Math is everywhere.
Everything can be assigned a number that has some meaning.
The rock you just picked up might have a mass of 40 grams with a volume of 15 cubic millimeters.
Your child might be 6 years old and in grade 1.
Your bank account has an account number and has a balance, a number of dollars and a number of cents.
At the last movie attended you may have sat in the 5th seat in the 10th row from the screen on the left side.
Not much thought is given to these numbers yet we use them day in and day out.
Numbers quantify; answering questions such as, "how far," "how many," "how much," etc.
Numbers allow us to answer these questions with no ambiguity. The concept of the number
itself is the same across cultures worldwide, i.e., 5 is 5 not 6.
Numbers form the basis of Mathematics. Mastery of addition, subtraction, multiplication
and division is prerequisite to understanding algebra. However, these operations are
intuitively valid and are proven correct using formal logic in the form of proofs.
Everyday we make 'logical' decisions without much thought. Yet, once you study Boolean Algebra you will
find that the 'logical' decisions you make daily aren't always sound, coming as a surprise to many.
Geometry sharpens decision making skills since the many theorems proved in the study of Geometry require sound logic.
Taking a Geometry course will not only result in a better understanding of geometric shapes
but it will also sharpen your decision making skills.
We use logic all day long that results in true or false.
Stating 2 + 3 equals 5 is a true assertion. Stating 2 + 3 equals 7 is a false assertion.
"If I step off this cliff I will fall." True enough, so we choose NOT to step off the cliff.
We automatically make these decisions; they are inherent to who we are. Mathematics is based on this
true false logic; one could say, mathematics is inherently part of us as well.
Studying the history of Mathematics gives you an appreciation of how civilization has
adapted over the ages. Technology and Science follow the developments in Mathematics;
most often, quite later. However, this is not always the case. Recent developments in
String Theory (Physics) require mathematics which require techniques we don't yet have to manipulate the equations involved.
Let's take a look at the ancient Greek's perspective on numbers.
The ancient Greeks, the Pythagoreans in particular, considered numbers to be reality.
Starting with, one, each number in turn had a very specific meaning and purpose in their world view.
You probably recall something about the Pythagorean Theorem, or perhaps were introduced to geometry
using a text based on Euclid’s Elements. The Pythagoreans used pictographs to represent numbers;
perhaps students (called initiates) used pebbles placed in the sand.
The number "one" was a single pebble, all by itself, a single point in the sand.
The number "two" was represented with two pebbles, three with three pebbles, etc.
However, these pebbles were laid out in a specific way. See
number shapes 1 and
number shapes 2. These
links also show how the Pythagoreans thought of numbers in terms of geometry.
Thinking this way, a single pebble is a point in space. Two pebbles defined a line.
Three pebbles defined a triangle, four pebbles a square, five pebbles a pentagon, etc.
But this is not all, the Greeks had other meanings for numbers.
The number 1 meant unity, not divisible, and the generator of all numbers (the modern Peano Axioms are
based on this concept), and more abstractly, 1 meant reason itself.
Monad (meaning unity in Greek) was their term for one.
The number 2 represented opinion, diversity, and represented
the first female number. Dyad was the word they used for 2.
The number 3 was the first possible sum of the numbers so far, monad plus dyad. But for the Greeks, unity combined with diversity
meant harmony and they called three the first male number.
(Yes, the Greeks were a male dominated society.)
The number 4 was represented as four pebbles arranged in a square,
a shape with four equal sides, and with all being equal,
four represented fairness and justice in particular.
The word "square" in “You treated me squarely,”
still rings true to its original Greek meaning.
In review:
One "monad" unity, not divisible, REASON
Two "dyad" opinion, diversity (FEMALE)
Three unity combined with harmony (MALE)
Four fairness and justice (four EQUAL sides)
One could stretch the point that Mathematics is the basis for all we do today.
"Number" pervades everything.
The beauty of Mathematics is, that with logical thought, we can extend the concept
of number to form logical frameworks to model reality itself. And this modeling
of reality forms the basis of all Sciences giving us the ability to predict events up to the
accuracy of our mathematical model. Unlike the Greeks we understand that these models
are not reality but very good approximations of reality.
All we do, and all we build involves numbers in one way or another, and the study of Mathematics
should be fun and rewarding all on its own. As one professor said to my Theory of Calculus
class, "Knowing WHY it works is far better than knowing HOW it works," which pretty
much sums it all up.
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