Are you sure they did this arithmetically? Keep in mind that they were not using arabic numerals. Even today (and by today, I mean before calculators and computers were ubiquitous) engineers commonly used look-up tables instead of calculating everything from first principles.
I’m not sure of anything, actually. I just don’t understand how anything built by something other than trial and error doesn’t use some kind of mathematics; it seems like, by definition, whatever techniques used would qualify as “mathematics”.
Ah, as TriPolar suggests:
Well, a very small percentage of writings have survived or been discovered. The monks may have been inspired to preserve the elevated thoughts of philosophers rather than the mundane ones of engineers, if a bit a speculation may be allowed.
Yeah, the math was more likely to be geometry rather than arithmetic.
At roughly 44:30 into this video, the narrator explains an ingeneuous way in which stonemasons who built the parthenon translated templates into carved colums by using large compasses. I don’t know if mathematics was involved in other aspects of the building process, but I’ve watched other documentaries showing early Greek and Egyptian engineers using non-mathematical ways to construct buildings.
The main, if not only, surviving work on architecture from Roman times is Vitruvius’ De architectura. Probably because of that - and it’s also 10 volumes - it became extremely influential in the Renaissance. I’ve only seen excerpts from it, but it was heavily descriptive. I agree with John Mace that for the Romans geometry was essentially math.
For road building, this source says it was done with “Roman Military Engineers”, but fails to discuss their training.
“The building of Roman roads was often planned and undertaken by the Roman military engineers, particularly in terms of the outer reaches of the empire, starting with the roads in Gaul, built under the command of Agrippa between 16 and 13BC. The building work itself would be undertaken by the soldiers themselves or by captives and local workforce they might access. The materials employed were usually those which were most readily available, ie stone such as neatly shaped granite slabs was not always readily available!”
Ok, trial and error.
We all know that Archimedes was a rambling wreck from Syracuse and a hell of a (military) engineer, besides being perhaps the most brilliant mathematician of the ancient world. I’m not really familiar with his work, and I’m certainly not an engineer, but didn’t his work touch on some points that would be familiar to present-day engineers? If so, did any Roman builders and engineers have access to his work, or would they never have thought of themselves of it?
In the remote past, I asked at one point how Roman engineering worked so well generally, and was told that their basic approach was to over-engineer everything. Which, I take it, means simply concluding, “if we make the walls this thick, that oughta be strong enough to hold the roof up”, based on the experience of past projects.
More like “Well, I’m not sure if this thick will be enough. Let’s make it twice that thick, just to be sure.”.
Even engineers today throw in a fudge factor, just in case, because if you design something for just the load you expect it will bite you in the ass. It is said that John Roebling, designer of the Brooklyn Bridge, doubled the amount of cable because he assumed it wouldn’t meet spec. I find that interesting because it was his company that made the cable, but it gives away that he was a True Engineer, planning around an understanding that the nincompoops in the shop couldn’t read or follow a spec to save their lives and the cable would ship understrength anyway, damn their eyes. Which it did, but not understrength enough that the bridge is not still standing and could probably laugh off a small nuclear bomb.
I read a similar notion in a book about the Black Plague. I don’t remember the title, but I think any book about the BP would go into detail about it.
Basically, the nobility depended on serfs and their own body of servants to handle their administrative duties. When the BP struck, these people died, leaving the nobles without help.
The middle class actually started forming itself at this point. Some peasants were tradesmen and merchants in their own right, and offered their services to the nobility for pay. Up until that point, such a prospect of nobility actually giving peasants money for services was unheard of. But, the nobles found themselves without options, so they capitulated.
Thus, the more enterprising commoners saw their fortunes and society status climb, leading to the establishment of guilds and creation of a middle class.
I don’t recall the details, but a factor 2:1 is used now where there has been limited testing of the materials used. This happens a lot with modern composite materials. If you want to build something using a unique layering of carbon fiber and matrix then you either need extensive testing on the physical characteristics of the material, or you use limited testing and double the number you get as a result. So if you find tensile strength of a material through a limited number of tests is 100 psi, your design has to assume it will fail at 50psi.
My experience is in elevators, where everything was designed for a weight rating twice that engraved on the control panel. Y’see, folks lie about their weight and it’s impolite to be obvious when you estimate the total weight of the passengers. And if an exotically beautiful woman tells you, “Room for one more, honey,” take the next car. Even if she does look like Spock’s slutty fiancee and you think you have a chance because if she fell for Stonn she will sleep with anybody.
Because CBS lets you watch this important safety documentary for free, and everybody should see it, here it is: http://www.cbs.com/shows/the_twilight_zone/video/622081103/twenty-two
Interesting points. To what extent did the Romans have formal vocational and/or educational qualifications? Iirc the concept of a university with bachelor’s degrees, master’s degrees, etc. didn’t really exist until the Middle Ages (and was based on trade guilds anyway), so I wouldn’t expect that. Did they have any qualifications you could get or was it pretty much connections (who you knew, networking, etc.), and job interviews with practical demonstrations? E.g. could you get a certificate rating you as “EDVCATVS MAXIMVS” or “MAGISTER TECHNOLOGIVS”?
IN so far as I can recall, no, they did not have any specific kind of certifications for any field. For the Roman, the test of whether you were any good at something was whether you succeeded. However, they were quite capable of suing the togas* off people who screwed up. I’m not sure if there are records of people demanding repayment from bad architects, but it wouldn’t surprise me.
*Yes, I know most people didn’t actually wear togas, but I thought it was funny.
Roebling only got the contract after a cable broke and killed and injured a number of workers. Before that contractors were supplying the cable. They were quickly replacing the certified cable with rejected spools of cable after it left the inspector’s area.
If you have Netflix, the BBC documentary Seven Wonders of the Industrial World has an excellent episode on the construction of it. It discusses this issue.
The Attorney General of Babylon worked that out a millenium before Rome.
Humans are not alone in using tools or speech, but we probably invented lawsuits while still in the caves.
They had law schools, and after the first century, a regulated legal profession that required certification to practice in various areas.
As regards engineering: We have several engineering manuals, and several others are mentioned, so at least to some extent, Roman engineers probably started with “book learning”.
For a lot of the grander projects, the Romans seemed to turn to Greek architects. We know several Greek architects were educated at the Musaeum at Alexandria, so that probably functioned as an architectural school, and it seems likely there might’ve been less famous schools elsewhere that used the same model.
A lot of the less grand, more functional construction projects were done by the military. The military had a bunch of job titles for various specialized engineers, but I don’t think we have much information on how they learned their trade.
Indeed, I guess I had forgotten 'ole Hammurabi. However, being that the OP asked about Rome, I was trying to see if we had any known court cases involving Roman law. So far I haven’t found one, but I can’t say I have anything like a comprehensive list.
Are you certain about that? From my sources it looks like that was more a late-era development.
There must be some somewhere. Lawyers dearly love their precedents, and I can fully imagine Rumpole pulling out an ancient book of case law to save some petty thief from jail. Er, gaol. I’ll look for some tomorrow, if I don’t get caught up watching Rumpole episodes on YouTube.
Wife had a class in which they read records from a Pharaonic (Ptolemaic? Doesn’t matter; regimes change but the bureaucracy lives on.) Egyptian night court. The usual things–mostly drunk and disorderly and not paying a legal prostitute–and the BC equivalent of “fifty bucks and time served” for the punishments. Daughter is jealous because night courts seem to be a thing of the past and she had to sit in Cook County until morning.