noodlings of a day:

grand slam season, especially Rafa in the finals, and we get to test whether the sleep timer on the electronics can beat out Rafa's match. The vast majority of the year, two hours is plenty, until it's F1 season, or racing season, or tennis season...

I've a handful of thought balloons on this article, about the universe, cosmology, and a couple of old ideas dating back to at least Feynman and Gell-Mann (M G-M just passed away about two weeks ago as of this writing):

1. Always with the unanswerable questions. If he did nothing else, one of Hawking's most useful contributions, in my observation, was to have recognized cosmological imaginings can be connected to real predictions, at least around black holes (Hawking radiation, if you're following along). Most of the rest of these sorts of things in this end of the pool are a long, long way from finding their way to testability. Well, except for those of us who write science fiction... 2. Ok, now a question. Hawking and Hartle were interested in the Wheeler-DeWitt equation, most especially "What's the simplest solution that looks like something we can all call a universe?" And they came up with one. With a boatload of assumptions, sure, but there's no question the solution they generated has a vaguely recognizable utility with respect to the thing we look out into the night and gasp over. How then the Turok et al (TFL) paper, which says "No, we like our approach much better" and then go on to show that Hawking/Harle's solution doesn't show up for a different set of assumptions? And, in the TFL assumptions, we find a solution that doesn't appear stable, doesn't even vaguely resemble a universe we experience... here where we're just us theorist chickens, gang this is fun, but I'm not seeing why I shouldn't default to "interesting but not useful, yet." 3. Related: I have to cry foul on the use of imaginary here. We're out here where the isomorphism to the matrix algebra (or at least a Wick rotation?) should be inherent; dragging "i" back into it smells like drifting to anthropomorphism. That it leads to what looks like a dynamically unstable long-term solution with unrealistic density distributions makes me wonder if we've gone too far here. Summing over all histories should mean summing over all histories, not just the ones that "look" or "feel" "right". I'm not saying HH didn't have a similar issue, but now we're into the realm of counting "who's used the least assumption" and that's where we can only come back to comparing against the empirical observation...

Completely different note/observation. Our daughter is taking a couple of extra classes this summer. She's trying to line up her regular schedule over the rest of high school. The math class she's taking is "the one". That is, the one that every budding mathematician runs into, the one that makes you work.

It goes like this: early classes, disciplines, and the young math geek can "see" the solutions easily. So she writes them down, and enjoys the experience. Dad nods along, waiting for the moment... when the solutions she sees don't make any sense. And she has to learn to work through the algorithms anyway. That's the tough part, because she's now having to learn habits Dad has been years pointing to, saying "You'll need to be careful, these tools will help." And now it's come. Easy becomes hard, and hard-headed now gets in the way.

It's short term but delicate. I went through it, from observation it happens in all disciplines, not just mathematics. The key is navigating the short term storm in such a way that she doesn't spend years "hating math" because of it. Which can happen. I don't think it'll be an issue here, she's only showing simple frustration. But I'll get to do some extra homework this summer, as well.

Theorem: science is two-sided, rational map and empirical map. The two go together. Yet, from observation, one or the other tends to get ditched. Get too married to the rational argument, the beautiful logic, without murdering your darlings, and it's amazing how easily one can ignore that you're having your nose rubbed into it by the universe.

Or, on the flip side, only "results" matter. And if you've never seen this one go wrong... one failure mode here is to jump from "result" to result and not realize the incidental successes are essentially random until you hit the wall.

I put empirical results in quotes there because data is noise unless there's an a priori rationale. Hypothesis and measurement are iterative, and skipping over one or the other just makes a mess.

No clues, here, except that learning to be humble in the face of uncertainty is often key to complex endeavors.