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Originally posted by uncommitted
And if,
as is suggested,
counting is so easy and natural,
please explain how the following sentence
lead to the Greco-Roman dominance of half the world for centuries.
"The shortest distance between two points is a straight line"
When that appears in Book 1 of Euclid's Elements,
but they don't get to number theory (counting) till Book 7.
Mike
Because the quote is stunningly eloquent, what has that got to do with anything at all? Do you disagree at the shortest distance between 2 points (and I'm sorry, I always thought two was a number) is indeed a straight line? What point are you trying to make? I'm fairly sure though that particular observation did not on its own lead to the Greco Roman dominance.edit on 29-8-2013 by uncommitted because: layoutedit on 29-8-2013 by uncommitted because: (no reason given)
Originally posted by BobAthome
dont know about u guys but i always thought that pi was the big breakthrough,, after zero.
Originally posted by Nyiah
OP, I was thoroughly confused by your opening post without citations and a reason for the post, but I eventually got the drift down the page some that you were showing examples of time keeping. I was with you up until you snapped on Spider's post about menstruation perhaps being an inspiration for timekeeping. WTH, man? Are you seriously going to chuck a theory out the window because it involved women? Really? You can't cherry-pick your favorites while ignoring all possible reasons that might have inspired timekeeping, that's not scientific at all. It is quite reasonable that monthly shedding of the uterine lining way back in the early days might have indeed inspired some semblance of timekeeping. Unless you're insinuating early peoples were too stupid to connect the dots of "female body does this thing males' bodies don't + days it does it + days without body doing this = ?" If back then, the group female rhythm of menstruation (and yes, women in groups can sync up) coincided with moon phases, they might have applied deeper thought to it.
Kudos to Spider, btw, for sharing. I didn't know about that, and learned something new, even if just a hypothetical.
Originally posted by Spider879
reply to post by mikegrouchy
A tally stick, though
in no way shows the existence of numbers greater than "one", "two", and "many"
It only proves that people could compare sticks and say
"I have more many than you"
It was more than a simple tally stick.it was a very early precursor to what was found in a much later Kemet in it's use of the doubling system.
At one end of the Ishango Bone is a piece of quartz for writing, and the bone has a series of notches carved in groups (shown below). It was first thought these notches were some kind of tally marks as found to record counts all over the world. However, the Ishango bone appears to be much more than a simple tally. The markings on rows (a) and (b) each add to 60. Row (b) contains the prime numbers between 10 and 20. Row (a) is quite consistent with a numeration system based on 10, since the notches are grouped as 20 + 1, 20 - 1, 10 + 1, and 10 - 1. Finally, row (c) seems to illustrate for the method of duplication (multiplication by 2) used more recently in Egyptian multiplication. Recent studies with microscopes illustrate more markings and it is now understood the bone is also a lunar phase counter. Who but a woman keeping track of her cycles would need a lunar calendar? Were women our first mathematicians?
www.math.buffalo.edu...
I am familiar with Ogham kinda like the Roman's use of letters for numbers, and the Rune script also although I haven't dug deep into either..but my main point was the Ishango bone connected to the Lunar cycle and women is the oldest known so far in the world.
But interestingly there was always this thing with magic and numbers world wide,
Originally posted by Hanslune
reply to post by mikegrouchy
Do you have link to that?
Besides,
The discovery of a leap forward in the history of counting
that skips completely over base 5, to land squarely on base 10/20 (with doubling! no less)
strains credulity.
An extraordinary claim.
I hardly think one baboon fibula is extraordinary proof.
Where are the calendars, the month names, the astronomy?
No, it is just one more wedge driving men and women apart.
Doubling series in Africa
In some accounts authors have stated that Africans use a “primitive” number system in which they count by multiples of two.It is true that many cases of African arithmetic are based on multiples of two, but as we will see, base two systems are not crude artifacts from a forgotten past. They have surprising mathematical significance, not onlyin relation to African fractals, but to the western history of mathematics and computing as well.
The presence of doubling as a cultural theme occurs in many different African societies, and in many different social domains, connecting the sacredness of twins, spirit doubles, and double vision with material objects, like the blacksmith's twin bellows and the double iron hoe given in bridewealth (figure 7.3). Figure 7.4a shows the Ishango bone, which is dated around 8,000 years old and appears to show a doubling sequence. Doubling is fundamental to many of the counting systems of Africa in modern times as well. It is common, for example, to have the word for an even number 2N mean "N plus N" (e.g. the number 8 in the Shambaa language of Tanzania is “ne na ne,” literally “four and four.”)A similar doubling takes place for the precisely articulated system of number hand gestures (figure 7.4b); for example “four” represented by two groups of two fingers, and “eight” by two groups of four. Petitto (1982) A similar doubling takes place for the precisely articulated system of number hand gestures (figure 7.4b); for example “four” represented by two groups of two fingers, and “eight” by two groups of four. Petitto (1982) found that doubling was used in multiplication and division techniques in west Africa (figure 7.4c).Gillings (1972) details the persistent use of powers of two in ancient Egyptian mathematics as well, andZaslavsky (1973) shows archaeological evidence suggesting that ancient Egypt’s use of base-two calculations derived from the use of base-two in sub-Saharan Africa.
Doubling practices were also used by African descendants in the Americas. Benjamin Banneker, for example, made unusual use of doubling in his calculations, which may have derived from the teachings of his African father and grandfather (Eglash 1997c). Gates (1988) examined the cultural significance of doubling in west African religions such as vodun, and its transfer to “voodoo” in the Americas
homepages.rpi.edu...
In the 1970's during the excavations of Border Cave, a small piece of the fibula of a baboon, the Lebombo bone, was found marked with 29 clearly defined notches, and, at 37,000 years old, it ranks with the oldest mathematical objects known. The bone is dated approximately 35,000 BC and resembles the calendar sticks still in use by Bushmen clans in Nimibia.
How can anyone call it either
numbers or counting, when
is plainly skips all odd numbers.
leads me to conclude that the "official sources"
are either lazy, or just trying to protect their
entrenched positions
Originally posted by Hanslune
reply to post by Spider879
..or due to chance [color=gold] no odd numbers are involved
Originally posted by Spider879
reply to post by mikegrouchy
How can anyone call it either
numbers or counting, when
is plainly skips all odd numbers.
Just different ways of problem solving
The thing with the Bones and why it may have been females..because if it was indeed connected to their monthly cycle then [color=gold] it would make sense that women carved it.
By all means be true to one's self.