<

Now you've stirred him up again.
If he wants to scribble nonsense on his padded cell walls, leave him to
it.
There is no need to defend yourself when you are not attacked.
Androcles.


|
| To DVM: The simple equation of x^2 = -2 does not have a root in the
| real number field. Do not confuse this with real numbers. when -2 IS
| a real number, as it often is, its square is |4|. +2^2 is also |4|.
| The sqrt of |4| can be either 2 or -2 depending on the application.
| Did you ever solve for x in two (or more) simultaneous equations?
|
| Do not confuse Einstein's math of relativity with simple math. He
| adorned his math with principle applications he misused as math and as
| applications to support his theory. Iow, he bent math to suit his
| theory and forgot about math theory.
|
| While math theory is, itself, incomplete, it is surprising that his
| application of the bending of that should represent a true objective
| reality. This is like a normaly cognizant man being infatuated by a
| younger blonde "siren". It is all built on the shifting sand of the
| immediate contemporary understanding rather than the rock of objective
| universal reality.
|
| You don't know what the real and objective study of physics is, and
| probably never will. I can say this to most "physicists" as well, so
| don't be too hurt. All you have to do is give up a certain amount of
| belief and replace it with basic logic that is firmly based on
| empiricism.
|
| Do not confuse empiricsm with reports of the same. Pound-Rebka is a
| fine example of how permiscuous an explanation of a theory can be.
| Time dilation, alone, provides the differing measurements of the
| frequency (energy) of light (em). It only through Einstein's faulty
| logic that light is also imbued with the attributes of losing
(gaining)
| energy through gravity in this measurement.
|
| The second assumed postulate (SR) is the culprit. If you begin to
| assume that OWLS in each and every frame is c, you have embarked on a
| one-way path of misunderstanding everything in this universe (except
| for how you may wish to describe it).
|
| As I have mentioned in an earlier post (probably within my last
three),
| if the top half of the structure of SR-GR were found to be false, a
| panic would ensue to prevent this.
|
| You are just simply unaware of this universe as an objective
happening.
| I hope that you are otherwise entertained and miss a real explanation
| of what gravity really is. Forever! (I hope you never find out)
|
| Back to Nth: Could you possibly UNDERSTAND some real physics instead
| of commenting about the peripheries?
|
| If you think my comments are scathing, wait until you really
understand
| more of this universe. (Of course THAT would not be considered
| scathing, would it?)
|
| Is the Earth a "moving frame"? Why or why not? What causes gravity
to
| exist besides a non-physical relationship of subjectively observed
| empirics?
|
| It appears that a true universal physics phenonemon is beyond our ken
| yet we pretend to decree it as what we want to believe. What's new?
|

Sometimes one (IMO sloppily) says that 4 has "two square roots",
namely -2 and +2, but when you see the square root sign in an

article (or the sqrt()-function in ASCII-based texts on Usenet),
then it is always that positive number.

So I repeat: you see that sqrt(anything) is a positive number.

You will find no technical or scientific article where a square
root appears in an equation and where it represents a
negative number by itself.

When Androcles sees this, he always turns mad, but since the
man is insane, that does not surprise me. If he once turned

<xxein@bellsouth.net> wrote in message news:1126145726.935797.18280@g44g2000cwa.googlegroups.com...

Nth Complexity wrote:

xxein@bellsouth.net wrote:

I will try to do this once more - but slowly and clearly.

In the context of the real numbers "*THE* square root" of a
number is defined as the positive number that produces the
original number when squared.

You might not like that, but just assume that this is the way
it is usually done.

Sometimes one (IMO sloppily) says that 4 has "two square roots",
namely -2 and +2, but when you see the square root sign in an
article (or the sqrt()-function in ASCII-based texts on Usenet),
then it is always that positive number.

What one can do to take into account the fact that there are two
numbers that produce 4 when squared, is this:

Still working in the reals:
x^2 = 5 <==> x = sqrt(5) or x = -sqrt(5)
x^2 = 4 <==> x = sqrt(4) or x = -sqrt(4)
x^2 = 4 <==> x = 2 or x = -2
So I repeat: you see that sqrt(anything) is a positive number.
And if you wish, you can sort-of say that each positive real
number has "two square roots". I would then personally add
the specification: yes, it has "two square roots", namely *the*
square root and the negative of it, the former being positive
by definition.

You will find no technical or scientific article where a square
root appears in an equation and where it represents a
negative number by itself.
Sometimes an article will tell you "that we use the negative
square root of something", but then they will write an equation
where a minus-sign precedes *the* square root expression
(which itself is positive), thus effectively making the combined
result negative. The logical structure of what takes place in the
article will then be something like
x^2 = 5 <== x = -sqrt(5)
Note the direction of the implication and compare with the
equivalences above.

So, still keeping the definition that every sqrt-expression
is positive, we can correctly write the following
sqrt(x^2) = x for all x >= 0
sqrt(x^2) = -x for all x <= 0
This way the result of the sqrt()-function is always
positive (or zero).

An example:
First let's take x = 2, so the first line directly applies:
sqrt( 2^2 ) = 2
Both sides of the equation are positive.

Now let's take x = -2, so the second line directly applies:
sqrt( (-2)^2 ) = -(-2)
Since x = -2 is negative, the result of the square root,
namely x = -(-2) = 2, is positive.
So again, both sides of the equation are positive.

Finally, lets' take x = 0, so both lines apply:
sqrt(0^2) = 0
sqrt(0^2) = -0
Indeed, in both cases both sides of the equation are zero.

When Androcles sees this, he always turns mad, but since the
man is insane, that does not surprise me. If he once turned
mad about something because he didn't take the trouble to
properly look at it, then he always turns mad over it. That
is Androcles' condition.
Do you suffer from that same condition? I.o.w. do *you* still
maintain that there is something wrong with me like you claimed
in
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/NegSqrt.html
?
Have you looked at the bottom of that page at the Maple and
Mathematica screenshots I asked a friend to create to
illustrate the point.
I think you just didn't take close enough a look at the point
I was making.

For now, I will not comment on the remainder of your post.
Perhaps later.

Dirk Vdm