## Absolutes are relative

I came upon a realisation in my first year of university. There are very few absolutes in the universe.

I was sitting in the lecture theatre, taking notes of the professor’s lesson. I was in my first year, and in my first semester, and I haven’t any friends I knew there. “Friends” were people I saw frequently (if you could call the first 2 weeks “frequently”). After two and a half years of being conscripted in the army, my brain was raring to go (about the most mentally strenuous activity I remember was figuring out how dBase IV and FoxPro work [those are database systems by the way]. Oh and how to make the records print nicely. That’s interesting, considering that I had to send letters to over 500 military personnel, and one choke of the printer sent hours and tons of paper to waste. Lining up address information on the paper could be quite challenging. Another story for another time…).

It was a maths lecture (not surprisingly…) about fundamental logic (I think). I learnt of the term “for all” (or “for every” or something similar), which is represented by an inverted capital A. For example, for all even numbers, one of the factors is 2.

This “for all” term is not used lightly. When you say, “for all”, it means for all conditions, circumstances, situations, universes, even alternate realities, that the next statement is true.

And as the professor said, all you need is one example of the statement being false, and the whole statement collapses.

A related concept is the negative. For example, “There is no such thing as a zombicorn.” First, there’s no such thing as a zombie. Second, there’s no such thing as a unicorn. Uh, I’m not going to contest you on that. Go Google it or something…

What you mean by “There is no such thing as XYZ”, is that for all conditions, circumstances, situations, universes, even alternate realities, that the statement is true. And all you need is the existence of XYZ for that statement to be false.

Because of this, the professor also said that it’s impossible to prove a negative. We just barely found Earth-sized, possibly habitable planets at the outer reaches of our exploration of space. How can anyone possibly search the entire known (and unknown) to find that one existence of proof? Have you searched all the planets out there? Do you know for sure, that there is absolutely no way that XYZ can possibly exist?

This is why I find maths interesting. Some of its concepts can be proven. For example, the statement “There is no such thing as an even number with a factor that’s 2.” All I need to disprove that statement is find the existence of an even number with 2 as a factor. For example, 6 (with 2 and 3 as factors).

Once I realised that about the only absolute statements are in maths (and possibly physics, but I suck at physics, so, yeah…), and even then those absolute statements are held in the strictest of scrutiny, I also realised that (almost?) everything is relative. Yes, I know I’m way behind some fellow named Einstein who mentioned some theory of relativity somewhat…

The notion that nothing is absolute scares the hashbrown out of some people. Those people need to know that this is right and that is wrong. That this is black and that is white. That there are clear cut lines with which they can stand behind of. That there are “right” arguments and opinions they can back themselves with.

For example, the statement “You’re always late.” really means the person is saying you’re always late in the person’s mind. Never mind the few times that you are early, because that person will conveniently forget about those instances (because of cognitive dissonance. The person had to convince herself that she’s right about you being always late, and thus fabricates proof that substantiates her opinion). Also, it presupposes that you will continue to always be late. And all you need is to be early once, and that statement is false (but cognitive dissonance will thwart your attempts at defending yourself).

This taught me to be tolerant of other people’s views. When nothing is absolute, then nothing is certain. Like I said, this scares the cranberry out of some people.

And this coming from a maths lecture. More interesting still, it came from a discipline that’s known for its strictness.

## Cantor sets and Invisibility cloaks

More specifically, it’s the Cantor ternary set.

## Don’t rely on just the average!

I made this video because I’ve always been skeptical about reports (such as population census and surveys) with the average as the only statistical measurement.

## Singapore ranked high in PISA 2009 survey

According to the latest PISA results, Singapore is ranked 5th overall in terms of reading capabilities (see executive summary in PDF). Singapore also scored high in mathematics and science.

“Better educational outcomes are a strong predictor for future economic growth,” said OECD Secretary-General Angel GurrĂ­a. “While national income and educational achievement are still related, PISA shows that two countries with similar levels of prosperity can produce very different results. This shows that an image of a world divided neatly into rich and well-educated countries and poor and badly-educated countries is now out of date.”

Wealth and level of education does not come hand in hand. You still have to work for it.

The best school systems were the most equitable – students do well regardless of their socio-economic background. But schools that select students based on ability early show the greatest differences in performance by socio-economic background.

I’m a bit cautious of this one. Skill honing at an early stage assumes that whatever a student is good at has already manifested itself. It’s a reasonable assumption. It’s only dangerous if the skill specialisation is to the exclusion of all else (or even “many” else). It gets worse if the student don’t like his “special” ability, and also has aptitude in another area that he likes. But the student is already shuffled into Box A for the first skill.

What do you think?