8 Matching Annotations
  1. Sep 2021
    1. I knew that Sol Golomb had been collaborating on a textbook going back almost fifteen years. It's great to see it not only finally come out, but to see it published with his name in the title!

      I had the pleasure of taking Sol's combinatorics class at USC several years before he passed away, so I also got an early look at much of the material as he was using it in class. It was scheduled at my lunchtime, so I took the time to drive over to USC at lunch twice a week to sit in. My favorite part was seeing proofs for various things I'd seen in other branches of mathematics, but done in a combinatorial way.

      Somewhere knocking around I think I've got audio recordings and notes of the class that I'll have to do something with one day.

      Many talk about Sol's ability to do calculations in his head, but like most mathematicians he knew the standard tricks and shortcuts. To me this was underlined by the fact that he always did long division on the board when there wasn't a simple short cut.

  2. Aug 2021
    1. We can use the itertools.combinations function to find all possible subsets of a chord for a given cardinality.

      Ha! Found a Ruby method to do the same thing in Sonic Pi. https://in-thread.sonic-pi.net/t/exploring-modes-of-pitch-class-sets-using-chord-invert/5874/10?u=enkerli

      Glad this is explicitly mentioned here as it was my initial goal as I got into musical applications of Set Theory!

  3. Feb 2021
    1. According to the historian Robert Darnton, this led to a very particular structuring of knowledge: commonplace users "broke texts into fragments and assembled them into new patterns by transcribing them in different sections of their notebook." It was a mixture of fragmented order and disorder that anticipated a particular form of scientific investigation and organisation of information.

      Might be an interesting source to read.

      Also feels in form a bit like the combinatorial method of Raymond Llull, but without as much mixing.

  4. Nov 2020
    1. Jan Zoń - A New Revolutionary Cards Method

      This highlights a question I've had for a while: What is the best encoding method for very quickly memorizing a deck of cards while still keeping a relatively small ceiling on the amount of space to memorize and work out in advance.

      I want to revisit it and do the actual math to maximize the difference between the methods.

  5. Oct 2020
    1. Experienced practitioners [...] don't have to plod step by step through such a listing of concepts and questions. When they encounter a set of ideas or engage in debate, they can speed through the familiar relationships and spot at a glance the concepts that haven't been taken into account and the questions that haven't been asked. When they work out their own arguments or ideas, they can look at each point from a galaxy of different perspectives that might never come to mind without the help of the combinatorial system and the mental training it provides. Like the Lullian adepts of the Renaissance, they supplemented the natural capacities of their minds with the systematic practices of the combinatorial art. This, in turn, the art of memory seeks to do with the natural capacities of the human memory.  De Umbris Idearum, 'Working Bruno's Magic', p. 164
    1. The important ideasof combinatorics do not usually appear in the form of precisely stated theorems, but moreoften as general principles of wide applicability.
    2. many clever techniquesinvented. Some of these can again be encapsulated in the form of useful principles. Oneof them is the following, known to its friends as Concentration of Measure:if a functionfdepends in a reasonably continuous way on a large number of smallvariables, thenf(x) is almost always close to its expected value.
    1. I was just helping a student with his AoPS homework, when I came across the following related problems: Eight people, including Fred, are in a club.  They decide to form a 3 person committee.  How many possible committees can be formed? So we are choosing 3 people out of 8 or . How many possible committees include Fred? Since Fred is taking one committee seat, that means we need to choose 2 more people from the remaining seven, or . How many possible committees do not include Fred? Since we can’t choose Fred, we need to choose 3 members from the remaining 7 or . Since the total number of committees is equal to the number of of committees with Fred plus the number of committees without Fred, then we can say

      Pascal's rule and is Fred on the committee