4 ms·

Why would you need numbers for right angles? You need a straight line and a string. But I agree with the second paragraph: there's a huge difference between a

by usrusr 3y ago

Why would you need numbers for right angles? You need a straight line and a string. But I agree with the second paragraph: there's a huge difference between a procedure that is handed down as part of "this is how we estimate a building project" and a theorem that is declared universal truth and base for all kinds of other theorems. Even if they are exactly the same thing.

detourdog 3y ago
How useful are universal truths compared to getting shit done? I only see theorems as useful for complex societies. The son of a gem dealer would have the time to work out universal truths. The reputation of everyone doing it without numbers would reveal the pattern of the universal truth. Finally this looks like it was all done using cuneiform. Which brings up questions of notation and the language to describe a square root.
- usrusr 3y ago
  Getting shit done is the antithesis of progress because it goes hand in hand with "if it was good enough for my father, it will be good enough for me, who are you to disrespect (the methods of) my father!"
  - detourdog 3y ago
    I agree but dying for ideals isn’t much progress. Progress is a luxurious goal.
- empath-nirvana 3y ago
  What everyone is talking past here is that the Babylonians discovered what engineers call a "rule of thumb", and engineering is focused on getting things done using rules of thumb. The best possible rule of thumb is a mathematical proof or a scientific discovery, but it's by no means necessary. . Observing that something always holds and even having a formula for it is not the same thing as having a proof, and the proof is what makes it mathematics and geometry and not "just" engineering. The babylonians had a rule of thumb -- the greeks discovered the theorem -- and more than that, they seem to have invented the mathematical/geometrical proof as a concept, along with formal logic. Without that mental framework, it's hard to say that the babylonians proved anything or had any theorems at all, only collections of rules of thumb. It's quite likely that lots of babylonians sort of independently and intuitively understood _why_ it must be true, but they don't seem to have ever written it down. Not that there's anything wrong with having rules of thumb -- it's a huge achievement to even notice and collect and teach those things, all the stuff around you is built relying on them. I encourage everyone to watch this series of videos. https://www.youtube.com/watch?v=_ivqWN4L3zU https://www.youtube.com/watch?v=_ivqWN4L3zU
  - detourdog 3y ago
    I think what you might be touching on is that the "rules of thumb" may have been so integral of the culture as to be hidden.
- ordu 3y ago
  > How useful are universal truths compared to getting shit done? As I understand Greeks invented proofs because "universal thruths" they exported from Babylon and Egypt sometimes explicitly contradicted each other. I believe such contradictions may be a great nuisance when you try to get shit done. Egypt and Babylon were sufficiently "complex" societies for proofs, but their tradition treated mathematics as a bunch of useful facts about numbers and shapes. New generation just memorized them. We should think it worked for them in most cases, and when it didn't work it was not so often for them to start thinking a lot of reforming mathematics. Plus they were indoctrinated by the math they learned (authority of a teacher is above of anything else, i suppose) and to reform math was not a natural idea for them.
andrewflnr 3y ago
I've personally worked on a project where we used a 3-4-5 right triangle to lay it out on the ground. Straight lines alone do not get you right angles.
- rcxdude 3y ago
  You can get right angles with a straightedge and compass, both of which you can make on a construction site with string and pegs in the ground. It's just an instance of bisecting the angle. Which is more convenient in practice is situational.
  - KMag 3y ago
    Right. The big problem with accurately bisecting a 180 degree angle is you need to have access to points rather far in both directions from both points. If you want an accurate right-angle corner near the edge of a property that's flanked on two sides by fences, rivers, busy roads, etc., then you might not have convenient access to one of the anchor points needed to perform your bisection. (Or semi trucks snagging your rope might be inconvenient.) The nice thing about Pythagorean triples for drawing out foundations is that you don't need access to any ground outside the foundation of your building. Being integers, you also don't need any measuring device apart from some rope. You just pace out a bit under 1/3 of the shortest side (or a bit under 1/5 the longest side, whichever is shorter) (call this an "'bout-right") length of rope. You then use your 'bout-right to make a 3'bout-right, a 4'bout-right, and a 5'bout-right piece of rope. Pull the three ropes tight in your perimeter, and you've got your right-angle for your foundation.
  - andrewflnr 3y ago
    Fair, I didn't realize they were using the string as a compass.
- mauvehaus 3y ago
  You can certainly get close enough with straight lines. If you create a parallelogram, you can get it square by making the diagonals the same length. And if you can determine that the diagonals are the same length, you have what you need to get close enough to a parallelogram in the first place.

by usrusr 3y ago

detourdog 3y ago

How useful are universal truths compared to getting shit done? I only see theorems as useful for complex societies. The son of a gem dealer would have the time to work out universal truths. The reputation of everyone doing it without numbers would reveal the pattern of the universal truth. Finally this looks like it was all done using cuneiform. Which brings up questions of notation and the language to describe a square root.

usrusr 3y ago
Getting shit done is the antithesis of progress because it goes hand in hand with "if it was good enough for my father, it will be good enough for me, who are you to disrespect (the methods of) my father!"
- detourdog 3y ago
  I agree but dying for ideals isn’t much progress. Progress is a luxurious goal.
empath-nirvana 3y ago
What everyone is talking past here is that the Babylonians discovered what engineers call a "rule of thumb", and engineering is focused on getting things done using rules of thumb. The best possible rule of thumb is a mathematical proof or a scientific discovery, but it's by no means necessary. . Observing that something always holds and even having a formula for it is not the same thing as having a proof, and the proof is what makes it mathematics and geometry and not "just" engineering. The babylonians had a rule of thumb -- the greeks discovered the theorem -- and more than that, they seem to have invented the mathematical/geometrical proof as a concept, along with formal logic. Without that mental framework, it's hard to say that the babylonians proved anything or had any theorems at all, only collections of rules of thumb. It's quite likely that lots of babylonians sort of independently and intuitively understood _why_ it must be true, but they don't seem to have ever written it down. Not that there's anything wrong with having rules of thumb -- it's a huge achievement to even notice and collect and teach those things, all the stuff around you is built relying on them. I encourage everyone to watch this series of videos. https://www.youtube.com/watch?v=_ivqWN4L3zU https://www.youtube.com/watch?v=_ivqWN4L3zU
- detourdog 3y ago
  I think what you might be touching on is that the "rules of thumb" may have been so integral of the culture as to be hidden.
ordu 3y ago
> How useful are universal truths compared to getting shit done? As I understand Greeks invented proofs because "universal thruths" they exported from Babylon and Egypt sometimes explicitly contradicted each other. I believe such contradictions may be a great nuisance when you try to get shit done. Egypt and Babylon were sufficiently "complex" societies for proofs, but their tradition treated mathematics as a bunch of useful facts about numbers and shapes. New generation just memorized them. We should think it worked for them in most cases, and when it didn't work it was not so often for them to start thinking a lot of reforming mathematics. Plus they were indoctrinated by the math they learned (authority of a teacher is above of anything else, i suppose) and to reform math was not a natural idea for them.

andrewflnr 3y ago

I've personally worked on a project where we used a 3-4-5 right triangle to lay it out on the ground. Straight lines alone do not get you right angles.

rcxdude 3y ago
You can get right angles with a straightedge and compass, both of which you can make on a construction site with string and pegs in the ground. It's just an instance of bisecting the angle. Which is more convenient in practice is situational.
- KMag 3y ago
  Right. The big problem with accurately bisecting a 180 degree angle is you need to have access to points rather far in both directions from both points. If you want an accurate right-angle corner near the edge of a property that's flanked on two sides by fences, rivers, busy roads, etc., then you might not have convenient access to one of the anchor points needed to perform your bisection. (Or semi trucks snagging your rope might be inconvenient.) The nice thing about Pythagorean triples for drawing out foundations is that you don't need access to any ground outside the foundation of your building. Being integers, you also don't need any measuring device apart from some rope. You just pace out a bit under 1/3 of the shortest side (or a bit under 1/5 the longest side, whichever is shorter) (call this an "'bout-right") length of rope. You then use your 'bout-right to make a 3'bout-right, a 4'bout-right, and a 5'bout-right piece of rope. Pull the three ropes tight in your perimeter, and you've got your right-angle for your foundation.
- andrewflnr 3y ago
  Fair, I didn't realize they were using the string as a compass.
mauvehaus 3y ago
You can certainly get close enough with straight lines. If you create a parallelogram, you can get it square by making the diagonals the same length. And if you can determine that the diagonals are the same length, you have what you need to get close enough to a parallelogram in the first place.