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A monoid is a category, a category is a monad, a monad is a monoid

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Re: A monoid is a category, a category is a monad, a monad is a monoid

#51

Post by pitaj »

tikhonj wrote: post #12
casion wrote: post #2

Are there really that many people on NH that can understand this? I'm not trying to be snarky, I'm legitimately interested. It seems like this class of knowledge is highly specialized, yet I see posts like these high up on NH frequently.

I work at Target and we have a weekly class on algebra, category theory and Haskell because people are interested. It's a mix of programmers learning some of the math and mathematicians learning some of the programming :). It's actually a lot more accessible than it seems at first—these ideas are not complex , just abstract. Thinking at a high level of abstraction is very much a skill which requires specific training…

This is the most unexpected thing I've ever heard about Target.

Re: A monoid is a category, a category is a monad, a monad is a monoid

#52

Post by irfansharif »

Waterluvian wrote: post #40
the_af wrote: post #39

Earlier quoted context omitted.

Learning Haskell, if you just want to hack and build a program, is not really complicated and you don't need a math degree or to be particularly smart. You just need to understand it won't be like writing other languages you learned before. That doesn't make it more difficult, just different.

Good to know. I think I get too into my head when reading about it all. Monads? Monoids? Functors? Oh my! Edit: thank you all for your wonderfully encouraging and useful responses. I know what I'm playing with tonight!!!

Philip Wadler published this paper[1] titled 'Monads for functional programming' that serves as a good introduction on the subject and is very accessible. It is enumerated through with concrete examples such as 'error handling' using Monads and maintaining 'state' via the State Monad.

[1]: http://homepages.inf.ed.ac.uk/wadler/papers/marktoberdorf/ba...

Re: A monoid is a category, a category is a monad, a monad is a monoid

#53

Post by bshimmin »

crawfordcomeaux wrote: post #45
bshimmin wrote: post #27

Earlier quoted context omitted.

accidentally stumbled on the Buddhist practice of deity visualization, which created a second conscious voice in my head. She helps me learn how to embody more than one new personality trait at a time easier than if I simply focused on being those things. It's weird/complicated, and I'm willing to go into more detail if people have questions. I would love you to go into more detail, though probably only for all the w…

Standard advice to learning a set of new personality traits: pick one each morning to choose to embody for the day & focus on it. How I do it: associate the set of traits with an identity somewhat separate from my own. She's essentially a clone of my personality, except she identifies as a woman & embodies the following personality traits: gentleness, patience, valuing relationships based on emotional support availab…

Thank you for taking my mean-spirited response in good part (I upvoted your initial comment because it entertained me - though you've since edited out the best bit! - and I'm upvoting your reply because it was interesting and delivered with gentleness and humility).

I'm far too much of a troglodyte to understand any of this stuff, but good on you for you trying to improve yourself (if that is indeed the intended goal).

Re: A monoid is a category, a category is a monad, a monad is a monoid

#54

Post by JHonaker »

crawfordcomeaux wrote: post #16
emsy wrote: post #7

Earlier quoted context omitted.

I'd be more interested to know whether there's a practical use of understanding it on this level. I wanted to learn about monads and wrote some smaller Java examples using streams and flatmap. You can see the benefit and understand how it's implemented very easily. However, the academic explanations and notations were not helpful and I'd argue made understanding the concept needlessly complicated.

I'm slowly developing a systematic framework for programming the human brain with foundations in category theory. I've gotten a lot of useful mileage out of what little I've learned about category theory. It contributes to my intuition about how to reprogram my brain. I'm convinced we'll be teaching it to children in the future, once the programming framework is better developed and understood. What could be more pra…

I'm curious to hear of a few examples of how you're doing that.

Would you mind sharing?

Re: A monoid is a category, a category is a monad, a monad is a monoid

#55

Post by zengid »

tikhonj wrote: post #12
casion wrote: post #2

Are there really that many people on NH that can understand this? I'm not trying to be snarky, I'm legitimately interested. It seems like this class of knowledge is highly specialized, yet I see posts like these high up on NH frequently.

I work at Target and we have a weekly class on algebra, category theory and Haskell because people are interested. It's a mix of programmers learning some of the math and mathematicians learning some of the programming :). It's actually a lot more accessible than it seems at first—these ideas are not complex , just abstract. Thinking at a high level of abstraction is very much a skill which requires specific training…

Is this at the HQ in Minneapolis? I hope to move back to MN someday (to raise the younglings) and you make Target sound awesome!

Re: A monoid is a category, a category is a monad, a monad is a monoid

#56

Post by maxiepoo »

Waterluvian wrote: post #38
casion wrote: post #2

Are there really that many people on NH that can understand this? I'm not trying to be snarky, I'm legitimately interested. It seems like this class of knowledge is highly specialized, yet I see posts like these high up on NH frequently.

I love pure programming. But the thing that makes me hesitant to try to learn something like Haskell is that it feels like I need a math degree to understand the concepts and terms. For a while I thought I was just not that smart. But I realise that all these things are just kind of really complicated.

Just a note, this post has nothing to do with Haskell.

Re: A monoid is a category, a category is a monad, a monad is a monoid

#57

Post by rocqua »

irfansharif wrote: post #50
jingwen wrote: post #8

For anyone interested to start on this subject, Philip Wadler's Category Theory for the Working Hacker [1] is an excellent introductory lecture for building an intuition. [1] https://www.youtube.com/watch?v=V10hzjgoklA

just to note this talk briefly alludes to another subject, the Curry–Howard isomorphism, something Philip Wadler had similarly given a talk about at Lambda Days (2016) titled 'Propositions as Types'[1] (slides [2] and the video recording[3]). [1]: http://www.lambdadays.org/lambdadays2016/philip-wadler [2]: http://www.lambdadays.org/static/upload/media/14562260715188... [3]: https://youtu.be/aeRVdYN6fE8

That youtube lecture was really interesting.

The very ending was awesome as well!

Re: A monoid is a category, a category is a monad, a monad is a monoid

#58

Post by rpcspillover »

crawfordcomeaux wrote: post #23

In most of the category theory posts on HN I've seen, there's at least one person asking ahead this stuff is useful for. This comment is about why I find it useful. Why I learn this stuff: to more effectively change things about myself. Category Theory is an abstract math of relationships. I use it to better understand how my mind and body work. How parts of me are related in the moment and/or across time. Understand…

could you elaborate on the energy orgasms? I realize you've edited that part out but it was the most interesting for me personally because I had similar experiences after I learned Idris and understood the Curry-Howard isomorphism.

Re: A monoid is a category, a category is a monad, a monad is a monoid

#59

Post by crawfordcomeaux »

rpcspillover wrote: post #58
crawfordcomeaux wrote: post #23

In most of the category theory posts on HN I've seen, there's at least one person asking ahead this stuff is useful for. This comment is about why I find it useful. Why I learn this stuff: to more effectively change things about myself. Category Theory is an abstract math of relationships. I use it to better understand how my mind and body work. How parts of me are related in the moment and/or across time. Understand…

could you elaborate on the energy orgasms? I realize you've edited that part out but it was the most interesting for me personally because I had similar experiences after I learned Idris and understood the Curry-Howard isomorphism.

I took it out cause it seemed egregious, but since you're somewhat familiar with the topic, here's a little more to build on:

Imagine yourself as a bounded poset if you don't make much money or a bounded proset if you do. By definition, you have both initial and terminal objects, called "bottom" & "top," respectively. For many, this concept may be tricky, as people's heads and asses are often indistinguishable. They're zero objects, so let's not worry about them. Also, don't confuse prosets with brosets (bounded prosets where all tops are fully faithful phalluses, ie. dickheads), as brosets do not preserve meaningful structure. Brosets use the "No homo" identity functor to demonstrate this property ("homo" being the notation for "homomorphism").

But I digress...

Identify a path from your bottom to your top. Apply the pullback of energy from the environment to yourself through your bottom and then use the pushout to the next object in the path. Make sure each object is an Abelian category or this won't work, BTW. It helps to sync the movement of your hips with your breathing, also. Same goes for hand gestures. When the energy reaches your top, tighten all of your muscles and hold your breath for the final pushout.

I find it helpful to visualize/fantasize a well-defined coeffects system for Idris.

(If your comment was serious, Google "energy orgasms" for way more than I can ever explain...I haven't really dug into it yet)

Re: A monoid is a category, a category is a monad, a monad is a monoid

#60

Post by crawfordcomeaux »

bshimmin wrote: post #53
crawfordcomeaux wrote: post #45

Earlier quoted context omitted.

Standard advice to learning a set of new personality traits: pick one each morning to choose to embody for the day & focus on it. How I do it: associate the set of traits with an identity somewhat separate from my own. She's essentially a clone of my personality, except she identifies as a woman & embodies the following personality traits: gentleness, patience, valuing relationships based on emotional support availab…

Thank you for taking my mean-spirited response in good part (I upvoted your initial comment because it entertained me - though you've since edited out the best bit! - and I'm upvoting your reply because it was interesting and delivered with gentleness and humility). I'm far too much of a troglodyte to understand any of this stuff, but good on you for you trying to improve yourself (if that is indeed the intended goal…

What I'm doing with my life is both serious and entertaining. I laugh at myself all the time because some of the things I do are genuinely hilarious!

I stopped showering for 4 days after initial success with trying to see a stick figure that moves with my body on the back of my closed eyelids.

The persistent thought haunting me?

"What if it's all in my head?"

Fucking with your mind fucks with your mind, typically in very funny ways.

As for not being able to understand any of this stuff, perception is key to learning. Perhaps practice choosing to believe things? Start with small, easy to believe things that are inconsequential to your life, but still meaningful. An example would be temporarily choosing to believe an opposing political stance has merit and then seeking the merit. Everyone has a reason for believing what they do, so go find perfectly valid reasons to believe something crazy. It'll get easier to do the more you practice.

If you want a simpler practice, go "look at the space between branches" and enjoy the different spaces you find. The skill progression comes from loosening your definition of the words in that phrase. Here's a starting point: go from finding 2D shapes to 3D ones.

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