6 ms·
> Also nice how they IMMEDIATELY ran into a continuing fraction 1/3, which is exactly the point of the 60-minute hour, 24-hour day, or 360-degree circle: lots o
by L3viathan 3y ago
> Also nice how they IMMEDIATELY ran into a continuing fraction 1/3, which is exactly the point of the 60-minute hour, 24-hour day, or 360-degree circle: lots of factors.
While I agree in principle, this example is not evidence of it. It's not like we measured the amount of sleep needed and it's precisely 8 hours. A more reasonable thing to say would be: You need to sleep for 3.5 metric hours.
- tomtomtom777 3y agoExactly. The exact amount of sleep needed on average is almost certainly an irrational number. (Because almost every number is irrational)
- Karellen 3y agoAre you sure? Isn't the average calculated by dividing by n, an integer? Edit: I mean, you're right that nearly every number is irrational. But I think averages are going to be some of the tiny fraction of numbers that aren't.
- red_trumpet 3y agoOnly if you take an average of rational numbers. Like e/2 is still irrational.
- ReleaseCandidat 3y agoWhile in theory you could measure sleeping time in fractions of 2 pi, I'd guess that you're using rational numbers in the actual calculation anyways.
- red_trumpet 3y agoWhy would sleeping time be a fraction of 2pi? > I'd guess that you're using rational numbers in the actual calculation anyways. Well, actually one uses floating point arithmetic, which isn't rational numbers either (as shown by the classic example a = 1/3, b = 3*a, then b != a)
- ReleaseCandidat 3y ago> Why would sleeping time be a fraction of 2pi? The rotation of a hand of the clock, expressed as the arc length of the curve of its endpoint :) A sleeping time of 0 is always a problem, though.
- red_trumpet 3y agoBut why would the second factor be a rational?
- 867-5309 3y agohttps://en.wikipedia.org/wiki/Turn_(angle) https://en.wikipedia.org/wiki/Turn_(angle)
- saalweachter 3y agoI mean, we could be measuring time in radians. We already subdivide degrees into minutes and seconds, might as well call the day 2 pi radians. We sleep for 2/3 pi radians of the day in that case.
- red_trumpet 3y agoThe whole argument started when somebody above claimed that we probably do not sleep exactly 8 hours, but some weird irrational number. That problem persists even if you measure in radians...
- Rayhem 3y agoDo the physicist thing and just define all your constants to be one. "How long is a day? 1 day." "I slept for .37 days." This nicely unifies things with the tao manifesto[1] people since 1 day = 1 turn = 1 tau = 2 * pi radians and reinforces the periodic nature of these things. [1]: https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto
- PawgerZ 3y ago
- littlestymaar 3y ago> Edit: I mean, you're right that nearly every number is irrational. The set of rational number is a “null set”: https://en.wikipedia.org/wiki/Null_set https://en.wikipedia.org/wiki/Null_set
- jstanley 3y agoActually averages are even more likely to be irrational than ordinary numbers. It only takes a single irrational input to make the average irrational.
- reliablereason 3y agoIt’s almost certainly a rational number as activity in the body is finite. There will be an exact point at which a certain molecule has interacted with another molecule marking the exact point of perfect sleep. Averaging many rational numbers can’t get you an irrational number. Also it is invalid to compare infinite series like you do in your paracentesis argument, there are infinitely many irrational numbers and infinitely many rational ones. If you do it, you run in to contradictions. (Something which is related to Cantor's paradox)
- yakubin 3y agoThe statement OP put in parentheses is a well-defined statement in mathematics. It means that the Lebesgue measure of the set of the rational numbers is zero in the space of real numbers.
- aydyn 3y agoThat's nice, but reality doesn't live on the real number line.
- _Algernon_ 3y ago"all models are wrong but some models are useful" You're not being clever by being pedantic.
- aydyn 3y agolol saying that a number in reality will be irrational is peak pedantry. Try again, sweaty.
- downvotetruth 3y ago> will be an exact point at which a certain molecule has interacted with another molecule marking the exact point of perfect sleep Just because the best current theory suggests a smallest observable time span does not mean as a consequence that time is discrete.
- willis936 3y agoI don't really care how much sleep I get as long as it's enough. I care greatly when the bus leaves and when my meetings are. Anything that hopes to replace a clock had better be adding precision rather than removing it.
- kybernetikos 3y agoDecimal seconds are slightly shorter than normal seconds, so times that use seconds are more precise. The other fun thing is that decimal time doesn't really need names for the levels, it's just numbers of significant figures so if you only want to give the first digit of the seconds that works too.
- willis936 3y agoIt's less precision for a given number of symbols. Fewer usable factors mean you can only reasonably divide up segments of time into larger, less precise chunks.
- kybernetikos 3y agoThis is far from the truth. The closest time before midnight you can conveniently represent in the current time system is 23:59:59 which is six symbols for a standard second before midnight. In decimal time the closest time before midnight you can conveniently represent would be .9:99:99 which is noticeably closer (0.163 of a second closer) to midnight and uses only 5 symbols. This should not be surprising - our current system is very inefficient in its use of digits.
- MagicMoonlight 3y agoYou’ve picked the only time where the systems overlap. Try converting something like 45 minutes into this convenient time system and let us know how efficient it is
- kybernetikos 3y ago
- itslennysfault 3y agoI blame the labor unions... "Eight hours for work, eight hours for rest and eight hours for what you will."