The idea is if you use those two shapes and try to colour the plane with them so the colours match, then the only way that you can do this is to produce a pattern which never repeats itself.
People think of these eureka moments and my feeling is that they tend to be little things, a little realisation and then a little realisation built on that.
And these little things may not seem like much but after a while they take you off on a direction where you may be a long way off from what other people have been thinking about.
This book is about physics and its about physics and its relationship with mathematics and how they seem to be intimately related and to what extent can you explore this relationship and trust it.
Well, I don't know if I can comment on Kant or Hegel because I'm no real philosopher in the sense of knowing what these people have said in any detail so let me not comment on that too much.
As you say, the way string theory requires all these extra dimensions and this comes from certain consistency requirements about how string should behave and so on.
My own way of thinking is to ponder long and I hope deeply on problems and for a long time which I keep away for years and years and I never really let them go.
Some years ago, I wrote a book called the Emperor's New Mind and that book was describing a point of view I had about consciousness and why it was not something that comes about from complicated calculations.
Well, gauge theory is very fundamental to our understanding of physical forces these days. But they are also dependent on a mathematical idea, which has been around for longer than gauge theory has.
In the book, I make the point that here we have string theory and here we have twistor theory and we don't know if either one of them is the right approach to nature.
So what I'm saying is why don't we think about changing Schrodinger's equation at some level when masses become too big at the level that you might have to worry about Einstein's general relativity.