Peace...
Problem
Hypothesis
Experiment
Observe
Conclusion
This was a scientific method given to me in 7th grade, by my science teacher. Some of the back story is, I was basically thrown out my elementary school in 4th grade, because they ran out of curriculum for me, & was planted into a school with a "gifted & talented" program, all without parental contact or permission. The irony that I didn't see until years later, was the name of the school, Golda Meir, named after the female Prime Minister of Israel @ one time...Why the fuck would a school in the Midwest USA, be named after a Jewish Prime Minster? Anyway, this led me to the "gifted & talented" Samuel Morse Middle school, where I learned to LOVE Science...I only remember one of the teacher's names though...He was a colored man with a pacemaker & scared of microwaves. He had given himself the name "Dr. Pheoc", as a way for us to remember the formula...and I refuse to eat microwaved food to this day...Anyway, the flaw in the above method is obvious to those of Us who use scientific method of Supreme Mathematics, and that's the lack of observation before the experiment (even though it's implied, it's not plainly stated)...the fact that the formula is wrong, isn't the point of this writing...
I'm around college & high school students daily, & some of them tell me that they don't like school. I can't really be mad @ em, I know there's some bullshit is being passed off as education just as well as they know it. I first remind 'em that they as least have the privilege to GO to school, and that even though they aren't promised anything, they one, better their odds, and two, if nothing else, learn the math & science (take the best part), because they can't lie about that too well...
Thinking scientifically is essential in this age of information...This day and time that We live in shows & proves that Knowledge is the Foundation...there's a so-called economic depression that's been called a recession ever since it started, and all that's telling me is that the 10% are playing with the numbers...also, I haven't seen or heard anyone mention the fact that all of this money being put into the US economy is going to DROP the value of the dollar like a hailstone, like it ain't already low enough...meanwhile, they distract Us with cartoons of chimps so that nobody's thinkin' bout that shit...& while all THAT shit is goin on, they either "taking over" your bank (so-called bailout), closing your bank (join a credit union instead), or trying to snatch the home from under your feet (if mortgage is being paid, the bank owns it outright). & don't forget, the 14th amendment was for corporations to be counted as people...& while I LOVE Living in America, I'm jus sayn, they continue DAILY...
Just like anything else though, the US & all other economies run by the 10%, are subject to the laws of mathematics...in fact, economics IS mathematics...history will show how this country was set up for this robbery/depression in the late '20s & early '30s for all of their gold (those "send us your gold" commercials ARE by design), & it's been done again...the Great Depression back then borned some of the Greatest Minds to influence recent history in America (Allah the Founder was born, then Fard came to visit, & Elijah learned how to hustle & win in that time), so what does that say for Us and how We make sense of & get through this Math in which we're "situated"? A question to ask yourself is where will "I-Land" in an economic system that's literally falling apart?
Right NOW though is a window of opportunity for the True & Living, because people NEED Good Orderly Direction amongst them through this tribulation. The job that I have is supervising, but the title is Coach, basically middle management slash training...While there's the administrative part of the job, the perk for me is that I walk & talk amongst 100+ people per day, and around 20 that I'm directly responsible towards (NOT for!!! People are responsible FOR themselves & their families). All they get from me is Mathematics, & I don't even have to say Wisdom Equality or God lol...That's 100+ opportunities to do the duty of a civilized person, so spend my day drawing people up AND I get paid for it! Teaching just happened to always be a talent of mine, that was part my problem in elementary school & forward, I got a high from embarrassing the teachers...I taught my classmates those subjects better than most of my teachers could, & I was this little kid from the hood with a mother who hadn't finished high school, they couldn't figure the shit out! Anyway, the point is, I see it as getting paid for just being myself.
We all have (or should have) talents that you can multiply with. One of my favorite parts of the bible is the parable of the talents...one man is given 1 talent by a king, another is given 2, and another is given 5. When the king returns some time later, he wants to know what the 3 have done with the talents...the one with 5 brought back 5 more, & the king gave him more... the one with 2 brought back 3 more, & got more. The one with 1 brought back 1, said he put it up & was was scared to lose it. The king called him slothful & sumthn else, & took the 1 talent back...as for the chapter & verse, I dunno, look it up...What I draw up from that though, is using what ever talents you have to make a profit. Stop following prophets, even they had trades. Use the Law of Inertia to stay in motion regardless to the time... a Trade is a plus lesson, not the other way around...
Peace...
Allah Universal
Au22
Friday, February 27, 2009
Monday, February 23, 2009
Wisdom Understanding...Show & Prove
Peace...
The Genius that Allah was, he applied 120 Degrees to Self and taught us to do the same. By doing so, one awakens to the Knowledge of Self veiled in said Lessons. And it's not about just memorizing. The advantage that We have of internalizing 120's subliminal messages (see 13*, 1-40 for that science), is being rooted in the Square of Truth. Truth, being the Wisdom of the Cipher, "naturally" expresses & impresses the Cipher, in the form of a Self-Styled Wisdom, that brings forth an Original Understanding. Other than Our Lessons, One can "internalize" just about any fucking thing else in the world and be at risk of becoming other than self...Conversely, internalizing the tools of 120 Degrees along with the Supreme Mathematics and Alphabet is the Way to Understanding Self, from Knowledge to Pluto and beyond...For real, think about it for a minute, how fuckin' amazing is that?
Allah Showed & Proved to his Nation what he said he would do. Prove that he was Allah. That's it. Other than that, there's NO "promises" with this, other than 240 more degrees if you want 'em...even if you don't, 240 is STILL there by default...otherwise known as the Unknown Ciphers...
Today's Supreme Mathematics is Wisdom Understanding...I see that as Showing & Proving...your Wisdom is what you express/Show to the world of self, your Understanding is the Proof of Self's Foundation being Right & Exact...One's Understanding of Self bears Witness to the Knowledge Self via the Wisdom of Self. Thus the placement of Wisdom in the Supreme Alphabet, the Language of those with Knowledge of Self, otherwise Known as Supreme Wisdom...Supreme Wisdom, is ways & actions speaking louder than words (Showing & Proving) as Living Mathematics...
23*, 1-40
The Wisdom Understanding degree of the Knowledge to Culture Cipher (aka Allah's Free Cipher aka Lost-Found Muslim Lesson #2 aka the 1-40) asks; "What did he promise his Nation he would do?"
That degree as Elijah gave it is "about" Yacub, yet applying the ? to Self, I ask "What did Allah Universal tell his Nation he would do?". That I would show (Wisdom) AND Prove (Understanding) my Power by taking the devil (negative influences) off the planet (my Plane of Truth), and in doing so, I Show & Prove to the 85%, 10% AND 5% that it CAN and WILL be done. It's about more than just telling people, you HAVE to Show AND Prove, or people "can hardly believe" (23*, 1-36) ANYTHING you say in the 1st fuckin' place!
Yacub told his people in detail what he would do, AND did it! This degree unlocks the ability within self to outdo Yacub...All you have to do is Show & Prove you are Allah. That's it. 'Cause only Allah can show & prove that he is Allah, and only Allah can take the devil off the planet. Period. You can tell who's who not by what they say but by what they do, and even MORE so by HOW they say and do whatever it is they say & do.
Only the True & Living can be True & Living, whether God or Earth...The Babies don't have that choice...They're already the Greatest...Everybody else is jus bullshittin...
Nowadays when examining a person that either requests 120 from me or that I think of giving 120 to, I ask myself questions like this: If I give this person a loaded gun, would they use it Righteously? Would they try to use it on me, or themselves even? Would they use it to save a baby? Or would they take it to the police when they occasionally talk people into bringing them guns for cheap? Will I literally drive this person crazy, or are they stable enough to handle the weight of examining self? (don't laugh, this Science does in-deed create some mad scientists & frankensteins...that's how the devil got here in the 1st place)
My point is, Sincerity is Key, and will allow you to get from Knowledge to Pluto and beyond...I've learned from experience that when teaching a person who is not 100% Determined to get the Lessons and Build, it backfires. Every time. I'm ALWAYS Willing, but NEVER so desperate as to give this away for nothing (6*, 1-36). And I don't understand one who would...What you Earn is What you Learn, What you Learn is what you Earn...
Peace...
Allah Universal
The Genius that Allah was, he applied 120 Degrees to Self and taught us to do the same. By doing so, one awakens to the Knowledge of Self veiled in said Lessons. And it's not about just memorizing. The advantage that We have of internalizing 120's subliminal messages (see 13*, 1-40 for that science), is being rooted in the Square of Truth. Truth, being the Wisdom of the Cipher, "naturally" expresses & impresses the Cipher, in the form of a Self-Styled Wisdom, that brings forth an Original Understanding. Other than Our Lessons, One can "internalize" just about any fucking thing else in the world and be at risk of becoming other than self...Conversely, internalizing the tools of 120 Degrees along with the Supreme Mathematics and Alphabet is the Way to Understanding Self, from Knowledge to Pluto and beyond...For real, think about it for a minute, how fuckin' amazing is that?
Allah Showed & Proved to his Nation what he said he would do. Prove that he was Allah. That's it. Other than that, there's NO "promises" with this, other than 240 more degrees if you want 'em...even if you don't, 240 is STILL there by default...otherwise known as the Unknown Ciphers...
Today's Supreme Mathematics is Wisdom Understanding...I see that as Showing & Proving...your Wisdom is what you express/Show to the world of self, your Understanding is the Proof of Self's Foundation being Right & Exact...One's Understanding of Self bears Witness to the Knowledge Self via the Wisdom of Self. Thus the placement of Wisdom in the Supreme Alphabet, the Language of those with Knowledge of Self, otherwise Known as Supreme Wisdom...Supreme Wisdom, is ways & actions speaking louder than words (Showing & Proving) as Living Mathematics...
23*, 1-40
The Wisdom Understanding degree of the Knowledge to Culture Cipher (aka Allah's Free Cipher aka Lost-Found Muslim Lesson #2 aka the 1-40) asks; "What did he promise his Nation he would do?"
That degree as Elijah gave it is "about" Yacub, yet applying the ? to Self, I ask "What did Allah Universal tell his Nation he would do?". That I would show (Wisdom) AND Prove (Understanding) my Power by taking the devil (negative influences) off the planet (my Plane of Truth), and in doing so, I Show & Prove to the 85%, 10% AND 5% that it CAN and WILL be done. It's about more than just telling people, you HAVE to Show AND Prove, or people "can hardly believe" (23*, 1-36) ANYTHING you say in the 1st fuckin' place!
Yacub told his people in detail what he would do, AND did it! This degree unlocks the ability within self to outdo Yacub...All you have to do is Show & Prove you are Allah. That's it. 'Cause only Allah can show & prove that he is Allah, and only Allah can take the devil off the planet. Period. You can tell who's who not by what they say but by what they do, and even MORE so by HOW they say and do whatever it is they say & do.
Only the True & Living can be True & Living, whether God or Earth...The Babies don't have that choice...They're already the Greatest...Everybody else is jus bullshittin...
Nowadays when examining a person that either requests 120 from me or that I think of giving 120 to, I ask myself questions like this: If I give this person a loaded gun, would they use it Righteously? Would they try to use it on me, or themselves even? Would they use it to save a baby? Or would they take it to the police when they occasionally talk people into bringing them guns for cheap? Will I literally drive this person crazy, or are they stable enough to handle the weight of examining self? (don't laugh, this Science does in-deed create some mad scientists & frankensteins...that's how the devil got here in the 1st place)
My point is, Sincerity is Key, and will allow you to get from Knowledge to Pluto and beyond...I've learned from experience that when teaching a person who is not 100% Determined to get the Lessons and Build, it backfires. Every time. I'm ALWAYS Willing, but NEVER so desperate as to give this away for nothing (6*, 1-36). And I don't understand one who would...What you Earn is What you Learn, What you Learn is what you Earn...
Peace...
Allah Universal
Saturday, February 21, 2009
Wisdom Knowledge...Chaos Mathematics
Chaos theory attempts to explain the fact that complex and unpredictable results can and will occur in systems that are sensitive to their initial conditions. A common example of this is known as the Butterfly Effect. It states that, in theory, the flutter of a butterfly's wings in China could, in fact, actually effect weather patterns in New York City, thousands of miles away. In other words, it is possible that a very small occurance can produce unpredictable and sometimes drastic results by triggering a series of increasingly significant events. 
CHAOS MATHEMATICS
The natural world has always had a chaotic way about it. The mathematical world has always been amazing complex. So why has Chaos theory just evolved as such a critical part of science, mathematics, and art?
Simple. Computers.
The calculations involved are repetitive, boring, and number in the millions. To produce the Mandelbrot Set on a single screen takes an estimated 6,000,000 calculations. Nu human would be stupid enough to endure the boredom. But a computer will. Computers are particularly good at mindless repetition. The computer is our telescope, our microscope, and now, our art gallery. We cannot really explore Chaos without it, and we certainly can't produce fractals unaided.
However, it is necessary to use the computer as an investigative tool. Most computer use is based on putting in data and instructing the computer on what output is required. Chaos Theory arose as scientists and mathematicians started to play. To put in numbers and watch as they careered around the plane, mostly the complex plane, in detailed patterns. They watched as the computer produced the numbers, and didn't just wait for the final result. And they tried different ways of plotting and exploring equations- mostly for the fun of it.
Playing with mathematicians, science and computer programming produced images which looked like nature. Ferns and clouds and mountains and bacteria. They indicated why we couldn't predict the weather. They seemed to match the behavior of the stock exchange and populations and chemical reactions all at the same time. Their investigations suggested answers to questions which had been asked for centuries- about the flow of fluids as they moved from a smooth to irregular flow, about the formation of snowflakes, about the swing of a pendulum, about tides and heartbeats and cauliflower and rock formations.
This new theory dealt with a vast range of intellectual domains. And they started plotting the fractals. Some mimicked nature. Some were stunningly beautiful. And some were just fascinating.
Chaotic Systems are not random. They may appear to be. They have some simple defining features:
1. Chaotic systems are deterministic. This means they have something determining their behavior.
2. Chaotic systems are very sensitive to the initial conditions. A very slight change in the starting point can lead to enormously different outcomes. This makes the system fairly unpredictable.3. Chaotic systems appear to be disorderly, even random. But they are not. Beneath the random behavior is a sense of order and pattern. Truly random systems are not chaotic. The orderly systems predicted by classical physics are the exceptions.
There is a strong link between chaos and fractals. Fractal geometry is the geometry which describes the chaotic systems we find in nature. Fractals are a language, a way to describe geometry. Euclidean geometry is a description of lines, circles, triangles, and so on. Fractal geometry is described in algorithms- a set of instructions on how to create the fractal. Computers translate the instructions into the magnificent patterns we see as fractal images.
Sunday, February 1, 2009
4*, 1-36
Peace...
I know, I know, I'm 2 days early in regards to today's degree, whatever, better ahead than behind...been doing more reading than writing lately, here's an excerpt from one of the titles on my list (The Language of Mathematics: Making the Invisible Visible)...It's more Eurocentric than anything (I took out some of those parts), but those that know, will take the best part...All Emphasis is My Own...Peace...Au
**************************
Excerpt from the prolouge of:
The Language of Mathematics: Making the Invisible Visible
Keith Devlin
ISBN 0-7167-3379-X (hardcover)
ISBN 0-7167-3967-4 (paperback)
1. Mathematics—Popular works. I. Title.
QA93.D4578 1998
© 1998, 2000
What Is Mathematics?
It's Not Just Numbers
What is mathematics? Ask this question of persons chosen at random, and you are likely to receive the answer "Mathematics is the study of numbers." With a bit of prodding as to what kind of study they mean, you may be able to induce them to come up with the description "the science of numbers." But that is about as far as you will get. And with that, you will have obtained a description of mathematics that ceased to be accurate some two and a half thousand years ago!
Given such a huge misconception, there is scarcely any wonder that your randomly chosen persons are unlikely to realize that research in mathematics is a thriving, worldwide activity, or to accept a suggestion that mathematics permeates, often to a considerable extent, most walks of present-day life and society. In fact, the answer to the question "What is mathematics?" has changed several times during the course of history.
After Newton and Leibniz, mathematics became the study of number, shape, motion, change, and space. By the end of the nineteenth century, mathematics had become the study of number, shape, motion, change, and space, and of the mathematical tools that are used in this study.
It was only within the last thirty years or so that a definition of mathematics emerged on which most mathematicians now agree: mathematics is the science of patterns. What the mathematician does is examine abstract 'patterns'—numerical patterns, patterns of shape, patterns of motion, patterns of behavior, voting patterns in a population, patterns of repeating chance events, and so on. Those patterns can be either real or imagined, visual or mental, static or dynamic, qualitative or quantitative, purely utilitarian or of little more than recreational interest. They can arise from the world around us, from the depths of space and time, or from the inner workings of the human mind.
Different kinds of patterns give rise to different branches of mathematics. For example:
• Arithmetic and number theory study patterns of number and counting.
• Geometry studies patterns of shape.
• Calculus allows us to handle patterns of motion.
• Logic studies patterns of reasoning.
• Probability theory deals with patterns of chance.
• Topology studies patterns of closeness and position.
One aspect of modern mathematics that is obvious to even the casual observer is the use of abstract notation: algebraic expressions, complicated-looking formulas, and geometric diagrams. The mathematician's reliance on abstract notation is a reflection of the abstract nature of the patterns he studies.
Different aspects of reality require different forms of description. For example, the most appropriate way to study the lay of the land or to describe to someone how to find their way around a strange town is to draw a map. Text is far less appropriate. Analogously, line drawings in the form of blueprints are the most appropriate way to specify the construction of a building. And musical notation is the most appropriate way to convey music, apart from, perhaps, actually playing the piece.
In the case of various kinds of abstract, 'formal' patterns and abstract structures, the most appropriate means of description and analysis is mathematics, using mathematical notation, concepts, and procedures. For instance, the symbolic notation of algebra is the most appropriate means of describing and analyzing the general behavioral properties of addition and multiplication. The commutative law for addition, for example, could be written in English as:
When two numbers are added, their order is not important.
However, it is usually written in the symbolic form:
m + n = n + m
Such is the complexity and the degree of abstraction of the majority of mathematical patterns that to use anything other than symbolic notation would be prohibitively cumbersome. And so the development of mathematics has involved a steady increase in the use of abstract notation.
Symbols of Progress
These days, mathematics books tend to be awash with symbols, but mathematical notation no more is mathematics than musical notation is music. A page of sheet music represents a piece of
music; the music itself is what you get when the notes on the page are sung or performed on a musical instrument. It is in its performance that the music comes alive and becomes part of our experience; the music exists not on the printed page, but in our minds. The same is true for mathematics; the symbols on a page are just a representation of the mathematics. When read by a competent performer (in this case, someone trained in mathematics), the symbols on the printed page come alive—the mathematics lives and breathes in the mind of the reader like some abstract symphony.
Given the strong similarity between mathematics and music, both of which have their own highly abstract notations and are governed by their own structural rules, it is hardly surprising that many (perhaps most) mathematicians also have some musical talent.
In fact, for most of the two and a half thousand years of Western civilization, starting with the ancient Greeks, mathematics and music were regarded as two sides of the same coin: both were thought to provide insights into the order of the universe. It was only with the rise of the scientific method in the seventeenth century that the two started to go their separate ways.
For all their historical connections, however, there was, until recently, one very obvious difference between mathematics and music. Though only someone well trained in music can read a musical score and hear the music in her head, if that same piece of music is performed by a competent musician, anyone with the sense of hearing can appreciate the result. It requires no musical training to experience and enjoy music when it is performed.
For most of its history, however, the only way to appreciate mathematics was to learn how to 'sight-read' the symbols. Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent of a pair of ears. Mathematics can be 'seen' only with the 'eyes of the mind'.
It is as if we had no sense of heating, so that only someone able to sight-read musical notation would be able to appreciate the patterns and harmonies of music.
In recent years, however, the development of computer and video technologies has to some extent made mathematics accessible to the untrained. In the hands of a skilled user, the computer can be used to 'perform' mathematics, and the result can be displayed in a visual form on the screen for all to see. Though only a relatively small part of mathematics lends itself to such visual 'performance', it is now possible to convey to the layperson at least something of the beauty and the harmony that the mathematician 'sees' and experiences when he/she does mathematics.
Without its algebraic symbols, large parts of mathematics simply would not exist. Indeed, the issue is a deep one, having to do with human cognitive abilities. The recognition of abstract concepts and the development of an appropriate language to represent them are really two sides of the same coin.
The use of a symbol such as a letter, a word, or a picture to denote an abstract entity goes hand in hand with the recognition of that entity as an entity. The use of the numeral '7' to denote the number 7 requires that the number 7 be recognized as an entity; the use of the letter m to denote an arbitrary whole number requires that the concept of a whole number be recognized. Having the symbol makes it possible to think about and manipulate the concept.
This linguistic aspect of mathematics is often overlooked, especially in our modern culture, with its emphasis on the procedural, computational aspects of mathematics. Indeed, one often hears the complaint that mathematics would be much easier if it weren't for all that abstract notation, which is rather like saying that Shakespeare would be much easier to understand if it were written in simpler language.
Sadly, the level of abstraction in mathematics, and the consequent need for notation that can cope with that abstraction, means that many, perhaps most, parts of mathematics will remain forever hidden from the nonmathematician; and even the more accessible parts—the parts described in books such as this one—maybe at best dimly perceived, with much of their inner beauty locked away from view. Still, that does not excuse those of us who do seem to have been blessed with an ability to appreciate that inner beauty from trying to communicate to others some sense of what it is we experience—some sense of the simplicity, the precision, the purity, and the elegance that give the patterns of mathematics their aesthetic value.
The Hidden Beauty in the Symbols
In his 1940 book A Mathematician's Apology, the accomplished English mathematician G. H. Hardy wrote:
The mathematician's patterns, like the painter's or the poet's, must be beautiful, the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test; there is no permanent place in the world for ugly mathematics. . . . It may be very hard to define mathematical beauty, but that is just as true of beauty of any kind—we
may not know quite what we mean by a beautiful poem, but that does not prevent us from recognizing one when we read it.
The beauty to which Hardy was referring is, in many cases, a highly abstract, inner beauty, a beauty of abstract form and logical structure, a beauty that can be observed, and appreciated, only by those sufficiently well trained in the discipline. It is a beauty ''cold and austere," according to Bertrand Russell, the famous English mathematician and philosopher, who wrote, in his 1918 book Mysticism and Logic:
Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
In an age when the study of the heavens dominated scientific thought, Galileo said, "The great book of nature can be read only by those who know the language in which it was written. And this language is mathematics."
Striking a similar note in a much later era, when the study of the inner workings of the atom had occupied the minds of many scientists for a generation, the Cambridge physicist John Polkinhorne wrote, in 1986,
Making the Invisible Visible
We have answered the question "What is mathematics?" with the slogan "Mathematics is the science of patterns." There is another fundamental question about mathematics that can also be answered by a catchy phrase: "What does mathematics do?" By this I mean, what exactly does mathematics give you when you apply it to the study of some phenomenon? The answer is "Mathematics makes the invisible visible.''
Let me give you some examples of what I mean by this answer.
Without mathematics, there is no way you can understand what keeps a jumbo jet in the air. As we all know, large metal objects don't stay above the ground without something to support them. But when you look at a jet aircraft flying overhead, you can't see anything holding it up. It takes mathematics to 'see' what keeps an airplane aloft. In this case, what lets you 'see' the invisible is an equation discovered by the mathematician Daniel Bernoulli early in the eighteenth century.
While I'm on the subject of flying, what is it that causes objects other than aircraft to fall to the ground when we release them? "Gravity," you answer. But that's just giving it a name; it doesn't help us to understand it.
It's still invisible. We might as well call it 'magic'. To understand gravity, you have to 'see' it. That's exactly what Newton did with his equations of motion and mechanics in the seventeenth century. Newton's mathematics enabled us to 'see' the invisible forces that keep the earth rotating around the sun and cause an apple to fall from a tree onto the ground. Both Bernoulli's equation and Newton's equations use calculus. Calculus works by making visible the infinitesimally small. That's another example of making the invisible visible.
Here's another: Two thousand years before we could send spacecraft into outer space to provide us with pictures of our planet, the Greek mathematician Eratosthenes used mathematics to show that the earth was round. Indeed, he calculated its diameter, and hence its curvature, with 99 percent accuracy. Today, we may be close to repeating Eratosthenes' feat by discovering whether the universe is curved. Using mathematics and powerful telescopes, we can 'see' into the outer reaches of the universe. According to some astronomers, we will soon see far enough to be able to detect any curvature in space, and to measure any curvature that we find.
Knowing the curvature of space, we can then use mathematics to see into the future to the day the universe comes to an end. Using mathematics, we have already been able to see into the distant past, making visible the otherwise invisible moments when the universe was first created in what we call the Big Bang.
Coming back to earth at the present time, how do you 'see' what makes pictures and sounds of a football game miraculously appear on a television screen on the other side of town? One answer is that the pictures and sounds are transmitted by radio waves—a special case of what we call electromagnetic radiation. But, as with gravity, that answer just gives the phenomenon a name; it doesn't help us to 'see' it. In order to 'see' radio waves, you have to use mathematics. Maxwell's equations, discovered in the nineteenth century, make visible to us the otherwise invisible radio waves.
Here are some human patterns we can 'see' through mathematics:
• Aristotle used mathematics to try to 'see' the invisible patterns of sound that we recognize as music.
• He also used mathematics to try to describe the invisible structure of a dramatic performance.
• In the 1950s, the linguist Noam Chomsky used mathematics to 'see' and describe the invisible, abstract
patterns of words that we recognize as grammatical sentences. He thereby turned linguistics from a fairly
obscure branch of anthropology into a thriving mathematical science.
Finally, using mathematics, we are able to look into the future:
• Probability theory and mathematical statistics let us predict the outcomes of elections, often with
remarkable accuracy
• We use calculus to predict tomorrow's weather.
• Market analysts use various mathematical theories to try to predict the behavior of the stock market.
• Insurance companies use statistics and probability theory to predict the likelihood of an accident during the
coming year, and set their premiums accordingly.
When it comes to looking into the future, mathematics allows us to make visible another invisible—that which has not yet happened. In that case, our mathematical vision is not perfect. Our predictions are sometimes wrong. But without mathematics, we cannot see into the future even poorly.
The Invisible Universe
Today, we live in a technological society. There are increasingly few places on the face of the earth where, when we look around us toward the horizon, we do not see products of our technology: tall buildings, bridges, power lines, telephone cables, cars on roads, aircraft in the sky. Where communication once required physical proximity, today much of our communication is mediated by mathematics, transmitted in digitized form along wires or optical fibers, or through the ether. Computers—machines that perform mathematics—are not only on our desktops, they are in everything from microwave ovens to automobiles and from children's toys to pacemakers for those with heart problems. Mathematics—in the form of statistic—is used to decide what food we will eat, what products we will buy, what television programs we will be able to see, and which politicians we will be able to vote for. Just as society burned fossil fuels to drive the engines of the industrial age, in today's information age, the principal fuel we burn is mathematics.
And yet, as the role of mathematics has grown more and more significant over the past half century, it has become more and more hidden from view, forming an invisible universe that supports much of our lives.
Just as our every action is governed by the invisible forces of nature (such as gravity), we now live in the invisible universe created by mathematics, subject to invisible mathematical laws.
I know, I know, I'm 2 days early in regards to today's degree, whatever, better ahead than behind...been doing more reading than writing lately, here's an excerpt from one of the titles on my list (The Language of Mathematics: Making the Invisible Visible)...It's more Eurocentric than anything (I took out some of those parts), but those that know, will take the best part...All Emphasis is My Own...Peace...Au
**************************
Excerpt from the prolouge of:
The Language of Mathematics: Making the Invisible Visible
Keith Devlin
ISBN 0-7167-3379-X (hardcover)
ISBN 0-7167-3967-4 (paperback)
1. Mathematics—Popular works. I. Title.
QA93.D4578 1998
© 1998, 2000
What Is Mathematics?
It's Not Just Numbers
What is mathematics? Ask this question of persons chosen at random, and you are likely to receive the answer "Mathematics is the study of numbers." With a bit of prodding as to what kind of study they mean, you may be able to induce them to come up with the description "the science of numbers." But that is about as far as you will get. And with that, you will have obtained a description of mathematics that ceased to be accurate some two and a half thousand years ago!
Given such a huge misconception, there is scarcely any wonder that your randomly chosen persons are unlikely to realize that research in mathematics is a thriving, worldwide activity, or to accept a suggestion that mathematics permeates, often to a considerable extent, most walks of present-day life and society. In fact, the answer to the question "What is mathematics?" has changed several times during the course of history.
After Newton and Leibniz, mathematics became the study of number, shape, motion, change, and space. By the end of the nineteenth century, mathematics had become the study of number, shape, motion, change, and space, and of the mathematical tools that are used in this study.
It was only within the last thirty years or so that a definition of mathematics emerged on which most mathematicians now agree: mathematics is the science of patterns. What the mathematician does is examine abstract 'patterns'—numerical patterns, patterns of shape, patterns of motion, patterns of behavior, voting patterns in a population, patterns of repeating chance events, and so on. Those patterns can be either real or imagined, visual or mental, static or dynamic, qualitative or quantitative, purely utilitarian or of little more than recreational interest. They can arise from the world around us, from the depths of space and time, or from the inner workings of the human mind.
Different kinds of patterns give rise to different branches of mathematics. For example:
• Arithmetic and number theory study patterns of number and counting.
• Geometry studies patterns of shape.
• Calculus allows us to handle patterns of motion.
• Logic studies patterns of reasoning.
• Probability theory deals with patterns of chance.
• Topology studies patterns of closeness and position.
One aspect of modern mathematics that is obvious to even the casual observer is the use of abstract notation: algebraic expressions, complicated-looking formulas, and geometric diagrams. The mathematician's reliance on abstract notation is a reflection of the abstract nature of the patterns he studies.
Different aspects of reality require different forms of description. For example, the most appropriate way to study the lay of the land or to describe to someone how to find their way around a strange town is to draw a map. Text is far less appropriate. Analogously, line drawings in the form of blueprints are the most appropriate way to specify the construction of a building. And musical notation is the most appropriate way to convey music, apart from, perhaps, actually playing the piece.
In the case of various kinds of abstract, 'formal' patterns and abstract structures, the most appropriate means of description and analysis is mathematics, using mathematical notation, concepts, and procedures. For instance, the symbolic notation of algebra is the most appropriate means of describing and analyzing the general behavioral properties of addition and multiplication. The commutative law for addition, for example, could be written in English as:
When two numbers are added, their order is not important.
However, it is usually written in the symbolic form:
m + n = n + m
Such is the complexity and the degree of abstraction of the majority of mathematical patterns that to use anything other than symbolic notation would be prohibitively cumbersome. And so the development of mathematics has involved a steady increase in the use of abstract notation.
Symbols of Progress
These days, mathematics books tend to be awash with symbols, but mathematical notation no more is mathematics than musical notation is music. A page of sheet music represents a piece of
music; the music itself is what you get when the notes on the page are sung or performed on a musical instrument. It is in its performance that the music comes alive and becomes part of our experience; the music exists not on the printed page, but in our minds. The same is true for mathematics; the symbols on a page are just a representation of the mathematics. When read by a competent performer (in this case, someone trained in mathematics), the symbols on the printed page come alive—the mathematics lives and breathes in the mind of the reader like some abstract symphony.
Given the strong similarity between mathematics and music, both of which have their own highly abstract notations and are governed by their own structural rules, it is hardly surprising that many (perhaps most) mathematicians also have some musical talent.
In fact, for most of the two and a half thousand years of Western civilization, starting with the ancient Greeks, mathematics and music were regarded as two sides of the same coin: both were thought to provide insights into the order of the universe. It was only with the rise of the scientific method in the seventeenth century that the two started to go their separate ways.
For all their historical connections, however, there was, until recently, one very obvious difference between mathematics and music. Though only someone well trained in music can read a musical score and hear the music in her head, if that same piece of music is performed by a competent musician, anyone with the sense of hearing can appreciate the result. It requires no musical training to experience and enjoy music when it is performed.
For most of its history, however, the only way to appreciate mathematics was to learn how to 'sight-read' the symbols. Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent of a pair of ears. Mathematics can be 'seen' only with the 'eyes of the mind'.
It is as if we had no sense of heating, so that only someone able to sight-read musical notation would be able to appreciate the patterns and harmonies of music.
In recent years, however, the development of computer and video technologies has to some extent made mathematics accessible to the untrained. In the hands of a skilled user, the computer can be used to 'perform' mathematics, and the result can be displayed in a visual form on the screen for all to see. Though only a relatively small part of mathematics lends itself to such visual 'performance', it is now possible to convey to the layperson at least something of the beauty and the harmony that the mathematician 'sees' and experiences when he/she does mathematics.
Without its algebraic symbols, large parts of mathematics simply would not exist. Indeed, the issue is a deep one, having to do with human cognitive abilities. The recognition of abstract concepts and the development of an appropriate language to represent them are really two sides of the same coin.
The use of a symbol such as a letter, a word, or a picture to denote an abstract entity goes hand in hand with the recognition of that entity as an entity. The use of the numeral '7' to denote the number 7 requires that the number 7 be recognized as an entity; the use of the letter m to denote an arbitrary whole number requires that the concept of a whole number be recognized. Having the symbol makes it possible to think about and manipulate the concept.
This linguistic aspect of mathematics is often overlooked, especially in our modern culture, with its emphasis on the procedural, computational aspects of mathematics. Indeed, one often hears the complaint that mathematics would be much easier if it weren't for all that abstract notation, which is rather like saying that Shakespeare would be much easier to understand if it were written in simpler language.
Sadly, the level of abstraction in mathematics, and the consequent need for notation that can cope with that abstraction, means that many, perhaps most, parts of mathematics will remain forever hidden from the nonmathematician; and even the more accessible parts—the parts described in books such as this one—maybe at best dimly perceived, with much of their inner beauty locked away from view. Still, that does not excuse those of us who do seem to have been blessed with an ability to appreciate that inner beauty from trying to communicate to others some sense of what it is we experience—some sense of the simplicity, the precision, the purity, and the elegance that give the patterns of mathematics their aesthetic value.
The Hidden Beauty in the Symbols
In his 1940 book A Mathematician's Apology, the accomplished English mathematician G. H. Hardy wrote:
The mathematician's patterns, like the painter's or the poet's, must be beautiful, the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test; there is no permanent place in the world for ugly mathematics. . . . It may be very hard to define mathematical beauty, but that is just as true of beauty of any kind—we
may not know quite what we mean by a beautiful poem, but that does not prevent us from recognizing one when we read it.
The beauty to which Hardy was referring is, in many cases, a highly abstract, inner beauty, a beauty of abstract form and logical structure, a beauty that can be observed, and appreciated, only by those sufficiently well trained in the discipline. It is a beauty ''cold and austere," according to Bertrand Russell, the famous English mathematician and philosopher, who wrote, in his 1918 book Mysticism and Logic:
Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
Mathematics, the science of patterns, is a way of looking at the world, both the physical, biological, and sociological world we inhabit and the inner world of our minds and thoughts. Mathematics' greatest success has undoubtedly been in the physical domain, where the subject is rightly referred to as both the queen and the servant of the (natural) sciences. Yet, as an entirely human creation, the study of mathematics is ultimately a study of humanity itself.
For none of the entities that form the substrate of mathematics exist in the physical world; the numbers, the points, the lines and planes, the surfaces, the geometric figures, the functions, and so forth are pure abstractions that exist only in humanity's collective mind. The absolute certainty of a mathematical proof and the indefinitely enduring nature of mathematical truth are reflections of the deep and fundamental status of the mathematician's patterns in both the human mind and the physical world.
In an age when the study of the heavens dominated scientific thought, Galileo said, "The great book of nature can be read only by those who know the language in which it was written. And this language is mathematics."
Striking a similar note in a much later era, when the study of the inner workings of the atom had occupied the minds of many scientists for a generation, the Cambridge physicist John Polkinhorne wrote, in 1986,
Mathematics is the abstract key which tums the lock of the physical universe. In today's age, dominated by information, communication, and computation, mathematics is finding new locks to turn. There is scarcely any aspect of our lives that is not affected, to a greater or lesser extent, by mathematics, for abstract patterns are the very essence of thought, of communication, of computation, of society, and of life itself.
Making the Invisible Visible
We have answered the question "What is mathematics?" with the slogan "Mathematics is the science of patterns." There is another fundamental question about mathematics that can also be answered by a catchy phrase: "What does mathematics do?" By this I mean, what exactly does mathematics give you when you apply it to the study of some phenomenon? The answer is "Mathematics makes the invisible visible.''
Let me give you some examples of what I mean by this answer.
Without mathematics, there is no way you can understand what keeps a jumbo jet in the air. As we all know, large metal objects don't stay above the ground without something to support them. But when you look at a jet aircraft flying overhead, you can't see anything holding it up. It takes mathematics to 'see' what keeps an airplane aloft. In this case, what lets you 'see' the invisible is an equation discovered by the mathematician Daniel Bernoulli early in the eighteenth century.
While I'm on the subject of flying, what is it that causes objects other than aircraft to fall to the ground when we release them? "Gravity," you answer. But that's just giving it a name; it doesn't help us to understand it.
It's still invisible. We might as well call it 'magic'. To understand gravity, you have to 'see' it. That's exactly what Newton did with his equations of motion and mechanics in the seventeenth century. Newton's mathematics enabled us to 'see' the invisible forces that keep the earth rotating around the sun and cause an apple to fall from a tree onto the ground. Both Bernoulli's equation and Newton's equations use calculus. Calculus works by making visible the infinitesimally small. That's another example of making the invisible visible.
Here's another: Two thousand years before we could send spacecraft into outer space to provide us with pictures of our planet, the Greek mathematician Eratosthenes used mathematics to show that the earth was round. Indeed, he calculated its diameter, and hence its curvature, with 99 percent accuracy. Today, we may be close to repeating Eratosthenes' feat by discovering whether the universe is curved. Using mathematics and powerful telescopes, we can 'see' into the outer reaches of the universe. According to some astronomers, we will soon see far enough to be able to detect any curvature in space, and to measure any curvature that we find.
Knowing the curvature of space, we can then use mathematics to see into the future to the day the universe comes to an end. Using mathematics, we have already been able to see into the distant past, making visible the otherwise invisible moments when the universe was first created in what we call the Big Bang.
Coming back to earth at the present time, how do you 'see' what makes pictures and sounds of a football game miraculously appear on a television screen on the other side of town? One answer is that the pictures and sounds are transmitted by radio waves—a special case of what we call electromagnetic radiation. But, as with gravity, that answer just gives the phenomenon a name; it doesn't help us to 'see' it. In order to 'see' radio waves, you have to use mathematics. Maxwell's equations, discovered in the nineteenth century, make visible to us the otherwise invisible radio waves.
Here are some human patterns we can 'see' through mathematics:
• Aristotle used mathematics to try to 'see' the invisible patterns of sound that we recognize as music.
• He also used mathematics to try to describe the invisible structure of a dramatic performance.
• In the 1950s, the linguist Noam Chomsky used mathematics to 'see' and describe the invisible, abstract
patterns of words that we recognize as grammatical sentences. He thereby turned linguistics from a fairly
obscure branch of anthropology into a thriving mathematical science.
Finally, using mathematics, we are able to look into the future:
• Probability theory and mathematical statistics let us predict the outcomes of elections, often with
remarkable accuracy
• We use calculus to predict tomorrow's weather.
• Market analysts use various mathematical theories to try to predict the behavior of the stock market.
• Insurance companies use statistics and probability theory to predict the likelihood of an accident during the
coming year, and set their premiums accordingly.
When it comes to looking into the future, mathematics allows us to make visible another invisible—that which has not yet happened. In that case, our mathematical vision is not perfect. Our predictions are sometimes wrong. But without mathematics, we cannot see into the future even poorly.
The Invisible Universe
Today, we live in a technological society. There are increasingly few places on the face of the earth where, when we look around us toward the horizon, we do not see products of our technology: tall buildings, bridges, power lines, telephone cables, cars on roads, aircraft in the sky. Where communication once required physical proximity, today much of our communication is mediated by mathematics, transmitted in digitized form along wires or optical fibers, or through the ether. Computers—machines that perform mathematics—are not only on our desktops, they are in everything from microwave ovens to automobiles and from children's toys to pacemakers for those with heart problems. Mathematics—in the form of statistic—is used to decide what food we will eat, what products we will buy, what television programs we will be able to see, and which politicians we will be able to vote for. Just as society burned fossil fuels to drive the engines of the industrial age, in today's information age, the principal fuel we burn is mathematics.
And yet, as the role of mathematics has grown more and more significant over the past half century, it has become more and more hidden from view, forming an invisible universe that supports much of our lives.
Just as our every action is governed by the invisible forces of nature (such as gravity), we now live in the invisible universe created by mathematics, subject to invisible mathematical laws.
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Knowledge of Self: A Collection of Wisdom on the Science of Everything in Life
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