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Used to walk to work, took 40 minutes, and with nothing else to occupy my mind I would think of some math problem and see what I could do. I remember cutting i

Used to walk to work, took 40 minutes, and with nothing else to occupy my mind I would think of some math problem and see what I could do. I remember cutting into the library one time when almost at work to see if my solution was the same as the classical one. It wasn't! I knew then the joy of discovery. Of course I wasn't the first to think of it but that didn't matter, the joy is the same.

JadeNB 4y ago
> Of course I wasn't the first to think of it but that didn't matter, the joy is the same. Thank you for emphasising this key point! There's pleasure and there can be prestige in being the first to solve a mathematical problem, but there's joy and accomplishment just in solving the problem yourself, even if your approach is exactly the classical one. I am a rock climber as well as a mathematician, and I compare it to that: the first person to summit a route will get the big-name recognition, but it's still worth it for me to come along and summit myself later, even if I use exactly the same sequence as tens of people who have gone before me.
glorioushubris 4y ago
>Of course I wasn't the first to think of it but that didn't matter, the joy is the same. Exactly right. When I was in undergrad physics, I signed up for the intro comp-sci course (which is recommended back then but not yet required). First we learned the basic syntax of C, and in the second unit we learned about sorting algorithms. The Prof introduced us to bubble sort, selection sort, and insertion sort, and also the idea that the efficiency of a sorting algorithm was proportional to how many comparisons it required. Being a physics student, I knew that there were physical process, like driven granular systems, that sorted objects by size without mathematically comparing anything at all. I wondered if I could beat the efficiency of all three of the algorithms by programming the computer to do something similar, treating integers like differently-sized grains of sand. Over the weekend I first coded an algorithm I called jostle sort that sent the unsorted integers flying across a 2D array a distance equal to their magnitude, then picked them up again from left to right, top to bottom. This worked, but slowly because it had to look at every cell of the 2D array. Thinking about it further, I imagined tipping the 2D array up from the bottom edge, so that all the integers in a column slid into a pile in the top row. I realized I only needed the count of how many integers ended up in each column, not the columns themselves. I could just initialize a 1D array of zeroes the size of the max value to be sorted, and increment the value in index n whenever I encountered n in the unsorted array. This worked really well, easily beating the other three algorithms in the criteria we'd been asked to test on our homework assignment. I'd invented counting sort. I would later learn that I wasn't the first, but that didn't lessen my pleasure. It's still my favorite sorting algorithm, because of that joy of discovery.

JadeNB 4y ago

> Of course I wasn't the first to think of it but that didn't matter, the joy is the same. Thank you for emphasising this key point! There's pleasure and there can be prestige in being the first to solve a mathematical problem, but there's joy and accomplishment just in solving the problem yourself, even if your approach is exactly the classical one. I am a rock climber as well as a mathematician, and I compare it to that: the first person to summit a route will get the big-name recognition, but it's still worth it for me to come along and summit myself later, even if I use exactly the same sequence as tens of people who have gone before me.

glorioushubris 4y ago

>Of course I wasn't the first to think of it but that didn't matter, the joy is the same. Exactly right. When I was in undergrad physics, I signed up for the intro comp-sci course (which is recommended back then but not yet required). First we learned the basic syntax of C, and in the second unit we learned about sorting algorithms. The Prof introduced us to bubble sort, selection sort, and insertion sort, and also the idea that the efficiency of a sorting algorithm was proportional to how many comparisons it required. Being a physics student, I knew that there were physical process, like driven granular systems, that sorted objects by size without mathematically comparing anything at all. I wondered if I could beat the efficiency of all three of the algorithms by programming the computer to do something similar, treating integers like differently-sized grains of sand. Over the weekend I first coded an algorithm I called jostle sort that sent the unsorted integers flying across a 2D array a distance equal to their magnitude, then picked them up again from left to right, top to bottom. This worked, but slowly because it had to look at every cell of the 2D array. Thinking about it further, I imagined tipping the 2D array up from the bottom edge, so that all the integers in a column slid into a pile in the top row. I realized I only needed the count of how many integers ended up in each column, not the columns themselves. I could just initialize a 1D array of zeroes the size of the max value to be sorted, and increment the value in index n whenever I encountered n in the unsorted array. This worked really well, easily beating the other three algorithms in the criteria we'd been asked to test on our homework assignment. I'd invented counting sort. I would later learn that I wasn't the first, but that didn't lessen my pleasure. It's still my favorite sorting algorithm, because of that joy of discovery.