Archimedes discovers Calculus

[chrispi]

Most of his manuscripts are lost to us, perhaps he did indeed come up with calculus (especially with the recent discovery of an Archimedean manuscript dealing with infinity.) His work on integrals (surface of a sphere = surface of the smallest cylinder containing it) and derivatives (parabolic projectile paths, etc) point to this. Could he have found their link?

What are the historical consequences of Archimedean calculus?

[carlton_bach]

Is calculus possible without a numerical system including zero? Could it be done with the mess the Greeks (and Romans) called their numbers? If so, he (por someone else) may well have and the idea been forgotten for want of practical applications. We keep finding all of these 'world-shaking discoveries' (blood circulation, heliocentric system, germ theory, round earth etc.) popping up all over the place whenever people had the time and leisure to think.

What implications would it have for history, though? What are the real-world applications in a world where engineering is run by rule-of-thumb and simple trig?

[DominusNovus]

Originally Posted by carlton_bach

We keep finding all of these 'world-shaking discoveries' (blood circulation, heliocentric system, germ theory, round earth etc.) popping up all over the place whenever people had the time and leisure to think.

Someone in antiquity came up with a germ theory? Enlighten me, please.

[Grey Wolf]

I can't remember what Calculus is or why its useful. I know Newton discovered it then locked it in his draw for 15 or so years (thanks to Bill Bryson for that knowledge) but I'm buggered if I know what it is

Interestingly, I remember DOING it at school, but I don't think the Maths teacher ever explained why anything existed or what it was supposed to do, only how to do it. My mind doesn't really work like that and it was a miracle that I got a Grade C at OA Level

Grey Wolf

[carlton_bach]

Originally Posted by DominusNovus

Someone in antiquity came up with a germ theory? Enlighten me, please.

I don't recall which papyrus it is, but there was the suggestion in one of the medical treatises dating most likely to the Middle Kingdom that diseases were caused by invisible agents travelling between people. Similar speculation is recorded in the contagion theories of Arab scholars which, in turn, made it into Western medicine. That is where we get the word 'germ' - something that germinates disease.

Unfortunately, without a proper understanding of microbiology, the miasma theory of disease actually makes more sense.

[chrispi]

Originally Posted by carlton_bach

Is calculus possible without a numerical system including zero? Could it be done with the mess the Greeks (and Romans) called their numbers? If so, he (por someone else) may well have and the idea been forgotten for want of practical applications. We keep finding all of these 'world-shaking discoveries' (blood circulation, heliocentric system, germ theory, round earth etc.) popping up all over the place whenever people had the time and leisure to think.

What implications would it have for history, though? What are the real-world applications in a world where engineering is run by rule-of-thumb and simple trig?

Calculus without zero may actually be an advantage, as you can't divide by zero and leave "ghosts of departed quantities" as Bishop Berkley complained. Unlike the Romans, it would be surprisingly simple for the Greeks to convert their alphabetic numeral system to decimals: just keep the first 9 numbers (alpha-theta) and change 10 (iota) into a 0*, and you have a Greek decimal system!

*the numbers 9, 10, 11, 12 and 13, written θ, ι, ια, ιβ, ιγ, would be written instead as θ, αι, αα, αβ, αγ.

[NapoleonXIV]

Originally Posted by carlton_bach

Is calculus possible without a numerical system including zero? Could it be done with the mess the Greeks (and Romans) called their numbers? If so, he (por someone else) may well have and the idea been forgotten for want of practical applications. We keep finding all of these 'world-shaking discoveries' (blood circulation, heliocentric system, germ theory, round earth etc.) popping up all over the place whenever people had the time and leisure to think.

What implications would it have for history, though? What are the real-world applications in a world where engineering is run by rule-of-thumb and simple trig?

I believe the Phoenicians had a place value system based on 6. (hence the 360 degrees in a circle and the 60 seconds in a degree etc). I also believe this would be known to the Greeks and the Romans. (6 has advantages over 10, chief among them being how many numbers are evenly divisible by 6. )

If the Romans did know Calculus they could calculate stresses and loads on structures and not have to overbuild. (The legend was that the foreman had to stand underneath the arch while the temporary supports were removed) However, recent (1978) work done on one of the more well-known surviving acqueducts indicated a safety factor of only two, the modern standard for such structures, when wind stresses were taken into account. Either the Romans were both extremely lucky and very slipshod or they had some way of calculating the stresses.

[Anthony Appleyard]

The Phoenicians spoke a Semitic language, and Semitic languages have the number system 1 10 100 1000. The 360 degrees in a circle likeliest came from astronomy and astrology: each day the sun seems to move about a degree against the stars, so someone in the Middle East used a day's sun movement as the unit angle, and then they noticed that 360 = 60 * 6, and for some purposes they started to count in 60's.