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Sun, Jul 15 2007 1100 Adding Gauss was six years old when,
one day the teacher was fed up
with the paper airplanes, so she told the kids to
add up all the numbers from one to a hundred
while she is going out for coffee.

5050, he said, before she left for the door.

How did you know? she panicked.

Its simple really:
Add the first to the last, you get 101.
Add 99 to 2, still 101.
.
Add all the way to 50+51.

Counting 50 times 101 in all.

1+ 2 + 3 +...+ n = n*(n+1)/2

Fri, Jul 13 2007 400 Functions The blending function is that which takes an apple
and turns it into apple juice.
You can also use the blending function on strawberries
and get strawberry juice.
But you can't blend oranges.

For clarity, we will call this function "blended()".

We use parenthesis, (brackets),
to show that a function acted on something
by writing like this:

blended(apple)

and then we can write down the result:

blended(apple) = appleJuice

and

blended(x) = xJuice

but only if x is in the universe where blended() operates.

the function:
double(x) = 2x
can be drawn easily on paper:

Make a horizontal line from one side of the paper to the other.
Divide it into 21 parts by drawing short vertical lines
across the line, and number them from -10 to 10.
Lets call this drawing "The X axis".
The Y axis is vertical, and is otherwise the same.
Once you draw it, we call the drawing, "The Axis System".

If X is 5, than double(x) is 10,
so we draw a dot above the 5 on the X axis, (where x=5),
at the height where y=10.

double(-6) = -12 and is not on the paper,
so we draw all the dots from x equals -5 to 5,
and connect the dots with a ruler.

Together with the axes, we call this drawing now:
"The graph of y = 2x".

What would you blend to get absolutely nothing?

Well, if you put nothing in, you'll get nothing back,
that's for sure.

But is it that obvious that you cannot put a few ingredients
that would cancel each other out and you'll still get nothing.
For example if you put in the blender
matter and anti matter in just the right quantities?

The root of a function is the value of X where the value of Y is zero.
So at least one root of blended() is also zero.

Finding the root of a function is like solving an equation:

blended(x) = nothing.
What is x?

y = double(x)
what is X if y is zero?
y = 2x
0 = 2x
2x = 0
x = 0

But with the function:
y = 2x - 2
the root is 1.

So what is the root of y = x*x?
Zero.

of:
y = x*x -4 ?
2, right.

Well if we look carefully, -2 is also a root of this function.

The equation:
square(x) - 4 = 0
Is the equation to find the root of the function:
y = square(x) - 4

If in an function definition x is squared,
but no higher powers are there,
we call the function a Quadratic function,
and the equation a Quadratic equation.

I you draw the line of the function, the roots of the equation
are those where y=0, or when the line crosses the X axis.

We also use letters for the numbers in the definition itself,
and not to be confused with the numbers from the axes,
we take the letters A,B and C for the Constants in the equation,
and X,Y for the variable numbers from the axes
we originally marked X and Y in our drawing of the graph.

y = a*sqaure(x) + b*x + c

The quadratic equation to find the roots of

a*sqaure(x) + b*x + c = 0

If all this down to earth mathematics
was a bit stressful,
nor Aquatic, which is more on the Oceanic side,
that math can predict the future,
that the suns will rise tomorrow,
in a galaxy, far, far, away....

Keep Up the Good Work.
 guitar
Fri, Jul 13 2007 155 Gauss His true genious was to connect mathematics and reality,
by prooving and classifying from reality,
the true axioms of mathematics.

In math, we first take axioms for granted to be true.

If we use a system of logic where the axioms are not true,
then the system can only be used for teaching logic:

What is true then, in an axiom, if we can not proove it is true,
to make it different from the axioms that lead to
no Aristotelian logic constructs that we will ever use?

This is in fact the difference. They pertain to reality,
and Gauss has shown us that,
through mathematics.

In complexity theory -
a field in computer science theory that deals with
the complexisty of computer programs -
there is this set of very complex problems called
NP complete.
These are defined by means of a concept called Reduction.

A reduction is a logical transofrmation of one problem
to another.
If one can reduce problem A to problem B,
then B must be a harder problem or equal,
and if B were soleved,
then A is considered solved,
because it is reducible to a solved problem.

Computer science theorist have collected a large set
of such problems, showing reductions in both directions,
thereby establishing equivalence of the problems,
without ever solving any.
They are too complex, probably, to be actually solved.
But if one is ever solved in the future,
then automatically all others are solved too.
From a theoritical standpoint,
this concept is very powerful.
A world of logic consturcts with many reductions
after long research, has been built,
atop a foundation yet to be discovered.

Reduction is a mathematical construct, not just a concept.
It is a methemtical description of what logically
constitutes what is termed by this, and proof
of why it is logically correct.

Gauss connects math to reality. It is implied
by looking at his conclusions from the mathematical point
of view of reductions, and follow aristotelian logic.

The primary concept is obvious:
Reality can be counted,
and pure mathematical deductions can be drawn.

But if a certain demographic of reality can be
prooven statistically to be correct,
whereas we know this fact also to be correct
from other observations of reality,
then we can take the statistical conlusion from Gauss
to be inhetrently correct, because we know it to be true
from other sources.

This being the case we start a process of reduction
that will in the end up saying the follwing:

The axioms are prooven to be true, (in as far as reality is true,)
in all cases where the conclusions regarding reality,
which we otherwise know to be true somehow,
where the axioms are used in mathematically
arriving at the same known conclusion.

The details of the reduction process itself are not important
in this case, but it is worth noting
that the same can probably be prooven
by other means, even though mathematical proofs
in general do not necesserily work if you reverse
the order of deduction.
"A prooves B" does not necessarily imply "B prooves A",
and so a reversal may or may not be logically correct.

In other words, Gauss has classified the axioms
of mathematics that were used for prooving the central
limit theorem as correct.

The axiom, and the thorem are equivalent,
to the extent that conclusions from the theorem,
can be shown from other means to be correct.

For example, if election poles match statistical predictions,
then it is proof that A+B always equals B+A.

Tue, Oct 09 2007 100 Heisenberg and Prokofiev Each sees their own image of reality.
One sees facts and mathematical proofs
that show that the reality of the other is elsewhere.
The other sees emotions and perceptions.

And what kind of bird are You - said duck - if you can't swim.
Wed, Dec 06 2006 200 Math Three years of irrelevant truths.
Ten years later,
Kathleen Turner reaches forty and teaches you that
the university was in highschool,
so you start studying politics.
Its really all about communication and psychology,
and that, nobody knows,
so you study evolution in animals for eight years,
and then you are happy for some lingering memories
of a small collection of irrelevant truths called math.

 Cheetah

 Evolution Theory For Kids

Fri, Jul 13 2007 140 The Origin of Racism A true disbeleiving Jew can mathematically prove the Protocols of Zion from The Origin of Species.

 Star Of David

 David Bowie
Wed, Jan 30 2008 100 The Thin Difference You look thinner.
You mean I looked fatter?
The math wizes would say its the same thing.
Freud would say its the opposite.

Ha Hevdel Ha Dak
Wed, May 24 2006 1100 Video Processing - Heisenberg take 2 Turns out it takes ages of CPU time to compress and decompress the files,
as compared with the near zero amount of work done by most filters.
So it goes like this, (Tir'eh):
you can due a step, saving a new file with just the resizing stage done,
which will take about 2 hours of cpu time, and once you got this part
over with, you are safe past that stage and can continue to the next, You do the math.
Heisenberg said:
You will grow old before your computer does, and die at young age of hunger so don't argue with me, please,
it can be fatal.

of course, if you have a culture of your own like I do,
you do argue of course,
and end up being convinced anyway,
after a long period of still excruciating mental pain,
when you don't have time to eat,
and later when you wake up from this nightmare
you smile and say:
"Yeah, but look how much more I know now"
Wed, May 24 2006 500 Video Processing - TAU Short association break in the flow,
(and yes, I know it doesn't seem like flow to you just yet):

I just remembered in accuracy the event where another student caught a professor
in a mistake, it was hilarious, it went like this:
the students said, "you are wrong, because this and that, etc"
the professor, being very smart and quick, immediately replied,
"you are right of course, I had just thought of it three seconds before you said it",
the student, most instinctively replied
"and I thought of it six seconds before I said it"
almost as if saying,

"get real, we're all mathematicians here,
Freud doesn't count or knows how to,
only numbers do"

and every student in class was literally laughing out loud, and so was the professor.

incidentally, this was also in the first semester, when none of us can
be even thought to be named mathematician later in life,
so the entire conversation was in fact totally Freudian.

anyway, where was I:
Mon, Dec 03 2007 500 Who Are You How do you know what you know?
How do you know math?
How do you know English?
How do you know Drums?
Where does your name come from?
How do you like your Music?
How do you know about the swimming pool in the middle
of the water at Gordon bay?