Working with programmer Noah Rubin, Damien Riehl built software capable of generating 300,000 melodies each second, creating a catalogue of 68 billion 8-note melodies.

the total number of ways you can scramble a Rubik’s cube: 43,252,003,274,489,856,000. Written in a more mathematical way, that number is (388!)(21212!)/12.

If Luhmann’s notebox system was not dynamic and fluid and not one of pure order, either, how can one think of Luhmann’s notebox system? In my experience using an Antinet Zettelkasten, I find it to be more organic in nature. Like nature, it has simple laws and fundamental rules by which it operates (like the laws of thermodynamics in physics); yet, it’s also subject to arbitrary decisions. We know this because in describing it, Luhmann uses the word arbitrary to describe its arbitrary internal branching. We can infer that arbitrary, means something that was decided by Luhmann outside of some external and strict criteria (i.e., strict schemes like the Dewey Decimal Classification). (12)12 This arbitrary, random structure contributes to one of its most distinctive aspects of the system–the aspect of surprises. Because of its unique structure, the Antinet is noted as “a surprise generator,” and a system that develops “a creativity of its own.” (13)

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

In his practice, Leiris wrote,Duchamp demonstratesall the honesty of a gambler who knows that the game only has meaningto the extent that one scrupulously observes the rules from the very out-set. What makes the game so compelling is not its final result or how wellone performs, but rather the game in and of itself, the constant shiftingaround of pawns, the circulation of cards, everything that contributes tothe fact that the game—as opposed to a work of art—never stands still.

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

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.

Jan Zoń - A New Revolutionary Cards Method

The important ideasof combinatorics do not usually appear in the form of precisely stated theorems, but moreoften as general principles of wide applicability.

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.

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