Open Data and Time.

Open Data has an assumed quality of fairness. Moreover, fairness is simple from a computational point of view. Models based upon latitude, with variations in seasonal effects are not symetric and therefore inherently more complicated. This model is based upon longitude, and symetric in time to the day level.

Sadly, Fairness is not all that exciting: ½ + ½ = 1 = 360°. Like sunshine and darkness, fairness is a resonance. Time is "coordinated" to measure a point in darkness (Midnight), but can be transformed to measure (an observable) Noon.

There is a "Business Rule" governing the behaviour of the resonance at intermediate values. However, the basic model is sufficient to see useful results. The model is compatible with scientific observations, where specific measurements must still be tied to point coordinates. The sign of the longitude and symetry are sufficient by themselves to measure openness and transparency.

The Model:

Two Weeks is all the historical memory fairness requires, because in the right coordinate system, ½ of Earth becomes indistinguishable from the other ½ Earth.

 

Day Zero

 x=

Units

Value

West

270° +

 

°

 

East

450° +

 

°

 

 

 

Global Rate of Change

°/day

 

 

 

Day Length Balance

hr.

 

 

The Metrics

Global Rate of Change (°/day)

The western day and the eastern day each span 180° for a total of 360°. (?: would %, 2 π Radians, or 400 Gradians be better)

Day Length Balance (hours)

The day length should always be 24 Hours. For some use cases, there is a disparity (an overlap in coverage), measured in hours. Asking who "wins" and who "loses" is the wrong question because the winner will be the loser in the next cycle.


Use Cases

Earth x ½, x= 1/2

Both factors are in balance.

Civil Time

Civil Time begins and ends when the sun is 6° below the horizon. As long as it is applied fairly in both east and west, there is no overall effect (x= (96 + 84)/360). Daylight Saving Time has no effect due to symetry - one could also call DST Darkness Borrowing Time.

If within the zones, it is used to extend sunshine hours there is a disparity (x=(96 + 90)/360). The further from the equator, the bigger the ratio of sunshine to darkness. At worst, the assumed need to compete will drive both zones (x=(96 + 96)/360) and the day will be compressed by 6.25%

An agricultural work day is "dawn to dusk" but disparity is also seasonal. An industrial work day is non-seasonal, and gives rise to a disparity at all latitudes.

Nautical Time

Nautical Time begins and ends when the sun is 12° below the horizon. The same comments about Civil Time apply. A ship at sea has no disparity, not having much choice in the "at sea" status (x= (102 + 78)/360). A day sail is longer in summer (x= (102 + 90)/360), but the balance remains since "at sea" does not depend upon latitude. Effectively, all work at sea is seasonal.

Astronomical Time

Astronomical Time begins and ends when the sun is 18° below the horizon. The name is somewhat misleading. This is the time of day when accurate astronomical observations are possible. It is always in balance, weather permitting. While there is no hard evidence the system was designed by small children wishing to delay bedtime, the conclusions are inescapable.

Climatologist Time, x= (90.8333 + 89.1667)/360

This is not an "official" designation, and yet, the only standard, the approximate angle below the horizon the sun must go to duplicate the bending of light (relativistic effects, Atmospheric Refraction). To measure Climate Change it is first necessary to find the normal value. However, that value is outside human experience. Just as we have little choice in average body temperature (~37 C°), we are aware that we need more than a few minutes sleep each day. This value is interesting because the resultant disparity is not large enough to observe on a daily basis, but could be seen on a yearly basis (x= (360/365.25)*(90.8333 + 89.1667)/360). The disparity is half an hour - close to the variation in the Equation of Time (Sundial Correction) over a year's time. The model predicts that the argument is not over whether it gets cold at night, an unsurprising, but necessary result.

White Nights, x= (1/2) * (0/24+12/24+12/24+0/24)

Far to the North and South, there is only a incomplete sunset in mid-summer balanced by a long winter night. It is fair too.

Leap Years, x= (1/2) * (((365*3)+(366))/1461)

The Gregorian Calendar, with a leap year every four years, is fair, and in balance (x= (1/2) * (((365*3)+(366))/1461)). It is interesting that it is only so after the full 4 year period - there is no such thing as a fractional reserve calendar and days must be added in whole chunks. Partial sums are in balance (x= 1/2*(((365*3)+(365))/1460)) or (x= 1/2*4*365/1460), but the entire disparity can be attributed to the Leap Day itself (x= 1/2*(((365*3)+(365))/1461)) or (x= 1/2*4*365.25/1460).

Resource Value and Retrograde Motion. (x= (1/2)*(365.25/365)*(365/365.25))

Resource allocation (fairness, balance) and Resource value are related, but independent variables. In this case, we deal with two points of view (frames of reference). Simple Interest (1+(i/100))N is always calculated as a forward-looking return, that is, retrograde motion from a Lender's Frame of Reference. Natural Science computes many a Reduced Mass in the same fashion, and there is nothing sinister about it, it is a sign convention. The term Retrograde Motion simply means that a mass is spinning faster than it is orbiting. In the case of "value", ethical concerns arise naturally if the resource is under control of an owner, regardless of whether that ownership is Public or Private. The ethical concern is simply that the resource in question is the Lender's to lend, that is, that accumulation precedes transfer. Confidence Games are not allowed, as a computational matter.

Time Value of Resources (Lender Frame of Reference)

This is the annual forward rate (365.25/365), as a percentage, 0.068(49)%.

Time Value of Resources (Borrower Frame of Reference)

The annual discounted rate (365/365.25) is the reciprocal (1/(365/365.25)), and numerically identical (as a forward rate). The other way of saying this is that the value of the resource at the time of transaction was discounted (365/365.25 = 99.93 (16) %) so that "at present" the value is 100%.

Fair Value of Resources (Government / Non-Profit Frame of Reference)

As was shown above (see: Leap Years), the fair value of a resource is not the annualized rate, but rather the rate over 4 years. As Simple Interest, forward, (1461/1460)4, in percent, 0.274(25)%. These rates are related in an unfortunately non-obvious way: The "time to double" the annual rate is the half-life of the 4 year cycle. There are two additional observations. First, Leap Days do make a difference, only after many generations, but for the same fundamental reason Climate Change is not observable on a daily basis. A small rate of change has the same visualization as a slow time to double. Second, Many resources are measured in Decimal (base 10). Both Temperature and Monetary resources are Decimal. In logarithm space, the results are the same, but as sums of circles based on π, this is not the case. When you divide a Decimal number by 2 you get an infinite combination of 9's complement remainder, when you divide by 2π it becomes much harder to see the initial software problem with your arithmetic.

The reason is a computational limit, not a failure in mathematics. A sum never uses all the digits of π and rounding errors, all in one direction, accumulate. A direct computation, as with logarithms, does not have this problem. Power Functions can have the problem. The Nth root of a number should mean something. An unofficial test is the question, "What's the Square Root of a cup of tea ?". If the square root is a half cup and the square is two cups, PASS. ½ Earth means something only when compared to the other ½. That said, the model is quantitative.

The Business Rule for Intermediate Values

A Trigonometric Identity

½ = Cos(24°) + Cos(48°) + Cos(96°) + Cos(168°) = Cos(60°)

Although the full development will have to wait for another time, the day resonance "Business Rule" is this identity. On any graph, a line passing through 24 °/Hours, 1 day, must also pass through 2 days, 4 days and 7 days. And, 1+2+4+7=14.

This amounts to solving the (motion) differential equations with partial fractions. For non-organic (=Decimal) parameters, the two equations both go flat at higher multiples of the 14 Day period. Day Evolution by 2 Week Frame (PDF)

Fourteen days is the double-period, which is to say that every 7 days, each ½ of the Earth goes through this cycle. Two weeks historical memory is not accidental, or arbitrary. It is resonant behaviour. Perhaps not unexpectedly, fiat policies have no effect on the measurements. This can be dangerous in two ways: A "broader view" can give the illusion of a longer and therefore "better" data collection time. Conventions like Civil Time have no effect on physical measurements. Yet the "broader view" can still mask unfairness since any initial peturbation decays eventually to a steady state. Willful ignorance has the maximum bad effect.

In addition, "Climate Time" itself has some unique issues around the calculation of fine structure effects.

When the identity is applied, there is a little problem. The sums only add up to a (very large) fraction of ½. This "error" is constant and small (< 1 part per 5000), but not an indication of fine structure or, the hallmark of chaos, sensitive dependence on initial conditions. This is a natural way to shed accumulated information entropy. Disparities can be quantified, but not in a step-wise way (adding refining terms). Instead, spectral visulizations and imaging techniques are all that are available. This simply demonstrates that local balance and fairness are always independent of global balance and fairness - an interesting result itself.

For Work-Life Balance, it is not quite possible for another to own another's time, since this entails the "creation" of time segments to balance. For example: To be balanced, your time must be your own: (1/2)*(5/7 + 2/7) etc. Slavery is always unbalanced, (1/2)*(7/7 - 2/7). Any claim to the contrary implies that the claiment can create time, since balance is (1/2)*((7/7+2/7) - 2/7). Money can buy neither Happiness nor Harmony, but it can come very close, in about 1,000 weeks (about 19.14 years): (1/2)*((7/7+2/7) - 2/7)*(999+1). Every other fraction except (2/7), "weekends", is balanced (try it).

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