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

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21–30 of 79 posts

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

#21

I've been studying Leibniz recently and I'm excited to get to his treatment of Monads. The following is a little irrelevant to this post, but the title of this post stirred a relationship. So to Leibniz, in the conception of an entity's identity, he posits that one must include all propositions related to that entity. So when we try to consider a property of an object of our mind, we are basically saying "it is what…

This is awesome! I am definitely going to read some Leibniz after this. Would you recommend his Monadology?

To say "only God can understand the future" is an unnecessary personification of our incompleteness. I think the future of declarative functions is pretty clear. Today foo(x) = 2x, tomorrow foo(x) = 2x. Anything we can't say is simply a dearth of information. How useful is it to say we've a dearth of "future information"?

Anyway, we give names to sets of propositions, and that's a neat trick.

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

#22

I've been studying Leibniz recently and I'm excited to get to his treatment of Monads. The following is a little irrelevant to this post, but the title of this post stirred a relationship. So to Leibniz, in the conception of an entity's identity, he posits that one must include all propositions related to that entity. So when we try to consider a property of an object of our mind, we are basically saying "it is what…

If god was all powerful, he could create a rock he himself could not lift.

If god was all knowing, he could create a cryptosystem he himself could not break.

God is a bad measure of physical properties. Some things are just unknown.

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

#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. Understanding how things in me are related is essential to me dealing with PTSD & recovering from addiction, both of which can color every aspect of a person. Untangling them is insanely hard and has gotten much easier through CT.

I apply my programming intuition to my brain & body through CT. There exists a path from neuroanatomy to theoretical computer science that passes through category theory. I've been experimenting on myself for 6 months with the goal of changing my mind and body. I've been doing it by developing an intuition for category theory, developing an intuition for how neutral networks learn, adapting machine learning models with concepts from neuroscience and psychology, and mixing it all with my intuition for programming.

So far, I've:

• changed how I walk through a handful of sessions lasting a few minutes and no longer experience back pain I'd been seeing a chiropractor (saw him weekly for 3-4 months with little improvement, ending about 10 months people changing my gait)

• began learning how to identify and stop believing anxious thoughts

• accidentally started developing the ability to focus and direct my attention (way beyond anything I've ever experienced on my ADHD meds)

• 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.

Here are some of the few bits supporting my claims about neuroanatomy and category theory:

https://www.researchgate.net/publication/280219255_Conciliat...

One of the coauthors wrote the only book on the brain and category theory:

http://tierra.aslab.upm.es/documents/PhD/PhD-JGomez.pdf

If you understand a good bit of CT and would like to help me flesh out my framework, my contact info is in my profile.

I live in the Seattle area and would love to meet up with anyone interested.

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

#24
post #21

I've been studying Leibniz recently and I'm excited to get to his treatment of Monads. The following is a little irrelevant to this post, but the title of this post stirred a relationship. So to Leibniz, in the conception of an entity's identity, he posits that one must include all propositions related to that entity. So when we try to consider a property of an object of our mind, we are basically saying "it is what…

This is awesome! I am definitely going to read some Leibniz after this. Would you recommend his Monadology? To say "only God can understand the future" is an unnecessary personification of our incompleteness. I think the future of declarative functions is pretty clear. Today foo(x) = 2x, tomorrow foo(x) = 2x. Anything we can't say is simply a dearth of information. How useful is it to say we've a dearth of "future in…

"an unnecessary personification of our incompleteness." Not unnecessary according to Leibniz. See e.g. https://en.wikipedia.org/wiki/Monadology

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

#25
post #11
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'd be surprised if there are more than a handful, but I often wonder the same thing about posts about systems programming and, well, basically anything that mentions Rust in the title. For my own part, I find this kind of post fairly easy to digest, but that's almost certainly because I'm a Mathematician by training (PhD in numerical differential geometry, but did a lot of abstract algebra as an undergraduate). To m…

I see. I'm coming from the other side. I do microcontroller and embedded development.

This post is basically Ancient Greek to me, as you put it.

I think I largely became curious since "these types of posts" tend to be highly ranked with relatively few comments, yet they still show up frequently.

I'm also surrounded by a large number of varying types of programmers and engineers, and I get to hear evangelizing and discussion of a wide array of technologies, but pure math type stuff like this never comes up. So combined that with the aforementioned observation and I become increasingly curious how these posts do well.

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

#26

I've been studying Leibniz recently and I'm excited to get to his treatment of Monads. The following is a little irrelevant to this post, but the title of this post stirred a relationship. So to Leibniz, in the conception of an entity's identity, he posits that one must include all propositions related to that entity. So when we try to consider a property of an object of our mind, we are basically saying "it is what…

If god was all powerful, he could create a rock he himself could not lift. If god was all knowing, he could create a cryptosystem he himself could not break. God is a bad measure of physical properties. Some things are just unknown.

I was expecting you to add: "Could Jesus microwave a burrito so hot that he himself could not eat it?"

https://youtu.be/JhhXCuUG2pw

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

#27

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…

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 wrong reasons (such as my own entertainment).

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

#28

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…

Fascinating, are you writing this up anywhere?

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

#29
post #4

Earlier quoted context omitted.

I only know this famous quote: http://stackoverflow.com/questions/3870088/a-monad-is-just-a... But I didn't really try to understand it.

It's hard to understand because it's utterly unenlightening. It's a restatement of the definition. It's like saying "the number two is just the sum of one and one." It's trivially true yet utterly fails as an explanation because it requires more concepts to convey the exact same content.

I would argue the concepts of monoid objects and the category of endofunctors on an object are simpler than that of monads, so this description does help. I come from a math background and had never seen this quote before, and I think it has given me a definition of (mathematical) monads that I can remember.

Haskell, unfortunately, is still quite opaque to me.

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

#30
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

This seems to presuppose a good deal of functional programming background.

Not a criticism, just a note to anyone thinking of spending an hour with it.

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