> Can you pilot a plane? > Can you strip down a jet engine and reassemble it? > Can you calculate the optimum shape of a wing? > > There is no rule that says you have to do all three to be competent at > any one of them, nobody can do everything. We all rely on the competence > of others and have some specialty ourselves.
Actually, when it comes to mathematical physics, I believe it is a sin to trust the judgements of others regarding the structure of theories. To a large extent we have to rely on the experimentalist to do a good job of providing us with the input data upon which we build, and by which we test our theories. But even there, we are obliged to be vigilant.
> I'll trust a computer to fly a plane before I'll trust myself or a human > pilot,
So was a computer flying AA77, or was flight-school flunky, Hani Hanjour? Do you really want to trust a computer which is programmed by an anonymous person whose Weltlinie is not approximately coincident and parallel with yours during the flight?
> just as I'll trust a calculator not to make an arithmetic mistake. > The child should learn algebra instead of tables, the real problem is > the teachers are not competent to teach algebra so they bore the kids to > death by teaching tables by rote and the kid grows up hating math, which > is a handicap.
I was a superb academic failure, partly because I was so good at ginning up the answers on the fly, without ever firmly memorizing them. I am the antithesis to the rote learner. There are many places where learning by rote is valuable. I regret that I took little advantage of them in my youth.
> If the teacher had learnt algebra at age 7 they'd be > teaching kids algebra at age 22.
I can teach preliterate children to add, subtract, multiply and divide, but I rarely have the opportunity.
> You have to teach to principle of > multiplication, count = row * column, but not tables. Arrange 7 rows of > 9 columns and count, 63. > 8^2 = 64, (x-1)(x+1) = 7 * 9 = 63 = x^2 -1 > 4^2 = 16, (4-1)(4+1) = 4^2-1 = 15 > That can be learnt by rote instead.
A child should learn to construct his multiplication table, and should memorize the table he constructs. He should explore the patterns in the table. For example 8+1=7+2=6+3=5+4=4+5=3+6=2+7=1+8=9. 81, 72, 63, 54, 45, 36, 27, 18 are multiples of 9.