Poll 53 - One squared (1^2) equals one. One to the power of three (1^3) equals one. What does one to the power of infinity equal? Poll ended November 29 2009. By far the most popular answer was "One", with 75.3%. "Infinity" was next, with 10.1%, "None of the Above" with 9.3%, and finally "Zero" with 5.3%.Interesting! Let's look at the most popular answer first. The logic of this seems pretty simple, doesn't it? One multiplied by itself equals one. No matter how many times you multiply it by itself, the answer is one. Right? Right.
But here's the tricky part. Infinity is not a number. So multiplying one by itself an infinite number of times is different from one multiplied by itself a specific number of times. Does that mean the second-most popular answer is correct? Is the answer infinity?
Here's a link that reveals what mathematicians say about this thorny question. The correct answer, it turns out, is that one to the power of infinity is like dividing zero by zero: in both cases, the answer is "indeterminate".It's worth noting here, though, that dividing zero by zero is not the same as dividing any other number by zero: the first is "indeterminate", the second is "undefined". What's the difference?
Indeterminate means all answers are possible. Here's a link to another mathforum.org discussion about this idea. It explains that the answer to one to the power of infinity could be one, could be infinity, could be undefined... it's indeterminate. One over zero, on the other hand is undefined only.
What's this all got to do with Imagining the Tenth Dimension? Because the zero we start from and the tenth dimension we end up with are indeterminate. Likewise, "before" and "after" the life of our universe is the same underlying state of indeterminacy.
Indeterminate is not the same as undefined, and that's an important distinction. As we've said recently in entries like You Are the Point, What's Around the Corner, and even last time in Strength of Gravity, Speed of Light, the underlying structures of our reality naturally balance everything out, to a place where all the simultaneous possibilities of that indeterminacy add up together into a big beautiful zero of perfect symmetry, where all answers are possible.
I like to call this underlying state the Omniverse. My followup book to Imagining the Tenth Dimension, O is for Omniverse, plays with these ideas in an unusual way, combining easily digestible poems with some stunning visuals created by Marilyn E. Robertson.
A direct link to the above video is at http://www.youtube.com/watch?v=AjR69ddBK78
Enjoy the journey,
Rob Bryanton
Next: Poll 54 - Is Time Moving Faster?
I loe the subject of infinity, I spent hours and hours thinking about it, this is something I wrote before regarding that, which is related to what you say here.
ReplyDeleteInfinity is today so well integrated into today's language that we can scarcely imagine many thoughts and expressions without it. However, despite its widespread use, infinity is one of those objects we scarcely understand. Most of us view time as infinite and space as infinitesimally decomposable and possibly infinite,, even though both involve unmeasurable, unfathomable dimensions that defy comprehension. Yet, infinities (yes, there are several) are very, very useful to "tie" things together, to provide comprehensible models, and for the mathematician to provide a completion of mathematical theories that actually simplifies statements, proofs, and applications.
Take care Rob
Hope you are doing great