3 ms·

Geometry and the imagination – Laying train tracks

1 points by samwillis 3y ago

eternityforest 3y ago
This problem illustrates perfectly the difference between engineering, tech, and everything else, and where they overlap. Tech tends to holonomic control. It's easier to think about and more versatile and people like it. Real life is full of stuff where you can't move without turning or turn without moving or unscrew one thing without something else falling off or that pesky Pauli exclusion principle gets in your way. I would almost say that being aware of the fact that systems have degrees of freedom and inputs you control and they aren't always 1-1 matched is the start of truly doing tech. It's like such a sharp dividing line. Things you control, and things you don't, it seems more philosophically interesting than almost anything else in math. Right now people talk about climate change, but CO2 is just a case of energy output being tied to fuel burning. Functional programming is all about separation and making sure doing stuff doesn't make other stuff you don't control happen. And then on the other side, there's lots of things that seem to be culturally significantly partly because they're nonholonomic. A sports player's performance depends on a ton of variables from genetics to mental state to how good their trainers are and none of it is a direct thing in the way gcode directly controls the CNC. If wine was made in a replicator from some exact chemical description file, I'm guessing it would be a lot less interesting. Things that you can't control every part of seem to give a sense of being a unified whole. And then, there's occasionally times when less control makes things better functionally, because you want some states that would otherwise be physically possible to be impossible or locked out, like a microwave that can't run with the door open. And on top of all that there's overconstraint, where everything can just go straight to crap if you have more inputs than degrees of freedom. Furniture that cracks when humidity changes because different attachment points fight each other is a big deal... but maybe the "Too many chefs and not enough line cooks" social problem is also an example of that.

1 points by samwillis 3y ago

This problem illustrates perfectly the difference between engineering, tech, and everything else, and where they overlap. Tech tends to holonomic control. It's easier to think about and more versatile and people like it. Real life is full of stuff where you can't move without turning or turn without moving or unscrew one thing without something else falling off or that pesky Pauli exclusion principle gets in your way. I would almost say that being aware of the fact that systems have degrees of freedom and inputs you control and they aren't always 1-1 matched is the start of truly doing tech. It's like such a sharp dividing line. Things you control, and things you don't, it seems more philosophically interesting than almost anything else in math. Right now people talk about climate change, but CO2 is just a case of energy output being tied to fuel burning. Functional programming is all about separation and making sure doing stuff doesn't make other stuff you don't control happen. And then on the other side, there's lots of things that seem to be culturally significantly partly because they're nonholonomic. A sports player's performance depends on a ton of variables from genetics to mental state to how good their trainers are and none of it is a direct thing in the way gcode directly controls the CNC. If wine was made in a replicator from some exact chemical description file, I'm guessing it would be a lot less interesting. Things that you can't control every part of seem to give a sense of being a unified whole. And then, there's occasionally times when less control makes things better functionally, because you want some states that would otherwise be physically possible to be impossible or locked out, like a microwave that can't run with the door open. And on top of all that there's overconstraint, where everything can just go straight to crap if you have more inputs than degrees of freedom. Furniture that cracks when humidity changes because different attachment points fight each other is a big deal... but maybe the "Too many chefs and not enough line cooks" social problem is also an example of that.