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history of indian mathematics

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Seva Lamberdar
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Post by MaxEntropy_Man Sun May 05, 2013 7:14 pm

https://www.youtube.com/watch?v=pElvQdcaGXE

https://www.youtube.com/watch?v=DeJbR_FdvFM

i'd like to watch the whole thing if it's available somewhere and would have been nicer without the exoticization.
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Post by MaxEntropy_Man Sun May 05, 2013 7:23 pm

madhava's sine table: http://en.wikipedia.org/wiki/Madhava's_sine_table

it totally makes my hair stand on end!
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Post by bw Sun May 05, 2013 7:41 pm

MaxEntropy_Man wrote:
i'd like to watch the whole thing if it's available somewhere and would have been nicer without the exoticization.










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Post by MaxEntropy_Man Sun May 05, 2013 7:55 pm

thank you!
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Post by rawemotions Sun May 05, 2013 11:56 pm

http://en.wikipedia.org/wiki/Jya

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Post by Seva Lamberdar Mon May 06, 2013 5:52 am

Earliest humans made use of numbering / counting in quite a variety of things and applications. According to a number of Vedic hymns, number 7 was very important (indicating that people were counting at least upto 7 at that time using different numbers, 1, 2, 3 ...) and people used 7 in laying down the sticks in yajna (7 sticks of wood per layer). Based on the 7 colors in the rainbow perhaps (amazing observation at that time), they also assigned 7 horses to Surya's chariot and might have concluded that the white light was composed of seven components (colors).
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Post by MaxEntropy_Man Mon May 06, 2013 7:06 am

most indians i have met keep harping about the indian discovery of zero or clever ways of doing arithmetic, but as i may have said here before, the discoveries the kerala school mathematicians made go far beyond all that. they discovered series approximations to pi and gave series representations of trig functions well before they were rediscovered (that's what one has to call it) in the west.

for example this series widely attributed to leibniz was discovered by madhava, the founder of the kerala school two centuries earlier!

pi/4 = 1-1/3+1/5-1/7+....

it is only recently people in the west have started calling it the madhava-leibniz series. this and other series came out of the discovery of calculus, which means it is very likely that kerala guys also figured out at least some calculus before newton and leibniz.
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Post by MaxEntropy_Man Mon May 06, 2013 7:32 am

rawemotions wrote:http://en.wikipedia.org/wiki/Jya

there is not much mathematics in that link. here is a more detailed link of the algorithm described by madhava's followers for calculating trig functions as series and attributed by them to him (again a full two centuries earlier than newton and leibniz):

http://en.wikipedia.org/wiki/Madhava_series
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Post by Seva Lamberdar Mon May 06, 2013 10:13 am

MaxEntropy_Man wrote:most indians i have met keep harping about the indian discovery of zero or clever ways of doing arithmetic, but as i may have said here before, the discoveries the kerala school mathematicians made go far beyond all that. they discovered series approximations to pi and gave series representations of trig functions well before they were rediscovered (that's what one has to call it) in the west.

for example this series widely attributed to leibniz was discovered by madhava, the founder of the kerala school two centuries earlier!

pi/4 = 1-1/3 1/5-1/7 ....

it is only recently people in the west have started calling it the madhava-leibniz series. this and other series came out of the discovery of calculus, which means it is very likely that kerala guys also figured out at least some calculus before newton and leibniz.

There shouldn't be any surprise about these great achievements by Indians in science and mathematics.

Indians had already demonstrated great inquisitiveness, logic and depth in their thinking related to philosophy.

Several thousand years ago Jaimini in India tried to systematize the entire Vedic literature on the basis of proper enquiry and reasoning in Mimamsa (Purva Mimamsa), http://www.geocities.ws/lamberdar/purva_mimamsa.html

The systematic development of knowledge related to the world of matter by Indians is further evident in Vaisesika (the philosophy of atomistic pluralism), http://www.geocities.ws/lamberdar/vaisesika.html

Similarly, the great exploration of mind in Samkhya by Indians was far ahead of its time. The practical aspects of Samkhya in the form of Yoga and Yoga philosophy are now being used all over the world to study and use the mind properly.

Even the expression of the Supernatural (Brahman) by Badarayana in the Braham Sutra (Vedanta Sutra) was extremely broad and deep. As Vedanta, it encompasses majority of the religious / theological considerations (thoughts) today.
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Post by MaxEntropy_Man Mon May 06, 2013 11:32 am

seva: your writeups have nothing to do with the mathematical work done by the kerala school of mathematicians, but with vedanta. i am sure your writeup is valuable to those interested in the subject, but i have no interest in vedanta or philosophy in general. my earlier posts in this thread have to do with the work indians did in mathematics. while it may not be surprising, their work is not well known in the west. i believe it is time they were given the credit due to them.
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Post by Guest Mon May 06, 2013 12:54 pm

tl;dr

[my lone post for today]

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Post by Seva Lamberdar Mon May 06, 2013 12:59 pm

Huzefa Kapasi wrote:tl;dr

[my lone post for today]

why?
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Post by Guest Mon May 06, 2013 1:04 pm

Seva Lamberdar wrote:
Huzefa Kapasi wrote:tl;dr

[my lone post for today]

why?
why did you highlight my "my lone post for today?" are you refering to that or to "tl;dr?"

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Post by Seva Lamberdar Mon May 06, 2013 1:07 pm

if I hi-lited something and then responded, then that's that.
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Post by Marathadi-Saamiyaar Mon May 06, 2013 1:20 pm

bw wrote:
MaxEntropy_Man wrote:
i'd like to watch the whole thing if it's available somewhere and would have been nicer without the exoticization.










Actually, it will be good to bookmark the page (I did) and let the kids watch the relevant sections before touring/visiting any of these sites. Some interested kids will be all excited and realize the importance of history, heritage, and their direct relevance to what they study today.

Most often, kids are not told why math, physics, or history/geography is relevant to the present day daily lives and incidents.

Thanks BW.

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Post by Guest Mon May 06, 2013 1:28 pm

Seva Lamberdar wrote:if I hi-lited something and then responded, then that's that.
the discussions/threads in this site are utterly butterly boring. sorry, but that is the way it is. things might change tomorrow if tomorrow ever comes.

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Post by Seva Lamberdar Mon May 06, 2013 1:31 pm

MaxEntropy_Man wrote:seva: your writeups have nothing to do with the mathematical work done by the kerala school of mathematicians, .....

Max, my comment highlighting the exhaustive, systematic and logical approach by ancient Indians in the development of various philosophies such as Mimamsa (ancient texts and practices), Vaisesika (world of matter), Samkhya (world of experience) and Vedanta (the supernatural) was not an effort to undermine or ignore the works of mathematicians, especially the work done by the Kerala school of mathematicians. I just wanted to add (in terms of ancient Indians' scholarly achievements) to what you wrote earlier, "most indians i have met keep harping about the indian discovery of zero or clever ways of doing arithmetic.... ".
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Post by Seva Lamberdar Mon May 06, 2013 1:46 pm

Huzefa Kapasi wrote:
Seva Lamberdar wrote:if I hi-lited something and then responded, then that's that.
the discussions/threads in this site are utterly butterly boring. sorry, but that is the way it is. things might change tomorrow if tomorrow ever comes.

We had an engineering student in our class. He said one day "why are we learning and going over these complicated and boring derivations for various formulas, since in most of our practical applications during job we will be just opening the Handbook, pick out a formula or equation and use it to solve our problem?"
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Post by Jeremiah Mburuburu Mon May 06, 2013 4:50 pm

Huzefa Kapasi wrote:
Seva Lamberdar wrote:if I hi-lited something and then responded, then that's that.
the discussions/threads in this site are utterly butterly boring. sorry, but that is the way it is. things might change tomorrow if tomorrow ever comes.
they won't, if tomorrow brings you and TMB to this site.

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Post by Idéfix Mon May 06, 2013 5:57 pm

Thanks Max and BW for posting these videos. This series looks very promising.
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Post by Guest Tue May 07, 2013 12:42 am

Jeremiah Mburuburu wrote:
Huzefa Kapasi wrote:
Seva Lamberdar wrote:if I hi-lited something and then responded, then that's that.
the discussions/threads in this site are utterly butterly boring. sorry, but that is the way it is. things might change tomorrow if tomorrow ever comes.
they won't, if tomorrow brings you and TMB to this site.
i am back and it appears so are you. let's rock the partyyyyy!

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Post by Seva Lamberdar Tue May 07, 2013 10:32 am

Btw if someone is wondering about why I didn't mention Nyaya when I briefly talked earlier about the other five Brahmanical / Vedic philosophies (Mimamsa or Purva Mimamsa, Vedanta, Samkhya, Yoga and Vaisesika), well, here it is...

Nyaya darshana (or the Logicism), like Vaisesika (philosophy of atomistic pluralism), relates to the material world. While the latter (Vaisesika) explores the world in detail at the minute (constituent) scale, the former (Nyaya) looks into the causes and processes applicable to the world on the whole. In other words, Vaisesika is a build up of the world from the elementary (microscopic) level, whereas Nyaya looks at things and processes in a more general way (at macroscopic level).
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Post by Propagandhi711 Tue May 07, 2013 11:50 am

Seva Lamberdar wrote:Btw if someone is wondering about why I didn't mention Nyaya when I briefly talked earlier about the other five Brahmanical / Vedic philosophies (Mimamsa or Purva Mimamsa, Vedanta, Samkhya, Yoga and Vaisesika), well, here it is...

Nyaya darshana (or the Logicism), like Vaisesika (philosophy of atomistic pluralism), relates to the material world. While the latter (Vaisesika) explores the world in detail at the minute (constituent) scale, the former (Nyaya) looks into the causes and processes applicable to the world on the whole. In other words, Vaisesika is a build up of the world from the elementary (microscopic) level, whereas Nyaya looks at things and processes in a more general way (at macroscopic level).

congrats seva on explaining how nyaya looks at process controls on a macro level while vaiseka does micro level analysis. putting these together it seems like we have a good system architecture and process to address issues arising due to elementary misunderstandings and malfunctionings of global supply chain of ideas

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Post by Seva Lamberdar Tue May 07, 2013 1:22 pm

Let's keep the things simple Propa, without dragging the latest computer oriented process controls and system architecture into the study of Vaisesika and Nyaya philosophies.
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Post by Seva Lamberdar Wed May 08, 2013 11:13 am

Seva Lamberdar wrote:Let's keep the things simple Propa, without dragging the latest computer oriented process controls and system architecture into the study of Vaisesika and Nyaya philosophies.
Btw if anyone is interested in reading more about the theological aspect (in terms of connection to Brahman) about these and other Indian philosophies, here is the link ....
https://such.forumotion.com/t11338-theistic-and-non-theistic-hindu-philosophies
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