10 ms·

Some years ago Wildberger gave some excellent lectures explaining quaternions using rational geometry, which, if I am not mistaken, is related to Clifford algeb

• imglorp 10y ago
  I've noticed Wildberger getting some grief about some of his unconventional ideas. I very much enjoy his lecture style, but as a layperson I'm never sure when he's straying away from accepted areas into controversial ones. Any feedback there?
  • blux 10y ago
    Yes, he sure is controversial. He does not acknowledge the existence of irrational numbers for example. In his lectures he avoids the use of any transcendental functions for the same reason, so no square roots, sine, or cosine. I'm no mathematician, so I'm not qualified to comment on this either. Would love to hear other opinions on this too. My personal opinion on this is that his rational approach does produce beautiful math, in the sense that it is really simple and intuitive.
    • nabla9 10y ago
      >the existence of irrational numbers for example. I think most of cases of "non acknowledging" are deeply personal aesthetic considerations. One likes to play with one set of objects and only with them. In the widest sense existence in mathematics means that mathematical object is well-defined and the system used is consistent (you can't derive contradictions). Of course mathematicians are free do limit themselves into any subset of axioms or concepts they feel is "natural" or "real" and work only with them. But if they make philosophical arguments against other using irrational numbers, axiom of choice etc. I think they should argue that they are not consistent or well defined.
    • jcranmer 10y ago
      > In his lectures he avoids the use of any transcendental functions for the same reason, so no square roots, sine, or cosine. Square roots are algebraic, not transcendental.
  • llamaz 10y ago
    The general consensus is that his videos are very good. It's just his insistence that the real numbers shouldn't be used that is not accepted. Some mathematicians (1% of 1% of mathematicians) agree with him, most don't. edit: Doing math without the real numbers is less elegant and harder, but it's philosophically more sound. It essentially means restricting yourself to math that can be described as a (possibly infinite) algorithm. The lay person is more likely to agree with what Wildberger has to say than a mathematician. In fact, most people think that infinity in math is a process (potential infinity). But in math, we use absolute infinity. A completed infinity. 0.999... does not tend to 1, it _is_ 1. Infinity is completed.
    • blux 10y ago
      > It essentially means restricting yourself to math that can be described as a (possibly infinite) algorithm. I'm confused. My impression is that it is the other way around where irrational numbers and operations like sine, square root etc. are infinite 'algorithms'?
      • empath75 10y ago
        Yeah, but there's a difference between saying there exists in reality some exact value for the square root of 2, and saying that it's possible to calculate the square root of 2 to arbitrary precision.