3,700-year-old Babylonian tablet rewrites history of Trigonometry

Maths is the true universal Language through time.

.. the first ancient culture that used the number zero was indian.

a reply to: anti72

Not to take away from the substantial contributions to mathematics by Indians like Brahmagupta in the 9th century, we have to give credit where credit is due and acknowledge that that Maya utilized zero as both a placeholder and a numerical concept hundreds of years prior to the Indians and Greeks. The Maya had a base 20 system that included zero by 650 CE with use of zero going back much earlier while the Indian mathematicians didn't start to utilize zero in such a way until the 9th century and over at least a millennia spanning Mesopotamia and Babylon, concepts of zero weren't really used, at least not as a numerical value and sporadically so a sense a place holder. For an interesting historical look at the topic, I would suggest reading this- www-history.mcs.st-and.ac.uk...

originally posted by: Blackfinger
Maths is the true universal Language through time.

I love it! I hate to say it but as a nerd, Trig and Calculus were very interesting because every line, curve or object you can think of can be defined with a mathematical equation. Chemistry and Physics thrive.

Math doesn't lie. The IPCC liars are exposed due to others doing their math....

originally posted by: punkinworks10
a reply to: Harte

It is absolutley a trig table.
You have every thing you need, the value of the tangent, the length of the sine leg and the length of the hypotenuse.

How can that not be a trig table?


The table increments from ~44-3/4° down to 32°ish, by ~1/2° increments but varies a little.

The base 60 system make for very cumbersome computation, using only integers and all.

It's not a "true" trig table because it only uses whole numbers for the hypotenuse of the triangles.
There are an infinite number of ratios not calculated there.
What I'm saying is that it only uses Pythagorean triples.
For example, Is there a ratio present for a triangle with legs of length 6 and 7?

The discovery of so many Pythagorean triples is far more impressive than the ability to divide two whole numbers though.

Harte

originally posted by: Harte

originally posted by: punkinworks10
a reply to: Harte

It is absolutley a trig table.
You have every thing you need, the value of the tangent, the length of the sine leg and the length of the hypotenuse.

How can that not be a trig table?


The table increments from ~44-3/4° down to 32°ish, by ~1/2° increments but varies a little.

The base 60 system make for very cumbersome computation, using only integers and all.

It's not a "true" trig table because it only uses whole numbers for the hypotenuse of the triangles.
There are an infinite number of ratios not calculated there.
What I'm saying is that it only uses Pythagorean triples.
For example, Is there a ratio present for a triangle with legs of length 6 and 7?

The discovery of so many Pythagorean triples is far more impressive than the ability to divide two whole numbers though.

Harte

Still if this is just Geometry, it would have to be the beginnings of Trigonometry. Do reporters of any news spend time thinking clearly anymore or avoiding grandstanding to make it better click bait so we will click it? Not many IMO.

originally posted by: peter vlar
a reply to: anti72

Not to take away from the substantial contributions to mathematics by Indians like Brahmagupta in the 9th century, we have to give credit where credit is due and acknowledge that that Maya utilized zero as both a placeholder and a numerical concept hundreds of years prior to the Indians and Greeks. The Maya had a base 20 system that included zero by 650 CE with use of zero going back much earlier while the Indian mathematicians didn't start to utilize zero in such a way until the 9th century and over at least a millennia spanning Mesopotamia and Babylon, concepts of zero weren't really used, at least not as a numerical value and sporadically so a sense a place holder. For an interesting historical look at the topic, I would suggest reading this- www-history.mcs.st-and.ac.uk...

The Graham Hancock and I suppose the Ancient Aliens program have some curious questions worthy of answer about the connections. Graham more scientifically accurate to look at it for what is on the ground and call it an ancient civilization. We know what AA preaches and that is not impossible just far fetched speculation to many.

originally posted by: Justoneman

originally posted by: Harte

originally posted by: punkinworks10
a reply to: Harte

It is absolutley a trig table.
You have every thing you need, the value of the tangent, the length of the sine leg and the length of the hypotenuse.

How can that not be a trig table?


The table increments from ~44-3/4° down to 32°ish, by ~1/2° increments but varies a little.

The base 60 system make for very cumbersome computation, using only integers and all.

It's not a "true" trig table because it only uses whole numbers for the hypotenuse of the triangles.
There are an infinite number of ratios not calculated there.
What I'm saying is that it only uses Pythagorean triples.
For example, Is there a ratio present for a triangle with legs of length 6 and 7?

The discovery of so many Pythagorean triples is far more impressive than the ability to divide two whole numbers though.

Harte

Still if this is just Geometry, it would have to be the beginnings of Trigonometry. Do reporters of any news spend time thinking clearly anymore or avoiding grandstanding to make it better click bait so we will click it? Not many IMO.

I agree that it IS trigonometry. What I'm saying is that it is not the trigonometry that gave (some of) us headaches in High School.
As far as reporters go, I imagine that the percentage of them that understand trig is small. But the headline is technically correct anyway.
Lastly, finding Pythagorean triples isn't really geometry. The way I see it, these triples show a more advanced mathematics than the trigonometry does.

Harte

originally posted by: SlapMonkey
Just imagine the knowledge that was lost with the destruction of the Alexandria Library.

Many people scoff at the idea that we are a people with amnesia about the knowledge from antiquity, but it seems like every year, there is more and more absolute, concrete proof of this reality.

I hear Yeah ,,, Lost of Knowledge let alone , Technology was Lost by Raiders, Conquerors , & from RELIGION!
just as ISIS has Done Today , and here in the States ( recently ) b

Here is a List : of the Cause :
List of destroyed libraries
en.wikipedia.org...



Maya codices of the Yucatán is One that is Bothersome

We could of Learned So Much , from the Mayan Civilization
instead of Guess Working of their Culture and HISTORY

Destroyed by the Spanish thought it was made by heretics!!

We found a large number of books in these characters and, as they contained nothing in which were not to be seen as superstition and lies of the devil, we burned them all, which they regretted to an amazing degree, and which caused them much affliction.

- Bishop Diego de Landa

Maya codices
en.wikipedia.org...

Diego de Landa
en.wikipedia.org...

originally posted by: Wolfenz

originally posted by: SlapMonkey
Just imagine the knowledge that was lost with the destruction of the Alexandria Library.

Many people scoff at the idea that we are a people with amnesia about the knowledge from antiquity, but it seems like every year, there is more and more absolute, concrete proof of this reality.

I hear Yeah ,,, Lost of Knowledge let alone , Technology was Lost by Raiders, Conquerors , & from RELIGION!
just as ISIS has Done Today , and here in the States ( recently )

b

Here is a List : of the Cause :
List of destroyed libraries
en.wikipedia.org...



Maya codices of the Yucatán is One that is Bothersome

We could of Learned So Much , from the Mayan Civilization
instead of Guess Working of their Culture and HISTORY

Destroyed by the Spanish thought it was made by heretics!!

We found a large number of books in these characters and, as they contained nothing in which were not to be seen as superstition and lies of the devil, we burned them all, which they regretted to an amazing degree, and which caused them much affliction.

- Bishop Diego de Landa

Maya codices
en.wikipedia.org...

Diego de Landa
en.wikipedia.org...

Several codices survived, you know. They are remarkable, but not that remarkable.
So it's not all just "guesswork."

Harte

originally posted by: IAMTAT
If it's so much more accurate than Base 10...Why don't we use Base 60 today?

Accurate doesn't mean easy to use. Could it be that we are losing intelligence as time progresses? Or maybe, back then, there existed hybrids or other beings or something different about the humans or at least some, maybe something in their diet, the water or air or their behaviors or rituals or daily lives that enhanced their minds to be able to use this system.

Base 10 is so easy... too tempting... what would possess them to try anything else? Its a mystery to me.

originally posted by: 3n19m470

originally posted by: IAMTAT
If it's so much more accurate than Base 10...Why don't we use Base 60 today?

Accurate doesn't mean easy to use. Could it be that we are losing intelligence as time progresses? Or maybe, back then, there existed hybrids or other beings or something different about the humans or at least some, maybe something in their diet, the water or air or their behaviors or rituals or daily lives that enhanced their minds to be able to use this system.

Base 10 is so easy... too tempting... what would possess them to try anything else? Its a mystery to me.

The advantage of using 60 is that it is divisible by so many numbers 2, 3, 5, 6, 10, 12, 15, 20, 30. Next big number is 360.

We use 60 minutes in an hour. How many intervals of 30 minutes are in an hour? 15 minutes? 10 minutes? 5 minutes? We haven't lost that intuition. That's calculating reciprocals. We just use it in a different way. Anything can learnt off by heart like times tables. It's just whether it's woth spending all that time learning that information.

What happens is that we find ways of doing things automatically. With weaving, it took four artisans sitting around a loom, constantly lifting up and lowering the treadle, shuflling the shuttle across from side to side, changing thread colors, and in the end no too garments would be exactly identical. Replace that with punched card looms, a waterwheel, automatic thread switching, precision engineering with metals, and all that can be done automatically, allowing more time to be spent adding frills and embellishments.

That carries onto mechanical computing. We used to employ people to calculate harbour tide tables by hand. Work would be sent out by post and then returned when the "computers" had finished their calculations. That was replaced by mechanical gear computers, then valve based systems, transistors, electronic computers, digital computers. Now we are onto supercomputers, cloud computing and neural networks.

With mechanical engineering, designing a new car would involve getting the designer to make a design using spline rulers - flexible pieces of wood that could be pinned into shape. By their physical structure, they would always create the most "relaxed" curve which spread all the tension across the curve rather than being pinched at any one place. Then that design would be sent to the modelling shop who would spend several weeks or months making a clay model. Once approved, that would go through to the windtunnel guys, who would put the model in a tunnel, record smoke trails going around the model, then send that back to the designer. That could take weeks or months. Then any changes would affect the space for door handles, locks, engine, wheel axles, and the process would repeat.

Now, designers have CAD/CAM/FEA/CFD software that lets them design the vehicle, test for any awkward joints, then run a virtual wind tunnel, all within a couple of hours. Virtual reality software allows for a vehicle to be inspected for ease of use before even a single panel is pressed out. Having systems that provide virtual tactile feedback is the next stage.

Harte,
More advanced than "trig", in that it appears to me to that they used some sort if progression to generate the values in the table, which by the way has a real world application, that nobody has hit on yet.
It is a table for the values of the angle of repose,
32° to 45° in 1/4 and 1/2 degree increments.
Since a good portion of the written record left by the mesopotamians is business related, I see how this partucular tablet is useful on a day to day basis.
Why would a business man need to know the angles of repose?

Because is used to estimate the volume of a large pile of a commodity, such as grains.

I would bet that this tablet had a companion table of conic volumes ratios.

a reply to: seasonal

You mortals carbon-dating system is off by 78% if not worst, that's all I have to say.

Ah, so brown people knew trigonometry before whites? Interesting. Oh, all foundations of civilizations were developed by brown people, not white?

This is news /end sarcasm

originally posted by: ImmortalLegend527
a reply to: seasonal

You mortals carbon-dating system is off by 78% if not worst, that's all I have to say.

Good thing that this tablet wasn't dated via 14C then right? But then again one would have to be invested in knowing something about the artifact in question prior to making dumbed down statements from a point of ignorance right? It's a pretty well known piece. One doesn't have to be well versed in all of Kramer's work for example, to get a basic understanding of it. But being a mystical and magical immortal you should know all of this right?

Just in case any of the mere mortals are curious, I'll break it down quickly for you. The piece was found at what was once the city of Larsa. Like all cuneiform, there are tell tale differences that can be attributed to not just geographical location but it's chronological origin as well. This tablet shares specific characteristics with many other administrative documents from Larsa during the period between 1822 and 1784 BCE that have dates inscribed into the tablets. Plimpton 322 was dated through comparative analysis, no radiometric dating was used on the artifact.

So perhaps you could give us all some insight as to why the dates are inaccurate being that were all just mere mortals and couldn't possibly compete with your personal insight into the matter?

a reply to: FelisOrion

Ah, so brown people knew trigonometry before whites? Interesting. Oh, all foundations of civilizations were developed by brown people, not white?

I know it was sarcasm, but if I remember well, the genetics for white skin came later, for adaptation to nordic low light for vit. D production. So basically, yes, colored skin came before, possibly already at work with triangle.

Practically speaking, this isn't as surprising as most people are saying.

Look at what they built: structures which seemed to entail advanced mathematical knowledge.

Math is great, but what a disastrous psychological error it is to believe that math corresponds to the nature of reality.

Reality is irrational. Non-Linear is the only way it can truly be described. We are analogical creatures first and foremost, followed by a recently evolved capacity to digitize our relatedness to the world in terms of ideal i.e. divisible numbers.

This definitely enables us to create in ways that allow us to learn more and more about the way reality operates, but it also exposes our limits in knowing completely i.e. without a remainder that lies "outside" our structures; It will always be the case that analogical processes, occurring within a finite, granular, and relational ontology, forms the way reality operates.

Again, religious fantasy - whether Pythagorean, Babylonian, or Kurzwelian - should be recognized as corrosive to the intellect.

originally posted by: Harte

originally posted by: Wolfenz

originally posted by: SlapMonkey
Just imagine the knowledge that was lost with the destruction of the Alexandria Library.

Many people scoff at the idea that we are a people with amnesia about the knowledge from antiquity, but it seems like every year, there is more and more absolute, concrete proof of this reality.

I hear Yeah ,,, Lost of Knowledge let alone , Technology was Lost by Raiders, Conquerors , & from RELIGION!
just as ISIS has Done Today , and here in the States ( recently )

b

Here is a List : of the Cause :
List of destroyed libraries
en.wikipedia.org...



Maya codices of the Yucatán is One that is Bothersome

We could of Learned So Much , from the Mayan Civilization
instead of Guess Working of their Culture and HISTORY

Destroyed by the Spanish thought it was made by heretics!!

We found a large number of books in these characters and, as they contained nothing in which were not to be seen as superstition and lies of the devil, we burned them all, which they regretted to an amazing degree, and which caused them much affliction.

- Bishop Diego de Landa

Maya codices
en.wikipedia.org...

Diego de Landa
en.wikipedia.org...

Several codices survived, you know. They are remarkable, but not that remarkable.
So it's not all just "guesswork."

Harte

I knew you would say something Harte .. LOL

of course I know that.. it Survived just 3 and a partial 4

I posted a link about them : Did I Not ?

Most of it is Guess Work you think the Mayans just made a Few of them ?

a Large Number of them according to the Sick Minded Bishop Diego de Landa

but how many!! were they, hundreds? thousands ?

that is a Fact what - Diego de Landa had written.

again Harte, seem like your Trolling .

Again Lost History that could of mentions about not only the Mayans but Aztecs and INCAS! Peru Bolivia... Tiwanaco / Puma Punku for example :

etc.. more Likely may of telling the tale they are descendants of a more Advanced Civilization.
like Egypt , Sumaria , INDIA , Greeks , as Most Stories had gone that Route..

Trigonometry : and PIE , but Egyptian math is so Awesome and Easier on the Mind


here ya go folks!!

you may learn something :

www.youtube.com...



Ive known this since for the last 30ish years

a reply to: Wolfenz

I find it far more probable (though for you, less palatable) that elitism provokes wishful and dissociative thinking i.e. results in collapse, then that anything that comes from such traditions i.e. "ancient civilizations" before our own, prove to be true.

Consider the conditions that are required for mathematics. Is it possible, perhaps, that the human brain, and that human beings working together in relatively developed contexts, are able to 'touch upon' a system of knowledge that, because it is rational and reasonable, is able to be reinvented again and again?

This seems far more plausible to me than to believe, without any significant evidence, that ancient cultures - fundamentally elitist, and therefore, structurally biased by their social-advantages-over-others - were somehow carriers of a civilization that preceded our own - again, with no evidence.

This is what is meant by the term, a "just-so story". It's coherent, given your own life history and emotional needs; but is true? You can't even relate to what you write without a fanatical emotionality - basically meaning, in effect, that you aren't comfortable speaking in ways that are more tentative - because its justified by reason of not having definitive proof.

Yet, being controlled by your emotions - and a religious faith in numbers - the belief in numbers is what makes you feel good; hence, you believe what you believe. The linguistically coded belief, a later evolutionary and development function of the brain-mind, exists merely to control and regulate the affective dynamics that have been released in you by interpersonal interactions i.e. you too are an object, with structuring principles - 86 billion neurons involved in the regulation and representation of 50-75 trillion cells. How this massive 'body' operates, not surprising, is a function of the the geometry of the physical self-organization of other human bodies - for the simple reason that human minds are an emergent function of intersubjective engagements with others.

In other words, and as simple and obvious as it may sound, what you believe is a myth. A myth you believe because it makes you feel better.