Sea level and freezing point: zero as a chosen reference, not an absence

0:00Here is a hill. And here, in the seabed, is a trench. The hill is a thousand metres high. Fine. But a thousand metres above what? That question sounds pedantic, and it is the whole of this video. Height is never a property of a place on its own. It is always a distance from something, and somebody has to choose the something. For the whole planet, the something that got chosen is the surface of the sea.

0:30Not because the sea is special, but because it is roughly the same height everywhere, and anybody can go and find it. So sea level is called zero metres. And that is a decision, not a discovery. Nothing about the sea makes it zero. It is a landmark. A line drawn across the planet, that everybody agreed to measure from. And the moment you draw a line like that, something follows automatically.

1:02There is land above it and there is land below it, and you need two kinds of number to say which. That is where negative heights come from. Not from anything going missing, but from a landmark with territory on both sides of it. Here is a cross section. That phrase needs a sentence of explanation, because most people meet the picture before the words. A cross section is a vertical slice through the ground, seen from the side. As if you had cut through the land with a knife and were looking at the cut face.

1:40Hills stick up out of it. Valleys and trenches drop down into it. And here is the useful part. Hills and trenches go on the same scale. You do not need one ruler for mountains and a different one for the seabed. One axis, with zero in the middle of it, measures both. So let us read some heights off it. The axis is marked every five hundred metres. Up to fifteen hundred above the line, and down to fifteen hundred below it.

2:13Seven points are marked along the profile. A, B, C, D, E, F and G. Take A. Follow it straight across to the axis. It lands between the thousand mark and the fifteen hundred, nearer the thousand. So A is about twelve hundred metres. Take B. Same move, but this time it lands below the line, between minus five hundred and minus a thousand. So B is about minus six hundred.

2:44And notice what we are doing here. We are reading, not calculating. About is the right word, and about is good enough. All seven, read off the same way. A is twelve hundred. B is minus six hundred. C is five hundred. D is minus thirteen hundred. E is fourteen hundred. F is minus two hundred. G is eight hundred. Now put them in order, lowest first. D is lowest, at minus thirteen hundred. Then B, at minus six hundred. Then F, at minus two hundred.

3:23Then we cross the line. C at five hundred, G at eight hundred, A at twelve hundred, and E highest of all at fourteen hundred. Look carefully at the first two. D is thirteen hundred and B is six hundred, and D is the lower of them. Bigger digits, lower place. Below the line, that is always how it goes. E and D are the extremes of this drawing. What about the extremes of the actual planet?

3:56The highest point on Earth is a mountain summit, about eight thousand eight hundred and forty-nine metres above sea level. The lowest point is not a valley. It is the floor of the deepest trench in the ocean, about ten thousand nine hundred and thirty-five metres below it. So the deepest place is further from sea level than the highest place is, and by quite a long way. Between them lies nearly twenty kilometres of vertical range, which is more than twice the height of that mountain.

4:31And one more thing worth saying. The lowest dry land, land you could stand on, is about four hundred and thirty metres below sea level. Below sea level does not have to mean underwater. Now something completely different, with exactly the same structure underneath it. Temperature. Here is a thermometer, of the kind you would find in a laboratory. Its scale runs from minus twenty at the bottom to a hundred at the top, marked every ten degrees.

5:06On a hot afternoon it might read forty. On a mild day, fifteen. Both of those sit above the zero mark, so both are easy to read and easy to believe. But now look at where that zero mark actually is. It is not at the bottom of the scale. It sits one sixth of the way up, and there are two marks underneath it. Minus ten, and minus twenty.

5:33Those marks are not decoration. They are there because there are temperatures down there, and people need to read them. If you believe that zero is the bottom of the scale, then the whole lower sixth of this instrument is unreadable to you. You will look at a reading of minus four and see a four. And you will conclude that minus four is warmer than minus two, because four is the bigger number. It is not, and this is where that mistake costs you something.

6:08So what does zero degrees actually mean? It means the temperature at which water turns into ice. That is the whole of it. Water freezes there, and somebody chose that point as the landmark, because it is easy to find and because it matters. It is not the absence of temperature. It is not the coldest that anything can get. It is a line drawn across a scale, in exactly the way sea level is a line drawn across a planet.

6:40And once a line like that is drawn, there is always something on the other side of it. Here is a real problem of the kind this is all for. A mountain town in November. Four temperature readings, taken at four different moments in one day. Fourteen degrees, eight degrees, minus two, and minus four. And four times, listed in no particular order. Two in the morning, eleven in the morning, two in the afternoon, and eleven at night.

7:15Match them up. And the way to do it is not arithmetic. It is to think about when a day is warm. A day is coldest in the hours just before dawn, and warmest in the early afternoon. So two in the morning is minus four. Eleven at night is minus two. Eleven in the morning is eight. And two in the afternoon, the warmest moment, is fourteen. Now the thing this whole video has been building towards.

7:47Watch what happens if we change the landmark. Suppose we decide to measure heights from a surface five hundred metres higher than the sea. Not for any good reason. Just to see what happens. Every single number on the chart changes. A was twelve hundred and now reads seven hundred. D was minus thirteen hundred and now reads minus eighteen hundred. C is the interesting one. C used to be five hundred metres above the line. Now C is the line. C reads zero.

8:24And here is what did not change. Not one grain of rock has moved. E is still the highest point and D is still the lowest. The drop from E to D is still exactly twenty-seven hundred metres. Every gap survived. Which tells you what the sign of a height really is. It is not a fact about the land. It is a fact about the line we chose. And now put three pictures side by side.

8:54A lift shaft, with the entrance floor called zero and floors below it. A height axis, with the sea called zero and land below it. A thermometer, with the freezing point of water called zero and temperatures below it. Three completely different things, and the same structure in every one. A landmark chosen because it is useful, and territory on both sides of it. That is what negative numbers are for. Not for counting things that are missing, but for saying which side of the line you are on.