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UGC recommendations for teaching IKS: some serious lacunae

C. K. Raju

c.k.raju@ganita.guru

Introduction

The recent UGC guidelines for IKS in the curriculum for higher education
as also reported in newspapers
have several lacunae.

I will take up three recommendation

Vedic mathematics
Vedic astrology
"Kerala" calculus

There is widespread confusion regarding traditional knowledge

To illustrate: E.g. on a recent visit to Australia
the Indian community invited me speak on Bharatiya ganita
and the Indian calendar.

Bharatiya ganita?

Much talk today on Bharatiya gaṇita.
Is there any other kind of gaṇita?
Or does the phrase Bharatiya mean that no other nationality should use it?
It is only for Bharata?

If you say only gaṇita

You are forced to acknowledge that gaṇita is not the same as math
for the simple reason that ganita accepts empirical proofs (प्रत्यक्ष प्रमाण)
as do ALL systems of Indian philosophy, without exception.

Western math prohibits empirical

When the Euclid book first came to Europe during the Crusades
and was falsely interpreted as containing axiomatic proofs
convenient to Christian rational theology invented during the Crusades.

Christian priests declared axiomatic reasoning without facts,
and, contrary to science, as a "superior" way of reasoning (convenient to Christian theology).
We foolishly accept that this is the best way to teach math FOR science and teach it.
In the language of the current class IX NCERT math text (p. 301)
"Beware of being deceived by what you SEE"

गणित accepts प्रत्यक्ष प्रमाण

As stated in in the Nyaya sutra 2
and elaborated with examples from Indian gaṇita texts in this slide.

as also explained in my Hawaii’i article of 1999/2001 in Philosophy East and West
or as explained in this video on the notion of proof in Indian gaṇita
or in this one in IIAS Shimla on ganita versus math
and in this one on practical ganita vs religious mathematics.

We must understand the different philosophies of gaṇita and math

if we intend to teach traditional gaṇita and use it.
Cannot just keep pretending that acceptance of prtayaksh
and prohibition of empirical are one and the same thing!!
when they are diametrically opposite.

But one can’t teach traditional ganita without this discrimination

between ganita and math
apparently the UGC objective is to inculcate pride by teaching history

but not to actually teach gaṇita or to deviate from existing colonised math courses
because that is the real colonial superstition ("dharam") propagated by colonial education
ape the West to the point of wearing suits in Delhi summer.

Apparently the UGC wants to promote tradition without

without any conflict with the other colonial tradition of aping the West.
this is an impossible proposition
even promoting Ayurveda brings it in conflict with West.

This is an open invitation people to make fun of pride in things
which are de facto rejected as useless today.
as for example the fear of teaching calculus as gaṇita
and the fear of even discussing it openly.

Vedic math

Some universities, such as Harisingh Gaur University, Sagar
have introduced “Vedic math” in the syllabus.

"Vedic math" has NOTHING to do with Veda-s

Everybody agrees! (Including original "Vedic math" book.)
As stated on its opening page and on p. xxxv/p. xxix bottom (in newer reprint)

"Obviously these formulae are not to be found in present recensions of Atharvaveda".(emph. added)

My past writings on this issue

Article in Hindu, and in Jansatta
Responses to critics on this blog
esp. admission by Atul Kothari that "Vedic math not found in Veda" is true.

The REAL math found in the Veda

is better described in this book
and its great importance is explained in my recent book on Aryan Race Conjecture.
Also अक्ष सूक्त (ऋग्वेद 10.34), my translation
in my paper on "Probability in ancient India" in Elesevier Handbook of Philosophy of Statistics.

No mention of any of above in "Vedic math" book

So, real math in Veda-s is NOT "Vedic math"!
It is authentic traditional Indian gaṇita
which "Vedic math" seeks to replace.
To reiterate, Gaṇita NOT a synonym for math: see my Himanjali article "गणित बनाम मैथमेटिक्स".

So, name "Vedic" in "Vedic math" misleading:

that "Vedic math" has some connection with Veda.
Using name of Veda to mislead, to sell, demeans the Veda.
A disservice to Hinduism.

Apologias

"Vedic in sense that all knowledge is in the Veda"
ALL knowledge?⁉
Manual for car repair?

"Ancient" hence "Vedic"?

(Atul Kothari said that so.)
WRONG claim. Everything ancient is NOT "Vedic"!
Lokayata, Buddhists, Jains REJECTED belief in Veda-s or related शब्द प्रमाण.
Lokayata said that moksha is laughable.

Lokayata said that authors of the Veda are धूर्त, and that Veda-s are false (अनृत) and contradictory (व्याघात).
Eng trans. (Cowell) that "three authors of the Veda were buffoons, knaves and demons".
Calling this "Vedic"!😖
JUST to justify misguided attempt to sell "Vedic" math, is going too far!

Anyway, no evidence "Vedic math" is ancient 😀

Our source modern: Bharati Krishna Tirtha.
Could not explain his sources when asked by K. S. Shukla, ca. 1950.
"Vedic math" NOT found in ANY traditional Indian math/astronomy text
from Vedanga Jyotiṣa (\(-1500\) CE) to Yuktibhāṣa (+1500 CE) across 3000 years.

Swami Bharti Krishna Tirtha

was undoubtedly a patriot and a freedom fighter.
His intentions were entirely honourable
(that is not necessarily true of those who promote or oppose Vedic math today)
But he was ill-informed that he was replacing an imported tradition of arithmetic by an Indian tradition.
Our duty is to correct him.

Arithmetic as currently taught IS of Indian origin

which went from India to Europe,
and was returned as part of colonial education.
So "Vedic math" wrongly seeks to replaces real Indian gaṇita by using a fake marketing label "Vedic".

"Vedic math" has VERY limited use

At BEST good for mental calculations in elementary arithmetic for primary school.
Perhaps for some competitive tests where a calculator is disallowed.
My point: teach mental arithmetic (many systems) if you want, but at least remove the false label "Vedic".

Any OTHER harm in teaching "Vedic math"?

Yes! Damages authentic Indian tradition of gaṇita in various ways
and its REVOLUTIONARY possibilities for future S&T which even Africans understand
But most Indians don't.

Colonialism taught us to ape Whites/West,
and we are easily fooled by one FALSE label "Vedic",
and related ELEMENTARY mental arithmetic
(teaching which does NOT threaten West)
as teaching gaṇita does

Graeco-Roman calculus: Arithmetic revolution

Greek (and Roman) names for numbers very similar to Persian and Indian (Sanskrit) names.
West claims this is because “Aryans” invaded India
drove the indigenous Dravidians to the South
On this fantasy See how many seat DMK won.

But NO evidence for Aryans!
West claims they also created the Veda-s (so much for the label "Vedic").
This the ultimate insult to Hinduism.
My simple, decisive answer to this 250-year old fantasy.

Grace-Roman counting INFERIOR;
their number names agree with Sanskrit ONLY for small numbers. Why?
Graeco-Roman number names stopped at the puny myriad (Persian beavan) \(10^4\)
still means uncountable, and connotes it as in "myriad stars" and other literary quotes

But Indian names went on to parārdha (=10¹²) Yajurveda 17.2,
tallakṣhaṇa (=10⁵³) and beyond (10¹⁰⁸, Buddha, Lalita vistara sutta, chp.12)
so these Aryan/European duffers could not have created the Veda!

But why did no one notice this for 250 years?

Why did no one point it out that "Aryan"/Greek/Roman knowledge of arithmetic was limnited to small numbers.
Because we study only our own tradition
and are afraid to attack the pūrva paksha (opponent’s point of view)
which is what our tradition demands.

Why were Greeks and Romans backward in math?

Conquest of Greeks by Persians (Aechemenid conquest after Lydian conquest) is a known fact.
Hence, early Greeks/Romans knew calculus
calculus=pebble=psephos: primitive pebble arithmetic = गिट्टी गणित
Two meanings of word calculus!

Early Greeks learnt pebble arithmetic from their Persian conquerors
to pay tax to them (tax collector scene from Darius vase −300 CE)

Large numbers

Roman numerals designed for pebble arithmetic.
How do you write 1888 in Roman numerals?

Pebble arithmetic very inefficient.
Small number 1888 needs 13 figures MDCCCLXXXVIII not 4
Indians could write large numbers
because Indians used efficient place value system.

that is Graeco-Roman pebble arithmetic is primitive/INEFFICIENT
compared to sophisticated place-value of Indian gaṇita.
Large numbers need place value.
Took smartest of Europeans over 1000 years to understand simple fact.

Transmission to Baghdad

First Indian arithmetic, because of its fame, went to Arabs.
al Khwarizmi of Baghdad translated it as Hisab al Hind.
Came to be known to Europeans as algorismus or algorithms after his Latin name: Algorithms.
From Baghdad it went on to the Umayyad Khilafat which ruled Spain, Morocco

Then in the 10th c. a pope (Gerbert) heard of it
and started learning Indian arithmetic
from Muslims in Spain and Morocco.
But FAILED to understand it
constructed an abacus which destroyed efficiency of Indian ganita.

Fibonacci

Took another 2 centuries for Christian Europeans to grasp the efficiency of Indian Gaṇita.
and its use for commerce.

Then Florentine merchant Fibonacci wrote Liber Abaci (13th c.).
based on al Khwarizmi's 9th c. Hisab al Hind.
Both (Fibonacci and al Khwarizmi) gave an over-simplified treatment of Indian gaṇita

As found in common Indian texts emphasizing commercial uses of gaṇita (instead of astronomy)
Compare contents of 9th c. Mahavira's गणित सार संग्रह (Gaṇita sāra sangraha),
with Fibonacci's contents (square/cube roots etc. only in chp. 14)
Note Fibonacci's chp. 4 on subtraction (only LESSER numbers)

Fibonacci's blunder

That is, still mired in the paradigm of pebble arithmetic like Gerbert
Fibonacci blundered: has no negative numbers (like al Khwarizmi)
because in primitive Graeco-Roman calculus (pebble arithmetic)
subtraction means removing pebbles from an existing hoard
and you can't remove more pebbles than there are on the board!

OF COURSE Fibonacci numbers stolen from India, he made NO original contribution.
Fibonacci's influence largely limited to Florence and neighbouring states
since zero (= sifr=cipher) puzzled Europeans] (and Florence passed a law against zero)
Finally, in 16th c. Gregor Reisz declared victory of algorismus over abacus

followed by Adam Riese.
Most importantly Jesuit general Christoph Clavius again imported gaṇita direct from India
wrote a text on practical mathematics,
introduced it in the Jesuit syllabus ca. 1575.
We copied it after colonial education.

Persistent confusion about subtraction and negative numbers

Fibonacci's confusion about negative numbers persisted in Europe right till 19th c.
Three quick indicative examples
Pascal (17th c.), Euler 18th c.), De Morgan (19th .)

Interim conclusion

Conclusion: Western math was PERSISTENTLY INFERIOR,
even in the matter of primary-school arithmetic
from early Greek times till end of 19th c.
contrary to colonial tales of Western supremacy.

Phylogeny is ontogeny

On the principle that “phylogeny is ontogeny”
these Western difficulties with elementary math are reproduced even in the primary school classroom today.
Hence, aping the West makes math difficult even in the matter of primary school arithmetic.
So the decolonial solution is to revert to the original methods of teaching ganita.

E.g. Assume child has learnt representation of numbers by objects at home.
START teaching arithmetic with place value, teach large numbers early.
Teach practical value of arithmetic as in Mahavira Ganita sara sangraha etc.

Also necessary to discuss difference between philosophy of ganita
and of Western (axiomatic) math which prohibits the use of empirical in proof
because of the churchification of mathematics in the West,
since the Crusades when Euclid first arrived in Europe.

But useless to talk of such matters to people who don’t know the basic history of arithmetic.
If interested see my 2nd recent talk in Australia
Note that the philosophy of axiomatic math enunciated by Christian priests
Peano’s axioms, formal real numbers

started by pronouncing their great curse (anathema) in 6th c. on the Hindu notion of soul
similar to the notion of soul which Plato linked to mathematics as mathesis
and which was copied by early Christianity of Origen.

So, follow your colonial dharam, fundamentally against Hinduism
and keep pushing what your neta-s (Congress or BJP) tell you to do.

Calendar and "Vedic astrology"

The calendar involves the motion of the sun against the background stars (year, नाक्षत्र वर्ष)
of the moon (month, चंद्रमास)
the phases of the moon (tithi, तिथि ≠ civil day = सावन दिन )
the weekday (वार)

Because the Greeks were so bad at math
their calendar involved a year of 375 days
as the learned Greek Solon
explained to the Lydian king of Greeks

Currently you learn the (Gregorian) calendar
The Julian calendar was adopted as the official Christian calendar in the Roman empire in 325 CE.
It was later (6th-7th c.) changed to the "Year of the Christian Lord" calendar
This religious calendar forces you to recite the name of the Christian Lord, AD-BC with every date.

Then it was earlier called the Julian calendar after Julius Caesar
who got the Egyptians to make it, after he conquered Egypt.
The original Roman calendar was so bad the correction needed an intermediate year of 448 day
because Romans, like early Greeks were bad in math

The months are unscientific with 28, 29, 30, 31 days
with no relation to the cycle of the moon
The year is still described using leap years, since Romans lacked fractions (of pebbles)
The Gregorian reform of 1582 still used leap years,since fractions were little known in Europe then.

In contrast, the Indian calendar is very scientific

Every month has exactly 30 tithi-s
because a tithi is mathematically defined as the time in which the moon moves ahead of the sun by 12° (celestial longitude)
so purnima to purnima = 360° = 12° × 30.

However, we never refer to that unscientific and religious calendar

as the Christian calendar
to hide the fact that our two secular festivals
Independence day and Republic day are defined ONLY on the Christian calendar.

However, UGC aims to defame the Veda-s

Therefore, it will also NOT talk of science with regard to the Indian calendar
instead wants to link the Veda to the pseudoscience of astrology.
This attempt has been going on for the last 20 years.
When the UGC first tried to open 16 University departments of Vedic astrology

At that time a debate was organized between scientists and astrologers
in India International center by Kapila Vatsyayana
the late Pushpa Bhargava, Raja Ramanna, and I participated on the side of the scientists.

I challenged the UGC, in front of the international press, to show me
a single verse on astrology in the Vedanga Jyotish.
No one could.

Vedanga jyotisha defines jyotisha as कालज्ञानं, and कालविधानशास्त्रं.
It does not have a single sentence on astrology1 or फलित ज्योतिष),

In fact traditional Indian astronomy texts from Vedanga Jyotish to Yuktibhasha
(including Varahamihira’s Panchsiddantica,
across at least 3000 years do NOT have a single sentence on astrology.

the confusion arises because Jyotish defined in the VJ as timekeeping
is misread as astrology.

perhaps this misreading is deliberate.
Because astrology is a source of money and also superstition
and the government wants to encourage that
without contesting Christian superstitions in the calendar.

What to do?

The correct approach is to avoid making a joke of Indian tradition
by teaching a pseudo science of astrology,
and to instead teach the scientific aspects of Indian tradition and the Indian calendar,
while emphasizing the religious and non-secular aspects of the Gregorian calendar.
This is being tried out initially in a school in Hyderabad.

Teaching Indian calendar requires rajju ganita

or a change in geometry teaching
to measure angles in space, such as the angle between sun and moon
which are rarely in the sane plane (ecliptic).

Measuring 3D angles not taught in current school geometry syllabus
which teaches useless angle measurement only with protractor.

Rajju ganita also needed to determine local latitude, longitude, size of the earth.
also never taught in school geometry since colonial education focuses on Euclid
and teaching the church method of axiomatic proof by prohibiting facts
falsely read into the Euclid book.

However, big task

zero support and much opposition from govt
whether Congress or JP
Very limited support from private parties.
So, it may or may not happen.

Kerala calculus

Again the UGC IKS recommendations speak of “Kerala calculus”.
Whish’s 1832 article on the Indian calculus mentioned only Kerala texts.
Good we are now taking cognizance of it AFTER 190 years.

But that does not mean calculus originated with the Aryabhata school of Kerala,
which only carried forward the work of Aryabhata.

This confusion is due to several reasons:
1. the focus of the UGC recommendations is only to develop a sense of pride in Indian culture,
and not to emphasize its current usefulness,

which directly challenges the West.
Pride can also be based on false assumptions
as the cases of Vedic math and Vedic astrology shows.

Calculus stolen by Newton etc.

How could the West have understood it
when it too a thousand years to understand elementary arithmetic and negative numbers?
Fact: West did not understand calculus!

Newton’s fluxions were not understood
Hence, Dedekind invented axiomatic reals.
Now the West claims that is that that is the only way to understand and do calculus.

Indian calculus as ganita was different did not involve a metaphysics of set theory etc.
but we know the rule: the West cannot be challenged
in keeping with our colonial temper!

Does Indian ganita make calculus better/

2. If one focuses on the current use-value of IKS,
the question would immediately arise whether the calculus can be taught better under IKS.
No one else except for me has actually attempted to teach calculus using IKS.

The moment one does so it is obvious that Aryabhata’s finite difference technique
now falsely called (“Euler’s method”) of solving differential (finite difference) equations

-is far better suited than mere infinite series

without any well explicated criterion of convergence.

the finite difference technique, first used by Aryabhata, is what is still use for all practical application
such as sending a man to the moon.
but we must do our colonial dharam, the most important aspect of it is to please the West.

3. Even if the UGC’s unstated objective is solely to inculcate pride minus use value,
a conflict would nevertheless arise in the glorification of the high caste Brahmins of the “Kerala school”
over the low-caste Āryabahaṭa a dalit from Bihar,

though there was no such conflict in the minds of people of the Aryabhata school in Kerala
who openly acknowledged Aryabhata as their guru.
which shows that the oppressive form of casteism is post-colonial.
So, let us call it the Aryabhaṭa calculus.

Ganit vs math again

4. Most importantly, there is a clear conflict between the philosophy of ganita
which accepts empirical proof (prtayaksh pramana)
and the philosophy of axiomatic mathematics, underlying which prohibits it.
And axiomatic real numbers regarded as essential to the teaching of calculus, which rejects empirical proof.

How calculus is taught with ganita

In my recent first (invited) talk at Pacific rim conference in mathematics
have reiterated the principles underlying my course on calculus without limits.
taught in 3 countries in 5 universities.

Three principles are

Finite difference techniques: calculus as solution of differential equations
Non-Archimeaden (polynomial) arithmetic of Brahmagupta
- which results in calculus without real numbers and without limits
Zeroism or inexactitude.

But the colonized are unwilling even to seeriously discuss the differences in a rational way,
to decide which is better,
because it exposes the religious (Christian) superstitions,
underlying the current axiomatic philosophy of mathematics.
Such a serious discussion would take several days, not 40 mins.

Summary and conclusions

UGC should modify its recommendations
to keep in mind the use value of tradition
and the difference in the philosophies of ganita and math.
We should teach authentic history and the scientific nature of Indian tradition,

Tradition understood for its use value is not the monopoly of Bharat
and could easily be grabbed by others, like Haldi patent.
So we need to understand that we do not have another 190 as we took in acknowledging Whish.

Created: 2024-09-12 Thu 21:56