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Why Did Thomas Harriot Invent Binary? (2021)
- cubefox 3y agoPrevious discussion: https://news.ycombinator.com/item?id=35663799 https://news.ycombinator.com/item?id=35663799
- dang 3y agoThanks! Macroexpanded: Why Did Thomas Harriot Invent Binary? - https://news.ycombinator.com/item?id=35663799 https://news.ycombinator.com/item?id=35663799 - April 2023 (48 comments)
- revertmean 3y agoInteresting 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 3y agoTo be fair, binary is foundational to computer programming so I would expect to find Knuth there.
- revertmean 3y agoI 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 3y ago> 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.
- dhosek 3y agoI think that the only reason this sentence isn’t part of the literature is that DEK is more of a software guy than a hardware guy.
- benatkin 3y agoMostly because he's a writer.
- permo-w 3y agoit 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: xy + 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 = 9147 + 4. so our number ends with 4 y=147 is not 0, so we do 147 = 169 + 3. so our number ends with 34 y=16 is not 0, so we do 16 = 19 + 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
- permo-w 3y agounable to edit it now, but where the text switches to italic there’s meant to be a "*"
- pier25 3y agoActually ancient Egyptians invented binary calculations much earlier. https://medium.com/@jillplatts/ancient-egyptians-the-original-computer-scientists-ab97322d48dd https://medium.com/@jillplatts/ancient-egyptians-the-origina...
- benatkin 3y agoThe 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 3y ago> I'd like to see an expert's analysis. Wikipedia seems like a good place to start: https://en.wikipedia.org/wiki/Binary_number https://en.wikipedia.org/wiki/Binary_number
- readthenotes1 3y agoOne 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...
- AdieuToLogic 3y ago> 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 ... I think of this as "hubris of the now." This is where people cannot fathom how previous generations could achieve what they did without the tools and/or knowledge which exists in the present. An example of this is found when contemplating how atmospheric differential equations were solved with computers having about 4k of RAM in the 1940's.
- kallistisoft 3y agoA 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
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- goatlover 3y agoWhat 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.
- pfg_ 3y agoChurch 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
- gerdesj 3y agoThat'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.
- jt2190 3y agoEdit: 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.
- deleted 3y ago[deleted]
- codedokode 3y agoI 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 3y agoFloats are just scientific notation in binary. Once you decide that's ehaty out want, the hard part is hw and error handling.
- dspillett 3y ago> I wonder how developers of computers came to idea to use binary numbers? Essentially a logical consequence of electronics and the equipment they were working with at the time. That 0 and 1 are not pure zero-volts and 5-voltsⁱ. There is a lower range that will definitely be ready as 0 and an upper range that will be read as 1, and hopefully the signal doesn't spend long between them. Also switching isn't absolutely instant, switches bounceʲ, debouncing methods smooth that but drag out the time to transition from 0->1 or 1->0. All of this is try for multi-level electronics but even more so, making it easier and more reliable to work in binary than 3, 4, or more levels per bit. Ternary (base 3) computers did exist, some using -1/0/+1ʰ and some using 0/1/2, and multi-level logic is used for some storage methods today, so binary isn't the be-all and end-all it is just most usually the most reliable & convenient tool for the job. ---- [i] or 3.3 or whatever other logic levels you are using [j] a lot less of a problem with microscopic transistors but think back to old chunky relays & tubes [h] not sure if that is just notation or there were negative voltages involved - I last read about these things properly at Uni ~2.5 decades ago
- codedokode 3y ago> All of this is try for multi-level electronics but even more so, making it easier and more reliable to work in binary than 3, 4, or more levels per bit. You don't need many levels. IBM's tabulators used pulses to represent numbers in decimal (e.g. 6 pulses to transmit digit 6). That's why it is surprising that computer developers didn't reuse existing technology and went with a new system.
- eternalban 3y agoI thought the Daoists invented binary. I-Ching is a binary system of size 2^6.
- dhosek 3y agoBut the numbering doesn’t really follow the usual positional aspects of binary. You would expect that the hexagram in the second position, given the first hexagram would be either 夬 (43) or 姤 (44) depending on whether you’re big-endian or little-endian. For that matter, the first hexagram should be number 0 for it to be a binary system. Just because you have an 2^n symbols doesn’t automatically make you binary.
- eternalban 3y agoThe numbers assigned to the hexagrams are not part of the actual I-Ching. You're free to consider the 'receptive' as 0 and the 'creative' as 63 if you wish. The sequence is also explicitly known as an 'arrangement'. That said, my comment was somewhat tongue in cheek.
- superb-owl 3y agoLeibniz himself was somewhat inspired by the Taoist I Ching, which has a beautiful binary counting system. https://en.wikipedia.org/wiki/I_Ching%27s_influence https://en.wikipedia.org/wiki/I_Ching%27s_influence
- AdieuToLogic 3y agoIn this context, "invent" is a poor choice of words. "Reify" or "document" perhaps would be better.
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- dwheeler 3y agoI'm skeptical that an "unpublished manuscript" should count. If someone quietly has an idea, but tells no one, it has no value to humanity. If the world wasn't told, then the world has every right to say "that does not count".