The
Very Christian Sphere (Revised)
The point where hard Mathematics and solid Philosophical and
Physics Theory meet! I like to think
about this solution, it is a lot of fun!
We typically had 8 minutes per question, (40 questions in 2
hours), and we were not told what that meant.
Nothing beyond that. I assumed
they were from 8 to 20 points each like most of our marks, so decided to go
really into the deep end on one. I
spent 20 minutes on this one. . . in 2 parts.
One for math, one for the farrows, and then some final notes.
4 questions correct was average for a grade 12 Math
Genius. They were all marked from 0 to
1 in the end. I got an 8 overall (but 4
were half marks) in grade 11, so a +1.
Even if 4 points were half points, and I got a solid 0 out of 0 on this
one, I can assume. BUT. . . I went for
the 1 out of 1.
Even if the weird math about it that you can come up with is
not remotely correct, and begs alternate possible universe questions. I think its also very Religiously and
Metaphysically sound. In Grade 11 I was
asked to represent my school in an intervarsity (between school) math
contest. One of the Questions blew my
mind, so I sought the spiritual advice of an angelic being, which consulted
with me on this matter in my head. To
phrase and frame an opinion sometimes one wishes to step out of their own soul
and form the opinion that an alien race might, when posed with questions which
become framed far too ordinarily and do not reflect the knowledge wisdom and
depth and breadth of our existence, and our intellectual education that can
come in from completely unexpected fronts.
The editor of this test called this, "The most
Christian way to possibly define a sphere." I came up with this strangely Zoroastroan and Judaic form of
describing the area within a sphere. I
have always liked that! Occasionally I
have had calls from other universities calling me the "Christian
Mathematician!" An on-file
favorite exam, they say!
I came in first place by the way, which put Campbell
Collegiate ahead of everyone. We
swapped out our grade 12s for the geniuses because Minot was involved for some
very strange reason, and this was the cold war era.
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The
Question
In traditional math the distance from the center of a
circle to the outside is its radius.
(pi)*r^2 is the classical definition of the area of a circle in 3-D
space. What do you think is the area of
a sphere in Four dimensional space?
Quick and Dirty Version:
A = (pi)*r^2
(2(pi)r^3[pppp])/3.
Roof Dooyen says that the inverse derivative of the area of
a circle
is the volume of a sphere.
(2(pi)r^3[pppp])/3.
And if you read his math it is a little like this.
Sometimes he multiplies by 2 for 2 dimensions or 2 angles.
So you might assume I got a zero on a 1/1 answer meant for
Post-Graduate Math Scholars. But the
marker decided that a farrow could be a one.
I forgot the two
on the front so
(pi)r^3 became multiplied by 4/3 and I got 1/1. Or a 0 of 0 because they could not
understand me and never could? :-{
There is a Rooph (French for Ralph)! There was a real article, the marker did
read it too! But.. . no! So either in
the end Rooph is just wrong, as he tends to be from those he has met.
[Editor's End Note: A traditional answer is that time is an
additional dimension, and thus has no effect on the area of a sphere, which is
(4/3)*(pi)*r^3. One could waggle about
and describe a circumference and the infinite triangles. . . yadayada. But this is not what was asked. Was this test leading me into Pythagoras
land and the world of infinite pink triangular trees. . . no let's not go
there.
A less traditional computer science answer would be: In
3-dimensional space the area of a sphere would be (4/3)*(pi)r^3. Using Cartesian Coordinates, it's points
when calculated extend across a computer screen with height, width, and depth
(usually in real time on a computer only the surface will be calculated but you
could do it this way to be weird). A
cube is formed from these points, the center point is really relative. And a weird way, but a common way to do the
math. These points extend into
4-dimensional space, the difference would be that this space is record across a
grid that is 4x4, and includes height, width, and depth, and time (as a
timestamp). That means each point is
there at that point in time. And thus
it must have the same area. . . as each point moves similarly across time and
space until some physical effect is applied to it.
My initial thought is that the inverse derivative
((dx)(dy))^-1 is the area of a sphere in four dimensions. [!]
Evident Proof:
This is because the derivative of the area of a circle is
2(pi)r. And the area of a circle is
3(pi)r^2. This also happens to be its
inverse derivative due to a recent proof by Rooph (Ralph) Dooyen (in Scientific
American, September or October of 1991(1992?)).
Think about how you would solve this problem perhaps, before
continuing. Don't think of the text
book answer at all. Can you think how
you might solve this problem in terms of a matrix universe, quantum computing,
string theory? [It might make my goofy
and charmingly young yet original math that much more interesting in the plus
or minus column.]
{My original answer was a bit off} Answer: 4*(pi)*r^3 [pppp]
(pi)r^2= the area of a circle, the textbook answer.
{Editor's Note: Rooph Dooyen was known to be a bit of a wild
and difficult to understand character who went off about things. So taken literally his math states that the
inverse derivative of the area of a circle is the area of a sphere, but it
doesn't quite line up. That is perhaps
the thing that has most kept me thinking about this equation for so long.
Thusly the inverse derivative of the quantitative area of
the sphere is: (2(pi)r^3[pppp])/3. This is the cartesian area of a sphere in
3D space.
{!!!Editor's Note:
The minus C takes some classes to learn. . . highly advance stuff, and a
bit theoretical. You learn this in your
6th University class or you take Physics 100 where everyone is a genius and
everyone drops out! This is the area of
a sphere.
V = (2(pi)r^3[pppp])/3 -C But 4/3*(pi)*r^3.
-C must somehow create a situation, or be explained
mathematically in a way that emulates. . .
the front. So it needs to
multiply into times two.
I don't think these weird farrows are nothing either. . .
The point in my head is not to describe metaphysics in 4
dimensions and forget about light etc.
It is to use a flat mathematics way to describe the intracasies of
physics,
and actual working relativistic physics in a mathematical
model, and lend weight to
the idea that wild and crazy math can work. As Roof would agree, and all mathematicians
and physicists if a formula doesn't work you can just work
it and work it until it does. And you can even convince yourself that something
works that doesn't and then you'd better stop.}
I will go through my proofs, and do the math altogether at
the end.
My initial thought is that the inverse derivative ((dx)(dy))^-1
is the area of a sphere in four dimensions.
This is because the derivative of the area of a circle is
2(pi)r. And the area of a sphere is
3(pi)r^2. This also happens to be its
inverse derivative due to a recent proof by Rooph (Ralph) Dooyen (in Scientific
American, September or October of 1991(1992?)).
(Editor's note: A quick proof is that the derivative of 3(pi)r^2. (Would be
(2r^2) / (2r) = r) (Classic!) Thusly (dx)/(dy) 3(pi)r^2 = 3(pi)r^2/
3(pi)r (-C) = r. . . which questions the fundamental basis. Where is -2(pi) but
it is close. . But you need to read the theorem, it is very beautiful and does
work out.)
As those who have mastered university math and computer
science know that math doesn't really work out sometimes. And underlines the fact that further
problems must occur if one is to inverse the theorem precisely. Anything to do with Sine has become suspect
as Simon Dyck, of the University of Calgary writes. As do many university authors.)
This therefore makes progress interesting and decidedly
theoretical. What is time exactly and
dimensionality? Einstein writes that
time is "a universal constant" and has been constantly criticized for
so saying. Heat is an expression of
time, as we all known. Time speeds up
as electrons and subatomic particles accelerate.
What the fourth dimension is requires five proofs to prove.
I will define a proof as the symbol: ∴
It would be too easy to say three dimensions of area are the
same. Within a four point matrix, the
matrix will not remain constant, but assuming that the universe was on a flat
grid, as on a compute memory chip, it will need a fourth pointer. What each point here is and means varies
greatly across the ever-moving-ever-evolving (growing more than shrinking
currently) universe.
The first proof is the proof of time. This is the fourth dimension and our
quantitative jump forward. And yet
dimensions are not created because they exist.
I will provide proofs of this combination effect which leads to the
creative process of a fourth dimension.
There is no Descartian God of dimensionality. There is the existence and its substrate and
a constant-ness within the ether which combines and recombines. The universal substrate does not suddenly
elicit a form which evolves forward, and creates a universal lightning without
a push, that combines and recombines forms beneath this substrate.
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∴ 1
I will define as the principle of a single dimension and its
quantitative complexity as a farrow, or a sheave, (I use Egyptian heiroglyph
sometimes), or the pawn symbol here: p
p
There is a single backbone projecting the existence of
dimensionality that is eternal, yet unchanging. Without movement, or motion, or growth. A creation, but not a realizable one without interaction.
(Editor's Note= With one p
the dimensions are mad. There is no
dimensionality merely an absence of dimensionality. We are sort of missing the Null Set [] Samosud. Which you are not allowed to say in ancient
Judaism, so that's okay, maybe.)
pp
One existence multiplied by another existence. There is a dual existence that is
penetrated, what was immortal is now intrinsically intertwined and flawed. It dies almost the moment it is born without
additional context and clarity.
ppp
Three existences multiply into a creative quantity, and
create a motion, movement and modality, which moves outward, yet is
destroyed. Perhaps eternally. [All that is created exists and fails over a
universal constant of time, yet time is a partially created structure, sutured
into the modality of an infinite moment of birth and death]
pppp
Four existences move the perceptive illusion of a solidity of
time, space, and the shadows, and perspective of other dimensionality and their
interference wave points. All creation
is at war with destruction. [We create
the illusion, yet a fragmented and displaced one of a non-constructed infinite
universe which will in time fail. Its
expansionary and destructive, strings and superstrings (or your version/vision
of them) begin to manifest and change shape.
Is light real or illusory? Black
exists. What else?]
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[Editor's note: Why
stop at 4? I guess a time limit. [[4[p]]]
is easily describable to a human being yet does not fully describe the fourth
dimension. There are further nuances
that must be substituted in and factored out.
I have since realized that it would probably take 120 volumes to
describe the [[8[p]]]? Maybe the best way to describe that would be
to have optional (farrowed sections).
It would be interesting to describe the rest of the proofs. This is where we are just getting into it
and it ends. What about [[16[p]]]?
∴ 2 The Concept of Area In Space
A circle is defined as a point with a center, around it are
equidistant points, these describe a sphere in three dimensions. [Editor's note: possibly in any four
dimensions, but not pharoahs]. The area
of a sphere is the space < or equal to those points. As Rooph Dooyen points out, it is infinitely
probable that another race or entity could view a sphere from an entirely
different way of viewing, perhaps having access to 5 or 7 dimensions of
evolved, dimensional, senses or scientifically constructed gear to assist said
senses. And yet it would still appear
to be a circle because of its unique even-ness.
Why does gravity
love a sphere so? You could define it
that way.
I am going to
define it as a construct of the background existences improbable, yet
infinitely active way of interaction.
And later on maybe I will sort on a subtractive constant to these
forces. Either way the fourth dimension
is very tragic for math. Computer
science blew away all the traditional theories of its structure in the 60s or
70s so lets make some new math for the new era.
[Editor's Note: Either way the main point is that all
dimensions are not even, and not constant across the universe. Yet could be created evenly for this area of
space. And calculated evenly within
that vicinity. . . when we study string theory.]
∴ 3
So quickly, the math is here:
This is because the area of a circle is 2(pi)r. And the area of a sphere is 3(pi)r^2
3*(pi)r^2= the area of a circle. Thusly the inverse derivative of the quantitative area of the
sphere is: (4/3)*(pi)r^3[pppp]
[Editor's note: is that where is the -C
is? When we learn third derivatives in
our fourth or fifth year of studying calculus in multiple university and other
studies (3rd year for me)... we learned
that adding C in inverse derivatives at the end of an equation in highschool
Calculus was a waste of time.
Immediately that section which is not calculated emerges as the
constant. As if magically... maybe far easier to learn down the
line. I didn't think so at the time. ((4(pi)r^4) + 3(pi)r^2)[pppp]
[Editor's Second Note: Earlier on I thought
(3r-8) should be divide out. . . [pppp]
. Is (3r-8)^-1 = [pppp] . Or its expression on this level of dimensionality???]
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It is interesting to note that in the first version of this
mathematical discourse I did not mention string theory or the curvature of the
universe, or that the universe might one day not be expanding in our relative
area. Also the relativity and structure
of time and universal constants was rather bold.
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