Shake it up baby now (shake it up baby) ...

Nu Zulun is supposed to be a duvuluped country.  Clean, green, serene ...

But check out the bus I have to travel on each morning ... a bone rattling, clattering, battering, shattering heap of a rust bucket.

(Well, that's not really the bus - my bus is much less comfortable)

Air conditioned ?? My .... arse ......  bottom.

North Star are the company responsible for for some of these monstrosities. I have been on a number that break down with consummate ease.

Now admittedly, North Star do have some modern buses. But the 863 at the allotted hour of my departure ain't one of them.

I used to travel by bus in the Philippines  and never came across what I endure on my daily commute into Auckland city.

Time for North Star to upgrade these tin cans on wheels.






Photo by Keith Edkins Wikimedia Commons

Call me irresponsible - call me unreliable, throw in undependable too ...

Let's add irrational to that mix ...



I have always been fascinated by what are known as irrationals numbers (numbers that cannot be expressed as a ratio or fraction). Now, before you leap on me, I know ratios and fractions are different conceptualizations.

The ancient Greeks, called the Pythagoreans (named after their leader Pythagoras), were entranced by whole numbers - unlike many kids in schools today.

For the Greeks, the whole numbers were 1, 2, 3, 4, 5, and so on ..... Zero had no been invented yet.
They also had the concept that there could be fractions made up of "ratios" of whole numbers 1/2, 3/4 ...

They reasoned quite reasonably, that whole numbers and fractions covered everything.

However one day, so the tale goes, on a boat, one Pythagorean demonstrated that you could not get a number (as fraction) multiplied by itself to result in 2.

You could get close  (7/5) x (7/5) = 49/25 (1.96) and (10/7)x(10/7) = 100/49 (2.041) ...

However, you never never get there  (a/b)*(a/b) can never ever equal 2


It was something that did not appeal the the Pythags or either to mathematicians up to fairly recent times. Some suggested that these irrational numebrs had suspect ontological status.

So they said √2 , √3, √5, √6 and infinitely many more …

Could not really be real numbers ...

Think of the number line. It seems reasonable, doesn't it dear reader, to assume that you can keep subdividing it up using fractions until you fill it completely.

Just take the gap between 0 and 1. Surely we can pepper it with fractions. 1/2, 1/4, 1/8, 1/16, 99/100, 999/1000 and so on and so forth.

And using fractions we can always put another point between two points ad-infinitum. So that this  ............ eventually becomes ________  !!!

So, where do these pesky irrationals come from?

Tis a mystery of religious proportions.

I finish with the proof (by contradiction) that √2 is irrational. Enjoy!!!