I have found the one-time-break for large numbers; the border betweenFinite vs. Infinity; call it Second-Zero #963 Correcting Math #308 Atom Totality

Hard to believe, I dare say, that a purely fictional and nonsensical
TV show is going to
help out a math genius. Anyway, last night was a TV show on PBS of Dr.
Who, of an
episode, I think was titled "Library" about some nonsense of shadows
devouring flesh.
And of course, in the Atom Totality, time travel is impossible. I
watch these things
to sort of speak take a microvacation from all the other things I have
in mind; entertainment.
But lo and behold, this episode helped foster the solution to the
vexing problem
of seeking the border between Finite and Infinity. Specifically, the
Dr. has two "sonic
screwdrivers". And then later on, I realized, zero in Old Math can be
"defined" not
undefined, if there were two acting zero numbers. Enough of TV talk,
for I never want
to leave an impression that anyone's time is well spent by watching
TV, and just the opposite.
We do know from science that as much exercise as one can get is
beneficial, and as little
of TV viewing as one can get is beneficial. I presume, also, that as
close to zero viewing
of TV is better than those that watch too much. I watch the news and
the weather reports as
a necessity. And about an hour or two of entertainment per day whilst
fixing dinner and eating
dinner. Also, last night was a Red Green episode where I had a good
laugh about this
animal control officer facing a muskrat that squirted him in the face.
About the funniest Red
Green while eating and made me laugh so fast that some of the food in
my mouth was
ejected was when Green was pretending to serve Mike Hammer a bed and
breakfast with
grapefruit juice. But I guess my alltime best laugh was the garage
that could not fit two full
cars, so Red engineered where he parks the second car on its side.

But getting down to business. Old Math has division by zero as
undefined. This is a cover up
for the lack of Old Math to well define the border between Finite
versus Infinity.

All of these items have one thing in common:
1) zero division undefined
2) log-spirals cannot start at the point 0 in the sequence 0, 1, 1, 2,
3, 5, 8, . . .
3) ellipses versus circles versus parabolas versus hyperbolas in conic
sections cannot
have unbounded numbers but must have a border between them
4) the rectangular-hyperbola Y = 1/x must have a bound as it
approaches zero
5) the square root and any roots of numbers must have a border between
finite versus
infinite or else Algebra and Number theory has no numbers that are
roots. The Old
Math believed that 1.4142...... was the square root of 2, when in
fact, it is easy to prove
that in Old Math such a number multiplied by itself can never yield
2.00000...... for it always
leaves messy nonzero digits or non9s (1.9999......) to the rightward.
In other words, in Old Math, they have no sqrt2. In New Math, where a
border is found between finite versus infinite, that all Finite
numbers have roots.
6) And finally, the number zero in Old Math where zero is the divisor
is undefined. It is undefined, because Old Math never defined the
border between finite versus infinity.
7) The number "e" is a special number, a one time break number for
Calculus, but today
I am going to provide a second log number that is the second one time
break number in
mathematics. It is the number 1/(19^(22*22)

This post is already too long so let me summarize.

Log-spirals are defined as equiangular. That is there sole abiding
main feature. The golden
ratio log spiral comes from the Fibonacci Sequence and involves phi
which involves sqrt5.
The golden ratio log-spiral must use the sequence 0, 1, 1, 2, 3,
5, . . . But that is impossible
because no golden ratio log spiral can start with 0 and have all the
angles equiangular. The
solution is that the start of the log spiral is not at the point 0 but
at the point 1/19^(22*22). If
the log spiral starts at 0, then its angle is not equal to all the
other angles of the golden ratio
log spiral.

Another example is the hyperbola in the first quadrant of 1/x which
has infinite area under the
curve. The only reason it has infinite area is because of Old Math
division by zero is undefined. So now, let us find that MicroWorld
Second Log or Second Zero. We construct the rectangular hyperbola so
that it is in all four quadrants and forms a open ended 4 pointed star
shape figure. We ask, at what
number between 0 and 0.1 can we start a golden ratio log spiral, and
simultaneously ask, at
what angle do we **offset** the rectangular-hyperbolas in those four
quadrants such that they
intersect and form a quadrilateral in hyperbolic geometry? Here we
have one number that offsets the golden ratio log spiral so that it
can exist and we ask for the same number that offsets the hyperbola of
1/x so that it forms a quadrilateral in hyperbolic geometry.

This is a "one time break number" just as "e" is a one time break
number for 1 in calculus.

This new number, call it Second Zero or Second Log is 1/19^(22*22).

In Old Math, they had a funny notion of negative infinity, since they
never defined what infinity
means in the first place, that their negative infinity was awfully
more ridiculous than their positive infinity.

In New Math, negative infinity is from Second Log to zero and that
whenever we are confronted with division by zero, we replace zero with
Second Zero.

So the area under the curve 1/x is a finite area because we have to
slip in
19^(22x22) = 8.2554901045277384397095530071882e+618

When we do conic sections, in Old Math, they had the ridiculous notion
that there where
an infinitude of ellipses between slices of an angle 0 to 1 degrees as
well as an infinitude
of ellipses between angle 1 and 60 degrees.

The flaws of Old Math:
a) refusing to precision define finite vs. infinity by stating its
natural borderline
b) with no precision definition of finite vs. infinity, zero divisor
had to be undefined
c) with no precision definition of finite vs. infinity, irrational
numbers were hallucinated
d) with no precision definition of finite vs. infinity, no golden
ratio log spiral could be
constructed or existed because of zero as starting point.

Now all of this makes sense, if we start from Physics and ask, was
physics ever bothered
by division with zero? No, and in fact, Quantum Mechanics says that
the vacuum of Space
and Time is filled with energy, so in physics, division by zero was
fair and square, but that zero in physics was not the 0 of mathematics
but rather this Second Zero of 10^-618.

Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies

Archimedes Plutonium wrote:
(snipped)

Log-spirals are defined as equiangular. That is there sole abiding
main feature. The golden
ratio log spiral comes from the Fibonacci Sequence and involves phi
which involves sqrt5.
The golden ratio log-spiral must use the sequence 0, 1, 1, 2, 3,
5, . . . But that is impossible
because no golden ratio log spiral can start with 0 and have all the
angles equiangular. The
solution is that the start of the log spiral is not at the point 0 but
at the point 1/19^(22*22). If
the log spiral starts at 0, then its angle is not equal to all the
other angles of the golden ratio
log spiral.

Another example is the hyperbola in the first quadrant of 1/x which
has infinite area under the
curve. The only reason it has infinite area is because of Old Math
division by zero is undefined. So now, let us find that MicroWorld
Second Log or Second Zero. We construct the rectangular hyperbola so
that it is in all four quadrants and forms a open ended 4 pointed star
shape figure. We ask, at what
number between 0 and 0.1 can we start a golden ratio log spiral, and
simultaneously ask, at
what angle do we **offset** the rectangular-hyperbolas in those four
quadrants such that they
intersect and form a quadrilateral in hyperbolic geometry? Here we
have one number that offsets the golden ratio log spiral so that it
can exist and we ask for the same number that offsets the hyperbola of
1/x so that it forms a quadrilateral in hyperbolic geometry.

This is a "one time break number" just as "e" is a one time break
number for 1 in calculus.

This new number, call it Second Zero or Second Log is 1/19^(22*22).

In Old Math, they had a funny notion of negative infinity, since they
never defined what infinity
means in the first place, that their negative infinity was awfully
more ridiculous than their positive infinity.

In New Math, negative infinity is from Second Log to zero and that
whenever we are confronted with division by zero, we replace zero with
Second Zero.

So the area under the curve 1/x is a finite area because we have to
slip in
19^(22x22) = 8.2554901045277384397095530071882e+618


Let me try to furnish some details for the above.

Let me make a ascii art sketch even though bad, it still helps.

The curve 1/x in first quadrant looks like this ( tilted about 60
degrees.
Now the full four curves in all four quadrants looks like this:

) U (
^

Sorry about the U and ^ but those were the only symbols close enough
to
what I want of four hyperbolas in the four quadrants with Y = 1/x
rectangular hyperbolas

And keep in mind that they do not intersect any of the axes, but that
is exactly what
this borderline between Finite and Infinity is going to end up doing
is making those
hyperbolas rotate so that they intercept and form a hyperbolic
quadrilateral.

So I want to rotate those three out of four hyperbolas so that they
form a hyperbolic
quadrilateral.

And how much of a rotation is required to do that fulfillment of
forcing those hyperbolas
to become a quadrilateral? Well if my estimates are correct, that
amount of rotation of
three of those rectangular hyperbolas will be 10^-618 per every
revolution of a log spiral
that emanates from the origin.

Now I shift subject to the Golden Ratio Logarithmic Spiral and tell
you what is wrong with
it. It involves phi and the Fibonacci Sequence of 0, 1, 1, 2, 3, 5,
8, . . . and the wrong
or flaw of it is that 0 is the origin but it is a "one time break" in
all of pure mathematics. It
is not arbitrary or convention but embedded into the fabric of
mathematics that it is
impossible to generate a Golden Ratio Log Spiral and use 0 as the
first starting point. Why is this? Because the log spiral is
equiangular and to start at 0 for the golden ratio log spiral is
impossible to have that first angle be the pitch of 17 degrees
(approx) at 0. So how is this
corrected or rectified so that the golden ratio log spiral can start
and come into existence.
And the answer is that the start of the golden ratio log spiral is
offset from the 0 origin point
and that number for the offset is 1/19^(22*22) approx equal to
10^-618.

So you see what I am doing. I find a flaw in mathematics that is
inherent in mathematics. The Golden Ratio Log Spiral is the sequence
0, 1, 1, 2, 3, 5, . . . so we cannot do anything about
the 0 and the fact that we have to use 0. But we cannot start at 0 for
it thence has an angle not equal to the angle the golden ratio log
spiral must have of 17 degree pitch. So pure math
has this special number of 10^-618 as the starting point, which is
slightly offset of zero in
order to have the golden ratio log spiral.

Now I use that golden ratio log spiral and transpose it onto the
Cartesian Coordinate System with those four rectangular hyperbolas of
1/x curves. I ask myself, if I make that offset with the Golden Ratio
Log Spiral, how will that affect those three rectangular hyperbolas?
And the
answer is that at the x = 10^618 and y = 10^618 that the rotation
would create a Hyperbolic
Quadrilateral.

So as you can see, this number is very special and intrinsic to pure
math. It is a one time
break number just as the number "e" is a one-time-break number. In
fact it is related to "e"
since "e" is a quantifier of rate of change and the windings of a log
spiral are rate of change
of size concomitant with same shape.

There is only one number in mathematics that allows the golden ratio
log spiral to come into existence and this same number closes the
hyperbola of 1/x forming a hyperbolic quadrilateral
at 10^618.

This number is very special, just as special as pi and e, and perhaps
even moreso, for it is the
number which is the natural and pure borderline in mathematics for
Finite versus Infinity. Anything above 10^618 is infinite and anything
below 10^-618 is infinite.

Now that creates a new problem, in that we have always considered 0 to
be superbly finite.
but now we are going to have to have a convention saying that 0 is an
infinite number and
not a finite number, just as our conventions that 0^0 = 1 and 0! = 1.

So it is a brand new day on New Math with a bright warm shining Sun
and clean fresh air.


Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies