Discovering Technical Math and the Tools of the Trades
Chapter 2: Discovering Technical Math and the Tools of the Trades
“It’s too hard.”
Another grand math myth is “It’s too hard.” This myth was probably started by a person who said that about everything. Life isn’t particularly easy, so the mantra probably got a big reception from everybody, not just those who were doing math. Survival isn’t easy. If you go back a zillion years (that’s an approximate date), you see that hunting for food was “too hard,” yet some- how the human race hunted, survived, and got civilized.
You know what’s hard? Walking is hard. A human being isn’t constructed all that well for walking, but the average child learns how to walk by the time she’s about 11 months old. She looks a little clumsy at first but later becomes very proficient at walking as she does more of it.
Driving a car is hard, but most people can do it. They learn how to drive, and then (get ready) they drive. Two things make you a good driver: knowing the fundamentals and practicing.
That concept, of course, is shared by every professional dancer and athlete in the world. And it applies to just about every action or operation a profes- sional does. It’s the same with mathematics. Know the fundamentals and practice. It’s a mantra you can live by. The carpenter’s first try at driving a nail probably bends the nail, and his first saw cut is probably crooked. But knowing the fundamentals and practicing eventually make the difference.
“I have a phobia.”
This misconception is a variation of the popular statements of denial in the preceding sections. Unfortunately, the argument doesn’t have legs, because all people approach new experiences with anxiety.
The distinction between anxiety and phobia is important. Anxiety is an everyday emotion. A phobia (a fear) is an anxiety disorder. Phobias are the most common form of anxiety disorders. In a study, the National Institute of Mental Health found that between 8.7 percent and 18.1 percent of Americans suffer from phobias.
You may have a phobia, but actual, legitimate math phobia (fear of not suc- ceeding at math) isn’t common, regardless of what Internet hucksters try to tell (and sell) you. To be fair, math phobia does exist, but it’s not a perma- nent condition; after sufferers experience even small amounts of math suc- cess, they usually overcome it. So really, having a math phobia is even more reason to do math.
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Remember: Somebody Else Already Did the Hard Work
Civilization makes math. But here’s a paradox. Math makes civilization.
Mathematics started a long time ago in a galaxy far away (well, actually, on this planet). In the beginning, math was just about counting. (See Chapter 3.) And for a time in human existence, that was all people needed.
Well, being a hunter-gatherer is all very fine, but (to tweak an old song), we can show you a better time. That “better time” was nice, stable agriculture, which required some basic math to make it work when it was established about 10,000 years ago. Farming settles people down. It starts cities growing and it also produces specialized trades.
Math lets a culture do more, have more, and be more. As cultures grew more civilized, they needed to measure land and trade with other cultures. That requires math, so technical math grew and got sophisticated.
In the mere thousands of years from the cave dwellers to texting, mathemati- cians made discovery after discovery. They not only figured concepts out but also did what are called rigorous mathematical proofs. To put it another way, if you read about something in a math book, it’s been proven true.
Ancient cultures from all over each provided something. Several cultures came up with the same concepts independently, and others passed concepts on to other cultures. Historians don’t know for sure exactly who did what when, because trustworthy history is based on written records, which don’t always exist.
The following list gives you an overview of some of these historic contribu- tions. There’s no mystery in this very brief history — just highlights, folks, because the full story is enormous, and some of the details come up in the other chapters of this book. The point of this cultural timeline is to show that the math has been developing for a long time. The concepts in this book have been used by billions of people.
✓ Prehistory marks the birth of counting and tally sticks.
✓ The Babylonians introduced arithmetic, algebra, and geometry around 3,000 BC. Math not only was handy for measuring the farmers’ fields but also helped the king collect taxes and astronomers look at the stars.
✓ The Egyptians gave humanity measurements, the math for agriculture (as early as 5,000 BC), and the math to build 138 pyramids (as early as 2,630 BC).
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Chapter 2: Discovering Technical Math and the Tools of the Trades
✓ The Indus Valley civilization produced the concept of the decimal system and the concept of zero (about 100 AD).
✓ The Greeks provided, among other things, the systematic study of math- ematics (between 600 BC and 300 BC). That includes rigorous arguments and proofs.
✓ The Romans, among their many contributions, developed the standards still in use today for the weight and purity of gold and for precious metals and gemstones.
✓ The Arabs were the conduit for the discoveries of China and the Indus Valley civilization to Europe. They formalized the concept of zero and made other brilliant discoveries on their own.
✓ The Chinese developed math independently and were making strides as early as 300 BC.
✓ The Europeans produced some wonderful math before and during the Enlightenment. Isaac Newton gets credit for calculus. Copernicus gets credit for modern trigonometry, and René “I think, therefore I am”
Descartes had many hits on the top-100 math charts. He’s especially known for Cartesian coordinates. Head to Chapter 14 to see more about Cartesian coordinates.
✓ The Mayans had a super calendar and an excellent number system.
They also had the concept of zero.
✓ All the other civilizations surely made unknown contributions. Where the historical record stops, the mystery begins. Perhaps the Hittites originated the credit card, or the Celts first developed the subprime mortgage.
The Trades, They Are A-Changing
Building technologies are probably the oldest trades, and they’re in no danger of disappearing. In fact, they’re more complex than ever. In addition, new trades are popping up regularly. As new careers come into existence and old careers evolve, the education and technologies that go with them must adapt. Trade schools (community colleges, technical colleges, and regional occupational programs) continue to offer vocational programs that expand as society’s needs expand, including creating green programs as environmen- tal consciousness becomes more socially important.
These expansions reflect three broad trends. First, once-new technologies, such as automobiles and air conditioning, are a permanent part of modern life (yes, Virginia, cars and AC weren’t always common), so society must educate
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people to handle them. The second trend is the need to provide more special- ized education for practitioners. The third trend is that education must offer training for the newest careers.
Here’s a tough assignment (NOT): Go see a movie. Make it an animated one if you can. At the end of the film, study the credits as they crawl by — you see the names of dozens of traditional Hollywood specialized crafts, but you also see many new careers. Some skill areas, such as computer generated imagery (CGI), were absolutely unknown not so long ago.
Technical careers continue to evolve. Some jobs haven’t been created yet, so we can’t exactly list them here. Other jobs are turning into professions right now as the required skills become more formalized and people need more advanced education in how to do them. As technology advances, your career will likely evolve into something other than what it is now. If you maintain your current skills — especially your math skills — and keep your eyes open for what a new career requires, you can transition with no problem.
Math Devices That Can Help You Do Your Job
Specialized calculators and measurement tools help you do your work more efficiently, but that doesn’t mean you should ignore general math skills.
General math skills are great because they are general.
General skills are in your brain, which is a handy place for them. And you never have to replace batteries. You can use the skills in more than one career, which is excellent because experts say that the average person changes careers several times in a lifetime. Lastly, unlike a lot of tools you use on the job, you take your math skills home or anywhere else.
That said, some specialists make the same kind of calculations all the time, so specialty calculators devoted mainly to calculations needed for a particu- lar trade are great additions to their math skills.
Some careers require more measurement than calculation; as a result, you can also find special measurement devices that give you exactly the infor- mation you need. Because some of them contain a computer chip (such as a nursing assistant’s body mass index calculator), the machine does both measurement and calculation automatically, and the technician just sees the result as a measurement. The following sections give you a look at some of these calculators and measuring devices.
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Chapter 2: Discovering Technical Math and the Tools of the Trades
Pocket (or phone, or computer) calculators
Although your mind is an excellent calculator, life is short and some calcula- tions are long. For complex math operations or any math operation on items with many digits you probably need a calculator.
Get off your wallet and buy a pocket calculator
A basic calculator (sometimes called a four-function calculator) is really simple and very inexpensive. This calculator does four basic math functions: addi- tion, subtraction, multiplication, and division. But even the simple ones often include percentage and square root functions.
A more complex calculator is called a scientific calculator, but you don’t have to be a scientist (or play one on TV) to use it. This calculator not only does basic math but also has more buttons so you can do trigonometry functions, exponents and roots beyond square roots, and logarithmic functions that use both base 10 and base e.
Both types are still called pocket calculators. They have come a long way, since the first ones ranged in size from a box covering your entire desk to a
“handy” unit the size of a large book. Eventually, they shrunk in size to fit in your pocket, and some are now so small they fit on a keychain.
You know your cellphone has one
That’s right! Your new mobile phone has a good calculator. For that matter, so does your older mobile phone. Just look for your phone’s application icon or go to the standard menu to look for the built-in calculator. It’s there.
Apple iPhones have a really cool calculator. When you hold the phone vertically (portrait mode), it’s a “regular” four-function calculator. When you rotate it to the horizontal position (landscape mode), it becomes a scientific calculator.
Do it with a mouse
Desktop and notebook computers have come with built-in simple calculators for a long time. In the Microsoft Windows operating system, the classic ver- sion was a four-function calculator, as shown in Figure 2-1.
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Figure 2-1:
Microsoft Windows four- function calculator.
Calculator Calculator Edit View Help
0.
Backspace CE C
sqrt / 9 8 7 MC
%
* 6 5 4 MR
1/x - 3 2 1 MS
= + . +/- 0 M+
Later versions of Windows have both a basic and scientific option. The scien- tific option is shown in Figure 2-2.
Figure 2-2:
Microsoft Windows scientific calculator.
Calculator Calculator Edit View Help
0.
Backspace CE C
Mod / 9 8 7 MC
Or
* 6 5 4 MR
Lsh - 3 2 1 MS
= + . +/- 0 M+
And Xor Not Int E D C B
A F
pi ] ln log n!
1/x [ Exp x^y x^3 x^2 F-E dms sin cos tan Sta
Inv
Ave Sum s Dat
Hyp
Hyp Dec Oct Bin Degrees Radians Grads
To run the calculator application in Windows, click Start→All Programs→ Accessories→Calculator.
The classic Apple Macintosh (Mac) calculator is a four-function calculator.
The dashboard calculator widget (an on-screen mini-application) that comes with the Mac OS X operating system has three options: basic, scientific, or programmable.
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