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Stream: community: general

Topic: category theory in human psychology

ADITTYA CHAUDHURI (Mar 28 2021 at 07:24):

Has there been any approach based on category theory, Topos theory.. etc to understand human psychology? I would be very grateful if someone can suggest some references or resources in this direction!
Thanks in advance.

Fawzi Hreiki (Mar 28 2021 at 07:27):

I don't know about any serious research in that direction but Ronnie Brown and Timothy Porter (famous homotopy theorists) have some interesting papers on the use of analogy in thought and the relationship to CT.

Fawzi Hreiki (Mar 28 2021 at 07:28):

For example, this and this.

Fawzi Hreiki (Mar 28 2021 at 07:32):

If you want something perhaps more substantial, there is the theory of 'Memory Evolutive Systems' by Andrée Ehresmann and Jean-Paul Vanbremeersch which is a categorical approach to biological/chemical/etc.. systems

ADITTYA CHAUDHURI (Mar 28 2021 at 07:33):

@Fawzi Hreiki Thanks a lot for the references.

Henry Story (Mar 28 2021 at 15:02):

I may have said this elsewhere but I think a topic for investigation would be how software professionals have specialised in different categories, and find it difficult to bridge those. E.g. Category of Sets for FP, Coalgebras for OO, Bicategories of relations for Semantic Web, Functors to Set for Relational DBs? Just a thought, that I'd be happy to read a paper on to clarify or even debunk this intuition.

Jules Hedges (Mar 28 2021 at 15:12):

This probably isn't what you have in mind, but there's at least one serious academic investigation into the use of category theory based methods in education, led by @Bob Coecke, which involves a not trivial amount of applying human psychology

John Baez (Mar 28 2021 at 17:38):

I think nobody has made real progress in using category theory to understand human psychology.... yet.

John Baez (Mar 28 2021 at 17:39):

It may happen someday, but it will take a lot of work.

Fawzi Hreiki (Mar 28 2021 at 17:45):

I imagine when that does happen, it will happen via category-theoretic approaches to network/systems theory more broadly

John Baez (Mar 28 2021 at 18:03):

Yes, I've been working on category theory first for electrical circuits and then chemical reactions - these already posed a lot of challenges! Next I'd like to tackle more biochemistry and evolutionary game theory. All these are much easier to study mathematically than psychology. Maybe someone can plunge straight into doing psychology with categories before doing all these "easier" sciences, but only if they know a lot of category theory and have some insight into psychology that lends itself to mathematical formalization.

ADITTYA CHAUDHURI (Mar 28 2021 at 18:53):

From our exposure to music we may assume that every scale (a sequence of musical notes ) when played in a particular time signature they somehow expresses a particular human emotion. Though the converse may not be true that is whether every emotion can be expressed through some sequence of musical notes or not. If I assume that the converse is also true then in some sense studying human emotions will be same as studying different scale patterns in music. But I guess that there are some good work on axiomatising music theory through category theory (for example The Topos of Music https://www.springer.com/gp/book/9783764357313). So in that case can the study of music theory will be considered as a study of human emotions(which is a part of human psychology)?

I apologise priorly if I sound very naive. I am a music enthusiast and play some musical instruments. I always felt the connection of emotion and music. So I am just curious.

Henry Story (Mar 28 2021 at 19:49):

I spend a year reading books on psychology around 2001 while in SF, from analytic philosophy to Jung (you can open all kinds of doors and have conversation in SF cafes with a good knowledge of him), to cognitive and existential psychotherapy, etc...
I think (some) emotions can be modelled in terms of epistemic modal logic: it is a shift in your indexing in the set of possible worlds. So in that logic a belief is a set of possible worlds. You tend to position yourself as inside the worlds you believe to be true. But new information can shift your understanding of where you are in the space of possibilities.
An example:
Jane is walking down a dark street going home after a hard days work. She hears footsteps behind her in the distance getting closer. At this point a number of possibilities could start coming up. Perhaps she is worried and so dangerous ones come to mind. Danger would requiring looking around, but that could reveal fear. So she goes on a bit. Her heart beats faster, she searches for possible escape routes if the worst were to come true. What door could she ring on? As she gets closer to her friends house she ventures to turn her head: it's her brother. Nothing to worry about. She smiles.
Facts can change emotions, as they change the space of possibilities in which one places oneself.

Henry Story (Mar 28 2021 at 19:52):

Now as I recall this positioning in space is what co-monads do. Every comonad has a co-unit, that extracts the object at that location.

ADITTYA CHAUDHURI (Mar 28 2021 at 20:05):

@Henry Story Thanks for the reply. I am still little confused about how co-monads come into play in describing the change of space of possibilites.

Henry Story (Mar 28 2021 at 20:12):

I am not sure how this works in detail, but the relation between monads, comonads and modal logic has been made in quite a number of papers. In possible worlds logic there is a pointer, the actual world, denoted @, that picks out a world out of the sets of all worlds. (so this works like the counit). That is an indexical, in that for any agent in any world, that world in which that agent is, is the actual one. (It is indexical just like "now" is always the time at which that token is spoken, "I" refers to the person who utters the word, "here" refers to the place of around the person speaking, etc...). One can when reading fiction change (by suspension of disbelief) the world which one considers actual. See the fun essay Truth in Fiction.

When thinking about psychology one has to take a phenomenological reading of possible worlds, which I think is how one has to read Philip K. Dick, who came up in a discussion in Febuary.

Henry Story (Mar 28 2021 at 20:49):

The idea of a shift in the space of possibilities also reminds me of what @David Corfield has said a few times speaking of Modal HoTT, where if I recall what is going on is geometric morphisms between infinite toposes. (He mentions monadic and comonadic modalities in this tweet).

@SchreiberUrs "While Modal HoTT is about both, monadic and comonadic modalities, most talks will be about monadic modalities." Sounds like they'll need a follow-up to restore the balance.

- David Corfield (@DavidCorfield8)

John Baez (Mar 28 2021 at 21:45):

@ADITTYA CHAUDHURI wrote:

But I guess that there are some good work on axiomatising music theory through category theory (for example The Topos of Music).

I'm not very impressed by that book. I would like to see someone who knows music theory and topos theory, other than the author of that book and his friends and students, say something concrete about what's good about this book. I know a fair amount of topos theory - not much compared to some people here, but more than what's in this book - and I'm not completely ignorant of mathematical music theory. But I don't see what that book does that's interesting.

John Baez (Mar 28 2021 at 21:48):

I'm more impressed by papers like these:

• Thomas Fiore and Thomas Noll, Commuting groups and the topos of triads.

• Alexandre Popoff, Moreno Andreatta and Andree Ehresmann, Groupoids and wreath products of musical transformations: a categorical approach from poly-Klumpenhouwer networks.

John Baez (Mar 28 2021 at 21:49):

But these focus on the mathematics of music theory - neo-Riemannian theory to be specific - and don't try to say anything about psychology.

John Baez (Mar 28 2021 at 21:51):

In short, they're taking a portion of music theory that's already been mathematized, and bringing in category theory to go further.

Valeria de Paiva (Mar 29 2021 at 06:48):

hi @ADITTYA CHAUDHURI the box or necessity operator satisfies two properties: $\Box A\to A$ and $\Box A \to \Box(\Box A)$. these can be modeled by a comonad as explained in https://www.researchgate.net/publication/226515897_On_An_Intuitionistic_Modal_Logic

Henry Story (Mar 29 2021 at 07:19):

mhh, just looking at that again, it looks like $\Box A \to A$ does not actually capture the @ actuality indexical operator for the actual world. I think that goes $@ p \to p$
Where does that come in?

Henry Story (Mar 29 2021 at 07:37):

Perhaps this does not come out so well in kripke modal logic. But the truth of a counterfactual statement depends very much on where the actual world is (counterfactuals are a graded modality) So if "If Kangaroos had not tails they would topple over" depends on what the closest world to the actual one is where they have no tails. Do they then have bigger feet?

ADITTYA CHAUDHURI (Mar 29 2021 at 07:55):

@John Baez Thank you Sir very much for the references. Can the mathematical music theory has the potential to understand/explore/ classify human emotions? For example one can argue that the same music may not induce the same emotional feeling to each person but I feel there is some universality too ( example major scales create some joyful feel whereas minor scales create a little darker feel , Different Raagas in Indian Classical music expresses different moods, same is true when we move from one genre, sub genre of music to another). But let's discuss a hypothetical situation(inspired from @Chetan Vuppulury ) say a person travels 100 years back and play hard rock then how would a person in 1921 react to it?
Generally Hard rock expresses some extreme aggression, rebel, Boldness....etc(hard to describe in words). But these feelings were still present in 1921 population but might not have the right music to express them. It's a kind of similar when Einstein found the use of Riemannian geometry(which were developed much before) useful to describe the universe. But there are also other instances like if someone plays smooth Jazz in saxophone(representing a city life) to a rural population of 1500 AD they may not relate to any of their emotions prevalent in their life. But if the same person from 1500 time travels to 2000 and leads a city life for some years then he/she may relate something to that music.

Now consider pure Mathematics. It generally explores all the logical structure that can be derived from the fundamental axioms using deductive logic. It generally does not care even if that logical structure fails to prove itself to be useful to the existing science. But it may be possible that someone from future can find some usefulness for that logical structure .

Keeping the discussion for pure Mathematics in mind , can we say that one can use music theory to explore/understand all possible human emotions irrespective of the fact that whether a particular human emotion can relate to some existing set of emotions in the contemporary population or not?

ADITTYA CHAUDHURI (Mar 29 2021 at 07:59):

@Valeria de Paiva Thank you very much for the reply and the reference.

Henry Story (Mar 29 2021 at 08:02):

So in your argument you keep moving between the space of all... and the particular. I think we need to model both, which we can do with a simple construct of pointed Xs.
We can have Pointed Sets, which are sets with a point in them. Or pointed graphs, which are pairs of Graphs with and a node in them. So we can have Pointed Spaces with a space and a point in it. (S,a). If x is closer to y in (S,a) this may not be the case in (S,b).
Similarily, the propositions true in (W,a) may not be true in (W,b) (here propositions can be thought geometrically as subspaces of W).
What is true at one time, may not be true at another. The music enjoyed at one period may not be understandable to those living at a previous one.
What you are imagining when you are imagining someone from the past coming to the future, is a morphism from one state to another. Children have to do this all the time, as they learn new concepts, and as their space of possibilities increases from the crib and the mother, to the family, to the village, country, earth, universe, and beyond. But we also have to do this moment to moment as we shift from one understanding of where in the space of possibilities were are (is it an antilope or a lion over there) to another.

Henry Story (Mar 29 2021 at 08:07):

And indeed where we understand ourselves to be in the space of possibilities will inform our actions, since emotions and actions are closely related.

Bob Coecke (Mar 29 2021 at 10:08):

I got one psychology paper: https://www.frontiersin.org/articles/10.3389/fpsyg.2020.527114/full

Bob Coecke (Mar 29 2021 at 10:10):

There is also some work on conciousness by @Sean Tull and @Harny Wang and others. Sean's even made the cover of New Scientist.

Bob Coecke (Mar 29 2021 at 10:10):

https://arxiv.org/abs/2002.07654

Bob Coecke (Mar 29 2021 at 10:10):

https://arxiv.org/abs/2007.16138

Bob Coecke (Mar 29 2021 at 10:15):

ADITTYA CHAUDHURI said:

From our exposure to music we may assume that every scale (a sequence of musical notes ) when played in a particular time signature they somehow expresses a particular human emotion. Though the converse may not be true that is whether every emotion can be expressed through some sequence of musical notes or not. If I assume that the converse is also true then in some sense studying human emotions will be same as studying different scale patterns in music. But I guess that there are some good work on axiomatising music theory through category theory (for example The Topos of Music https://www.springer.com/gp/book/9783764357313). So in that case can the study of music theory will be considered as a study of human emotions(which is a part of human psychology)?

I apologise priorly if I sound very naive. I am a music enthusiast and play some musical instruments. I always felt the connection of emotion and music. So I am just curious.

We are currently using our quantum natural language framework, which is categorical, to generate music on quantum computers in collaboration with https://www.plymouth.ac.uk/staff/eduardo-miranda This must be the wildest thing I have ever done.

Bob Coecke (Mar 29 2021 at 10:16):

We are also upgrading our DisCoCat NLP framework to a cognitive architecture. A series of papers is on the way, but here is already an old one: https://arxiv.org/abs/1703.08314

Henry Story (Mar 29 2021 at 11:09):

Given that there is at least a school of possible worlds interpretation of quantum theory, these views must be related at some point.

ADITTYA CHAUDHURI (Mar 29 2021 at 11:19):

@Bob Coecke Thank you Sir very much for the references.

ADITTYA CHAUDHURI (Mar 29 2021 at 11:21):

Bob Coecke said:

ADITTYA CHAUDHURI said:

From our exposure to music we may assume that every scale (a sequence of musical notes ) when played in a particular time signature they somehow expresses a particular human emotion. Though the converse may not be true that is whether every emotion can be expressed through some sequence of musical notes or not. If I assume that the converse is also true then in some sense studying human emotions will be same as studying different scale patterns in music. But I guess that there are some good work on axiomatising music theory through category theory (for example The Topos of Music https://www.springer.com/gp/book/9783764357313). So in that case can the study of music theory will be considered as a study of human emotions(which is a part of human psychology)?

I apologise priorly if I sound very naive. I am a music enthusiast and play some musical instruments. I always felt the connection of emotion and music. So I am just curious.

We are currently using our quantum natural language framework, which is categorical, to generate music on quantum computers in collaboration with https://www.plymouth.ac.uk/staff/eduardo-miranda This must be the wildest thing I have ever done.

Wow!! Thats amazing!!

Valeria de Paiva (Mar 29 2021 at 12:42):

Henry Story said:

mhh, just looking at that again, it looks like □A→A\Box A \to A□A→A does not actually capture the @ actuality indexical operator for the actual world. I think that goes @p→p@ p \to p@p→p
Where does that come in?

@Henry Story the actuality operator is part of hybrid logic, an extension of modal logic. I've done a bit on that with Torben Brauner (Roskilde University) https://www.academia.edu/674216/Intuitionistic_hybrid_logic, but we didn't write about categorical models. if you have time, I'd love to do it, but it isn't a tiny project.

Valeria de Paiva (Mar 29 2021 at 12:46):

Henry Story said:

Perhaps this does not come out so well in kripke modal logic. But the truth of a counterfactual statement depends very much on where the actual world is (counterfactuals are a graded modality) So if "If Kangaroos had not tails they would topple over" depends on what the closest world to the actual one is where they have no tails. Do they then have bigger feet?

hmm, the maximum that I'm willing to accept is 'counterfactuals can be modeled as a graded modality', and even that is a tall order.

John Baez (Mar 29 2021 at 15:55):

Can the mathematical music theory have the potential to understand/explore/classify human emotions?

I think if you want to understand the emotional aspects of music you should look, not at mathematical music theory (which doesn't have much to say about emotions, at least not yet), but the work of psychologists, like this:

• Yasmin Anwar, Ooh là là! Music evokes at least 13 emotions. Scientists have mapped them, Berkeley News.

See the works of Alan Cowan for more.

ADITTYA CHAUDHURI (Mar 29 2021 at 17:14):

@John Baez Thank you very much Sir for the references. What are the aspects of music that mathematical musical theory covers generally? I am assuming that it must cover the formation of different scales as well as similarity in patterns between different scales in a mathematical way. If each scale represents a particular set of emotions then naturally indirectly mathematical music theory should have a connection to the study of emotions. Am I misunderstanding anything here ?

Tim Hosgood (Mar 29 2021 at 17:27):

i think the idea that a scale correspond to an emotion is a bit too reductionist, since you could pick two pieces of music written in the exact same key but that relay entirely opposite emotions

ADITTYA CHAUDHURI (Mar 29 2021 at 17:39):

@Tim Hosgood I got your point. What I meant by scale here is actually a sequence of notes played in a particular time signature. Ok, I agree that that may be the music has some connection with emotions but may not be much useful to understand emotions. Has there been any attempt in the past to study human emotions rigorously through a Mathematical model (preferably using category theory)?

Jules Hedges (Mar 29 2021 at 17:41):

Incidentally most people can't distinguish between the same piece transposed into different keys. You need at least approximate absolute pitch to be able to associate anything to keys, including emotions

Jules Hedges (Mar 29 2021 at 17:41):

(Which is a fact that I find really weird, because the key of a piece really does convey a lot of emotion to me)

Joshua Meyers (Mar 29 2021 at 17:43):

Before equal temperament, different keys actually sounded different (because the intervals would be different sizes), so the key would convey emotion even to people with relative pitch. This gave keys emotional connotations, which they still have today even now that we use equal temperament.

ADITTYA CHAUDHURI (Mar 29 2021 at 17:43):

Jules Hedges said:,

(Which is a fact that I find really weird, because the key of a piece really does convey a lot of emotion to me)

Yes, for me too. I play harmonica. Harmonica in different keys feels very different.

Jules Hedges (Mar 29 2021 at 17:46):

Since the human brain is extremely good at recognising patterns across all out different senses without us noticing, my guess is that when you play an instrument, the key of a piece gets associated to other pieces in the same key (and thus their emotions) via a "side channel" of the physical movements you have to do to play in that key

ADITTYA CHAUDHURI (Mar 29 2021 at 17:48):

@Jules Hedges I understand your point.

Oscar Cunningham (Mar 29 2021 at 17:48):

Another factor is that different pitches on a single instrument are not necessarily perfect transpositions of each other. They will have different timbres.

Jules Hedges (Mar 29 2021 at 17:49):

And some instruments also respond differently in different keys, eg. a violin resonates more when you play in a key close to G major

ADITTYA CHAUDHURI (Mar 29 2021 at 17:50):

hmm.. thats true..

ADITTYA CHAUDHURI (Mar 29 2021 at 17:53):

That means you are saying that music may not have a Universal meaning but it depends on the instruments in which we are playing. But is it not similar to the fact that " the feeling of Sadness" is universal to all people but its manifestation varies from person to person?

Fabrizio Genovese (Mar 29 2021 at 17:54):

I don't think music has a universal meaning

Fabrizio Genovese (Mar 29 2021 at 17:54):

Not emotionally, not technically

ADITTYA CHAUDHURI (Mar 29 2021 at 17:56):

@Fabrizio Genovese Ok.. So you are saying that in music there is nothing like bouba-Kiki effect https://en.wikipedia.org/wiki/Bouba/kiki_effect? (which we have for geometrical shapes)

Jules Hedges (Mar 29 2021 at 17:56):

Not universally. I can't imagine any conceivable way that it could happen. But culturally, in the context of "a bunch of standard works that everyone knows" is a different matter, much more plausibly true and not completely inconceivable to be able to say something about it mathematically

Fabrizio Genovese (Mar 29 2021 at 17:58):

bouba-kiki itself is not universal, in the very same page you linked it is said that the majority, but not the totality of people identifies things in the same way.

ADITTYA CHAUDHURI (Mar 29 2021 at 17:59):

@Fabrizio Genovese Hmm.. I agree.

Jules Hedges (Mar 29 2021 at 17:59):

I would guess that consonance and dissonance (which are mathematically definable) are universal-ish (but I'd be interested if anyone can correct me based on academic studies!) ... but the way that people respond to different amounts of consonance and dissonance is surely cultural. Music without any dissonance is music without any tension, so it's like eating English food

Spencer Breiner (Mar 29 2021 at 17:59):

Maybe not an absolute coordinate system, but it seems to me there is definitely some universal difference (for humans) between Beethoven's 5th and the Moonlight Sonata, even if only based on volume and tempo. (forgive my sparse knowledge of classical music)

Fabrizio Genovese (Mar 29 2021 at 17:59):

Music is mainly art, only then maths and science. Art could be described at best, as a loose ensemble of vaguely organized heuristic practices. To my knowledge, every effort to describe art from the point of view of science has led to very uninteresting science, and nearly always to very uninteresting art. :smile:

Fabrizio Genovese (Mar 29 2021 at 18:01):

You can definitely, say, for instance, how harmony struggles with this. The near totality of rock music should be considered as cacophony from the point of view of classic music.

Fabrizio Genovese (Mar 29 2021 at 18:01):

There isn't "one" harmony. Again, it's a set of sparsely organized practices, to which one can subscribe or not

Fabrizio Genovese (Mar 29 2021 at 18:01):

Even better, you can subscribe only to part of it, which is basically how music evolves over time.

Henry Story (Mar 29 2021 at 18:52):

Valeria de Paiva said:

Henry Story said:

Perhaps this does not come out so well in kripke modal logic. But the truth of a counterfactual statement depends very much on where the actual world is (counterfactuals are a graded modality) So if "If Kangaroos had not tails they would topple over" depends on what the closest world to the actual one is where they have no tails. Do they then have bigger feet?

hmm, the maximum that I'm willing to accept is 'counterfactuals can be modeled as a graded modality', and even that is a tall order.

The image on p11 from David Lewis' Counterfactuals is a very helpful illustration of how counterfactuals are to be conceived. Ignore the red circles that I have added to start with. If we take his example with the following 4 propositions shown as areas on the map
$\psi$: The party is Lively
$\phi_1$: Otto comes to the Party
$\phi_2$: Anna comes to the Party
$\phi_3$: Waldo Comes to the Party
Then we have from the actual world $i$ at the center of the black concentric circles that

• If Otto were to come it would be a lively party (because the closest grey area where $\phi_1$ is true is a $\psi$ area)
• if Otto and Anna were to come it would be a dreary party (the is the second closest grey area)
• if Otto, Anna and Waldo were to come it would be a lively party (the third gray area)

But now imagine that the person making that statement is wrong about the actual world being $i$. Perhaps the actual world is the center of the red concentric cicles. (A bit like Trump supporters were wrong about the result of the election). There the closest $\phi_1$ worlds where Otto comes to the Party it is a dreary one (ie a $\lnot \psi$ world - perhaps he is depressed). But the closest worlds where Otto and Anna come contain both dreary and non dreary worlds: i.e if Otto and Anna came to the Party it could be a lively party (perhaps some other turn of events happens that shows Otto's depression to be unfounded, and Anna gets on better with Otto).

I think that this shows conclusively that in Lewis' analysis of Counterfactuals the truth of a counterfactual statement depends on the actual world. I am pretty sure that the proof theory at the end of the book would substantiate this.

Counterfactuals.jpg

John Baez (Mar 29 2021 at 20:32):

ADITTYA CHAUDHURI said:

John Baez Thank you very much Sir for the references. What are the aspects of music that mathematical musical theory covers generally? I am assuming that it must cover the formation of different scales as well as similarity in patterns between different scales in a mathematical way.

It covers things like scales, chords, voice leadings, rhythms, etc. In Western music there aren't so many scales as there in Indian music (ragas), but there's also a lot more work on chords (bunches of notes within a scale, played simultaneously) and voice leadings (how to go from one chord to another chord).

So, a huge amount of mathematical music theory focuses on studying chords and voice leadings. This is especially true for neo-Riemannian theory, which has been studied using categories. I pointed you to two papers on that. If you want to get a feeling for what mathematical music theory using categories looks like, take a look at those papers:

• Thomas Fiore and Thomas Noll, Commuting groups and the topos of triads.

• Alexandre Popoff, Moreno Andreatta and Andree Ehresmann, Groupoids and wreath products of musical transformations: a categorical approach from poly-Klumpenhouwer networks.

John Baez (Mar 29 2021 at 20:39):

If each scale represents a particular set of emotions then naturally indirectly mathematical music theory should have a connection to the study of emotions. Am I misunderstanding anything here ?

Most Western music in the "common practice period" from 1650 to 1900 used mainly just two scales: major and minor. So, the mathematical music theory I know doesn't have a lot to say about scales and emotions. Everyone says "major is happy, minor is sad". That's an oversimplification, but it's not really a good basis for the study of emotions! It's also not very interesting mathematically.

There are probably music theorists who study emotions much more deeply. But anyway, the use of category theory in music seems focused on neo-Riemannian theory, which is a detailed study of chords and voice leadings.

John Baez (Mar 29 2021 at 21:17):

So, I guess what I'm saying is that anyone who wants to apply category theory to psychology has a lot of work to do. It's good to try, but it will require that some experts on psychology and some experts on category theory work together for a few years. I don't think existing work on category theory and music will help a lot.

ADITTYA CHAUDHURI (Mar 30 2021 at 06:56):

@John Baez Thank you Sir very much for the detailed explanation.

ADITTYA CHAUDHURI (Mar 30 2021 at 11:53):

Has there been any approach to understand cognition or consciousness using the language of infinity categories ? At least to me it seems that the language of simplicial sets can be helpful in understanding any kind of network system involving higher dimensional networks.

Javier Prieto (Mar 30 2021 at 13:48):

Jules Hedges said:

I would guess that consonance and dissonance (which are mathematically definable) are universal-ish (but I'd be interested if anyone can correct me based on academic studies!)

Ask and you shall receive: https://www.nature.com/articles/nature18635 (disclaimer: never read the paper, but I vaguely remembered it existed so I could google it fast)

Robert Seely (Mar 30 2021 at 18:05):

Jules Hedges said:

Incidentally most people can't distinguish between the same piece transposed into different keys. You need at least approximate absolute pitch to be able to associate anything to keys, including emotions

That's only if you are using equal temperament (e.g. as on a piano). Such use is actually quite "modern", and isn't really a good reflection of music "through the ages"! If interested, try this book: "How Equal Temperament Ruined Harmony" by Ross Duffin. ($10 in Kindle on Amazon)

John Baez (Mar 30 2021 at 19:16):

The human voice can transpose music to any key without changing the ratios between tones; if you do this the different keys don't have different "flavors". I bet most ordinary singers throughout the ages weren't well-trained enough to do anything else. I think you need a bunch of well-tuned instruments around to associate different emotions to different keys. I think most pianos in the world have generally been out of tune.

John Baez (Mar 30 2021 at 19:23):

Now that most (?) music is generated electronically, we're getting used to really precise tuning. With high-quality electronic instruments it should be easy to explore different tuning systems, but most people don't.

My electronic piano has a bunch of different tuning system options. I used to wonder if I could tell the difference, but it turns out to be easy: they all sound bad except for equal temperament. And then, if I use another tuning system for a while, equal temperament sounds bad too. When I reached the point where all tuning systems sounded bad, I decided I had to stop exploring this.

Robert Seely (Mar 30 2021 at 19:28):

I think you have this backwards, John, or else I misunderstand what you are saying. Till the (late?) 19th century, equal temperament was unusual - the intervals between the semitones were not all equal. That was a relatively "modern" development. And so the keys did have different flavours till then. One frequent misunderstanding is what Bach meant by "Well Tempered Clavier" - most scholars now agree that he didn't mean "Equal Tempered Clavier". There were several different tunings around then which attempted to allow one to use different keys without sounding "out of tune", but were not intended to have the same equal semitones. But one can dispute that! ;-) One can actually prove this historical claim pretty convincingly by investigating church organs from before the 19C, and apparently they are differently tuned in different places. Each town (or whatever) having its own "preferred tuning", it seems.

And whatever this amounts to, certainly ordinary singers were well trained by all accounts - they gave each key its own flavour deliberately, as did (and do) players on instruments without fixed intervals (like the violin family) - I've been told by some violin-playing friends that when playing with other strings (like violas and cellos) that they do _not_ use equal temperament, because they get a better sound with "natural" intervals, and they prefer the sound.

John Baez (Mar 30 2021 at 22:53):

I think you have this backwards, John, or else I misunderstand what you are saying. Till the (late?) 19th century, equal temperament was unusual - the intervals between the semitones were not all equal. That was a relatively "modern" development.

I didn't make myself clear.

For different keys to have different flavors, we need a tuning system where individual notes (e.g. A, B, C, D,...) have specific frequencies attached to them. Then a perfect fifth in the key of A will involve a different frequency ratio than a perfect fifth in the key of C.... unless we happen to use equal temperament.

But I'm suggesting that for a lot of musicians throughout a lot of history, it would be hard to have a setup where individual notes have specific frequencies attached to them!

Imagine the bare-bones situation: a group of people singing, with no instruments. If they've got good ears it's easy for them to sing an octave, or a perfect fifth, etc. So they can easily do something like Pythagorean tuning. But unless they're really trying to make things complicated, their perfect fifth starting on one note will have the same ratio as their perfect fifth starting at any other note: 3/2. That's because 3/2 is easy to do and it sounds great.

This is not equal temperament, but it also means that different keys won't have different flavors, unless they work to achieve that.

If they're singing in a church with an organ, then it's different: the organ will probably dictate the tuning system they use, as you suggest, and a song in the key of A will sound different than a song in the key of C. But this is different from the highly mathematical approaches beloved by tuning freaks - you know, the kind who say "Kirnberger III is better than meantone temperament". This is just people working with the instruments they have.

I've been to a village in Bali that had a gamelan with an unusual tuning system: that is part of the charm of that village. I think there's no real way to tune most of the instruments in a gamelan after they're built. To what extent can you tune a pipe organ?

Jules Hedges (Mar 30 2021 at 23:15):

John Baez said:

This is not equal temperament, but it also means that different keys won't have different flavors, unless they work to achieve that.

(Except to listeners with absolute pitch!)

Jules Hedges (Mar 30 2021 at 23:18):

John Baez said:

To what extent can you tune a pipe organ?

Pretty sure it's impossible, you'd have to change the shape of every pipe individually. (I can imagine an organ design where every pipe has a "piston" and they're all attached to a rack whose height can be adjusted to pitch-bend every pipe at once. That might be something I just invented. Also it might sound terrible)

Fabrizio Genovese (Mar 30 2021 at 23:32):

Indeed, organs have registries, that vary in tune and tone

Fabrizio Genovese (Mar 30 2021 at 23:32):

So you do not tune them, but you can have multiple sets of the same thing tuned in different ways :smile:

John Baez (Mar 31 2021 at 02:10):

Jules Hedges said:

John Baez said:

This is not equal temperament, but it also means that different keys won't have different flavors, unless they work to achieve that.

(Except to listeners with absolute pitch!)

Right! But I was talking about a world without lots of precisely tuned instruments - the world of most people before electronics became cheap. In that world, how much attention would people pay to absolute pitch? If I'm an Inuit in ancient Greenland, or a poor peasant in medieval France, and I'm the only guy around with absolute pitch, am I going to complain that everyone else is singing a half-step sharp? What does that even mean?

Am I going to think a song sounds really different if it's sung a half-step higher? (Quite possibly.)

John Baez (Mar 31 2021 at 02:16):

Anyway, I'm getting a bit carried away talking about the Inuit. A better example might be Gregorian chants, back before organs. Did those monks have tuning forks, or did they just sort of wing it? If the latter, they still could be really careful about getting the relative pitches within a chant exactly right.

Eduardo Ochs (Mar 31 2021 at 03:27):

@John Baez, this playlist (in the Early Music Sources YT channel) may have what you are looking for...
https://www.youtube.com/playlist?list=PLWoQ_Z2-dWRmXI7KiHep_kG6BPqLEjl0K

John Baez (Mar 31 2021 at 04:10):

Those looks nice! Right now I'm talking about the dark realm of music where there aren't keyboards and tuning forks to firmly lock down tuning systems... but whether or not those YouTube videos get into that realm, they look really interesting. I'm trying to learn more about early music and baroque music.

Robert Seely (Apr 01 2021 at 03:11):

John Baez said:

Those looks nice! Right now I'm talking about the dark realm of music where there aren't keyboards and tuning forks to firmly lock down tuning systems... but whether or not those YouTube videos get into that realm, they look really interesting. I'm trying to learn more about early music and baroque music.

So this is where we disagree - I'll let you look up some authorities on tuning before the 19th century. But here is my understanding. This is not a question of having tuning forks, or other tuners, since it wasn't the exact frequencies that were important (it's a fact that something like "middle C" was interpreted as a different frequency in different locales - even within the same country or society - this has been verified by checking the tuning of organ pipes, which once in place are rather difficult to retune!) The question was of relative intervals - what a mathematician would regard as ratios of frequencies (so e.g. an octave is 2:1, etc). And there were several tuning systems in place during the period before the 19th C - And still today there are are different tuning systems (e.g. as I said before with string quartets, etc). So the different keys actually had different intervals between the notes of an octave - and hence different "qualities" - some thing that was lost with equal temperament.

So, in short: we have nothing to teach musicians (say) before the 18th C - they knew how to tune their instruments "perfectly", and no electronic tuners were necessary - indeed, ask any solo guitarist today if they need such tuners!! Certainly I never did - if the intervals between the strings were right (that can be done by ear), you're ready to go. If you're playing with other guitarists, you all agree on (say) A, and go from there. It gets more complicated the more instruments you're playing with, of course, and that's where a tuning fork or whatever is useful. Or else just agree to agree with the violas!

Jason Erbele (Apr 01 2021 at 06:17):

@Robert Seely, I think you and @John Baez are possibly talking past each other. Either that or I'm misunderstanding what one or both of you are saying. The tuning forks etc. nail down a base frequency to a particular note, and that nailing down, specifically, seems to be what John is avoiding. If indeed "middle C" was interpreted as a different frequency in different locales, that would support not nailing down a base frequency to a particular note. And I know enough European music history to know that you are absolutely correct that "middle C" was interpreted as a different frequency in different locales.

Jason Erbele (Apr 01 2021 at 06:18):

Given a tempering and a base frequency for that tempering (e.g. the same equipment in the same conditions is used between trials), I'm sure many people could discern the differences when you transpose a piece to a neighboring key if the tempering is not equal. I don't think there is any disagreement there. I would also suggest that's not really the interesting phenomenon here – different things are perceived as different, which is practically useful, but not very interesting.

Given a tempering, but allowing the base frequency to change between performances of a piece (suppose A is 425 Hz for one performance, but 440 Hz for another performance – perhaps you listen to an organ performance in one locale, then listen to it again in another locale) will probably give "isomorphic" performances to most people, since most people do not have absolute pitch. As long as the relative frequencies are identical between performances, I don't think most people would notice a difference (especially if the piece features a positive number of changes in key). By the way, I'm using the word isomorphism loosely here, hence the scare quotes. I doubt there is an honest isomorphism here; see below.

I find this to be a more interesting phenomenon, as different things are perceived as the same. It would be interesting to see what is the threshold ratio of frequencies before that "isomorphism" breaks. I doubt most people would fail to recognize the difference if the transposition is by an octave, for instance!

Henry Story (Apr 01 2021 at 06:46):

I have updated the picture from David Lewis' book with a morphism which would correspond to a change of belief, and which would have an accompanying emotional change, as possibilities and plans that were reachable from one state turn to be unreachable in another. For example a friend dies, and can no longer be spoken with.
(Note that the pictures don't show up on the archive)
Counterfactuals.jpg

Henry Story (Apr 01 2021 at 06:54):

One can of course in this topological view of the space of possibilities, have points be possible worlds (a whole state of a universe). But it could also be temporal views with divergent futures and divergent pasts. David Lewis defines a counterpart relation on objects so that one can speak of objects that have some sort of identity relation across worlds. The relation between Kripke and Lewis' notion of identity across worlds is analysed in Kohei Kishida's CT based thesis Generalised Topological Semantics for First-Order Modal Logic. (He does not look at Counterfactuals though, which brings a whole new dimension to the picture). One major interest is how Counterfactuals shows how non-monotonic reasoning works. And that is what we humans are best at. We are tuned for contextual shifts.

Henry Story (Apr 01 2021 at 07:06):

In Man, Android, Machine one can see how Philip K. Dick takes this counterpart view seriously. There are many of our counterparts that have exactly the same view and beliefs of the world. These are subjectively indistinguishable: that is you could not tell where on a map one is located. (This sounds like Homotopy Type Theory 's view of equality could be usefully applied here). One is streched out so to say across worlds, or over this space. (In classical view we are in exactly one world, but Lewis' view can easily take quantum indeterminacy into account). Still beliefs being spaces of possbilities, reality may force us to the realisation that the world we thought we inhabited is just "a dream"). Such transformations correspond to such morphisms. And as I believe these can be seen to have an accompanying emotional value.

John Baez (Apr 01 2021 at 07:12):

Robert Seely said:

John Baez said:

Those looks nice! Right now I'm talking about the dark realm of music where there aren't keyboards and tuning forks to firmly lock down tuning systems...

So this is where we disagree - I'll let you look up some authorities on tuning before the 19th century. But here is my understanding. This is not a question of having tuning forks, or other tuners...

You keep saying things I agree with, and acting like I disagree. I think our misunderstanding comes from the fact that I'm talking about the realm of music where keyboards, and tuning forks, and other such devices aren't available, so that it gets harder to lock down any sort of tuning system.

So: I'm not talking about 19th century or 18th century or 17th century or 16th century European art music, where they had keyboards easily available. I'm talking about music like Gregorian chants, or pickup bands where a bunch of people start singing or playing the fiddle: music where you get to decide on the tuning afresh each time you play a piece. I was trying to say most of the music played by most people for most of history was like this, and I was trying to say that in this situation it gets hard for different keys to have different "personalities".

On a keyboard, the different keys will have different "personalities" (sets of frequency ratios) unless you adopt equal temperament. Equal temperament lets you transpose any interval however you like and get another interval with the same frequency ratio. But without equal temperament, a major third (for example) in some key must have a different frequency ratio than a major third in some other key. So I completely agree that before the rise of equal temperament, keyboard music gave different keys different personalities. This era goes back at least to 1511, it seems:

https://www.youtube.com/watch?v=nLa7GOKGMaQ

But this is exactly not what I was trying to talk about. I was talking about music where people strike up a tune purely with their voices, with no keyboard - or tuning fork, or anything else - to regiment them. In this situation they can choose the tonic to be at any pitch they like, and choose to sing in Pythagorean tuning - or whatever tuning they like - starting from that tonic. If they then sing starting from an A, a major third above that can have a frequency 4:3 as high... and if they sing starting from a B, a major third above that can have a frequency 4:3 as high... etc. If they do this, different keys won't have different "personalities" (sets of frequency ratios).

Of course if they want they can choose to sing in such a way that different keys have different personalities, but without the aid of an instrument like a keyboard this seems harder.

Henry Story (Apr 01 2021 at 07:14):

Continuing on the topological view of emotions above:
A very good example of such subjective trip through space, is from the famous computer animation Ratatouille, where right at the end of the film the stern art critique tastes the dish made up by the mouse, and is transported back to his childhood, in a way reminscent to the famous work by Marcel Proust In Search of Lost Time where the whole book unfolds from his eating a Madeleine. From there I think one could start tying this into music too.

Simon Burton (Apr 01 2021 at 14:26):

I remember going to this talk at the Australian categories seminar, "What can category theory say about cognition?" by Steven Phillips. Abstract here: http://web.science.mq.edu.au/groups/coact/seminar/cgi-bin/abstract.cgi?talkid=1463

Robert Seely (Apr 01 2021 at 17:13):

John Baez said:

Robert Seely said:

John Baez said:

Those looks nice! Right now I'm talking about the dark realm of music where there aren't keyboards and tuning forks to firmly lock down tuning systems...

So this is where we disagree - I'll let you look up some authorities on tuning before the 19th century. But here is my understanding. This is not a question of having tuning forks, or other tuners...

You keep saying things I agree with, and acting like I disagree. I think our misunderstanding comes from the fact that I'm talking about the realm of music where keyboards, and tuning forks, and other such devices aren't available, so that it gets harder to lock down any sort of tuning system.

... I'm talking about music like Gregorian chants, or pickup bands where a bunch of people start singing or playing the fiddle: music where you get to decide on the tuning afresh each time you play a piece. I was trying to say most of the music played by most people for most of history was like this, and I was trying to say that in this situation it gets hard for different keys to have different "personalities".

... I was talking about music where people strike up a tune purely with their voices, with no keyboard - or tuning fork, or anything else - to regiment them. In this situation they can choose the tonic to be at any pitch they like, and choose to sing in Pythagorean tuning - or whatever tuning they like - starting from that tonic. If they then sing starting from an A, a major third above that can have a frequency 4:3 as high... and if they sing starting from a B, a major third above that can have a frequency 4:3 as high... etc. If they do this, different keys won't have different "personalities" (sets of frequency ratios).

---

Ok - this clarifies the point of difference, thanks! But I would still beg to differ - I wasn't talking about keyboards (hence the explicit reference to guitars etc), but rather the intervals between tones. And that remains the issue I think. Singers, string players, and especially wind instruments (before keys!) all are very aware of the "natural" intervals between notes, and in the era of "natural temperaments", it really does make a difference where you put the various "big" and "small" semitones. So: it really doesn't matter what your A is (as a frequency), but it does matter where the large and small semitone intervals occur. And so different "keys" (even if they're not called that) will sound different. They might not say they are singing in A or C or whatever, but different "scales" would still be something to be aware of.

But at this point I suspect we've drifted from the topics at hand .... ;-) On this we'll agree, probably: different keys became a bigger deal with the advent of popular keyboard instruments. (Remember my story of the harpsichordist who changed tuning and so temperaments several times during her concert of Elizabethan music.)

John Baez (Apr 01 2021 at 18:32):

I really don't think we disagree about anything.

it really does make a difference where you put the various "big" and "small" semitones.

Since I play music, I know this. It completely changes everything.

So: it really doesn't matter what your A is (as a frequency), but it does matter where the large and small semitone intervals occur. And so different "keys" (even if they're not called that) will sound different. They might not say they are singing in A or C or whatever, but different "scales" would still be something to be aware of.

I think I still haven't managed to convey my point.

I think you are trying to say this: different modes sound extremely different: major, minor, Phrygian, Mixolydian, whatever. Yes, because as you climb up any one mode the placement of tones and semitones differs! But I was talking about something subtler.

Robert Seely (Apr 01 2021 at 19:05):

John Baez said:

I really don't think we disagree about anything.
I think I still haven't managed to convey my point.

I think you are trying to say this: different modes sound extremely different: major, minor, Phrygian, Mixolydian, whatever. Yes, because as you climb up any one mode the placement of tones and semitones differs! But I was talking about something subtler.

Well, I wasn't talking about different modes - without equal temperament, not all semitones are the same intervals, and so different keys (in the modern sense) actually do sound different, even with the same "tone-semitone distribution".

But maybe we've said all we can, so maybe we can leave this till someday we meet again and can discuss this over a glass of beer or wine, or a cup of coffee! ;-)

(In the meantime, take a look at Duffin's book (if you've not already done so)).

Valeria de Paiva (Apr 01 2021 at 19:15):

Henry Story said:

The relation between Kripke and Lewis' notion of identity across worlds is analysed in Kohei Kishida's CT based thesis Generalised Topological Semantics for First-Order Modal Logic. (He does not look at Counterfactuals though, which brings a whole new dimension to the picture).

Thanks, I did not know about the thesis and it's interesting. I guess I don't remember it, because I was not interested in FOL in 2011. now I am, so much appreciated, thanks! (about counterfactuals, my work is very different and adds more structure to Kripke models, as set-theoretical models.)

John Baez (Apr 01 2021 at 19:23):

Robert wrote:

It really does make a difference where you put the various "big" and "small" semitones. So: it really doesn't matter what your A is (as a frequency), but it does matter where the large and small semitone intervals occur.

I wrote:

I think you are trying to say this: different modes sound extremely different: major, minor, Phrygian, Mixolydian, whatever. Yes, because as you climb up any one mode the placement of tones and semitones differs!

Robert wrote:

Well, I wasn't talking about different modes - without equal temperament, not all semitones are the same intervals, and so different keys (in the modern sense) actually do sound different, even with the same "tone-semitone distribution".

Well, you were just now talking about different modes, because you were talking about where the large and small semitone intervals occur. Now you're saying something else, which I also agree with.

John Baez (Apr 01 2021 at 19:24):

Indeed I said the same thing a while back:

On a keyboard, the different keys will have different "personalities" (sets of frequency ratios) unless you adopt equal temperament. Equal temperament lets you transpose any interval however you like and get another interval with the same frequency ratio. But without equal temperament, a major third (for example) in some key must have a different frequency ratio than a major third in some other key. So I completely agree that before the rise of equal temperament, keyboard music gave different keys different personalities.

John Baez (Apr 01 2021 at 19:25):

But this is well-known, and I only mentioned it to distinguish it from what I was actually trying to say.

Eduardo Ochs (Apr 02 2021 at 22:27):

Do we have any string players here? I studied viola a bit, but on a very basic level... I remember spending many, many hours once trying to learn how to make a diminished fifth sound right, and then going to the next lesson feeling that I was totally incompetent - and then my teacher saying that I had made a huge progress and that my intonation was much better...

I think that "real" string players should have lots of stories on how to find the right tuning for pieces - and it would be fun to hear how they tell these stories to an audience of mathematicians.

Jules Hedges (Apr 03 2021 at 09:46):

I believe that category theory has a much higher than expected number of viola players

Jules Hedges (Apr 03 2021 at 09:47):

It's funny to explain it by saying that category theory plays a similar role in mathematics that violas play in an orchestra

Timothy Porter (Apr 08 2021 at 07:04):

Back to the general theme of this thread, I tried to use Chu spaces and related ideas for things relating to Information in a paper with J. Gratus, A Spatial View of Information, Theoretical Computer Science, 365, (2006), pp. 206 - 215. Some of this has been picked up and taken much further by
Chris Field and Jim Glazebrook, eg. in A mosaic of Chu spaces and Channel Theory I: Category-theoretic concepts and tools. J. Expt. Theor. Artif. Intell. 31(2), 177-213. doi:10.1080/0952813X.2018.1544282. They have other interesting papers in the same general direction. I do not know if this helps.

Spencer Breiner (Apr 08 2021 at 15:30):

Neat! Here's the arXiv link for the lazy:
https://arxiv.org/abs/1803.08874

Verity Scheel (Apr 11 2021 at 04:53):

Late to the discussion, but I play in string quartets a fair amount, and I have a faulty but nonnegligible sense of perfect pitch.

Our default pitch tendency probably is equal temperament, but when we really sit down to tune a chord, it’s more about negotiating that particular chord at that moment in time (usually in the order of root, octave, fifth, third, seventh – i.e. more consonant intervals first). It’s much more dynamic than how a keyboard would be tuned: in a string quartet, the same note will sit in different places in different chords.

So I don’t think we end up with markedly different characters in different keys, mostly because it isn’t globally coherent. But sometimes we do have to negotiate chords with open strings differently, and the relationship there would vary by key.

Thus I tend to agree with John that I wouldn’t expect marked differences in different keys, unless the singers/performers were led to emulate it for some other reason than pure consonance/blending.

Disclaimer: we cellists usually “get” to win the tuning disagreements ;)

José Siqueira (Apr 24 2021 at 11:23):

Musical anhedonia is a thing, so the way music interacts with the human brain seems to be a tad more complicated.

Henry Story (Jul 05 2021 at 18:18):

Bob Coecke said:

ADITTYA CHAUDHURI said:

From our exposure to music we may assume that every scale (a sequence of musical notes ) when played in a particular time signature they somehow expresses a particular human emotion. Though the converse may not be true that is whether every emotion can be expressed through some sequence of musical notes or not. If I assume that the converse is also true then in some sense studying human emotions will be same as studying different scale patterns in music. But I guess that there are some good work on axiomatising music theory through category theory (for example The Topos of Music https://www.springer.com/gp/book/9783764357313). So in that case can the study of music theory will be considered as a study of human emotions(which is a part of human psychology)?

I apologise priorly if I sound very naive. I am a music enthusiast and play some musical instruments. I always felt the connection of emotion and music. So I am just curious.

We are currently using our quantum natural language framework, which is categorical, to generate music on quantum computers in collaboration with https://www.plymouth.ac.uk/staff/eduardo-miranda This must be the wildest thing I have ever done.

I guess it would be interesting to have a music and mathematics thread. I'd be interested to know if there anyone has used the work from "The Topos of Music" to create new music that could not have been thought of before, or indeed if any music had come out of it.

Not sure if the quantum computer work is related, but can one listen to anything?
(I know nothing about music theory so perhaps it is just that learning of it from the CT Side would be a good way to learn a new way to think of category theory)

Jon Awbrey (Jul 05 2021 at 18:34):

Henry Story said:

I guess it would be interesting to have a music and mathematics thread. I'd be interested to know if there anyone has used the work from "The Topos of Music" to create new music that could not have been thought of before, or indeed if any music had come out of it.

♩ On A Related Note ♪ The Music Of The Primes ♫ Riffs & Rotes ♬

Now there’s a progression of progressions I could enjoy, musically speaking, ad infinitum, and yet this pilgrim would consider it progress, mathematically speaking, if he could understand why the sequentiae should be sequenced as they are.  Would that understanding add to my enjoyment?  On jugera …

Jon Awbrey (Jul 05 2021 at 21:50):

Jon Awbrey said:

Henry Story said:

I guess it would be interesting to have a music and mathematics thread. I'd be interested to know if there anyone has used the work from "The Topos of Music" to create new music that could not have been thought of before, or indeed if any music had come out of it.

♩ On A Related Note ♪ The Music Of The Primes ♫ Riffs & Rotes ♬

Now there’s a progression of progressions I could enjoy, musically speaking, ad infinitum, and yet this pilgrim would consider it progress, mathematically speaking, if he could understand why the sequentiae should be sequenced as they are.  Would that understanding add to my enjoyment?  On jugera …

There is also this blog I follow ☞ Alpof

Jon

Jon Awbrey (Jul 16 2021 at 12:24):

Re: Math & Music :1234: :musical_score: this just in …

Alpof • Strange Spaces of Networks and Chords

https://www.youtube.com/watch?v=wDWRFWb9Gqo

Alpofblog (Jul 16 2021 at 12:55):

Jon Awbrey said:

Re: Math & Music :1234: :musical_score: this just in …

Alpof • Strange Spaces of Networks and Chords

https://www.youtube.com/watch?v=wDWRFWb9Gqo

Hey ! That's me ! :) I'm not sure I could follow most of the discussions here, but I'd be glad to discuss about math/music/category theory....

Henry Story (Jul 24 2021 at 18:23):

I came across this NPR interview of Ian McGilchrist (wikipedia page) on a book of his from 2010 "The Master and His Emissary; The Divided Brain and the Making of the Western World". The author of the book according to medical journal article, was 2009 Fellow of the Royal College of Psychiatrists and fellow of All Souls College, Oxford.

Let me assume that what he has written is generally correct - and I am sure there are people here who will have much better informed opinions on this. There is an interesting claim that the asymmetry in responsibility between left and right brain goes back 800 million years, that is that extremly simple creatures also have this asymetry. The thesis is to simplify that the right part of the brain looks at generalities - one could call it context - and the left is geared more to precision, analytic, goal directed thought. The left hemisphere's focus helps the animal catch the prey, the right hemisphere helps the animal be aware of its surroundings to stop it from being prey.

If this asymetry is so old, one may wonder if apart from being evolutionary based, which of course it has to be, if it is not also evolution discovering or using mathematical structures.

Henry Story (Jul 24 2021 at 18:30):

For example it seems remarkably close to dualities one finds between say monads focused inside a context, and comonads which have a position but operate on contexts.

John Baez (Jul 24 2021 at 20:46):

Somewhat unrelatedly, the asymmetry in vertebrate anatomy can be traced back to the fact that cilia twist in one direction, not another. There have been a lot of papers about this; I'm just linking to a random one.

John Baez (Jul 24 2021 at 20:47):

This of course does not deny that the way left-right asymmetry gets used by organisms is heavily affected by natural selection!

Simon Burton (Jul 25 2021 at 17:21):

@Henry Story Thanks for mentioning this. I agree & also think it looks a lot like some kind of adjunction/duality.

From what I've noticed there are two kinds of mathematical thinking: manipulating abstract syntax, versus direct experience/perception of concrete mathematics. These two are intertwined in various ways, but in my experience people generally excel in one of these two styles of thinking and not the other. I think that many famous collaborations between two mathematicians are divided along these lines.

Jon Awbrey (Jul 25 2021 at 21:55):

@Simon Burton said:

Henry Story Thanks for mentioning this. I agree & also think it looks a lot like some kind of adjunction/duality.

From what I've noticed there are two kinds of mathematical thinking: manipulating abstract syntax, versus direct experience/perception of concrete mathematics. These two are intertwined in various ways, but in my experience people generally excel in one of these two styles of thinking and not the other. I think that many famous collaborations between two mathematicians are divided along these lines.

Dear Henry, Simon, et al.

Susan Awbrey and I have worked a lot and written a little on a variety of “two-culture” and “cognitive style” questions from a broadly pragmatic perspective informed by the work of C.S. Peirce, John Dewey, and like-minded thinkers.  The three dimensional spaces of Peirce’s triadic sign relations afford a perspective on the ways diverse thinkers can specialize their thought to different planes or facets of a sign relation’s full volume.   Sue has taught at all levels from middle school to graduate school and understands educational development and organizational diversity far better than I have any hopes of doing so I may try to talk her into joining in.  Various issues along these lines are discussed in the following paper.

• Conceptual Barriers to Creating Integrative Universities

Henry Story (Aug 03 2021 at 06:05):

Here is a complete different kind of possible relation between maths and psychology. This article argues that the fractal nature of the brain could allow it to make use of quantum states thus supporting Roger Penrose's hypothesis in "The Emperor's New Mind"
The author gives a conversation overview in this multimedia page on the web and is based on this paper Quantum transport in fractal networks

Jon Awbrey (Aug 04 2021 at 18:00):

∅