February 21, 2006
I confess to be one of those people who hate math. I can do my basic arithmetic all right (although not percentages) but I flunked algebra (once), barely passed it the second time — the only proof I’ve ever seen of divine intervention — somehow passed geometry and resolved, with a grateful exhale of breath, that I would never go near math again. I let others go on to intermediate algebra and trigonometry while I busied myself learning how to type. In due course, this came to be the way I made my living. Typing: Best class I ever took.
Here’s the thing, Gabriela: You will never need to know algebra. I have never once used it and never once even rued that I could not use it. You will never need to know — never mind want to know — how many boys it will take to mow a lawn if one of them quits halfway and two more show up later — or something like that. Most of math can now be done by a computer or a calculator. On the other hand, no computer can write a column or even a thank-you note — or reason even a little bit. If, say, the school asked you for another year of English or, God forbid, history, so that you actually had to know something about your world, I would be on its side. But algebra? Please.
I’ve often said that writing is a good thing. Writing allows one to clarify ones thoughts. Writing takes what is often floating ideas in our heads, and forces us to place it into proper order. At that point, we can evaluate whether or not it is “logical” and/or meaningful. What’s missing from Cohen’s writing? Logic, obviously…
First things first. Typing is no more than an ancillary skill to Richard Cohen’s career. At worst, he could write his columns by hand, and pay someone else to type them for him. Slightly less worse would be that of the “hunt-and-peck” variety, who type, only less quickly than Cohen. To show just how much of a logical fallacy it would be to say that a journalist’s typing skills are how they make their living would be to hear a computer scientist say the same thing. But by Cohen-logic, it’s true. You must be able to type to write computer programs, right? And learning to type, then, is a crucial skill in the programming of computers. All Cohen has acheived by taking classes in typing is to get his muddled thoughts out of his head more quickly than if he were hunting and pecking for keys. Judging by this column, perhaps thinking more and typing less would have served him better. After all, if typing is the key to becoming a successful writer, there are about a million secretaries across the country about to steal his job!
Second, I hate to even address the fact that he claims to never use algebra in great detail, except to say that he either uses algebra on a nearly-daily basis (albeit without writing out equations in detail), or I hope for his sake that he’s not in charge of his finances. At the very least, if he’s that bad at percentages, by which I assume he’s including those dreaded “fractions”, I dearly hope he doesn’t cook his own meals. If a recipe serves 4, calling for 1/4 cup of this, 2/3 cups of that, and he’s trying to expand it to feed 12, I don’t want a seat at that dinner, because I can be assured that someone who doesn’t do algebra is going to screw it up. Since I’ll bet he manages to survive through his daily life, I’m guessing he does use algebra. If he doesn’t, of course, I’d love to let him have a seat at my poker table!
Following his logical misstep in the claim that learning to type is the basis for becoming a journalist, and his clearly false claim that he has “never one used” algebra in real life, you’d think that would be enough for two paragraphs. But he has to follow it by showing ignorance of the difference between math and calculations. Humans do mathematics. Computers do calculations. Computers and calculators follow a very simple formula: GIGO. You put Garbage In, you get Garbage Out. As an example, the hardest academic class I’ve ever taken in my life was Electromagnetic Fields and Waves. If you’ve ever had the misfortune to take a calculus-based physics class on electricity and magnetism, it’s that class– on methamphetamines with a PCP chaser. In fact, any Purdue EE’s that are reading this are already feeling the migraine start. If you could figure out how to accurately describe the problems in that class based upon the information given, you could quite easily (well, after a double or triple integral) solve the problem. If you could figure out how to describe the problem, you could probably get a computer or a very advanced calculator to give you the correct answer. But the difficult part, and the mathematics involved, is the setup of the problem, not the calculation of the problem. Computers can’t do the math for you, they can only do the grunt-work of calculation. One aspect of learning math, of course, is that it allows you to see through TurboTax’s Guarantee of “100% Accurate Calculations!”, when you understand that all they’re advertising is the ability to add, subtract, multiply and divide. They’re not advertising 100% accurate returns, but someone who doesn’t understand the difference between mathematics and calculations won’t easily make that distinction.
So he’s thrown up three fairly major problems in a mere two paragraphs… I think I’ve already learned enough to know that I’ll never need to read a Richard Cohen article again. Yet, I am digressing by picking his writing into little shreds. What I really would like to do is explain just how important math and/or logical instruction is to the world. Thankfully– as I’ve already written enough– a few other people have beat me to it.
Logical reasoning is connected because logic follows from mathematical rules that start in algebra. He says “writing is the highest form of reasoning” or something like that, and math wizzes can’t write. What hogwash. The LSAT, the test to get into law school, has four parts: logical reasoning, reading comp, short arguments and a writing portion.
The highest LSAT scores come from the following majors: (1) Math/Physics; (2) Philosphy/Religion (philosphy typically teaches logic rules that are based in algebra and other math concepts and rules); and (3) Economics (similarly, teaches logic reasoning and uses a lot of algebra and calc).
Not that the world necessarily needs more lawyers, of course! But ask yourself about the times you’ve debated a lawyer versus the times you’ve debated a writer: Which one was a stronger debater? Which one had the stronger logical reasoning skills? While many writers believe passionately and are well-versed on a particular subject, if you had to switch sides in a debate, who would scare you more? That’s what worries me about most lawyers, who can argue both sides of a debate impeccably, because they know how to find and expose flaws in reasoning.
Strong logical reasoning is a key component found among good lawyers. It is not surprising, then, that the people who do well on the LSAT are disproportionately those in majors that rely heavily on those skills. Now, only a small portion of lawyers become litigators, which is what we think of when we hear the word “lawyer”. Litigation takes certain skills of public speaking and oration in addition to those listed above. The foundation of the legal profession, though, is logic and reasoning.
KJ was responding to the claim made by Cohen that “writing is the highest form of reasoning”. I, of course, take issue with a pathetic claim like that. Thankfully, again someone else has done the heavy lifting, and I thank KJ for pointing me his way. Cog at The Abstract Factory:
This leads me to my next point, which is the intrinsic ludicrousness of the claim that writing is the highest form of reasoning. I love writing and I love reading, but no finer device was ever invented for deception, obfuscation, sloppy thinking, and straight-up nonsense than natural language. The proof of this is Cohen’s column, which is a mile-high pile of crap, but is written in a sufficiently entertaining style that many readers will not be put out by the glaring errors of fact and reasoning within it.
People who study reasoning — i.e., logicians — rapidly abandon natural language and develop formalized notation using algebraic rules. (Note that “algebraic” here denotes something broader than high school algebra.) In formal logical systems, one is forced to state one’s premises and rules of inference explicitly; and, given an explicit enough derivation for a conclusion, one can usually determine via syntactic inspection alone whether the reasoning is valid. The tools of formal logic are so useful that non-logicians in philosophy have adopted aspects of them more generally. In fact, formalizing Cohen’s argument above would make it immediately clear how silly it was.
This is why, throughout history, so many of our best philosophers were also mathematicians. Liebniz, the founder of calculus (at the same time Newton was working separately in the same field), was a very well-known philosopher. Descartes, arguably a much better mathematician than philosopher, is more famous for the latter, coining the phrase Cogito ergo sum (I think, therefore I am). And the “double threats” of olden days were hardly the exception. Mathematics and philosophy spring from the same well: logic. They are only different applications of the same basic skill set.
The problem with the world today is not that our students spend too much time on math, which so many of them won’t directly use in their careers. The problem is that our schools spend too much time teaching specific knowledge, rather than teaching the basics of thinking.
I personally believe that in addition to teaching algebra, all high schools should teach at least one semester, more likely two, in basic logic and debate. One semester could be devoted to the basics of logic: take an argument, reduce it to symbols, evaluate its validity. Explain what a syllogism is. Explain that for an argument to be valid, the conclusions must flow from the premises according to natural rules. Then show valid but unsound arguments, to ensure that students understand the flaw behind constructing a valid argument based on false premises. The second semester would be devoted to logical fallacies. Explain the correlation/causation problem. Explain why an appeal to authority is false. Explain how people trying to lead you one way or another are prone to giving you a false choice, and how to spot a non-sequitor. This course will be the easiest way to ensure that people aren’t bamboozled by politicians, salesmen, and every other huckster and swindler looking to exploit them.
To prepare students for life in the real world, you can never expect to arm them with all the knowledge they’ll need. The breadth and depth of knowledge necessary to live a successful life is ever-changing and always growing, and is far too wide and deep to cover in four years. What you must do is to arm them with all the tools they need to find and understand the knowledge waiting for them in the world. Reading and writing are crucial tools, because they are the means to acquire and pass on knowledge and ideas. Math, science, and logic, however, are just as crucial, because they are means to understand, evaluate, and differentiate good knowledge from bad. While Richard Cohen may not believe that math in necessary to do this, I think that should cast into doubt any words he writes about economics, taxes, and budgetary matters. Basically, for a political op-ed columnist, if something he writes is more in-depth than a gossip column, consider it suspect.
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