Big day, developmentally speaking. Also, not all stretches of 5 hours are equal.
Yesterday was a pretty big day for us developmentally speaking. Teddy made some big steps along the developmental path. But before that, let's talk about the subjective nature of time. When I was around 16, Jason (my brother for those who don't know) and I would drive to Boy Scouts together. Jason was an Assistant Scout Master and a math major at the time. We'd talk about all sorts of stuff, but I remember one conversation in particular. It was about the mathematical concept that there are different sizes of infinity. For example, there are infinite integers greater than zero. There are also infinite real numbers greater than zero. However, there must be more real numbers than integers. There are infinite real numbers between 1 and 2, for example.
What this has to do with Teddy is this: I was reminded of this conversation the other morning at 4:40, when Teddy woke Amy and me up. He'd been asleep since around 11:30, which is a good 5 hour stretch. By some definitions, that means that Teddy sleeps through the night. I'm not sure I agree with those definitions. But it occurred to me that this was not a 5 hour stretch that I'd prefer. Waking up between 4 and 5 is a pretty awful thing. No matter what, if Teddy is crying at that time, it's going to take at least a half hour to get him back to sleep, if you're lucky. If you have to change him, feed him, burp him, and calm him back down, it's probably closer to an hour. At that point, if it's a week day, you're basically done sleeping for the night, because you're not likely to get back to sleep and get any useful sleep before the alarm goes off. Getting him to sleep from 11:30 to 4:30 is not equivalent to getting him to sleep from 9 until 2, or 10 until 3. It's not even close.
First off, bravo for actually remembering something mathematical. Secondly, you're sleep deprived (bravo, nephew), and a humanities major, so you can be forgiven, but since this is for posterity, I thought I should point out that your description of the different "sizes" of infinity (mathematicians call the concept "Cardinality" http://en.wikipedia.org/wiki/Cardinality) is somewhat misleading. The rational numbers also have an infinite number between zero and one, but they are the same cardinality as the natural numbers. The difference relates to being able to create one-to-one mappings between them. The proof of this is really interesting and pretty accessible, it's called Cantor's diagonal argument, it's on wikipedia as well.
ReplyDeleteSo, you're saying that the natural numbers have the same cardinality as integers, but the real numbers don't? This reminds me of when you tried to teach me multiplication when I was 4.
ReplyDeleteWhat I'm saying is that the natural numbers {1,2,3,4,5,...}, the integers {...,-2,-1,-,1,2,...} and the rational numbers (i.e., the fractions) all have the same cardinality, but the real numbers are bigger. (They're the same size as the set of all subsets of the natural numbers, or any of those other sets.) And stop whining about multiplication. You can't tell me you never use it.
DeleteI am so glad that your time in to car to and from Boy Scouts was a learning experience as well as brotherly bonding. Although I do understand the reality of getting up at 4 am as opposed to 7 am, my motherly brain is saying, "Yes! The mother's curse is alive and well!" ...paybacks are heck, aren't they?
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