# For the Hunter, in NSW Australia @ the Smart Ideas Competition, 17 April 2016. I will travel to France to learn French from humans, 24 July 2016. Apologies are offered for the computer generated translations.

I am a visiting American who has spent enough time in the Hunter region of New South Wales Australia so that - when I return to the Quest on Hunter street in Newcastle, they greet me with "Welcome home!" I am probably not eligible to enter the competition, but the winning outcome for me would be interest to sponsor me to come here to live. In fact, when a cab driver asked me what I think of Newcastle, I said that I could happily spend the rest of my life here. I am presently visiting a friend in Kotara.

I don't know about here in Australia, but back in the USA I like to ask this question: "If the education establishment has not done a horrible job during the last 80 years or so, then why do so MANY people have so MUCH trouble with numbers?" Is there no such, or at least much less such, trouble in Australia? (And please: What about France?)

I have a numerical project idea to begin with the older people - the 'great' and 'grand' parents, and work down in age to the adult children and then to the youngest ones. In its seemingly impossible entirety, it would be to calculate, from the sheet music, the theoretical time length of Olivier Messiaen's "Catalogue of the Birds". But in one of its smallest versions, it might just involve only the first three sounds of the 3rd piece - as shown in this picture:

The image, uploaded with permission, shows the beginning of the third piece: 'III. LE MERLE BLEU'.
See the score in print:

The dot after the middle note in the first measure lengthens the note to which it is attached by one half the note's normal length.

This is why the time duration of the eighth note, in the calculation below, is multiplied by three plus one half, rather than just by three.

Then, to find the time duration of the first measure, with a metronome mark which equates an eighth note to 116, we use the hand written calculation shown below.

The metronome mark, , means that one hundred and sixteen eighth notes sound for one minute:

Now please, let me explain why I have left the time in the form of the improper fraction (3 x 5 x 7) / (2 x 29) seconds.

I propose that we do this problem, not as engineers or scientists - who would use decimal numbers to approximate the intermediate times - but as mathematicians using exact rational numbers (which is to say improper fractions). The numerators and denominators will grow large so that it will be best to express them as products of prime factors raised to powers. So far, in the numerator, we have the prime numbers   3,   5,   and   7 . In the denominator we have   2   and   29   .

There are a great many calculations that would be required to find the theoretical time length of Messiaen's entire catalogue. But the number of people who have trouble with numbers is so great that they could make short work of the problem - if they succeed in combining their labors. The business happens when people start making the transition from being helped to helping others. It is the magnitude of the problem (project) that puts an end to peoples' problems (difficulties) with numbers.

The project I describe above conveys powerful concrete experience.
The abstract theory gives more power @ my spoken reals project.
The current version of the time calculation is here.