Appendix: Measure of a... Something

The measurement system in Octas is designed to keep the maths as simple as reasonably possible. This means keeping numbers small, but not too small!

I actually find some of the units of measurement on modern Earth quite unwieldy. Particularly the metre, which is too big for a lot of human-scale use, requiring the use of decimal fractions. Meanwhile the next commonly-used size down, the centimetre, tends to be too small and too big at the same scale, often requiring both the use of multiple digits above the decimal point, and a fractional component below it. Being decimal, this isn't particularly difficult to manage mathematically, but the scales of the units just don't seem to mesh with what the human mind can easily visualise - I am 175cm tall, or 1.75m tall. Neither are particularly easy for me to quickly visualise in my head - and I have been using these units since before I started school, so you can't claim it is just that I am not used to them!

I actually find the old Imperial unit of measurement, the foot, to be in my sweet-spot for visualisation, and I suspect this is more generally true, and why even in fully metric countries, the unit is often still popularly used in an informal way. The way feet are divided by 12 to inches, yet multiplied by 3 to yards, is an abomination however, so I am not singing the praises of Imperial measurements here, just the length of around 25-35cm as being a more human-centric base from which to derive a measurement system, whether in decimal, octal, or any other numeric base.

The metre is also an extremely Earth-chauvinistic unit, being originally based on a (pretty accurate) estimate of the polar circumference of the Earth divided by 4 million (so equator to pole divided by 1 million). Metric angular degrees, a system that - like metric time - was never adopted, divided the circle into 400 degrees, 100 degrees per quadrant, so it made perfect sense, and was even a good idea in terms of ocean-navigation via sailing ship, as it potentially made the maths involved a lot simpler. But that is Earth-scale advantages, not human-scale.

Since Octas was designed to work in a numeric base of 8, it makes sense to use a measurement system that likewise works in base-8, otherwise you get all the same issues as you do with the rather ad-hoc Imperial measurement system trying to force divisions by 12, 8, 24, 36 etc. into a base-10 system.

The big question is what to use as the base unit of measurement? Dividing the circumfrence of the Earth up into a nice round base-8 number, as was originally done to define the meter, is a bit Earth-centric for a game system that is intended to not be restricted to Earth settings (the default Octas/fallen world is explicitly not Earth, or even much like it in some significant ways). The foot is a nice human-scale-friendly unit, that many people are familiar enough with, but is still entirely arbitrary, not to mention tied up in the baggage of one particular human culture at one particular time in human history.

I wanted a truly universal measurement base. Ideally one that multiple cultural groups with no knowledge of each other might be able to come up with independently. For that we have to look into the laws of the universe itself.

One option is the so-called Hydrogen Line, which is a specific wavelength of (IR) light that a Hydrogen atom will emit when its electrons flip from one energy state to another. This is constant (as far as we know, and have no reason to think otherwise) across the entire universe, and the wave-length itself is 21cm, which is at the short end of the ideal human-friendly range. I spent some years a while back playing with measurement units based of this length, and it was quite good to work with.

It is also the unit of measurement used for the human forms depicted on the back of the Voyager Probe records, due to its cultural neutrality, and the ease with which it can be described via pictographs to any alien civilisation with enough science to get themselves into space to encounter it.

More recently I discovered Planck units which are quantum units that seem to tie into the fundamental nature of the universe (though there is still some unanswered questions of exactly how they do so). The Planck Length, for example, is about (we haven't been able to precisely meanure it) 1.616255×10^-35m. This is really really tiny. Unusably tiny for pretty much everything (even too tiny for measuring individual atoms)!! But it simplifies a whole bunch physics equations a good deal when used instead of an arbitrary unit of distance. It seems (still some argument on this) to be a fundamental lower limit to how fine it is actually possible to measure things in our universe before quantum uncertainty makes things too blurry to measure at all. The maximum 'resolution' of the universe, if you will. It is about as universal and fundamental as you can get. And there are equivalent fundamental units for mass, temperature, electrical charge and all the other basic things we measure, called Planck Units. All of these units represent either the smallest, or the biggest measurement that appear possible in the currently-known laws of the universe, making them stupidly unwieldy for any use outside of the aforementioned physics equations!

The Planck Length is unusably small for human-scale. But we have multiplication. By multiplying the plank length out (in our case in base-8, since that is what we want to use here), we get 8^38 Plank Lengths, which comes in at around 335.6mm, a little over our beloved 1 foot, and also very close to 1/3 of a meter. Right on our sweet spot for human use. (You could also do this in base-10, but the number you get would - of course - be different, and really, why would you?: Base 10 is already pretty arbitrary and human-centric, so an arbitrary Earth-centric measurement unit like the meter is just right for it!)

So there we have it. The Octas base unit of measurement, the Length, is 335.6mm long. Its similarity to the foot is a happy almost-coincidence. Almost, because we deliberately chose the 8^38 multiplier to put us in the general area we wanted, but that it was that close is coincidence.

Since we have now decided to use Plank Units as our base for distance measurement, it makes sense to do the same for any other units. So for weight, we multiply the Plank Mass by 8^10 to get the Block of around 24kg, or 50 pounds, which is actually a little coarse for real-world human use, but perfect for in-game use where we don't care about bogging ourselves down tracking the weights of lighter things anyway.

And before someone points out that mass and weight are not the same thing, I explicitly made the surface gravity of the default Octas world to be exactly what it needs to be so that weight and mass are numerically equivalent, just as they are on Earth in SI-units for the same reason. Octas is a made world: I made it up in my head, but even canonically, it is an artificial planet, so the fact that the local gravity (and size, and many other attributes) work out to result in nice easy-to-work-with numbers is not in any way coincidence!

Inline with the artificiality of the Octas world, time is likewise normalised to Planck Time, with the day being around 22 hours long. The artificial planet was deliberately spun-up to match this exactly!

I am not even going to specify the exact length! You can go calculate it yourself if you like: it is the Plank Time multiplied by 8^53 for half a day, so double it again for the whole-day length.

The unit was chosen as it is close enough to the Earth day we are all used to that it isn't even worth noting the difference in the game rules. Treating an Octas day as 24-hours won't make any difference to the game and so it isn't even mentioned.

Divisions of that day, however are important. For simplicity, we will give times as divisions of Earth-days, the difference to Octas 'reality' being too small to be worth complicating things over for a game.

The Octas day is divided into four quarters (around 6 Earth-hours each), being predawn, morning, afternoon, and evening:

Day Cycle Quarter Name Half Name
Midnight-Dawn Predawn Night
Dawn-Noon Morning Day
Noon-Twilight Afternoon Day
Twilight-Midnight Evening Night

Each quarter is then divided into 8 Octas-hours, each Octas hour being around 45 Earth-minutes.

Octas hours are further divided into 8 minutes, each being very approximately 5 Earth minutes.

Further division of minutes into 64 seconds (of around 4 Earth Seconds each) is possible, but common people of Octas rarely have any need for such precision in their daily timekeeping.

A year on Octas is likewise divided into 4 seasons (Octas was deliberately given a 22.5 degree axial tilt relative to its orbit to provide Earth-like seasons). Each season is 64 days long, so the year is 256 days long. Again, this isn't normally going to impact the gameplay, so if you forget and start treating the Octas year as the same as Earth, it is unlikely to matter, so, like the difference in day-length compared to Earth, it generally doesn't even get mentioned in the rules, but you can make a thing of it if it suits your game play needs.

In-game, a year on Octas is whatever length of time a major adventure plus a bit of a rest before/afterwards takes, or a chapter of a major campaign spanning multiple years, unless making it one season per chapter works better, or whatever else suits the narrative of the story the players are creating, in the end!

Octas doesn't have months. The 7 moons of Octas all orbit at different speeds, none of which conveniently fit any rational division of time, so there is no universal division of the year like this. Individual cultures may, however, obsess over one particular moon and so advanced games could include individual places that have somewhat-arbitrary month-like divisions of time, and probably messing up their agriculture trying to adhere to them rather than the seasons until the farmers all revolt! (Hi again, Ancient Rome, and your fleeting attempt at 10-month years!)

Direction is based on the same whole-circle divisions as planetary-rotation-based time, so has a lot in common with daily time. The circle is divided into 4 quadrants with compass points at each boundary, exactly as happens on Earth. For North, South, East and West. The default Octas world has a magnetic field and rotates in the same direction as Earth, so these are exactly as players are used to.

Note that the precedence we give to compass points is somewhat arbitrary. North-as-top is no more valid than South-as-top, but just a convention (and not a bad one, even coming from a Southern-hemisphere dweller such as myself). Ancient Asia tended to draw their maps with East (sunrise) at the top, so even North vs South isn't the whole range of possibilities!

Occasionally giving players maps from foreign cultures that just assume the reader knows which direction top represents is a relatively harmless way for a GM to mess with their players!

Each quadrant on the compass is formally divided into 8 minutes, being 11.25 degrees on a modern Earth protractor, and then into 8 seconds of around 1.4 degrees. So there are 256decimal degrees (400octal) in a circle, and 64decimal degrees (100octal) in a single quadrant.

The inhabitants of the Octas/Fantasy realm don't use Radians: their needs in angular measurement are not that sophisticated. But radians, being based off the ratio of diameter to circumference of a circle, don't actually change anyway, you would just express them in octal rather than decimal.

Pi is expressed in octal as 3.11037552...., 3.11 being accurate enough for most uses even by today's standards.

Informally, the compass can also be divided into 8 parts, being N, NE, E, SE, S, SW, W, NW exactly like on Earth. 16 divisions (NNW, etc.) are also sometimes used, again exactly like on Earth.

In the game, the informal units are generally sufficient, particularly the 8-way N, NE, E, SE, S, SW, W, NW. So players don't really have to care about all the other details of angular measurement. Again, unless that is their thing!

Informal Relative Direction generally states direction in eights of a quadrant. So 45 (Earth) degrees right of forward would be "4 (eighths) right (of front)."

Other units

The supplied fantasy world of Octas doesn't have much use for other units, such as electrical voltage, but if you are setting your game in a world that does, such a unit might be:

Name Abrev. Planck Multiplier SI-equivalent
Octal Plank Voltage oPV PlankVolt / (8^29) 6.8V

Possible common usage (oPVs in octal, where 0.4 is exactly 1/2, SI Volts in decimal):

Realistically, there would also be 1000oPV (28kV), 2000oPV (56kV) and 10000oPV (220kV) transmission lines too, but I can't think of any game-narrative reasons to go there, since they all look similar enough and a character touching any of them is equally charcoaled!

Note that most things above are on half-units (0.4 is 1/2 in octal). Using whole units resulted in many of the convenient voltages being well outside what over a century of human experience has demonstrated is the ideal range for each usage, so even using oPVs from the start things would likely have eventually settled on such values.

Sometimes other factors apply, for example:

A lot of electronics used to operate at 5V, because a particular type of early common transistor operated best at around that voltage. As a result 5V is still one of the main voltages fed to computer mainboards, even though few, if any, of the modern chips still use that voltage anymore, but instead the mainbord down-converts to whatever its chips need. With 5V already available on-board, it was then a sensibly cheap option for USB voltage when that technology came along.

In oPV-land, that original transistor technology would have operated at 0.6oPV (5.1V), which is also in the sweet-spot for a little line-loss on a 2m cable, then regulating down to 0.4oPV for circuit use in more modern usages (many USB devices do exactly that, regulating the incoming 5V down to 3.3V to use internally).

The more-common-today 3.3V general logic voltage is due to a later transistor technology which works happily from 3V to 15V, with the lower end being more energy efficient. The 3.3 was chosen, presumably, because it is the nearest clean fraction (1/3) of 10V at the efficient end of the range, so choosing a very-close-by 0.4oPV (3.4V) is just as valid.

Lead-acid vehicle batteries are considered 12/24V because the 6/12 cells from which they are made are close to 2v each. That's just battery-chemistry: you can't change it. The alternators on cars/trucks could be designed to be any (reasonable) voltage but work at around 13.8/27.6V (4oPV for the latter, by coincidence), because they need to output slightly higher than the battery float voltage to charge them.

Likewise, 1.5V zink batteries (non-rechargeable AA, AAA, etc.) are around 1.5 volts due to their battery-chemistry. Technologies such as this just won't normally have nice convenient oPV values, and they only generally get nice-looking SI ones from rounding the real value, sometimes quite significantly: NiCad Batteries designed to substitute for zinc (A)AAs operate at 1.3V, but most equipment such batteries are used in is designed to still work with somewhat-depleted regular zinc batteries anyway so don't care about a little bit of under-voltage.

Technology V (rounded) oPV (rounded) Notes
Zinc Battery cell 1.6 (↓1.5) 0.17 (↓0.14) 3 cells to make a bit over 0.4oPV
Nickel Battery Cell 1.3 (↑1.5) 0.15 (↓0.14) 3 cells to make slightly over 0.4oPV
Lead Battery cell 2.1 (↓2) 0.23 (↑0.24) 12 cells to make the below "4oPV" battery.
Truck Battery Bank 25.2 (↓24) 3.6 (↑4) Rounding justified as "For 4oPV system"
Truck Alternator 27.6 (↓24) 4.0 (4)


Okay, that went on a bit! Electronics is my professional-field, so I get carried away! Just don't expect me to be able to put that much thought into most units!

You can look up the other Plank Units (and their derivatives) and do the maths yourself as needed, choosing 8ⁿ multipliers/dividers that put you in the desired 'sweet spot' for easy-to-work-with numbers for your application. Remember that some Planck Units (like length and mass) are tiny, so will need a big multiplier, while others (like voltage and temperature) are huge, so likewise need a big division to get into human-scale ranges.

If it is something you are personally interested in (such as me and electronics, above) feel free to do a bit of historical back-tracing to see if anything interesting falls out of using slightly different standard units, but that isn't in any way obligatory.

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