Non-zero technology?

Not a mathematician, so this may be a stupid question.:p

AIUI, some kinds of maths are impossible without the concept of zero. So, what kind of tech is possible for a society that never invents zero? Not ones that have no concept of "nothingness" (& I suspect there are those, too), just ones that don't actually have the numeral. (Ancient Rome, frex.)
 
A surprising amount, actually. You can get to roughly mid-nineteenth century tech flying by the seat of your pants. The problem is that you have to invent things differently because so many drivers of modern technology (modern accounting, statistics, demographics, engineering etc.) depend on maths being relatively easy to implement. There is only so much that geometry and fractions can do for you. But you don't really need complicated mathematics to build railways, steamships, breechloader rifles and printing presses.

You can forget about mature chemical industries, electronics, or just about any advanced materials engineering, though.
 
carlton_bach said:
It surprises me, frankly, you get to the 19th Century.:eek:
carlton_bach said:
modern accounting, statistics
This, I'm less sure of. AIUI, the tally stick stopped being able to cope with increasingly sophisticated (complicated) businesses, whence (more/less) modern accounting. Am I wrong this needs zero?
carlton_bach said:
You can forget about mature chemical industries, electronics, or just about any advanced materials engineering, though.
That's about what I figured. Post-classical physics generally? Genetic engineering?
 
Honestly, the concept of zero is going to become obvious to at least one bright spark as soon as you develop a society which records a lot of data, because eventually there's going to be places where one set of data recorded some figures and another set of data based on the same criteria but taken from a different sample (i.e. tax numbers in different locations etc) has nothing, and you need a way of showing this. So for a start you're looking at anything which does not require lots of note-taking. Thus, financial stuff is out of the window and so is anything requiring formulae to calculate. Even if it would technically be inventable without the concept of zero, there comes a point where zero is just so useful that it would almost automatically be conceptualised as a by-product of the invention process.
 
It surprises me, frankly, you get to the 19th Century.:eek:

Almost all of the know-how involved in making basic steam engines - even fairly high-pressure ones - and building most early Victorian infrastructure is artisanal. You need someone with an understanding of basic physics to figure it out, but the maths required to do that are fairly simple. Once you have it figured out, you vcan teach it hands-on. Of course all that technology will be built with big margins of safety (and still be dangerous), but so much mid-19th century tech was. Did you see the bridges they built for the transcontinental railway in the 1860s? Like that.

The main problem, of getting to the nineteenth century IMO is that so many of the things that motivated technological development depended on modern maths. The technology itself, not so much. Remember that well into the second half of the century, many engineers were self-taught, often with only basic school education but a wealth of practical knowledge. You didn't need to be ablke to solve for x to build, maintain or drive a train. The problem ism, you needed to be able to do that to manage a railway line.

This, I'm less sure of. AIUI, the tally stick stopped being able to cope with increasingly sophisticated (complicated) businesses, whence (more/less) modern accounting. Am I wrong this needs zero?

You can have a good deal of functioning accounting with fractions and non-zero numerals. If you look at papyrological evidence from Ptolemaic Egypt, you see stuiff that sounds susapiciously like modern tax consulting. But there is a limit, both in the practicality of the system and in its ability to model things. I'm not an expert by any stretch of the imagination, but I know that without decimal points and the operations they allow, adding up, dividing and multiplying fractions is major PITA already. Designing a mathematical model of even the simplest economic transaction becomes horribly difficult.

THink of it by the nanlopgy of building high structures. You can do surprising much with cut stone. The pyramid of Khufu was the tallerst man-made structure on earth for ages. But to get even a little higher requires an enormous amount of additional labour, which may well explain why people stopped building taller pyramids. If you have a system that solves your basic problem more elegantly - like arch vaulting, steel beams, or reinforced concrete tubes - height can be added with much less difficulty. A zero system give you that ability. Once you have it, you can do algebra, and with that, you can build stuff like space shuttles, nuclear reactors and structured debt obligations. Without it, your ability to track and model economics, populations, and observed phenomena stays fairly basic.

That's about what I figured. Post-classical physics generally? Genetic engineering?

Very unlikely IMO. I doubt you could get a working Newtonian model. Elements of it, maybe, and geometric approximations of the thing. Certainly no stochastics. I suspect almost anything to do with modern chemistry is out.
 
Falastur said:
Honestly, the concept of zero is going to become obvious
Read the OP again. I accept the concept is obvious: just not the fact of it. Mexica had the concept of zero; IIRC, not the description of it, a placeholder for it. Romans, too, probably.
Falastur said:
there comes a point where zero is just so useful that it would almost automatically be conceptualised as a by-product of the invention process.
There comes a point where the need to invent it arises, yes, but that's not inevitable.
carlton_bach said:
The problem ism, you needed to be able to do that to manage a railway line.
For sheer complexity?
Falastur said:
If you have a system that solves your basic problem more elegantly - like arch vaulting, steel beams, or reinforced concrete tubes - height can be added with much less difficulty.
Some of that is materials science; stone could only carry so much load, while wrought iron (later steel) offered opportunities. Part of the problem is the "cut & paste" of building without blueprints/plans. That can be solved, at least in part, by scale models & quite simple scaling up. (This kind of thing was already in play by the time Notre Dame was built.)
Falastur said:
Very unlikely IMO. I doubt you could get a working Newtonian model. Elements of it, maybe, and geometric approximations of the thing.
I suspected not. I confess, it's hard to appreciate how sophisticated even Newtonian physics is, looking back.
 
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