This originally started out as a paper on Zeno's paradoxes but the more I researched the problem of infinite regression, supertasks, and fundamental mathematiics (its been a while, ok?) the more fallacies I discovered. This first entry in the "Infinite Things" series will be devoted to the concept of infinite regression, i.e. 1/infinity, which is at the root of each of Zeno's paradoxes.
It Isn't Zero Dammit
1/infinity does not equal zero. Going on the record for this one because as much as I hate math, it should be done right. If infinity is to be treated as an unending series of numbers, or the highest of all possible numbers, it must still be treated as a number. Therefore, 1/infinity does not equal zero but a number really, really, really, REALLY close to zero. The answer I most approved of was "undefined" since infinity itself isn't exactly a true number to speak of. Why, you may ask? Ok, Zeno.
If we walk a line to get from point A to point B, we must get to 1/2 AB, then get to 1/4 AB, then to 1/8 AB, etc. Essentially, we will never get to point B because we always have to go halfway from where we are measuring from to point B, and that distance can always be cut in half "infinitely." Now, I actually read up on this because I didn't want to post a "GUYS! I SOLVED IT!" entry only to read about how wrong I am a few hours later. It actually led me to this entry on supertasks, which started this whole train of thought. (Thank you Chihara, whoever you are.)
This line dividing business makes a lot of paradoxical sense when you start with the whole numbers, i.e. 1, 1/2, 1/4, 1/8... they're fractions, whatever. BUT! let's start at the other end. Say you get allllll the way to 1/infinity and decide to turn around. Well, doubling 1/infinity gets you... oh, look at that. You get 1/infinity again. Doubling it again gets you... 1/infinity. Yet again. Cynicism aside, this poses a very real problem for the argument. We started out taking real numbers and hypothesizing them into an infinite number, but you can't really do that. You can divide a number by half or double a number as many times as you like; it will never truly reach infinity. It will get small, but no matter how small it gets it will still be a numerical value. The same concept can be applied to matter; cutting a cake in half 100000000000 times still leaves you with a very small piece of cake.
Whoever that douche was in one of the forums I checked before writing this article who said, "for all practical purposes, 1/infinity equals zero," you can't math and you shouldn't math. There are certainly problems in the Arabic mathematical base-10 system that cause problems when applying it to our universe (where else would Zeno get his paradoxes from?), but "pretty much equals" isn't math; it's guessing. I could "pretty much" stop at a red light, and I'll use your logic when the police officer asks me how the car crash happened.
There Was Only One Section in This Post
LOOK AT ALL OF THIS EMPTY SPACE
Its Like It Goes On Forever
When Do You Use "Its" and "It's"?
This cleared things up.
Screw You, BD
Steve
No comments:
Post a Comment