Running into giants

Ya know how the quote goes...
"I only saw further by standing on the shoulders of giants"

The trick is you actually have to climb the damn giants to do that. Instead, there are two contrary paths that an awful lot of people take...one of which is up close and personal right now.

1. Make the giant squat...stand on his back, and see almost as far as he did. I worry that a good chunk of academia does this.

2. Work your ass off, finding one new idea after another, learning and clawing, dragging ideas out of the mud, and then sit down exhausted and find...Euler did it first.

I don't care much about the first option, but the second option is interesting to me because I've run into it twice in 24 hours, and semi-frequently before.

When I was in college being all math-geeky...I got a senior thesis assignment from my professor: a problem he was kind of working on (q-analog of the problem of derangements). 6 weeks later, I brought him a solution...6 weeks later, he figured out what I had done. After a bit, he searched the literature, and found that the simple version of my result was already out there, in a military application. And then he found an interesting equality in my results (Infinite product = infinite sum)...and then later we determined that Euler had been there first. It was fun...but science rewards precedence, not rediscovery. It makes me feel like a real mathematician though, to do original work, and discover Euler got there first.

Yesterday, I was reading Vernon Smith's book: Rationality in Economics, and was smacked in the face again by work by geniuses that got there first. First, Smith talks about Hayek's discussion of constructivist vs. ecological rationality. Guess what...that's Sowell's constrained vs. unconstrained visions, sitting in Hayek's The Fatal Conceit. Then he goes into a discussion of know-that vs. know-how, and again cites Hayek, and indeed Adam Smith.

Ok...so deflated, I go home, put the kids to bed, and call my friend Bob, the education guru. While I've worked loosely in education for 20 years, Bob has worked explicitly in education, and teaching education and publishing on education and ... for longer than ... I've been alive? And he has an undergrad in econ, and he just knows everything. I present my education software pitch to him...he goes through, and lists in 15 minutes, concerns that I'd taken 6 months to hash out, and then proceeds to list some more that I haven't thought of. Damn experts.

But along the way, he brought up (in a sidebar) something that I wasn't thinking about, which oddly made me feel better.

Bob is a constructivist in the educational sense instead of the Hayekian sense. Constructivism roughly means that in order to understand something, you have to build the meaning yourself. The simple version of that is frequently when someone is making mistakes at math...they don't understand the correspondence between math concepts and reality. Addition difficulties are frequently due to a misunderstanding of some deeper concept: Correspondence (4 means like 4 apples) , number permanence (4+6 is always the same answer), etc. Incidentally, both Bob and I have found lots of people who are COLLEGE GRADUATES!!!! who have problems with these things. Mostly those college graduates with these problems are people in masters/teaching credential programs who are going to be pre-school or elementary teachers.

So what...? We know you ramble, Aretae, but you are usually going somewhere.

Well...this reminded me that in general one needs experience to be able to apply the theory. If one has only theory, one has only a proposition, and not the elements from which the proposition is built. This means that the reasoning that one does from the proposition is likely to be faulty. Instead, what we should all want is enough experience in a field in order to have run into, cataloged, and identified the problems we face. AFTER one does enough work attempting to solve problems, then it is appropriate to hand someone the standard solution.

So I feel better. Sure, Hayek, Euler, Adam Smith, Vernon Smith, and my friend Bob got there first. HOWEVER, I wouldn't have a depth of understanding of the topics if I hadn't gotten there basically solo.

The good news is that I've been giving the under-theorized version of this pitch at work, when arguing about how Java training should proceed. Now I not only feel better about re-discovering topics that Hayek and Euler solved, but also, I can apply this at work. And...from a memory...Feynman seemed to believe the same thing, as his approach to understanding physics (and some other stuff) was known to involve going back to the beginning and trying to derive the whole mess of it.

Experience doing...don't try to believe you understand something without it.