I just found out about this video series today. As someone who codes regularly using fp-ts, I've spent quite a bit of time teaching people about these concepts, but from now on I'm just going to point new people at this playlist. These videos are really well done. Thank you for making them.
The explanation is pretty great, in physics we use group theory for almost every modern theory, that's why functional programming is pretty useful in that science. Nice video.
Thanks a lot for this great quality course! I hope that you would also consider adding or creating a new course for Effect-TS, as fp-ts is moving and becoming part of it now, and it looks very promising to me, and there is almost no content about it now.
Thank you Hayder, I checked out Effect-TS and as you said it looks promising. It seems that it’s in its first stages, but cool stuff I definitely keep an eye on it.
Looking forward to the next video. In fact, this is one of the only channels I actually also enabled notifications for :) Praise aside, this video for me was the hardest to understand so far. Not because of the group itself but the examples you provided. From my perspective it would've been far better if you colored or labeled the nodes in the first two examples (triangle and permutation). When all nodes look the same and you rotate it or mirror it such that the overall triangle also looks the same then this morphism should also be an identity at least that's what my brain tells me just from the visual state I am able to read. This way it would even be more intuitive to see that from a group's perspective both examples are identical because when you project the top node onto the bottom edge it is also visually identical to the permutation example. So yeah, maybe I'm getting this totally wrong but from my perspective all morphisms in the first example pointed to the same object when you think about it in terms of categories. I guess there is some rather large room for interpretation, so maybe you're just interested in the way I interpreted this :)
Now that I'm thinking about what you said, there could be an improvement I could make in my next iteration on this course, so thank you for mentioning this. What I really wanted to convey is, objects (like circles in permutation and edges in the circle, or character that you actually encrypt) is not important. The important thing is not the objects but transitions and actions. Transitions and actions are your Group elements and not the example objects. When you use Group to model triangle movement (using set, binary operation, associativity, identity element, inverse method) nowhere in our definition we used the concept of edges of triangles. the reason I didn't use different colors was to direct viewer’s mind towards that. As you saw, when 2 groups are isomorphic, it means that we can forget about the circles, edges, ... These become unnecessary details which we abstracted them in our Group definition. But still color coding could help to understand the composition of transitions which I think that was what you were referring to as well, so absolutely thank you for your feedback :)
@@webvv Yes that was exactly what I was referring to :) I did get the abstraction, but demonstrating the abstraction on a real world example requires labeling the nodes or edges from my point of view. Anyway, that's just nitpicking, glad if it gave you some ideas to improve the series :)
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This series of videos is truly a treasure trove of videos.
I just found out about this video series today. As someone who codes regularly using fp-ts, I've spent quite a bit of time teaching people about these concepts, but from now on I'm just going to point new people at this playlist. These videos are really well done. Thank you for making them.
This is really heart warming to hear. I’m so glad you like my videos and referring it.
The explanation is pretty great, in physics we use group theory for almost every modern theory, that's why functional programming is pretty useful in that science.
Nice video.
Thank you Andoni! I’m really interested to learn about the use cases in your field. Can you please list some of them?
I really love the way you explain about the group theory.
I’m glad you enjoyed the video.
Great explanation, keep doing these videos!!
Thanks a lot for this great quality course! I hope that you would also consider adding or creating a new course for Effect-TS, as fp-ts is moving and becoming part of it now, and it looks very promising to me, and there is almost no content about it now.
Thank you Hayder, I checked out Effect-TS and as you said it looks promising. It seems that it’s in its first stages, but cool stuff I definitely keep an eye on it.
Looking forward to the next video. In fact, this is one of the only channels I actually also enabled notifications for :)
Praise aside, this video for me was the hardest to understand so far. Not because of the group itself but the examples you provided. From my perspective it would've been far better if you colored or labeled the nodes in the first two examples (triangle and permutation). When all nodes look the same and you rotate it or mirror it such that the overall triangle also looks the same then this morphism should also be an identity at least that's what my brain tells me just from the visual state I am able to read. This way it would even be more intuitive to see that from a group's perspective both examples are identical because when you project the top node onto the bottom edge it is also visually identical to the permutation example.
So yeah, maybe I'm getting this totally wrong but from my perspective all morphisms in the first example pointed to the same object when you think about it in terms of categories. I guess there is some rather large room for interpretation, so maybe you're just interested in the way I interpreted this :)
Now that I'm thinking about what you said, there could be an improvement I could make in my next iteration on this course, so thank you for mentioning this.
What I really wanted to convey is, objects (like circles in permutation and edges in the circle, or character that you actually encrypt) is not important. The important thing is not the objects but transitions and actions. Transitions and actions are your Group elements and not the example objects. When you use Group to model triangle movement (using set, binary operation, associativity, identity element, inverse method) nowhere in our definition we used the concept of edges of triangles. the reason I didn't use different colors was to direct viewer’s mind towards that.
As you saw, when 2 groups are isomorphic, it means that we can forget about the circles, edges, ... These become unnecessary details which we abstracted them in our Group definition.
But still color coding could help to understand the composition of transitions which I think that was what you were referring to as well, so absolutely thank you for your feedback :)
@@webvv Yes that was exactly what I was referring to :) I did get the abstraction, but demonstrating the abstraction on a real world example requires labeling the nodes or edges from my point of view. Anyway, that's just nitpicking, glad if it gave you some ideas to improve the series :)
Excelent👍
Please keep going if possible 🙏
Absolutely, I’m planning to upload the next video in the next couple of days. Thank you for following 🙏
Amazing!
❤️
13:50 except there is an imposter '!' that is not a part of your group
The characters are not your elements in the group, the “action of rotating”s are the elements.
cool!