I mentioned in another post that Leo is obsessed with Where’s my Water. Yesterday we were exploring gravitational lensing, and Leo turned it into a “where’s my laser” game. I don’t think I need to explain this any further; the pics are pretty self-explanatory (except that the thing in the middle is a black hole — but maybe that’s obvious).
As promised in this previous post, I’m going to report the basic plot of Thinking Machine stories after I relate them to Leo — usually at bedtime, so you’re getting this a day late (at least). I’m only summarizing the plots, because If I tried to write them out as actual stories it would take me way too long, and would never happen. I’m also not going to go into much background; you’ll pick up the cast of characters and general idea pretty quickly. In line with the goals of this blog I’m also going to over-describe the STEM-related content in the stories. I usually don’t actually get more than a few sentences into these technical aspects of the topics so as not to interrupt the flow of the story. However we do occasionally end up in an extended discussion, even breaking out the iPhone in bed sometimes to look stuff up.
In last night’s episode Dr. Evil was creating tornadoes to wreak havoc upon various state capitals for the purpose of shorting the stock market and making lots of money.
[Dr. Evil’s specific goal wasn’t really the point here — he’s Evil, after all, so he doesn’t need another goal! — but we did talk briefly about why being able to predict the future was very important for a lot of things, not the least being making money. We also didn’t talk at all about the stock market, nor what selling short means. Next week! 🙂 ]
Anyway, so the National Weather Service computers, which do weather prediction, check their predictions in order to tweak their parameters to improve their predictions. We discussed this sort of machine learning in some greater detail because it’s central to the story line. The computers had begun to notice major anomalies in their predictions, way outside of the normal prediction error … not to mention that tornadoes were showing up in places where they had never been seen before (unlikely), and state capitals were being specifically whipped out by class F4 tornadoes (VERY unlikely).
So the NWS called in Leo and Ada to use The Thinking Machine to help them figure out what was going on. Many previous Thinking Machine stories have involved weather prediction, so Leo knew that weather was mostly controlled by heat, which is mostly controlled by the sun. (Ensued a somewhat long iPhone WunderMap session looking at fronts, and our own near term rain predictions, and how a cold front bearing down on us is probably mostly what this prediction is based on, etc.)
But in this case, the weather was going crazy, so instead of calculating the forward problem, they had to program The Thinking Machine (which is, of course, done by changing the gear settings — remember, it’s essentially a Babbage Machine!) to solve the inverse (backward) problem: That is, given a pattern of phenomena, find out what pattern of heating was creating the observed pattern of tornadoes. Although we didn’t go into any more detail than this in <em>how</em> to solve the inverse problem, we did talk a little about why it’s way harder than the forward problem. I used simple math equations to exemplify this, for example, it’s really easy to do say what 5+4= … he either knows it, or can do a simple (forward) calculation to solve it more-or-less immediately. But the “inverse” problem, e.g., ?+5=11 is harder, because unless you algebraically transform it into ?=11-6, and then solve the subtraction form (which would be easy), you basically have to try a bunch of numbers, and then run the calculation forward and check the result. We did some examples. (I didn’t go into the algebraic transformation part of this discussion; we’re only starting into Algebra, but he got the general idea of forward and inverse problems, and could see that the inverse one was harder than the forward one because you had to try a bunch of numbers.)
Okay, so Leo and Ada programming the thinking machine to take the observed tornado pattern and compute the pattern of heating and cooling required to create it. (Incidentally, I have an idea for a terrific iPad game based on this scenario, in case anyone wants to collabroate on it! 🙂 )
The next thing was to recall (which Leo does, but you won’t) that Dr. Evil has a tunable laser in his hidden lair, and that he had tuned it to infrared (to heat things), and was bouncing the infrared laser beam off his fleet of reflecting satellites to create the heating pattern predicted by the inverse solution. (I didn’t get into the problem that the reflectors would have to be tuned to the laser’s wavelength as well…another time!) Then we did a little rough angle of reflection = angle of incidence, and found the satellites, which the space shuttle went out to collect in order to thwart Dr. Evil’s evil plan.
Remember, all of this was being done in the context of a bedtime story all that physics, meteorology, and computer science seems like it would destroy the interest in the story line, but Leo loves that stuff, and if I let him, we would be exploring every topic in great depth in the middle of the night.
I’m sure that it’s just a ploy to get to stay up later. 🙂