Steven Weinberg - Is Mathematics Invented or Discovered?

Steve the efficacy of mathematics in explaining the physical world in explaining physics is really remarkable first of all how accurate is mathematics in explaining physics I don't think mathematics can be ever regarded as a an explanation in itself of anything and this is not always been well understood perhaps it's even still controversial physical theories aren't the way they are because of principles of mathematics principles of mathematics are they are the language in which we state our physical principles and they are the way the intellectual tools we use for calculating the consequences of those principles but nothing is the way it is because of some mathematical principles that was not historically well understood Plato had over the door of his Academy according to legend the inscription let no one who was ignorant of mathematics enter here but his idea of mathematics was as the deep explanation of things for example he wanted to explain the five elements fire earth air water and the fifth one he called quintessence which is the material out of which the heavenly bodies are made in terms of the five regular platonic solids the five bodies that are this that we're every face in every vertex are the same the cube the tetrahedron octahedron dodecahedron and icosahedron and you know it was really not mathematical science in the way we understood it and that was more mathematical mumbo-jumbo and some even some moderns talk about mathematics that way direct I think was responsible for exalting mathematics to a level I don't think it really deserves I mean he regarded his equation the Dirac equation which is the basic equation we use to describe the electron in quantum mechanics as being the way it is because it was mathematically beautiful and I don't think that what that was right actually we now have a better understanding of why the direct equation is the way the direct equation is but it is still true as Plato was hoping and as Dirac was hoping that when we make advances in in science we often find the mathematicians who've been there before us we find that beautiful mathematics which pre-exists the developments in physics turns out to be extraordinarily useful what are some examples well a classic example is is the theory of symmetry the theory called group theory which is the mathematical underpinning of physical principles of symmetry symmetry principles describe how things describe the ways in which things have appearance which doesn't change when you change your point of view and the set of all ways of changing your point of view which leaves the appearance of something unchanged is called the group the symmetry group and the theory of symmetry groups existed for a hundred years before it was applied in physics because it was developed as a solution of purely mathematical problems by every scale wahhhh without any practicality we're not over no that's right or it's certainly none that had anything to do with physics I once used the analogy that theres a spooky quality about the ability of mathematicians to get there ahead of physicists and i said it's a little bit as if when niels Neil Armstrong first landed on the moon he found in the lunar dust the footsteps of jules verne and the question has naturally occurred to many people why is mathematics so potent and I have a few tentative ideas about why that might be true and one of them is that we're nature is described by laws which to the human mind have to be expressed mathematically and although the mathematics that is needed to describe those laws isn't natural to us because we live in the real world we've gradually gotten beaten into us by nature by our effort to understand things that this is the way the world is not some other way that the world is well described for example in terms of symmetry principles that was not apparent for millennia of scientific effort and became apparent in the 20th century because the effort to understand elementary particles forced us to introduce symmetry groups so the universe is our math teacher that's right but it's not a very efficient teacher we're not taking a well organized set of lectures which it's trial and error but we're gradually getting there another possibility is that we only look for theories that are mathematically beautiful of course sometimes we can't be so lucky sometimes we need theories because the problems are practically important we have to freak for example be able to calculate the flow of air past an airplane the turbulence produced because we want to know how much drag that will be on the airplane it's not a fundamental scientific problem it's a practical problem so we need complicated theories once a very leading plasma physicist said to me plasma physics is the theory that describes gases where the electrons have departed from the atoms and are travelling freely so the gas becomes electrically conductive and plasma physics plays an essential role in trying to design thermo nuclear reactors for instance because the way you make a thermonuclear reaction go is to get a plasma of hydrogen hot enough so that reactions take place well he said to me if you have an elegant theory in plasma physics that describes what might go on with beautiful elegance it's guaranteed to be irrelevant with a real world I mean plasma physics is driven to a large extent by the practical need to understand well some Astrophysical phenomena but also to try to make thermonuclear fusion work and so the plasma physicist does not search for mathematical beauty my friend runs away from but when the aim is not practical but conceptual when you're you're trying to understand why we live in the kind of world we do the kind of theory that is going to be useful to us would be a theory that has great mathematical Beauty because it's only in that way that it could have explanatory power if it's ugly that means it has a lot of various discordant elements and you haven't really explained much because you have to say why is it that way and not some other way you haven't gotten very four ways if it's beautiful you have a feeling ah this explains it even even though the beauty may itself be a consequence of something much deeper which doesn't have that particular kind of beauty may have some other kind of beauty so that's another thing we look for we look for theories that are beautiful and there is a hope that at the very bottom there will be something completely beautiful that there is a hope that you know as as the poet Vaughn said if any beauty I did I'm not sure I'm quoting this exactly if ever any beauty I did see which I desired and got twas but a dream of thee we dream of a beautiful theory that will be completely beautiful

Channel: Closer To Truth

Views: 264,441

Keywords: Steven Weinberg, Closer To Truth, Mathematics, Reality, Physics, Philosophy, Cosmology

Id: NpMk9G-ddiM

Length: 8min 41sec (521 seconds)

Published: Mon Feb 22 2016