Are Gloranthan Counting Systems Decimal?

[Rodney Dangerduck]

Since a real world friend is having a "significant" birthday, it begs this exceptionally nerdy and geeky question:

In Glorantha, do most cultures use base 10 for their counting and math?  Base 12 like some ancients?  Or something else?  (Thumbless Morokanth?)

 

[Agentorange]

57 minutes ago, Rodney Dangerduck said:

Since a real world friend is having a "significant" birthday, it begs this exceptionally nerdy and geeky question:

In Glorantha, do most cultures use base 10 for their counting and math?  Base 12 like some ancients?  Or something else?  (Thumbless Morokanth?)

 

Thumbless morokanth as a counting unit base, i can't see it catching on.

[soltakss]

2 hours ago, Rodney Dangerduck said:

In Glorantha, do most cultures use base 10 for their counting and math? 

Coinage is in multiples of 10 or 20, so 10 Bolgs to a Clack, 10 Clacks to a Lunar and 20 Lunars to a Wheel, or 10 Lunars to a half-Wheel, so base 10 seems right.

Also, Hoplites are arranged in squads of 10, Agimori Impis use 10s, 100s and 1000s.

Lunars, however, might use Base 7 for ritual counting. In My Glorantha, 7 soldiers make a Squad, 7 Squads make a Company (49), 7 Companies make a Cohort, and 7 Cohorts make a Legion (2,401).

[mfbrandi]

1 hour ago, Rodney Dangerduck said:

In Glorantha, do most cultures use base 10 for their counting and math?  … Or something else?

Ooh, I like this!

Do they have a positional system? With zero? With a “decimal” (adjust to suit base) point?

Does it make any real sense to talk about base with Roman numerals? (I am just asking: it is clear fives and tens are important, but …)

If we say “three-score years and ten”, are we breaking out of our base ten system, or is it just a colourful way of saying “3 × 20 + 10”? (See also “soixante-dix.”)

Shepherds count sheep like this: yan (1), tan (2), tether (3), mether (4), pip (5), …, jigget (20). But they count “goats” like this: yan, tan, teher — run!

I am going to guess that counting systems vary to suit the tasks and sophistication of the users. If no computers, no need to bother with low bases, right? But the Morokanth might have a binary thumb–no thumb system for magic.

[Joerg]

Pamaltelans like to use base 17, Lunars like base 7, Dara Happans use base 8 or base 10 (especially Plentonius).

In our world, Germanic counting systems know the small hundred (10x10),. the large hundred (12x10) and the gros (12x12). The French and the Danes count and number in twenties rather than tens all the way to 100. And we all use base 12/24/60 for time (except people using SI units, which have decimal seconds and multiples thereof).

Given the history of British coinage (which had the guinea, worth a pound plus a shilling, or 21 shilling, or 252 pence), the Gloranthan system for 1:20:200:2000 is pretty easy to remember.

[Bill the barbarian]

2 minutes ago, soltakss said:

Lunars, however, might use Base 7 for ritual counting. In My Glorantha, 7 soldiers make a Squad, 7 Squads make a Company (49), 7 Companies make a Cohort, and 7 Cohorts make a Legion (2,401).

This sounds quite likely for the Orlanthi as well... Seven day weeks (before moonrise), 7 lightbringers... My games Issaries contracts divide shares into 7ths...

 

[mfbrandi]

11 minutes ago, soltakss said:

Lunars, however, might use Base 7 for ritual counting. In My Glorantha, 7 soldiers make a Squad, 7 Squads make a Company (49), 7 Companies make a Cohort, and 7 Cohorts make a Legion (2,401).

Interesting: so officers come from within the basic count? So if each squad is six soldiers plus a squad leader, then a company is led by a “first among equals” from the squad leaders, not an extra “senior” officer (for a total of 50)?

Edited January 7, 2023 by mfbrandi
from -> by

[soltakss]

4 minutes ago, mfbrandi said:

Do they have a positional system? With zero?

Apparently the Egyptians had 0 for accounting purposes and the Babylonians had zero as a placeholder in the Bronze Age, so Zero as a concept is fine. 

I am not sure if Glorantha have a positional system, though. In my games they do, as it is easier.

7 minutes ago, mfbrandi said:

With a “decimal” (adjust to suit base) point?

Almost certainly not.

In the real world, the Chinese had them in the Iron Age, so I suppose it could be suitable for Glorantha. If so, only specialised sages would use them.

10 minutes ago, mfbrandi said:

Does it make any real sense to talk about base with Roman numerals? (I am just asking: it is clear fives and tens are important, but …)

Not really, and it is a nightmare to do arithmetic using them.

11 minutes ago, mfbrandi said:

If we say “three-score years and ten”, are we breaking out of our base ten system, or is it just a colourful way of saying “3 × 20 + 10”? (See also “soixante-dix.”)

A score is a unit of counting, so is the same as twenty, so maybe it is similar to base 20 but is not the same.

 

[soltakss]

5 minutes ago, mfbrandi said:

Interesting: so officers come from within the basic count? So if each squad is six soldiers plus a squad leader, then a company is led by a “first among equals” from the squad leaders, not an extra “senior” officer (for a total of 50)?

Yes, but I flip-flop all the while on that.

[Brian Duguid]

13 hours ago, soltakss said:

13 hours ago, mfbrandi said:

Does it make any real sense to talk about base with Roman numerals? (I am just asking: it is clear fives and tens are important, but …)

Not really, and it is a nightmare to do arithmetic using them.

Presumably much easier using a Roman abacus, though i.e. a tool adapted specifically to that task.

https://en.wikipedia.org/wiki/Roman_abacus

[David Scott]

17 hours ago, Rodney Dangerduck said:

Since a real world friend is having a "significant" birthday, it begs this exceptionally nerdy and geeky question:

In Glorantha, do most cultures use base 10 for their counting and math?  Base 12 like some ancients?  Or something else?  (Thumbless Morokanth?)

The Dara Dappan sacred alphabet (GtG 394), states: The first eighteen characters of the Sacred Alphabet are also a quasi-decimal numeric system. It operates on the additive principle in which the numeric values of the letters are added together to form a total.

[Darius West]

18 hours ago, Rodney Dangerduck said:

Since a real world friend is having a "significant" birthday, it begs this exceptionally nerdy and geeky question:

In Glorantha, do most cultures use base 10 for their counting and math?  Base 12 like some ancients?  Or something else?  (Thumbless Morokanth?)

The currency at least seems to be a variant of decimal.  So do keymiles for that matter.

[Jeff]

Pelorian languages are all strongly base 10. 

Theyalan languages give a number for each of the days of Sacred Time, so 1-14. 15 gets represented as 1-1, 28 as 1-14, and so on until we get to 210 which gets a new signifier. 

 

[Nick Brooke]

In my Glorantha, Lunar mathematicians have come up the innovative numeral "zero," much as Arab mathematicians did. Its use transforms arithmetic, except that fuddy-duddy bearded Lhankor Mhy types think it's somehow "tainted by the void of chaos" and insist on keeping their craptastic traditional numbering systems: more fool them.

This insight was inspired by Sir Kay's musings in John Steinbeck's The Acts of King Arthur and his Noble Knights (on p.269f. of the Book Club edition):

Quote

"They say the pagan has invented a number which is nothing -- nought -- written like an O, a hole, an oblivion. I could clutch that nothing to my breast..."

[Bill the barbarian]

1 hour ago, Nick Brooke said:

In my Glorantha, Lunar mathematicians have come up the innovative numeral "zero," much as Arab mathematicians did. Its use transforms arithmetic, except that fuddy-duddy bearded Lhankor Mhy types think it's somehow "tainted by the void of chaos" and insist on keeping their craptastic traditional numbering systems: more fool them.

Not sure about your attributing the zero to the arabs, same part of the world... Mesopotamia though they did not use zero as we do... I believe it was an Indian who brought the zero up to date... lets see...

yep found this:
https://www.history.com/news/who-invented-the-zero

It might seem like an obvious piece of any numerical system, but the zero is a surprisingly recent development in human history. In fact, this ubiquitous symbol for “nothing” didn’t even find its way to Europe until as late as the 12th century. Zero’s origins most likely date back to the “fertile crescent” of ancient Mesopotamia. Sumerian scribes used spaces to denote absences in number columns as early as 4,000 years ago, but the first recorded use of a zero-like symbol dates to sometime around the third century B.C. in ancient Babylon. The Babylonians employed a number system based around values of 60, and they developed a specific sign—two small wedges—to differentiate between magnitudes in the same way that modern decimal-based systems use zeros to distinguish between tenths, hundreds and thousandths. A similar type of symbol cropped up independently in the Americas sometime around 350 A.D., when the Mayans began using a zero marker in their calendars.

These early counting systems only saw the zero as a placeholder—not a number with its own unique value or properties. A full grasp of zero’s importance would not arrive until the seventh century A.D. in India. There, the mathematician Brahmagupta and others used small dots under numbers to show a zero placeholder, but they also viewed the zero as having a null value, called “sunya.” Brahmagupta was also the first to show that subtracting a number from itself results in zero. From India, the zero made its way to China and back to the Middle East, where it was taken up by the mathematician Mohammed ibn-Musa al-Khowarizmi around 773. It was al-Khowarizmi who first synthesized Indian arithmetic and showed how the zero could function in algebraic equations, and by the ninth century the zero had entered the Arabic numeral system in a form resembling the oval shape we use today.

 

The zero continued to migrate for another few centuries before finally reaching Europe sometime around the 1100s. Thinkers like the Italian mathematician Fibonacci helped introduce zero to the mainstream, and it later figured prominently in the work of Rene Descartes along with Sir Isaac Newton and Gottfried Leibniz’s invention of calculus. Since then, the concept of “nothing” has continued to play a role in the development of everything from physics and economics to engineering and computing.

 

 

Edited January 8, 2023 by Bill the barbarian

[Nick Brooke]

Please forgive my shorthand. Zero found its way to Europe via the Arab world, and we adopted it as what is popularly called an “Arabic numeral.” Previous numbering systems including the Roman and Greek methods were phenomenally crap by comparison. There is an intriguing anecdote about what happened to the Greek scribes in Damascus when it became the capital of the early Caliphate, but I fear I would annoy you by continuing, so I will stop.

[Soccercalle]

I use 10 as a base for most cultures but 7 for the Lunars.

10 explains both the coinage and the Humakti military.

[Ormi Phengaria]

Rather than base-7, I suspect if the Lunars have made their own count, it might be base-27, since that could at least see calendrical use, and can go by the ancient "Twenty-Seven Carvers". Maybe some Carmanian numerology, too. Base-12 might be found in Pamaltela with the Hoolars offering a folkloric explanation.

[Nick Brooke]

OK, this is from memory. In the first heady rush of the Jihad, the Umayyads seized the Byzantine city of Damascus and made it the capital of their new Caliphate. The administrators of Damascus both wrote and counted in Greek.

Now, Greek numerals were a weird secondary application of the Greek alphabet, plus various squiggles, underlines etc. Arabic numerals (please see my earlier post before quibbling) were considerably more useful: the use of a Zero to mark varying numbers of “tens” makes numbers far more powerful and flexible. And the Arabic language and script were utterly unlike anything the Greek scribes were familiar with.

So, in a decision that will surprise nobody who’s ever worked for a large organisation, the Caliphate decided that its accounts should be written in Arabic script and Greek numerals.

Edited January 9, 2023 by Nick Brooke

[soltakss]

On 1/8/2023 at 6:15 PM, Nick Brooke said:

Please forgive my shorthand. Zero found its way to Europe via the Arab world, and we adopted it as what is popularly called an “Arabic numeral.”

I think that Fibonacci championed Arabic Numerals but I can't remember if they became popular then.

[Sir_Godspeed]

On 1/7/2023 at 9:58 PM, Joerg said:

Pamaltelans like to use base 17

I'm sorry hhhWHAT?! O.o

I wanna hear about this!

[Darius West]

On 1/8/2023 at 7:58 AM, mfbrandi said:

Do they have a positional system? With zero? With a “decimal” (adjust to suit base) point?

This is a really good point.  I initially thought "No, the decimal point was a very late invention in our own society, so there is no way it would be an early adoption in Glorantha".  But that is simply not the case historically.  There was always a form of notation to indicate decimal fractions.  The Indians used a bar, Muslims used a comma, and eventually Europeans discarded a Vertical Line, in favor of John Napier's use of the full stop we employ today.  There has always been some sort of columnar indicator for fractionation in the decimal system since its inception in India, so there is no reason there wouldn't be one in Glorantha.  Hooray for bronze age decimal points it seems.

[Nick Brooke]

On 1/9/2023 at 12:01 PM, Ormi Phengaria said:

Rather than base-7, I suspect if the Lunars have made their own count, it might be base-27, since that could at least see calendrical use, and can go by the ancient "Twenty-Seven Carvers". Maybe some Carmanian numerology, too. Base-12 might be found in Pamaltela with the Hoolars offering a folkloric explanation.

The Foundation TV series brought this to my attention: base-27 makes sense, and is in use in our world.

“The Oksapmin people of New Guinea have a base-27 counting system. The words for numbers are the words for the 27 body parts they use for counting, starting at the thumb of one hand, going up to the nose, then down the other side of the body to the pinky of the other hand, as shown in the drawing. 'One' is tip^na (thumb), 6 is dopa (wrist), 12 is nata (ear), 16 is tan-nata (ear on the other side), all the way to 27, or tan-h^th^ta (pinky on the other side).”

I think this would have delighted Greg; I can see no indication (despite the later prominence of Pelandan Finger-goddesses) that he used it when coming up with the Lunar calendar, with its 27-year waxing and waning epicycles.

[French Desperate WindChild]

I will not base my answer on irl but on a gloranthan question

what do you need to understand then practice sorcery, alchimy, dwarf plans  and such complex tasks. So for me there are a lot of options. what mathematic base ? depends probably on number of runes, or number of form runes, or power runes, or ... other runes

[Sir_Godspeed]

6 hours ago, Nick Brooke said:

The Foundation TV series brought this to my attention: base-27 makes sense, and is in use in our world.

“The Oksapmin people of New Guinea have a base-27 counting system. The words for numbers are the words for the 27 body parts they use for counting, starting at the thumb of one hand, going up to the nose, then down the other side of the body to the pinky of the other hand, as shown in the drawing. 'One' is tip^na (thumb), 6 is dopa (wrist), 12 is nata (ear), 16 is tan-nata (ear on the other side), all the way to 27, or tan-h^th^ta (pinky on the other side).”

I think this would have delighted Greg; I can see no indication (despite the later prominence of Pelandan Finger-goddesses) that he used it when coming up with the Lunar calendar, with its 27-year waxing and waning epicycles.

Body parts are also the root of base-10 (ten fingers, obvs.), base-20 (ten fingers and ten toes, iirc.,) and base-12 (number of joints on the fingers of one hand except the thumb - this was a common way to count in ancient Sumeria, apparently, which is why we have 12 hours in one day and 60-minutes in one hours - 12 joints times the five fingers on the opposite hand.)

So you're bringing up a good point, number systems can come in a wide variety even without bringing in esoteric reasons.