Re: On the muliplication of negative numbers
- From: "Spaceman" <spaceman@xxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Tue, 5 Aug 2008 23:52:38 -0400
Uncle Ben wrote:
On Aug 4, 5:50 pm, HW@....(Dr. Henri Wilson) wrote:
On Sun, 3 Aug 2008 19:58:19 -0700 (PDT), Uncle Ben
<b...@xxxxxxxxxxx> wrote:
On Aug 3, 6:42 pm, HW@....(Dr. Henri Wilson) wrote:
On Sun, 27 Jul 2008 14:18:06 -0700 (PDT), Uncle Ben
<b...@xxxxxxxxxxx> wrote:
It might seem strange to consider this plebian topic in a
newsgroup having to do with such an esoteric subject at the
theory of relativity, But, believe it or not, a controversy has
arisen between certain frequent posters in this newsgroup as to
the result of multiplying negative numbers, a topic generally
treated in the U.S. educational system before the 6th year
(12-year-olds).
Numbers have interested people for both practical purposes and
amusement for centuries. The negative numbers arose to provide
solutions to questions such as "What number, if any, added to 5
gives 3?" Before the invention of negative numbers, there was no
such number. With negative numbers admitted, there is.
Negative numbers pose no problem in addition and subtraction. And
multiplication of a negative number by a positive integer is
quickly understood as repeated addition. But multiplication of
two negative integers is not so quickly dismissed as a problem. I
admit that I groped for a while to think of a way to make the
solution obvious in terms of more elementary operations. One
doesn't want to say: It's a rule! Obey it!
The way I came up with may not be simplest (if you kinow something
simpler, tell me about it), but it works:
Consider 5 * 5 = 25. If one is silly enough to write 5 as 6+(-1),
one would have
(6+(-1))*(6+(-1)).=25
By the distributive law, one could expand that to
6*6 + 6*(-1) + (-1)*6 + (-1)*(-1) = 25
We all agree that 6*6=36. Now 6*(-1) =
(-1)+(-1)+(-1)+(-1)+(-1)+(-1) which reasonable people will agree
amounts to -6. Similarly (-1)*6 = -6 again. So far, we have
Therein lies your logical mistake.
You are assuming 6 'minus 1s' are the same as -1 '6s'
We all know it works...but the basic question remains. What
physical significance can be attached to multiplying by a negative
number?
Consider this, which someone sggested to me as a heuristic
explanation:
Let direction to the right be positive, direction to the left be
negative.
We agree that the work done by a force moving an object a distance x
is Fx in one dimension.
If the force is to the right and the displacement is also to the
right, the work is positive.
If the force is to the left and the displacement is also to the
left, the work again is positive.
That is a consistent application of the multiplication by a negative
number. It also shows that a negative times a negative is a
positive.
No. Direction is not absolute.
In the physical sense, both your directions are positive.
Uncle Ben
Henri Wilson. ASTC,BSc,DSc(T)www.users.bigpond.com/hewn/index.htm
All religion involves selling a nonexistant product to gullible
fools. Einstein cleverly exploited this principle with his second
postulate.- Hide quoted text -
- Show quoted text -
Just for kicks, let's take this one step further. Suppose in a
discussion I begin an argument with:
"Let x=5. ..."
If my discussant replies:
"But is x really 5? From another point of view x = -5. How do you
know that x is really 5?"
The answer is obvious. I know that x is 5 by hypothesis.
Similarly with the number line. The number line is not a physical
object. It is a logical construction. To make the left side
negative, all we have to do is to say "let the left side be
negative," and that is what we normally do. It is part of the
construction. It is part of the hypothesis.
The numberline is on a table inbetween You and I,
You tell me left, I mark the left, you say, no that is the right,
I say no, that is my left.
You say..
No..
I say Yes.
Which way is truly Negative Ben?
Do you always ignore "relativity" to support relativity?
How do we know which side is "really" negative? By hypothesis, that's
how.
I just showed you even that is "relative".
So.
Relative or "not relative and left is left to every frame?
If someone wants to make the right side negative, all he has to do is
to say "let the right side be negative." Then the right side will be
negative by hypothesis, and anyone who wants to join the discussion
normally understands that or can be dismissed as an idiot.
Hypothesis violates relativity then.
Facing each other, you can not prove that left is left.
You can say such all you want but the guy on the
other side of the line facing you has the same hypothesis.
His left is the left side of the line.
Your is not.
Who is correct?
Would you like to try this with forward and backwards also?
We will place a sphere in between us and move it
one direction.
Who will know that "forward" is the direction the sphere is
moving?
:)
--
James M Driscoll Jr
Creator of the Clock Malfunction Theory
Spaceman
.
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