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Unreasonable Effectiveness

I think most people would have to agree that there is just one reality and that we can at least approximately know what that reality is. I’m not saying that we understand everything about the universe or that we ever will, but it is possible to form a rough idea about what’s going on.

How do we know we are right? Well it’s all about predictability. If obscure theories such as quantum theory and relativity weren’t at least good approximations to reality then technology which relies on them (like GPS) wouldn’t work. And it does, with remarkable precision (in fact with perfect precision as far as we can tell) so saying these theories are true is justified.

They may not be absolutely, irrefutably true but they are at least close enough to being true that it makes no difference. After all, Newtonian physics was “true” until little anomalies started becoming apparent which lead to better theories. But saying Newtonian physics isn’t true is a bit harsh. It’s “quite true” (if that means anything) and is still good enough for most physics calculations.

And it may be that we can never understand the full truth about many things. For example, I have always wondered about wave/particle duality. This is the quantum theory concept that particles act like waves and waves act like particles depending on the type of measurement being made.

I have always thought that the most likely explanation for this is that what we are trying to explain are neither waves nor particles (two phenomena which are clear in the macro world) but that both are good models to explain something which we have neither the language nor the conceptual framework (apart from maths) to explain otherwise.

So many phenomena can be explained with maths but trying to explain them using “plain language” seems to be impossible. I have heard the claim that if something cannot be explained without maths then the maths is just a model of something which is probably not real, but what if it’s the other way around?

I think it is more likely that maths is the true standard for reality and if a phenomenon can also be explained using language and “common sense” then that is just a bonus. As the subject under discussion becomes more fundamental (in the sense of explaining the true underlying nature of reality) then it may be that common sense and language, which have simply evolved over long periods of human interaction with the everyday macro world, are just not relevant any more.

There was a famous article called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” published in 1960 by physicist Eugene Wigner where he noted that the maths behind a physics theory often leads to advances and predictions in the real world.

Of course, you cannot just make up any old random maths theory and expect it to be a model of the real world. The Intelligent Design crowd tried that in the 1990s but the maths presented by William Dembski was clearly flawed and has been discredited.

So maths is often the only “language” which can explain the real world but it doesn’t follow that maths always explains it correctly. Another doubtful example is string theory where (I am assured) the maths is beautiful but no one knows yet if it’s true.

I want to finish this post with some excellent quotes on the subject of the explanatory power of maths (some of which are completely contrary to my thoughts above)…

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. – Albert Einstein [Not so sure about this except that maybe everything is ultimately statistical.]

Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover. – Bertrand Russell [This is basically what I am saying above. Russell is one of my favourite philosophers ever]

There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology. – Israel Gelfand [I disagree]

We should stop acting as if our goal is to author extremely elegant theories, and instead embrace complexity and make use of the best ally we have: the unreasonable effectiveness of data. – Peter Norvig [I think we need both, but data is the final arbiter]

Yeah after reading those you’ve got to wonder if we will ever know anything!

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