chance?

« on: December 11, 2007, 06:40:44 AM » Reply #6

Re: Tangents

Quote from: tuple on December 11, 2007, 06:21:24 AM

* tuple searches fruitlessly for a tangential subject and finds no literary branch to hang such a construct on.

Don't talk about branches, the maple in my backyard seems to like to deposit dead ones on the roof, usually during a windstorm while we're upstairs trying to sleep.  Which is difficult to do when you hear the loud "thump" of something hitting the ceiling above your bed..

* Rocinante wonders if that helped

« on: December 11, 2007, 07:42:09 AM » Reply #7

Re: Tangents

Quote from: David on December 11, 2007, 06:26:22 AM

Quote from: Rocinante on December 09, 2007, 05:34:20 PM

Though some of the more interesting discussions have come from evolution of the original topic

Bollocks.  The threads change because there is a great overseer who is intelligently designing them.  Do you really think all these threads could have gotten so screwed up by pure chance?

They have been touched by His Noodly Appendage.

« on: December 11, 2007, 09:32:55 AM » Reply #8

Re: Tangents

Is it weird that when I read the topic title I immediately thought of lines that touch a curve at only one point?

Speaking of which (almost), my kingdom for anyone who can tell me what the graph of

y = (-1)^x

looks like.

« on: December 11, 2007, 11:10:02 AM » Reply #9

Re: Tangents

I would have to agree topics do like to git off at some points.

*ben does the x variable = anything or is it just there?

« on: December 11, 2007, 12:24:14 PM » Reply #10

Re: Tangents

Quote from: benmachine on December 11, 2007, 09:32:55 AM

Speaking of which (almost), my kingdom for anyone who can tell me what the graph of

y = (-1)^x

looks like.

Well, consider this.

etc
-1^-3 = -1
-1^-2 = 1 // that is to say... 1 / (-1)^-2 = 1/1=1
-1^-1 =-1
-1^0 = 1
-1^1= -1
-1^2= 1
-1^3= -1
-1^4= 1
-1^5= -1
etc

Note: fractions of a negative number do not exist in the real number system. They are complex. (ex, sqrt(-1) = i)

Therefore, your graph looks like a series of dots alternating between -1 and 1. There are no lines joining them... that all doesn't exist.

Note: I'm a terrible mathematician, but this is what I believe is correct. Please get someone to verify this claim.

« on: December 11, 2007, 01:26:39 PM » Reply #11

Re: Tangents

-1^0.5 is i, as you said, because x^(p/q) is the qth root of x ^ p and the square root of -1 is imaginary.
However, -1^(2/3) is the cube root of -1 squared, which IS real: -1.
see http://www.google.co.uk/search?q=(-1)^0.2
It becomes clear with a little investigation that all -1^(p/q) where p and q are coprime and q is odd are real, and equal 1 where p is even and -1 when p is odd. However, this doesn't really resolve the situation since the graph is still discontinuous and now seems to have an infinite number of distinct real results between x = 0 and 1, despite having an equally infinite number of x values where clearly no real y exists. I still have no idea what the graph looks like.

« on: December 11, 2007, 01:40:43 PM » Reply #12

Re: Tangents

Stop it I say stop it. That stuff hurts my head

« on: December 12, 2007, 11:40:32 AM » Reply #13

Re: Tangents

well if its an if you have an equally infinite number of x values where clearly no real y exists you'll just have a straight line.

« on: December 12, 2007, 12:28:08 PM » Reply #14

Re: Tangents

Hmm, yes indeed.

Well, in that case, I theorize that...

0 exists
Everywhere where the fraction's numerator is:
  Is greater than the denominator
  Is even
Exists.

Everything else does not.