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## Units and order of magnitude estimates.

One of the most important skills a physicist can have is to estimate the size of various effects without doing a detailed calculation. This basic skill is one of the hardest ones to learn, mostly because it is very easy to disbelieve: after all, you didn’t do a real calculation. But at the same time, it is one of the most important skills one can have. These estimates will tell you if you are going to be wasting your time doing a calculation or not. On the other hand, they migt give you an enormous amount of information without having a fundamental system of equations to solve: let us say, you don’t know if there is a relation between some set of phenomena, but order of magnitude estimates migt be able to do that for you. I will now describe various instances of these order of magnitude estimates to show you how powerful they are.

## Everyday physics: the stress tensor.

You might think I have gone bonkers. When have you ever heard of the stress tensor being everyday physics? Don’t let nomenclature fool you. The stress tensor is as a matter of fact something that we have a lot of familiarity with, just not by that name. Consider for example a steel cable made of filaments as in the figure. What is the total tension on the cable? You can say that the tension is built filament by filament, so the total tension (the capacity to pull an object evaluated as a force) is proportional to the number of filaments if all the filaments have the same individual tension.

Each filament contributes to the tension

Since the number of filaments is another way to count areas, we find that the total tension is proportional to the area. If we calculate the tension per unit area, we call that the stress of the material. Now it starts to sound familiar, doesn’t it?

This post was written three days in the future from now. I have been informed that it is still not possible to send information to the past without messing it up. I hope this warning message makes it to you: do not travel to the past, I repeat, do not travel to the past. It’s messed up man….

As you can see, the laws of physics are still holding. The last of the three elementary concepts is time. Time seems to be different than space, and also than mass. Time is always there, never stopping, not once, not ever. Well, except in some seminars I attend to where time does seem to stop. I must check into that and see if I can profit.

So how do we notice that time is there? There seem to be these things that happen again and again and again and again. We call them days. Then we notice that there are these things called years: you notice because of the seasons, and if you happened to be a hunter-gatherer, the winters seem to have very little gathering available. Well, maybe a lot of wood-gathering to keep warm. But I digress. In some sense time is this little beast that lets us repeat stuff. However, there seems to be no rewind button, and let me tell you, there are times where I wish I had one…

## My sword is longer than yours.

Well, that is what I imagine a friendly bet over beer in the middle ages would look like. Let us say two vikings taking a break after some invading of Europe. Not that things have changed that much. We still have silly bar bets over the sizes of *ahem*…

Graff and Olaff are in desperate need of a meter stick.

So after some potato bliss, I had to think at great length about how to introduce some other elementary (in the sense of being fundamental, not easy) physics concepts. You see, it is hard to talk about physics without the three basic elementary irreducible concepts: mass, length, time.