Post-Scarcity Economics

[alexjrgreen]

I'm as big a fan of the Greeks as anyone, but they were severely limited by even Early Modern standards.

We probably passed them in about 1700, perhaps a few years later.

In what aspect?

Human rights? Technology? Economy? Military? Science? Arts?

See, I agree that medieval times are sort of boring and depressing, but I do not really see many areas where Greeks would be really better than westerners in say 1500 (more likely much earlier).

Let's see. In 1700 we still had slavery, we didn't yet have lighthouses and the Industrial Revolution was yet to start.

You can probably make a case for Michelangelo equalling the Greeks at sculpture, but not many others.

[Luzr]

We probably passed them in about 1700, perhaps a few years later.

In what aspect?

Human rights? Technology? Economy? Military? Science? Arts?

See, I agree that medieval times are sort of boring and depressing, but I do not really see many areas where Greeks would be really better than westerners in say 1500 (more likely much earlier).

Let's see. In 1700 we still had slavery, we didn't yet have lighthouses

Yeah, right

http://en.wikipedia.org/wiki/Lighthouse#History

So what else?

[alexjrgreen]

Let's see. In 1700 we still had slavery, we didn't yet have lighthouses

Yeah, right

http://en.wikipedia.org/wiki/Lighthouse#History

So what else?

Fair comment. Cordouan certainly qualifies and possibly the Lanterna of Genoa. Otherwise the Greek era lighthouses are bigger.

Accurate clocks don't appear in the modern era until 1584 (Jost Bürgi, accurate to a minute a day) and only improve on the best water clocks with the use of the pendulum after 1656.

[Luzr]

Let's see. In 1700 we still had slavery, we didn't yet have lighthouses

Yeah, right

http://en.wikipedia.org/wiki/Lighthouse#History

So what else?

Fair comment. Cordouan certainly qualifies and possibly the Lanterna of Genoa. Otherwise the Greek era lighthouses are bigger.

Accurate clocks don't appear in the modern era until 1584 (Jost Bürgi, accurate to a minute a day) and only improve on the best water clocks with the use of the pendulum after 1656.

E.g.

http://en.wikipedia.org/wiki/Salisbury_cathedral_clock

IMO, more technologically advanced than waterclocks. Besides, waterclocks were known in medieval ages too..

[alexjrgreen]

Accurate clocks don't appear in the modern era until 1584 (Jost Bürgi, accurate to a minute a day) and only improve on the best water clocks with the use of the pendulum after 1656.

E.g.

http://en.wikipedia.org/wiki/Salisbury_cathedral_clock

IMO, more technologically advanced than waterclocks. Besides, waterclocks were known in medieval ages too..

The Greeks had dials and mechanisms too.

In mathematics, we didn't supass Euclid until Newton's Principia of 1687.

[pfrit]

Accurate clocks don't appear in the modern era until 1584 (Jost Bürgi, accurate to a minute a day) and only improve on the best water clocks with the use of the pendulum after 1656.

E.g.

http://en.wikipedia.org/wiki/Salisbury_cathedral_clock

IMO, more technologically advanced than waterclocks. Besides, waterclocks were known in medieval ages too..

The Greeks had dials and mechanisms too.

In mathematics, we didn't supass Euclid until Newton's Principia of 1687.

Good God, Man! The greeks didn't have zero or any real idea of Pi!

[djolds1]

Good God, Man! The greeks didn't have zero or any real idea of Pi!

They were also limited to word problems instead of symbolic mathematics. The fact that Archimedes almost created calculus (method of progressive approximations) using only word problems is... amazing.

[alexjrgreen]

In mathematics, we didn't supass Euclid until Newton's Principia of 1687.

Good God, Man! The greeks didn't have zero or any real idea of Pi!

The Greeks did have a symbol for zero - a small circle with a long overbar - introduced from Babylonian sources by Hipparchus in the second century BC and used by Ptolemy in the second century AD.

Archimedes (third century BC) proved that the ratio of the circumference of a circle to its radius was between 223/71 (3.140845) and 22/7 (3.142857). The symbol Pi was introduced by William Jones in 1706 and popularised by Euler in 1737.

Euclid's Elements remained the main textbook for geometry until the twentieth century.

[Luzr]

Accurate clocks don't appear in the modern era until 1584 (Jost Bürgi, accurate to a minute a day) and only improve on the best water clocks with the use of the pendulum after 1656.

E.g.

http://en.wikipedia.org/wiki/Salisbury_cathedral_clock

IMO, more technologically advanced than waterclocks. Besides, waterclocks were known in medieval ages too..

The Greeks had dials and mechanisms too.

True, but basing the pace on mechanic oscilation rather than drops or quantums of water is considered more advanced approach anyway. It is less wet in any case.

In mathematics, we didn't supass Euclid until Newton's Principia of 1687.

Are you joking?

Positional zero, decadic system, actuall rules to COMPUTE expressions with large numbers.

Well, these were Arabic and Indian inventions, but widely accepted in west way before 1500. For Greeks, it was almost impossible to compute things like 12345678 / 334533634. Well before 1500, it was something that mathematics in west (and India and perhaps Arabia) could do in minutes.

Then, negative numbers, quadratic and cubic equations and thus complex numbers - all around 1500.

http://en.wikipedia.org/wiki/Complex_number#History

After 1500, but before 1700, west discovered functions, function graphs and analytical geometry. These were the real foundation of modern science. Calculus was something that Greeks perhaps understood intuitively, but they were far from any formal theory - if nothing else, they did not have notion of functions.

So anything else Greeks were better than the west around 1500?

[Luzr]

In mathematics, we didn't supass Euclid until Newton's Principia of 1687.

Good God, Man! The greeks didn't have zero or any real idea of Pi!

The Greeks did have a symbol for zero - a small circle with a long overbar - introduced from Babylonian sources by Hipparchus in the second century BC and used by Ptolemy in the second century AD.

When we are speaking about zero, there are actually two issues.

One is symbol for empty quatity. They might have had it.

Second is "positional zero". It is required to build modern decadic numbers system. This one is way more important as decadic system allows for easy formalized computational methods. Greeks definitely did not had positional zero.

Euclid's Elements remained the main textbook for geometry until the twentieth century.

Yeah, they were quite good at geometry. But they were particulary bad at numerics.

[alexjrgreen]

When we are speaking about zero, there are actually two issues.

One is symbol for empty quatity. They might have had it.

Second is "positional zero". It is required to build modern decadic numbers system. This one is way more important as decadic system allows for easy formalized computational methods. Greeks definitely did not had positional zero.

They had positional zero, they just rarely needed it: A history of Zero.

[Luzr]

When we are speaking about zero, there are actually two issues.

One is symbol for empty quatity. They might have had it.

Second is "positional zero". It is required to build modern decadic numbers system. This one is way more important as decadic system allows for easy formalized computational methods. Greeks definitely did not had positional zero.

They had positional zero, they just rarely needed it: A history of Zero.

Means they really sucked at numerics..

[alexjrgreen]

quadratic and cubic equations

Look up Diophantus (third century AD).

Calculus was something that Greeks perhaps understood intuitively, but they were far from any formal theory - if nothing else, they did not have notion of functions.

Nice point, and and a consequence of Greek grammar which treats actions differently.

The same issue caused the split between the Greek Orthodox and Roman Catholic churches over the doctrine of the Trinity. Grammatically, an action (breathing) cannot be a person.

[Luzr]

quadratic and cubic equations

Look up Diophantus (third century AD).

Diophantus looked at 3 different types of quadratic equations: ax2 + bx = c, ax2 = bx + c, and ax2 + c = bx. The reason why there were three cases to Diophantus, while today we have only one case, is that he did not have any notion for zero and he avoided negative coefficients by considering the given numbers a,b,c to all be positive in each of the three cases above. Diophantus was always satisfied with a rational solution and did not require a whole number which means he accepted fractions as solutions to his problems. Diophantus considered negative or irrational square root solutions "useless", "meaningless", and even "absurd". To give one specific example, he calls the equation 4 = 4x + 20 'absurd' because it would lead to a negative value for x.

Does not look like he was better than Italians around 1500.

[alexjrgreen]

They had positional zero, they just rarely needed it: A history of Zero.

Means they really sucked at numerics..

Check out Archimedes' Sand Reckoner, where he constructs the number ten to the power of eighty quadrillion.