From Ancient To Modern - Mathematics

I want to assume for just a moment that base 60 is the desirable system. Let's just argue, for arguments sake, that this system serves a greater purpose. Perhaps we are not expanding the ancient systems capabilities to include our present needs, but that in fact the ancient form will indeed solve the modern need.

The Babylonians use Sexagesimal from about 2000 BC. Various wedge shape symbols were deployed that I can't get into the CR4 editor. They had no 'zero' figure and just used a space, which must have been a bit confusing. Despite that they could work with fractions.

For an excellent read on number systems grab a copy of "Mathematics From the Birth of Mankind" by Jan Gullberg. A truly excellent book, which gives all round coverage of math stuff.

I could rant on more about various number systems, but would rather not plagerize too much. Read the book, it's very good .

This is just my opinion, just not too much off topic.

one of the thing I have noticed, is what held back the advances of not only math but science as a whole. Which is religion.

One would wonder if this would have redefined higher math as you know it.

I agree. If in fact science were to reveal the truth of religion then the religious power would be for wont of control of said truth.

So, by that line of thought the 2 are inclusive, not exclusive. The McLain paper (I am citing this paper only because the link is already posted. There are innumerable supporting resources available in addition) does a sufficient job of bridging the gap and showing how Sumerian/Babylonian religion (as were the Mayan's and Egyptian's) are dependant on science - they are one in the same!

This 'Oneness' is also described in Tao, Zen, Hindu, the Q'oran and other religious teachings - but again let's not be distracted. Which I see will be difficult, as the first responder offers only a difference where in the stated context I am interested in unity.

This is my favorite math history web site.... St Andrews University.

http://www-groups.dcs.st-and.ac.uk/~history/

So that will make for a good thread.

What of base 60 as it applies to modern day. Is it too primitive? Not fully appreciated? Too tarnished by the fringe? Too elegant to be understood? Too archaic?

Look at the trouble the the U.S. has in converting to the metric systems,

Now ask how ingrained is society is in their current system, and the ask them to change to the base 60.?

economy, schools, industry, government, .... difficult, not matter how.

C_Rummel3,

My first thought on number bases is that base 10 was naturally adopted because of our 10 fingers. Then that base 2 was adopted for our current computer architecture, based on a transistor, which has 2 states (on-off, hi-low, etc). A newer architecture may come along that uses multiple states for it's basic building block. At that point a different number base could be very desireable.

LG_DAVE

I just noticed this article further on in today's CR4.

base 4?

http://cr4.globalspec.com/blogentry/4304/Researchers-create-light-based-quantum-circuit-that-does-math?frmtrk=CR4digest

This is an eye-opener.

I spent 5 years getting my degree (applied physics) at St. Andrews, and keep in touch (very intermittently) with one or two alumni, but nobody told me about the maths history site!

Thanks Steve.

You're welcome John. I have used that site many times... one of my favorites...

And no the title should not read dodern, but rather 'Modern'. Isn't that interesting.

Forum Thread: From ancient to modern - Mathematics

See this is how it was originally posted, under it's correct title. Before a third party change.

Thanks, after getting a few minutes to read the links I learned something new.

I like the base 60 math, but I am not convinced that it would buy modern man much to use it instead of our current system. But I also can't say I have thoroughly thought it through.

I expect that the idea that a circle is divided into 360 parts is based on the observation that there is about 360 days in a year (I said about, not exactly). The realation to music is interesting as well...

As I have said elswhere (but a little differently) on this site, I think that science, math, theology, philosophy, music, and poetry should be fused (as per McClain). But I keep getting the reaction that they (at least science and theology) are incompatible. I am not buying it.

If you started from 'scratch.' i.e. a very young age and were brought up on base 60 math you would be acclimated to the multiplicity of symbols required. Programming computers requires Octal or base 8 and Hexadecimal base 16 which aren't too difficult. Binary base 2 is 'Duck Soup.'

If base 60 is to be assimilated and used for practical purposes there must be some reasons and applications to demonstrate its uses.

To complicate your life try Egyption math with hieroglyphics and strange notations. Not to mention obtuse word problems.

I imagine Roman Numerals would be a PIA!

Read A "History of Mathematics", forgot the author. Base 60 is used because you can divide easier using " head math". Can't divide by 7 or 11, or 13. Probably the source of mythology about these numbers.

Just my 2 cents. I enjoy ancient math as well. Some ancient Sumarian problems are very difficult!

Problem is that no one in the younger generations does math in their head anymore. Ask a young person to add 5+4 and they will reach for a calculator.

those number are also prime if that would have anything to do wih it.

Those are in fact primes. Division is not performed by the means we are familiar, but the results are obtained otherwise.

It seems that the notion of working by ratios was of great interest to the ancients. McLain indicates that the understanding of these ratios sired music. Not that music caused the understanding of ratios. It is theorized that waves were realized and understood and then described by the ratios illustrated. In turn, wave calculations, and further harmonics. This is of interest to me as there is a great deal of interest in modern physics and quantum theory to wave and particle theory.

It seems that in ancient time, time itself was a function of the wave - frequency. Today geometric shapes and a clock - time itself continue to exist on base 60 math.

There is the possibility that the expanding universe is under laws that ancient calculations could shed some light on. I wonder how many theorists in the scientific community have really 'crunched the numbers'. Let us entertain the idea that we do not know all that they knew, and that they knew much more about the behavior and origins of the universe than we do now.

Strange not to find any response to your thread!!

Here is something to stir the pot!!

Enjoy!

Note: Augustine(354-430 CE) wrote, 'The good christian should avoid mathematicians and all those who make empty prophecies. the danger already exists that mathematicians have made a covenant with the Devil to darken the spirit and to confine man in the bonds of Hell'

Mathematical Star Signs

A Mass of Aries rams describes a Curl
Potentially connected to a Field
Some Fractal of Mechanics may unfurl
A Calculus of fuzzy-logic yield.

Quadratic Taurus bulls do not Equate
So don't get Knotted arguing the toss
Although with cows they'll gladly permutate
Inverting them with Product makes them Cross.

Most Geminis are tied in Causal Loop
Because their brains are Hypobolic Plot
So if you Add their salad to their soup
It anti-matters them and matters not.

Cancerians love Cartographic law
Their kind presents a Strange Attractor risk
But should their Bifurcations start to bore
They make delicious Metamathic bisque.

The Cumulative Frequency of Leos
Thrice multiplies their skill at Quantum Jump
But if they start to overRule your Peanos
Just poke them with a Compass in the rump.

Harmonic Virgos may be tempt to play
By flattery Tangented to their ear
'I love the Curve Elliptic of your sway
Thou art the Cuboid destined for my Sphere'.

X Librans makes a Quantity of prate
Now double it for Power Y to Zen
Subtracting Z produces vacillate
Divide by thumps to clear and start again.

Shy Scorpios in Logarithms hide
With Relativity which they embrace
They fly by taking Parabolic ride
With aliens from Fibonacci Space.

As Sagittarians Abstractly run
On no Account engage in Matrix dance
Whilst they may find it Exponential fun
You'll forfeit toes to their Kinetic prance.

To Orbifold a Capricorns Converse
Distract by 'citing enth- most place of Pi
But if the Complex Plane remains adverse
Contuse with Games of Cryptograph eye-spy.

Aquarians are Fluidly Inclined
To saying stupid things like 'catch a Wave'
Illogic'lly Entangled in the mind
Their Hemispheric Orbits won't behave.

The Roots of Pisceans obliquely Lie
Within an Escher Tesselated bowl
They're blessed with Countless Postulated fry
And Scaled with Quasicrystal fungal sole.

Note: Augustine(354-430 CE) wrote, 'The good christian should avoid mathematicians and all those who make empty prophecies. the danger already exists that mathematicians have made a covenant with the Devil to darken the spirit and to confine man in the bonds of Hell'

-but he was really talking about astrologers-

Diane Hine

"One may therefore assume that, as a result of a great law of nature every bit of energy of proper mass 'mo' is intrinsically related to a periodic phenomenon of frequency 'no' in such a way that hno = moc2, no being, evidently, measured in the system attached to a bit of energy. This hypothesis is the basis of our system: it is valid, like all hypotheses, as much as are valid the consequences which one can deduce from it.

~~~~Louis de Broglie

I stumbled across this thread just now and so haven't delved into the resources you mention, but I do have a question: in your studies have you discovered why the Babylonians preferred a base 60 number system over some other base? Were there compelling reasons to do so and can you say what these are? Also - and this is just a thought - were we to take this study to an abstract level where the base B is unspecified, might we be in a better position to see if there exist hitherto unknown, fundamental reasons why one (or more) bases might be preferred over others? Some are no doubt forced upon us by certain practical constraints such as two-state transistor switches making a binary system the natural choice for digital computers, and so forth. But what of a system that is natural for humans? If this is a silly, naive question, then please disregard. -e

Fingering, dear chap;

"Read on for an idea from J.J. O'Connor and E.F. Robertson of the University of St. Andrew's in Scotland.

Their theory says: the Sumerians counted to 60 using both hands like we do but with a difference. They used finger parts instead of whole fingers.

Consider the four fingers of your left hand: ignoring the thumb. The joints divide each finger into three parts. So, we can count finger parts to reach 12. Here's the trick: I use the fingers and thumb on my right hand to point. Using my right thumb, I point at each finger part on my left index finger. That gets me to 3. I continue pointing with my right thumb at all the other finger parts on my left hand. That's how I can count to 12.

Next, I point at each left-hand finger part with my right index finger to raise the count to 24. I've got 5 digits on my right hand and five 12s are 60. That's how I count to 60."

I forwarded this to my Sumerian friend who confirmed that this is indeed the case. He said, "Yes, when I count my fingers in the old way, I come up with 10*"

-e

------

* Base 60

The finger theory sounds plausible, but why not include the bones on left thumb to arrive at base 70 ? On a personal level I understand - I'm always sucking my thumb .

Look at what Hinduism, one of the world's ancient living religion,

claims to have contributed to ancient math and science...amazing!!

http://commonworldinheritage.blogspot.com/2009/06/achievements-of-ancients.html

Amazing, indeed! Here's a little snippet:

Mahabharat is dated at about 6000 years before present, Shrimad Bhagwat ~1000 - 1500 years bp (as far as I can determine).

Just as well they're only claims.

How much research did you do on this fellow (Vartaks) before you posted his list of so-called 'achievements'? And you're calling this 'Hinduism'?

You're kidding, right?

Was there any need to research on him, Vartak, the child of the Moon??? No. Check out the references and they all point to Hindu scriptures, mainly Bhagwat Geeta.

It's the claims which have to be checked for validity otherwise what else are we supposed to be doing here??

The pain is all too much - I'm gonna find me a long forgotten thread and have an entire discussion with myself. Something like 'supping microwave water in a bathtub with my socks on' .

Funnily enough, arriving back at this old chat has been fun. The links are interesting. It's worth getting this archived, but I'm not sure of the official process for doing so.

Just so I don't get skinned, I mentioned a mathematics book somewhere in this thread Scandanavian sounding guy). It's a bit 'light' for many of CR4 calibre, but if you ever get your kids a book on maths it's in my top 10. #1 is a giant picture book, pitched at pre-teens. No ****, the book is excellent. Can't recall the title offhand, but I still read it for inspiration. To this day I am still trying to get my head around the mathematics in Jaeger and Cook's classic tome.