Zero: A philosophical history of an Indian Idea – II
Written by Shivprasad // August 27, 2010 // Philosophy, Religion, Culture, Uncategorized // 36 Comments
The Men Who Knew Infinity
Zero and infinity are curious beasts; they defy our logical understanding of the world. Try this: could you name an infinitely large number? Any number you think of, however large, will be a finite number. See how a similar problem creeps in when we deal with time related notions of ‘the present’ and ‘eternity’. We tend to think of eternity as an ‘endless’ duration of time. But if it is some duration of time, however long, it cannot be eternity- just the same way as we cannot think of an infinitely large number. What is eternity then? Ludwig Wittgenstein cautioned us against the trap of treating the present and eternity as moments in time. Rather he said they symbolize timelessness: the absence of time. (more on eternity and Wittgenstein some other day)
The properties of Zero are just as logically absurd as that of eternity. It is common knowledge now that one divided by Zero is infinity and one multiplied by Zero is Zero. I fear however most of us don’t actually grasp the profundity of these simple formulae, perhaps because we are so familiar with them. To understand Zero better, we first need to shrug off the anaesthetic soporific of familiarity with this thought experiment suggested by Charles Siefe. Imagine an elastic band as the number line. When you multiply you stretch the band. When you divide you relax the band. This is what happens with routine divisions and multiplications with numbers other than zero. However, the bizarre happens when you operate with zero. Now when you multiply by Zero the band is so stretched that it explodes: and nothing remains as Zero sucks any number into itself. Similarly when you divide by zero the band so contracts that it implodes; nothing of it remains. Such are the properties of the Zero. These operations represent the end of logic as we know it: any equation in the world can be proved by multiplying both sides by Zero. In what philosophical world view could any of these make sense?
All of this absurdity made perfect sense in the Indian world view. The Indians not only embraced the idea of Zero, they actually celebrated it. What follows is the gist – oversimplification even- of the idea of emptiness at the heart of Indian philosophy. The central idea of Indian philosophy was that the infinite phenomenal world (apparently) emerges from emptiness. And when the appearance of the infinite phenomenal world – which is illusionary- is realized to be nothing but mere appearance, the individual consciousness is restored to its real state of attributeless and formless emptiness: Brahman (not to be confused with the caste Brahmin). By a perceptual illusion (maya) the apparently individual consciousness (atman) perceives the phenomenal world of names and forms- with the individual being the subject and the phenomenal world being the object of perception. Realization or enlightenment is end of this illusion – with there being no differentiation between the subject and the object- and state where this obtains is that of emptiness (Brahman).
Different Indian schools of philosophy give different names to this ineffable and nameless emptiness. Some called it Sunya (Zero or emptiness) others called it Nirguna Brahman (attributeless truth) some others, Sunya Brahman. This idea forms the philosophical core of Buddhism and the many branches of Vedanta. Much has been written about whether the Buddhist Sunya and the Vedantic Nirguna Brahmana are metaphysically identical. But this is not the occasion to get into such logomachical and ultimately -I dare say- futile debates. Truth according to both Buddhism and Vedanta is ineffable, being beyond illusionary sensory perception, beyond thought, and eventually beyond language. Both assert that the truth or emptiness is neither equivalent to existence nor to non existence. And finally both assert that enlightenment is the restoration to that very truth; and the path to that involves thoughtlessness and surrender of the false sense of ego.
In short, emptiness or zero was thought to be the truth of human existence and indeed the meaning of life. In Douglas Adams’ Hitchhiker’s Guide to the Galaxy, the supercomputer, Deep Thought, after seven and a half million years of computation, computes the meaning of life to be a meaningless number: 42. This may sound amusing in a humorous fictional work. But here was a philosophy that asserted seriously that the meaning of life was a number: and the number was Zero (Sunya). Sunya is one of the many words for Zero in Sanskrit. Another Sanskrit word for Zero was Poojyam. In Tamil, Zero is still referred to as Poojyam. Poojyam in Sanskrit also means the object of worship. The goal of human life was indeed worship (surrendering the illusionary sense of individual ego) for the realization of the ultimate emptiness (Sunya ). Thus in Zero was to be found the whole meaning and goal of existence.
When Indian Mathematicians introduced Zero they made it clear that they were applying this very philosophical idea in the realm of mathematics. They asserted that Zero ( Sunya or Poojyam) was Nirguna Brahman (attributeless truth) and infinity (Poornam or ananta) was Saguna Brahman ( truth with attributes). Infinity was a manifestation of Zero. No doubt all this sounds too mystical and far removed from modern mathematics. Yet no less a genius than Srinivasa Ramanujam( 20th Century) also held this view, and expressed it in precisely the same Vedantic terminology. After Ramanujam died, amongst his papers at Trinity College, Cambridge was found a note where Ramanujam equated Zero and Infinity with Saguna and Nirguna Brahman. That note provided the inspiration for Robert Kanigel to name his biography of Ramanujam as The Man Who Knew Infinity. But Ramanujam was just one in a line of Indian mathematicians who for over 1300 years understood Zero and infinity in this way. Brahmagupta ( 7th Century AD) who formalized most of the properties of Zero we visited earlier, understood these concepts in just this way. Bhaskara (12th Century AD) who improved upon Brahmagupta’s formalization by introducing the idea that any number divided by zero was infinity also relied on the same Vedantic equation.
36 Comments on "Zero: A philosophical history of an Indian Idea – II"
What a great resource!
Profound!
Magnificent pieces- both of them. Had always wondered, why the zero had to be ‘discovered’- and put it down to my limited understanding of maths.
Looking forward to post number 3.
Lovely post Shiv.
I really loved reading your blog. It was very well authored and easy to undertand. Unlike additional blogs I have read which are really not tht good. I also found your entries very interesting. In fact after reading, I had to go show it to my friend and he ejoyed it as well!
I agree with others that your prose is, shall we say, priceless and very illuminating. I have not gone into Wittgenstein much but Ramanujan was a genius to who continued fractions and the like was child’s play and he may have also looked at infinity and zero along those lines – then the question arises what those individual terms in such an infinite series mean – people, events, perceptions…
You have summarised the information on zero and infinity in a formulaic form based on our ancient wisdom of Indian thinkers. I came across your article when I am working on perceptual time and philosphy. As a professor of philosophy your article stimulated my thinking and will certainly direct others to this article. So your article is an inspiration to lay persons and students of philsophy — all in one…keep writing!
Awesome thinking & analysis…
esplly 1/0 =infinity & 1*0 = 0 !!!!
Keep the mixture cooled and pat it on your lips as often as
necessary. Having a well hydrated body is a sure way of having your energy levels high at all times.
It must be protected well if the body is to be kept safe and healthy without any serious problems.
Feel free to surf to my page; bliss products on sale
There are those who don’t like the shopping experience.
The XXI century is certainly century fashion, where existing trends have a strong influence on society.
Perhaps you are a model who wants to expand your portfolio with a range of startling shots that show off your versatility and individual flair.
Here is my site – pink bodycon dress tumblr
The main way you are likely to get sick while at camps is only if you cook wrongly at camps.
Summertime at Parris Island, South Carolina is a sweltering mix of
heat, humidity, sand fleas and continuous chaos.
The attack on this naval base also reinforces the belief that Pakistan at least knew the
location of Bin Laden. “We are passionate about providing indoor-outdoor play and amenities that keep dogs happy and healthy. Time to fuel up for that daunting task of packing up and heading home. Frankly, there’s not much of a rush to do this at a low level, so you can just wait until you have the necessary points (you need to be able to clear out Nelson in the next mission, so you may have to wait a bit anyway). This is not a practice allowed, in fact strictly against the rules, but what could a few bones tossed over the fence harm an animal that crushed bones with its massively powerful jaws. I knew then that I wanted to motivate and inspire the neediest students whom many have written off just because of the circumstances they were born into. Fees are $150 for each session, although there is a $5 discount if you register and pay the entire tuition more than 30 days prior to the camp. The teacher can pass out the boxes and eat lunch around the campfire, outdoors, in the cabins or tents.
Have a look at my website: day summer camp boca raton
These significant changes give an opening to a market of specialists when it comes to tax preparation, auditing and bookkeeping.
In a photography business in particular, here are a number of items that are assets to be
listed for your business. As an Accountant with an MBA Degree in you
will be able to use your skills to analyze a company.
Here is my web site – john costello Boca Raton CPA duane morris
Pick and choose from these activities based on your students’
needs and interests. Strong arms help balance the body under pressure help when shielding the ball.
In your daily travels, you may see signs in windows of stores or
restaurants that say “Now Hiring”. Some camps even offer day options,
which can be the perfect time length for some kids.
Begin this summer art camp project by discussing line drawings with students.
As spring gets into full swing it is time to start thinking
about summer and planning all of those typical summer activities for you and your family.
ll need to plan ahead to make the most of your trip. Some cooking utensils may be kept in a nearby container or just in a cupboard where they can be accessed as need be.
The amount of money you earn at a camp varies depending on various factors,
such as your experience and the number of years you have previously
worked at the camp. Mega-experienced local and English speaking surf coach, Ulisses, will have you
with the best spots and also have you standing in no time.
Feel free to visit my webpage – Boca raton summer camp Boys
Strona świadczy o interesujących zagadnieniach,
zachęcam do rozmowy
Here is my weblog … zmarszczki pod oczami
Article Source: more information on how to regrow your hair check out Total Hair
Regrowth Review. Purchase shampoo or other hair care products that
are meant specifically for people with thinning hair. Any
cosmetic plastic procedure could be a worthwhile and
extraordinary experience for both the patient and surgeon,
if this is done in the light of surgical standards in term of safety.
Feel free to visit my page laser hair growth fda approved
These services are designed to make your moving experience
a good one. These companies have professional staff which carried
your goods from one place to another. The expense apart from
covering the vehicle also involves in spending for the moving boxes.
My site self storage companies london
The note provided that all principal and accrued interest
was due in a single balloon payment at the end of the note term, and neither principal nor interest
could be prepaid. Educating these customers in how to handle
their tax affairs in the future can save them many thousands of
dollars. For conducting the additional analysis on the specific
CPA network, which will assist you to earn funds, all you
want to do is you will need to place in the identify of that network along with some other applicable keyword phrases
that could possibly assist you in discovering out if there is any precise challenge with that individual organization.
Feel free to visit my blog Boca Raton CPA side
Comfort comes in the form of the beautifully upholstered reclinable deck seats and bow seats, and a drive.
With the high temperature sensitivity of some perishable goods, it’s easy to understand why
so many companies rely on vacuum insulated panels such a Thermo –
Cor to ensure the quality of their products. Her husband, Ian, is a pilot at the New
River Air Station near Camp Lejeune.
Take a look at my web page … deck box seating
The hair follicles are not receiving the right balance of nutrients they need
to grow. Data coverage: market sizes (historic and forecasts),
company shares, brand shares and distribution data.
We live in a climate that gets hot and humid and there
are many activities to choose from.
Feel free to surf to my website … laser hair growth fda approved
Great blog here! Also your website loads up very fast! What web host
are you using? Can I get your affiliate link to your host?
I wish my website loaded up as fast as yours lol
Will the doctor performing blind dissection be able
to adequately account for this variability in the average patient and
will he risk operating on an unwary patient in whom these differences
might be profound. Data coverage: market sizes (historic and forecasts), company
shares, brand shares and distribution data. However, pulling on a scab that was adherent to the skin usually dislodged the graft –
often several days after pulling on a hair was safe.
Here is my web site – yoga for hair growth for men
Local climate, outdoor shading, windows, home orientation, and insulation quality should be taken into consideration when coming up with a detailed plan for HVAC installation. To begin with, get everyone who is helping you move a
back brace. Such storage facilities have created sensations among people
owning loads of things. Having said this, it will
do you well to get the help of professionals
if you plan to extend of remodel your abode. Mastering adds significant value and quality control to
a musical artists releases. There are some plans which offer quality speaking,
Real DVD backup the:1 and great video clip quality. Yasuo Fukuda
was the first son of a former Japanese Prime Minister Takeo Fukuda.
Thus, employees’ active listening skills assist a company to build rapport with customers and help them
obtain the relevant information they need.
If you are out in bad weather or just don’t like moving from
block to block, valet parking can be a welcome facility
needed at that time by saving you the hassle in finding a spot
when parking is scarce. Randy Neville, one of the pilots said that the plane has operated as they hoped.
my homepage: american moving and storage association newsletter
Even frequent blow-drying at extreme heat or brushing obsessively can cause your hair to
become extremely fragile causing it to break
and fall out. Electrolysis – Electrolysis is a solution which utilizes a needle to
kill the hair at its root. Such devices as KTP,
ERBIUM, Pulse DYE and Alexandrite have short length of laser light waves,
and they are very effective for removing unwanted hair on a light
colored skin.
Look into my website :: igrow 800
You can keep your spray tan longer by using products that will not only preserve its color but also enhances it.
Often the cancer can be removed from the skin, but 2,000 people still die annually, according to the American Cancer Society.
Frederick Mohs in the 1930′s who began this treatment
for skin cancer.
My web page Self tan uk
To keep you in the most comfortable and peaceful state
of mind possible, Dr. Laser procedures are also used to diminish the emergence of age spots and
wrinkles and also to resurface your skin. At $10,000 it was exactly one
tenth cheaper than the same surgery in the United States, which would have
cost him $100,000.
My web-site entertainment news
Tall high profile model escorts indore, and simply smart escorts in Indore can forever be retrieve at your service! We have the most amazing collection of gorgeous Escorts available for incall and outcall engagements. And not only they are picturesque and friendly � they are broad minded and eager to give their clients full pleasure.
I celebrity escorts , Independent Escort always waiting for you. so please come fast and make me feel comfortable by taking care of the body from you own hands and please grab me tightly so that i can also feel the hardness and warmth which is found only in some of the handsome man which are very much hard to find and to find that particular love and man hood
Smart indore escort service, and simply smart escorts in Indore can forever be retrieve at your service! We have the most amazing collection of bold Escorts available for incall and outcall engagements. And not only they are picturesque and friendly � they are broad minded and want to give their clients authentic pleasure.
Our independent escorts service is the service of unbeatable beauty and discretion a differenceescorts in. Our clients believes on us just because of the excellent services provide by us with full satisfaction. We also serve the Elite class society people where maturity is must. Our high profile escorts will full cares about you and your satisfaction You must also ensure that the photos of the girls that you see online are recent and genuine. Our escorts are truly one of a kind each one is educated, a good conversationalist, sophisticated and charming, so you are not embarrassed to go out with them to a dinner.
Our independent escorts service is the service of unbeatable beauty and discretion a difference Delhi escort agency. Our clients believes on us just because of the excellent services provide by us with 100% satisfaction. We also serve the High class society people where maturity is must. Our high profile escorts will full cares about you and your satisfaction You must also ensure that the photos of the girls that you see online are recent and genuine. Our escorts are truly one of a kind each one is educated, a good conversationalist, sophisticated and charming, so you are not embarrassed to go out with them to a date.
Każdy z nas zetknął się z faktem, zalecam zapoznanie się z problemem.
Place zabaw dla dzieci
Yes! Finally someone writes about Androderm.
These could also prize you additional money for forex trading in applied online games.
French, Italian, Turkish, Argentinian, Cuban eateries, blend nicely with tiny ice cream areas,
and sport bars. It doesn’t take information and competence to
win in the prizes within this pleasure.
I do not know if it’s just me or if perhaps everybody else experiencing problems with your blog.
It appears as though some of the text on your content
are running off the screen. Can someone else please provide feedback and let me know
if this is happening to them too? This may be a problem with
my web browser because I’ve had this happen previously.
Many thanks
This piece of writing is really a good one it assists new
the web viewers,who are wishing for blogging.
As you are searching for the best different companies that came up in your search results, there
are a few more things to keep in mind. When combined with a very low
calorie diet, the person is subsisting more on their stored fat than on what they are
eating. During the first week a person could expect to loose anywhere from
7-10lbs. For a couple of drops of the HCG supplement you’re paying two dollars each and every
single day. All it takes is for you to add at least fifteen minutes
of cardio exercises into your daily routine.