Symmetries

5 responses so far ↓

•   db137033 // Mar 14th 2013 at 12:43 am

  I searched the web for what a mandala is and found that a definition of a mandala is “a symbol in a dream, representing the dreamer’s search for completeness”. A math problem (in my mind at least) is a sequence of marks on a piece of paper manipulated according to stated rules with the goal of reaching a final ground ie a completion. Mathematicians and mathematics as a science has in its heart the sanctity of proof. Taking something more or less simple and adding and inferring as we go along in the hopes of proving a final piece. I think the definition is very fitting because this journey of proof can be so difficult and alluring it almost seems like a dream. But I, like all other people fascinated by mathematics must keep trying to reach these proofs even though the distance to the final destination (proof) may seem out of our grasp – Denis Buci

•   an125231 // Mar 16th 2013 at 3:56 pm

  Mandalas resemble the proof of the completeness theorem. The mandala, {3,5,0,8}, shown on page 2 of the mandala handout, shows the triangle being contained inside the pentagon, the pentagon being contained inside a circle, and the circle being contained inside an octagon. The proof of the completeness theorem involves a set of axioms being contained in a larger set of axioms, this larger set of axioms being contained in a more larger set of axioms, this more larger set of axioms being contained in an even more larger set of axioms… By analogy, the octagon in this mandala may stand for the maximal set of axioms required for completeness.

•   an125231 // Mar 17th 2013 at 8:31 pm

  The medicine buddha mandala at the center can represent the statement that is to be proved, and the different regions of the mandala can each contain a logical deduction that must be discovered in order to be given passage to the next consecutive region.

•   ag120857 // May 22nd 2013 at 10:34 pm

  The analogy between proofs and mandalas is one that I would like to consider further.

  The question of concern is: what is a proof?

  “a formal series of statements showing that if one thing is true something else necessarily follows from it.”

  But for most mathematicians, showing that these formalizations can be done is sufficient. Does this mean that what mathematicians construct aren’t proofs? If not, then we need to revise our definition.

  Suppose instead we called it a “convincing argument made by someone who knows math.” The “who knows math” part implies that it’s dependent on particular people – mathematicians. Does this mean that before I decide whether X is a proof, I have to figure out who the mathematicians are?

  What if someone doesn’t have an aptitude for math? Does a mathematician need to be convinced by an argument ? Does this mean that the people who decide what a proof is are the mathematicians? Suppose there were only a handful of people could understand a proof. Is this argument a proof because a handful of people understand it and are convinced by it? If the few people that claim to understand are the only ones convinced, is it still a proof?

  If a proof is this “formal series of statements,” then a mandala is very similar to a proof. We are “finding the gates to ascend to successively higher and more central levels of enlightenment.” But if a proof is a “convincing argument,” then a mandala isn’t quite the same. To informally prove something (to present a convincing argument) is analogous to jumping across higher levels in a mandala, skipping steps to arrive at enlightenment.

•   Xin Lin // May 25th 2013 at 12:39 am

  Mandalas is similar to problem in several ways. In geometry, mandalas can be triangles, squares, circles and many other shapes. The shaped included many mathematical problems, such how to find the angles, the ratios between the lines. In a different angle of looking at the mandalas, its patterns is similar to the process of finding a theorem and proving it to be consistent.