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A Model of the Cosmos in the Ancient Greek Antikythera Mechanism

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Re: A Model of the Cosmos in the Ancient Greek Antikythera Mechanism

#91
Can anyone help me understand why gears with prime numbers of teeth would not be mechanizable?

For Venus the original designer faced a dilemma: the known period relation (5, 8) was very inaccurate, whereas the accurate (720, 1151) was not mechanizable because 1151 is a prime number, requiring a gear with 1151 teeth.

I thought that gears with prime numbers of teeth would be advantageous because it would spread the wear evenly across the gear that it contacted.

Re: A Model of the Cosmos in the Ancient Greek Antikythera Mechanism

#92
post #45

Earlier quoted context omitted.

In the case of the Antikythera mechanism, it turns out the knowledge and technology weren't entirely lost. There's a fairly well-established throughline now from Babylonian observation-based astronomical tables to Greek philosophical views and mathematics (and craftmanship) to Arabic astrolabes (retaining some of the gear-train tech) and then back to Europe, to the monastic astronomical clocks. Then the escapement wa…

The Roman were truly a successful agrarian civilization, but became lackluster in progress from there. They never made an overwhelming shift to mathematical / science based civilization. They took over Syracuse with a mandate to keep Archimedes alive, but that failed. Some scholars say the only roman contribution to math was numerals. Basically they reaped the profits of empire, and fell into the cargo cults of opule…

You mean slave labor society right, if you can't expand the empire fast enough, you "human capital" stream dries up, its like taking on too much debt and not being able to keep up with paying.

Re: A Model of the Cosmos in the Ancient Greek Antikythera Mechanism

#93

Sadly or maybe only interestingly, the Clickspring folks' recent article[1] arguing that the mechanism used a lunar calendar doesn't seem to be cited in this new article. [1] https://bhi.co.uk/antikytheramechanism/

Given how recent his publication is, it is quite likely that the authors of this were already in the final edit stages when they became aware of it, and so it didn't affect anything in their paper and so wasn't cited.

Re: A Model of the Cosmos in the Ancient Greek Antikythera Mechanism

#95

Forgive the naive question, but does this mean these ancient Greeks knew the world was round thousands of years ago?

Eratosthenes even measured earth's circumference with astonishing accuracy. They knew more than we think they knew...

Re: A Model of the Cosmos in the Ancient Greek Antikythera Mechanism

#96

Can anyone help me understand why gears with prime numbers of teeth would not be mechanizable? For Venus the original designer faced a dilemma: the known period relation (5, 8) was very inaccurate, whereas the accurate (720, 1151) was not mechanizable because 1151 is a prime number, requiring a gear with 1151 teeth. I thought that gears with prime numbers of teeth would be advantageous because it would spread the wea…

1151 is too many teeth for a gear. The teeth would not be deep enough to transmit power effectively. You can't make this exact ratio using gears with fewer teeth because 1151 is prime (more generally, whenever the numerator and denominator are coprime).

Re: A Model of the Cosmos in the Ancient Greek Antikythera Mechanism

#97

Earlier quoted context omitted.

> which are hopefully sometimes improvements The death of Latin is very upsetting.

Why is that out of curiosity?

Reading the English for Catullus 16 (pretty dirty) and feeling jealous that they could put it so succinctly in their own language. Also this TED talk https://www.ted.com/talks/lera_boroditsky_how_language_shape....

Re: A Model of the Cosmos in the Ancient Greek Antikythera Mechanism

#98

Can anyone help me understand why gears with prime numbers of teeth would not be mechanizable? For Venus the original designer faced a dilemma: the known period relation (5, 8) was very inaccurate, whereas the accurate (720, 1151) was not mechanizable because 1151 is a prime number, requiring a gear with 1151 teeth. I thought that gears with prime numbers of teeth would be advantageous because it would spread the wea…

You can't split them up into several smaller gear pairs, so you actually need two gears with 720 and 1151 teeth. A gear with 1151 teeth is impractical to make, both in terms of size and in terms of the manufacturing capability at the time.

Re: A Model of the Cosmos in the Ancient Greek Antikythera Mechanism

#99

Can anyone help me understand why gears with prime numbers of teeth would not be mechanizable? For Venus the original designer faced a dilemma: the known period relation (5, 8) was very inaccurate, whereas the accurate (720, 1151) was not mechanizable because 1151 is a prime number, requiring a gear with 1151 teeth. I thought that gears with prime numbers of teeth would be advantageous because it would spread the wea…

It's tough to make gears with that many teeth, especially if you want them to mesh with smaller gears.

Also, meshing against a 1-tooth gear is problematic, so you would need to probably increase that to >4 teeth to have it work. Then your bigger gear needs to have >4x the teeth to get the desired ratio.

Re: A Model of the Cosmos in the Ancient Greek Antikythera Mechanism

#100

I always wonder what future archaeologists in will read into artifacts from our time when they find them in 2000 years...

We really like trash made of plastic.

I'm not so sure. A lot of trash plastic degrades over long periods of time. They might find the plumbing (which is a type of plastic that lasts longer), but that isn't trash in general.
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