Engineering rule

Any idiot can build a bridge that stands. It takes an engineer to design a bridge that barely stands.

Tbh, I want my memes with sources. and this one is strange...
https://civilizationchronicles.com/roman-engineering-and-mathematics/ claims that mathmatics were essensial to roman engineering.
whereas this (only abstract avaliable...) https://link.springer.com/chapter/10.1007/978-3-662-66494-0_25 claim that mathmatics were but an auxillary science? 🤔
nontheless mathmatics seems to have been quite understood and used by the roman engineers building among other things, aqueducts
- The joke is that calculus as a field of mathematics didn't exist until millennia after the fall of the empire
  
  Astrology was so important to the Greeks, they figured out the elliptical orbits of the planets (up to Jupiter) and how to compute them without calculus.
- Calculus is a specific field of mathematics, mostly to do with limits, integrals and derivatives. Those all feature very heavily in working out loads and stresses.
  But it's unfair to say the Roman didn't have calculus. It wasn't formal calculus, but they absolutely had mathematics, and the Greeks worked out the exhaustion method a century before the Via Appia was even started.
  You don't need calculus to do some very impressive building, you can go very very far with experience, rules of thumb and basic maths. Hell, ask any civil engineer and they'll gladly show you some common formula that makes physicists cry.
  
  Put simply, you don't need to know of, or what a certain field of math is to be able to apply the different fundamentals of it.
  As an example. You ever see a basketball player bring out a chalkboard to calculate the trajectory, mass, spin, or force to throw the ball to get it in the basket? No. Over time they all eventually create a physics model in their heads and are able to subconsciously calculate all of that with relative accuracy based on experience, training, and practice. Yet, a lot of those players never took a lick of physics.
  
  Do you happen to know any civil engineers, I would like to see these formulas
- Calculus was invented in the late 1600s, almost 2000 years after the Roman aqueducts were built. The Roman engineer would know some geometry, but certainly not calculus.
  
  That calculus as a modern field wasn't established until the 1600's does not mean the Romans only had geometry. That's not how technology works. It doesn't fit neatly into containers defined by modern thought. They likely developed what they needed and thought nothing of calling it something else because their purpose for it was different. For example Calculus is often called the study of change, not something the Romans were super interested in. Unlike the Greeks who were figuring out astronomy math. If you want to see how far they were before things started falling apart you'd have to get a historian to tell you what they even considered the mathematical fields to be and look at how they used it.
- The engineer guy on YouTube did an episode the engineering method explaining how ancient and medieval Masons built stuff without math. https://youtu.be/_ivqWN4L3zU?si=2N_iyZiBD8eDpltR
  Though I am sure the Romans used plenty of math during the construction of many of their projects.
  
  and medieval Masons built stuff without math. https://youtu.be/_ivqWN4L3zU?si=2N_iyZiBD8eDpltR
  That video shows that all of those ancient engineers relied heavy on math. What do think math is, if not all of the engineering principles laid out in that video?
- Romans had a basic understanding of proportions and general vibes of design, but they couldn't really create calculations to verify their design as we do today. For instance, the designers of the Pantheon understood they needed to lighten the concrete as it went up and had novel techniques of doing so that we use today, but they didn't really know.
  The state of the art for understanding basic stresses didn't become known until the 19th century. The design of the Eiffel Tower was impressive, in part, because that structure has a calc book defending it. A lot of early railroad bridges were still designed based on ratios and vibes.
  That said, not all loads were understood by that time. The Tacoma-Narrows Bridge collapsed in part because of a gross misunderstanding of wind loads combined with the ability to design structures light enough that wind loads controlled.
- The mathematics mentioned in the first source have nothing to do with engineering though.
  Ratios, a little trigonometry and geometry, all of which are essentially under the geometry category and arithmetic are not what concerns the engineering field. They are architectural tools if you will. Of course they utilized geometry, that's not something innovative. Maths in general does not mean anything here, maths can be about number theory(completely unrelated to any practical application).
  What differentiates them and engineers now is essentially mechanics. Forces, torques, stresses, materials, masses, moments of inertias etc. They never applied quantitative engineering principles, their structures were only sound from experience and intuition, the geometry mentioned was for architectural purposes.

Oh yeah. The chad slavedriver vs the virgin computer guy. Tale as old as time
- Slavery is the most impressive form of engineering. Ever wonder how they built the pyramids?
  
  I'm begging people to actually educate themselves on how the pyramids were built. They were built by paid workers, but then later, the Greeks saw them and assumed they were built by slaves because that's what the Ancient Greek did with their building projects.
  
  Is it slave labour if they can choose to strike?