The oldest "0" in India for which one can assign a definite date

http://www.ams.org/samplings/feature-column/fcarc-india-zero

by richeyrw • 13 years ago

119 28 13 years ago

dclowd9901• 13 years ago

So if 0 wasn't a concept, you couldn't count to 10?

I'm not sure I understand. I thought the significance of 0 was the recognition of an absence of existence. Just because numbers use 0 (270, 50, 20, etc.) wouldn't seem to indicate that it was understood at that significance...

andrewcooke• 13 years ago

think roman numerals. or hash (tally) marks by five.

olavk• 13 years ago

It is two distinct concepts, both important. The one concept is the use of a positional or "place-value" notation for numbers.

Place-value notation means you use a base set of symbols, and then the position when using multiple digits is a multiplier. Compared to say Roman numerals this have the advantage that you can write arbitrarily large numbers. (The Romans didn't have a symbol for numbers larger than 1000, hence larger numbers became cumbersome to write.) More important though, arithmetic is much simpler using a place-value notion, because you can place numbers vertically and then perform the operation on one row at a time.

Place-value notation requires a symbol for "nothing at this place", the "0". The post is about the oldest known use of "0" in a place-value system. (Which probably means the oldest use of a place-value system per se, since you cannot have a place-value system without "0".)

However, using a place-value notation like decimal notation does not mean that you have to accept zero as a natural number. That is a separate issue.

breadbox• 13 years ago

The Babylonians got by using a place-system without zero for a long time. People relied on context to disambiguate.

(It probably helped that with a base-60 system, one was six times less likely to have a zero.)

glurgh• 13 years ago

The disambiguation from context was disambiguation of scale because there was no radix point. They did have a way to indicate a zero-valued position in a number, without that you can't really 'disambiguate' or have a positional number system at all.

pfortuny• 13 years ago

No, the problem is not '0' not being a concept. There are two issues here, which are related but not the same. The conecpt of 'nothingness' is irrelevant to both:

1) Dealing with '0' as an ordinary number.

2) Using a positional number system, which requires a symbol or context for telling '1230' from '1023' and '1203', etc.

One tends to think that solving the first issue leads to the second. Solving the second implies in some way having already solved the first, due to the nature of positional systems.

zdean• 13 years ago

would it be fair to differentiate the two concepts as:

1. using "0" as a digit

2. using "0" as a number

KMag• 13 years ago

> Solving the second implies in some way having already solved the first, due to the nature of positional systems.

Untrue. (Edit: actually true). It works perfectly well to have a decimal number system using digits 1-10 instead of 0-9. For sake of notation, let's say A is the digit representing 10.

"A" = 10, "11" = 11, "19" = 19, "1A" = 20, "21" = 21, etc.

Edit: actually, I misread your argument. What you argued is definitionally true.

peter303• 13 years ago

"New numbers" are invented to complete a group for a particular arithmetic operation. Zero is not necessary the addition operation because all cardinals one and above suffice. Zero is created for the subtraction operation of a cardinal with itself.

There were empty place holders signs in place-number systems of Babylonia and ancent China that function like our zero numeral. But this placeholder did not enter arithmetic operations. So it is not considered the "modern" zero.

Ditto creating negative numbers for cmpleting the subtraction operation group. Ratios for cardinal division. Real numbers for some ratios that are not cardinals. Infinity for zero divisors. Irrationals for roots of cardinals. Imaginaries for roots of negatives. Infinitesmals in differentiation and integration. And so on ...

At some point in medevial times each of these new numbers were considered the work of the Devil because they did not have concrete existance in the physical world. Later on accountants showed how zero & negative numbers were usefule for business. And physicists showed how these new numbers could predict the physical world.

phaemon• 13 years ago

>At some point in medevial times each of these new numbers were considered the work of the Devil because they did not have concrete existance in the physical world.

Really? Do you have a cite for this? It sounds made up.

oz• 13 years ago

I can't speak for math, but I know that a few centuries ago, certain musical notes were regarded as 'The Devil's Music':

https://en.wikipedia.org/wiki/Tritone#Historical_uses http://news.bbc.co.uk/2/hi/uk_news/magazine/4952646.stm

fusiongyro2• 13 years ago

Especially since under neoplatonic thought lots of things are considered more real because they lack physical existence.

chris_mahan• 13 years ago

Very interesting!

Of course, reading "Those who can access JSTOR can find some of the papers mentioned above there" demonstrates once more that, alas, the digital divide still exists.

contingencies• 13 years ago

RIP. http://en.wikipedia.org/wiki/JSTOR#Aaron_Swartz_incident

alainbryden• 13 years ago

"The history of zero is a bit complicated."

I see what you did there

onto• 13 years ago

I see what you did there.

tokenadult• 13 years ago

A recent article of related interest is the story of the recovery of the oldest datable inscription that shows a numeral zero used in base-ten place-value notation, "How I Rediscovered the Oldest Zero in History,"

http://blogs.discovermagazine.com/crux/2013/05/20/how-i-redi...

which links to the article kindly submitted here.

The submission title here is NOT the original article title, as preferred by the Hacker News guidelines, and the other recent article suggests that the title shown on the submission here is not fully accurate for all regions of the world.

salimmadjd• 13 years ago

OT: in Arabic Zero is "Ciphr" or "Cipher" where we get the words decipher or cipher from.

carlob• 13 years ago

In many romance languages it is the root of the word we use for digit. It, es: cifra, fr: chiffre, ro: cifrǎ. In Portuguese the word is algarismo and it comes from al-Khwārizmī [0], who gives the name to algorithm as well.

raghuinc• 13 years ago

In Tamil, its still called cyber.

cpleppert• 13 years ago

I'm not sure what the article claims here. This is the first dated inscription but the positional arabic notation (with a zero like glyph) had been in use for at least 300 years earlier. If you consider other place value systems the concept of a 'separator' goes back much farther.

This isn't necessarily evidence that they understood zero as a number as opposed to a concept. By 1000 in Europe they used a symbol as a placeholder that looked superficially similar to our modern glyph of zero. When explaining it, however, it was clear it was simply a placeholder that could always be omitted and was "sometimes useful" and was absolutely not really a number. It isn't clear that the glyph used here or in Europe was anything more than an elaborate 'dot.' It certainly didn't seem to be be transmitted as a recognizable glpyh but each culture rendered it in the way most convenient as a counting and placeholder aid.

JoeAltmaier• 13 years ago

Yeah;all this talk of 'placeholders' that don't matter. Every digit is a 'placeholder', standing in for the count that it represents. Not convinced.

If it was used in a power-of-ten (or power-of-anything for that matter) for 'nothing here' then it was a digit, it was zero, and it should be considered a legitimate heir to our zero.

beloch• 13 years ago

An earlier use of zero (as defined in the article) for which one can assign a definite date was in 357 AD. The gotcha is that it's not the circle we're so familiar with. This is the first Mayan (Olmec) long-count recorded containing a zero, although long-counts showing a clear positional number system were recorded in the first century BC.

http://books.google.ca/books?id=TzrNgAsJY1MC&lpg=PP1&...

While the use of zero in India may have been influenced by earlier cultures (e.g. Babylon), it's pretty unlikely there was any direct contact that could have spread the use of zero to mesoamerica. Thus, positional number systems with a zero place-holder have been invented independenly at least twice in human history!

swatkat• 13 years ago

Apparently, this article is about oldest known depection of symbol of zero (i.e. a circle), which is found in Gwalior's Chatur Bhuja temple.

But, zero in decimal place-value system[1] and zero's usage as a number[2][3] are much older.

[1]http://en.wikipedia.org/wiki/Lokavibhaga

[2]http://en.wikipedia.org/wiki/Br%C4%81hmasphu%E1%B9%ADasiddh%...

[3]http://en.wikipedia.org/wiki/Brahmagupta#Zero

realrocker• 13 years ago

Also notable here is Aryabhatta who used a base of 10 symbol for zero[1]. Though he didn't use the notation '0'. [1]http://en.wikipedia.org/wiki/Aryabhata#Place_value_system_an...

The oldest "0" in India for which one can assign a definite date

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