A wooden mechanical calculator
- Thread starter BillC
- Start date
if you like mech calcs:
im a fan of the Curta and how it wraps the input output line around a cylinder again, the digital version of a circular slide rule.
if you are keen on Curta there is this very complex 3d print project.
at least two full reels of PLA.
im a fan of the Curta and how it wraps the input output line around a cylinder again, the digital version of a circular slide rule.
if you are keen on Curta there is this very complex 3d print project.
Curta Calculator Type I scaled at 3:1 by mwu | Download free STL model | Printables.com
3x scale Curta Type I for FDM 3D printing | Download free 3D printable STL models
www.printables.com
Very interesting those mechanical calculators. You hear the terms,enter, hold, carry, read, etc. Often wondered about the origins of our number systems and the logic which is attached. I wonder if the parts of the human body such as fingers and toes (digits) might have played a part in the development of our numerical system. If we count the human digits we get 20 fingers and toes and if we add the major extremities two legs two arms and one head we get another five which takes us to a count of 25, if we then multiply 25 by the four major extremities (two arms and two legs) we reach the number of 100. Which as we can see is made up of a one and zero,s. I Wonder if there is on some far away planet in a remote galaxy a monopede slug which when calculating uses its body part for a count of 1 if present and if not present it could yield a count of 0. Again we see one,s and zero,s The origins of numerical logic still a complete mystery.
from a good read:
"A key clue to the nature of Stone Age mathematics was unearthed in the late 1930s when archaeologist Karl Absolom, sifting through Czechoslovakian dirt, uncovered a 30,000-year-old wolf bone with a series of notches carved into it. Nobody knows whether Gog the caveman had used the bone to count the deer he killed, the paintings he drew, or the days he had gone without a bath, but it is pretty clear that early humans were counting something.
A wolf bone was the Stone Age equivalent of a supercomputer. Gog’s ancestors couldn’t even count up to two, and they certainly did not need zero. In the very beginning of mathematics, it seems that people could only distinguish between one and many. A caveman owned one spearhead or many spear-heads; he had eaten one crushed lizard or many crushed lizards. There was no way to express any quantities other than one and many. Over time, primitive languages evolved to distinguish between one, two, and many, and eventually one, two, three, many, but didn’t have terms for higher numbers. Some languages still have this shortcoming. The Siriona Indians of Bolivia and the Brazilian Yanoama people don’t have words for anything larger than three; instead, these two tribes use the words for “many” or “much.”
Thanks to the very nature of numbers—they can be added together to create new ones—the number system didn’t stop at three. After a while, clever tribesmen began to string number-words in a row to yield more numbers. The languages currently used by the Bacairi and the Bororo peoples of Brazil show this process in action; they have number systems that go “one,” “two,” “two and one,” “two and two,” “two and two and one,” and so forth. These people count by twos. Mathematicians call this a binary system.
Few people count by twos like the Bacairi and Bororo. The old wolf bone seems to be more typical of ancient counting systems. Gog’s wolf bone had 55 little notches in it, arranged into groups of five; there was a second notch after the first 25 marks. It looks suspiciously as if Gog was counting by fives, and then tallied groups in bunches of five. This makes a lot of sense. It is a lot faster to tally the number of marks in groups than it is to count them one by one. Modern mathematicians would say that Gog, the wolf carver, used a five-based or quinary counting system.
But why five? Deep down, it’s an arbitrary decision. If Gog put his tallies in groups of four, and counted in groups of four and 16, his number system would have worked just as well, as would groups of six and 36. The groupings don’t affect the number of marks on the bone; they only affect the way that Gog tallies them up in the end—and he will always get the same answer no matter how he counts them. However, Gog preferred to count in groups of five rather than four, and people all over the world shared Gog’s preference. It was an accident of nature that gave humans five fingers on each hand, and because of this accident, five seemed to be a favorite base system across many cultures. The earlyGreeks, for instance, used the word “fiving” to describe the process of tallying.
Even in the South American binary counting schemes, linguists see the beginnings of a quinary system. A different phrase in Bororo for “two and two and one” is “this is my hand all together.” Apparently, ancient peoples liked to count with their body parts, and five (a hand), ten (both hands), and twenty (both hands and both feet) were the favorites. In English, eleven and twelve seem to be derived from “one over [ten]” and “two over [ten],” while thirteen, fourteen, fifteen, and so on are contractions of “three and ten,” “four and ten,” and “five and ten.” From this, linguists conclude that ten was the basic unit in the Germanic protolanguages that English came from, and thus those people used a base-10 number system. On the other hand, in French, eighty is quatre-vingts (four twenties), and ninety is quatre-vingt-dix (four twenties and ten). This may mean that the people who lived in what is now France used a base-20 or vigesimal number system. Numbers like seven and 31 belonged to all of these systems, quinary, decimal, and vigesimal alike. However, none of these systems had a name for zero. The concept simply did not exist."
- Zero: The Biography of a Dangerous Idea by Charles Seife
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A similar related topic to numerical systems and machines is calendrical reconning. It is fun to think that we as human culture have not lost count of the days of the week for thousands of years (a Sumer invention). And, we still count the time and angles in ancient Sumer base 60 units, because they had all the best astronomical observations. (with exception to the revolutionary french obsession to decimalise everything.)
CURRENT DECIMAL TIME
Calendrier Républicain:
Quintidi 15 Nivôse an CCXXXIII
à 0h 59′ 57″ t.m.Paris
probably the most famous, calendrical calculator is the Antikythera mechanism.
CURRENT DECIMAL TIME
Calendrier Républicain:
Quintidi 15 Nivôse an CCXXXIII
à 0h 59′ 57″ t.m.Paris
probably the most famous, calendrical calculator is the Antikythera mechanism.