Of Syntax and Grammar from English to Math and Science

Adapted from J. Engr Education, 2008, 97(3), 301 - 302.

Consider this:

It is very important that you learn about traxoline. Traxoline is a new form of zionter. It is montilled in Ceristanna. The Ceristannians gristeriate large amounts of fevon and then bracter it to quasel traxoline. Traxoline may well be one of our must lukized sneziaus in the future because of our zionter lescelidge.

Directions: Answer the following questions in complete sentences. Be sure to use your best handwriting.

1. What is traxoline?

2. Where is traxoline montilled?

3. How is traxoline quaselled?

4. Why is it important to know about traxoline?

- Judith Lanier

Now, anyone who is decently competent in English can answer the questions above without having any idea what the terms mean. But this judgement neglects the important point that a significant amount of grammatical and syntatic knowledge is being tested here. One could not solve these problems without understanding the differences between subjects and objects, how to identify verb tenses and endings, the role and implication of helping verbs etc.

There is a strong analogy between (the above) example and the use of mathematics in science. The mathematics in itself is about grammatical and syntactic relationships, and permits the drawing of complex conclusions about the placeholders (variables) without having any idea what those placeholders stand for.

...We not only expect students in science and engineering to be able to understand mathematics (syntax); we expect them to combine this knowledge with knowledge of what the math is talking about in a tightly integrated way to see the meaning of the symbols. This is different from straight math and can even lead to differences in the way equations are interpreted.

The Differences Between Meanings in Physics and Math: A Shibboleth

One of your colleagues is measuring the temperature of a plate of metal placed above an outlet pipe that emits cool air. The result can be well described in Cartesian coordinates by the equation

T(x,y)=k((x²+y²)

where k is a constant.

If you were asked to give the following function, what would you write?

T(r,q)=?

The above is a problem whose answer tends to distinguish engineers and physicists from mathematicians. An engineer or physicist who works regularly with polar coordinates is likely to give the response T(r,q) = kr², a result obtained by assuming the variables are related by the familiar polar to Cartesian relation r² = x² + y². A more mathematical colleague is likely to respond, T(r,q) = k(r² + q²). The function is defined mathematically by saying, “Add the squares of the two variables and multiply by k.”

The engineer will object. “You can’t add r² and q²! They have different units.” The mathematician might reply, “No problem. I see what you mean. You just have to change the name so that each symbol represents a unique functional dependence. For example, you could write T(x, y) = S(r,q) = kr².” Unfortunately, your more concrete friend (imagine a chemical engineer at this point) is still unlikely to be satisfied. “You can’t write the temperature equals the entropy! That will confuse everything.”

Many engineers, physicists, and mathematicians are surprised by this story. Each side believes that its way of using equations is the “obvious way” and that surely even a mathematician (or an engineer) would agree. Unfortunately, that is not the case. Each group strongly prefers its own interpretation of how to write an equation.
These two examples dramatically illustrate that in science and engineering, we tend to look at mathematics in a different way from the way mathematicians do. The mental resources that are associated (and even compiled) by the two groups are dramatically different...using math in science requires the blending of distinct local coherences: our understanding of the rules of mathematics and our sense and intuitions of the physical world.

Dedicated to those of you readers who did not get this joke.

Career options

You are given two choices:

1. A full time industry R&D position in a Fortune 100 firm which pays you very well (we are talking about being in a pay bracket at least at the 90th percentile of personal income in US), all the more so given today's tough deteriorating ecnomic conditions and in an area you are keen on plunging into or;

2. A postdoc in a well-respected lab whose PI was recently acknowledged by the US federal government for the scientific work coming out of there. The project(s) I am offered is challenging enough that will expand my scientific repertoire, and previous group members have had considerable success in finding excellent teaching positions (e.g. Imperial college, UIUC, UT-Austin to name a few).

Received a lot of conflicting opinions amongst my friends whom I consulted for their advice.

Day of rememberance

7 years ago, I remember stepping out of my "Transport Economics" class (at 9 am in the morning) and hearing fellow students in the hallway urging us to go watch cable TV. Apparently something big had happened in NYC and DC. I spent pretty much the rest of the day glued to the huge TV set the university had put up in the Memorial Union, and called home to assure my folks that I was safe and secure.

Tuesday, Sept 11, 2001. To the victims and survivors:

It is important to commemorate this day not only to pay tribute to those who lost their lives, but also to honor those who continue to live with this tragedy.

第一个

This past week for two nights in a row I dreamt about my 1st gf. The details are fuzzy, but it is awful to wake up and to start the day in a lousy mood.

A quick check on this blog told me why. I am amazed by the ability of my subconscious mind to remember dates anniversaries.

Two years later, I still stand by the title of this entry.

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Olandario, who has since deleted his blog, wrote this in 2006.

A neverending story

Now and then, I may meet an interesting new girl, and being single and desperate, I take the opportunity to get to know her better. It’s tiring; trying to know someone new always is. And as we grow older, so do the people we meet (unless you are a cradle snatcher), and there’s more to find out. And then there is the usual background research to be done.

Primary school. Secondary school. Junior college. University. Major. Favourite colour. Favourite book. Favourite animal. Favourite number. Favourite song. Favourite movie. Favourite flower. Unfulfilled dream. Biggest regret.

You labour at it, so that you may reap the rewards later in case things work out. But one after another, they fall by the roadside, and even though you stay as friends, when her birthday comes around again, you can no longer recall what her favourite cartoon character is, or what she likes to eat at a restaurant.

I no longer ask, because I no longer care to find out. No more hedging of bets, just to clog up my brain with more useless tidbits of information I won’t be able to recall when the occasion arises. But for you; I can never forget.

Jin Shan Primary School. River Valley High School. Raffles Junior College. University of Melbourne. Medicine. Red. To Kill a Mockingbird (one of them). Dog. Five. Right Here Waiting. Serendipity. Lilies (or at least it used to be). To be a singer. Not getting together with me.

It’s almost ten years since we set eyes upon each other in that classroom, almost nine years since we traded rubber bands with straws between our lips, eight years since you looked through the fourth-storey window and watch me kick a ball, and I saw you stand and sing on stage in that most memorable of Talentimes, and we got ‘married’ in civics and moral education class, seven years since I heard you cry your heart out on the phone, and we stepped through the gates of the same college, five years since you laughed at my clean-shaven head, four years since I bade you farewell at Changi, and you first got attached, almost three years since I did, one year since I broke up, and four months since you did.

A decade of memories.

There have been many times in those years when I have wondered about us, and where we will be in another decade’s time. Whether the meandering journeys we have taken since those heady secondary school days were meant to test us, and whether fate will bring us together again some day. Or as you once put it, whether we will return to square one after everything that we have been through together. If, we will ever end up together.

I already know the answer.

Happy Birthday.

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And my greetings to another girl on the west coast.