Hawking’s Genius

How do people reach conclusions? How can these conclusions be swayed? How do you know you are correct, as opposed to being manipulated? How could a TV programme about physics and cosmology tell us something about our current way of life, including politics?

I have recently been watching a series of TV programmes entitled Genius, in which Stephen Hawking starts out by suggesting that anyone can answer the big questions of nature, given a little help. He gives them some equipment for them to do some experiments, and they are supposed to work out how to use it and reach the right conclusion. As an aside, this procedure greatly impressed me; Hawking would make a magnificent teacher because he has the ability to make his subjects really register the points he is trying to make. Notwithstanding that, it was quite a problem to get them to see what they did not expect. In the first episode there was a flat lake, or that was what they thought. With more modern measuring devices, including a laser, they showed the surface of the lake was actually significantly curved. Even then, it was only the incontrovertible evidence that persuaded them that the effect was real, despite the fact they also knew the earth is a sphere. In another program, he gets the subjects to recognise relative distances, thus he gets the distances between the earth and the moon by eclipses, then the distance to the sun. The problem here is the eclipses only really give you angles; somewhere along the line you need a distance, and Hawking cheats by giving the relative sizes of the moon and the sun. He makes the point about relative distances very well, but he overlooks how to find the real distances in the first place, although, to be fair, in a TV program for the masses, he probably felt that there was only a limited amount to be covered in one hour.

It is a completely different thing to discover something like that for the first time. Hawking mentions that Aristarchus was the first to do this properly, and his method of getting the earth-moon distance was to wait for an eclipse of the moon, and get two observers some distance apart (from memory, I believe it was 500 miles) to measure the angle from the horizontal when the umbra first made its appearance. Now he had two angles and a length. The method was valid, although there were errors in the measurements, with the result he was out by a factor of two. To get the earth-sun distance, he measured the moon-earth-sun angle when the moon was precisely half shaded. The second angle would be a right angle, he knew the distance to the moon, so with Pythagorus, or, if he were into trigonometry that was not available then, secants, he could get the distance. There was a minor problem; the angle was so close to a right angle and the sun is not exactly a point, and the half-shading of the moon is rather difficult to get right, and of course his actual earth-moon distance was wrong, so he had errors here, and had the sun too close by a factor approaching 5. Nevertheless, with such primitive instruments that he had, he was on the right track.

Notwithstanding the slight cheat, Hawking’s demonstration made one important point. By giving the relative sizes and putting the moon about 5 meters away from the earth (the observer) to get a precise eclipse of the given sun, he showed what the immense distance really looks like proportionately. I know as a scientist I am often using quite monstrous numbers, but what do they mean? What does 10 to the power of twenty look like compared with 10? Hawking stunned his subjects when comparing four hundred billion with one, using grains of sand. Quite impressive.

All of which raises the question, how do you make a discovery, or perhaps how do discoveries get made? One way, in my opinion, is to ask questions, then try to answer them. Not just once, but every answer you can think of. The concept I put in my ebook on this topic was that for any phenomenon, there is most likely to be more than one theoretical explanation, but as you increase the number of different observations, the false ones will start to drop out as they cannot answer some of the observations. Ultimately, you can prove a theory in the event you can say, if and only if this theory is correct, will I see the set of observations X. The problem is to justify the “only if” part. This, of course, goes to any question that can be answered logically.

However, Hawking’s subjects would not have been capable of that because the first step in forming the theory is to see that it is possible. Seeing something for the first time when you have not been told is not easy, whereas if you are told what should be there, but only faintly, most of the time you will see it, even if it isn’t really there. There are a number of psychological tests that show people tend to see what they expect to see. Perhaps the most spectacular example was the canals on Mars. After the mention of canali, astronomers, and Lovell in particular, drew lovely maps of Mars, with lines that are simply not there.

Unfortunately, I feel there was a little cheating in Hawking’s programs, which showed up in a program that looked at whether determinism ruled our lives, i.e. were we pre-programmed to carry out our lives, or do we have free will? To do this, he had a whole lot of people line up, and at given times, they could move one square left or right, at their pleasure. After a few rounds, there was the expected scattered distribution. So, what did our “ordinary people” conclude? I expected them to conclude that that sort of behaviour was statistical, and there was really choice in what people do. But no. These people conclude there is a multiverse, and all the choices are made somewhere. I don’t believe that for an instant, but I also don’t believe three people picked off the street would reach that conclusion, unless they had been primed to reach it.

And the current relevance? Herein lies what I think is the biggest problem of our political system: people can be made to believe what they have been primed to believe, even if they really don’t understand anything relating to the issue.