I was watching "Alexander" on DVD the other day and noticed a quote... for got the exact quote but, as Alexander was entering Babylon he was impressed by the "architects and engineers" who built the city. I had to chuckle.
Romans probably had equivalents of architects who actually had "engineering sense". The term architect (one involved with art and science of buildings and built environment) is more appropriate than engineers for those in the Roman days but those involved in design of aqueducts and colosseum can also be considered engineers in todays terms.
For todays engineers, mathematics is definitely important, but more than that, knowledge of physics is a prerequisite. I believe one can be an engineer with mediocre math skills but equipped with exceptional physics skills. Legally though, you do not need either. You just need to pass the license exam which isn't too difficult with proper preparation.
In some cases, yes. But the question is ill-asked. Can you be a GOOD engineer without higher math skills? Probably not.
To a large degree, engineering today is based on using tools that insulate the engineer from the bulk of the math required to actually do the problem. Simulators, FEA, etc., all provide results without the user necessarily knowing or understanding what's going on under the hood. Thus, someone with minimal understanding of math can indeed run the programs and engineer solutions that are within the confines of the existing parameters or routines.
However, such as person will probably have a limited ability to know when the answer coming back is incorrect. Also, this person will likely be unable to do an engineering analysis that's not already canned and waiting for him.
One of the engineers at work is considered a hack, because he has not grasped using VHDL as it was intended, thus producing designs that are unsimulatable, untestable and undebuggable. He's an engineer, but we will NEVER use him do to a new design every again.
The Romans and Babylonians had excellent engineers, better than most today. Those structures took more than artistic sense, there were practical calculation of dimensions and load capacity that were done by the builders of the aquaducts and great monuments, not to mention figuring out the logistics and construction methods.
I don't think that buildings of the scale that the Romans, Greeks, Egyptians, etc., built are possible without some level of engineering.
Even though they might not have had the math, the designers had at least an intuitive visualization of the loads and how they were distributed. They had sufficient understanding of surveying to square up their buildings and aligned the edges to specific angles.
Do you think any of the roads built in the last 150 years or so will last 2000 years? The Romans built many.
Did you ever watch a road construction site where they were using a sheeps foot roller?
They are called sheeps foot rollers because the Romans compacted road base material by driving herds of sheep back and forth over the area.
The Roman roads were built to move the Army around quickly, increased trade and commerce was a secondary benifit.
Architects and builders of Gothic Cathedrals did not have much more math than the Romans. Yes, they had Arabic numbers and the zero, but not much advanced math. And, still, who would dare to build anything like a cathedral today? There was no prestressed concrete in those days. No gas or electric welding and no computers.
Just to add to zeitghost's comment - there is a tendency to assume a high level of engineering and architectural skill when looking at old cathedrals and other ancient structures. But we're only seeing the structures that have survived. These structures were designed and built empirically, without any underlying understanding of the basic physics or material characteristics. They learned by trial and error. Vast numbers of cathedrals collapsed during construction or shortly thereafter. Through trial and error, the builders developed rules of thumb for building proportions, materials, spans, etc, but they did not really understand the basic principles.
Just as wine and beer makers learned to make wonderful stuff without ever knowing about yeast or enzymes.
Gaudi designed his cathedral by hanging appropriate weights from an overhead framework. The threads that were used to suspend the weights gave the line of action of the forces, so should form the centre of each column.
It is not inconceivable that the Romans, or some Gothic cathedral masons, used a similar technique.
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
Step back in time a back a bit further: did the ancient Egyptians employ engineering techniques and principles to construct the pyramids? Or the Mayan people before them? I think they must have had some understanding of the materials they worked with and of how to go about assembling these vast structures. The designers of them must surely be the forefathers of todays civil engineers.
As for learning empirically, weren't the Tay Bridge, the Titanic, the Tacoma Narrows Bridge, the Comet airliner, and the space shuttle all designed by engineers? They all incorporated inherent weaknesses whose significance was not understood or fully appreciated at the time of design: learning through trial and error is still going on in modern times.
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One day my ship will come in.
But with my luck, I'll be at the airport!
Main Entry: 1en•gi•neer
Pronunciation: "en-j&-'nir
Function: noun
Etymology: alter. of earlier enginer, from Middle English, alteration of enginour, from Middle French engigneur, from Old French engignier to contrive, from engin
1 : a member of a military group devoted to engineering work
2 obsolete : a crafty schemer : PLOTTER
3 a : a designer or builder of engines b : a person who is trained in or follows as a profession a branch of engineering c : a person who carries through an enterprise by skillful or artful contrivance
4 : a person who runs or supervises an engine or an apparatus
Main Entry: en•gi•neer•ing
Function: noun
1 : the activities or function of an engineer
2 a : the application of science and mathematics by which the properties of matter and the sources of energy in nature are made useful to people b : the design and manufacture of complex products <software engineering>
3 : calculated manipulation or direction (as of behavior) <social engineering> -- compare GENETIC ENGINEERING
So did the Roman road and structure designers and constructors meet these definitions?
"the application of science and mathematics by which the properties of matter and the sources of energy in nature are made useful to people"
That does not seem an unreasonable definition.
It does not say that engineers have to understand analytically every last nuance of their design, all you have to do is use the available maths and science to make useful things.
So, rules of thumb and books of proportion (how ships were designed), represent the accepted practice at the time. By that standard, the Romans had engineers.
To take a later example, think about Brunelleschi's dome. He didn't know how to solve one part of the design, and as we have seen, he could not have analytically solved a beam equation, none the less, it is a /designed/ structure. It would be interesting for someone to reverse engineer it to find out how close to the mark the design was by modern standards.
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
i've always thought that scientists study things to understand how/why they are that way, and engineers apply science to make things.
like greg, i don't think engineers have to understand the basic physics in order to make things. tho' the better the understanding, the greater the likelihood of getting something usefull.
look at the development of the airplane. i'm pretty sure that the wright bros never understood (certainly not in a mathematical way) prandt's lift theoory; but they were able to make an airplane through experiment (and insight). look at all the failed airplane designs, and the free thinking going on, in the early days of aviation. everyone had ideas at the beginning, some were good, most weren't, but once the underlying science was understood better then the success ratio went up a lot.
can you be an engineer without math skills ... certainly if you've the insight as to how something's going to work, and the patience to develop your ideas though experiment. someone mentioned that today's mathematical tools isolate the users from their creations ... i would add isolate them from understanding the underlying fundamentals ... how often do we see people proficient at driving the software (designers CAD, analysts FEM) without really appreciating what's going on ?
This book is an excellent description of engineering from the ancient Egyptians, up to the Renaissance. Whether or not Imhotep qualifies as an engineer depends upon your standard. He knew as much or more about the subject than any of his contemporaries. He knew the value of PI to one digit, 3, and he did not know anything about calculus, which would not be worked out for another four and a half millenia.
I was under the impression that the Wright brothers advanced aeronautical engineering, at least in the practical sense. They did accurate calculations of lift and drag versus velocity. They recognized the importance of a high aspect ratio wing. You have to consider the possibility that the technology was at a low enough level that a couple of bicycle mechanics could improve it.
The part of De Camp's book that amused me was the revelation that artists and engineers were one and the same person in medieval Europe. After years of joking about artsies in college! It explains a lot about Leonardo Da Vinci.
Skim through some of the ancient literature, Vitruvius, Archimedes, Ptolemy, and you will quickly come to appreciate that the ancients excelled in both engineering and mathematics. Roman construction materials were manufactured to an Imperial standard. Construction methods reflected an understanding of physics.
The arithmetic used by the Egyptians, Greeks and Romans was derived from the Babylonian sexigesimal counting system. This system, in turn, derived from an ancient finger counting technique, and can still be recognized in applications which use 12,60,or 360 divisions of a whole. By the time of the Romans, finger counting techniques had reached the point where surprisingly complex mathematics could be worked out using "digital" techniques. The Romans also used a device called a counting table, similar in concept to an abacus, to extend the range and complexity of their calculations.
The concept of zero, one of the keys to modern mathematics, seems to have taken seed in many places and times. But it wasn't until the middle ages that it was generally accepted in Europe. Whether the Romans understood zero is a matter of some question.
Trigonometry was well advanced by Roman times, and was probably the "highest math" practiced by engineers. They were pretty good at using trig for surveying: water tunnels were dug from both ends, often extending many hundreds of feet underground, and meeting within a small margin of error. Newton was far in the future, as was calculus.
Good reading on this topic, as Drawoh pointed out, is L Sprague De Camp's book on ancient engineers. Also check out Vitruvius's "Ten Books on Architecture", and George Ifrah's books, "From One to Zero", "Universal History of Computing", and "Universal History of Numbers".
