New research: The history of Timekeeping

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 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: layout

edit on 29-8-2013 by uncommitted because: (no reason given)

For thousands of years math education started with division,
then multiplication,
only much later and after mastery of the first two did addition and subtraction start.

This is a common problem with people educated in the modern world when looking back
at the past with they eyes they currently have,
instead of seeing things with the eyes our ancestors had.



Chiron The Centaur Tutor: Alright pupil. Is there any way to slice this pie so that we both get exactly equal portions.

Achilles: Ummm, down the middle?

Chiron: How do you define middle.

Achilles: Ummmm, the widest part.

Chiron: That right. As Euclid wrote "A diameter of the circle is any straight line drawn through the center and terminated in both directions by the circumference of the circle, and such a straight line also bisects the circle."

Achilles: I see. So the widest line possible that crosses the circle will also guarantee that both parts are equal.

Chiron: You have a future my boy.




Number theory (what we call counting) doesn't come until much much later in the lessons.





Oh and as to the sentence quoted above,
and the answer to the question
How did it allow the Grecco-Romans to dominate for centuries?

The answer is simple and only one word long.

Roads.




Has anyone ever noticed that the old Roman roads are painfully straight,
unnecessarily straight,
going straight through swamps,
chopping straight through mountains and hills,
almost like it was their purpose in life?


Mike

Originally posted by BobAthome

dont know about u guys but i always thought that pi was the big breakthrough,, after zero.

But have we solved it yet?

Being a transcendental number it does not terminate,
having an infinite number of decimal iterations.


.........pi = 3.141592653589793240

.......22/7 = 3.142857142857142790
......error = 0.001264489267349555

....355/133 = 3.141592920353982520
.....error. = 0.000000266764189282

52518/16717 = 3.141592390979242480
.....error. = 0.000000262610550761


If I run my own computer analysis of the pi formula
to generate any number of iterations
this is what I find...


Pi = 4 -4/3 +4/5 -4/7 +4/9 +4/11 . . .
cycles computed 3,807,918

..Pi. = 3.141592653589793240
error = 0.000000262610494117


It takes three million eight hundred seven thousand, nine hundred and eighteen cycles
to be more accurate
than simply dividing 52518/16717.


And anyway,
Euclid already solved this problem millennia ago.


"In a circle, equal arcs subtend equal chords"
- Euclid's Elements


Mike

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.

Good,
I'm happy you were offend.

Obviously this information is not meant for you.

So get out,
and stay out!

I'll continue discussing Spiders posts with Spider
who seams neither
as easily offended,
nor as willing to quickly dump me into the trash.


Mike

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,

Ok you have cornered me in some dangerous territory,
and there is no way I can see to say this without sounding preachy,
so I'll just be preachy.


In the ancient world there is no difference between being "whole" and "1" (one).

A man was not considered a man...
A woman was not considered a woman...
Until they were whole.
Mated, one flesh, that is to say ... one.

/ begin preachy rant

There are only two super geniuses of science that I am aware of.
Lavoisier and Einstein. In both cases these men were blessed
the very rarest of occurrences. A lab assistant that they were
both deeply in love with and who were their wives. Back in
those days finding a woman with a love for science and a
knack for being a lab assistant, wheather a chemistry lab
or a laboratory of the mind, was as common as finding
a supernova. And a great many potential geniuses
died alone and unloved by any woman, as their wives
usually hated their work or were jealous of their time
spent in the lab. It was a different world back then.

I do find it interesting though, that here in the post
feminist world the story is being revised to suggest
that those men stole the work from their wives when for
hundreds of years one of the great laments of science has
been about how much genius has been lost because of the
rarity of finding a good husband and wife team.

And now that we have generations of empowered scientific women
capable of participating in just such a relationship the drum beat for
castigation of men in general is being whipped up to a louder and faster beat.

Disgusting if you ask me.
/ end preachy rant


/ personal diatribe
Claudia Zaslavsky is a post modern agenda pusher.
It is no surprise to me that she has the hubris to think
that it is her mission to restore some sense of history
to the Congo, as though they are not capable themselves,
and that she is a champion of feminist causes.
/end personal diatribe

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.


Mike

The calendar of ancient Minos was divided up into the Year
based on the Moon going through five phases.

62 phases = 1 year

Each phase had it's own color.

Many of the moon colors have filtered down through myth, legend, and Religion to us.

The phrase Blue Moon these days means "any 30 day month with 2 full moons",
but to the Minoans this meant the last quarter moon after the full moon,
that the moon was turning blue and would soon be gone.



In Revelations 6:12 we find this passage.
"And I beheld when he had opened the sixth seal, and, lo, there was a great earthquake; and the sun became black as sackcloth of hair, and the moon became as blood;"
Which to a Minoan would translate as "On the first quarter moon there shall be an eclipse of the sun."


An interesting thing about this five phases of the moon
and using 62 of them to measure a year.

It is incredibly accurate,
and naturally produces a kind of leap year function.

Where the Tropical year is about 12.333 months long
this Minoan method gives 12 x 5 = 60, with 2 extra 1/5ths of a month
Not quite the 1/3 required, but light years beyond any other calendar
in use anywhere in the world at the time.


Mike

reply to post by mikegrouchy


Do you have link to that?

Additionally the Minoan used an Administrative calendar
based on "The Great Year", or 8.5 years.

Every 8 and half years the old ruler would be sacrificed
and an new ruler installed.

It worked like this,
when the Red Moon, (the first quarter moon)
fell exactly on the Winter Solstice, a new ruler was installed.

Then when the Red Moon, (first quarter)
fell exactly on the Summer Solstice,
the old ruler was bleed out, and a new ruler installed.

This ruler would be replaced during the next
Red Moon on a Winter Solstice.




So it changed from winter to summer every 8.5 years.

Here are some of the Duties the Ruler oversaw.

5 days: Snake of Winter, out of 91.3 days of winter
3 days: Bull of Spring, out of 54.8 days of spring
7 days: Lion of Summer, out of 127.8 days of summer
3 days: Grapes & Olives of Fall, out of 54.8 days of Fall

Mike

Originally posted by Hanslune
reply to post by mikegrouchy

 

Do you have link to that?

Sure,
here ya go.

Creet Gazzet: Discovery & Demonstration of the Minoan Calendar








And here is a nice picture
of the Thera Wall Mural it was decoded from,
for those who don't want to visit the link

Though I have done more cross checking
and cross cultural analysis than is available
on just that page, it was the starting point and
I encourage anyone "who's got the bug" to do
more research on their own. There is so much left to learn.


Mike

reply to post by mikegrouchy


Thanks for the link. I wouldn't agee with Dempsey's conclusion. His background is not in Minoan studies and he has not (AFAIK) tested this idea in a PRP, ie put it out where Minoan experts could discuss it. However its seems to have been informally looked at. See below

A link discussing the theory

reply to post by Hanslune


Yes I'm aware of that.

But nothing is this entire thread
is either approved of by "official sources"
nor willing to wait around for them to tell-me
what the truth is.

My own conclusions, analysis to the metrics,
computer simulations of the data and
comparison to the actual astronomical data
leads me to conclude that the "official sources"
are either lazy, or just trying to protect their
entrenched positions.

No one has to agree with me,
but at least now, the few people
who have read this thread, are
getting a different perspective.

Take the information, and use
it anyway you wish. Or ignore it.

In the opening post I put a specific date
on the invention of numbers.

That move all on it's own is heresy in
the modern era.



Mike

If the reader thinks that the experts
disagree with me now, just wait
till I show how letters were invented.


Mike

reply to post by mikegrouchy

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.

I don't get why it would strain credulity doubling is very common in large parts of Africa the Bones only pushes it back to an extremely early age.

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...

Check this vid out

Actually other bones exist

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.

I think you read too much into the motive of Claudia Zaslavsky after all her job is an ethno mathematician
And don't look at this as debating, dabating have that confrontational ring to it we are just sharing info and comparing notes.

reply to post by Spider879


Well said,
some great information.
A top notch contribution.

I'm tempted to leave the post untouched.

But I can't, and remain true to myself.

How can anyone call it either
numbers or counting, when
is plainly skips all odd numbers.


Further,
why does it have to be just women,
who carved the bone, why couldn't
it have been a husband wife team?

Does the reader realize that division
of labor is a modern invention, one
we seem to have no trouble
projecting onto the past. Even when
the earliest evidence of it dates to
Sumeria, in the 18th Century b.c.?


Mike

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 it would make sense that women carved it.

By all means be true to one's self.

reply to post by mikegrouchy


There aren't any 'official sources' that you think their are is telling. Science advances by consensus, if no one believes you your idea doesn't get accepted.

Do think that you might be more concerned with rebelling that providing anything of value?

leads me to conclude that the "official sources"
are either lazy, or just trying to protect their
entrenched positions

Could you perhaps link to a person who demonstrates what you call an 'OS' who is lazy, protective and has an 'entrench position' on the Minoan calendar?

reply to post by Spider879


..or due to chance no odd numbers are involved

reply to post by mikegrouchy

It was told to me that in the beginning when humans started time, it could have had a choice, if smarter, to start time, at a time, when at the beginning, to make humans live longer, by aging slower ,and

Originally posted by Hanslune
reply to post by Spider879

 

..or due to chance [color=gold] no odd numbers are involved

Don't mistake my frustration for
any kind of validity to the sliding
innuendo that somehow I'm more
concerned with rebelling.

I'm frustrated because suddenly
I realize I am discussing this
with math illiterates.

Which means I will have to wait
for a better educated generation
to realize the profound value of
the research being shown here.

Thank you.

I can now continue on unconcerned,
as it is very clear that unless some-
one tells the reader how "chance"
applies, or doesn't, to the existence
of odd number when one is going
all the way to 28, that the reader
wont know how to feel about it.

/not my problem


Mike

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.

No it wouldn't.

It would make sense if a married couple
were communicating between each other,
then yes, record keeping might evolve.

But for the so-called Ethno Mathematician
(an oxymoron if there ever was one) to
miss out on the possibility of it not being
just a woman, is the worst kind of historical
revisionism.

She commits two grave offences.

1) implying that viewing the efforts of men and women as separate is natural
2) implying that men and women have always been separate

I have wasted enough energy pointing
out the bias and flaws in some deceased
persons work and their crimes against
mathematics and humanity.

That is the last I shall say about that.




If you have some of your own research
you would wish to show or flesh out
I would love to see it.


Mike