1. What I Understand of Math
Neifert, B. K.. Three. Kindle Direct Publishing, ©2022. pp. 136 - 138
One only exists if it represents a real object.
Half of one is equal to one if one makes the new half its own distinct form.
Addition, subtraction, division and multiplication
Comprise the four functions which describe all natural laws.
Pi is equal to the circumference of a circle, if the diameter is one.
The area of a circle is equal to Pi, if the diameter is two.
There are laws to how lines interact, which limits physical shapes.
i exists in three dimensional space only if the x, y, and z axis represent three dimensional space.
e only exists in motion.
Pi is calculated from lines of calculus atop lines of calculus, and infinite formulas over infinite formulas, and cannot be calculated by a single equation.
The quadratic equation can be used to calculate any four sided object's area.
Negative numbers only exist if physical objects are bisected by axis.
E=MC^2 means the energy which comprises an object is equal to the mass of that object times the speed of light squared---then, if any energy is added to that object and makes it move, one adds the velocity of that object times the speed of light squared.
All laws of physics can be represented in physical space.
The parabola of Quadratic Equations displayed on a graph correspond to real world arches, and the laws of gravity.
The axioms of Trigonometry create finite solutions for real world objects, and so do all other axioms of geometry.
The axioms of Trigonometry and the axioms of Geometry can be combined to find more complex shapes.
In the polynomial x^2+2x+34; x^2 is the solution to the equation squared, 2x is the solution to the equation times two, and 34 is how many more units of one can fit into a four sided object. If this can represent a real object, the solution will have at least one positive answer. If not, the answer will be either negative, or have i within the solution.
The quadratic equation works based on the geometry of four sided objects, and within the algebra, one can understand the very workings of quadrilaterals.
Calculus can be used to determine a square root, because it is a simplistic logarithm of division, which can be represented by calculus.
Newton's Laws of Motion and Even The Laws of Thermodynamics can all be represented by division, multiplication, addition, and subtraction. These basic functions can be used to represent all forces in the universe, including chemistry, motion and the laws of matter and quanta.
The Laws of Euclid state that all finite matter, with finite lines, can only divide into a finite object a finite amount of times.
The Planck Length is the smallest unit of solid matter known to man, however, energy exists beneath it as infinite vibrations. Therefore, all matter is vibrations in an infinite vacuum of space, both macro and micro.
Infinity is the only rational way to explain the Universe---for, even if the universe expands, there is that which it expands into. For, there is no place, rationally, where empty space will not be. There will not be a place where there does not exist.---Therefore, infinity is the only means by which we can determine the universe... true infinity, not numerical infinity.
Chess is not truly an infinite game---not in the true sense.
Aleph Null, being the infinite set for one universe and all the multiverses within it, can be duplicated by a second Aleph Null of another universe with multiverses within it.
The Higgs Boson Field is discovered because a Muon, if calculated to be equal with the ratio of the mass of electrons, only appears at less of a percent than the electron when a beauty particle splits. Meaning the Higgs field is the difference of that which binds the subatomic forces.
2. Ellipses
Neifert, B. K.. Three. Kindle Direct Publishing, ©2022. pp. 200-201
The Ellipsis is a beautiful shape
Its area can be calculated simply,
Yet, its circumference---the less difficult
Of the two calculations, presumably---
Needs calculus to be discovered.
Wouldn't math be much better taught
With a ruler
A piece of string
And a compass?
Calculus first taught
By the circumferences of Ellipses?
Algebra first taught through the Pythagorean Theorem?
Order of Operations taught through Quadratic Equations?
And Grade Schoolers taught arithmetic by measuring lines?
Euclid's Elements taught,
So students aren't indoctrinated in baseless deductions?
Math might then be a little bit of fun,
If Order of Operations were taught with Einstein's Theory of Relativity
Or algebra taught by the formulas for Electricity?
What could be harmed by it?
If more advanced math were learned on chemistry
Instead of rote deduction?
Rather, the student would be taught all the minutia of algebra
Without the absurd notion that endless deductions must always be true.
Simply put, algebra and logic both break down
When entered into the realm of imaginary physics.
The largest problem with the modern world
Is the student's ability to thoroughly explore deductive proofs for their own beliefs,
Yet haven't been educated
To see whether it really works.
The moral philosopher sees only what she wants
While the wisest mathematician believes in the pure fantasy of algebra.
3. Gödel's Theorem on Why God Exists
Neifert, B. K.. Three. Kindle Direct Publishing, ©2022. pp. 214
Gödel's theorem at its simplest,
Is this, "If it is necessary for God to exist,
"Then God must exist."
Simply put, civilization is falling apart without belief in Him.
Basic human constructs of right and wrong are ignored.
People are attempting to abolish basic human rights such as freedom of speech, mobility and religion through the absence of belief.
Goodness cannot exist---purely---if there is not a God
Because then Goodness would always be relegated back
To men and their faulty judgments.
We seem unable to even define gender without belief in God
The most basic and obvious of all truths.
People don't understand what love is without Him.
It seems, that it is necessary for there to be a God, therefore, He exists.
4. The Test of Apollo and Apollos
Neifert, B. K.. Three. Kindle Direct Publishing, ©2022. pp. 32-33
Athena, when trying to differ who was the wiser of the two men, took Apollos and Apollo to Greece, and brought them both before Euclid. Athena knew the wiser of the two men was Apollo, yet the more intelligent of the two men was Apollos.
Thus, Paul accompanied them to the philosopher, and set them to answer three questions, each of varying degree of more difficulty.
First, Apollo was asked the very first principle of the Elements. Apollo answered, “If the two equal circles are made, so points of the line A and B are the two circles' centers, where their circumferences conjoin together, lines drawn to it shall make equilateral triangles. For the circles, therefore the lines, are equal.” Apollos answered the same.
Then, came to the next question. Apollos was the first to answer, without the others' knowledge. He had said, “There shall never be an end to prime numbers. For, each one discovered, there shall always be a new one. For there is always one number greater still, than even the combined products of any number of primes in succession.” To which Euclid was well pleased, and so was Athena.
But, when it came to Apollo, Apollo had said, “There is no way to prove that prime numbers do not end. Therefore, what we know of them cannot be complete.” Athena furrowed his brow, and knew this was not enough. Surely, Apollos knew this too, yet had faith that prime numbers would never cease, for he believed in order. It was evidence that Apollo might be the wiser of the two; therefore, the fool among them.
The third question was posed to Apollo first. “Can there be lines drawn within a circle any number of times?”
Apollo gladly answered, “Why yes, of course. For there is infinite space between the gaps of all matter. There is always a shorter and shorter distance in which a line can be drawn. There shall always be space by which measuring degrees shorten.”
Athena thought wisely, “This was a very wise answer.” Surely this is a man of understanding. Yet, what about his twin brother?”
Thus, Apollos answered, “Given that the quill's ink has finite dimensions, too, and the circle itself is finite, no matter how many lines you draw, there shall always be a limit to the lines. For, the ink with which we create carries forth its own dimensions in space and time, otherwise it would be naught. Therefore, there can only be a finite number of lines drawn in any given circle.”
Athena was wildly impressed by this answer. Euclid had thought to add it to his elements. Yet, Apollo's was wiser, still. Surely, Apollos understood it well, and even mused on it, but Apollo was wiser in his conceit, to have godlike imagination and thereby see the gaps between everything.
Yet, Apollo professing to be wise, had cheated off of Apollos, thus, he would claim to understand the finitude of the universe. Yet, even there he was too wise; for, Apollos never said the universe was finite, nor did he ever ascribe limitations to man's measurements. He, rather, ascribed that where there is a finite thing, there can only be finitude.
5. Homer's Theorem
Neifert, B. K.. The Wisdom of B. K. Neifert. Kindle Direct Publishing, ©2022. pp. 243 - 244
I learn from this,
"The square roots of the two shorter sides' sum
"Of a Right Triangle
"Is equal to the square root of the longer,"
In purely logical form...
The equality breaks down
And Algebra ceases to function.
Take the Pythagorean Theorem.
If one square roots the C variable, and square roots it again,
The same must be done to the opposite side.
Creating Homer's Theorem.
Frighteningly, I see the problem with modern mathematics,
In that when we are taught pure deduction,
We are never taught the practical applications.
Thus, Algebra breaks down where there is nothing
Extant to base it on... or at least it can, as proven by Homer's Theorem.
Coincidentally, the Pythagorean Theorem also
Breaks algebra in itself, that it wouldn't exist
If one could merely square root both sides of an equation.
Then, necessarily, A+B=C is the same as A^2+B^2=C^2
If this axiom holds true.
Which, if it did, well, then there'd be no discovery.
Of course, I'm probably not the first to have trifled with this.
So, I'm confident there is an explanation.
6. Euclid's 35th Law
Neifert, B. K.. The Wisdom of B. K. Neifert. Kindle Direct Publishing, ©2022. pp. 246 - 247
Intersecting Chords Theorem---
Again I have encountered something
I cannot understand.
It's as plain as day that this works.
I had it proven to me
By Presh Talwalkar,
Yet, my mind is incapable of knowing why
It works as a first principle.
How can anyone say God doesn't exist?
If God is infinitely wiser than any man---
I don't know why this simple axiom works...
I, like you,
Have to rest on faith that it does...
Errata---
I do now understand Intersecting Chords Theorem.
It is not the lines which are being measured as equal
But the segments of the circle as a whole.
However, some minds cannot attain to this knowledge
Therefore the previous is still a cogent argument.
And there are many things my mind cannot attain to, as well.
Errata again: The products are equal, due to the geometry
Of a circle; it will limit the dimensions of the line's segments,
And due to the perfect symmetry of a circle,
The factors of the two products of line segments will be equal.
They will make equal products.
7. A Squircle
Neifert, B. K.. The Wisdom of B. K. Neifert. Kindle Direct Publishing, ©2022. pp. 268
A rounded square
Which to determine its dimensions
Is so laborious a calculation,
Yet, nonetheless, simply exists
In many utilitarian ways.
There are many innocuous things
We take for granted in life.
Even in some simple shapes,
There are such eccentricities
That it would take a Doctor of Math
Just to figure them out.
Of which, I am not one.
But, I pleasantly muse
Over their formulas
Knowing that greater minds than mine
Are hard at work.
8. Triangle
Neifert, B. K.. The Wisdom of B. K. Neifert. Kindle Direct Publishing, ©2022. pp. 278
One would think the triangle
Be a simple shape to plot
In algebra.
Nope... its simplest requires calculus.
Its most elegant requires three lines of equation.
One can, indeed, make any shape
From linear equations;
I'm confident of this.
A good poem is formed like an equation---
Instead of numbers, one pieces together
Psychology and Sociology;
Nature and History;
Philosophy and Religion;
Wisdom and Action.
And like a triangle, simple
Things we take for granted,
Such as the existence of God
Or the why of good and evil,
Can be very difficult to figure out on our own.
9. Heron’s Formula
Neifert, B. K.. The Wisdom of B. K. Neifert. Kindle Direct Publishing, ©2022. pp. 347
An inner circle with a radius of 1
Within a triangle, so said the Mathologer,
Where every two lines meet by one radius on the perimeter of a triangle,
Their corresponding angles follow the pattern “A+B+C=A*B*C”
Where each value is equal to the length of each of the two equal lines of one angle
Which make line segments at the three points of the radii.
There must be other oddities like it,
Found in other patterns.
Just like Quadratic Equations figure for values squared,
But will also correspond to real world quadrilaterals;
As that’s how they’re actually solved.
10. The Limit
Neifert, B. K.. Bread of Harvest, Opal Steeples, ©2022. Kindle Direct Publishing, ©2022. pp. 238 -239.
We can find the limit.
But, we cannot cross it.
It's the fundamental crux
Of calculus.
There are limitations to human
Imagination.
Limitations to human science.
Limitations to human understanding.
Because, there are limitations
In the real world...
We can simply understand the limit.
We can calculate the Bible
That Jesus' Morals are good...
From there, solve through Sine
That the rest of the Bible speaks
The Law---but, we'll never reach the limit.
We'll never know the full measure.
We'll continually approach it...
Yet, each infinitesimal distance
Is infinitely wide.
The limit is Christ,
And like calculus,
We must have faith that it solves---
We'll never feasibly touch infinity.
11. Pyramids
Neifert, B. K.. Bread of Harvest, Freedom Steak ©2023. Kindle Direct Publishing, ©2022. pp. 305.
The reason there are pyramids
On different continents,
Is the same reason there are sleds
And feathered arrows
On different continents.
It is not a conspiracy
Of an ancient, Aryan civilization
Which academia is hiding.
It is because what's possible
Will always produce similar structures
Of Logos.
12.Calculus in Tanka
Neifert, B. K.. Bread of Harvest, Freedom Steak ©2023. Kindle Direct Publishing, ©2022. pp. 352 - 353
A limit can be
Calculated, true; but the
Calculations can
Never approach the limit---
It's where infinities touch.
A sine function works
On the logic of Pi. So,
The sine function will
Work off considerations
Of circles' geometry.
Zeno's Paradox
Is calculus. The leaps are
The calculations
While the limit is the place
Where man and reptile meet.
One can measure the
Sermon on the mount, and like
Calculus, measure
The Golden Rule to fully
Calculate and find Jesus.
13. Why P Cannot Always Equal NP
Neifert, B. K. Artemis XX. WordPress.com. 2023. https://brandon.water.blog/2023/07/06/artemis-xx-2/.
It's the proverbial Squaring of the Circle.
The limits of Coefficients in a system,
Which would create NP, cannot always
Be described by P, due to the limitations on geometry.
Every system of equation is defined by a shape.
And simply put, there are limits to every shape
Which makes it impossible to conform some shapes into other shapes.
I think anyway.
In fact, through further rumination,
If P could always equal NP,
It would break down the very notion of equalities.
P equaling NP
Would be the same as saying
πr^2=l*w.
Fundamentally, the axioms of one shape,
Cannot translate to another.
If they could, there'd be no use for mathematics.
In fact, I'd further say,
That if P equaled NP,
One would have a universal equation
And System for solving all axioms of Geometry.
Which, fundamentally, cannot be true.
As Pi is no more described in a square
As Length and Width are described by a radius.
The shapes have different axioms
By which they must follow,
Which require new calculations on their part
To describe each geometric figure.
So with, any Nondeterministic Polynomial
Cannot always be equated into a Polynomial.
As each Nondeterministic Polynomial
Will be defined by its unique shape and dimensions.
Simply, it cannot be so.
Therefore, Some NP cannot be equal to P.
14. I Am By No Means a Mathematician
Neifert, B. K. Artemis XX. WordPress.com. 2023. https://brandon.water.blog/2023/07/06/artemis-xx-2/.
I am by no means a mathematician.
However, when I come to P = NP---
Dazzled by the complexity of the equations---
I look at each equation like a shape.
As if each equation represented a simple shape;
Or, even a very complex shape.
In my limited exploration of geometry,
I know a few very basic things.
One cannot take the shape of a Right Triangle,
And use the Pythagorean T heorem
To explain an Isosceles.
And seeing that NP and P
Can be reduced to this principle,
At its most basic level,
The most fundamental thing to learn
From this system, is that we CANNOT
Generalize a rule for all shapes.
We cannot, for instance,
Call an equation a polynomial
If it has three dimensions, for example.
If there is a cubed variable,
The equation no longer is a Polynomial.
I think people approach the problem
From the angle of where I approached
Pythagorean Theorem.
It seems intuitive,
To think the proof lies
In the hypotenuse being like a crossed section
Of a quadrilateral.
But, that is not why it solves.
It seems possible...
Even very likely,
To where you'll be duped into thinking it.
But, upon keen observations,
And studying the equations and dimensions,
You find it cannot be so
As it would break down equalities and the laws of algebra.
So, also, I think NP equaling P
Would be the same notion,
Of it seeming intuitive,
That a solution can be made.
But, generally, what's intuitive can be deceptive,
And what's more, you cannot define
The Pythagorean Theorem for a Circle,
Any more than Pi would apply
To a Square.
Sure, one can make equal anything,
But by means of deduction,
There is no way outside of empirical observation
To determine a shape, and how the laws
Of objective space apply to it.
Adding the dimension of time
Further complicates this, and makes even more complex shapes,
Which I believe, its geometry, must be studied independently
For each individual problem.
Much like the philosophers of auld would study shapes
To determine axioms and principles.
Thereby, one must study the shapes
And derive new axioms for each individual shape.
And possibly, that will be the occupation of many brilliant minds come the future, what will.
15. Quadratic Equations
Neifert, B. K. Artemis XX. WordPress.com. 2023. https://brandon.water.blog/2023/07/06/artemis-xx-2/.
A difficult mystery...
Every Polynomial represent
A shape---
Thus, the Quadratic Formula
Breaks down those shapes into two dimensions.
Hence, why it gives a length and width
For its answer---
Also, how Cubic equations
Give, the added dimension of breadth.
Thus, by reducing the equation down to one dimension,
One can figure what they need in that one dimensional space.
This is also why P cannot always equal NP
As NP can often work in multiplicities of more dimensions.
16. Fibonacci Numbers
Neifert, B. K. Artemis XX. WordPress.com. 2023. https://brandon.water.blog/2023/07/06/artemis-xx-2/.
Symmetry---
You Fibonacci numbers appear in nature
Because of your symmetry.
You appear because of the soundness of your structure.
Phi---you are Nature's Rectangle;
You are Nature's Symmetry---
You are Nature's sounding board
For the entire structure of the universe.
17. Circles
Neifert, B. K.. My Collected Writings. Kindle Direct Publishing, 2021. pp. 255 - 258
Mr. Emerson, may I just attain
What you said about circles.
It makes me first get offended.
As is true with all wisdom and
All truth, we resist it at first.
We do not like things to be
So simple, nor do we appreciate
Patterns we ourselves have not attained.
Yet, looking at the mountains
The trees, my palm, my fingers
My gloves, the rocks,
My calves, the cow’s horns
The lizard’s ovular body
The worms, the flies which are
Shaped like eggs,
The grasshoppers which are shaped
Like fingers, the birds
Which are shaped almost ovular
The frogs, which when scrunched
Are like a little oval
The bushes which are ovular too...
And cats and dogs and horses when they lie down.
I do say I see the pattern as well.
And I do believe I have a theory on why.
Pi---being infinite, as is the infinite measurement of the curve---
Must inherently be the natural order of geometry.
So everything, running off, and smoothing over by rain
And evolving over time,
Naturally must produce a circle.
As, Pi is the natural shape, the natural
Number of nature, by which all other things are dictated.
Surely, it has its subtle imperfections
Making each specimen different,
But given the natural shape of all things
Are likened to a circle---
And what is straight
Often we can assume was man made,
How men create things in squares
And nature its circles---
I do say it’s an
offensive little thought.
That I hadn’t attained it first---
Maybe I equal you in genius
For giving an explanation as to why---
Is it the infinite reality of Pi
Which causes this?
That number naturally representing
The geometry of a curve
Therefore, randomness must
Inherently, be shaped into curves.
For, the patterns in nature show
That all things, built by God,
Are as a curve. Men build in squares
And God builds with circles.
Because men must shape our environment
To order, and God must shape His environment
To the natural world toward that infinite
Shape, that infinite number Pi.
And Mr. Emerson I do not plagiarize you
Rather, as you said about great poets
Writing in an age where there are few,
We take all things and make them our own.
But, my solemn task is finding in the past
Things which ought to be remembered by all
For a better future.
Another peculiar thought.
It seems that man is the only creation
Of God’s which is like a rectangle.
For, the Golden ratio
By which men create and shape their world,
Is dictated by the rectangular shape of our body.
No other creature is dictated by its rectangular
Form. None which I know.
For, they are either cones, spheroids
Or outright shaped like circles.
The Human body, when standing upright
Exhibits the Golden Ratio;---
That being Five to two.
So do trees, so do bushes,
But only human bodies seem to be nature’s rectangle
Which may be why we prefer them in our creations.
But this strange ratio has been told to me
By a much beloved professor
When describing the Acropolis
Which is fitted to our human shape;---
Which does appear in nature;---
Perhaps it is nature’s rectangle
Which we men are formed closer to----
Yes, it is most defined in our human form.
For, perhaps these two measurements
The measurement of Pi
And the measurement of Phi,
Perhaps these numbers are scientific
Facts, oblong and shaping the world
Through their infinite order.
Perhaps Pi is nature’s curve
And Phi is nature’s rectangle
Both working together
In their infinite measurements
As if planed and scaled by God
Like the Bible said,
"Wisdom was with God when he Planed the Scale of the Earth".
For, by observing this order,
I am confident that God exists.
For, these measurements create
Upon the earth, and define all Aesthetic Beauty.
That, and of course, Fibonacci’s sequence;
Which repeats itself through all natural shapes.
For some reason, these numbers lay down the law
Of how our natural world gets shaped by the
Eons of textures and winds, and rains.
And, certainly, to have such geometric certainty
As this---for randomness cannot truly occur in nature
According to these principles---
It must be that an architect, by design
Created our world.
And as certain as these mathematical principles are
Which are observed in everything from trees
To mountains, to rock formations
And even the Grand Canyon and Niagara Falls,
So are the moral principles laid down by Christ
As certain. Which, Mr. Emerson,
Is my scientific foundation for believing in Him.
18. Fibonacci and Pythagoras
Neifert, B. K. Artemis XX. WordPress.com. 2023. https://brandon.water.blog/2023/07/06/artemis-xx-2/.
Fibonacci, your secrets are serene---
We can spend a lifetime studying you
As the Cat on the Mathologer's shirt
Bends to your hurricane of Phi.
Even Pythagoras, yes...
Bends to your will.
For, take four of your numbers in a square
Lined up in their sequence from the lowest on top
And the highest on the bottom,
Left to right,
And when cross multiplied completely,
Make legs and the hypotenuse of a right triangle;
Yes, one value even must be doubled, but how serene!
Know its inner circle, like a soul
Tangential to the Right Triangle's form.
And what's this?
Do you know the squares made
From the exterior of each line of the triangle?
That's how Pythagorean Theorem works?
So, the radii of exterior circles
Also, by cross multiplication,
Fit by three Euclidean Squares of Pi.
So also, counting by Fibonacci,
While working through Fibonacci
Creates Pythagorean Theorem's roots also;
Even when a number counted
Is not a Fibonacci number.
19. Two Black Maidens
Neifert, B. K. Artemis XX. WordPress.com. 2023. https://brandon.water.blog/2023/07/06/artemis-xx-2/.
Two black maidens set their minds to proof...
They do their math, and prove
Calculus, they use, to prove Pythagorean Theorem,
Yet Calculus is proven so much, so
That Pythagorean Theorem is proven too!
And Pythagorean Theorem proven so, that Calculus is proven new!
It is a biconditional,
Two Tautologies that necessitate.
The very crux of Equalities,
And the very crux of all mathematics and logic.
It is how, oh my souls,
That science knows.
20. Squaring a Circle
Neifert, B. K. Artemis XX. WordPress.com. 2023. https://brandon.water.blog/2023/07/06/artemis-xx-2/.
Squaring the circle
Is impossible; take aught
That exists... still can't.
To break the circle into
Quanta, it still can't be done.
21. Square and Square Roots
Neifert, B. K. Artemis XX. WordPress.com. 2023. https://brandon.water.blog/2023/07/06/artemis-xx-2/.
Take one square and take
A line, and cut it down the
Middle. Then do it
Again perpendicular.
See each line segment's a half.
Then, note that the areas of two lines
Is equal to one fourth the square.
Then note 3+4=5 is not
True. But 9 + 16 = 25 is true.
Thus, by square rooting the variables
You incur the dimensions of one dimensional
Lines of a right Triangle.
Also, the quadratic equation reduces
Polynomials to one dimension.
How? By intuiting the axiom of
Of a square or rectangle, by the three
Coefficients. So that the equation
Breaks down into length and width
And represented by the two factors.
Know that length and width breaks down
To one dimensional lines.
So also, negative and positive
Numbers square into the same numeral;
Thus, also into length and width.
Why P won't equal
NP, is that some NP
Cannot be a square.
Reflections on Math as Poetry; Blog Exclusive
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