Think Archimedes - The Student Development Company

I am 27 years old – it’s not my job to be political. I can’t even run for the presidency until I am at least 35 years old. At my age, it’s supposed to be my job to continue educating myself, to give to my fellow man in any way that I am able, and to continue growing my business so that I can afford to have a wife, so that I can start a family, so that we can, as a team, add to and benefit society. My job is not supposed to be to think for the government and do their jobs for them. Nevertheless, I have already written one short proposal for how to intelligently modify the current broken school system, and have provided some additional solutions in this piece.

**It is important to note that I don’t really care if you agree with all of my ideas or not. If you have better, more cost effective, or more practical approaches we can talk about then bring them to the table – otherwise just sit in the bushes and watch. People who only know how to complain take away from any conversation because complaining simply recognizes that there is a problem which is not yet taken care of. If you recognize yourself as this kind of person, really just stop reading now and move on to something else (you might feel insulted and probably won’t like our company mission, or vision anyway). This article is not politically correct – it is real life right now. People seem to have forgotten that Americans are butt kickers, whose butts we primarily kick are our own. Whenever the government takes actions, or makes plans to take actions that threaten the general good of its people we must take matters into our own hands and STOP relying on Big Ben to take care of our problems.**

So What Is South Carolina’s Education System Planning To Do Anyway?

If we have learned anything today it is this: Government is NOT going to actually help us solve the education crisis in South Carolina. In today’s (October 15th) edition of The Post & Courier we find a very confounding recommendation by our state’s education superintendent – one that will, “save money and provide the least amount of harm to students’ learning,” as if we are to assume that it is necessary, in the first place, to cause any amount of harm to our children. Here are the five proposals that are supposed to be in the best interest for South Carolina families:

1. Lowering the state’s minimum required number of days from 180 per year by requiring that students be in class 4 days a week instead of 5. (Ever heard the phrase, “Idle hands are the devil’s workshop”? It doesn’t really matter that students will be in class a little bit longer each day, the point is that they will have THREE full days off from school now instead of two. In the real world, I work longer, harder days than I ever have before – and I have to fight and demand to get one day off.)
2. Reduce testing to the minimum of that which is required by federal law. (Violating one of the most obvious success principles of sports, academics, business, and life: You cannot get maximum results out of minimum efforts … brilliant!)
3. “Eliminating 2009 ratings for schools and districts on the state report card.” (ie, we are not going to hold schools accountable for results anymore. Why are they doing this? Reportedly, “With this degree of cuts, test results may not reflect what schools are capable of doing, [Jim Rex] said. So while eliminating report card ratings wouldn’t save money, it would address the issue of fairness and accuracy.”)
4. Giving each school district the ability to use government funds as they see fit. (ie, we are not going to hold schools accountable for their discretionary use of tax-payer’s money either.)
5. Allowing each school district to pick and choose which of the mandated government programs they will implement. (ie, you had BETTER get involved in your school’s Parent-Teacher-Student Organizations (PTSOs) if you want to have any say in what your children will be taught and have available to them.)

Not only are these officials not asking the people they are supposed to be protecting and serving for input, suggestions, or ideas (thereby sheltering themselves from great thinkers within the community) – they are demonstrating their reactive nature to problems, thus focusing on the problem rather than the solution. What’s worse, they are setting a poor example to our citizenry of what it means to think outside the box for clever, intelligent, and innovative ways of solving problems.

So If The Government Won’t (Or Can’t) Help, What Can We Really Do? One Word: Leverage.

Leverage Allows Us To Create Incredible Power With The Same Amount of Force

How about leveraging the internet by creating interactive web-based video tutorials by the best teachers in the state? The lessons and work only need to be done one time and then we don’t have to continue paying 10,000 teachers to teach each lesson, because it has already been taught the best way, by the best teacher once, and is available to every student in the state with internet access. It could even be a collaborative project among many teachers, taking extreme care to craft each lesson from multiple angles. I know it sucks that all of these “education majors” who are functioning in our schools as teachers will become obsolete to some degree, but the truth of the matter is that we will still need them more than ever – we just won’t be paying them to teach the bulk of the lessons.

We still need a lot of effective tutors and teachers to mentor and develop character in our students, we still need role models who can push us and drive us to achieve more than we ever thought possible, we still need coaches to kick our butts in sports, clubs, and organizations. We need mentors who can help us find internships and discover our talents and abilities so that we can find and do what we love as we enter the working world. Why do we feel so strongly that we must hold on to the old, broken way that school has always been in an age where technology and information has given us more opportunity to solve our problems than ever before in the history of mankind?

What About Students Without Internet Access?

No Computer? No Problem.

“Toughen up butter cup” – go to the library and use one within the free public domain, or find a friend who does have access, or spend a few hundred bucks on a laptop and go to a coffee shop with internet access. Where there is a will there is a way. It is said that you can make excuses, and you can make money – but you can’t make both. By allowing students to make excuses for why they can’t find a solution to a simple problem like finding internet access is to continue encouraging them to be victimized and remain powerless. After all, if you can’t solve a problem as simple as getting internet access in today’s wired world, then maybe you should consider learning how to think for yourself and be resourceful as part of your balanced education?

I know it is a lot to ask that a poor family save up drug and alcohol money, discontinue the cable bill for a few months, sell the television set, or take any other sacrificial measure to provide themselves with a proper laptop. Especially (God forbid) getting a second job – that would definitely be out of the question. So in the case that a family would not be able to get a computer for themselves, I am sure that a generous politician will naturally rise up to take your cause (if you would but vote for him or her) and use our tax money to buy your student one for you. The “I don’t have a computer or internet” excuse is just stupid. Really, society will make sure little Jimmy has a laptop.

What About Providing Tax Benefits To Families With Students Making The Cut?

Tax Cuts Motivate Us To Take Action

We could even encourage and motivate more parents to care about and be involved with their own childrens’ educations by rewarding families with tax credits of parents who have students on the honor roll, or who score well on standardized tests. Who can be sure exactly how much this might be or how it might be enforced (perhaps schools reporting which students qualify to the IRS directly) but in just a few hours each week, parents could hold their kids accountable for school work and be compensated for it – perhaps thousands of dollars – since better students take less work in the classroom. And doesn’t this just make sense because accountable parenting is really one of the biggest parts to the solution anyway? Few would argue that successful students start at home.

For those more motivated by pain, we could also impose a tax penalty to parents of students who are failing out of school or not making the cut. Doesn’t it also make sense to penalize negligent parents who are disinterested in their own child’s education – creating MORE time and energy on behalf of the school’s staff in tutoring, mentoring, and behavioral problems? It sure is at least something to think about. That way, every parent is affected in some way, either positively or negatively, and they won’t have anyone to blame or praise but themselves.

Isn’t that what tax credits and penalties are supposed to be used for anyway: To either encourage or discourage certain actions and behaviors made by a citizenry? That is, of course, why we allow home owners to deduct their mortgage interest on Schedule A of their tax return – because home ownership increases the net worth of any community’s citizenry. Likewise, we also impose fines for pulling money out of retirement accounts before age 65 and a half to discourage this behavior.

We need to start holding ourselves and neighbors as accountable as we wish to hold the government. After all, ultimately it isn’t really the government’s responsibility to see to it that your kids are educated – it’s yours. And anyway, now more than ever you should be taking an active interest in what your children are learning and how well they are mastering their studies, because the school system sure isn’t. And the last thing you or anyone else needs to do is continually place blind faith into the government as an effective system for educating our youth – because it isn’t. As with most things, privatized companies will always produce greater value and results than government run organizations.

Actions Speak Louder Than Words

We Dont Have To Wait For The Government To Take Action To Do The Right Thing. "Ask Not What Your Country Can Do For You."

Since our governing body will do nothing about the problems we are faced with – other than retreat – we have decided that we will take a proactive stance in taking responsibility for this task. Our company is now dedicated to maintaining this high standard of excellence, and our vision is to see South Carolina students rise from 49th in the nation into the top 10.

Education is no accident. The problem with the system is more a matter of the environment in which students are placed and the standards to which they are held than it is a problem with the kids themselves. Children are brilliant – they will rise to whatever standard you set for them. They need guidance, direction, coaching, and butt kicking. They need to know that laziness is unacceptable, that slackards starve to death and have loser friends. And they also need to know that there is a champion within all of us if we will but dig deep and give life all that we’ve got.

Performing well in high school, college, or on standardized tests requires three primary strengths: Reading, Logic, and an elementary blend of mathematics (Arithmetic, Algebra, and Geometry). Most seniors have had eleven school years to be exceptional at these, only to still be poor at adding and multiplying numbers in their heads, inefficiently slow readers, and illogical in many arguments used in writing essays. The reason for this is, quite simply, three fold:

1.) Our schools have never taught students that there is any other way to perform mathematical calculations other than some of the longest, boring, inefficient, uncreative, step-by-step, archaic ways imaginable.

2.) Schools have failed to offer speed reading courses to teach students the science of the brain’s processing abilities, good reading habits, and advanced comprehension techniques.

3.) Not once have government schools even offered elementary logic courses discussing how to look for fallacious arguments, how to counter them, and how to construct logical, intelligent, irrefutable arguments.

Is it any wonder that we have students who still feel so insecure about their own ability to make calculations that they have to rely on something outside of themselves (a calculator) for even simple operations? That isn’t confidence. Should we be surprised that we have students who don’t even finish reading comprehension and verbal sections of tests because they don’t read fast enough AND fail to discern what the passage is even talking about? That is border-lined “illiterate”. Can we now begin to recognize how it is that we graduate students in droves who fall prey to simple fallacious arguments, are easily fooled into picking wrong answer choices, and who cannot build strong, supported cases in their own essays and arguments?

Enough is enough. We recognize that we cannot make students learn what they need to know in order to achieve this goal, but what we, as a company, can do is kick their butts by getting rid of every excuse they can give for not knowing something so that they are forced to admit they are just lazy if they do not make the cut. Think Archimedes has officially made the decision to provide high-quality, cost effective math and logic lessons to grade school students so they can own, crush, and dominate standardized tests. Students – if you want it, come and get it. We will do everything we can to help you become the scholars of today and leaders of tomorrow.

In a time when there is more at stake than ever, it is time to kick some butt – our own butts. The world needs demonstration more than it needs teaching, and we will demonstrate how mathematics is more relevant and applicable than ever.

Article: Should Fractions Be Confined To The Dustbin Of Math History?

Habitually we scan the top of the morning paper, “USA TODAY – THURSDAY, JANUARY 24, 2008 – 11D”. Scan the page, let’s see…Mayan sacrifices…amphibian extinction…fractions to the DUSTBIN?! In the first place, what is the deal with all of these articles concerning death? And second, what branch of academic pursuit has actually brought up the question, “Should fractions be confined to the dustbin of math history?” (<–???!!)

Who Needs Fractions Anyway?

If you have ever seen a 1/1000 scale model of a ship in a jar; if you have ever measured 3/4 of a cup of flour while baking chocolate chip cookies; if you have ever given the time saying something like, “Quarter ’til Eight;” if you have ever earned 8% on an investment; if you have ever found an average; if you have ever split anything into equal groups; then you understand the value of fractions in an educated and fast-paced world. Furthermore, if you have ever studied number theory at any level then you know that to challenge the position of the fraction at any theoretical level is to challenge one of the very four primary operators and the very foundation of numbers themselves.

Ever Driven In Miles Per Hour?

Fractions are a fundamental part of the study of mathematics and absolutely a necessary component to the modern day curriculum. They allow us to compare two unrelated measurements (distance divided by time – miles/hour as an example – to understand the idea of speed). Fractions are an integral part of understanding everything from rates of change to models of growth and decay. We use them in nearly every profession whether reading and understanding your electric bill in “kilowatts PER hour” or studying the proportions of the human body to create a masterpiece like Michelangelo’s David.

Fractions Have Always Been An Integral Part Of Technological Advancement

In the late 1600s Gottfried Leibniz and Sir Isaac Newton showed the world that a fraction could be challenged to the very limits of its definition. Dividing by the actual value of zero we call “Undefined” as in “there is not a way to combine words, thoughts, or ideas in such a way that the human mind can conceive of this operation.” The discovery of Calculus, without a doubt, has been one of the single greatest mathematical achievements mankind has ever accomplished and it could not have been done without the concept of a fraction.

Fractions Let Us Use EXACT Values

While the idea of teaching children only the decimal system appears to be wise on the outside, it robs children of gaining an early understanding of “number”. Fractions allow me to be EXACTLY correct in representing certain numbers like 1/3, since no matter how many .333333 decimal places I can extend out to, I will always be estimating. Furthermore, as I count to ten I begin with one digit values (i.e. 1, 2, etc) until I get to ten and then a new digit appears to the left (the tens place). This is an illustration of what its like to work in base-10 mathematics: with every group of ten I add another increment to the next place to the left.

Fractions Allow Us To Easily Understand Multi-based Mathematics

Fractions are one of the main ideas to working in multi-base mathematics. As an example, if we are working in terms of thirds, this is like working in a base-3 system where every time we count three more we add one more to the place immediately to the next place to the left. If we are working in 7ths (base-7 i.e. days of the week), then every time we count 7 7ths we add one more to the ones place (by the way, this concept is tested on the SAT). Simple as this might seem, it is perhaps more important than ever to ensure that the modern student understands these classic fundamentals.

Dumbing Down American Curriculum Is Not The Answer To The Problem

We are at a point in history where we define “technology” to a large degree in terms of programming, web aps, and database management. Historically the most technologically advanced civilizations have always had an edge in global commerce and it certainly seems as if the internet will continue to be the cutting edge of technology for years to come. It really doesn’t make sense to discourage the use of fractions, and hopefully this article will serve as a great refute the this idea.

Even In Sports We Go Back To The Fundamentals

Ask 1,000 students if they know what a number is and you will get 1,000 affirmatives. Now ask those students if they can properly dissect a number and explain it piecewise … Sadly, in the modern school curriculum’s race to Calculus many students cannot explain this fundamental question about mathematics. Any great coach knows that when a player gets into a slump, one of the best places to start in bringing him/her out of it is to go back to the fundamentals and break the dynamics down, step-by-step, analyzing each component of a move, swing, or play until the root of the problem is solved. Thus, let’s reconsider the idea of what a number is.

The Anatomy Of A Number

Numbers only exist because we say they do, and it is important to recognize that mathematicians, over thousands and thousands of years, have come to define numbers as having 5 components to them (there are actually 6 since every number has an imaginary component also, but for practical purposes we shall disregard the ±bi).

Every number has five components: a base (b), a coefficient (c), a divisor (d), a power (p), and a root (r)

As a simple example, 24 is a number: It exists as an independent, specific, and unique value and has eight “factors” or “numbers that evenly divide” into 24: 1, 2, 3, 4, 6, 8, 12, and 24. The amount of 24 is the same as 1 x 24, and this is such an important idea in mathematics that we have a name for it: The Multiplicative Identity. And by the way, this is the idea we are able to exploit in mathematics when adding fractions with different denominators, etc. as we use The Master of Disguise. So whereas we started with 24, now we have:

We call a number that sits just out front of the a set of parenthesis a “coefficient”. If you break down that word it gives you more of a clue to what it means: “with” + “efficiency”. It is a simplified way of dissecting and thinking of a number. As an example, rather than thinking of the number 24 as a solid, concrete value of “24″ it might be better to think of it as 8 x 3. In this case, I could think of it two different ways: 8(3) where 8 is my coefficient and 3 is the base number or 3(8) where 3 is my coefficient and 8 is the base number. This is all, of course, very simple – and that is exactly the point. This is the first step in understanding what numbers are. We have covered 2/5 of the components of a number which brings us to our third idea: the divisor.

Every Number Is A Fraction Anyway

Any number you can imagine is a fraction, because at the very least every imaginable value is always “over 1″. The number 5? It’s really 5/1. The number 14? It’s really 14/1. -8? You guessed it: -8/1. Even fractions (i.e. 3/5 = (3/5)/1), constants (i.e. π = π/1), imaginary numbers (i.e. 2i-3 = (2i-3)/1), or even algebraic variables (i.e. x = x/1) may ALWAYS be written as [insert every number you can imagine]/1. In the case of our number 24, it is equivalent to write it as:

1(24)
—–
1

Symbolically I might code this as:

c(b)
—–
d

where d = divisor

Even the obelus (”old school” division sign: ÷) looks like a fraction! Mathematicians are so literal, but that is the advantage of mathematics! There really is no guessing involved.

The Power of Working With Roots

The last two components of numbers are the power and root. Powers and roots are used in financial equations as a way of looking into the future to see what an investment will grow to, and as a way of seeing into the past to see what amount we must have started with in the first place.

Of course, most people are familiar with where powers are written – as superscripts to the right of the base number (ie, the 2 in 4²). But what might cause a bit of confusion is the location of the root value. The radical sign was used back in the day before computers and calculators took over as a method for solving root values (square roots, cube roots, etc). The way it was done looks similar to how long division is performed now, so it made sense to write the root value inside the v shape of the radical sign √.

It looks beautiful, so we still use it today when writing formulas, but for all practical purposes it is much easier to place in the denominator of the exponent, so that the √4 can be written as 4^1/2. It’s just really convenient to have both the power and the root values listed together, so that in very long equations you don’t have to look back and forth across the page to see what the roots and powers are – it keeps everything in one place. And anyway, the modern exponential value, itself, is a fraction!

So Our Final Dissection Of Numbers Gives Us Our Final Structure Of How They Really Look

c(b)^p/r
—–––
d

Where c = Coefficient
b = Base Number
p = Power
r = Root
d = Divisor

What is important is to walk away understanding another reason why not teaching fractions in school is just a bad idea. Contained within the very definition and understanding of “what it means to be a number” is the concept of fraction. To stop teaching this is to hinder students from understanding the foundation of mathematics itself. We rest our case – the answer is no.

Considering how the internet and globalization are changing the way business is done faster than at any other time in the history of the world, I am here to tell you that you better invest in yourself. You are no longer just competing with your next door neighbor Tom for business, you’re competing with Amal from India and Chao from China. And however many billion others are out there. Make yourself more valuable by reading great books by people who have spent a lifetime studying and applying whatever it is you want to learn.

It is true: You have the right to not go to college, but you don’t have the right not to have an education.

If you think that you might be interested in the book at all, we can guarantee that it will knock your socks off. The books marked with an asterisk represent texts that contain profound wisdom, incredible value, and should be read by every student who plans on being intelligent, efficient, wealthy, and successful – Period.

College Admissions & Test Prep

Looking Beyond the Ivy Leagues, by Loren Pope
The Official SAT Study Guide, by College Board

Biographical

*The Autobiography of Benjamin Franklin
*Benjamin Franklin, by Walter Isaacson
Lincoln the Unknown, by Dale Carnegie
The Autobiography of Andrew Carnegie

Science

*A Brief History of Time, by Stephen Hawking
Power to Save the World: The Truth About Nuclear Energy, by Gwyneth Cravens
The 10 Most Beautiful Experiments, by George Johnson
Plan B 3.0: Mobilizing to Save Civilization, by Lester Brown

Math & Logic

Beyond Numeracy, by J.A. Paulos
*Innumeracy, by J.A. Paulos
The Language of Mathematics, by Keith J. Devlin
God Created the Integers, by Stephen Hawking
A History of Mathematics, by Carl Boyer
The Constants of Nature, by John Barrow
The Golden Ratio: The Study of Phi, The World’s Most Astonishing Number, by Mario Livio
*Being Logical, by D.Q. McInerny
*Speed Mathematics, by Bill Handley
One, Two, Three … Infinity, by George Gamow

Language

Grammar Gremlins: Taming the Mischief-Makers of the English Language, by Don Ferguson
Under the Grammar Hammer, by Douglas Cazort
I Always Look Up the Word Egregious, by Maxwell Nurnberg
*Proust & The Squid, by Maryanne Wolf
Read & Grow Rich, by Burke Hedges
The Gremlins of Grammar, by Toni Boyle & K.D. Sullivan

Globalization

The Lexus & The Olive Tree, by Thomas Friedman
The World is Flat, by Thomas Friedman
The Elephant & The Dragon, by Robyn Meredith
A Whole New Mind: Why Right Brainers Will Rule The Future, by Daniel Pink
How Soccer Explains The World: An {Unlikely} Theory of Globalization, by Franklin Foer
Billions of Entrepreneurs, by Tarun Khanna

Business

*Ready, Fire, Aim, by Michael Masterson
*The 21 Irrefutable Laws of Leadership, by John Maxwell
*The 17 Indisputable Laws of Teamwork, by John Maxwell
*Good to Great, by Jim Collins
*The Breakthrough Company: How Everyday Companies Become Extraordinary Performers, by Keith McFarland
*The eMyth Revisited, by Michael Gerber
*The 4-Hour Workweek, by Timothy Ferriss
*Built to Last: Successful Habits of Visionary Companies, by Jim Collins
*No B.S. Time Management for Entrepreneurs, by Dan Kennedy

Financial

*One Up On Wall Street, by Peter Lynch
*The Science of Getting Rich, by Wallace Wattles
*The Richest Man in Babylon, by George Clason
*Missed Fortune, by Douglas Andrew
*Rich Dad, Poor Dad, by Robert Kiyosaki
*Cashflow Quadrant, by Robert Kiyosaki
The ABC’s of Gold Investing, by Michael Kosares
*Gold: The Once & Future Money, by Nathan Lewis
Wealth of Nations, by Adam Smith
Why We Want You To Be Rich, by Robert Kiyosaki & Donald Trump
The Automatic Millionaire, by David Bach
Blind Faith: Our Misplaced Trust in The Stock Market, and Smarter, Safer Ways to Invest, by Edward Winslow
The Advantage of Real Estate, by Patrick Riddle, Dusty Keefe, and others

Thought Process

*As A Man Thinketh, by James Allen
The Art of War, by Sun Tzu
Our Sacred Honor, by William Bennett
*The Science of Being Great, by Wallace Wattles
*The Power of Focus: What the World’s Greatest Achievers Know about The Secret of Financial Freedom and Success, by Jack Canfield, Mark Victor Hansen, & Les Hewitt
The Secret, by Rhonda Byrne

Psychology

Snoop: What Your Stuff Says About You, by Sam Gosling
Blink: The Power of Thinking Without Thinking, by Malcolm Gladwell
Predictably Irrational: The Hidden Forces That Shape Our Decisions, by Dan Ariely
Why We Buy: The Science of Shopping, by Paco Underhill
Personality Plus: How to Understand Others by Understanding Yourself, by Florence Littauer
The Color Code, by Taylor Hartman

Personal Development

***Unlimited Power, by Anthony Robbins
*Awaken the Giant Within, by Anthony Robbins
*The Master-Key to Riches, by Napoleon Hill
The Brain That Changes Itself: Stories of Personal Triumph from the Frontiers of Brain Science, by Norman Doidge
*Think & Grow Rich, by Napoleon Hill
*Maximum Achievement, by Brian Tracy

Web Technology

AJAX Design Patterns, by Michael Mahemoff
The Art & Science of Javascript, by Cameron Adams, James Edwards, Christian Heilmann, Michael Mahemoff, Ara Pehlivanian, Dan Webb & Simon Willison
Wikinomics: How Mass Collaboration Changes Everything, by Don Tapscott
ProBlogger, by Darren Rowse
Big Switch: Rewiring the World, From Edison to Google, by Nicholas Carr
Head First SQL, by Lynn Beighley
Head First PHP & MySQL, by Lynn Beighley & Michael Morrison
The Essential Guide to Dreamweaver CS3 with CSS, Ajax, and PHP, by David Powers

Sales & Communication

Act Natural: How to Speak to Any Audience, by Ken Howard
The Back of a Napkin: Solving Problems & Selling Ideas With Pictures, by Dan Roam
How I Raised Myself From Failure to Success in Selling, by Frank Bettger
*How To Win Friends & Influence People, by Dale Carnegie
*Negotiate This, by Herb Cohen
*Am I Making Myself Clear?, by Terry Felber
*NLP Workbook: A Practical Guide to Achieving the Results You Want, by Joseph O’Connor
*No B.S. Sales Success, by Dan Kennedy

Spiritual

Disclaimer: I don’t care what religion you are a part of…these books are excellent and will rock your world.

The Final Quest, by Rick Joyner
Understanding the Purpose & Power of Prayer, by Myles Monroe
Tender Warrior, (for dudes) by Stu Weber
*The Four Agreements, by Don Miguel Ruiz
*The Dream Giver, by Bruce Wilkinson
*The Prayer of Jabez, by Bruce Wilkinson
*Secrets of the Vine, by Bruce Wilkinson
Mere Christianity, by C.S. Lewis
The Screwtape Letters, by C.S. Lewis
The Problem of Pain, by C.S. Lewis
The Great Divorce, by C.S. Lewis
Can Man Live Without God?, by Ravi Zacharias
The End of Reason: A Response to the New Atheists, by Ravi Zacharias & Lee Strobel

Misc

*Tipping Point, by Malcolm Gladwell
Thinking For a Change, by John Maxwell

A Logical Approach To A Big Question

Lately there has been a lot of discussion around town regarding the overcrowding of Wando High School. I haven’t really heard any other ideas on how we might solve this problem other than to build another school, so I have taken it upon myself to think of at least one proactive solution.

There are already a large number of nationally accredited colleges offering entire degrees and certifications through an online curriculum, and one has to ask the question: Why can’t we do this for high school students also? It is just a matter of adoption. When the first fax machines and cell phones came out there were only a few hundred people around any given community that had them. But as these technologies became more cost effect and, certainly, as more and more people used them, everybody else had to have them also.

The internet community is about to grow to 3 billion as the earth becomes more and more hard-wired. The workers of the future aren’t just going to be competing with Joe down the street, or John who graduated from Harvard Business School – they will be competing with Harish from India, Xiao from China, and the billions of other workers all over the world. It’s called Globalization, and when we say “The workers of the future”, what we really mean is, “The workers of tomorrow.” User-adoption of the internet continues to grow at exponential rates, and we still have yet to see the mobile internet take off in the US, even though countries like Japan are years ahead of us with mobile computing.

Earlier this year Verizon Communications gained permission to land their Trans-Pacific fiber optic bandwidth cable in Oregon, linking mainland China with mainland US. Several weeks later Google, along with six other companies in the Unity conglomerate, announced their plans to link Japan to California. The world is becoming more and more wired at an extraordinary rate, and China already has all the capabilities it needs to become the next silicon valley – raw materials, giant factories, technological know-how, and all.

There is little, if any, doubt as to the vital importance of being web-savvy in today’s working community, and it would be difficult to argue that students should not be learning how to learn online at earlier ages anyway. I have already heard many talks about the construction of another massive complex – as if this is the only solution. Have we learned nothing from the great mathematician of Antiquity, Archimedes, who once said, “Give me a place to stand on and I will move the Earth.” Of course, he was speaking in terms of leveraging that which he already possessed, which allowed him to generate incredible force with very little effort.

In a time when technology has given us the ability to tap into the collective brilliance of mankind through the internet, why not explore this medium, as so many other colleges have successfully done already, to educate our youth?

Not only would it take a fraction of the time to develop the online platform (probably available by next fall), it would only require a fraction of the cost. After all, how much does it cost to hire an architect, construction crew, engineers, and materials for constructing a new educational facility? Here’s a hint: $65,000,000. As a private educator who has been leveraging web technologies for almost two years now, it has become entirely clear to me that web languages and technologies have finally become sophisticated enough to transform information into personal, meaningful lessons. To be sure, we have spent far less than even $30,000 to develop our own platform to a utilitarian degree. Granted, we have done a lot of the work ourselves, but isn’t that the point anyway?

For ten million dollars, as an example, not more than 2% of that ($200,000) should be adequate for programming the online community, 20% ($2,000,000) really should be enough to “subsidize” enough hardware and equipment to support students, teachers, parents, and admin, and 20% ($2,000,000) would increase the amount of money teachers should be paid for the additional skills they would have to develop to accomplish this task. The rest could be spent for incidental expenses and could serve as a treasury to fund IT support, networking, and other expenses. It might cost a little more than that, but not really much – if at all. It is far more likely that this will be way more than is needed. Logically, we might handle it this way:

1.) Split Wando High School into two halves: 1: Freshmen and Sophomores, and 2: Juniors and Seniors.

2.) Freshmen and Sophomores would attend school on Mondays and Wednesdays, and Juniors and Seniors would attend school on Tuesdays and Thursdays.

3.) Fridays would alternate between the two groups so that Freshmen and Sophomores would attend this week, as an example, and next week Juniors and Seniors would go.

4.) On days when students were not physically in class, they would be at home and online – meeting with their teachers and fellow students just as they would during any online course.

5.) After school extra-curricular activities would move forward as “business as usual.” Students who attend school online during the day would still go after school for soccer practice, additional tutoring, and so forth.

This would save on gas, traffic jams, and travel time for students, and even though it might be tedious to develop an adequate transportation system for students who rode the bus, this really is just a detail.

As a society we have invested so much time, energy, and resources to develop computing and information technology to where it is today, it sure does seem like we could Think Archimedes, so to speak, as a way of addressing the issue. Why not leverage resources that are readily available NOW.

In a time when the economy has been blind-sided by the government having to bail out Fannie Mae, Freddie Mac, the state of Texas after Ike, and AIG … when 284 major lending institutions have collapsed since 2006 … when government debt service payments are the third highest bill of the government and climbing … isn’t it just time to ACTUALLY change how we think about solutions to problems. In this political climate of promises and showboating, let us remember that it isn’t the politicians that have historically solved our problems.

Collectively, we have the ability – there is no shortage of imagination and brilliance within all of us to develop real, meaningful solutions outside of the box. It doesn’t take the government – it just takes a little courage and determination. After all, what better lesson can we teach our own children other than to dream big, dream hard, and never, ever give up.

Just a thought…

Imagine being brought into the world at a time when Alexander the Great has just conquered Egypt. He dies and is replaced by King Ptolemy I who establishes the Library at Alexandria – the first intellectual Mecca to EVER be established in the history of mankind. This same King hires Euclid to compile all of the known mathematics in the world, which has recently been published. You are born to an astronomer anyway, and at the age of 4 you are sent from Syracuse to this great city of knowledge, Alexandria, to study for twelve years under many teachers, not the least of whom may have been Euclid himself! While you are there you get to see the Pyramids, Sphinx, the annual flooding of the Nile, the irrigation canals, and ALL of the splendor that was the height of, arguably, the greatest civilization to ever inhabit the Earth. He would have seen all of the mechanics of the wine and olive presses, the methods of leverage used by the Egyptians to construct such monumental pyramids, and learned all of the other royal subjects of philosophy, astronomy, and logic.

This was the childhood of The Greatest Mathematician of Antiquity. It is no wonder that Archimedes would advance mathematics so far that he would nearly invent Calculus within one generation of Euclid! In his lifetime he would:

• witness three full-scale wars involving the surrounding cities and provinces of the Mediterranean,
  
• be appointed as chief military advisor to King Hiero II,
  
• discover the laws of displacement,
  
• hack known mathematics to mimic calculus – thus greatly improving mankind’s approximation of pi after 4000 years,
  
• discover the exact area of a circle,
  
• the exact surface areas and volumes of the sphere and cylinder,
  
• discover mathematical representations for buoyancy and the properties of floating objects,
  
• create a mechanical way for moving water uphill,
  
• and devise countless war machines that would protect Syracuse for THREE years during the Roman siege in 214.
  

He would witness the death of his beloved King and was entrusted with the protection of all that was Syracuse. His legacy serves as a living testimony to the many joys, accomplishments, and rewards of a life spent dedicated to mathematics.

Archimedes lived to the ripe old age of 87, and was deeply respected by even his enemies, for they knew of his notorious abilities that absolutely annihilated enemy troops that would breech the peace at Syracuse. The ancient commentator, Plutarch, once wrote:

“In the meantime huge poles thrust out from the walls over the ships and sunk some by great weights which they let down from on high upon them; others they lifted up into the air by an iron hand or beak like a crane’s beak and, when they had drawn them up by the prow, and set them on end upon the poop, they plunged them to the bottom of the sea; or else the ships, drawn by engines within, and whirled about, were dashed against steep rocks that stood jutting out under the walls, with great destruction of the soldiers that were aboard them. A ship was frequently lifted up to a great height in the air … and was rolled to and fro, and kept swinging, until the mariners were all thrown out, when at length it was dashed against the rocks, or let fall.”

What was he like?

We don’t know a great deal about the type of person that he was in character. We can only infer the types of qualities that those of great intellectual strength tend to have and put it into historical perspective.

Syracuse was founded 8th century BC as an annex of Corinth at the epicenter of the Mediterranean. Because of its strategic position on the South-Eastern tip of the province of Sicily, it became a great city of trade and commerce, and a constant target for opposing forces. From the town’s inception until the rule of King Hiero II in 3rd century BC, constant turmoil swept the province as Rome constantly sought control of the strategic port. In 263 BC, Hiero II secured a peace treaty with Rome that lasted until his death in 215 BC. It was not until this time that the Great Mathematician of Antiquity came on the scene. Archimedes enjoyed peace and prosperity in his hometown for most of his life and this probably allowed him much of the time he needed to develop his discoveries.

Syracuse sits on the Southeast tip of Sicily

Sicily sits at the epicenter of the Mediterranean

Archimedes probably studied at the Library of Alexandria, Egypt where nearly all of the world’s written knowledge existed at that time. Egypt boasted the great Pyramids of Giza, the Sphinx, great architectural structures, irrigation canals, and a host of other technologically advanced mechanical applications from which Archimedes could observe and contemplate. Alexander the Great had recently (100 years since) conquered the Persians and mandated that a great learning center be constructed with the charge of amassing everything known to the Eastern and Western worlds.

We know that Archimedes was extremely dedicated to his craft and reaped great rewards because of it. Archimedes was, himself, very wealthy and likely wanted for nothing – for most certainly anyone with such critical responsibilities would have been very highly compensated. He probably woke up very early and went to bed later in the evening while taking periodic naps during the day as needed – just like many of our contemporary thinkers do.

It is said that, “Small minds talk about people, average minds talk about events, and great minds speak of ideas.” Because of this, Archimedes likely did not hold a great many true friends, but something more akin to a small band of intellectual thinkers with which he could leverage his own knowledge and bounce ideas off of (Napoleon Hill would call this a “mastermind group”). He probably shunned idle chatter, exhibited a great deal of sobriety, and spent a large portion of his time alone. To accomplish so much in one lifetime he must have been excellent in practicing time management, and likely was in great physical shape since it takes great strength and stamina to work upon engines and stay energized, let alone to live to 87.


What did he teach us?

The story of Archimedes is the testimony of a life spent dedicated to excellence, achievement, and innovation. Before his time there were no textbooks to be read on mechanics (though one existed for geometry), no internet how-to videos for fabricating a home-made potato bazooka, or electric power as we know it today. Archimedes lived by imagination – tying the abstract world of pressures, forces, and mathematics to the physical world of mechanics, pulleys, and levers. He brought us the great joy and deep satisfaction in understanding a quantified world. He brought enjoyment and application back to a study that, historically, has been dull, boring, and uneventful.

-Archimedes taught us that to truly accomplish anything we must immerse our minds in continuous thought. Plutarch wrote, “Often times Archimedes’ servants got him against his will to the baths, to wash and anoint him, and yet being there, he would ever be drawing out of the geometrical figures, even in the very embers of the chimney. and while they were anointing of him with oils and sweet savors, with his fingers he drew lines upon his naked body, so far was he taken from himself, and brought into ecstasy or trance, with the delight he had in the study of geometry.”

How many people ever think to apply something like this? An example might be if someone had the desire to learn Spanish. What is the best way to do this? Well, certainly the path most traveled to this end is going to college, spending $50,000 and four years of time, and then walking away with a degree, which may or may not mean you are completely fluent in a language. And anyway, while in college you are still speaking English – this is not immersion. Archimedes might not think too highly of this path for a number of reasons:

1.) In the first place, it takes a long time
2.) Secondly, that is a lot of money just to learn something
3.) Archimedes didn’t need the approval of others to value himself

Instead, he might have taken $5,000 down to Mexico, moved to a village where nobody spoke English, and lived life for six months; being sure to read their newspapers, listen to their music, and actively absorb the culture. He might have even found himself a Spanish Philly to date and learn from while he was there (of course, being entirely respectful). That is what it is like to be immersed in something.

-See with the mind … be creative to the point of invention. He often solved proofs through the “method of exhaustion”, sometimes referred the “indirect passage to the limit.” In this way, he would inexorably seek greater and greater accuracy in his work, being sure to think of every single detail. To him, being close enough wasn’t good enough. Before his time the closest estimation of pi was calculated by the Egyptians 4,000 years previously by estimating the area of a circle to be approximately equal to the area of a square whose side is eight ninths the length of the diameter. Archimedes needed greater accuracy so that he could be confident that all of the mathematics he spent so much time developing would be the absolute best it could possibly be. As a result, he didn’t just get it close – he nailed it.

By computing the area of a circle using this method
we get an estimation of pi that is a half of a percent off of its actual value.

The way that he did this was to cut the circle into an infinite number of slices and alternately align them tip to crust. The picture below only cuts the circle into eight pieces so it may be difficult to immediately discern the logic used to show this, but of course, as the circle is cut into more and more slices (to the point of infinity), the bumpiness of the line becomes perfectly straight. This concept became the birth of the infinitesimal, a numerical amount so incredibly small you literally cannot conceive of it’s value.

” … for certain things first became clear to me by a mechanical method,
although they had to be demonstrated by geometry afterwards
because their investigation by the said method did not furnish an actual demonstration.”
-Archimedes

**It is clear from this that, though he did not have the actual mathematics available to him, he trusted his gut that he was correct.**

- Archimedes accepted nothing less than perfection. It is said that if you are willing to accept anything less than the best, you often get it. We know that Archimedes used the method of exhaustion to check his work. In this way he would inscribe and circumscribe a polygon with n-sides about a circle and average the two together (below). By doing this, he certainly must have seen that, as he added additional side lengths to each polygon, each one began to look more and more like a circle. If he could add an infinite number of sides to the polygon, it would literally BE the circle. This realization that the number of sides could be, theoretically, infinite would create inconceivably small slices of the circle that could be reconstructed in such a way as to become the area of a rectangle. Archimedes pushed the boundaries of infinity to reach perfection.

This understanding of minuscule values is what led, ultimately, to the development of calculus. In fact, Archimedes probably would have invented Calculus himself if there had been ANY ground work for him to work from at all. On this topic however, there were no textbooks, no nomenclature (that is, existing symbolic representations he could use as shorthand), no class he could take at the local community college.

It is amazing to think of the fact that tens of thousands of students, every year, take and understand calculus before the age of 20 – a subject that Archimedes, himself, would never know, even at 87. It wouldn’t be for another 1800 years when Sir Isaac Newton and Wilhelm Leibniz would independently discover calculus (from the integral and derivative perspectives, respectively) that humanity would have mathematical methods to solve these equations. Nevertheless, he must have known he was incredibly close to developing the idea himself, and were his life extended an additional fifty years who knows what more would have been discovered.

– Archimedes must have taken personal responsibility for all things related to the protection of his city. At some point in every champion’s life there is a realization that success is up to the individual. Surely Archimedes realized that he, alone, had the mental capacity and ability to use known physics and mathematics to protect the city. Everything and everyone that he held so dear – his family, his friends, his home – counted on him to ensure their safety. After all, if he didn’t devise a new way to protect the harbor, if he couldn’t figure out how to leverage the forces that be to his advantage, if he didn’t develop and improve new and existing war machines, then the Roman Army, which beat at his doorstep, would sweep through and sack the city.

Who else could he or anyone else trust to oversee this task? Absolutely nobody, and that is why King Hiero II of Syracuse named Archimedes, a mathematician, as chief military advisor of the entire city! Is it really any wonder, then, how he could get so lost in his work that he forgot to even eat?


– Archimedes’ greatest lesson taught us to do more with less. Archimedes was clearly a holistic thinker. He made sure to see with his mind and not with his eyes – seeing machines before their manifestation, and he taught us to work smarter instead of harder.

In Stephen Hawking’s book, God Created The Integers he mentions how:

Yes, it’s true*! Through a few simple laws of Algebraic Rule we can now make this claim with 100% confidence**! How you ask? It is all quite simple:

Assumption #1: The first concept you have to understand is the Identity Property, which states that any number is equal to itself.

As an example: 15=15, 33=33, and 101=101. That doesn’t seem so difficult does it? Thus, let us claim that any two integers , x and y, are equivalent in value when: x=y, where x is equal to y (redundant, I know).

As an example I recently heard somebody tell me that he was paid “biweekly.” But I really knew that he was not paid twice per week because that was not the context used. Interestingly enough the word “biweekly” actually does hold dual meanings. It can mean, “twice a week,” or it can mean, “every two weeks.” There are really two things to say about this.

The first is that this is a classic example of where social-wide ignorance has created ambiguity. Truly it is rare to come across a well-spoken individual: One skilled in oratory and definition. Rare indeed is the person who actually says something (just listen to any politician). I am sure all of you can remember a time when you have had a conversation with somebody for several minutes and walked away wondering what it was you just spent all that time talking about. The world is filled with people who can tell you all about something they have no real knowledge of.

Secondly, don’t assume that just because you have heard a word before or seen it in a book that you own the word in your repertoire. One of the only dangers of reading is that when you see a word repetitiously you can get a false sense of confidence in its meaning. The band 311 has a song entitled, “Reconsider Everything” which really sums up the idea here:

“What if the truth is that there is no truth
The only thing I can prove is there is no proof
Don’t be so sure that your source is correct
People believed it before, before they had checked”

Since the foundation of mathematics is arithmetic, it would be great to have an understanding of the different types of numbers that you will be working with in the first place. For lack of a word that actually exists, let us call this realm of all possible numbers the Numberverse.

For the SAT, the Numberverse is only as large as Real Numbers (you will never be tested on imaginary/complex numbers on the SAT). The following diagram I found at wlonk.com:

I like it because it is simple and does a great job at showing examples within each set. However, you will notice that in Natural Numbers it contains the value zero. I picked this as an example because it makes the assumption that zero is a Natural Number. I have always been taught, and continue to teach, that zero is NOT a Natural Number because I cannot actually possess zero of something. I simply do not have it. I have always called the set containing zero, “Whole Numbers” and showed Natural Numbers as a subset of Whole Numbers.

Even in mathematics there are philosophical debates at every level about simple things like this. All I can tell you is to assume nothing and Reconsider Everything.

Fractional values allow you to work with absolutely perfect values – that is, 1/3 can be multiplied and worked with perfectly, however it’s decimal equivalent of .333333333 will never be a perfect value. No matter how far out I take the decimal places it will always be an approximation (this is why the discovery of C/d for pi was so important).

Irrational numbers were to be the great crisis of the Pythagoreans – who believed that every number could be expressed as the ratio of two other numbers. At the time, Pythagoras had discovered that if a string had a length of 634mm (as an example) and tuned to the note C, then by cutting the string in exactly half (317mm) he would again find the same note C – just an octave higher.

The Pythagoreans’ assumption that all numbers could be expressed geometrically as the relationship between two whole number values would be for naught. The demonstration of applied mathematics has always served as a point of validity for mathematicians, and certainly Pythagoras was seeking to demonstrate the relevance of mathematics by, at the very least, perfecting the musical scale.

Of course, the discovery of the octave left the Pythagoreans scratching their heads. After all, how do you exactly measure a distance whose decimal values extend forever? To obtain a perfect pitch they discovered that frets on a guitar, as an example, needed to be placed in such a way that the string length played on each fret would diminish by successive powers of the twelfth root of 2 – which is an irrational value.

In this case, if L₀ is an E note, then L₁ is the next note on the musical scale: F, L₂ is an F#, L₃ is a G, L₄ is a G#, and so on.

According to legend, the Pythagoreans put one of their own to death for revealing to the outside world that the square root of two is an irrational value and, thus, that irrational numbers did in fact exist.

It is amazing to think that mathematics, irrational numbers to be more specific, could have such a valuable place in the things we love the most. Anyone who has enjoyed music, art, and nature has been blessed by the discovery and application of irrational numbers, which would never have been discovered in the first place were it not for the hard work and dedication put forth by history’s mathematicians.