everybody take turns

Math

I’m reading a book about infinity (DFW's Everything and More). Let’s try to forget the part about why anyone would read a book about infinity. Instead let’s concentrate on one of the things I’ve learned.

First, consider the good old number line, as depicted below. As imagined, it continues to count up and up forever, to infinity.


Now, or course the number line also consists of a bunch of other numbers inbeween the tick-marked intergers that aren’t shown here. Even ignoring irrationals (numbers that can’t be expressed as a fraction, like √2), there are literally an infinity of numbers between each integer. Zooming in provides evidence:


By combining these, you could say that there are actually an infinity of infinities, or ∞^∞, on the number line.

Now we have three infinities, all of which are actually equal:

This all reminds me of a quote I once heard about Quantum Mechanics, slightly altered:

“If you say you understand infinity, than you don’t understand infinity.”


Q.E.D.

No really, thank YOU

In the mail today, I received a small envelope. It was addressed to Cassidy and Kyle Schneweis. The latter name is identical to mine, but my wife's name is Laurel Maslowski. The address was ours. Inside was a thank you card. Handwritten on the inside, it says:

"Cassidy & Kyle,
Thank you for our kitchen towels. It will complement our Asian theme nicely.
Erin Warrick & Justin Denta"

Neither Laurel or I know anyone by these names, and we don't recall giving anybody kitchen towels.

I have a cousin named Cassidy, but her last name is Emery. Or at least it was. Maybe she got married. Maybe she got married to one of our other hundred or so cousins with my last name. I have a big family, but think I would have heard about that.

Maybe this is one of those blips in the space time continuum. Perhaps in an alternate universe I'm married to someone named Cassidy and living at the same address, and this is one of the blips that connects the two.

Or maybe it's just an example of American culture getting the best of Erin and Justin. They got some tacky towels as a wedding gift, but didn't know who gave them. They decided it would be better to thank the wrong people than not to thank anyone at all. Living life with a clear conscience certainly makes it much easier to sleep at night.

If you happen to know Cassidy and Kyle, please pass on Erin and Justin's thanks for the fine asian themed kitchen textiles.

Or if you want to try to use the card as a wormhole to a different universe, I'll hold on to it for awhile.