Olivia wrote:Before you damn the Greeks to mathematical mediocrity, you might want to take a look at this.

It's my understanding that, like the Hebrews, they had the Phoenician alphabet at their disposal.

That they could do it, when forced to do so, I do not doubt. That children were so trained in school - as they are now - is not true. In your example, really great scholars are giving the formula for what we would consider to be a merely difficult example. To Theon, this was at the limits of human ability. An order of magnitude greater than what we would think.

When you look at ancient numbers you see, over and over again, a much simpler, much cruder world. What is Ptolemaic latitude? It is expressed like this: 12:45, 14:12, 16:03. Ptolemaic latitudes in fact run from 12:00 to 24:00. What sort of strange system is this?

A very simple one, in fact. Latitude was expressed in hours and minutes of the longest day of the year. As the length of an hour, in fact, varied with the season, that means that the hours, as measured at the equinoxes, were used to measure the day of the summer solstice. Thus, 14:42 means a latitude at which the longest day of the year was 14 hours and 42 minutes in length. As it happens, ancient latitudes translate directly into modern clock time, since at the equinoxes, days are always 12 hours long. On the equinoxes, modern civil hours are exactly the same as ancient sundial hours. Or darn close.

Why was it done this way? Because water clocks were simple to make & read, whereas astrolabes were not. I wikied astrolabe just now, and, as expected, got the usual mush, that astrolabes were invented by the Greeks, long, long ago, but were then "improved" by the Arabs. And then lots & lots of pictures of Arab astrolabes. No Greek originals. Glossed right over was the fact that Arabs got a hold of "Arabic" numbers centuries before Europeans did (they got them from India, where they were developed around 400 AD), so OF COURSE put them to work in all manner of ways. Sometimes this willful ignorance of how numbers came to be & what they can do simply drives me up a wall.

This is very clear in algebra itself. Why did the Greeks substitute letters for numbers? Because simple letters were so much easier to manipulate than Roman numbers.

a squared plus b squared equals c squared was a lot easier than

XLIV squared plus CCCXXXIV squared, equals ???

Work out the relationship with ABC's and once that's clear then you can put actual numbers to it. To us, algebra is abstract. To the Greeks, it was practical.

This is aside from the fact that the Greeks historically used Attic numbers (go Wiki). Attic numbers are worse than Roman numbers. Roman numbers can also be expressed as simple hand signals, another advantage.

By contrast, Chinese numbers were simply dreadful. Go Wiki.

Does this have relevance?

YES IT DOES.

It explains, in one stroke, why Chinese astrology is largely symbolic & not based on the sky at all. Ditto for Tibetan astrology, which, in fact, could be counted on the fingers of the left hand - which I suspect is true of Chinese astrology as well. It also tells us about Mayan astrology.

The number system you use matters. Indian, aka Arabic, aka Western numbers have replaced all other counting systems. On earth there are thousands of languages, but there is ONLY ONE number system. (Romans have not been used seriously for seven centuries, at least.) Much of the history of human advancement can be traced directly to the formulation & spread of that one system. We all owe India a debt of gratitude.

GR wrote:

I'm not going to put words in Deb's mouth, but I think she's hinting at the problem, which is that the Riley is a 1st draft of a translation, and thus is riddled with errors. Curtis has pointed out a glaring one.

Riley says it's a draft, but even so, he put more than a year's work into it.

I went looking for Curtis, to see what the error was, but so far as I can tell, Curtis doesn't officially go by that name, as I cannot find it. Can anybody help?

Dave of Maryland wrote: I went looking for Curtis, to see what the error was, but so far as I can tell, Curtis doesn't officially go by that name, as I cannot find it. Can anybody help?

Hi Dave. Curtis goes by zoidsoft on the forum.

Dave of Maryland wrote: Yes, I know they're profections. I edited Lilly's Book 3, where you will find all 12 of the Merchant's profections. I was surprised, and a little suspicious, to see the same thing in Valens.

??? Why? This is a standard technique from the Hellenistic period to the Reformation.

Dave of Maryland wrote: For example, here on Skyscript I've read that "Valens uses equal houses." No, he doesn't. He uses Porphyry, and was doing so centuries before Porphyry got his name on them. Valens would have used something like Placidus, but that his system of notation - Roman numbers - were inadequate for the task. Porphyry was the best he could do, and in Klima 6 (as far north as Lyon, France), equal does not work.

Ye gods there's so much wrong here.

First, no one uses "equal houses" AFAIK except FAS trained astrologers. Valens uses the signs for topics & "Porphyry" for planetary "strength", as do many.

Second, writing in Greek, Valens would have used Greek letters as numericals. I don't understand how you keep asserting this!

Third, signs for topics works just fine. You continuely assert otherwise, all with no evidence to back you up besides vitriol.

Dave of Maryland wrote: Dorotheus gives no instructions for calculating planetary positions, did you ever wonder why?

Since what we currently have of Dorotheus is a translation of a translation of a translation, who's to say what he said?

Dave of Maryland wrote: So let's compare Dorotheus to Valens. Valens is a master, in full command of the subject. He proves it, right down to the details. Dorotheus is rich - or has a rich uncle - and lazy or maybe just not as bright. He has a machine. He hasn't checked if his charts are accurate because he DOES NOT KNOW HOW.

This is all rather pointless speculation.

Dave of Maryland wrote: It is for us - not Mark Riley - to decipher the text.

Then we would be better off starting from the critical editions.

Astraea wrote:

Dave of Maryland wrote: I went looking for Curtis, to see what the error was, but so far as I can tell, Curtis doesn't officially go by that name, as I cannot find it. Can anybody help?

Hi Dave. Curtis goes by zoidsoft on the forum.

It's Curtis M*******g. I remembered after I posted, went to his site & worked out that he's Zoidsoft. But Skyscript's search is not very good, so I will email him directly. Thanks -

Dave

Gabe's definitely right about Dorotheus - we don't even have all of what he wrote. Though one might want to look at Masha'allah's Book of Aristotle and Rhetororius's Compendium to fill in some gaps, but even that isn't a dead certain 'we know they got it from Dorotheus' deal.

There are similarities, though.

But even then, nothing's definitive, and certainly it's not complete.

Why not use Schmidt's translation of Valens (and his many, many footnotes) as a starting point to deciphering some of the obscurities in Mark Riley's translation?

The Pingree edition would be a help, too, and I'm sure we have some Greek-speaking person here who's got it. I can't be much help to you there, because I don't have it, and Greek is my worst language by far.

Fortunately, many people here don't have those problems

I know Steven Birchfield has studied Valens extensively (and I kind of suspect that both Gabe and Curtis have done, too), but I don't know what their schedules are like these days.

Dear Contributors at Skyscript,

I am preparing a critical edition of Mark Riley's translation of Vettius Valens' Anthologies.

Those who have studied Riley's text and who have comments or questions about it are welcome to contact me privately:

dave@astroamerica.com

My best to you all

David R. Roell