New York Times on the Web Forums
Science
Technology has always found its greatest consumer in a
nation's war and defense efforts. Since the last attempts at a
"Star Wars" defense system, has technology changed
considerably enough to make the latest Missile Defense
initiatives more successful? Can such an application of
science be successful? Is a militarized space inevitable,
necessary or impossible?
Read Debates, a new
Web-only feature culled from Readers' Opinions, published
every Thursday.
(3923 previous messages)
rshow55
- 10:16am Aug 23, 2002 EST (#
3924 of 3932)
Can we do a better job of finding truth? YES. Click
"rshow55" for some things Lchic and I have done and worked for
on this thread.
I've added this to the text you see when you click
'rshow55" above:
If you're looking at random combinations, and only one
possibility is right, how big is the search? How much does
it help to eliminate possibilities, in this random case?
Let's compare N! , N!/(N/2)! , and N!/(N/5!) for three
values of N . . . 10, 20, and 40
10! = 3,628,800 . . . . . . . 5! = 120 . . . . . . . . . .
. .2! = 2 20! = 2.433 x 10e18 . . . 10! = 3,628,800 . . .
. . 4! = 24 40!= 8.16 x 10e47 . . . . 20! = 2.433 x 10e18
.....12! = 4.79 x 10e8
For N= 10 . . N!/(N/2)! =3.024 x 10e4 . . .
N!/(N/5)! = 1.814 x 10e6 For N= 20 . . N!/(N/2)! =
6.704 x 10e11 . . . N!/(N/5)! = 2.027 x 10e16 For N= 40
. . N!/(N/2)! = 3.358 x 10e29 . . . N!/(N/5)! = 1.703 x
10e39
or, looking at reciprocals
2!/10! = 5.513 x 10e-7 . . . . . . . 5!/10! = 3.307 x 10e-5
4!/20! = 4.932 x 10e-17 ....... 10!/20! = 1.492 x 10e-12
12!/40! = 5.871 x 10e-40 . . . . 20!/40! = 2.978 x 10e-30
When things become known, and the number of remaining
variables gets smaller, finding answers is hugely
easier in "random" cases.
Suppose one child is trying to read a text, and knows 80%
of the words? Suppose another child approaches the same text,
and knows 20% of the words? Who has a chance?
Getting the most basic, most frequent facts and relations
straight is very important.
For fundamental reasons, for the most common things, it
is also very hard. The odds are overwhelming that both
individuals and cultures have made, and will make, many
mistakes - - many of them important and deeply embedded in
areas where performance is not good. That's both a challenge
and a source of hope.
We can do much better than we're doing in reading
instruction - and we have strong reasons to want to do so.
The kinds of things that can make reading
instruction better can make a lot of other things better, too.
When we learn basic things, the odds of our successfully
solving problems can get much better - and impossible
jobs can become possible, and sometimes even easy.
rshow55
- 10:29am Aug 23, 2002 EST (#
3925 of 3932)
Can we do a better job of finding truth? YES. Click
"rshow55" for some things Lchic and I have done and worked for
on this thread.
Adams, Marilyn Jager's BEGINNING TO READ: Thinking and
Learning about Print MIT Press 1991 is an impressive book,
and has been influential. I deeply respect it.
I've read it carefully several times.
Adams documents the prodigious amount of work and thought
that has gone into reading instruction.
As Brent Staples points out, we know a great deal, and do
some things much better than we used to - and some things
better in some places than others.
I'm going to argue, precisely from the complexity of the
situation - and the agony of many of the students -- that
there is room for large improvements - from the point of view
of almost everyone concerned - and preserving the good, warm,
useful things that are already well done.
Though there would be the need for some exception handling
at the level of doctrine.
If I'm wrong, I'll try to be clear about it - and propose
simple, testable things. I'll be doing so in the course of
making a statistical argument that is very important to basic
issues of getting fact systems to correct closure.
Including missile defense as a good and important example
much discussed on this thread.
(7 following messages)
New York Times on the Web Forums
Science
Missile Defense
|