For a smart material to be able to send out a more complex signal it needs to be nonlinear. If you hit a tuning fork twice as hard it will ring twice as loud but still at the same frequency. That's a linear response. If you hit a person twice as hard they're unlikely just to shout twice as loud. That property lets you learn more about the person than the tuning fork.
About Thomas Hobbes He was 40 years old before he looked on geometry which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and 'twas the 47 El. libri I' Pythagoras' Theorem. He read the proposition 'By God', sayd he, 'this is impossible' So he reads the demonstration of it, which referred him back to such a proposition which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that truth. This made him in love with geometry.
In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it if too wandering, they fix it if too inherent in the sense, they abstract it. So that as tennis is a game of no use in itself, but of great use in respect it maketh a quick eye and a body ready to put itself into all postures so in the mathematics, that use which is collateral and intervenient is no less worthy than that which is principal and intended.
Einstein is an analytical mathematician seeking to give a physical interpretation to the conclusions of his mathematical process. In this he is hampered by a load of contradictory and absurd assumptions of the school that he follows, which throws him in to all manner of difficulty. Einstein has such a faculty for embracing both sides of a contradiction that one would have to be of the same frame of mind to follow his thought, it is so peculiarly his own. The whole Relativity theory is as easy to follow as the path of a bat in the air at night.
'I think you're begging the question,' said Haydock, 'and I can see looming ahead one of those terrible exercises in probability where six men have white hats and six men have black hats and you have to work it out by mathematics how likely it is that the hats will get mixed up and in what proportion. If you start thinking about things like that, you would go round the bend. Let me assure you of that'
I had a feeling once about Mathematics that I saw it all. Depth beyond depth was revealed to me the Byss and Abyss. I saw as one might see the transit of Venus or even the Lord Mayor's Show a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go.
... it is interesting to note that the original problem that started my research is still outstanding - namely the problem of planning or scheduling dynamically over time, particularly planning dynamically under uncertainty. If such a problem could be successfully solved it could eventually through better planning contribute to the well-being and stability of the world.