Wildfalcon

Ok, so it’s important that we understand that there is a distinction between the models, or paradigms that scientists use and the real world. But when I first started to think about these things I got a bit confused. What about computers? Computer people always say “that’s not possible” without any hint that there is a chance that their understanding of how a computer works could be wrong. Unlike scientists, they are, normally, right.

The reason for this is that computers are a special case of building a model. In contrast to science, where we are actually theorising that maybe this model describes the world, when we design computer systems we are building a model, and then deciding to accept whatever the model says as fact.

Let me switch examples now - many people find computers too confusing to follow. The same is true of an election, such as the UK general elections. A model for how to count the votes and how to interpret them has been created. It is available from the government, and its intricacies have been studied in great deal. It’s not a perfect model, though for elections, there is no such thing.

This model gives us a prediction. Once we know how everyone in the country has voted, we can predict who will be the “most fairly elected winner”. At this point, in a scientific model, we would go and measure who the “most fairly elected winner” was, and compare that to our model. In elections, we take the answer from our model, and enforce it in the real world. Computers are the same, although the models are more complex.

The reason I got confused when I first came across this, is surely computers are real, physical things, which obey the real world, why should they obey our models any more than anything else does? It took me a while to figure this out.

Computers are at their most basic level built on semi-conducting transistors. We have a very good (scientific) model of how these work, but perhaps more importantly, for a reasonably small range of conditions (those that exist in a computer) we have looked at them, and observed them, and measured them in enough detail to know how they respond. They have a nice set of properties: they can be configured take two yes/no inputs and produce a yes/no output, in a variety of behaviours. These ways behave exactly like some of the basic logical concepts (AND, OR and so on). So we can use transistors to build a logic engine. A machine that is capable of manipulating our logical models. All that is required is that the behaviour of our transistors doesn’t suddenly change. We then build out logical models in the computer (programming). The “Microsoft Word” model says that when it receives an input showing that the “A” key has been pressed; the state of the screen should be updated to add the letter “A” at the cursor position. We then accept this as reality. Because the model in the computer says there is an “A” there, then there is.

Bookmark to:

Finally I have managed to describe what I want to say about how science works. The concept of a model, that can be manipulated by some tools, and that there are similarities (isomorphism if you want to be pompous) between the model and the way the real world works. I have also explained, though probably not very clearly the problem that logic, the tools science uses to manipulate its models, cannot be proved to be consistent – though no inconsistencies have ever been found.

The next problem is that of what exactly the similarities (isomorphism) to the real world mean, and can we rely on them. Something almost every school child is taught are Newton’s Laws of Mechanics. These describe a model of, say, a tennis ball being struck by a tennis racquet. When you look at a real tennis ball, being hit by a real tennis racquet, then the results are the same. If the model ball goes 106 meters, then the real world ball does too. At least, it does when you make sure your model includes all other factors that apply in the real world, like air.

For a long time, this was fine, and everyone thought that it would always be fine. This is called the problem of induction. It works as follows: “We have compared our model to the real world on many previous occasions, and it was always similar. So it will always be similar.” This is a bit of a leap of faith. We do not know the future, and so we don’t know that the next time we test it it will still work. In reality we assume that it will work, and the first time we find a case that it doesn’t work in, we have to modify our model.

Newton’s Laws of Mechanics, as it turns out, did not work for all time. They only worked until we were able to look at things moving very fast. Then Newton’s model starts to give answers that do not match what we see in the real world. But we can use a more complex model – one that Einstein created called Special Relativity, which still gives the right answers.

The same problem might be there for every single scientific theory we have. They might well only agree with the real world for a range of situations, those that we are able to recreate and then examine. There is even the (probably very remote) chance that they only work agree with the real world on dates before tomorrow…..

Most of this is purely academic though - unless it turns out that the models are only of any use before a certain date. We have spent a lot of time recreating scenarios in the real world, and checking to see if the models agree. Those that don’t are forgotten.

Bookmark to:

An orrery is a mechanical device. It has a big sphere – representing the Sun, at its centre. Connected to a clockwork mechanism are arms that rotate about the “Sun”, at the end of each arm is a smaller globe, representing one of the planets. You can wind the mechanism’s cogs backwards to see the positions of the planets relative to each another in the past, and you can wind it forward to see the future alignments.

Regardless of how well it is designed or built, an orrery will have two problems. It’s not consistent, and it might be fundamentally wrong. As a mechanical device it suffers from wear and tear. Each time you set it up, and then wind it forward one “day”, you get a different answer. The cogs will have worn down; turning a different amount, imperceptibly small bits of the teeth will have been smoothed down. The first time you get one configuration of the planets, the next time you set up the device to show you the same configuration, you will get a slightly different answer. What use is a model that doesn’t consistently give the same answer when asked the same question?

We can ignore that though, the small changes in answer are insignificant really, they are small and irrelevant. But there is potentially a bigger problem - the arms could be the wrong length, maybe on of the arms goes in the wrong direction. More realistically, they would not change in speed when two planets get nearer each other, or they might move in a circle rather than an eclipse. Even when it works as intended, it might be an imperfect recreation of the solar system.

Old fashioned as this may seem, it perfectly describes the way all “rigorous” science works. For anything we wish to explain, we construct a form of orrery: a model. We can wind it forwards or backwards to tell us the past, or the future. Today we don’t build a physical model. We build a conceptual model. A model made up of ideas. It doesn’t use cogs, or gears, but it uses predicates, axioms and theorems – the tools of logic. Scientists build conceptual models, using logic, of everything they try to explain.

These conceptual models suffer from the same two big question marks as the real orrery: Those of consistency and accuracy. That is to say, do they always give the same answer to the same question, and does the answer they give actually tell you the right, real world, answer?

Bookmark to:

Normally I don’t like to talk much about religion, but I came across an idea last night that was so interesting I thought I had to write it down. Simply put, the idea is that science is an unintentional side effect of a religious system that believes in a single god.

The argument goes something like this. Think of a society that believes in lots of gods, one that believes each rock, tree, animal, river etc has its own spirit to diety controlling it. You could easially think of two rivers, one flowing upstream, and the other flowing downstream, because that’s how each god wanted to run their river. If you accept that as a part of the belief system, you will never try and look for common behaviour in all rivers, because it just wouldn’t make sense. Every river has its own god, and every river has its own behaviour, based on that god.

Then by contrast, think about a society such as Christianity, which believes in (one) God. God decides how all the rivers work, and because of this, all rivers work the same. Once you have the concept that all things sharing some property also share behaviour, you start trying to explain that behaviour, to understand it, to predict it. As soon as you start trying to do that, science as we know it soon follows.

The familiar process then often follows, whereby we look at something, create some ideas as to how it works, that seems to successfully predict it, and then we think “hey, this explanation doesn’t need a God to make sense”. Before long there are all sorts of tensions between the scientists and the religious believes, but that’s another story…

Bookmark to: