The Five Sciences and Buddhism

[Indrajala]

In ancient Mahāyāna there developed an appreciation for the five sciences (pañca-vidyā), a kind of extracurricular set of pursuits that a bodhisattva could pursue for the benefit of beings. They include:

-grammar and composition (śabda-vidyā)
-the arts and mathematics (śilpakarma-sthāna-vidyā)
-medicine (cikitsā-vidyā)
-logic-epistemology (hetu-vidyā)
-philosophy (adhyātma-vidyā)

This perhaps reflects a more intellectual side to Indian Buddhism, but nevertheless the idea is that if someone is able they can and should pursue such studies as it enables a practitioner to further understand and benefit the world while more efficiently operating within it. It may not be directly aimed at liberation, but such knowledges are still useful nevertheless.

So how do you personally feel about studying such subjects? Do you think they would be worthwhile? If you have studied them, do you feel it benefits you as a practitioner? Have you helped others as a result?

[Malcolm]

In ancient Mahāyāna there developed an appreciation for the five sciences (pañca-vidyā), a kind of extracurricular set of pursuits that a bodhisattva could pursue for the benefit of beings. They include:

-grammar and composition (śabda-vidyā)
-the arts and mathematics (śilpakarma-sthāna-vidyā)
-medicine (cikitsā-vidyā)
-logic-epistemology (hetu-vidyā)
-philosophy (adhyātma-vidyā)

This perhaps reflects a more intellectual side to Indian Buddhism, but nevertheless the idea is that if someone is able they can and should pursue such studies as it enables a practitioner to further understand and benefit the world while more efficiently operating within it. It may not be directly aimed at liberation, but such knowledges are still useful nevertheless.

So how do you personally feel about studying such subjects? Do you think they would be worthwhile? If you have studied them, do you feel it benefits you as a practitioner? Have you helped others as a result?

Having studied them all, they are useful, especially medicine and adhyātma-vidyā

[Sherlock]

What constitutes the fine arts exactly? In the Tibetan context there is painting and sculpture of course but is mathematics included as well?

[Indrajala]

Having studied them all, they are useful, especially medicine and adhyātma-vidyā

What prompted you to study medicine? Was it a long-term interest or something that was sparked at some particular point?

[viniketa]

It may not be directly aimed at liberation, but such knowledges are still useful nevertheless.

I've studied all, as well. But then, I've never understood the concept of 'useless knowledge'.

So how do you personally feel about studying such subjects?

Personally, I've never met an area of knowledge I didn't like.

Do you think they would be worthwhile?

All of these can be particularly worth while in understanding our own minds and in generating bodhicitta.

If you have studied them, do you feel it benefits you as a practitioner?

Yes, although certainly not as a 'basis' of practice.

Have you helped others as a result?

Time will tell, but, yes.

[Dave The Seeker]

So how do you personally feel about studying such subjects? Do you think they would be worthwhile?

I believe studies to further our knowledge is a great benefit to us as well as other living beings.

If you have studied them, do you feel it benefits you as a practitioner? Have you helped others as a result?

I have studied them all, some to greater degrees than others, and yes I think it has benefited me. Before I began practicing Buddhism and much more since. Also I think knowledge is power, that power is the ability to help others. So the more one knows the more one can benefit all living beings

[Malcolm]

Having studied them all, they are useful, especially medicine and adhyātma-vidyā

What prompted you to study medicine? Was it a long-term interest or something that was sparked at some particular point?

I became interested in herbal medicine, and then the opportunity arose to study tibetan medicine. Glad I did.

M

[Sherlock]

This is a Chinese summary of silpakarmasthana-vidya from Baidu

工巧明
　　包括的范围很广，据《瑜伽师地论》卷十五“工业明处”称：农，商，事王，书、标、计度、数、印，占相，咒术，营造（雕塑），生成（豢养六畜等），防那（纺织、编织、缝纫），和合（调解争讼），成熟（饮食业），音乐等十二种均属此。

It includes agriculture, trade, printing, mathematics, craftsmanship, cooking, music and more according to the Yogacarabhumisastra. Interesting, when I go to university I plan to base my education around the panca-vidya as far as possible.

[kirtu]

In ancient Mahāyāna there developed an appreciation for the five sciences (pañca-vidyā), a kind of extracurricular set of pursuits that a bodhisattva could pursue for the benefit of beings. They include:

-grammar and composition (śabda-vidyā)
-the arts and mathematics (śilpakarma-sthāna-vidyā)
-medicine (cikitsā-vidyā)
-logic-epistemology (hetu-vidyā)
-philosophy (adhyātma-vidyā)

This perhaps reflects a more intellectual side to Indian Buddhism, but nevertheless the idea is that if someone is able they can and should pursue such studies as it enables a practitioner to further understand and benefit the world while more efficiently operating within it. It may not be directly aimed at liberation, but such knowledges are still useful nevertheless.

So how do you personally feel about studying such subjects? Do you think they would be worthwhile? If you have studied them, do you feel it benefits you as a practitioner? Have you helped others as a result?

Having studied them all, they are useful, especially medicine and adhyātma-vidyā

Having studied all of them except medicine, mathematics and logic are the most useful.

Of course this just means that particular people have particular affinities with different fields of study.

Kirt

[Malcolm]

Having studied all of them except medicine, mathematics and logic are the most useful.

Of course this just means that particular people have particular affinities with different fields of study.

Kirt

Adhyātma vidya means Buddhism i.e. the inner sciences.

Math does not really mean math as you understand it -- it means calculating calendars, mostly.

[kirtu]

It may not be directly aimed at liberation, but such knowledges are still useful nevertheless.

I've studied all, as well. But then, I've never understood the concept of 'useless knowledge'.

Then you aren't an American because American culture has radical utilitarianism (and a fair dose of anti-intellectual feeling - really a more anti-learning feeling combined with an explicit ceding of responsibility for decision making to experts in the guise of X knows more about this than we do) at it's very core. Malcolm in the past has said that my observation of these kinds of things is due to a limited experience of the US - well, this kind of radical utilitarian concept can be found all over the US - it is more commonly met with middle and hs kids but in fact can be found in fair amounts with college.university students and with adults well into their life.

So beware all ye' who tread in the intentional ignorance land of middle North America.

Kirt

[kirtu]

Having studied all of them except medicine, mathematics and logic are the most useful.

Of course this just means that particular people have particular affinities with different fields of study.

Kirt

Adhyātma vidya means Buddhism i.e. the inner sciences.

Math does not really mean math as you understand it -- it means calculating calendars, mostly.

I am aware of that and was about to address it.

Kirt

[Malcolm]

Malcolm in the past has said that my observation of these kinds of things is due to a limited experience of the US

we live in different countries. I don't live in the America you live in.

[kirtu]

What constitutes the fine arts exactly? In the Tibetan context there is painting and sculpture of course but is mathematics included as well?

We should be very clear that the Tibetans either did not develop mathematics except at least to the point of a form of modulus arithmetic that they developed or borrowed to create calendars, or they lost their knowledge of mathematics. But they seem to have not developed mathematics beyond modular arithmetic. This is is stark contrast to Indian and even Chinese mathematics. Southern Indians almost certainly developed both differential and integral calculus between 1000-1500 AD, well before Newton and Leibnitz. This knowledge as well as geometry, trigonometry and algebra apparently never made it to Tibet )or was ignored over time). Chinese mathematics stagnated but recovered after 1300 AD (after their period of expansion and after the assimilation of the Mongols) and proceeded into real geometry and algebra with interesting results in infinite sequences (which meant, math to explore math).

Later the Indians stagnated, perhaps due to the occupation by the English and then recovered in the 18th century. But centuries of Indian mathematics had been distilled in versified form in order to teach construction.

No one knows how Tibetans performed construction but it's all based on rectangular forms and likely it is based on trial and error although they may have had real math dealing with load bearing for engineering before something like 1500 AD or so at the latest (really well before that). Tang Tong Gyalpo may have been educated in mathematics and engineering (indicating a survival of math to the late 1400's) or he may have rediscovered mathematics sufficient to build serious iron bridges (but other people did the iron smelting and refining and that is unlikely to be a product of trial and error).

Kirt

[kirtu]

Malcolm in the past has said that my observation of these kinds of things is due to a limited experience of the US

we live in different countries. I don't live in the America you live in.

You can hear Americans from everywhere make statements about some branch of knowledge being useless. You can't whitewash it. The average knowledge of math and foreign languages is symptomatic of the attitude and we find the lack of these knowledges all over the US although it does appear that the generations before my father's had better general knowledge of practical math, so perhaps there was some massive problem induced into American education after WW 2.

Kirt

[kirtu]

Having studied all of them except medicine, mathematics and logic are the most useful.

Of course this just means that particular people have particular affinities with different fields of study.

Kirt

Adhyātma vidya means Buddhism i.e. the inner sciences.

Math does not really mean math as you understand it -- it means calculating calendars, mostly.

As Malcolm indicates, math all least came to mean arithmetic to support basic calendar calculation, at least in Himalayan Buddhism. But that is not definitively true because Indian's developed real math before they stagnated sometime after the 1500's and the Chinese kept developing real math after an earlier stagnation. So I would expect the historical interpretation of mathematics as one of the branches of the five sciences to have varied within Northern Buddhism.

A strong example inside Indian Buddhism and a strong support for a Tibetan loss of mathematics is the inclusion of weapons in writings related to the Kalachakra tantra detailing catapults. Catapluts can be constructed using trail and error but probably weren't. Why? Because trial and error is a solution that humans have used world wide to begin study but then transition to some mathematics universally. No society that developed catapults failed to employ algebra to some minimal degree and it suggest this in India would mean that one was asserting that the Indians had by the 1200's or so not begun to employ algebra which is a stunning statement. The only way around this is the fact that India was not one society (which was true). But we know that the Mahayana was spread all over Northern India at least by the 1200's.

Another issue is that Western Buddhism is heavily dominated by liberal arts people who are often proudly ignorant of mathematics (although this forum has a much more balanced make up). So there may be an unconscious tendency in Western Buddhism from the 19th century to ignore math.

A history of mathematics as known in Indian Buddhism still awaits publication by someone. Something like Morris Kline's history of mathematics from the 70's.

Kirt

[Malcolm]

You can hear Americans from everywhere make statements about some branch of knowledge being useless.

You might, I never do.

[viniketa]

You can hear Americans from everywhere make statements about some branch of knowledge being useless.

You might, I never do.

You're both right!!

[Dave The Seeker]

Adhyātma vidya means Buddhism i.e. the inner sciences.

Math does not really mean math as you understand it -- it means calculating calendars, mostly.

I have done a serious study of the lunar calenders and actually spent a year making a lunar/star calender.
Spent an hour each night, from 2-3am in a field I could walk to, and used a sexton to keep accuracy of location of the most dominant stars from the horizon.

[kirtu]

Adhyātma vidya means Buddhism i.e. the inner sciences.

Math does not really mean math as you understand it -- it means calculating calendars, mostly.

I have done a serious study of the lunar calenders and actually spent a year making a lunar/star calender.
Spent an hour each night, from 2-3am in a field I could walk to, and used a sexton to keep accuracy of location of the most dominant stars from the horizon.

That's a good point. You can create very accurate calendars and keep very accurate track of planets and stars. The Tibetans do not seem to have done this and by their own admission their calendars aren't very good. The Indians and Chinese did definitely use astronomical instruments and did construct calendars that were good for more than a year at a time. Calendar making can be a massive boost into the future because even with a geocentric view of space, trig arises. Also the Chinese and Indians were navigating oceans while the Tibetans were landlocked so there just weren't as many motivations to solve problems up in the Himalayas.

For that matter, you can develop more serious math, perhaps needing some trig, even in astrology (and astronomy and astrology were still related in the West up to Kepler who was noted as a skilled astrologer in school). I take Tibetans at their word when they assert that they have an advanced form of astrology but have certainly not looked at it (I'm not even sure that it is currently accessible outside of Tibetan). Perhaps they did utilize some math beyond modular arithmetic and perhaps this is encoded in astrology.

Kirt