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 Roman roads - how did they get them so straight?

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Meles meles
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PostSubject: Roman roads - how did they get them so straight?   Fri 24 Mar 2017, 11:23

A map of the Roman Britain shows that all the major towns and cities, sometimes hundreds of miles apart, were connected by a network of very direct/straight roads. Laying out the route for a straight path over a short distance can be done with taut string or for slightly longer distances by sighting along a line of poles. But clearly that is impossible for long distances across country where one cannot see from one end to the other. So how did the Romans survey the route for their roads to get them so straight/direct over long distances?



The only route of a Roman road with which I have some familiarity is Stane Street which runs from London to Chichester (Noviomagnus) on the South Coast. The road is only about 80 miles long but has to cross five lines of hills: the North and South Downs, and concentrically within them the North and South Greensand ridges of the Weald, and in the middle the central spine of the High Weald. Accordingly Stane Street does a couple of dog-legs firstly to take advantage of the gorge of the River Mole cutting through the North Downs adjacent to Box Hill at Mickelham, and then further south to use easy crossings of the River Arun in the vicinity of Pulborough and to follow a lower gradient route over the South Downs than would be needed by the direct route. But between these two fixed points and on towards the final destinations, the sections are remarkably straight, and overall the road is close to the direct line (nowhere is further than 6 miles from the direct line), despite being crossed by lines of hills and in the central portion, even now, being mostly covered in dense oak forest. In short you cannot get a clear line of sight for more than a few miles along the majority of the route. Stane Street is one of the shorter Roman roads in Britain and as I've said is actually sub-divided into three sections between the four fixed points (the ends and the two river gaps/crossings). The problems would be considerably more difficult over some of the longer distances elsewhere in Britain and throughout the Empire.

   

Without telescopic sights combined with a precisely graduated means to measure angles (ie basically a theodolite) the only way I can see to survey such long routes would be to raise tall markers every few miles, maybe less if you can put them on prominent hills, and then go back and forth along the whole line adjusting the position of these beacons  until each successive group of at least three were aligned, and so eventually the whole section would be straightened. But that's an awful lot of trial and error and still potentially prone to considerable error. Is that the way it was done or did they have some other method?


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PostSubject: Re: Roman roads - how did they get them so straight?   Fri 24 Mar 2017, 11:46

MM, you may be interested in this PDF document Roman Surveying which outlines the techniques used in grand engineering feats, including road location, that we can deduce from the scant records left by the lads themselves.

They were brilliant in both algebra and trigonometry, and both were used to amazingly great effect given that they were restricted to naked eye range when calculating projections of straight roads (and aqueducts which posed an even greater challenge as even slight deviations from the straight and narrow were horrendously expensive to incorporate into the design and structure). They didn't have calculus though - a legacy of their Euclidian mathematical principles inherited from the Greeks (who in turn had formulated them based on Egyptian practices).

The road they laid out from Rome to Terracina (90km) is still bloody impressive. It's part of the Appian Way and absolutely straight the entire run - most of it is still in use today, traversing hill and swampland along the way.

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PostSubject: Re: Roman roads - how did they get them so straight?   Fri 24 Mar 2017, 12:17

Adam Hart-Davies did a programme on this in "What the Romans did for Us" about a decade or so ago - https://www.youtube.com/watch?v=pUoSO5Rip7I - I have linked to the YouTube video of part I of the relevant programme about roads - the "how" bit is roughly at 4.00 mins in - might be a little before.
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PostSubject: Re: Roman roads - how did they get them so straight?   Fri 24 Mar 2017, 13:15

The Groma seems to have been the basic Roman surveying tool;

Groma






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PostSubject: Re: Roman roads - how did they get them so straight?   Fri 24 Mar 2017, 13:21

The Groma was an absolute must for working out right-angled intersections. Not much use however when plotting a straight road over rough terrain for miles on end. That's where the trigonometry kicked in, and lots of string. There's some debate about chains having been used - they definitely knew how to make them to a high standard - though just lugging them about in the quantities/lengths required would have probably meant they were impractical apart from during urban surveying - streets and alleys and the like. That's where you'd have seen a lot of Gromas too, I reckon.
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PostSubject: Re: Roman roads - how did they get them so straight?   Fri 24 Mar 2017, 13:32

Another link:

Roman Road Building

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PostSubject: Re: Roman roads - how did they get them so straight?   Fri 24 Mar 2017, 13:36

Thanks for all those links.

So yes I was basically right in thinking that it was essentially a method of 'trial and error' (although that expression rather fails to do justice to the sophistication of the technique) in that it required the intermediate markers to be adjusted back and forth until all were precisely aligned using the groma as a sighting device (and which, although simple and rather dismissed by Nordmann, would I'd have thought still be pretty good at getting alignment over a distance of a few miles). Like Adam Hart-Davis I'd rather thought that in practice it must have been done by stationing a surveyor at each intermediate marker to allow each subgroup of markers to be adjusted essentially simultaneously, and that of course means that there must have been a system for communicating between positions (ie "left, left, left ...stop ... right a bit ... stop. Mark!" etc), such as by semaphore, to communicate to the adjacent positions which might be a few miles away and so outside of vocal range. Interesting that Adam Hart-Davis says records suggest Roman surveyors could typically map out a mile of road every 3 to 4 days, which I reckon is pretty good going even when compared to a modern surveyor armed with a theodolite and GPS.

What I hadn't realised until I read Normann's link was that Romans also surveyed by creating a base grid and using angular measurements and trigonometry (which as Nordmann says is generally a more accurate method than just using linear alignment). I'd rather thought that this method only came into use sometime around the 16th century. But of course it really only needs a knowledge of Pythagoras, Euclidean triangular geometry and the ability to divide a circle into sufficiently small angular increments (Babylonian mathematics) all of which were well known to the Romans. And, now I think about it, accurate angular measurment must have been well understood by them as they routinely were able to build aquaducts running for many miles with a constant slight gradient.

I am however still intrigued how the Romans dealt with division. They could perform division by a method of proportions, but I feel they could only have expressed the results in terms of the summation of simple fractions (as I think the Greeks did), as, having no understanding of a floating decimal point, zero and place notation, they couldn't write decimals ... but that is another point entirely.


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PostSubject: Re: Roman roads - how did they get them so straight?   Fri 24 Mar 2017, 13:53

Division was a process of multiple subtraction of the divisor from the total having removed all the subtractives from the numeric expressions in use. This is necessary to ensure the comparative size is understood and the sum worth even starting. After that it's pure agony - especially with high values. Here's a good example from a tutorial:



There was evidence found on Crete, I remember, that caused great excitement when I was there in the 1980s as it seemed to indicate the Minoans understood zero and base ten calculation, and this even led to conjecture that this was so useful a knowledge that it could never have just disappeared, and therefore even the Romans had access through certain slaves to it - in fact it might even have been the arcane basis of certain religious cults throughout Greek and Roman times. One inscription found in Rome scratched by an architect on a stone foundation wall seems to employ Roman numerals along with other symbols in a calculation showing the radius and pitch of a vaulted dome ceiling. The calculation, if the other symbols are ascribed numeric values, still only makes sense in decimal. I'll see can I find it somewhere.
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PostSubject: Re: Roman roads - how did they get them so straight?   Fri 24 Mar 2017, 14:54

Yes doing division long-hand on paper using Roman numerals is very tedious ... but in practice I think most Roman calculations would have been done using a type of abacus or reckoning board. The typical Greek and Roman abacus had balls moving in grooves, or more simply could be just loose pebbles placed in grooves scratched in the dirt ... doesn't the word 'calculation' derive from calx, the Latin for a pebble?



But the problem with Roman numerals is how one expresses the answer ... ie how one writes it down or tries to communicate it to someone else.

For example, what's 562 divided by 84 (or DLXII divided by LXXXIV)? In decimal notation the answer is simply expressed as 6.7276

But using either an abacus or the above long division method you still end up with an answer of 6 with 61 remaining (ie 6 and 61 84ths). Intuitively that's somewhere between six and two-thirds, and, six and three-quarters ... and so it can be expressed as six and two-thirds and a bit. Alternatively, as Romans were used to using twelths, unciae, in weights, lengths and currency (hence ounce, inch and the uncia coin of the republican era), they might have preferred to express the answer in terms of twelths ... so somewhere between six and eight-twelths, and, six and nine-twelths, giving exactly the same answer as above but now expressed as six and eight-twelths and a bit.

To be completely accurate, if one is to express the remainder in terms of the summation of 'standard' fractions, one has to express the answer as six and one-third and one-quarter and one-seventh (and it's no easier to express even using the Babylonian base-60 number system).

That's a fairly easy calculation and the answer can be expressed accurately using simple fractions all of whose denominators are less than ten. But what about more complex calculations and those whose answers are irrational numbers (eg the hypoteneuse of a right-angled triangle whose other two sides are each one unit long, or the circumference of a circle measuring one unit across the diameter)?

But we are drifting a bit 'off road'.
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PostSubject: Re: Roman roads - how did they get them so straight?   Sat 25 Mar 2017, 10:50

@Meles meles wrote:
But the problem with Roman numerals is how one expresses the answer ... ie how one writes it down or tries to communicate it to someone else.

It's a good question, and the simple answer - especially with complicated fractions - is probably that they just didn't bother, at least using rudimentary notation. Geometry threw up the challenge repeatedly and mathematics wasn't always up to the task of expressing it. A lot of the "golden ratio"  stuff, for example, at least as it applied to building design and scaling up from rudimentary plans etc, was probably down to a need to avoid such complicated calculations, and one could even say - looking at the extant evidence - that Greek and Roman engineering (especially the Roman version) were prime examples of the KISS* principle in action.

But still you can't get away from the fact that along the way they developed a huge proficiency in theoretical projection when faced with massive engineering tasks which have - quite literally - stood the test of time. Stress distribution, material strength, "invisible structure" composition and design (such as foundations to roads and monumental buildings), and all the other aspects to these huge engineering undertakings, were obviously accurately calculated in their projection at the planning stage, and one must assume quite adequately expressed also to those involved in getting the thing done.

We are definitely missing something if, as with the Romans, we assume that everything we would quite reasonably insist should be expressed numerically today would have been necessarily expressed solely using their rudimentary numeric notations then. They must have used other means to compensate for the limitations of their standard notation system.

Mary Beard in one of her books referred to a grave inscription from Rome which went along the lines of "Josephus Bloggus, Master Builder. We didn't understand him, but we liked him". It could mean anything, I suppose, but I like to think it gives us a clue that these guys had developed an arcane language of mathematics unique to their profession. It's no accident, it seems, that "masons" took on the reputation for cultishness for millennia afterwards that they did.

*"Keep It Simple, Stupid!"
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PostSubject: Re: Roman roads - how did they get them so straight?   Sat 25 Mar 2017, 13:02

I was not by any means belittling the Romans for their inadequate maths, quite the contrary in fact, I stand in awe of what they (and other ancient peoples) achieved with the limitations of their number systems.

But actually I think your comment does correctly highlight the fact that "maths" isn’t just about numbers and calculations, and indeed that mathematical relations are so fundamental (I want to write true or pure but I fear that might be seen as a bit pretentious) that one can actually "do" maths in all sorts of different ways. Like a typical Roman carpenter, I mark out a metre long plank to be cut into 3 pieces by measuring 33cm "and a tad" (the fraction over isn't significant so there's no need to deal with irrational numbers), but if dividing a plank into two I rarely even measure it at all but rather just find the midpoint of balance.

I suspect that the Roman method of designing and constructing big civil engineering projects was much like the medieval mason’s approach when putting up a cathedral or similar large building, in that it was all done with scaling dividers and templates, with very little need to do any numerical calculations or write down any actual numbers.

For example medieval cathedrals are often typically 12 units long and 2 wide, with  the square tower (2x2) built above sections 7 and 8 which divides the total length into a nave 6 units long and an apse 4 units long. The relative dimensions  2:4:6:8:12 of course conform to Pythagoean philosophical ideas of "perfect" ratios, but more practically the whole floor plan requires no numerical measuring (it is independent of measuring system) and can be laid out using just string and pegs (even to get perfect right angles and a straight alignment). When it comes to doing medieval arches and even exquisitely beautiful and functional things like rib and fan vaults … again the whole lot can be sketched out on the design board using just a straight edge and a compass, then scaled up to full-size part drawings using scaling dividers, and finally these drawings used to create wooden templates to guide the masons in carving the individual blocks. Essentially one can build a cathedral, such as Chartres or York, without needing a graduated tape measure or doing any "sums" at all. The written records generally bear out the fact that the actual number crunching for such a project was usually limited to matters of how many carts were needed to move the required quantity of stone, and how much ale would be needed for the carters. Plus of course how much it would all cost!
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PostSubject: Re: Roman roads - how did they get them so straight?   Sat 25 Mar 2017, 15:45

@Meles meles wrote:
I was not by any means belittling the Romans for their inadequate maths

Me neither, but it does have to be said that their notation system, while perfectly adequate for accountancy purposes (99% of its use, most likely) was woefully inadequate when it came to philosophical conjecture - probably as pithy a summary of the difference between Roman and Greek values as any other that can be found. There is no Roman equivalent, for example, of that famous debate (which we believe raged for nearly a hundred years) regarding how many grains of sand would it take to fill the universe and which occupied the greatest Greek thinkers of the period. While it sounds rather stupid a thing to quibble about, for these guys it had almost as much to do with challenging existing methods of counting and measuring as any great desire to find a definitive answer.

The two most famous participants in the great debate were Apollonius of Perga and Archimedes. Both were hamstrung by the Greek numeric system - essentially the Roman one but with more succinct a use of alphabetic symbols and even with an occasional zero when things got really hairy and conjectural - so that they, like all who contributed to the debate, each felt obliged to come up with a practical way of extending the counting system so that absolutely huge amounts could be logically represented without using up all the papyrus in the world just to write one answer down.

A guy called Aristarchus got the ball rolling when he devised a shorthand method of writing large numbers by placing a value set combination, represented by existing symbols for lower ordinance values, over another - so that M (being the "myriad", or 10,000, which was one iota above the largest "useful" number) with "PKG" over it, for example, became 1,230,000. This introduction of "forms" which opened the door to astronomical values being expressible, was probably what kick-started the "sand in the universe" debate too, but what Aristarchus's system still could not solve was the problem of how to express the really really REALLY big stuff, the very stuff astronomical debate still challenges mathematicians to express cogently today.

Archimedes, we know now, hit on the best answer. However being Archimedes he kept it pretty much to himself and so fifty years later it was Apollonius who got the credit for combining the "forms" symbolism (hitherto a "times" value added to the base value below) with the "power" concept. Now the qualifier could be used to express "to the power of" and the liberation of numerics from purely sequential representation was complete.

You can see why they raved about Apollonius from this remnant we have of his work:



This uses the simple formula "10,000 = 10 to power of 4" as its basis for employing the symbols already familiar to everyone in a new way. Archimedes, struggling with an even greater total to express, quite independently developed a "100,000,000 = 10 to the power of 8" raised to powers as his basis for reinterpreting the existing symbols. It also allowed him therefore to say with no fear of contradiction that the number of grains of sand which could fit in the universe was 10 to the power of 64, or as he would have said "of the order of the eighth octet".

While all this sounds very theoretical and esoteric, it is still worth noting that the medieval cathedral builders you mention, who may indeed as you say have worked as much using visual and tactile escalation methods as mathematical modelling in their projections, could well have benefited from using Archimedes' methods of calculation and expression when projecting stress, weight and mass in their designs. Unfortunately - even with their superior arithmetical tools - they worked for an employer who still officially discouraged anyone from thinking in really high numbers, especially ones which might be used to quantify or get to grips with (and thereby remove the divine mystery from) the extent and nature of God's universe. The resulting catastrophic disasters, when they occurred, were instead used in a "trial and error" approach to future projects, elongating the whole process by centuries and ensuring the worshippers' fatalities themselves became mere integers in that process, a candid and telling admission of a value system which - at least as expressed through its mathematics - itself could be traced back to Roman roots and which ultimately elevates accountancy above all else. At least no one had to die working out the grains of sand thingy.
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PostSubject: Re: Roman roads - how did they get them so straight?   Sun 26 Mar 2017, 12:26

Back to the roads: MM, this short paper has a good stab at working out how the Romans overcame the limitations of their principal tool, the Groma, in extending its accuracy beyond its main function - surveying of camps, urban quarters, and similar enclosures: How did the Romans achieve straight roads? by Richard J. Hucker

He mentions the Dioptra, the true precursor of the theodolite, but is understandably vague about its precise use. Its application in aqueduct building is well understood, its usefulness in two plains having been documented by the Romans themselves. However the same logic used to deduce consistent height could also be used to calculate depth and this might have been crucial in the initial survey of a planned route when assessing hilly terrain and the materials required to traverse steep valleys. Using triangulation and with sufficient time to plan before actual construction the Dioptra could well have been the most important tool in calculating the longest possible distances traversable in absolutely straight lines and then staking them out. Once under construction the Groma would certainly have come into its own in keeping each new stretch in line with the one before.

In heavily wooded terrain the Dioptra also had a crucial function. The erection of a very high sighting pole over the treeline could be used through triangulation as an "absolute point" of reckoning not only for distance but also to ascertain the true topography of the concealed ground within its radius of sight. One needed a good grasp of geometry to work out gradient, true height and depth, so whoever used it must have been considered something of an elite amongst surveyors. Anyone with good eyesight and minumum training could operate a Groma, but the Dioptra techies must surely have commanded a high fee, especially if they succeeded in linking two Roman forts in an absolutely straight line - the main purpose of the bulk of road building in conquered territories. Being some of the first on the scene after conquest must have also placed them into the "danger money" category too in many instances.

The fact that so few illustrations of their mechanics during Roman times exist points to a deliberate policy of classifying their use as "secret" in a military intelligence sense. But it is reckoned they had come a long way from their original Greek astronomical measurement use and were probably as sophisticated as they would remain until superseded by the theodolite much later.

Someone's guess:
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PostSubject: Re: Roman roads - how did they get them so straight?   Sun 26 Mar 2017, 14:10

@Meles meles wrote:
Without telescopic sights combined with a precisely graduated means to measure angles (ie basically a theodolite) the only way I can see to survey such long routes would be to raise tall markers every few miles, maybe less if you can put them on prominent hills, and then go back and forth along the whole line adjusting the position of these beacons  until each successive group of at least three were aligned, and so eventually the whole section would be straightened. But that's an awful lot of trial and error and still potentially prone to considerable error.

Roman road building would indeed have been a case of trial and error in its initial phases. Only when the starting point and the ending point had been decided upon and then linked could any straightening have been attempted. The roads would literally have been works in progress for quite a while before finally being hardened – and even then there would have been subsequent fine tuning and maintenance.

Once the 2 ends of a stretch of road had been confirmed and linked to, however, it would have been relatively easy using polar and solar positioning to accurately straighten the road as is noted in the essays by Isaac Moreno Gallo and Richard J Hucker provided by nordmann. The Roman use of the gnomon (sundial) afforded them a very high degree of precision in terms of initial topographical surveying.

Several years ago I remember pondering this very issue after being almost blinded by the sunset one December afternoon while driving south-west on the A429 between Warwick and Cirencester. By chance on that particular day the sun seemed to be setting at exactly the point where that dead strait road met the horizon. Needless to say that the A429 follows a long section of Fosse Way the ancient Roman road between Lincoln and Exeter.
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PostSubject: Re: Roman roads - how did they get them so straight?   Sun 26 Mar 2017, 19:44

@LadyinRetirement wrote:
Adam Hart-Davies did a programme on this in "What the Romans did for Us" about a decade or so ago - https://www.youtube.com/watch?v=pUoSO5Rip7I    - I have linked to the YouTube video of part I of the relevant programme about roads - the "how" bit is roughly at 4.00 mins in - might be a little before.


Lady,

I watched it too in the time and wanted to reply it now, while I was on holiday this weekend, but you were the first:


Kind regards, Paul.
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PostSubject: Re: Roman roads - how did they get them so straight?   Sun 26 Mar 2017, 20:06

Great minds think alike obviously PR - couldn't possibly be fools seldom differing, could it.

When I was at primary school I remember one book about English grammar (though they didn't call it that at primary level) having a list of proverbs or sayings and "Great minds think alike" and "Fools seldom differ were placed one under the other.
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