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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
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(3789 previous messages)
rshow55
- 06:27am Aug 18, 2002 EST (#
3790 of 17697) 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.
About looking at a case, looking at a pattern, figuring
The Odds of That http://www.nytimes.com/2002/08/11/magazine/11COINCIDENCE.html
and making a judgement about whether the pattern is real, or
coincidental.
Facts about the number of combinations of possibilities are
crucial. The factorial series is THE most basic of these
facts.
A sense of how big the factorial series is - and how it
grows is basic - - both practically and morally, too,
because results have moral consequences. It is absolutely
central to understanding how human reasoning can possibly work
- and how closure, by reasonable standards, is actually
possible.
To know how necessary it is to eliminate possibilites - and
check. To know how easy it is to be wrong. But also, to know
how real and reassuring our chances are, quite often, of being
right. (Chances, not certainties.)
When we ask, in a defined case, what truth is, what are our
chances of finding it?
Numbers matter. Some numbers matter so much, it seems to
me, that everybody, including politicians and clergymen,
should have a sense of them.
rshow55
- 06:56am Aug 18, 2002 EST (#
3791 of 17697) 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.
When we ask, in a defined case, what truth is, what are
our chances of finding it? That depends on a lot, for any
particular case. But chance plays a part, and often a big
part.
Here's a simpler question, basic to evaluations of the hard
question bolded just above.
. When we're "looking for a needle in a
haystack" "How big is that haystack?"
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!)
Here they are 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
These are huge (or tiny) numbers.
Narrowing down the number of possibilities makes a HUGE
difference - even when we're just talking about random
searches - and when there is order in the system, narrowing
down the possibilities can be MORE important.
The differences that come with simplification are so great
that they make differences of life and death -- and the
difference between learning and not learning.
Focusing matters.
rshow55
- 07:12am Aug 18, 2002 EST (#
3792 of 17697) 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.
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?
How much can it change the odds, when basic
relationships get mastered, in a situation which really does
have basic order?
3696 rshow55
8/13/02 2:23pm ... 3697 rshow55
8/13/02 2:27pm 3698 rshow55
8/13/02 2:35pm ...
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. That's both a challenge and a source of
hope.
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.
Statistics isn't everything - but it is a lot -- and some
basic sources of fear and hope can become clearer if we
understand how The Odds of That http://www.nytimes.com/2002/08/11/magazine/11COINCIDENCE.html
change as information is focused to near-certainty. There is a
lot of coincidence in the world, but much order, too. If we
work at it, we can very often tell the difference when it
matters.
On missile defense, and on other defense issues which are
matters and life and death, and matters of $1200 per year per
american, it is worth the work to get much clearer than
we are. For all sorts of practical, moral, and aesthetic
reasons. Survival being one of them.
MD1075-1076 rshow55
4/4/02 1:20pm
My chances of getting the proposal described in many links
in MD1075-1076 isn't great just now. But if I could get my
security problem solved - get my situation clarified in
writing --- how those chances would improve !
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