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after decillion
Message #1 Posted by anna marie on 9 Dec 2005, 9:42 a.m.

What comes after decilion??? NOT INTEGER!!! i just wanna know

      
Re: after decillion
Message #2 Posted by John Cadick on 9 Dec 2005, 9:50 a.m.,
in response to message #1 by anna marie

A pretty complete table can be found at

http://mathworld.wolfram.com/LargeNumber.html

John

            
Re: after decillion
Message #3 Posted by Matt Kernal (US) on 9 Dec 2005, 4:46 p.m.,
in response to message #2 by John Cadick

The Wolfram table skips over "googol".

Where: 1 googol = 1.0 10100

Example: "I'll sell you my HP 42S for 1 googol dollars".

Factoid: The "Google" search engine name came from the number "googol". While still in college, the soon to be founders of Google both used the number as an answer on an exam.

Matt

      
Re: after decillion
Message #4 Posted by Ed Look on 9 Dec 2005, 11:52 a.m.,
in response to message #1 by anna marie

This numerical nomenclature is based on Latin. In Latin languages extant today, numbers like 11 or 24 are still spoken as "ten and one, or twenty and four", much like the four and twenty blackbirds of the nursery rhyme.

So, for such systems, after "10"-illion would be "11"-illion, so after decillion would come undecillion, dodecillion, trisdecillion, etc.

Trisdecaphobia, anyone? After all, you're all calc folks!

            
Re: after decillion
Message #5 Posted by Thomas Okken on 9 Dec 2005, 12:08 p.m.,
in response to message #4 by Ed Look

Quote:
In Latin languages extant today, numbers like 11 or 24 are still spoken as "ten and one, or twenty and four"

Actually, they have special words for 11 and 12 (e.g. "onze" in French, not "dix-un"). Probably a legacy from the times when humans still had six fingers on each hand.

(Of course French must be the weirdest language for counting -- who the heck came up with the idea of pronouncing 95 as "four twenties fifteen"? Good thing the names of those large numbers are not based on that...)

                  
Re: after decillion
Message #6 Posted by Valentin Albillo on 9 Dec 2005, 12:26 p.m.,
in response to message #5 by Thomas Okken

Hi, Thomas:

Thomas posted:

"Of course French must be the weirdest language for counting -- who the heck came up with the idea of pronouncing 95 as "four twenties fifteen"?"

    You've never heard of the English "fourscore", did you ?

    Or Abraham Lincoln's quote:

    "Fourscore and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal."

    What do you suppose that "fourscore and seven" stands for ?

    In other words (Matthew 7): "Why do you see the straw in your brother's eye, and the beam that is before your eye you do not notice?"

Best regards from V.

Edited: 9 Dec 2005, 12:32 p.m.

                        
Re: after decillion
Message #7 Posted by Etienne Victoria on 9 Dec 2005, 12:44 p.m.,
in response to message #6 by Valentin Albillo

Hi Thomas, Valentin,

Agreed!!

And this way of using "scores" (English) or "vingt" or "fiche" (irish according to my wife) reminds us that we've been using our hands and feets "fingers" to count & compute for a long time before RPN was invented.

All the best from France!

Etienne

                        
Re: after decillion
Message #8 Posted by Crawl on 9 Dec 2005, 1:01 p.m.,
in response to message #6 by Valentin Albillo

Lincoln was trying to be poetic (some might say pretentious) due to the occasion. No English speaker would ever say "fourscore" for eighty under normal circumstances.

                  
Re: after decillion
Message #9 Posted by bill platt on 9 Dec 2005, 12:35 p.m.,
in response to message #5 by Thomas Okken

Quote:
Of course French must be the weirdest language for counting -- who the heck came up with the idea of pronouncing 95 as "four twenties fifteen"?

That's why the Belgians and the Acadians simplified it: septante, huitante, neuvante etc --I can't remember exactly the constructions--mine are a little off but this is the basic idea in both cases :-)

Dozen and douze and onze and eleven and twelve are interesting.

Onze is clearly using the root for the word "un"

Douze is clearly using the root for "deux" as is trez, quatourze etc and so in this sense in french it is a consitent system...Jus that the "teens" don't start until seventeen (dix-sept).

(please forgive my spelling--it has been awhile...)

Compared to deutche is interesting, where

elf zwelf

are followed by dreizien (sp?) fierzien etc. and so is just like english in this respect. where the "zien" is "teen".

All three languages bifurcate the nomenclature of numbers in the set 11-19 into two sets linguistically--why they broke at different places is a good question.

Edited: 9 Dec 2005, 12:37 p.m.

                        
Re: after decillion
Message #10 Posted by Peter Geiser on 9 Dec 2005, 4:40 p.m.,
in response to message #9 by bill platt

English also has special words for eleven and twelve. They are etymologically even stranger than French:

Eleven comes from old English endleofan, meaning "one left over", and twelve is "two left over".

In German: elf, zwölf (zwoelf), dreizehn, vierzehn, ... (zehn being the equivalent to ten).

In this regards, Chinese is very logical, where you have shiyi (ten one), shier (ten two), shisan (ten three), etc.

Best regards
Peter

                  
Re: after decillion
Message #11 Posted by Gerson W. Barbosa on 9 Dec 2005, 12:43 p.m.,
in response to message #5 by Thomas Okken

Quote:
Actually, they have special words for 11 and 12 (e.g. "onze" in French, not "dix-un"). Probably a legacy from the times when humans still had six fingers on each hand.


Actually, there's nothing special in French words for 11 and 12, onze and douze: they come from Latin undecim (one and ten) and duodecim (two and ten).

                        
...latin
Message #12 Posted by Massimo Gnerucci (Italy) on 9 Dec 2005, 12:51 p.m.,
in response to message #11 by Gerson W. Barbosa

Hi Gerson,
please be careful with latin... ;-)

I was going to post my contribution but I stopped when I realized that I could easily fly away off topic.

'nuff said!

Greetings,
Massimo

Edited: 9 Dec 2005, 12:52 p.m.

                              
Re: ...latin
Message #13 Posted by Gerson W. Barbosa on 9 Dec 2005, 1:12 p.m.,
in response to message #12 by Massimo Gnerucci (Italy)

Ciao Massimo,

There's no way to explain "onze" is not a special word, as some might think, without showing its latin root.

But you're right, this thread has gone off-topic.

Regards,

Gerson

P.S.: I should actually be studying il congiuntivo presente, imperfetto e trapassato for my Italian test tomorrow :-)

Edited: 9 Dec 2005, 1:15 p.m.

                                    
Re: ...latin
Message #14 Posted by Massimo Gnerucci (Italy) on 9 Dec 2005, 3:54 p.m.,
in response to message #13 by Gerson W. Barbosa

Quote:
P.S.: I should actually be studying il congiuntivo presente, imperfetto e trapassato for my Italian test tomorrow :-)

Ciao Gerson,
my best wishes for your test!

However you'll be probably disappointed by knowing that these tenses are less and less used in normal conversation...
Thanks television! Alas, more elaborate speaking is forbidden when the audience is in the millions.

In bocca al lupo/break a leg!
Massimo

                        
Roman (Latin) numbers
Message #15 Posted by Marcus von Cube, Germany on 10 Dec 2005, 5:25 a.m.,
in response to message #11 by Gerson W. Barbosa

IIRC, Latin starts more consistent (in our modern eyes) than it ends:

11 - undecim, one and ten
...
17 - sedecim, seven and ten
but
18 - duodeviginti, two before twenty (!)
19 - unodeviginti, one before twenty.

The last two arne't too strange, given the fact that the Romans wrote their numbers in a similar way: IIXX and IXX.

Marcus

                              
Re: Roman (Latin) numbers
Message #16 Posted by Gerson W. Barbosa on 10 Dec 2005, 7:48 p.m.,
in response to message #15 by Marcus von Cube, Germany

Hello Marcus,

If you think numbers in Latin are awkward, what about fractions?

Excerpt from Ars poetica (by Horace):

http://tabula.rutgers.edu/spectator/text/june1711/ars_poetica.html

"Romani pueris longis rationibus assem discunt in partis centum diducere.
'dicat filius Albini: si de quincunce remota est uncia, quid superat? Poteras dixisse.'
'triens!'
'eu! rem poteris servare tuam. Redit uncia, quid fit?'
'semis!'"

"Through long calculations, Roman children learn to divide the as (the unity) in hundredths. 'Tell me, son of Albinus, if an uncia (1/12) is removed from a quincunx (5/12), what remains? Can you tell me? 'triens! (1/3)' 'Very good! You'll be able to manage your things. Were an uncia (1/12) added, what would you have?' 'A semis! (1/2)'

5/12 - 1/12 = 4/12 = 1/3
5/12 + 1/12 = 6/12 = 1/2
I think they'd learn this by heart as we do with multiplication tables. For everyday calculations they would use abbaci. Too bad the traditional abbacus maker at the time, Hector Paccatus, sold his skillful greek servants in order to reduce costs and imported less expensive slaves from the East. As a result, in the new abbacci the beads would not slide so smoothly on the rods as before and people started complaining... :-)

Edited: 10 Dec 2005, 7:51 p.m.

                                    
Re: Roman (Latin) numbers
Message #17 Posted by Richard Anderson (in Athens) on 12 Dec 2005, 7:00 a.m.,
in response to message #16 by Gerson W. Barbosa

Hello from where those Greek slaves might have come from!

I thought it was worth mentioning, since Roman numerals and abaci have been mentioned, that those numerals (that everyone points out are so clumsy) are a system of abacus notation. They tell you how to set the beads on an abacus with 4 beads + 1 bead on each bar. I & V on the first bar, X & L on the second, C & D on the third, etc. I suppose that the "subtractions" IV instead of IIII are tricks to save "keystrokes".

A skilled abacus user can outperform any old mechanical calculating machine...and maybe not actually need the abacus. It always annoys me when people say the Romans were deficient with numbers.

Kali Dynami (Good Strength),

Richard

                                          
Re: Roman (Latin) numbers
Message #18 Posted by Gerson W. Barbosa on 12 Dec 2005, 11:32 a.m.,
in response to message #17 by Richard Anderson (in Athens)

Quote:
Hello from where those Greek slaves might have come from!

Hello Richard,

I may have used the word 'servants' wrongly, instead of 'workers' or 'employees'. I don't have the foggiest notion what an abacus factory looked like. In fact it appears there were no abacus factories at all, these calculating devices being made by skillful artisans, most likely not from Greece, in low quantities. By what I know the Greek played an important role in ancient Rome as educators.

Quote:
I suppose that the "subtractions" IV instead of IIII are tricks to save "keystrokes"

If am not wrong, these later notation appeared in the Middle Ages as a way to save space in manuscripts.

Kal imera! (Good-day!),

Gerson

                                                
Re: Roman (Latin) numbers
Message #19 Posted by Richard in Athens on 15 Dec 2005, 10:00 a.m.,
in response to message #18 by Gerson W. Barbosa

Hello Gerson,

I'm sure there's a good abacus book or two out there. When I was a kid I learned how to use a "modern" Japanese abacus with 4 & 1 bead per bar rather than the Chinese 5 & 2 kind. I never learned what the Chinese do with those extra beads, nor do I know what kind of abacus the Romans typically used.

Both would be pretty easy to find out.

I typed "slaves" without thinking and then saw that you had said "servants" to begin with. I decided to leave it because slavery was so much a part of the Greek and Roman world.

Greek learning was much esteemed by the Romans. Many Romans sent their sons to be educated in the "Philosphical Schools" of Athens. An English friend of mine suggested that the Romans viewed a Greek education much as Americans think of Oxford or Cambridge. Athens, of course, wasn't the only place to get a Greek education. Alexandria was famous for its library and Euclid is thought to have studied in Athens but "taught and founded a school in Alexandria". (Heath)

Geometric tools are the compass and straight edge. I guess the abacus was the original "number-cruncher" but they went out when Arabic numerals came in. A good abacus cost much more than some scraps of papyrus...probably relatively more than those "dream-come-true" early 70's HPs. As a poverty-stricken archaeological surveyor I just dreamed of owning one of those but eventually jumped on the 42s. A wise jump and luckily I jumped more than once because one of my 42s's seems to have "walked" from my office last week. Nobody steals your old scraps of papyrus.

Richard (this posting counts as "general information")

                                                      
Re: Roman (Latin) numbers
Message #20 Posted by unspellable on 15 Dec 2005, 3:53 p.m.,
in response to message #19 by Richard in Athens

The Japanese style abacus is called a soriban. I have one, complete with English instructions although I have never gotten around to learning how to drive it.

But it is to be noted that the Roman number systemn relate to the abcus in the same way that binary numbers relate to the computer.

If you know the history behind the various nymbering systems, and oddities like a dozen, score, pence, shillings, and pounds, etc. they make a good deal more sense.


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