Timeline for How advanced can a civilization get without zero?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jul 7, 2018 at 7:51 | comment | added | mattdm | Imagine this system developing with counting on hands in base five, with the thumb as X and one hand as the ones column and the other hand as the fives column. This is (um) handy because now we can count to 30 on our fingers — and the thumb is already clearly a "special" sort of digit. I just tried counting that way, and it's actually more intuitive-feeling than counting in base 6 with two hands and zero. | |
| Jul 6, 2018 at 16:31 | history | edited | plasticinsect | CC BY-SA 4.0 |
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| Jul 6, 2018 at 16:25 | comment | added | leftaroundabout | Great answer. This system feels crazy because we are so used to ours, but I actually find it somewhat compelling. I suspect it would actually not bad if we used such a consequently zero-free system, as opposed to having zero but still always starting to count from one. (I think however seriously the best approach is to always start counting from zero, as most programming languages do.) | |
| Jul 6, 2018 at 11:41 | comment | added | AlexP | @Steve: "Roman-style" numerals have never been used for mathematics. They were used for writing numerical values in text. For mathematics the Romans used the Greek system, which is very similar to what this answer describes. (And which included a symbol for "nothing", used in mathematical tables.) | |
| Jul 6, 2018 at 8:37 | comment | added | plasticinsect | @Steve The major disadvantage of roman-style numerals is that they are not place-sensitive. Because of that, it is very difficult to do arithmetic with them. Place sensitive numerals (including both the system we are familiar with, and the system described in my answer) make it possible to do things like long multiplication, division, addition, subtraction, etc. This is a huge advantage. | |
| Jul 6, 2018 at 8:01 | comment | added | Steve | I don't see a need to force a number system similar to our own, where a zero digit would more naturally fit... consider something based on a loose analogue of Roman numerals in base 9... I, II, III, IIII, IIIIN, IIIN, IIN, IN, N, NI, NII, NIII, NIIII, NIIIIN etc. "nothing" / "empty" is just a blank, and isn't a number. Powers of 9 (or maybe 3) get unique symbols. Simple fractions with powers of 9 as the denominator are equivalent to "scientific notation". As zero cannot appear as the demoninator of a simple fraction, this further confirms the concept does not correspond with a number. | |
| Jul 6, 2018 at 6:52 | history | edited | plasticinsect | CC BY-SA 4.0 |
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| Jul 6, 2018 at 6:46 | history | edited | plasticinsect | CC BY-SA 4.0 |
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| Jul 6, 2018 at 6:26 | comment | added | plasticinsect | @hyst329 Thanks. I added a mention of simple fractions to the answer. | |
| Jul 6, 2018 at 6:18 | history | edited | plasticinsect | CC BY-SA 4.0 |
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| Jul 6, 2018 at 5:10 | comment | added | trolley813 | @plasticinsect Instead, you can just stick to the simple fractions (they were known long time before decimal ones, and are in fact more universal) | |
| Jul 6, 2018 at 5:09 | comment | added | plasticinsect | @Draconis I don't find it too hard to imagine. Exponents are just an extension of the concept of multiplication, and multiplication works fine without zero. Plus you don't really need to understand exponents to use the idea behind scientific notation. All you really need to know is that this number needs to be shifted over three places when you add it to that number. | |
| Jul 6, 2018 at 4:47 | comment | added | Draconis | It's difficult to imagine scientific notation (which requires exponents) being developed without the concept of zero. | |
| Jul 6, 2018 at 3:49 | history | answered | plasticinsect | CC BY-SA 4.0 |