June 23, 2005

Deltas and Ratios 

In mathematics, often the difference between two quantities is written with the Greek letter Delta:

Δ(x) = x2 - x1

Being it a difference, it tells little or nothing about the absolute values of x1 and x2; there is the same difference (90) between 100 and 10 as there is between 100100 and 100010 although in the second case the numbers are 1000 times bigger.

So, recently I read a leaflet inviting people to join the anti-G8 protests, and this leaflet said "the gap between the rich and the poor is getting ever wider". For argument's sake, suppose that this statement is both true and accurate; however it tells nothing about the baseline - or how poor are the poor. If anyone has enough income to live a decent life, what's wrong with some people being filthy rich? Nothing, unless you are a socialist or even worse a communist (I think in this case it's a difference of degree more than kind).

To make a practical example: there is a bigger income gap between Bill Gates and me than between me and a Brazilian farmer, but my living standard is much better than the Brazilian farmer. The income (or wealth) gap is almost meaningless in any serious discussion about poverty - unless you have an agenda, that agenda being a more "just" distribution of wealth.

The ratio between two different quantities generally has no specific name, but it can be called R:

R = x2 / x1

Again, also R says little about absolute values: 10/5 is equal to 1000 000/500 000 (the result is 2, if you wonder). Update 24/06: Probably in this case it would be better to say that a number, even if big, can be a rather small fraction of a huge one. But the emotional impact of a number with many zeroes is stronger.

So, this morning I looked at The Indipendent's first page and it featured alarming news: electric and electronic appliances left on standby consume so much energy to cause the emission of 1 Mt of carbon dioxide per year in Britain alone. This figure seems big, and the comparisons (enough energy to power Birmingham etc) reinforce the idea. But then let's look at the ratio, as published in the same article: approaching 1% of the nation's total.
Yes, 1%; one hundredth; in science when we can calculate a quantity with a 1% error it's rather good (it can be better, but even worse).

And what's being proposed to solve this problem? Regulations, of course, and even international ones.

Now, I think that turning off (not just standby) appliances when not in use is a good idea, and it takes only minimal time and effort to do it - when the appliance has a true ON/OFF button; some do not. I turn devices off when not in use (TV and computer monitors especially), and try to keep lights off when not required. But I wouldn't beat my chest about 1% of the total - especially considering that there is still a great uncertainty about the exact role of carbon dioxide emissions in the global warming.

On the other hand, I know personally people who are much more environmentalist (you know, the "No war for oil" types) but also waste electricity at every turn: computer monitors left on for hours even when not in use; they keep all lights always on even if nobody needs them etc. Or, they use a lot of candles: where does paraffin wax come from, in their opinion?? Update: Now I recall, my ex-flatmate kept the central heating on at max all day - but his room's window open too!


Ottime considerazioni, condivido in pieno.
Peccato che la matematica dispiaccia quasi quanto la fisica all'ambientalista tipo.....


The "poor" in America often have a car, T.V., VCR, and CD players. Just as anyone in Hitler's camps or even in Marine Corps Boot Camp would gladly switch places with the detainees at Gitmo, any really poor person in the third world would give their right arm to be poor in America. The left loves to highlight the difference in income but does not include Government benefits such as HUD, which pays for housing, Medicaid, food stamps, etc. Plus the fact they don't pay taxes but actually get a healthy refund over and above what they had withheld.

Anyone really poor in the Third World would give a limb to live in Europe as well - and indeed they pay hefty sums and face treacherous journeys at the hands of ruthless smugglers, only to enter in Italy as clandestines.
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