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Hi everyone, I'm Cam. My interest in category theory comes from my profession, which is programming. Several people who I believe to be smart and trustworthy have told me that learning some category theory might be helpful. I'll set a goal here of being able to understand the Yoneda by course end, those in the know can let me know if that's a reasonable goal.
I tried reading Conceptual Mathematics: A First Introduction to Categories by Lawvere and Schaunel about a year ago and, while I found the "flight of a bird as a map from time to space" diagram to be very charming, I was ultimately unable to really understand the text. I'm hopeful that this course and forum will be able to guide me (and others!) through Seven Sketches.
I live and work in Brooklyn, where I spend as much of my time as possible seeing live music and drinking with friends. I studied architecture (as in buildings, not software) in undergrad, and it is probably the subject I enjoy talking about the most. If you have an interest, let's talk bricks!
My only other active side project is a visual demo of sorts for the Raft consensus algorithm using a few raspberry pis and some LED matrices to represent state. I just finished up the LED control code in Python and am moving on to Raft itself now. I'm on the fence for language choice, but may give Elixir a go.
Thank you for hosting the course John! Excited to give category theory another crack.
Comments
Hey cool that you're working on Raft! Do you have a demo? Do you have an ETH-address? I have the right to reward anyone doing interesting work on blockchain-related topics with tokens from my company (https://crowdstart.capital). This is not meant as advertisement or anything, just want to give you some tokens ;)
Hey cool that you're working on Raft! Do you have a demo? Do you have an ETH-address? I have the right to reward anyone doing interesting work on blockchain-related topics with tokens from my company (https://crowdstart.capital). This is not meant as advertisement or anything, just want to give you some tokens ;)Hi, Cam! The Yoneda Lemma is dead easy if you think about it the right way: it's a way of making precise the intuition that everything only is itself by virtue of its relation to other things. However, it seems to require a guru to really explain this!
I could explain it... but unfortunately it seems not to be discussed in Seven Sketches of Compositionality. We'll probably have our hands full - for a while - covering that book. So, you'll learn about sheaves, topoi, monoidal categories and other awesome things, but not Yoneda. Not right away.
I've had little luck getting non-category-theorists to learn category theory from Lawvere and Schanuel's Conceptual Mathematics, even though it seems charmingly simple and direct to me. Maybe it doesn't lead the readers through enough grubby calculations... maybe it's too slick to even register as mathematics to most people! I don't know, but we have to learn by experience to figure out what works.
Sounds like you're doing cool computer stuff. You will at least meet other interesting people here, even if Yoneda remains beyond reach.
Hi, Cam! The Yoneda Lemma is dead easy if you think about it the right way: it's a way of making precise the intuition that everything only is itself by virtue of its relation to other things. However, it seems to require a guru to really explain this! I could explain it... but unfortunately it seems not to be discussed in _[Seven Sketches of Compositionality](https://arxiv.org/abs/1803.05316)_. We'll probably have our hands full - for a while - covering that book. So, you'll learn about sheaves, topoi, monoidal categories and other awesome things, but not Yoneda. Not right away. I've had little luck getting non-category-theorists to learn category theory from Lawvere and Schanuel's _Conceptual Mathematics_, even though it seems charmingly simple and direct to me. Maybe it doesn't lead the readers through enough grubby calculations... maybe it's too slick to even register as mathematics to most people! I don't know, but we have to learn by experience to figure out what works. Sounds like you're doing cool computer stuff. You will at least meet other interesting people here, even if Yoneda remains beyond reach.Hi Cam, Jonatan, John, I've been in a study group using Conceptual Mathematics as our text. Most of the members are Haskell and other functional programmers. I am so far the only person who wants to apply category theory to the real world. So this book and class is really interesting to me. (But I still think Conceptual Mathematics is really good for the underlying math.)
Hi Cam, Jonatan, John, I've been in a study group using Conceptual Mathematics as our text. Most of the members are Haskell and other functional programmers. I am so far the only person who wants to apply category theory to the real world. So this book and class is really interesting to me. (But I still think Conceptual Mathematics is really good for the underlying math.)Jonatan -> No working demo yet, as I've only finished a small part of the display code. I do have an ETH address, but I know very little about blockchain tech, if I'm being honest. While consensus is important in the space, the work that I'm doing is just for personal gratification–I'm not sure I can accept your offer, though I do appreciate it and it made me smile knowing someone is out there trying to foster interesting work.
John -> Thanks for your detailed reply, this must be taking up quite a lot of your time. I hope you don't get overwhelmed by the response!
With regard to the Yoneda, your description of it meshes with my basic understanding of it. It's OK that it won't be covered directly, I'm not afraid of a little self-directed learning. Let's just hope working through the material can give me a strong enough foundation to work on it.
I'm not really sure what the issue was for me with respect to Conceptual Mathematics. My math background is woefully lacking, and so I generally struggle with even basic notation at times and constantly find myself having to try to get a grasp on things as I go. Doing the book with no living outside resources was just a bit too much for me I think.
Bob -> Cool to see so many FP people in here. I've yet to really dip my toes in the water, I think my first foray outside of the realm of making toy-programs is going to be the raft implementation I mention above.
My understanding of category theory is so limited that I can't even imagine its pragmatic or "real world" uses, so I'm mostly excited to get some perspective! I'll keep Conceptual Mathematics in mind for a second pass after this course, maybe it will click on second read.
Jonatan -> No working demo yet, as I've only finished a small part of the display code. I do have an ETH address, but I know very little about blockchain tech, if I'm being honest. While consensus is important in the space, the work that I'm doing is just for personal gratification–I'm not sure I can accept your offer, though I do appreciate it and it made me smile knowing someone is out there trying to foster interesting work. John -> Thanks for your detailed reply, this must be taking up quite a lot of your time. I hope you don't get overwhelmed by the response! With regard to the Yoneda, your description of it meshes with my basic understanding of it. It's OK that it won't be covered directly, I'm not afraid of a little self-directed learning. Let's just hope working through the material can give me a strong enough foundation to work on it. I'm not really sure what the issue was for me with respect to Conceptual Mathematics. My math background is woefully lacking, and so I generally struggle with even basic notation at times and constantly find myself having to try to get a grasp on things as I go. Doing the book with no living outside resources was just a bit too much for me I think. Bob -> Cool to see so many FP people in here. I've yet to really dip my toes in the water, I think my first foray outside of the realm of making toy-programs is going to be the raft implementation I mention above. My understanding of category theory is so limited that I can't even imagine its pragmatic or "real world" uses, so I'm mostly excited to get some perspective! I'll keep Conceptual Mathematics in mind for a second pass after this course, maybe it will click on second read.Welcome to the forum. Until a couple of days ago, this has been a sleepy sleepy town.
I also work as a programmer, live in Brooklyn, and do lots of stuff with music. I'm in the Brooklyn Community Chorus (BCC), which is lots of fun and has lots of folks in it -- and I work on jazz guitar and singing.
I've had a long term interest in learning about category theory, but it's hard to keep going when there is no practical context surrounding the study. But now we have a context to work in, right here!
Welcome to the forum. Until a couple of days ago, this has been a sleepy sleepy town. I also work as a programmer, live in Brooklyn, and do lots of stuff with music. I'm in the Brooklyn Community Chorus (BCC), which is lots of fun and has lots of folks in it -- and I work on jazz guitar and singing. I've had a long term interest in learning about category theory, but it's hard to keep going when there is no practical context surrounding the study. But now we have a context to work in, right here!Thanks David! Happy it is picking up, and glad to see another New Yorker.
I'm not familiar with the BCC, but I am fond of choral work. Do you all perform for the public?
I've been listening to Veljo Tormis' a bit lately, have been particularly sweet on Laevas Lauldakse for a few months now. This rendition by Musica Intima is the best I've been able to find.
https://www.youtube.com/watch?v=49KbGJ7qVdo
Have also been enjoying R Murray Schafer's work, all of which seems to have beautifully rendered scores. I'm a fan of his explicitly stated desire to better control sound and noise in our daily lives. A difficult task in NYC, but something that I'm starting to try to pay more attention to in my day to day life.
https://www.youtube.com/watch?v=GiOhtgR1T0k https://www.youtube.com/watch?v=VIBfdBe369I
Thanks David! Happy it is picking up, and glad to see another New Yorker. I'm not familiar with the BCC, but I am fond of choral work. Do you all perform for the public? I've been listening to Veljo Tormis' a bit lately, have been particularly sweet on Laevas Lauldakse for a few months now. This rendition by Musica Intima is the best I've been able to find. https://www.youtube.com/watch?v=49KbGJ7qVdo Have also been enjoying R Murray Schafer's work, all of which seems to have beautifully rendered scores. I'm a fan of his explicitly stated desire to better control sound and noise in our daily lives. A difficult task in NYC, but something that I'm starting to try to pay more attention to in my day to day life. https://www.youtube.com/watch?v=GiOhtgR1T0k https://www.youtube.com/watch?v=VIBfdBe369I@Cam. I am not a FPer. That's the other people in my study group. I might learn from them, though. And I pointed them at this class, so maybe somebody else might join.
P.S. love the "singing aboard the ship". The other study group is in Secure Scuttlebutt, where nautical metaphors abound. https://staltz.com/an-off-grid-social-network.html
@Cam. I am not a FPer. That's the other people in my study group. I might learn from them, though. And I pointed them at this class, so maybe somebody else might join. P.S. love the "singing aboard the ship". The other study group is in Secure Scuttlebutt, where nautical metaphors abound. https://staltz.com/an-off-grid-social-network.htmlHi Cam, a RAFT side project sounds fun, I could end applying RAFT or blockchain in my job.
Hi Cam, a RAFT side project sounds fun, I could end applying RAFT or blockchain in my job.Hi Cam, re: Brooklyn Community Chorus, yes we do a show twice a year. Next one is in June. I know this isn't FB, but I post a message about it in chat when the time comes. Here's one from January: https://www.youtube.com/watch?v=y7M_t2PuND4
Hi Cam, re: Brooklyn Community Chorus, yes we do a show twice a year. Next one is in June. I know this isn't FB, but I post a message about it in chat when the time comes. Here's one from January: https://www.youtube.com/watch?v=y7M_t2PuND4Where are your favorite spots to hear music in Brooklyn? I go to Barbes alot. Also a big fan of Winnies jazz bar in the lobby of the Refinery Hotel, 38th st in Manhattan. No cover, unpretentious, small stage, conversational atmosphere; every night a different jazz band.
Where are your favorite spots to hear music in Brooklyn? I go to Barbes alot. Also a big fan of Winnies jazz bar in the lobby of the Refinery Hotel, 38th st in Manhattan. No cover, unpretentious, small stage, conversational atmosphere; every night a different jazz band.I usually go for specific sets that I'm interested in, rather than just hitting a spot. If I am going to just hear someone play, I tend to go to Fat Cat which is in the village–$3 cover, music every night but can get a bit hectic on weekends since it's right near NYU. I've got a friend who swears by Tomi Jazz, also in the city, but I've yet to go.
I think the Brooklyn venue I've been to the most in the past year or two has been National Sawdust. It's a bit pricey and not really the vibe I'd shoot for 24/7 but they have some really excellent concerts.
Hopefully I can come out for the next BCC show!
I usually go for specific sets that I'm interested in, rather than just hitting a spot. If I am going to just hear someone play, I tend to go to Fat Cat which is in the village–$3 cover, music every night but can get a bit hectic on weekends since it's right near NYU. I've got a friend who swears by Tomi Jazz, also in the city, but I've yet to go. I think the Brooklyn venue I've been to the most in the past year or two has been National Sawdust. It's a bit pricey and not really the vibe I'd shoot for 24/7 but they have some really excellent concerts. Hopefully I can come out for the next BCC show!Fellow Brooklynite here. I've seen amazing bands at Bar LunAtico (https://www.barlunatico.com) in Bed-Stuy. It's a one of kind place.
Fellow Brooklynite here. I've seen amazing bands at Bar LunAtico (https://www.barlunatico.com) in Bed-Stuy. It's a one of kind place.@John In fact, Fong and Spivak did mention the Yoneda lemma in passing (Oct 12 version, p.20), though restricted to the case of preorders and using the contravariant (upper set) version for some reason. :-? (I dug this out when one of my professors comments on my work suddenly brought Yoneda into my mind though it had absolutely nothing to do with category theory or mathematics...)
@John In fact, Fong and Spivak did mention the Yoneda lemma in passing (Oct 12 version, p.20), though restricted to the case of preorders and using the contravariant (upper set) version for some reason. :-? (I dug this out when one of my professors comments on my work suddenly brought Yoneda into my mind though it had absolutely nothing to do with category theory or mathematics...)