Did Ancient Farming Needs Shape Math and Language Development?

[Isaacsname]

Did mathematics and symbolic and natural languages arise from the necessity of keeping track of astronomical cycles ?

~Population growth cannot be sustained unless you can successfully farm

~You cannot successfully farm unless you keep track of various cycles

~You cannot keep track of anything without natural and symbolic langues

If you look at the ancient system of Mesopotamian { Babylonian, Sumerian, Akkadian } metrology , you can see that both units for measuring time and units for measuring cropland are based on the exact same thing, what they observed in the sky { seconds of time were counted off on the fingers as Lunar arc seconds }

https://en.wikipedia.org/wiki/Ancient_Mesopotamian_units_of_measurement

Ts it a reasonable assumption that mathematics { and natural and symbolic languages } were necessary to allow populations to flourish at all ?

Thanks, just trying to settle a debate I'm having with some friends

 

[micromass]

Any sufficiently complex society will have to develop mathematics in some way or another. Sure, there are many primitive cultures nowadays which do not know mathematics and cannot even count to 10. But once you have a culture which stretches over several big cities, you'll need mathematics.
For example, the need for counting and numbers comes directly from the need of the rulers to calculate and organizing taxes. The need for geometry comes from the need to build complex building, and from dividing land between farmers. Of course, astronomy also plays a big role, since astronomy tells us (for example) when to sow this plant and when to do reap, and whatever.

A lot of civilizations have developed a very solid system of mathematics: the Indians, Chinese, Egyptians, Mesopotamian cultures, the Maya, etc. But it is curious that there is only one civilization which organized math in a deductive form, and which saw math as more than a tool. This was the extra-ordinary accomplishment of the Greek culture.

 

[sophiecentaur]

I think Mathematics developed into a bit of a Frankenstein's monster because it started, as the above posts suggest, as a tool to achieve a defined end. But then it developed a life of its own. The symbols and operations took off in directions that were never anticipated. Amazingly, Maths has now taken the lead in many / most scientific developments and now does the actual driving.
I have a vague uneasiness about this, despite being a total convert to Maths. Could we be missing out on progress in other directions because of the contrictions that Maths imposes on us?
This is a very un -PF topic, of course.

 

[mathman]

I think Mathematics developed into a bit of a Frankenstein's monster because it started, as the above posts suggest, as a tool to achieve a defined end. But then it developed a life of its own. The symbols and operations took off in directions that were never anticipated. Amazingly, Maths has now taken the lead in many / most scientific developments and now does the actual driving.
I have a vague uneasiness about this, despite being a total convert to Maths. Could we be missing out on progress in other directions because of the contrictions that Maths imposes on us?
This is a very un -PF topic, of course.

I disagree completely. Math has a strong role in physics and is very important for some engineering. However biological sciences get by with rather elementary branches, such as basic statistics.

 

[sophiecentaur]

My worry is that Maths, because of its major role in all Science, may be dictating the way we are moving. If you read my post and concluded that I am Maths phobic then you did not get my message. It just concerns me that it is such a major tool in Science that it just could be obscuring some of the possible ways forward. Meanwhile, in the absence of a better tool, I will use and believe the Maths.
Statistics, in its present form, is highly influential in Biology and Medicine. It is the only known way of assessing the reliability of results. I also think that many Biologists could benefit from better Maths ability. But could that start to modify how they work?

 

[Isaacsname]

My apologies if this is off topic, but the only place I will get an educated response is here, I know it's not a pure math topic

Obviously I think it's safe to say, generally,as a growing civilization, if you cannot math you will not eat, would you agree ?

That Stellar, Lunar and Solar calendars { along with intercalations } were counted off on the hand is also quite impressive, imo

 

[Hornbein]

Did mathematics and symbolic and natural languages arise from the necessity of keeping track of astronomical cycles ?

~Population growth cannot be sustained unless you can successfully farm

~You cannot successfully farm unless you keep track of various cycles

~You cannot keep track of anything without natural and symbolic langues

If you look at the ancient system of Mesopotamian { Babylonian, Sumerian, Akkadian } metrology , you can see that both units for measuring time and units for measuring cropland are based on the exact same thing, what they observed in the sky { seconds of time were counted off on the fingers as Lunar arc seconds }

https://en.wikipedia.org/wiki/Ancient_Mesopotamian_units_of_measurement

Ts it a reasonable assumption that mathematics { and natural and symbolic languages } were necessary to allow populations to flourish at all ?

Thanks, just trying to settle a debate I'm having with some friends

I would think that natural languages preceded farming. They are useful for many other things.

I don't think math is needed to keep track of natural cycles. You can just plant when it gets warm enough. It isn't terribly exact.

Counting is needed for barter. Addition and subtraction are needed for bookkeeping any business.

My guess is that math got it's start when land ownership came in. Then surveying was necessary to determine boundary lines exactly. Geometry literally means "measurement of the Earth."

There is a tablet from ancient Babylonia that has a list of Pythagorean triples: integer solutions to a^2 + b^2 = c^2.

 

[micromass]

I don't think math is needed to keep track of natural cycles. You can just plant when it gets warm enough. It isn't terribly exact.

I think you severely underestimate the planning that goes into this. Many ancient texts link farming to astronomical phenomena. See for example Hesoid's "Works and Days". Here is a small part of the poem:

When the Pleiades and Hyades and strong Orion set, remember it is seasonable for sowing. And so the completed year passes beneath the earth.

In the same way, the time for picking grapes arrives

When Orion and Sirius come into mid-sky, and rosy-fingered Dawn looks upon Arcturus

Source and more information: Evans' "The History and Practice of Ancient Astronomy". In fact, I don't think it is very outrageous to say that interest in astronomy comes directly from our interest in time-keeping and farming.

 

[Hornbein]

I think you severely underestimate the planning that goes into this. Many ancient texts link farming to astronomical phenomena. See for example Hesoid's "Works and Days". Here is a small part of the poem:
In the same way, the time for picking grapes arrives
Source and more information: Evans' "The History and Practice of Ancient Astronomy". In fact, I don't think it is very outrageous to say that interest in astronomy comes directly from our interest in time-keeping and farming.

Yes. But you don't need math to see the Pleiades.

 

[micromass]

Yes. But you don't need math to see the Pleiades.

Again, see the book I linked to answer that question!

 

[symbolipoint]

People also developed Mathematics topics just from the desire to explore - even if this meant some kind of exploring other than travel to distant regions or lands.

 

[DiracPool]

This is what always cracks me up about mathematical physicists. They are way better than me at crunching the numbers and always seem to think that, just because they know math better than the average dog, then they are qualified to be experts in every area of science or even every area of life in general. Sorry. This is not the case.

This thread is a case in point. Here we have expert mathematicians who have no idea where the evolution of their trade comes from. This thread is a case in point. The mind wants to fill in the gaps, and if we have some tool that we are somehow miraculously able to wax like complex analysis, then we may naively say, this is the result of some need to do the taxes of traders in ancient Mesopotamia. Didn't happen like that. What about the traders 27,000 years earlier? Or 270,000 years earlier? Why wasn't the needs of their culture at that time the driving force to create a more sophisticated mathematics. You probably don't have an answer for that, do you?

 

[micromass]

This is what always cracks me up about mathematical physicists. They are way better than me at crunching the numbers and always seem to think that, just because they know math better than the average dog, then they are qualified to be experts in every area of science or even every area of life in general. Sorry. This is not the case.

This thread is a case in point. Here we have expert mathematicians who have no idea where the evolution of their trade comes from. This thread is a case in point. The mind wants to fill in the gaps, and if we have some tool that we are somehow miraculously able to wax like complex analysis, then we may naively say, this is the result of some need to do the taxes of traders in ancient Mesopotamia. Didn't happen like that. What about the traders 27,000 years earlier? Or 270,000 years earlier? Why wasn't the needs of their culture at that time the driving force to create a more sophisticated mathematics. You probably don't have an answer for that, do you?

Please enlighten us then.

I do have sources to back up any claim I make.

 

[micromass]

Also, I would be happy if you could give me evidence for any trade between large cities 300,000 years ago...

 

[DiracPool]

Well, let's start here, why was cuneiform invented 5500 years ago and not before then? What was the precipitate that fomented that?

 

[DiracPool]

Also, I would be happy if you could give me evidence for any trade between large cities 300,000 years ago...

I'm have no evidence for trade back then because there were no large cities before 6000 BCE.

 

[micromass]

Well, let's start here, why was cuneiform invented 5500 years ago and not before then? What was the precipitate that fomented that?

Can we not play games? Just tell us your point of view.

 

[micromass]

I'm have no evidence for trade back then because there were no large cities before 6000 BCE.

Right, exactly my point ;)

 

[DiracPool]

Can we not play games? Just tell us your point of view.

Absolutely. Here's the skinny. Mathematical ability in humans derived from operational motor skills abstracted to internal thought process...

 

[micromass]

Absolutely. Here's the skinny. Mathematical ability in humans derived from operational motor skills abstracted to internal thought process...

Any more detail?
Any evidence to back this up?
Any explanations why humans developed mathematics only recently, while they did have the ability for a long time?

 

[DiracPool]

Let's just say, that, as children we play with blocks and tinker toys, and Lincoln logs, and we develop motor patterns to manipulate things. In the mind, we represent the addition of two number as the psychomotor manual operation of combining two objects together, We represent subtraction as separating two objects. It's the feedback of the manual on the perception that makes the math gears work. Higher mathematical abstraction just go from there. If you want references, I can provide them.. But I've said too much already..

 

[micromass]

OK, so you have got nothing substantial. Got it.

 

[DiracPool]

OK, so you have got nothing substantial. Got it.

I've got plenty substantial, what do you want?

 

[DiracPool]

Any evidence to back this up?

You can read Jean Piaget's "Psychology of the Child" or "Genetic Epistemology" for starters. There's an journal called "Cognitive development" that I can refer you to many articles there if you want to further peruse.

 

[micromass]

You can read Jean Piaget's "Psychology of the Child" or "Genetic Epistemology" for starters. There's an journal called "Cognitive development" that I can refer you to many articles there if you want to further peruse.

And how is any of this relevant to ancient civilizations?

 

[DiracPool]

Any explanations why humans developed mathematics only recently, while they did have the ability for a long time?

Yes, I do have an explanation. In fact, I'm writing a paper on it right now. However, per PF guidelines, I'm not going to talk about model. Let's just say, though, it has to do with the recent genetic evolution of ASPM and other related microcephaly genes, and I'm not forgetting duplicons such as DUF1220 and dozens of others. I do my homework;

http://www.scientificamerican.com/article/a-missing-genetic-link-in-human-evolution/
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4114149/
http://www.ncbi.nlm.nih.gov/pubmed/17604569
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2409108/pdf/joa0212-0337.pdf
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2988714/pdf/1471-2121-11-85.pdf
etc.

 

[micromass]

So there is a genetic cause to math ability, you say? Of course. But that means we only evolved to obtain this ability 5000 years ago? If not, why didn't we develop math earlier?

 

[DiracPool]

And how is any of this relevant to ancient civilizations?

It's relevant to ancient civilizations in the fact that you have you no idea how you are able to manipulate symbols in the manner that allows you to wax functional analysis yet you want to make a comment on how you do so. I'ts not a cultural thing. It has nothing (or little after the fact) to do with keeping the books the ancient Mesopotamia. So I'm just trying to right the record.

 

[DiracPool]

So there is a genetic cause to math ability, you say? Of course. But that means we only evolved to obtain this ability 5000 years ago? If not, why didn't we develop math earlier?

As I said, this goes into my personal theories, but. let me turn the question to you, why didn't we develop the ability prior to 5000 years ago?

 

[micromass]

As I said, this goes into my personal theories, but. let me turn the question to you, why didn't we develop the ability prior to 5000 years ago?

I have no idea, but I would be interested in an answer that isn't personal theory.

 

[DiracPool]

I have no idea, but I would be interested in an answer that isn't personal theory.

Lol. Well, this is the cutting edge micromass, there is no answer right now other than my personal theory. At least from where I sit. If you want me to go further, I'd be happy to

 

[micromass]

Lol. Well, this is the cutting edge micromass, there is no answer right now other than my personal theory. At least from where I sit. If you want me to go further, I'd be happy to

OK cool. Next time, could you please indicate that you don't have any (accepted) solution to this yourself? It seemed in your post that you disagreed with my interpretation and that you had a better one. It would be fun to know beforehand that you don't.

 

[symbolipoint]

As I said, this goes into my personal theories, but. let me turn the question to you, why didn't we develop the ability prior to 5000 years ago?

No. This is the wrong thinking. We humans must take mathematics through its evolution. Mathematical explorers can only use what they have and is available to them at that time. Once in a while, a genius or other hardworking person makes a strikingly significant development.

 

[DiracPool]

OK cool. Next time, could you please indicate that you don't have any (accepted) solution to this yourself? It seemed in your post that you disagreed with my interpretation and that you had a better one. It would be fun to know beforehand that you don't.

Ok, I'll grant you the "accepted" status

 

[DiracPool]

No. This is the wrong thinking. We humans must take mathematics through its evolution. Mathematical explorers can only use what they have and is available to them at that time. Once in a while, a genius or other hardworking person makes a strikingly significant development.

I completely agree with this, but this is an after the 5500 years ago argument. After 5500 years ago, you are perfectly right, but why was there nothing prior to 5500 years ago?