
How the number zero was ‘discovered’ - ohjeez
http://www.bbc.com/future/story/20161206-we-couldnt-live-without-zero-but-we-once-had-to
======
inopinatus
We really are quite unkind in naming the numbers, or at least the difficult
ones. We call them Zero (via Fibonacci's "zephiram", from the Arabic "sifr"
meaning "empty"). Negative (from the Latin "negare", "to deny"). Irrational.
And so on, in an escalation of denial: Imaginary. Transcendental.
Supernatural. Surreal. There's more than a suggestion here that, on
encountering the construction of each, the gut feeling is to reject their
right to exist.

(Counterpoint; the ones we like are the ones we can grasp intuitively, and
they receive more complimentary names: positive, natural, rational, prime.
"integer" is Latin for "complete, sound, healthy")

It won't end, we'll always be discovering new number systems, so perhaps we
should reserve terms now. Paradoxical numbers, anyone? Or repugnant?

~~~
conistonwater
My dictionary gives "integer" as

> _early 16th cent. (as an adjective meaning ‘entire, whole’): from Latin,
> ‘intact, whole,’ from in- (expressing negation) + the root of tangere ‘to
> touch.’ Compare with entire, also with integral,integrate, and integrity._

Indeed, whole numbers is another word for integers, dated in English, but
that's what they are called in some other languages like German and Russian.

I also suspect _natural_ is like in _natural philosophy_ : occurring in
nature, not like the other meaning of _innate_ , although the two meanings are
closely related.

 _Imaginary_ is due to Descartes
([https://en.wikipedia.org/wiki/Complex_number#History](https://en.wikipedia.org/wiki/Complex_number#History)):

> _[...] sometimes only imaginary, that is one can imagine as many as I said
> in each equation, but sometimes there exists no quantity that matches that
> which we imagine._

It says Descartes didn't like them, but _imaginary_ literally means _not
occurring in nature_ , and this was presumably before people accepted
mathematical concepts as being as real as anything else.

 _Transcendental_ also literally means _beyond the algebraic numbers_ , since
that's the definition, that's what they transcend.

Surreal numbers are surreal because somebody (Conway?) needed to attach a
prefix to _real_ , and my dictionary says _sur-_ is the same as _super-_. My
dictionary says it is _surreal_ that is the odd word here: a backformation for
_surrealism_ , which is some kind of art movement (I wouldn't trust some
French painters to get English etymology right, eh? ;)).

Also, what about dyadic, and p-adic, numbers? Ordinal numbers? Hyperreal?

~~~
SilasX
To add to this, "rational number" comes from "ratio" [2], not "rationality".

They look similar because (per [1]) they both come from Latin _ratio_
("reckoning, accounting"), which derives from _reri_ (think, judge).

[1]
[http://www.dictionary.com/browse/ratio?s=t](http://www.dictionary.com/browse/ratio?s=t)

[2] They're the numbers expressible as one integer divided by another.

~~~
thefalcon
I realize not everyone is the same as myself, but I really wish that this
etymology was explained when the concept of the rational number was
introduced. I have trouble with rote memorization, but little trouble so long
as I can derive a thing from first principles. Realizing that rational number
comes from ratio seems so obvious in hindsight, but would have been so very
helpful to my in-school self oh so long ago.

~~~
lawpoop
When I took math in high school, our textbook had little blurbs that pointed
out historical curiosities in regards to math. (The only one I remember
clearly is an ancient Greek Queen? maybe Middle Ages, who did a lot of work on
conic sections. So maybe it's not such an effective teaching tool since I
didn't remember who exactly she was or when or where she lived).

Anyway, all the people who said stuff like "When are we going to use X math
topic in real life" were even more flummoxed by random math historical facts
that weren't going to be on the test.

Anyway, at least for me, I think I passed a point of maturity where I don't
feel "bombarded" when I encounter additional information in regards to a math
topic. I did poorly in math in high school, and, at the time, I felt that the
less information, the better-- I could only integrate so much. But now at my
age (almost 40) learning additional historical facts seems to help me
understand the topic better.

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pavel_lishin
I'm going to take this opportunity to plug this series of videos on imaginary
numbers, which covers the discovery/invention of zero to a small extent:
[https://www.youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703...](https://www.youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF)

I think it's just under an hour's worth of videos, in five minute chunks,
covering both mathematics and history.

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esnible3
Nice photo of the oldest zero known, at Angkor Wat, Cambodia, dated 683 AD
[http://www.smithsonianmag.com/history/origin-number-
zero-180...](http://www.smithsonianmag.com/history/origin-number-
zero-180953392/)

The previous contender was the zero at Gwalior in India, dated 876 AD
[http://www.ams.org/samplings/feature-column/fcarc-india-
zero](http://www.ams.org/samplings/feature-column/fcarc-india-zero)

~~~
contingencies
Wow... thanks, I never knew about that. As background to those unfamiliar with
the region, ancient Southern Indian voyagers established Hindu kingdoms
throughout this region (Indonesia, Cambodia, Vietnam). As such it follows that
Indian systems of numeracy had also penetrated what is now central Vietnam
(the Champa kingdom) and Indonesia (Srivijaya/Palembang).

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Amorymeltzer
I've commented on this on a previously-posted story[1] but the history of zero
is really worth digging into. I'll repost the little poem I mentioned
previously:

>U 0 a 0, but I 0 thee

>O 0 no 0, but O 0 me.

>O let not my 0 a mere 0 go,

>But 0 my 0 I 0 thee so.

As noted in the comments here, "cipher" used to be another name for zero/0, so
the above reads as:

>You sigh for a cipher, but I sigh for thee

>O sigh for no cipher, but O sigh for me.

>O let not my sigh for a mere cipher go

>But sigh for my sigh, for I sigh for thee so.

Which, of course, explains why Neo, The One from the Matrix, had an enemy
named Cypher.

1:
[https://news.ycombinator.com/item?id=9196813](https://news.ycombinator.com/item?id=9196813)

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happy-go-lucky
The etymology at
[https://en.m.wikipedia.org/wiki/Śūnyatā](https://en.m.wikipedia.org/wiki/Śūnyatā)
is helpful.

> "Śūnyatā" (Sanskrit) is usually translated as "emptiness," "hollow,
> hollowness," "voidness." It is the noun form of the adjective śūnya or
> śhūnya, plus -tā:

> śūnya means "zero," "nothing," "empty" or "void". Śūnya comes from the root
> śvi, meaning "hollow".

> -tā means "-ness"

There are many loanwords meaning shunya or zero in many Indian languages and
they are all adopted from Sanskrit.

~~~
kazinator
Any cognates (even distant ones) in any Indo-European tongues?

~~~
happy-go-lucky
Are these what you're looking for? [https://en.wikipedia.org/wiki/Indo-
European_vocabulary](https://en.wikipedia.org/wiki/Indo-European_vocabulary)

------
zingermc
> In 1299, zero was banned in Florence, along with all Arabic numerals,
> because they were said to encourage fraud. Zero could easily be doctored to
> become nine, and why not add a few zeros on the end of a receipt to inflate
> the price?

I'm really curious about this part. It sounds like they were already using
Arabic numerals. How did they intend to express numbers like the ones
mentioned in the first paragraph, like 101?

~~~
0942v8653
They were using Roman numerals. It's true that with Roman numerals and writing
out the number using words, it's harder to forge. See
[https://m.reddit.com/r/AskHistorians/comments/49z4d6/why_did...](https://m.reddit.com/r/AskHistorians/comments/49z4d6/why_did_florence_ban_hinduarabic_numerals_in_1299/)

------
kxyvr
I find zero to be an interesting concept in the applied math world because
depending on how you want to visualize it, it leads to different numerical
methods. For example, think of how we represent a zero vector on a computer.
Basically, we have an array of floating point numbers, but it's sort of hard
to exactly pin down when we want to define this array as zero. We could look
at all of the individual elements; we could sum them; etc.

Anyway, the two most used methods are to call a vector zero when its norm is
zero or to call a vector zero when it's orthogonal to all other vectors in the
space. The first approach leads to least-squares approaches, which gives
things like GMRES or QMR in linear algebra or first-order system least-squares
(FOSLS) finite element methods. The second approach leads to Galerkin and
Petrov-Galerkin algorithms, which gives things like CG in linear algebra or
more standard Galerkin or Petro-Galerkin finite element methods.

Anyway, that's just an aside, but I wanted to add that how we visualize zero
has a definite computational, algorithmic affect.

------
visarga
> shunya

Straight from Buddhist meditation, meaning "emptiness" -> and now it's the
basis of math and science. And it's not just zero, take a look at the
pronunciation of numerals in Sanskrit:

0 śūnya - Arabic "ṣifr" -> Latin "zephir" -> "zero"

1 éka - Greek "ena" -> Latin "unus" -> English "one"

2 dvi - like the prefix "di-" or "bi-" meaning double, German "zwei" ->
English "two"

3 trí - like "three"

4 catúr - like "quatre" in French

5 pañca - like Greek "pénte"

6 ṣáṣ - like six, or "șase" in Romanian

7 saptá - like seven, or "șapte" in Romanian

8 aṣṭá - like German "acht", English "eight"

9 náva - like nine, or "nouă" in Romanian, which also means new in both
languages (new sounds like nine)

10 dagan - like Latin "decem"

It's amazing how much Sanskrit is in our languages.

~~~
aap_
Greek _ena_ has nothing to do with that. It comes from _sem-_ , the same root
as that of lat. _semel_ 'once' and other words. If you want a Greek cognate to
_unus_ and _one_ there is only (ancient greek) _οἰνή_ 'one on a dice'.
Sanskrit _eka_ has _ka_ instead of expected _na_ for some reason, otherwise it
agrees with the rest.

~~~
visarga
I worked on intuition and Google :-)

~~~
kaishiro
Can you give some more context regarding what your response means?

~~~
visarga
It means I recognized the similarities and researched them on Google.

------
kazinator
> _In 1299, zero was banned in Florence, along with all Arabic numerals,
> because they were said to encourage fraud. Zero could easily be doctored to
> become nine, and why not add a few zeros on the end of a receipt to inflate
> the price?_

No doubt, the ban was supported by arguments about how it's making everyone
more productive by catching problems early and eliminating a whole class of
errors.

And so that would be where we can trace the origins of static typing.

------
_nrvs
A fantastic longer read on the topic is "Zero: The Biography of a Dangerous
Idea" by Charles Seife – highly recommended!

~~~
sedachv
I love popular math book recommendations, but that particular one gets pretty
terrible reviews: [http://www.ams.org/notices/200009/rev-
gray.pdf](http://www.ams.org/notices/200009/rev-gray.pdf)

~~~
andars
For an alternate take on it, see this positive review:
[http://www.maa.org/press/maa-reviews/zero-the-biography-
of-a...](http://www.maa.org/press/maa-reviews/zero-the-biography-of-a-
dangerous-idea).

------
known
Timeline of Ancient history
[https://en.wikipedia.org/wiki/Timeline_of_ancient_history](https://en.wikipedia.org/wiki/Timeline_of_ancient_history)

------
jorgeleo
From the picture in the article "The Babylonian symbol for an absence of
numbers".

Then that is not 0, that is null!

