Sundry Miscellanea

A point of view which was no doubt shared by another great Carl...Sagan.

During the recent winter "vacation" (which wasn't really, for me at least, as I have explained otherwise/elsewhere), I broke off what I was doing long enough to watch the movie Contact. Which—whatever its other merits and flaws—at least serves to emphasize the point that mathematics will be the only human language likely to be comprehensible to alien intelligences...should they exist and we ever make contact.

Why ever did you think I wouldn't like this? :)

I'm not surprised that innumeracy is widespread, and here is the reason...
Could it be that mathematical/scientific/logical ability is more rare and requires more natural talent than reading ability? Maybe some people are just not born with it... Maybe it's not entirely cultural, and that there are simply less people who are talented at math than there are who are talented at reading or writing.

This reminds me of a comment made by management guru CK Prahalad. Prahalad said that communication ifrastructure was more important than physical infrastructure. In other words, cellphones are more important than roads. To support this argument, he gave the example of farmers in the third world. Before cell phones, they were always squeezed by the middlemen, but now they can call around for the best deal. I had to ask myself; why did this new form of communication achieve what others had not? Why didn't writing, the printing press, universal literacy, radio, or even television help the poor farmers?

It occured to me then that all previous forms of communication were essentially one way. The few write, the many read. The few speak, the many listen. The few film, the many watch. These same technologies, which allow for the preservation and dissemination of knowledge, also promote the concentration of ideological power. Literacy, like television, greatly enhances the ability of a small elite to promote their own ideology.

That is one reason why being without literacy is unacceptable; it doesn't keep people from communicating with other people, but it does limit the one way communication they can have with the elite. Being without a cellphone, on the other hand, is not viewed as unacceptable; instead of facilitating centralized control of society, cellphones promote two way communication between people. Similarly, numeracy is acceptable because cuts people off only from knowledge, and the ability to communicate with other common people, and not from propaganda oriented communicaton. Furthermore, the internet as it stands facilitates two way communication, so the elite have little interest in promoting computer competency.

Taking the idea further...

The liberal arts have always been associated with the idea of "high culture", an implicit premise of which is that members of said "high culture" are in some way the vanguard of society, perhaps even superior. The point is that valuing and glorifying the liberal arts can be viewed as essentially a way to *legitimize* the ruling class.

Scientific knowledge, on the other hand, is associated with the advancement of all mankind, generally towards some kind of more equal society. Science bears the promise of god like powers...not for the elite few, but for all. Far from legitimizing the existing order, new technology threatens to catalyze revolution, to lay low the strong and empower the weak.

Scientific knowledge can also be legitimizing, at least to the individual, but the no class of society has a monopoly on scientific knoweledge. That is to say, liberal arts knowledge can be learned by osmosis, easily passed from parent to child, but scientific knowledge requires hard work and talent, and those are not always attributes with which the ruling class is endowed.

As an example, the recently added essay section of the SAT increases the emphasis on writing, and thereby devalues science. Interestingly enough, a person brought up in an upper class family, with two college educated parents, can score fairly well on the English secton of the SAT based only on what they learned through osmosis from their parents. The English sections of the SAT serve to raise the scores of students whose first language is upper class WAVE, and lower the scores of those students whose first language is BVE, regardless of intelligence.

So when we wonder why education, especially in the USA, places so little emphasis on science, we have to ask, "who is in charge, and what are their real motives?"

Isn't computer science the most important second language (assuming that individual languages such as C++ and Java can be considered dialects)?

Computer science emphasizes a number of key concepts which rank so low in the language of math that they are not taught explicitly before seventh semester of calculus (and possibly never, but I speak from personal experience). To name a few: recursion and iteration (recursion is taught implicitly for proof by induction. A very limited type of iteration is taught through summation notation and integration), tree recursion, order of growth, indentation, abstraction, commenting of code, scope, and descriptive naming (I know for a fact that the field of math is totally ignorant of this last concept!).

To prove my point, I was recently helping another student study calculus. They were given a value of "f(x)", which they tried to squeeze with the squeeze theorem. They had trouble because their book referred to the lower bound function as "f(x)", and the squeezed function as "g(x)". Had the book used descriptive nameing (e.g. lowerBoundFunction(x)), or had they understood scope, they would have had no trouble.

Another example: most physics students have trouble with complicated problems because they do not make use of indentation or abstraction.

For most real world applications, the concepts and language of computer science seem more useful. Math is really useful for...computer science.

To the Former Student who stated "Maybe some people are just not born with it... Maybe it's not entirely cultural, and that there are simply less people who are talented at math than there are who are talented at reading or writing." I would like to mention that any ability is trained not born. Ability and talent both require a certain amount of discipline and training. I would like to note that while I may not be well versed in Numeracy, I do note that it is an important skill to understand (as Carl's post suggests).

A case in point. I was born American, for several years the only language that I understood and spoke was English. It was not until later that I decided to study the Russian language. From that point on I studied the language of many other specialized fields such as Music and Computer Programming. It comes to me that if you wish to learn an area such as the sciences then you should understand the language that they speak.

I interpreted Carl's meaning behind this post as being more of a thought that we should teach people when they are young to "speak" in math. Many countries require two or three spoken languages before they even hit high school now, America only requires 1 during that period. There are many interesting articles in the U of MN's psychology library that go over developmental psychology where they have correlated that studying foreign languages are imperative at an early age.

To that end I would also like to say that I agree with Carl 100%. Teach children how to speak math at an early age, otherwise they will end up like me trying to stagger through complex math ideas while wondering what the ∀ character means.

To Matt I would like to argue that it is important to know all disciplines and not just focus on one. I think that it is wise for the SAT to require reading / writing and math. This is fundamental for anyone who is scientifically minding because the very nature of science is to learn. Also, be careful when you say revolution because science should not wish to uproot the status quo per say, but rather to improve what we currently have working.

Carl, keep posts like this comming I enjoy reading your perspective on life.

i think that anybody can be anything they want to be and a career in science is a great choice, it can open so many doors for you and make you a very successful person and if you look forward to a good life this is the place to be!!!!!!!!!!!

Recently, while volunteering at my local co-op, we got on the subject of language and math. My co-worker, convinced that we are missing out using English, asked me "What does math look like in Chinese?".