Wednesday 6 April 2005

Pic of the day: Since I have no idea how to illustrate today's topic, I include this picture with trees.

Orders of magnitude

You know what an order of magnitude is, right? Actually that depends on who is talking. When politicians use the expression, they just mean "size" or some such. But when engineers say "order of magnitude" they mean how many times 10 it is. So 10 is one order of magnitude larger than 1, which is one order of magnitude larger than 0.1, and so on.

Nature may not be quite so exact, but there is something to it. It seems that so many things in nature are made within a certain order of magnitude. A human, for instance, would not be able to survive if 10 times larger than now, and not if 10 times smaller. In fact, even for babies to survive, their bodies need to function slightly differently from adults. Their heart beats faster, their whole metabolism is sped up so they digest and burn the food faster. Otherwise they would lose too much heat ... when the body is smaller, it has more surface compared to the volume, so loses heat faster.

An ant and an elephant, despite the similarity of name, would be unable to even breathe if their size was swapped around. They would both quickly die. Science fiction writers in the past ignored this, but the current generation takes it into consideration, being smarter and better educated, as are most of us.

Plants are more scalable, but even then you can clearly see from a picture whether it is of a 6' or 60' tree.

Even on cosmic scales, size does matter. A planet 10 times as large as our Earth would be very different indeed. Due to the increased gravity, it would attract gas rather than letting it slowly leak into space, so it would have become a gas giant. Examples of such planets are Jupiter and Saturn. When the mass of the planet increases tenfold, it doesn't just have 10 times as much atmosphere. It changes to a type of planet that is mostly atmosphere, with a solid core that is totally hid from the outside world by a sea of gas, literally, as the pressure compresses the lower atmosphere into liquid form. Conversely, if our Earth was 1/10 its current size, it would have no atmosphere at all. Nor would it have a molten core, thus no magnetic field to protect it from the radioactive solar wind.

A star that is 10 times as large as the sun does not last 10 times as long ... due to the higher pressure in the core, nuclear fusion is more efficient, and the star becomes much brighter and burns out much faster. Also, when its life is over, it is likely to become a black hole, while our Sol seems destined to become a white dwarf.

***

As now all things in nature are made to their own scale, it should surprise no one that our mind also is. Intuition is a wonderful thing, and due to the way our brains are made, we can often make a reasonably correct assumption on the fly. We were after all made to live in this world, whether by design or natural selection. But there is a catch. When confronting things outside our order of magnitude, our gut feeling may be totally, utterly wrong.

This, I believe, is why people don't think of houses as consumer goods, as I mentioned on Sunday. But they are – they are just consumed so slowly. But even with tender loving care, a lifetime of living in a house will leave it somewhat worse for wear. And so on with all things. Your strategy for investment would be very different depending on whether your time horizon is 1 year, 10 years or 100 years.

As with time, so with numbers. People have a good idea about their daily expenses, or at least most have. But large numbers confuse them. What's really the difference between a million and a billion? They're both a lot of money, aren't they? I sometimes hear on the radio reporters or politicians accidentally mix the two, one way or the other. That's because to their mind, both are synonyms for "lots of money". Even so, there is a difference. A million is enough to build a nice house; a billion is enough to build a nice town. Because people don't understand how much a billion is, they don't even blink when politicians waste another billion on some kind of pointless posturing.

On the scale of the family, a childbirth is a unique and precious thing. But on the scale of humanity, population growth is ... well, what is it? Let's say we gather the people who were born exactly to the second ten years ago, and make them line up to shake your hand. Now, since we are talking population GROWTH, we also arrange that whenever someone dies somewhere, one of the children step out of the line and walk away. Only the extras, as it were, remain. All you have to do is shake their hand briefly. Think you can do that? No. Even if you don't tire, even if you don't take breaks for food and bathroom, you cannot shake their hands as fast as new ones arrive. The queue will be longer and longer the more you do it. Not that this is a bad thing, necessarily. We just have to be aware of it and plan for it.

Being aware of and planning for things outside our normal scale is hard. This is why some people only believe in what they see. Sadly, people don't see bacteria and viruses, such as the HIV virus that your one- night partner is infected with. These things are literally orders of magnitude outside our field of view. If attacked by a rabid lion, people would run for their lives. But facing the invisible death, they don't run from it, they run toward it and embrace it literally.

What I try to say is this: Outside our "order of magnitude", intuition does not help us. Reason may help, if sufficiently informed. But who listens to reason? Its voice is small and distant, and it takes a lot of training to even hear it, much less follow it.