[HN Gopher] Why Did Thomas Harriot Invent Binary?
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Why Did Thomas Harriot Invent Binary?
Author : adityaathalye
Score : 43 points
Date : 2023-05-17 06:31 UTC (3 days ago)
(HTM) web link (fermatslibrary.com)
(TXT) w3m dump (fermatslibrary.com)
| cubefox wrote:
| Previous discussion:
| https://news.ycombinator.com/item?id=35663799
| revertmean wrote:
| Interesting to me:
|
| "So far as I know, the only person who has attempted to explain
| Harriot's transition from weighing experiments to the invention
| of binary is Donald E. Knuth, who writes"
|
| It's amazing how the name of Knuth pops up in such a variety of
| different subjects!
| bombcar wrote:
| To be fair, _binary_ is foundational to computer programming so
| I would expect to find Knuth there.
| revertmean wrote:
| I wouldn't, just because it's so long ago. It's like reading,
| "the only person who has attempted to build Babbage's
| Difference Engine is Donald E. Knuth"!
| vanderZwan wrote:
| > _just because it 's so long ago._
|
| That's precisely why I would expect him the most. If anyone
| would dig deep into the history of mathematics to find and
| understand all of the origins of fundamental concepts in
| computer science, it's Knuth.
| benatkin wrote:
| Mostly because he's a writer.
| permo-w wrote:
| it seems inevitable to me that someone would invent binary, or
| ternary, or likely nonary
|
| bases are just the number of symbols you're allowed to use to
| represent a number. so base 10 has ten symbols: 0123456789.
| base 2 has two symbols: 01, base 3 three: 012, etc etc.
|
| someone will eventually look at a system with 10 symbols and
| think "what if we have x symbols instead of 10?"
|
| once you realise the basic mechanism through which decimal
| represents a number - i.e. you can write any natural number as
| "some y multiples of x + [a number z between 0 and x-1]" - with
| a bit of nesting you can derive any number of any base
|
| take 1327. let's write it in base 9. the way I would do this is
| to write 1327 in the form:
|
| x _y + z = 9y + [0,8]
|
| then if y != 0, we rewrite y itself in this form, then again
| with each new y, until y = 0. each z we produce is the next
| most significant digit in the answer. when y=0, the z produced
| is the most significant digit
|
| 1327 = 9_147 + 4. so our number ends with 4
|
| y=147 is not 0, so we do 147 = 16 _9 + 3. so our number ends
| with 34
|
| y=16 is not 0, so we do 16 = 1_9 + 7. our number ends with 734.
|
| y=1 is not 0, so we do 1 = 0*9 + 1. our number ends with 1734
|
| y=0 is 0 so we terminate and our number is 1734
|
| you can do this with any number and any base as long as you
| have the symbols for it
| [deleted]
| pier25 wrote:
| Actually ancient Egyptians invented binary calculations much
| earlier.
|
| https://medium.com/@jillplatts/ancient-egyptians-the-origina...
| readthenotes1 wrote:
| One thing that occurs to me is that we often fail to believe
| that people 3000 years ago were just as smart as we are,
| blinded both by our knowledge of them and our certainty of
| their limited knowledge. Limited knowledge does not mean that
| one is not innately smart though, and unable to figure some
| stuff out...
| benatkin wrote:
| The title is from the article. I dunno why you think the author
| who took the time to write the article deserves this gotcha or
| why we should divert focus from the article. If it was
| editorial by the submitter then yeah maybe...
|
| Edit: on review it does seem to be on topic, sorry. It seems
| unconvincing to me because it has only multiplication and
| division, where addition and subtraction point more to
| recognizing it as a workable number system. I'd like to see an
| expert's analysis.
| CharlesW wrote:
| > _I 'd like to see an expert's analysis._
|
| Wikipedia seems like a good place to start:
| https://en.wikipedia.org/wiki/Binary_number
| vanderZwan wrote:
| I suspect this article refers to binary _positional notation_ ,
| specifically, although it could have been more explicit about
| that.
|
| Having said that it would indeed have surprised me a lot if
| powers-of-two based calculations wouldn't be among the oldest
| ones we have. Doubling or halving things seems quite natural.
| kallistisoft wrote:
| A few gripes...
|
| Binary is impossible to 'invent' as it is just an application of
| established arithmetic rules to a base 2 number system.
|
| If i declared an arbitrary base of 73 you wouldn't say I just
| 'invented' septuaginta-tresinary??
|
| People have been using base 2 for thousands of years prior to
| Thomas Harriot, see egyptian multiplication, and to assume that
| these early mathematicians didn't understand the concept of base
| is naive!
|
| /get off my lawn
| water-your-self wrote:
| Im updating wikiedia for septuaginta tresinary, how would you
| like to be credited?
| swayvil wrote:
| So it's implicit in counting. It emerges naturally from mathy
| ideas. Like multiplication and calculus.
|
| Maybe we could say that he discovered it like Columbus.
| goatlover wrote:
| What about base infinity? Every number gets a unique digit.
| Would need something that generates a unique digit pattern for
| reach number that isn't a base.
| gerdesj wrote:
| That's a tricky one. Should we be able to actually write down
| each and every digit? If so then you'll need to invoke some
| sort of infinite related concept to allow it to happen. I'm
| not a mathematician but:
|
| Let the digit for one be a single pixel (the simplest mark I
| can make), two is two lots of one pixels etc. Now we need an
| infinite number of these.
|
| I don't think we can change over to say symbols made up from
| pixels either, nor mess with multi dimensions to add extra
| "depth". In the end we still need an infinite number of
| pixels or pixel properties - we could mess with colours but
| that is simply adding dimensions.
|
| We can conceive of base infinity but I don't think we can
| actually use it as such except symbolically. We can decree
| that a particular symbol or construction for a symbol
| represents a particular digit within base infinity that we
| can define by other means, and we can do that a lot but can
| we do it infinitely often? If we relax the physical
| representation requirement, then I'd say yes, otherwise no.
|
| I've no doubt that this concept is well understood and dealt
| with already by the pros.
| pfg_ wrote:
| Church numerals are kind of like this
|
| I don't think it's possible to represent decimals this way
| though - 8.1 = "8 + 1/infinity" = 8.0 and so is any other
| number for the decimal
| [deleted]
| codedokode wrote:
| I wonder how developers of computers came to idea to use binary
| numbers? As I remember, early calculating machines used decimal
| system (e.g. Babbage's machine, IBM's tabulators). For example,
| did Konrad Zuse invent floating-point binary representation
| himself when developing his machine or there were previous works
| which described how numbers can be added in binary system using
| relays or tubes?
|
| So, were there any works on floating-point binary numbers and
| implementing operations with them before 1938?
|
| Also, did he invent logic gates or there also were previous
| works?
| andromeduck wrote:
| Floats are just scientific notation in binary. Once you decide
| that's ehaty out want, the hard part is hw and error handling.
| eternalban wrote:
| I thought the Daoists invented binary. I-Ching is a binary system
| of size 2^6.
| jt2190 wrote:
| Edit: Reading further, it's clearly about the written form used:
|
| > [I]t is unlikely that Harriot hit upon binary notation simply
| because he was using weights in a power-of-2 ratio, something
| that was a well-established practice at the time. _Equally if not
| more important was the fact that he recorded the measurements
| made with these weights in a power-of-2 ratio too_. For when
| recording the weights of the various part-ounce measures, Harriot
| used a rudimentary form of positional notation, in which for
| every position he put down either the full place value or 0,
| depending on whether or not the weight in question had been used.
|
| My original comment:
|
| I'm a little unclear, as the article mentions "binary numeration"
| several times. Am I to understand that the Harriot is the first
| _written_ evidence of binary in a _modern_ form, that is, using
| arabic numerals like we do today? (example we 'd write four as:
| 100) Other commenters are noting that base 2 has been known for
| far longer than the last 500 years.
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