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.
-----------------------------------------------------------------------------------
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.
---------------------------------------------------------------------------------
∴ 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?]
-------------------------------------------------------------------------------
[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???]
---------------------------------------------------------------------------------
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.
---------------------------------------------------------------------------------
