## Roadmap

- Preface
- Pedagogical Practices
- Platonism
- Well Formed Concepts
- Origin of Numbers
- Calculus without Limits
- Time as a Concept
- Closing Remarks

## Preface

There is nothing inherently evil

about a traditional liberal arts
education. In fact, what poses as a well rounded education

today *pales* in comparison to the wisdom taught in ancient
times. The original seven arts first require a mastery of grammar, logic, and
rhetoric. The next four arts are more specialized which include: arithmetic,
geometry, music, and astronomy. It doesn't matter that these skills
were taught 2,000 years ago; they will always be relevant and are
demonstrably not taught well enough in public education.
The majority of students at big universities would find better purpose
in their abilities by pursuing a vocational craft rather than fall
for the debt traps of academia because self studying and a sharp mind are free.

But as high school students are propagandized to pursue higher
education, the ones who are passionate enough about pursuing the truth see
no other choice than to sign up for the innocent

and
objective fields such as Math or Engineering. We see this now as
many college programs report an increase in STEM
applicants. They want to learn a practical skill they imagine they'll be able to use in their
professional careers only to realize it's all corporate grooming.

Academia, irrespective of field, is a tit for tat game.
If you help a professor prove

his research, he will
be more likely to advertise and vouch for yours in peer review

. There's
also fiscal corruption where money laundering incentivises academics
to look the other way

when a new ill-formed
concept is being pushed. These ideas are taught as if they were truth with a capital T.

Academia used to be a privilege for the gifted, but thanks to
the standardization of everything, colleges are available to
all walks of life, the difference this time is the rigor or the
lack there of in curriculums and the moral shortcomings of those who
teach them.
The spells and deceptions of academia do not
stop at genders studies or CRT. Not only are fields such as math, physics,
and computer science (not a science and was studied before computers)
filled with mental masturbation but the way they are
*taught* contests the original meaning of *liberal*
in liberal arts: *liber*, free and unrestricted

.

## Pedagogical Practices

The flip side of the previous point showcases what teachers
ought to do: provide a grounding or a framework for students to
stand upon to see a glimpse of Truth. Teachers must
balance student's understanding of the material and their fluency
in problem solving. Old school methods of rote memorization are great for
cranking out problem after problem. For example if we had to rigorously determine simple arithmetic
like ⅔ ÷ ^{4}⁄_{9}, nothing
would ever be accomplished. Using muscle memory frees our minds to
work on harder problems. That doesn't mean we
should neglect to understand what the question is asking: how many

^{4}⁄_{9}'ths can be repeatedly subtracted from two thirds of the unit?

On the other hand, in common core there's too much emphasis put on the understanding
side of things. Kids have to know 10 different methods of doing a
simple calculation, only one of which is the accepted

way on
the exam. Everyone theoretically knows what they need to do,
but it takes them to long to do it. Ideally you should know what
fraction division is and be able to answer a question on it
instantly. You need both the fluency with basic operations which comes with drills and
the deep understanding of why the operations are valid in order to graduate on
to the harder and more abstract problems or you'll be lost. The more calculations one does
the greater their intuition becomes; the more intuition one has the
better at calculations they become.

### Learning Styles

A rather large amount of time used to be spent on training teachers
to cater to learning styles

. VARK (visual, auditory,
reading/writing, and kinesthetic) are the four main alleged
learning archetypes for each person. While it is true that not everyone
learns the same way, when students are taught with their own
style preference, exam scores do not indicate any advantage. In fact,
when someone says they learn by seeing or doing they are just confirming their past
biases and successes, when a teaching environment that uses all modes of learning
could've been equally or even more effective.

Learning styles makes learning worse. It gives teachers
unnecessary things to tend to, and makes students reluctant to
engage with certain types of instructions. So not only is
involving multiple ways of understanding the same concept important,
but integrating many concepts to arrive at the correct way

,
or approach to seeking knowledge, is *the* fundamental skill. Philosophy, the
field of which STEM's built on,
will provide this approach

and a slew of other tools students need to apply their skill
set to something beyond profits and utility.

## Platonism

Disclaimer: The actual identity and personhood of the man we know of as "Plato" is
independent of the metaphysics he presented. Lets take a look at an
article by the lecturer Balaguer from the Stanford Encyclopedia of
Philosophy who does not take kind to his thinking. Note, many academics
will bring up topics that are completely irrelevant to the argument as we'll see. First
off, *Platonism
in Metaphysics* is redundant. Platonism *is* metaphysics:
the discussion of what's independent of the human mind. Next, he defines it as:

Platonism is the view that there exist such things as abstract objects - where an abstract object does not exist in space or time and which is therefore entirely non-physical and non-mental.

While this definition is a somewhat amateur take, it's good
enough to give anyone a basic grasp on the concept. Here's
where it goes wrong: neither space nor time are relevant where
abstract objects are concerned. In fact, time is meaningless
without matter, so to include these in the definition in an
encyclopedia shows how tethered the author is to the
material world. A better definition would be: ... - where an
abstract object is entirely non-physical, inanimate and
independent of the human mind.

Abstract objects being
inanimate, have always existed and continue to exist, whether
anyone chooses to think about them or not. These objects are referred
to as perfect concepts or noumena

(non-mental) coined by
Kant, where *phenomena* are objects of the five senses
and used in the scientific method.

Balaguer's first example, Consider the sentence '3 is
prime'

is objectively a bad choice to illustrate what
it means to be an abstract object. Numbers are already abstract
objects and primeness is a property of only certain kinds of
numbers. It also assumes you know some math which by what I've
been saying so far would not be likely as STEM students aren't
supposed to go anywhere near philosophy. Other red herrings
are creatures like unicorns

or the flying spaghetti monster

which borrow from the material world and are most certainly *not* abstract objects.
A better example would be π as the length of the
circumference compared to the length of the diameter. As
described here circles are on
the higher order of reality: a universal form, and so even an
alien civilization would be able to derive an identical
understanding of π.

Another strawman is as so:

Consider the property of being red. According to the platonist view of properties, the property of redness exists independently of any red thing.

Wrong! Properties of color do not apply to an abstract
object because color requires physical substance and light.
Abstract objects do not take on the same attributes of physical
objects: it's the other way around. Known as
*reification* or mimicry, physical symbols or objects
are used to represent abstract ideas. There is no way to reify
color because abstract objects cannot be seen.

So he goes on and on about redness

, and finally gets
to his argument: the Epistemological one, which goes:

- Human beings exist entirely within spacetime.
- If there exist any abstract mathematical objects, then they do not exist in spacetime.
- This means human beings could not attain knowledge of said objects.
- If mathematical Platonism is correct, then humans can't attain mathematical knowledge.
- Humans have mathematical knowledge therefore, Platonism is not correct.

The last two claims are so fanatical they aren't even worth analyzing. Platonism is the only worthwhile philosophy and is how the Ancient Greeks came to realize all of their well formed mathematics; You cannot think properly without understanding it. Undoubtedly, without philosophy there would be no realization of any other knowledge or science, hence why it should be included in STEM curricula, especially ones heavy in math.

## What Defines a Well Formed Concept?

### Circularity

So before we go into what it means to be well defined, we should note that in
philosophy, circularity or circular reasoning is
*acceptable*. To understand why take a look here. Essentially
math cannot prove itself, and so philosophy fills this epistemic gap by
anchoring what it *means* to be true, and accounting for why we can construct
arguments in the first place. Truth is the ultimate circular
concept. It permits its own existence.
We will be defining what it means to define a concept, so obviously
we have to appeal to circularity.

*Sometimes* circular definitions are acceptable in math.
For example, one is one. This is the law of identity, and does not need
rigorous proof. Generally speaking, mathematicians do not care
about circular definitions because it's not describing anything new.
While not incorrect, it's generally bad form and creates tautologies.
Circularity in science is strictly forbidden and is completely incorrect. This
leads us to then ask why we care about well defined concepts in the
first place.

STEM students are presented with dump trucks full of propositions and theories often without any in depth explaining. It is up to them to see why they are all supposedly true. Here is how one can systematically see for themselves if a concept is well defined:

### Conditions

- Must be reifiable either intangibly or tangibly.
- Must be defined in terms of attributes which it possesses, not of which it lacks.
- Must not lead to logical contradictions.
- Must exist as a perfect concept, independent of the human mind.

As an example, let's analyze irrational numbers. Well
we could compare the measure of the hypotenuse of any isosceles
triangle to one of its legs and call it,
√ 2 , so
we pass step one. However, in step two, we realize irrational numbers are defined as
being *not* rational, and are therefore defined by something they lack i.e. a ratio. Irrationals are
incommensurable meaning impossible to measure, therefore we could never define
them to be numbers, the official definition of which we will now move on to.

## Origin of Numbers

number - coming to the realization that the notion of number is a difficult if not impossible idea to define precisely.- Edwin Clemenz, PhD

We will absolutely demolish this claim.

It's rather surprising math major's and even computer science
majors aren't taught the formal definition of number, and even more
outrageous the professors don't know it. When studying how
numbers came to be, one must realize that *ratios* and
magnitudes (short vs long, light vs heavy) came way before the discovery of
numbers as an abstract object, just as division came way before multiplication.

One has to read Euclid's Elements, the second most printed piece of literature after the
bible, to even start to understand the number concept. In Ancient Greek
there was no word for *abstract* and it was assumed scholars
should know math is a concept of the mind, so the direct translations can get hairy / circular. By
book seven, a weaker form of geometry called algebra is introduced
through the *abstract* unit. Why is algebra weaker? In
geometry we can arbitrarily choose what our unit length shall be,
so we can physically construct the length of something like π
×
√ 2 .
In algebra, our reference length is abstracted to a dimensionless
unit, called 1

making it impossible to know the exact value
of the aforementioned quantity. Before
we can say what 1

or any number is for that matter, we need
to discuss magnitudes.

### Magnitudes

Magnitudes are measuring attributes such as length, weight or
density. They are an exact measure of a physical or visual
quantity with dimensions. They can also be used qualitatively such as, A tree is
bigger than a sapling

but this doesn't tell us by how much. For
more exact language, we need to compare the magnitude of what we're
measuring to something else for reference.

### Ratios

A ratio is simply a comparison of two homogeneous magnitudes. By
homogeneous, we mean the two lengths have a common measure. For
example, _ : _ _ and _ _ _ : _ _ _ _ are both valid ratios because both
their antecedent and consequent pieces are measured with the unit of size
_

. If they didn't have a common measure then they would not be considered numbers.
In the case of π, the ratio of the length of the circumference
compared to the length of the diameter is measureless. This is
because there is no common measuring unit or building block which can
compare them. This is why π cannot be written as a ratio or
rational number and is consequently irrational (not a number). When p : q both
have a common measure we can write p / q as the name of the
measure, and the name is what we call a number.

### Number

Number, [*nombres* in French: number. *nombre* in
Spanish: name] is the **name** given
to a measure which describes a magnitude. So, _ _ : _ is a ratio
with a common measure of _

, and so _ _ / _ is the name of this
measure. In algebra we refer to this number as 2/1 or simply 2.

In algebra there is no distinction made between ^{1}⁄_{2} and
^{2}⁄_{4}, but in geometry
while they are proportional they aren't congruent since their measure's are
different. Look at the case where we have two right isosceles
triangles whose leg's are different magnitudes. In either triangle,
we see the ratio, hypotenuse : leg =
√ 2 . But which measure yields the *real*
√ 2 ? Really neither, since there is no ideal unit in geometry. More importantly, we see that
√ 2
≠ hypotenuse / leg, because in algebra there is no such thing
as length

. So of course when we abstract out a definition
which depends on a unit length (the leg) we will get an
indescribable magnitude (1.414...).

This makes you wonder what other concepts throughout STEM are most likely intentionally left incomplete or inadvertently taught flat out wrong.

## Calculus Without Limits

It is without doubt that many calculus students dread the first few weeks of class. Why? Because it is nothing but limit theory. The idea that an object can be equal to the limit of itself is not only incorrect but extremely confusing for new students. Dancing around the idea of zero divided by zero being indeterminate yet the basis of the fundamental theorem of calculus is silly. What if I told you all of calculus could be done with no knowledge of infinities, infinitesimals, or even knowing what a limit is?

### Derivatives

Here is the mainstream single variable definition of a derivative which any calculus student knows by heart:

If you haven't taken calculus the geometric meaning of the derivative
is as follows: given any smooth and continuous curve, the secant line
(a line which touches the curve twice) eventually *becomes*
the tangent line (touches the curve once) at the coordinate *(x, f(x))*, as Δ goes to zero. Here's
a visual:

The definition certainly gives you the correct answers but why confuse students with the zero divided by zero nonsense? Also, they find it rather cumbersome to learn a different derivative rule for each type of function. Surely there is a systematic method which does not involve limits.

In this diagram we can observe by similar triangles that the
slope of *any* tangent line
is given by the slope of a parallel secant line. The secant line is
given by connecting the coordinates
*(x - m, f(x - m))* and *(x + n, f(x + n))*, where *m, n* are the
distances to the left and right of *x*, the spot
we are trying to find the slope at.
We will derive an auxiliary equation which gives us *m* with our
arbitrary choice of *n* at any *x* in an example.

So from the total rise over run in the diagram, we can yield an alternate definition of the derivative without limits:

Different values for *m* and *n* are possible, but
what isn't is *m + n = 0* because m + n represents
the distance of the leg of a triangle. If m were to equal n
we wouldn't have a secant line. Two non-zero positive rational numbers cannot be combined
to equal zero, meaning our denominator never equals zero.
This demonstrates our definition can never be undefined.
Now we have to work out how we get *m* and *n*, then we're done.

Let's find the general derivative of *x*^{3}:

We can now hopefully see we have our answer in the form:

Q is the auxiliary function which always equals zero. Instead
of throwing this extra information away like in mainstream calculus
we can use it to find values of *m* or *n*. By completing the square,
we can express m in terms x and n or vice versa.

Using the quadratic forumla:

Obviously if all you care about is the general derivative itself,
the last part is not mandatory. For functions like sin(*x*) we'd
plug in the Taylor series expansion. Keep in mind the discovery of the derivatives to
the trigonometric functions had to come AFTER the discovery of
their Taylor series expansions. Note that
Newton worked out these Taylor series by trial and error in *De
Analysi*, but Brook Taylor
formally generalized polynomial expansions for all functions.
To prove derivatives without first appealing to derivative rules the function in mind
needs to be in polynomial form.

Going back to differentiating sin(*x*), all the odd degree terms
will cancel and we'd be left with the even middle terms, giving cos(*x*).
This will work for any function which is smooth and continuous. Sure,
memorizing the rule via drill might be easier, but if you wanted to gain
a deep understanding without limits it is certainly possible and even more powerful.

Here is some C which uses the root approximation method to calculate *n*
given *x* and *m* for sin(*x*):

```
#include <stdio.h>
#include <math.h>
#define e 2.7182818284590452353602874713527
#define pi 3.1415926535897932384626433832795
double f(double x, double m, double init_n) {
double r=init_n, t=0, t1=0, n;
do {n=r;
t = ( sin(x+n)-sin(x-m)-m*cos(x) ) / (n*cos(x)) - 1;
t1= (-(1/cos(x))*(sin(m-x)+sin(n+x))+m+n*cos(n+x)/cos(x))/(n*n);
r=n-t/t1;
} while ( fabs(r-n) > 0.00001 );
return r;
}
int main() {
\\ Function is called with angle, m and an initial value for n
double res=f((double) (pi/3), (double) 0.1, (double) 0.1);
printf("\n%lf", res); \\ res contains the value of n
res=(sin(pi/3+res)-sin(pi/3-0.1))/(0.1+res);
printf("\n%lf", res); \\ res contains the value of cos pi/3.
return 0;
}
```

With integrals, something clever can be done which relates to this alternate definition of the derivative. It removes the need for differentials and infinitesimals, but it's best if we save that for another day. What one should take from this is calculus was discovered in a brute force fashion as physicists in the seventeenth century were searching for a better toolkit. And thus calculus was not founded in a purely rigorous mathematical environment but from an empirical one.

One last misconception in STEM that needs to be addressed is a concept which directly relates to calculus, notably in physics. So what specifically about time in Einsteinian physics does academia get so undoubtedly wrong?

## Time as a Concept

In order for anything you say about time and theories
in physics to make sense, you must first *define*
what time is.

Right off the bat: no, time is not the indefinite continued progress
of existence and events in the past, present and future; time is not
defined by the jittering of cesium isotopes; and no, time is not the
mystical *fourth dimension*. We need to return to what makes a concept
well defined. For time to be reified we need two conditions:

- The existence of matter
- Constant repeatable action/motion called events

Take a sandglass for example, we take some sand (matter) and create
a glass tube which is constricted in its center. When ALL the sand passes
through from one end to the other at a **constant rate** we
call this an event.

Just like in geometry we can make our unit of measurement anything we like. For simplicities sake let's call the event just mentioned a cycle. Now we can measure how many cycles it takes to drive to the supermarket or for the sun to rise and set. This process determines time intervals in terms of cycles. When dealing with distances we can get a grasp of how fast we're going by forming the ratio distance : cycle.

One drawback is not everyone can reference our sandglass and know how long a cycle is. However, there is one event everyone becomes used to because it's always happening: it's the rotation of the cosmic heavens. The sun tells us the time of day, the moon tells the day of the month and the stars reflect the time of year or even the ages (eons).

If you thought astronomy being apart of the original seven liberal arts was foolish, think again. The ancients knew the intimate link between the motion of the heavens and the passage of time:

And God said: Let there be light made in the firmament of heaven, to divide the day and night, and let them be for signs, and for seasons, and for days and years. To shine in the firmament of heaven, and to give light upon the earth. And it was so done.

The book of Revelation even describes the end of time

coinciding with stars falling out of the heavens or the pausing of
their movement.

So, we use the cosmic rotation event as the standard unit of
time. We notice how one complete rotation consists of light and darkness.
The fact that these actions or motions in the sky are
*constant and repeatable*, we can verify that time can be reified.

After this, we define time as so: it is the name given
to a distance that describes the motion of a certain body of matter
from one position to another at a **constant rate**. Note
the definition of time almost identically lines up with the concept
of numbers. This is exactly Aristotle's view: time
is a number of motion.

In our definition we could easily have focused on *mass* instead of
*distance*. If we define a second as the number of times a
cesium-133 atom performs 9,192,631,770 oscillations,
we are STILL describing a mass, and a constant repeatable action,
although this is the materialist's view on time. The definition would be:
time is the name given to a mass
that describes the decay of a certain radioactive material from one
state to another, not as intuitive. Whichever scalar we choose, we more importantly should know
the concept of time describes the occurrence of an event and
distinguishes the event from all other events that do not occur
simultaneously or concurrently.

Now that we have defined time in terms of what it possesses, we can check off step two from the
well definedness criterion. For step three, lets assume the
previous definition of the concept led to logical contradictions. Then it would follow
that we would **not** be able to distinguish one event from any other, which if true,
you would not be able to read this article. Reading requires distinguishing one event
of processing a word or group of words from the next event. So obviously, the concept of
time couldn't lead to a logical contradiction (paradoxes are not necessarily contradictions).
Finally, we should confirm time is non-mental i.e. a noumena.

When we measure time we use a physical device like a clock
or a sun dial. That does not mean time is a physical quantity.
There is no particle made of *time*, and if there were you'd have to
be outside of time to manipulate it which by the first requirement of
reification, would imply you are not made of matter. You'd be timeless, spaceless and all eternal.
So just like numbers we know that time exists independent of the human mind. Therefore
we have passed step four and have rigorously shown time is well
formed. It isn't up for debate or a mystery

that needs string theory to be explained.
Einstein did not understand what time is, and consequently anyone
who teaches his guess work is also deceiving you.

## Closing Remarks

Do not think you're protected because you're enrolled in a STEM program. Anything which modern academia touches turns to filth. In no way should you disregard pursuing a degree but always remain skeptical of what is being taught. All it takes to commit an atrocity is to teach and instill one absurdity. Given that the left brain dominant occupy the corporate ladder, the pharmaceutical industry, the industrial military complex, space agencies and the intelligence community: STEM students have the utmost responsibility of not succumbing to their ideologies by challenging the convenient lies told to them in school and beyond.

These lies are used as a grooming ritual to render students useless on their own,
especially in corporate environments.
Thinking for one's self is only encouraged for menially niche tasks and often
ostracizing when it isn't
in the range of acceptable discourse. Stem's broad range of disciplines
breeds busy bees

, a destructive and containerized hive mind network, which is already here
and will be the demise of what we know of as Western Culture. How so? We don't need more
engineers, we need people who can fix stuff. The fear mongering that being a jack of all trades is risky,
has produced worker bees who can only do one thing well. The stigma that
trade skills and the arts are antiquated will inevitably turn people into useless-meaningless
husks of nothing when left to their own devices. White collar jobs are a spiritual dead end.

What can you do? Rise to the occasion. Challenge professors or other peers when you are presented with an ill-formed idea. See past deceptions by learning real philosophy. Learn a side trade / skill. Start thinking about how you can gather multiple streams of income and focus on building a family. God bless.