 Jan 2024
 Aug 2023

www.independent.co.uk www.independent.co.uk

Cuthbertson, Anthony. “Musician Uses Algorithm to Generate Every Possible Melody to Prevent Copyright Lawsuits.” The Independent, February 28, 2020, sec. Tech. https://www.independent.co.uk/tech/musiccopyrightalgorithmlawsuitdamienriehla9364536.html.

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

 Apr 2023

www.popularmechanics.com www.popularmechanics.com

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.
The total number of ways one can scramble a cube is
(3^8 * 8!)(2^12 * 12!)/12
the first term is for how the 8 corner pieces can be rotated by three before returning to their original orientations and the eight! places they can be placed<br /> the second term is for the two ways that 12 edges pieces can be inserted into their 12 locations The bottom 12 is for the 322 ways that algorithms can't solve for a single rotation of a corner piece, or the other algorithms can't swap a pair of corners or a pair of edges.

 Jun 2022

zettelkasten.de zettelkasten.de

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)
There's some magical thinking involved here. While the system has some arbitrary internal branching, the surprises come from the system's perfect memory that the human user doesn't have. This makes it appear that the system creates its own creativity, but it is really the combinatorics of the perfect memory system with use over time.
Link to: serendipity of systems based on autocomplete

 May 2022

ecotechnicinklings.blogspot.com ecotechnicinklings.blogspot.com

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

 Apr 2022

Local file Local file

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 outset. 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.
particularly:
but rather the game in and of itself, the constant shifting around of pawns, the circulation of cards, everything that contributes to the fact that the gameas opposed to a work of artnever stands still.
This reminds me of some of the mnemonic devices (cowrie shells) that Lynne Kelly describes in combinatorial mnemonic practice. These are like games or stories that change through time. And these are fairly similar to the statistical thermodynamics of life and our multitude of paths through it. Or stories which change over time.
Is life just a game?
there's a kernel of something interesting here, we'll just need to tie it all together.
Think also of combining various notes together in a zettelkasten.
Were these indigenous tribes doing combinatorial work in a more rigorous mathematical fashion?

 Sep 2021

www.springer.com www.springer.com

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.

 Aug 2021


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://inthread.sonicpi.net/t/exploringmodesofpitchclasssetsusingchordinvert/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!

 Feb 2021

publicdomainreview.org publicdomainreview.org

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.

 Nov 2020

forum.artofmemory.com forum.artofmemory.com

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.

 Oct 2020

www.dpmms.cam.ac.uk www.dpmms.cam.ac.uk

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.


mathproblemsolvingskills.wordpress.com mathproblemsolvingskills.wordpress.com

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
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