Langhorns deadliest blow - Killing Zero

My comment about bankers and a functional equivalent of negative numbers was partly intended as a reminder that Maths doesn't just come up in science, but in many everyday situations. IMHO no one can have run the large banking houses by exactly matching up loan and credit letters for each pair. NTM dealing with payments by instalment. They sure also calculated interest payments, it was certainly much harder in Roman numerals and without decimals, but where there is a will there's a way.

As to whether they had geometry, it kind of depends on what you mean by geometry. They built houses, castles, bridges, cathedrals etc pretty successfully. All that implies a good deal of building square and true, creating functional arches, some understanding of stresses and loads. They built some of the canals post the Angelic era. Its very difficult to see how you could do it without some level of surveying. Their geometry may not have been very abstract or as extensive as Euclid - who also didn't have Arabic numerals, may I just point out. But you can do a lot with similar triangles, Pythagoras theorem (for which there is a perfectly acceptable geometric proof) etc.

evilauthor wrote:I dunno. While Langhorne might have removed zero as a mathematical concept, people still needed to have the concept for "nothing" as an everyday thing. "I have no food!" "I have no gold!" etc etc.

And people still needed to SAY numbers and count large numbers of things, and they still spoke a form English. One through nine are still one through nine. Ten through nineteen are as unintuitive as Langhorne could ask for. But twenty and beyond?

"Twenty" "Twenty one" "Twenty Two"... "One hundred and thirty five" "Fifty two hundred and ninety six"

Everything past twenty? The VERBAL rules for speaking such numbers is straight up pure decimal positional notation. The only thing Merlin introduced was a symbol system that translated those verbal rules into something you could read.

And by the time Merlin first shows up, Safeholdians were routinely counting well past twenty.

In short, I don't think the introduction of Arabic numerals was as nearly a big leap as the OP seems to think it is. It is a big leap, but all the groundwork to understand it was already laid in the English language handed down from the Archangels and the Safeholdians own experience.

Also, we're never told that Merlin officially introduced negative numbers. The introduction of those were likely made as a "discovery" by the Charis university after its head was taken into the Inner Circle. He had already been working out new math before that happened and discovering new meaning in random phrases that the Archangels had said.

The thing about the "Roman numerals" is that the system came from the Archangels, and nobody questioned if there where a better way - especially considering the Schuelerites penchant for putting inquisitive people to the test.

Fun fact, Romans more or less spoke numerals the same way as English speakers do.

It's speculated that the number zero was first invented in Sumeria 3000 BC and it took almost 4200 years for the concept to reach Europe. And that without a scripture telling people how to write down numbers, how much longer would it have taken if there was an unassailable scripture telling people that numbers is written Roman style?

From that perspective the introduction of Arabic numerals was a big leap.

Silverwall wrote:To help those who are not well versed in the history of Math you may find the following essay on the history of zero interesting.
http://www-history.mcs.st-andrews.ac.uk/HistTopics/Zero.html

It differentiates between the two uses of zero, being a placeholder in the number system and being a number in it's own right.

P.s. one thing you can't do without zero? Graphing and map making using cartesian co-ordinates, which as the name suggest was invented the famous french mathematician René Descartes in the 1600s. This makes me wonder makes you wonder if the maps in the holy books had lines of latitude and longitude on them If they did I assume zero longitude would run through Zion as the prime meridian.

There is a mention in one of the earlier books that logitude was written on the maps( in Roman numerals) - I dont know if zero ran through Zion, and it so, how it handled East and West.

fallsfromtrees wrote:There is a mention in one of the earlier books that logitude was written on the maps( in Roman numerals) - I dont know if zero ran through Zion, and it so, how it handled East and West.

Irony of ironies. "360 degrees making up a circle" is preserved via the Holy Writ's map system, albeit in Roman Numerals.

The Zero line for both latitude and longitude is probably given some formal name to avoid saying it's zero. Equator and... "Temple time"?

evilauthor wrote:
Irony of ironies. "360 degrees making up a circle" is preserved via the Holy Writ's map system, albeit in Roman Numerals.

The Zero line for both latitude and longitude is probably given some formal name to avoid saying it's zero. Equator and... "Temple time"?

"Beginning" or some synonym would be a good choice.

Julia Minor wrote:

evilauthor wrote:
Irony of ironies. "360 degrees making up a circle" is preserved via the Holy Writ's map system, albeit in Roman Numerals.

The Zero line for both latitude and longitude is probably given some formal name to avoid saying it's zero. Equator and... "Temple time"?

"Beginning" or some synonym would be a good choice.

Line of Langhorn?

Baseball stats in Roman numerals sound fun...

jchilds wrote:Baseball stats in Roman numerals sound fun...

Actually stats would be quite simple!

Without zero and the place based system you can only do simple count stats e.g. Home Runs hit, Strikeout thrown, Runs batted in etc.

More advanced stats such as ERA, Strike rate, etc would be effectivly undoable. The problem is that you have no decimal fractions that these calculations need. All you could do is say he has a ratio of 114 hits out of 415 at bats as you can only express things as ratios of whole numbers. Without an easy way to normalise these stats would not be worth tracking.

Quick quiz, which batter do you want, Mr CXI/CCCCXV or Mr CCXLIV/CMXI there is just no way to eyeball the un-normalised number.

Answer: 111/415 = .267 hitter vs 244/901 = .271 hitter without being able to convert to decimal your stuffed.

I have just finished Tonio Andrade's Gunpowder Age, which contrasts Chinese and European development of gunpowder technology, especially 900-1900. Two points of interest to the way Peerless Author handled technology development:

1. In reaction to learning about advances from the Dutch, the Chinese figured out how to make cannon by encasing cast iron in either wrought iron or bronze, which was both cheaper and produced more effective weapons. I don't think the West ever picked this up. Had PA known about this I suspect he would have had Charis go for this instead of his straight iron casting.

2. The Chinese were unable to reproduce the advances made in gunnery from the late 16th century to the early 18th because they weren't a matter of simple copying. To understand them, they needed to understand that because of the gases interfering with missile velocity and the effect of air resistance, a cannon ball that should have gone 16 miles would only go three. In fact, it was determined that lower muzzle velocities would lead to much more power, hence Napoleon's use of the carronade to slaughter the Mamelukes in Egypt. The disparity was particularly notable in artillery, leading to drastic disparities in accuracy (because given the slightest change in weaponry, even experimentation with a reproduced weapon wouldn't give a good picture of range, while a way of determining range required a Western ballistic pendulum and knowledge of the way to compute the resulting ranges from Euler's formulas -- also unknown) and speed to reload/power. This disadvantage led to horrendous Chinese defeats in the Opium Wars, and was not overcome until the Chinese implemented a full-scale training in the new sciences (as did Japan in the late 1800s and the Ottoman Empire in the mid- and late 1800s).

My feeling is that PA -- understandably, given the Western focus of most military-technology history -- gave too short a shrift to the real difficulties COGA would have had -- especially in artillery, but also in accuracy in general -- in coming anywhere close to matching Charis, without knowledge of the science involved. In other words, accuracy, in particular, would have been worse than PA indicated and slower to improve, and despite the extra firepower -- which wasn't that much, considering their slowness to adopt the 17th-century idea of machine tools to make tools -- they still would be missing almost all their shots (less so at sea).

A horrible indication of this is the incident in the Opium Wars when the Manchu Dynasty attacked a Scottish garrison of 100 men with tens of thousands of troops, 18th century vs. late 16th century (muskets). The garrison slaughtered many thousands, until the dead became piled so high the remainder couldn't get over them. The garrison lost 25.

p.s. There's also an indication that the "smokeless powder" introduced by Charis late in the war was to the Chinese intimidating not so much because it allowed the enemy to see where they were shooting, but because the Chinese could not see where the enemy was shooting from: they couldn't figure out where to aim.

Anyway, just some thoughts.