Hacker News Reader

> I wouldn't be so sure there is nothing special about the duration of a second. It comes from dividing a day into two sets of 12, then those 12 into five sets of 12 (12x5=60), then those 60s into 60 each.

That's exactly why, actually. This is what the second was once defined as, but the problem is that the length of a day varies slightly - up to ~8s depending on the time of year and other seconds. As the article mentions, the amount of time that is defined as one second is now taken as an arbitrary fraction of the decay time for Cs-137 that is close the mean value of the length of the second defined relative to the time it takes the planet to rotate.

In terms of keeping time in our common lives it's not really a problem for there to be a little bit of ambiguity in how long a day/minute/second is, but this is important for things that rely on precision timing - like tuning in music. It'd also be crazy hard to keep track of how long a second is at any given moment, since some of the variation is random from tidal forces.

>"It'd also be crazy hard to keep track of how long a second is at any given moment, since some of the variation is random from tidal forces."

I think you could use something like this, which may be accurate enough:

https://en.wikipedia.org/wiki/Sunrise_equation

It may be more accurate to use something like the JPL ephemerides to convert between the two though:

https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/FORTRAN/req/...

Finally, the current definition of a second is meant to approximate the previous definition of a second. I am saying the previous one may have some correlation with biological activity.

If I understand you correctly, you are advocating for defining the second such that its length varies, but its connection to a day does not? And you would also introduce locality to the definition?

edit: Or perhaps you meant to tune variably, and not redefine the second. That sounds more sensible, but not as practical.

Here is the scheme which I am thinking may better link timekeeping to biological clocks:

  A day is defined as sunrise to sundown.
  A night is defined as sundown to sunrise.

  Every day consists of 12 hours.
  Every night consists of 12 hours.
  Each hour consists of 60 minutes.
  Each minute consists of 60 seconds.

  There are always 60*60*12 = 43,200 seconds each day and night.
  Within a given day or night every second is of equal length.*

  On the equinox (length of day = length of night) we will have a "base unit" s0.
  At times/places when there is more daylight than that, the duration of a second 
  during the day s_d > s0 and during the night s_n < s0.

  *It may be better to continuously vary the duration of a second so there 
  is not a sudden change at sundown/sunup. It can perhaps be linked to   
  https://en.wikipedia.org/wiki/Solar_zenith_angle. I think the Egyptians used 
  to use Sirius at night for this, but don't remember where I heard that. 
  Anyway now we can always be monitoring the position of the sun even when we 
  cannot see it at the moment.

The second part of what I am suggesting is there may be aesthetic or health benefits to varying periodic phenomenon along with the relative duration of a second. So if frequency is f = cycles/sec and we want to maintain the same numerical value, the f/f0 should scale with s_d/s0 and s_n/s0 (or just s/s0 if we are continuously varying it). Consider if f0 = 432 is ideal at the equinox, and we are wondering about f = 440. I would say that we look for when/where s = 440/432 x s0 x k. Setting the scaling constant k =1 and using an R package that in turn uses noaa sunrise/sunset data[1], I got 3/26/2016 at + 18 degrees latitude. You could do the same calculation in reverse from a given time/latitude to choose a preferred frequency.

[1] http://www.esrl.noaa.gov/gmd/grad/solcalc/

I see. I can't really get on board with a system where half an an hour at lunch is twice as long as half an hour at dinner, and I have a suspicion that it would actually further mire arguments about music pitch, but it's certainly a funny thought.

>"I can't really get on board with a system where half an an hour at lunch is twice as long as half an hour at dinner"

Move to the equator? J/k, I would not think this system would be law, or used for all purposes. Despite the huge pain that dealing with timestamps from various locations can sometimes be today, I suspect my scheme would make it more difficult to synchronize long distance activities.

It would more be a chill, get back to nature, type of timekeeping. Used at resorts and rehab centers.

Here is what I mean, nothing needs to be vague. My model predicts that the preferred pitch should track something like this with date and latitude: https://s11.postimg.org/mkw753lpf/image.jpg

The only free parameters are:

  F0 = the pitch of A4 on the when there are 12 hours of day/night
  k  = a scaling factor that determines how much to change the pitch based on duration of the variable second

Here I used F0 = 432 and k = 1, but those values will probably need to be determined by experiment.

Except that our day length is also changing -- very slowly, but changing it is. Further, given that the human clock, disconnected from day/night feedback, apparently treats 24.2 hours as a day.... https://en.wikipedia.org/wiki/Circadian_clock

>"the human clock, disconnected from day/night feedback"

I am saying the second was originally linked to length of day, so the calibrated clock should be used. Also, at some point the differences due to latitude changes, etc will be biologically indistinguishable from stuff like the effect of clouds.

So, we could say that a "circadian second" is about 1.008 seconds? (On average)

How precisely is that 24.2 known I wonder..

From the referenced Wikipedia link:

By recording the daily rhythms of hormones and body temperatures in 24 healthy young and old men and women over a one-month period, the researchers conclude that our internal clocks run on a daily cycle of 24 hours, 11 minutes.

...

Researchers previously reported a range of 13 to 65 hours, with a median of 25 hours, 12 minutes. The variation between our subjects, with a 95 percent level of confidence, was no more than plus or minus 16 minutes, a remarkably small range.

http://news.harvard.edu/gazette/story/1999/07/human-biologic...

I did refer to this with the Babylonian thing but I didn't want to get sidetracked into a review of ancient number bases. I love your reference about non-constant time though, most interesting.

According to NIST It's slightly more arbitrary than that:

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

Not sure of the numerological significance of 9192631770.

> Not sure of the numerological significance of 9192631770.

It has none. It just happens to make the new cesium-based definition of a second roughly equal to the historical definition of a second as 1/86400 of a mean solar day.

12 is a funky number, but arbitrarily grouping them into 2's and 5's takes the shine off.