"Hetware" wrote in message news:B9ydnbLZL9RKbx_PnZ2dnUVZ_hSdnZ2d@megapath.net...
On 11/12/2013 1:44 AM, Lord Androcles wrote:
> 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? ========================================================== I'm not talking of a test flight in some puddle jumper here, but a fully tested operational machine meeting all the rigorous requirements of the CAA in Britain or the FAA in the United States or the military. The very existence of drones shows aircraft can be pilotless and having worked for many years in flight simulation I know the capabilities computerized flight. Pilots taxi from gate to runway, the plane flies itself from runway to runway, pilots taxi from runway to gate. they are needed to avoid collision with other planes on the ground or in the air, but if ALL planes were FULLY computerized the pilot would be redundant, the control tower would take over with each plane reporting its position and velocity from its GPS. Yes, I have no problem with the programmer being anonymous, I use London Transport's Dockland Light Railway which has driverless trains.
> 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. ======================================================= We are all different and that is our strength. The Spruce Goose was a sea plane because nobody made tyres big enough for it. You learn by rote that an aircraft needs tyres, the details you leave to the tyre manufacturer who you trust to make for you.
> 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. ========================================================== Preliterate children are usually entrusted to young women hardly out of school themselves. Soon they are thinking finding a partner and raising their own, math is not a priority to them.
> 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.
==================================================== As another contributor said, computers don't think, they calculate. If you want to gaze in awe at a pattern look at the Mandelbrot set, which is entirely computed generated in the complex plane. z = (x+iy), z^2 +z is a rotation and a translation. http://mathworld.wolfram.com/MandelbrotSet.html That may be your forte.