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Hello all! I am very happy to be a part of this class! I do paintings, compose music and improvise on a solo guitar. I have a MA in music (classical guitar performance). I also teach guitar and a small music composition class where we try to bring mathematics and music together, for example by "playing" matrix multiplication tables as combinations of notes, of left and right hand fingers. Mapping notes onto powerset lattices and thinking on possible ways to form tonal spaces and how players could interact with them. I am learning categories to abstract performers thinking processes, finger movements, music composition and improvisation patterns. I find the language of it very musical and relaxing. It somehow occupies a spiritual, meditative space without objects and it has greatly influenced my life by moving the attention from endless objects and labels to pure relations.

Last Summer I read "half a Plato" to experience the square root of 2. It is quite shocking. I need to read the other half this Summer. It would be interesting to map the Parmenides dialogue into a categorical platonic map, or in such case any other thinker or a writer..

## Comments

Hello, Domagoj! What's "half a Plato"?

It's good to see another musician in this course! There are some interesting works on category theory and music, including by Maria Mannone, a classical musician and theoretical physicist who is attending this course. I sometimes correspond with Alexandre Popoff on this subject - he has a bunch of interesting papers.

`Hello, Domagoj! What's "half a Plato"? It's good to see another musician in this course! There are some interesting works on category theory and music, including by [Maria Mannone](https://forum.azimuthproject.org/discussion/2044/introduction-maria-mannone/p1), a classical musician and theoretical physicist who is attending this course. I sometimes correspond with [Alexandre Popoff](https://www.researchgate.net/profile/Alexandre_Popoff2) on this subject - he has a bunch of interesting papers.`

Thank you, Professor Baez, for the reference! Hi Domagoj, it'll be fun sharing ideas. Categories are quite a powerful tool to re-think even basic elements from music, moving the attention from single objects to transformational processes. So far, there are applications of categories to music theory, to musical performance included gestures, and to music-image interactions.

`Thank you, Professor Baez, for the reference! Hi Domagoj, it'll be fun sharing ideas. Categories are quite a powerful tool to re-think even basic elements from music, moving the attention from single objects to transformational processes. So far, there are applications of categories to music theory, to musical performance included gestures, and to music-image interactions.`

Hi John! Hi Maria! "half a Plato" as in half of all Plato's dialogues. Background: getting into the soft, natural, relational ancient mindset, a different kind of awareness. Reading Homer's Iliad for example where attention seems to be given to different body parts as separate entities rather than one

sufferingbody. I noticed, Plato sometimes copies certain abstract relations by mapping onto them different arguments in different works. Thank you for the references.Maria, your papers are inspiring, It will be fun!

Iliad

`Hi John! Hi Maria! "half a Plato" as in half of all Plato's dialogues. Background: getting into the soft, natural, relational ancient mindset, a different kind of awareness. Reading Homer's Iliad for example where attention seems to be given to different body parts as separate entities rather than one *suffering* body. I noticed, Plato sometimes copies certain abstract relations by mapping onto them different arguments in different works. Thank you for the references. Maria, your papers are inspiring, It will be fun! > There was a world, or was it all a dream?.. Iliad`

Hi Maria, I am curious to know about the connections between music and category theory that you have drawn. Would it be possible for you to post a link to a paper or two that you consider to be of interest?

I tried to download a couple from your page linked above, but didn’t succeed in getting the ResearchGate account. Alternatively you could email me dave.tanzer at the Google mail.

Thank you

`Hi Maria, I am curious to know about the connections between music and category theory that you have drawn. Would it be possible for you to post a link to a paper or two that you consider to be of interest? I tried to download a couple from your page linked above, but didn’t succeed in getting the ResearchGate account. Alternatively you could email me dave.tanzer at the Google mail. Thank you`

Hi Domagoj! This isn't category theory related, but I recently read a book called A Motif of Mathematics by Scott Guthery which was my first introduction to the Farey sequence and the mediant.

Apparently some folks have tinkered with a connection between those mathematical ideas and music. I know very little about music, so I don't know if this turns out to be an interesting line of investigation. Perhaps Googling for "Farey sequence music" will find you something to catch your attention.

It's interesting that you mentioned Plato. Apparently the mediant is related to antique views that distinguished between fractions, ratios, and proportions, a separation lost in our modern real-numbers-are-everything way of looking at quantities. Guthery references work by David Fowler called The Mathematics of Plato's Academy: A New Reconstruction that theorizes about this "pre-arithmetized" view.

There is a reference to the mediant appearing in "Plato's Parmenides 154bd". I know even less about Plato than I do about music! Perhaps you've already seen this. I was amused that a completely random math book I picked up happens to intersect with your nonmath interests.

`Hi Domagoj! This isn't category theory related, but I recently read a book called A Motif of Mathematics by Scott Guthery which was my first introduction to the [Farey sequence](https://en.wikipedia.org/wiki/Farey_sequence) and the [mediant](https://en.wikipedia.org/wiki/Mediant_(mathematics)). Apparently some folks have tinkered with a connection between those mathematical ideas and music. I know very little about music, so I don't know if this turns out to be an interesting line of investigation. Perhaps Googling for "Farey sequence music" will find you something to catch your attention. It's interesting that you mentioned Plato. Apparently the mediant is related to antique views that distinguished between fractions, ratios, and proportions, a separation lost in our modern real-numbers-are-everything way of looking at quantities. Guthery references work by David Fowler called The Mathematics of Plato's Academy: A New Reconstruction that theorizes about this "pre-arithmetized" view. There is a reference to the mediant appearing in "Plato's Parmenides 154bd". I know even less about Plato than I do about music! Perhaps you've already seen this. I was amused that a completely random math book I picked up happens to intersect with your nonmath interests.`

I noticed there was an interesting discussion going on here, so I went ahead and made a musical based discussion group. Simply out of curiosity, I would really like to learn how music and category theory relate. Hopefully, because the thread's easier to see, more people will join in there. :)

Applied Category Theory for the Musician

`I noticed there was an interesting discussion going on here, so I went ahead and made a musical based discussion group. Simply out of curiosity, I would really like to learn how music and category theory relate. Hopefully, because the thread's easier to see, more people will join in there. :) [Applied Category Theory for the Musician](https://forum.azimuthproject.org/discussion/2091/applied-category-theory-for-the-musician)`

BTW, on Plato and category theory, see this paper.

`BTW, on Plato and category theory, see [this paper](http://www.ellerman.org/on-self-predicative-universals/).`