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Unknown Digit

For sig figs, or anything.
  (+12, -3)(+12, -3)
(+12, -3)
  [vote for,
against]

It took mankind quite a while to come up with the zero, but it's been a huge success ever since. I propose a new digit, meant as unknown. Unknown is not the same as zero, and the number 198,000 is currently indistinguishable from the estimate 198,000 without specifically adding an uncertainty factor (done in some scientific realms, but unwieldy and mostly ignored elsewhere). The new digit would let you know at a glance the number of significant figures. 198,XXX tells you that you just don't know (or maybe care) about digits beyond the 8. Of course, we could keep the rigourous and precise uncertainty for scientific persuits, but this would be useful anywhere.

I came upon this idea when forced to choose a date for a picture from the past when I scanned it into my computer. Despite only knowing that it was in June of '98, I had to type in 6/1/1998. Some future ancestor will think this was a precise date, and perhaps base assumptions on that bad information. Had I the option, 6/X/1998 would have been perferred. In other cases, X/X/1998 or even X/X/199X would have been appropriate.

Worldgineer, Jul 01 2012

The problem with new 'sensible' standards. http://xkcd.com/927/
[AusCan531, Jul 03 2012]

http://www.cambridge.org/9780521424639 [pocmloc, Jul 03 2012]

[link]






       Here's X buns (0<X<9).   

       There'd need to be some convention as to how "X" behaved in sorting, ranking etc - maybe it could be assigned a value of 0. Actually maybe not, since that would cause problems with the "0th of July", or "month 0". Maybe have it count as a 1, since 1 can exist in any position in a date.
MaxwellBuchanan, Jul 01 2012
  

       Yes, but zero only works after the decimal. How do you distinguish 150 from one-hundred-and-fifty- something?   

       When the height of Everest was first measured accurately, the poor surveyor found it to be 29,000ft exactly. Fearing that people would assume he had just estimated it to the nearest thousand feet, he reported it as 29,002ft.
MaxwellBuchanan, Jul 01 2012
  

       let's all.   

       <random blather>
As [bs] mentioned, "?" is already in use.
A squiggle can be used to denote approximation ~186,000.
Database designers can subdivide a field into placeholders.
So where does the "?" or "X" go in the sort order ?</rb>
FlyingToaster, Jul 01 2012
  

       There's a already a very useful concept of nullity in databases. This is an elegant refinement of it. [+]
pertinax, Jul 02 2012
  

       The tomb of the unknown digit, being the smallest site of remembrance within Her Majesty's Commonwealth.
calum, Jul 02 2012
  

       [FT] This is not a let's all. Yes, for it to be useful it would have to be generally adopted, but the idea is solid without the general adoption.   

       As far as sorting, it should generally sort as if it had zeros in all x columns, as this would place near the nominal center of uncertainty.
MechE, Jul 02 2012
  

       //sort as if it had zeros in all x columns//   

       But then how do "12340" and "1234X" sort, relative to eachother?
MaxwellBuchanan, Jul 02 2012
  

       In an Oracle environment, 1234X would come last, in a Microsoft environment, it would come first. Come on, you knew that really, didn't you?
pertinax, Jul 02 2012
  

       I can digit. If not sigit or figit.
bungston, Jul 02 2012
  

       //Despite only knowing that it was in June of '98, I had to type in 6/1/1998//   

       I think I see your problem... you've tagged it as the 6th day of January, 1998.   

       You'd have been better off marking it 19980601, to give you 1 June 1998, with the added benefit of being able to sort all properly appended dates chronologically.
UnaBubba, Jul 03 2012
  

       But this is extraordinarily close to proper usage of significant figures.   

       Your 198,000 example (being either 198000 +/- 1000 OR 198500 +/- 500 - you didn't say) is better expressed as 1.98E5. Eliminate the unknown information altogether.
Custardguts, Jul 03 2012
  

       As a former North American who used to write dates as Month/Day/Year but now conforms to the more sensible Day/Month/Year format I agree with [Unabubba] that the Year/Month/Day format is the most sensible of all as it is sortable by chronological order. XKCD [link] does point out the problem with adopting the most sensible solution.   

       As for the //how do "12340" and "1234X" sort, relative to eachother?// question, "12340" should sort first as "X" is either equal to zero or greater. (with a 90% chance of being greater).   

       As for the original idea, I wish I could give a 2nd bun.
AusCan531, Jul 03 2012
  

       [Aus] Not true, though I made the same mistake initially. X is actually equal to 0 +/-5, it's uncertainty, not unknown.
MechE, Jul 03 2012
  

       //0 ±5//
ackshully X (though I still think ? is more accurate) should slot in as 0.49999999... .
FlyingToaster, Jul 03 2012
  

       Yes, you're quite correct [MechE]
AusCan531, Jul 03 2012
  

       //As a former North American who used to write dates as Month/Day/Year but now conforms to the more sensible Day/Month/Year format I agree with [Unabubba] that the Year/Month/Day format is the most sensible of all as it is sortable by chronological order.//   

       Actually, the D-M-Y format is the least sensible of all. The One True Date Format is indeed Y-M-D, which means that M- D-Y conforms more closely to the way dates should be written in order to sort properly. The only thing D-M-Y has going for it is internal consistency, but it is far better to be more correct than more consistent in this case. At least with M-D-Y, dates within a given year will sort correctly.   

       Incidentally, when I switched to generally writing dates in Y- M-D format, I eventually discovered an unexpected benefit: In the early part of the year, I noticed that I never absentmindedly wrote down the previous year as long as I was writing the year first.   

       //ackshully X (though I still think ? is more accurate) should slot in as 0.49999999...//   

       0.49999999… is exactly equal to 0.5 .
ytk, Jul 03 2012
  

       Can you write *infinity* in Roman Numerals?
They don't have a zero, which makes it very confusing...but I do like this idea. [+]
xandram, Jul 03 2012
  

       What [Custardguts] said - existing scientific notation covers this quite nicely, and, since it was formalised in IEEE 754, it has been the technical standard for all floating point arithmetic since 1985.   

       Consisting of 3 parts, a sign, coefficient, and exponent - you can describe any number you wish, to any level of precision you like. e.g. +123XX would be listed as +1.23 x 10^5 providing both a workable value and an indication as to the known degree of accuracy.   

       It would be neat to apply the same concept to dates as well - although that is already sort of done to some extent in dates vs datetimestamps if only by convention.
zen_tom, Jul 03 2012
  

       // It could even vary depending on what program you're running.//   

       Which would be very bad. The beauty of the idea here is that there would be a standard character which can stand in for any digit, but which would have the same breadth of validity as the digits 0-9.   

       The closest to a widely-accepted convention would be "?", or perhaps "*".
MaxwellBuchanan, Jul 03 2012
  

       Per your example with a date format, I have seen and used systems that allowed for unknown date data by using zero in place of the unknown element. In this case you could enter 6/0/1998 and the system, recognizing the zero to indicate the unknown day, would display "June 1998" as the date. These were specialized systems however and I don't know how widespread this practice is.   

       Outside of dates, I have seen "?" used frequently for unknown digits.
tatterdemalion, Jul 03 2012
  

       [bigsleep], shouldn’t the percentage error remain the same if you multiply by a known number? .i.
4x(198000±500)=792000±2000
<link>
pocmloc, Jul 03 2012
  

       //date [...] specialized systems//   

       Yep, I've used genealogy software that can handle dates with "about", "before", "after", "between", and so forth. Been trying to chase down what the internal data format was; no luck so far. Suspecting stored-as-text, and processed with a lotta extremely ugly code.
lurch, Jul 03 2012
  

       If you can write a consistent set of rules for sorting “fuzzy” dates, the actual programming is fairly simple. All you have to do is write a comparison method for your fuzzy date object that will determine whether it's less than, equal to, or greater than another fuzzy date object. You can then sort them like any other date.
ytk, Jul 03 2012
  

       Is it too late for a 'whose finger is that?' joke?
Alterother, Jul 04 2012
  

       Well... er, that _was_ the joke, actually.
Alterother, Jul 04 2012
  

       I liked the 'Array of negative size' post earlier last month, but I don't really understand what wrong with the good ole 'X' in 198,XXX in this case.
not_only_but_also, Jul 05 2012
  

       //what wrong with the good ole 'X' in 198,XXX//   

       That indicates an unknown variable, not uncertainty. That is, you would expect the result to be in the range 198,000 to 198,999. 198,?00, on the other hand, would provide a range of 197,500 to 198,499.
MechE, Jul 05 2012
  

       //198,?00, on the other hand, would provide a range of 197,500 to 198,499.// Would it? How so? Would it not instead indicate that the answer was one of the following options:
198,000
198,100
198,200
198,300
198,400
198,500
198,600
198,700
198,800
198,900
and no other possibility?
pocmloc, Jul 05 2012
  

       No, uncertainty is different than a variable.   

       If I measure that a car is clocked at 90 miles per hour, with a device that has an uncertainty of +/- 2, it could be going from 88-92 mph. In standard engineering practice, your last digit is always uncertain. For decimal numbers (including scientific notation) the uncertainty is specified by the last written digit. In this case 1.980x10^5. What this idea allows is the ability to write non-decimal numbers (with trailing zeros) the same way. That is 198,?00 has an uncertainty of +/-500, but 198,0?0 has an uncertainty of +/-50 (1.9800x1-^5).
MechE, Jul 05 2012
  

       In writing that, however, it occurs to me that the uncertainty should append to the preceeding digit. This means that 1.98x10^5 would be written as 198,?00, and have an possible range from 193,000 to 203,000. This could further be expanded by allowing the size of the uncertainty (up to +/-9) to be written after the uncertainty digit. This would allow for 198,?20 to cover a range of 196,000 to 200,000, for instance. For my car example it would be 90.?2.   

       (European readers, please excuse the American decimal points and comma separators.)
MechE, Jul 05 2012
  

       I think we've forked a bit: there's a distinction between   

       "my driver's license number is one two three four five something seven eight nine" : 12345X789   

       and "approximately 18,000": 18,XXX
FlyingToaster, Jul 05 2012
  

       Of course there is no variable, and it's not an equation. It's a number in scientific notation. But in an engineering measurement, there is uncertainty. If I measure something that is 1.98 meters long, with a device that is accurate to 2 centimeters, I don't know where it is between 1.96 to 2.00m. If I measure it with something that is accurate to 2 millimeters, then I know it is between 1.978 and 1.982 meters. That is the signficant figures application mentioned in the original post. And by standard practice, in scientific notation, the uncertainty is in the last written variable, exactly as I showed it in the post before that one.   

       I'll admit that the date application mentioned calls for a variable, not an uncertainty, but yes, they are two different things.
MechE, Jul 05 2012
  
      
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