The Weekend Australian - Review - - Viewpoints -

IT starts in pri­mary school. I hate hav­ing to learn mul­ti­pli­ca­tion ta­bles. I fail men­tal arith­metic, this sort of thing: if Johnny is six years older than Mary, and the sum of their ages is 20, and I am two years older than Mary, how old am I?

Some smart lit­tle kid would im­me­di­ately an­swer: nine. How did he do that? I’m fail­ing math­e­mat­ics, right?

But wait. Fast for­ward to age 12. I learn about el­e­men­tary al­ge­braic equa­tions: let Mary’s age be x, then Johnny’s age is x + 6; af­ter a cou­ple of lines of equa­tion book­keep­ing, all is trans­par­ent. I love it.

Move on to sec­ond- year high school, we are study­ing me­chan­ics. New­ton’s laws of mo­tion: a par­ti­cle oc­cu­pies a point in space and has a mass. Law 1: a par­ti­cle will con­tinue in a state of rest or of uni­form mo­tion in a straight line un­til it is acted upon by an im­pressed force, the text in­forms me.

I ponder this state­ment. I know about force: big­ger boys bul­ly­ing me in the play­ground. I was OK with the no­tion of a par­ti­cle with mass. I imag­ine ten­nis and cricket balls. But how could a par­ti­cle pos­si­bly travel with uni­form mo­tion in a straight line? I un­der­stand about the ve­loc­ity of a par­ti­cle and how to cal­cu­late it, so this must mean the ve­loc­ity of the par­ti­cle is con­stant or zero. No ob­ject in my lim­ited ex­pe­ri­ence trav­els in a straight line near the earth’s sur­face. All the ten­nis and cricket balls I have ex­pe­ri­enced are acted on by the force of grav­ity, or some­one throw­ing them or hit­ting them with a bat.

Curious, I think it’s very hard to imag­ine one of th­ese New­to­nian par­ti­cles trav­el­ling in a straight line. I ponder and ponder. Sud­denly I un­der­stand. Sud­denly I can do New­ton’s thought ex­per­i­ment and imag­ine a sin­gle lonely par­ti­cle mov­ing in free in­fi­nite space with no force act­ing on it.

With un­der­stand­ing comes a tremen­dous ad­mi­ra­tion for New­ton. The ge­nius who had been able to imag­ine the mo­tion of this lonely par­ti­cle in in­fi­nite empty space. A thing that doesn’t ex­ist in the phys­i­cal world. The law is a pure ab­strac­tion, the re­sult of an ex­per­i­ment that can only be car­ried out in the mind. But, cou­pled with his sec­ond law, that the re­sul­tant force on a par­ti­cle is equal to its mass mul­ti­plied by its ac­cel­er­a­tion, it ex­plains so much. All the prob­lems in the me­chan­ics text, cer­tainly.

I start work­ing out the prob­lems at the end of the chap­ter ( an­swers in paren­the­sis at the end of each ques­tion). To my de­light I keep get­ting the cor­rect an­swers.

Imag­ine my in­tox­i­ca­tion, and my dis­ap­point­ment, when my mates do not share my en­thu­si­asm for the joy of New­ton’s laws. That laws of na­ture could be ex­pressed con­cisely in math­e­mat­i­cal for­mu­lae is won­der­ful to me.

Then, in my fi­nal year of high school, we learn cal­cu­lus. Here’s the prob­lem that gets me hooked: Johnny ( he’s al­ways the naughty one) pours ink on his desk­top at a steady rate of x cu­bic inches per sec­ond. The ink spreads on the ta­ble in a cir­cu­lar pool of uni­form depth, h. Find a for­mula for the ra­dius of the pool as a func­tion of the time. Cal­cu­lus solves this and many other prob­lems. The power of New­to­nian me­chan­ics ex­plodes and I am hooked for life.

My ob­ses­sion at the age of 70 is a the­ory for wrin­kling sheets of steel. There is no cure, but I do get paid for it.

this­life@ theaus­tralian. com. au

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