“The mathematics behind Aishwarya Rai” (edited version in Fiji Times, 3 Oct. 2015)
The Mathematics behind Aishwarya Rai
While in cold Melbourne, I could not help but follow the Fiji media furor about the Ministry of Education decision to make mathematics compulsory.
I was also watching Australian high drama with Malcolm Turnbull explaining why he did a coup and replaced Tony Abbott as Prime Minister.
Seeing some parallels, I titled my Saturday article “The Abbott/Turnbull lesson for compulsory mathematics”.
But sensible Fiji Times editors thought that an Aishwarya title would be a better lesson for popularizing mathematics.
Opposing compulsory maths
The maths debate began when a worried secondary school principal complained that maths should not be compulsory and included in the “aggregate marks” to decide students’ futures.
No doubt there was a worry that low achievers might be shut out of scholarships or even from progressing to tertiary qualifications useful for other fields.
Many of us at USP used to feel the same when students excelling in science or mathematics could not get scholarships because of their poor English marks, often due to bad English teachers and lack of library resources, especially in rural schools.
Fergus Garrett, an experienced mathematics teacher pointed out (Fiji Times, 25 Sep. 2015) that there was little use teaching trigonometry, calculus, or quadratic equations to students who would eventually work only as garment workers, builders or labourers. Correct to some extent, although not completely.
Garrett thought that all they needed was a bit of arithmetic, an ability to record their budgets (incomes and expenditure) and know the real interest rates charged by money lenders. Correct to some extent, but not completely.
Supporting compulsory maths
The principal’s view was rejected out of hand by an MoE official, perhaps understandable given the national and the MoE concern at the declining standards in mathematics and even basic numeracy.
Dr Ropate Qalo wrote (FT 22 Sep. 2015) passionately in support of the MoE pointing to the critical importance of mathematics in all walks of life, from birth to work to retirement to death and the need to reeducate school principals and teachers to understand the importance of mathematics even for students “not good at it”.
Dr Jito Vanualailai then took the debate into the stratosphere (FT 26 Sep. 2015) by informing that the mathematics learnt in primary and secondary schools was more than enough to explore the universe, build the internet and Facebook, and end wars with a nuclear bomb governed by Einstein’s theory of relativity (E=mc2), thought by him to be understood by every Form 4 student today.
Hmmmm. Silly old me. I thought hormone driven adolescents at that age largely thought about the detailed mathematics underneath pleasant shapes of the opposite sex.
But Dr Vanualailai advised that mathematics was important if people were to properly know God and religion. Hmmmmm.
Despite the contributions of these two academics, the MoE still said little to allay public fears and address legitimate concerns.
The Turnbull and Abbott lesson
While Australia was recently aghast that an elected Prime Minister was once again being replaced without the benefit of a national election, Turnbull calmly explained that while Abbott’s policies might have been correct, he was not adequately explaining them and more fatally for a national leader, he was failing to take the Australian people with him.
Proof for Turnbull was that thirty consecutive opinion polls had shown that the Liberal Party was lagging so far behind the ALP that they were likely to lose the next election, a disaster for any ruling political party, and hence Abbott had to be sacrificed.
While the jury is still out, Turnbull and supporters now point to the polls which immediately showed that the Liberal Party had gone ahead of the ALP and that Turnbull himself was by far the most preferred Prime Minister with ALP’s Bill Shorting way behind.
Fiji lesson: why did the MoE not adequately explain to the Fiji people why they were taking the difficult decision to make mathematics compulsory, and in what form?
Once mathematics could be put into little boxes like arithmetic, geometry, algebra, calculus, statistics, probability, etc. But not any more.
Bertrand Russell very accurately joked “Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”
Why did the MoE not clearly explain that their curriculum experts were addressing (as I am sure they are) the legitimate concerns of public critics such as Fergus Garrett and others about what should be taught to all lower down and at higher levels?
They even had recently engaged in a massive public relations exercise extolling the need for and virtues of financial literacy being included in school curriculum, from the earliest ages.
They do not need to point out the obvious that “higher maths” is used every day and is absolutely necessary in fields such as medicine, engineering, accounting, and economics.
But MoE could point out that hundreds of thousands of subsistence farmers must know some maths: eg that 1 part of pesticide with 40 parts of water will save their vegetables from pests, while 1 part pesticide to 4 parts of water will kill the vegetables; eg spending too much on farming inputs may mean a financial loss when prices plunge with a glut.
Hundreds of thousands of cooks intuitively know that 2 tablespoons of salt will wreck a meal when the recipe calls for 2 teaspoons.
Of course, Garret’s concerns are legitimate: exactly what level of maths needs to be taught at the lower levels to ensure that our citizens are able to cope with the numerical demands of life?
Nevertheless, the MoE could point out that all people must engage in “life long learning”, often realizing the importance of school work late in life when their life circumstances change.
That even those in humble occupations can enrich their lives through higher mathematics which they do not have to pass, and that learning is not only about jobs, incomes and applicability at work.
It can often be the case that students may not like and devote enough time to the maths that they are exposed to in secondary schools and even universities, only to find twenty years later that that it is precisely the most useful mathematics to them.
I can personally vouch that while at University almost fifty years ago, I passionately plunged into the pure and applied theories of relativity and higher mathematics while ignoring what seemed at the time to be tedious and boring “statistics”.
But of course, at that time there were no desktop computers with the powerful statistical software that we have today, while computer programming was then done by punching holes in hundreds of cards and running them through a card-reader.
For me personally, for decades now, statistics and the theories of probability have been the most useful and intriguing of the mathematics I ever learnt and used in my career, especially when one has to decide whether an estimate of a number we are looking at is a “good number” or just garbage because of statistical errors.
Popularize maths with the bad news
MoE might find it difficult to explain the importance of mathematical “bad news” that powerful people do not want the public to understand, but there is no doubt about the importance to Fiji people’s everyday lives.
For instance some employers do not want wage earners to understand that if the percentage increase in the CPI is higher than the percentage increase in their dollar incomes, then their real incomes are falling at great cost to their standards of living (look at Father Barr’s fruitless struggles with the Employers Association over the Wages Councils Orders.)
Some banks do not want depositors to understand that a half percent interest rate on deposits while the CPI is increasing by 4%, means savers are being “robbed” tens of millions by banks and borrowers. Look at the failed attempts by Sada Reddy (former Governor of Reserve Bank) to reduce the interest rate spread of our powerful commercial banks.
A pension fund may not want pensioners to understand that reducing their legally contracted pension rate from 16% to 9% is effectively stealing tens of millions per year from hapless retirees by decrees forced down the judiciary’s throat by the Bainimarama Government, and they will strive very hard not to release any reports on pension fund viability, which might contain this useful mathematics.
A government may not want voters to understand that in doubling the Public Debt, the good times are being enjoyed by all today, while tomorrow’s taxpayers will pay the costs. Look at the refusal of the Bainimarama Government to acknowledge that it is piling on Public Debt far too rapidly, without any evidence of growth in the real productive sectors.
Look at our people’s inability to understand that Budget freebies given to the poor by one Government Hand are more than matched by the much larger VAT takings with the other Government Hand, while the rich are getting far bigger freebies through reduced corporate and personal tax.
There are many more examples where mathematics is needed by ordinary people to understand what is going on in their lives but will teachers try?
Popularize maths with fun
Perhaps the MoE needs to popularize mathematics applications to the real Fiji religions.
In rugby, why not objectively analyze the performances of coaches, teams and athletes with statistical analysis and graphs of tries and points scored for and against, or tackles made and missed or tries and penalties converted and missed, say over a period of twenty or thirty years.
How about explaining the performance of our athletes at Commonwealth or Pacific Games in relation to population and GDP of our country?
Explain how Fiji musicians of all cultures use mathematical exactness in their choices of harmonious notes and chords, the regularity and discipline of time in tempos, rhythms and beats.
A few of us might even join Dr Vanualailai in his philosophical journeys exploring the relationship between the beautiful mathematical world of numbers to God and Nature and science.
But I suspect that everyone would rather explore the mathematical beauty of Aishwarya Rai or Liz Hurley or Naomi Campbell (or to be gender neutral, Salman Khan and Brad Pitt).
The maths behind Aishwariya
While the common cliche is “beauty is in the eye of the beholder”, mathematicians might joke that “Beauty is in the phi of the face”.
This is going way beyond the simple 36-24-36 numbers analysis of curvy women, popularly bandied about.
“Phi” is the “Golden Constant” (1.618) or the “Divine Ratio” that brilliant painter Leonardo Da Vinci (The Da Vinci Code) supposedly used in structuring his magnificent paintings, also linked to “Fibonacci numbers” (known in ancient India well before Fibonacci supposedly discovered them), plant biology, geometrical shapes in nature, and even music scales.
It is even “alleged” that most people find a face “beautiful” if it has physical dimensions and ratios that are related to the Golden Constant or the Divine Ratio.
Read this article here arguing that the Divine Ratio geometry of phi can explain why most people would find Liz Hurley or Angelina Jolly, or more interesting for Fiji people, Aishwarya Rai might be considered beautiful.
Does this theory have a racist agenda glorifying Caucasian features?
Apparently not, as even “beautiful” African faces are given in the examples.
But skeptics will note that there are beautiful women whose features are not in the same proportions.
Skeptics will note that there are also women with the Divine Ratio proportions but who would not be considered particularly beautiful.
Skeptics will naturally ask, so what is the point to the phi and beauty?
Science historians will answer that many a time new discoveries are found to have no use at all at the time, until years or decades later, sometimes when complementary discoveries or innovations are made or conditions have changed.
The originators of email never ever dreamt of today’s massive expanding universe of the Internet.
The originators of the number zero in ancient India or Persia (today’s Iran) never dreamed that it would be an essential element in today’s world of computers of all kinds of shapes and sizes.
There is a wonderful literature on the use of the Divine Ratio by artists, consciously or unconsciously.
Watch this fascinating Youtube video on Leonardo da Vinci:
But a modern application is modern product designers and advertisers using the Divine Ratio to create highly successful global product symbols, including a most popular car and soft drink.
There are many fascinating examples on the Internet relating to the Fibonacci numbers and phi, the Golden Constant or Divine Ratio.
Whether the mathematical phi applies to Aishwarya Rai or not, for certain, The Fiji Times editors surely know that a mathematics article with Aishwarya Rai in the title is more likely to popularize mathematics than an article with Turnbull and Abbott in the title.
A no-brainer, you might well say?
[For those interested, read Birch Fett ‘An In-depth Investigation of the Divine Ratio’ TMME, vol3, no.2, p.157. The Montana Mathematics Enthusiast, ISSN 1551-3440, Vol. 3, no.2, pp. 157-175. 2006©The Montana Council of Teachers of Mathematics] available here: