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Exactly. The exact amount of sleep needed on average is almost certainly an irrational number. (Because almost every number is irrational)
by tomtomtom777 3y ago
Exactly. 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 agoYes, but in reality, you slept .37827387654329617345987613475130465019873458612386459012374587203475. . . days
- saalweachter 3y agoDoesn't that depend on whether time is quantized?
- PawgerZ 3y agoYes, but with no viable theories of a minimal unit, I'll assume that no such thing exists until given proof otherwise.
- nyrikki 3y agoBase 12 being 3-smooth, any number with 2 or 3 as a factor has a reciprocal with a terminating expansion. base 60 is 5-smooth, so any number with 2,3,5 as a factor has a terminating expansion. Just as SI has to add in deg min sec for fields like astronomy. As the practical numbers are quite dense up to 60, they could divide by multiplication of the reciprocal for many more numbers. Floating point is more complicated than just the base as the radix also matters. C(++) finally got decimal radix support this year in the standards and IBM has had decimal floats for a long time. FFT and encryption often use mixed radix despite being a binary base too. It is a far more complicated subject than it appears on the surface. But there are problems that aren't easily solvable in base 10. The degrees of a circle are an example and why navigation uses the nautical mile, where 1 nautical mile= 1 minute of latitude is an example. 12,60,360 are Superior highly composite numbers and 12 is the smallest 3-smooth and 60 is the smallest 5-smooth. This also means that with using 360 degrees one can divide a circle or semicircle in 12 sections with just a square, 345 triangle and equalatrral triangle. Where decimal or even radians requires the square root of 2, pi, etc... I am a fan of universal units of measurement, but had they been base 12 it would have been better IMHO. SI could be more broadly adopted if it has been base 12.
- xigoi 3y agoBase 6 is better than base 12. https://www.seximal.net/ https://www.seximal.net/
- nyrikki 3y agoPretty light on details, but if it works for you that is great. Quartiles and hand counting would be my argument for 12 but am probably biased based on familiarity.
- xigoi 3y agoSeximal is actually great for hand counting. You can use fingers the classical way for one digit per hand or base 6² compression for two digits per hand, allowing you to count up to 1296 with two hands.
- 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.