Ten Hundred Words of Science

If you haven't seen it before you should search YouTube for Feynman Fun to Imagine. I am extremely impressed with how accessible his explanations are, and I would have loved to see what he could have done with the given restriction. Probably not as well as he did without it but probably better than most could do with it.

edit: http://www.youtube.com/watch?v=v3pYRn5j7oI&list=PLC351CC566C...

That's exactly what it says. It's favicon is also an xkcd drawing.

When we tell a computer how to do something, we write a set of orders for the computer in a way that the computer can read. These orders can ask the computer to remember things, like numbers and names and places and so on. We can ask the computer to set up spots where it will remember things for us, and each such spot will have its own name. When we write down a thing for the computer to figure out, and the computer goes on to actually figure out what we are talking about, the thing can turn out to be either of two types. It can be the name of a place to store things, or it can be a thing to be stored (like a number or word or letter or a few of any of these). If it is a place to store things (which we can call a "left hand type of thing"), we could ask the computer to store other things in that place. If it is a thing that can be stored (which we can call a "right hand type of thing"), we could ask the computer to store it somewhere.

The reason why we use the names "left hand" and "right hand" in this way is that we can write orders for the computer like

cat should become two times two

In this case, the word "cat" appeared on the left hand side of the order, before "should become" (or "gets"), while the words "two times two" appeared on the right hand side of the order, after "should become". This makes sense because in this order we use "cat" as a name of a place to store things, while "two times two" (which turns out to be the number four) is a number that could be stored so that it can be used later on. Here, we would call "cat" a left hand type of thing, and "two times two" a right hand type of thing.

In some orders for the computer, the way to talk about where to store things is much more confusing (like we could say something like "right after this place", "right before this place", "ten spots after this place"), but still, if something works out to point to a place where you can store facts, then that thing is a left hand type of thing.

OK, what about light propagation according to the path-integral formulation of quantum electrodynamics? That's complex in quite a literal sense, though unfortunately "complex" isn't a top-1000 word so I had to say it a different way. Anyone who's read Feynman's lovely book "QED" will recognize the approach.

To find how a bit of light goes from one place (at one time) to another (at another time), look at every way it could take, straight or not. Imagine a little line that starts by pointing to the right and that turns as the bit of light goes along: if it goes two times as far, the line turns two times as much, and so on. But the line is always, say, one foot long. Now, do this for every way the light could go. Take all those lines and lay them end to end, and see how far the two ends are. The further they are from one another, the more light gets to that place at that time. (Of course you can't really do this because there are too many lines to lay end to end, but you can look at only some of the ways the bit of light could go, and then look at more, and more, and you will find that the answers change less and less. As long as you look at enough ways, you will get about the same answers for where the light goes.)

You may have heard that light goes in straight lines, and how far it goes in a given time is always the same. You can work that out using these ideas: what happens is that for a way the light could go that is not straight, or that goes too far or not far enough for the time it takes, if you change them a bit then the turn in the line changes a lot, so when you add up the lines for these slightly changed ways the lines all point different ways and when you lay them end to end you get something much shorter than if they all pointed the same way. But for the straight line that goes just far enough for the given time, it happens that a small change in the way the light goes makes a smaller change in the way the line turns, so when you add up the lines for these slightly changed ways you get something that is still very long because the lines all point about the same way.

And that means that, if you fix how long it takes, the places the light can go in a straight line, going just far enough for the given time, are places that make the lines add up well, so lots of light goes there. But for all the other places in the world the lines do not add up well because they all point different ways, so very little light goes there. And that is why light goes in a straight line and always so far in a given time.

The same ideas tell you why light does what it does when it meets a mirror. And they tell you why, by blocking off some parts of the mirror so that light that reaches them disappears, you can actually make more light go to some places than if the whole mirror were still there.

The color of the light comes from how fast those little lines turn around. When you block off some parts of a mirror, the ways the light likes to go (that is, the ways for which the little lines end up all pointing about the same way) will change with how fast the lines turn. So light of different colors goes different ways, and if light falls on one of these blocked off mirrors you see red in one place, blue in another, and green in the middle, like when it rains and you look away from the sun.

Those round things with music on are like mirrors but with little bits blocked off (that is how the music is stored on them, but that is another story), which means that when light falls on them you get the same red-then-green-then-blue thing. Pretty! And all because of the way those little lines go around and you add them all up.

The same is true of, e.g., "one" and "two".

According to the frequency list at www.wordfrequency.info (the free top-5000 one; for more than that you need to pay them), the only numbers below 1000 for which all the words making up n are among the n most common English words are 800..808.

Proof: the ranks of numbers 1..9 are 50,79,134,250,299,425,735,743,1163; the ranks of 10..19 are 840,4318,3246,X,X,3019,X,X,X,X (where X means "bigger than 5000"); the ranks of 10,20,...,90 are 840,2103,2855,3767,3064,X,X,X,X; the rank of "hundred" is 621.

So: all number-words have rank >= 50 so nothing below 50 is "good". Anything from 20 to 99 has rank >= 2000 because of "twenty" etc., so nothing below 100 is "good". For the same reason nothing below 2000 whose tens digit isn't 0 or 1 is "good".

Nothing from 100 to 620 is "good" because of "hundred". Nor any higher 6xx, as above; nor 700..720 because of "seven"; nor higher 7xx, as above. The small 8xx are as stated; higher 8xx are no good as usual; no 9xx is good because of "nine".

This word list actually puts "thousand" in position 650, which makes lots of 1xxx numbers good: the little Common Lisp program that actually gave me the results above says it's these: 1000 1001 1002 1003 1004 1005 1006 1007 1008 1010 1100 1101 1102 1103 1104 1105 1106 1107 1108 1110 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910.

Of course all large enough numbers are "good". I can't tell where "large enough" starts because that wordlist doesn't go far enough to include even "thirteen" or "sixty". Perhaps somewhere around 10000 onwards?