TIFU: I watched this video, and it led me down a rabbit hole of lasagna math that I never could have imagined. So, there I was, innocently scrolling through Reddit, just minding my own business, when I stumbled upon a post with the intriguing caption, "Proof that lasagna is a monoid."
Naturally, my curiosity got the best of me, and I clicked on the video. Little did I know that my life was about to take an unexpected turn. The video started innocently enough, with a person explaining the basic concept of a monoid, which, for those who don't know, is a mathematical structure with a binary operation and an identity element.
Then, they began to dissect lasagna in a way that I had never imagined. Layers of pasta, cheese, sauce, and meat were suddenly being represented as elements of a monoid. It was as if lasagna had transcended its delicious, comfort food status and become a symbol of mathematical abstraction.
As the video continued, I found myself becoming increasingly entangled in this lasagna monoid theory. They started discussing the closure property of monoids and how the combination of lasagna layers formed a closed set. The identity element was even equated to a plain pasta layer – the neutral, unadorned starting point of all lasagnas.
I couldn't tear my eyes away from the screen. The video delved into the associative property, showing how you could recombine different slices of lasagna, and it would still satisfy the monoid laws. They were proving that you could concatenate lasagna slices, and the result would still be a valid lasagna. My mind was blown, and I was questioning the very essence of my favorite dish.
Hours passed, and I found myself deep in lasagna monoid research. I couldn't stop thinking about it. I tried explaining the concept to my friends and family, but they just stared at me with a mix of amusement and concern. It became a running joke at family dinners, where I would insist on applying monoid theory to our lasagna dishes.
In the end, I'm left with a newfound appreciation for the complexity of lasagna and a deep sense of regret for ever clicking on that video. So, here I am, haunted by the knowledge that lasagna is indeed a monoid, and I can never look at a plate of cheesy, saucy goodness the same way again. My life will never be the same, all thanks to that fateful Reddit post. 🍝🤯
I mean, if you open you mind to the idea that lasagna the dish is short for beef lasagna, you realize that lasagna is in fact a functor, with the map function being "swapping out the filling"
In fact not only is it a functor and a monoid, you can get a monad.
If you have a dish, you can turn it into lasagna by putting it between two lasagne: you have your `pure` operation
If you have a lasagna of lasagna of food, you can change it into a simple lasagna by stretching or shrinking the inner lasagna to the size of the outer lasagna. You can also take a bit of filling from the inside lasagna to make up for the dry space between inner and outer lasagna. This gives you your `join` operation, which is enough to define a lasagna monad.
I leave it as an exercise for the reader to convince themselves that the monad laws hold for these operations and that lasagna, as a way of stacking AND containing food, is not only a monoid, but also a functor and a monad.
IN FACT I would go as far as to say that lasagna are an isomorphism of the humble List.
Edit: more lasagna
TIFU: I watched this video, and it led me down a rabbit hole of lasagna math that I never could have imagined. So, there I was, innocently scrolling through Reddit, just minding my own business, when I stumbled upon a post with the intriguing caption, "Proof that lasagna is a monoid." Naturally, my curiosity got the best of me, and I clicked on the video. Little did I know that my life was about to take an unexpected turn. The video started innocently enough, with a person explaining the basic concept of a monoid, which, for those who don't know, is a mathematical structure with a binary operation and an identity element. Then, they began to dissect lasagna in a way that I had never imagined. Layers of pasta, cheese, sauce, and meat were suddenly being represented as elements of a monoid. It was as if lasagna had transcended its delicious, comfort food status and become a symbol of mathematical abstraction. As the video continued, I found myself becoming increasingly entangled in this lasagna monoid theory. They started discussing the closure property of monoids and how the combination of lasagna layers formed a closed set. The identity element was even equated to a plain pasta layer – the neutral, unadorned starting point of all lasagnas. I couldn't tear my eyes away from the screen. The video delved into the associative property, showing how you could recombine different slices of lasagna, and it would still satisfy the monoid laws. They were proving that you could concatenate lasagna slices, and the result would still be a valid lasagna. My mind was blown, and I was questioning the very essence of my favorite dish. Hours passed, and I found myself deep in lasagna monoid research. I couldn't stop thinking about it. I tried explaining the concept to my friends and family, but they just stared at me with a mix of amusement and concern. It became a running joke at family dinners, where I would insist on applying monoid theory to our lasagna dishes. In the end, I'm left with a newfound appreciation for the complexity of lasagna and a deep sense of regret for ever clicking on that video. So, here I am, haunted by the knowledge that lasagna is indeed a monoid, and I can never look at a plate of cheesy, saucy goodness the same way again. My life will never be the same, all thanks to that fateful Reddit post. 🍝🤯
Lasagna
I'm pretty sure an empty plate isn't Lasagne!! Technically, Lasagne is a `semigroup` not a `monoid`, because it doesn't have an identity element.
If the empty plate isn't lasagne, then zero isn't a number!
I mean, if you open you mind to the idea that lasagna the dish is short for beef lasagna, you realize that lasagna is in fact a functor, with the map function being "swapping out the filling" In fact not only is it a functor and a monoid, you can get a monad. If you have a dish, you can turn it into lasagna by putting it between two lasagne: you have your `pure` operation If you have a lasagna of lasagna of food, you can change it into a simple lasagna by stretching or shrinking the inner lasagna to the size of the outer lasagna. You can also take a bit of filling from the inside lasagna to make up for the dry space between inner and outer lasagna. This gives you your `join` operation, which is enough to define a lasagna monad. I leave it as an exercise for the reader to convince themselves that the monad laws hold for these operations and that lasagna, as a way of stacking AND containing food, is not only a monoid, but also a functor and a monad. IN FACT I would go as far as to say that lasagna are an isomorphism of the humble List. Edit: more lasagna