A reminder that this is primarily ART, and plain-old fun. I am not trying to re-invent the world here! (That is well beyond my motivational capapacity!)

As always, when I go to the trouble of custom designing and making stuff, I try to avoid just re-creating things that I could more easily buy ready-made off-the-shelf. The more divergent the better! ....

Octal Planck unit measures - art that rules!

As touched on elsewhere in this site, I rather like the numeric-base 8, otherwise known as octal. A lot more than the cludgy old decimal we ended up with! (Thanks Ancient Rome!: There is inconclusive trace evidence that a good chunk of Europe was actually using a numeric base of 8 before the Romans 'civilised' the place.)

And if I am using an alternate numeric base, 10-based metric measurement loses its nice convenience the moment you leave base-10 anyway, so I may as well make myself a new one. (Note: this isn't any sort of problem with metric, which works well for the numeric base in which it was intended to operate, but an issue with trying to force it to do something it wasn't intended for!)

Rather than doing something arbitrary like measuring a bit of my (or Henry I's) body, or something rather-local like dividing up the polar-circumference of the planet I currently happen to live on (actually a very clever idea in context, and would have been very useful in oceanic navigation if metric-degrees for measuring angles had ever caught on!), I looked about for something a bit more universal.

There are a few 'universal' units about. Based on things that are (as far as we know) the same everywhere in the universe. I played around with the 'hydrogen line' at 21cm for a bit. Then I discovered Planck units - units at the very extremes of what is physically possible to measure! We can't actually even measure them, they are so extreme, but we (think we) know about them because they keep falling out of various physics equations. Being at the extreme, they are largely useless for more than simplifying some of these physics equations: a Planck length is so small it makes atoms look like planets, and a single Planck temperature unit encompasses all the heat in the universe! Not particularly useful in daily life! Until you multiply or divide them by huge numbers. In my case huge numbers in numeric-base 8.

So, if we multiply the Planck length by 838 (1046 expressed in octal, where digits '8' and '9' don't exist) we get around 335.6mm, which (unlike the centi/meter!) sits really nicely in the sweet spot for human perception/comprehension/visualisation, that sweet spot being from around 20 to 40cm. Divide or multiply by 8's to get sub/super-units.

Ruler with Octal Planck Units.

Above we have a basic ruler. Actually, it is a rather featureful ruler! I cut and engraved it on our maker-space laser cutter/engraver using 3mm polycarbonate sheet. Polycarbonate is often used for plastic window panes as it is quite tough and fairly scratch-resistant (for a plastic, at least). It is on my list of things to not put in the laser cutter, though - unlike most of the things on that list - this isn't so-much because it generates highly toxic/corrosive fumes if lasered, but because it burns (quite messily) rather than engraves. So you end up with brown-on-transparent results, and rather a lot of orange candy-floss-like gunk to clean out of the laser cutter! (Do not try to eat candy-floss-like gunk!) But sometimes brown-on-transparent is just what you want (or is at least acceptable), and along with the general toughness of the material, it is highly suitable for a plastic ruler.

I didn't end up (yet) putting any numeric symbols on the ruler. This was primarily because I don't want to use decimal numeric symbols and haven't come up with a satisfactory (to me) alternative symbol-set yet. But having physically created, and then used a bit, the ruler without marks, it seems that eight (sub) divisions across this length range is pretty easy to eye-count out, so numeric symbols are possibly not necessary anyway. They might even be a distraction - more than once the numbers on a metric ruler have slowed me down if I had to mesure between two points where the ruler couldn't be positioned with zero at one of them. So if I ever do come up with a good symbol set, I may decide not to add them to my ruler anyway!

I have developed several numeric (and complete alphabetic) symbol sets over my life. Some quite clever ones even. Too clever, it turns out: their cleverness invariably concludes in some very very very fatal flaw making them ultimately unfit for purpose!

There is also the dot-system I use in my 8-sided dice, but while that has proven excellent for dice, it isn't really practical for something that you might want to write with a pen. Also, the dot system is wide-open to forgery as it makes it very easy to just add extra dots to something already written to alter it!

This is usually the issue with any symbol system I invent - my mind loves all kinds of clever symetry and constructive/additive symbol-generation, which is not actually a good thing at all in a writing system as it makes it far too easy to alter already-written text! Not to mention that symmetry biting you when you encounter words - particularly short strings - up-side-down or viewed in a mirror and don't necessarily have any context to know that! But I just can't seem to kick the habit!

Update: I have recently come up with what might be a usable Latin-like symbol set. I didn't manage to get away from my obsessive-composite issue, but by generating a whole set, then carefully eliminating several, I was able to get the needed asymmetry and alteration resistance needed. I think! Stay tuned.

The ruler has 1/8ths 1/64ths and 1/512ths (10ths 100ths and 1000ths in octal, of course). I also engraved a 1/8th mini-ruler on the end, so it can be used as a tiny set-square in some situations, since the edge was there anyway, so I may as well use it for something! And a protractor at the other end for even more integrated usefulness! (more on that below). I am rather proud of packing so many useful features on to my ruler!

 

And why not a dedicated (and usefully larger) protractor, while we are at it? Again in lasered polycarbonate.

Octal Protractor.

Rather than just dividing the whole circle up into 64 units, I first divided it into four quadrants (trigonometry relies on quadrants a lot). I then divided each quadrant into 8 major units and 64 minor units, which provided a good 'resolution' for daily use.

Another side-effect of doing quadrants first, is that a circle now has 256 divisions exactly, fitting into a single 8-bit byte of binary data, without any space, so will, in digital applications, automatically wrap at zero without any extra program-code or transistor logic, which is neat.

The one thing octal cannot do so well is thirds (then again, neither can decimal, which is probably why we still use pre-decimal units for degrees!). I did toy with the idea of first dividing the quadrants into six, then each sixth into eight divisions. It is a sensible way to divide up a circle, but looses the nice byte-fit. Then I ran the numbers and found out that - in octal - ⅓ is 0.25252525... and ⅔ is 0.52525252..., so on my divisions that puts 30° at 25.25252525 and 60° at 52.52525252, which while not super-neat, is relatively memorable, so I decided to stick it out with my 64 divisions per quadrant, and add extra markings on the protractor for 15, 30, 60 and 75 degrees (45 degrees, the other very-common angle, naturally falls out of octal divisions, as does 22.5 and 11.25 degrees, two that don't fit the Sexagesimal system any better than 30 and 60 degrees fit octal).

I also put a ruler along the strait bottom of the protractor, because that can always be useful, as well as three holes, slightly over-size, for drawing unit-conformant circles with a pencil. The holes also have quadrant marks for drawing part-circles accurately.

As with the ruler, I didn't put any numeric symbols on the protractor: The major and minor divisions are relatively easy to count by eye and you can count between any two arbitrary angles without having to align one edge to use marked numbers.

Why so easy?!

Why is sight-counting in base-8 so easy? I have no idea, or any realistic way of finding out for sure!

But forced to guess, I would wildly-extrapolate that it is mostly the natural ease of repeated divisions by two, and possibly the human subsidising limit on the side: subsidising is being able to tell at-a-glance (ie: without actually counting) how many of a thing is present in view. For humans, this tends to naturally max out at four items (though you can train yourself a bit higher with lots of practice). 8 subdivisions is well above this, but there are only 4 subdivisions either side of a major mark, so you can stay within the subsidising range up or down from any major division mark. WARNING: Pure speculation! By a field non-expert, too!


Other things I measure!

I also have derived human-range-useful Octal Planck Units for some other things, such as weight, time, temperature, voltage, and a few more. Some, like my unit of length, seem to be a better fit for human-use than current mainstream units, while others are just equally-arbitrary. I sometimes even use them when what I am doing is pretty arbitrary anyway, but mostly they are just for fun/interest. Or to use in some sci-fi-ish fictlonal work if I want to stress the alien-ness of things a bit. Scale modified for oPU

I recently had some laser-printable A4 adhesive-backed vinyl at work for making door signs, and ended up with something-and-a-half pages to print, so I filled the otherwise-wasted space with something of my own. Having recently (and finally!) settled on a alpha-numeric glyph system that might be okay, I whipped up a quick 'octal-plank-weight' ring to stick over the rather-useless-to-me Imperial pounds-weight one on my bathroom scales. The yellow edge also represents my own target weight range.

Octal Earth Time (example)

Although obviously Earth-centric, if you are living on Earth, firstly my condolences, but more importantly, this is sensible for dealing with daily time! Trying to force Octal Planck Time on a natural Earth day would be about as sensible as trying to force a ten-lunar-month year! (Hi, Ancient Rome, again! .... Your decimal obsession really sucks!)

The below Earth 'second' isn't too-far-off half of an Octal Planck Time unit of 1.202s (Planck-time x 8^48), so I guess you could instead of dividing the Earth day by 4 quadrants, divide into two (day/night or prenoon/afternoon) if you wanted to keep them close, but it breaks compatibility with circle quadrants in angular measurement above so you can't convert directly between the angle of the sun in the sky and (approximate, according to season) time of day, and then sun-dial manufacturers won't invite you to their parties!

Divide the (Earth) day into 4 quadrants: Pre-dawn, Post-dawn, Pre-dusk, Post-dusk (or, since language is only arbitrary labels anyway: predawn, morning, afternoon, evening, if you prefer. Or even pre-coffee, post-coffee, pre-booze, post-booze if that describes the sum of your civilisation's core values and aspirations!)

Divide each quadrant into 8 'hours' (which would actually be 45 conventional minutes long)

Divide each 'hour' into 64 'minutes' (which would actually be 42.1875 conventional seconds long)

Divide each 'minute' into 64 'seconds' (which would actually be 0.6591796875 conventional seconds long - also towards the high-end of normal human resting heart-rate - conventional seconds are right at the lowest end, for comparison.)

Days-into-years on Earth fits nothing useful in octal (or decimal, or sexagesimal!). I would likely just divide the year into 13x 28-day months (1-15octal) and each month into 4x 7-day weeks (1-7) (Gaah! Prime Numbers are not friendly to measurement systems!) and tack an extra day (day 0) onto the start of the first week of any leap-year. Not pretty, but a good bit nicer than our current system, which even manages to break lunar cycles badly in an effort to force 12 months!

If you really want a 12-month year (not actually unreasonable, since we have 4 natural seasons, at least away from the tropics!), I guess you could chop up the extra month and add an extra week to each of the months associated with solsti and equini. Make them festival weeks! (There is, of course, nothing new under the sun: J.R.R.Tolkein's Shire calendar did something quite similar to this).

For things not directly related to time-of-day, (which is realistically the only place I actually use them anyway, since I still have to interact with the real world in standard clock/calendar time for my day-to-day life), I might use the octal Planck Time version in which the base unit is around 1.202s (848 x Planck time). For example, my AC power frequencies below are derived from this.

Physical Artefact?

Maybe one day when I retire from having to regularly interact with the real world I could make an electronic digital clock. Or just program an app for my computer and/or phone. Though I would have to invent the numeric glyphs first, or go full-analog, I guess!

Or make a sundial! Hmmmm....

Octal Earth sundial plan.

Above is a rough plan made by grabbing a sundial off a random online sundial-design-calculator. It is specific to my current latitude, of course, so unless you live at a similar latitude, you would need to re-do your own! I imported it into a background layer in Inkscape, and drew over it. Blue is my cutting layer and red my marking layer. The template from the online generator provided ¼ hour divisions, which line up perfectly with my 45-minute time-units.

I haven't done ⅛ subdivisions yet. Still deciding if I want to. And I'd have to eyeball them.

Now I (possibly, still subject to testing) have a numbering system, I might look more seriously into making one.

....

Octal Planck Voltage (example)

When I made my octal dice, people kept asking me what game they were for, and I soon got sick of having to answer 'none'. So I made a (dodgy) Fantasy Role-Playing Game system to go with them (release pending me finishing, play-testing, then probably having to completely re-write it!). The game works in octal and uses octal-Planck-units, though only units for length and weight* are needed in the game's base form. Below is adapted from one of the rule-book appendices detailing how to create new Octal Planck Units for extending the game into areas where such might be useful.

* The unit of weight in the game is two orders of magnitude (64x) bigger than the one I normally use, because that suits the game better, by removing the need to use unnecessarily large numbers, and so simplifying the associated maths: It's a role-playing game, tracking the oPU equivalent to grams would be tedious, the encumbrance rules track the few-kilogram-equivalent and ignore the weight of light equipment!

Electronics is my professional field, so I went just a bit overboard below (but it was fun)!:

The Planck Voltage is HUGE, at 1.04295×1027 Volts! It is (assuming I actually understand this stuff, which is not guaranteed!) the highest absolute voltage possible without breaking known standard physics! We need to divide it down quite a bit to get something actually usable, say dividing by 830 (expressed in decimal) to obtain a value of around 1 oPV (octal Planck Volt) = 0.842V (Standard International, decimal).

As a pure world-building exercise, applying some historical context from actual human technological development to a base-8-using people who somehow discovered the Planck Voltage before they developed electricity enough to already have settled standards, we can derive some possible common usage values (oPVs are in octal, where 0.4 is exactly ½, SI Volts are in decimal):

Note that most things above are on half-units (remember: 0.4 is ½ in octal, 0.6 is ¾). Trying to force whole-units (1, 10, 100) results in many voltages being well outside the ranges set by certain realities of how electricity works. So even using oPVs from the start, things would likely have eventually settled around such values anyway:

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, modern chips still use that voltage anymore, but instead the mainboard down-converts to whatever its chips now need. Later, with this 5V still readily available from the main power supply, it was a sensibly cheap option for (the original) USB power-wire voltage.

In oPV-land, that original transistor technology would have operated at 6oPV (5.1V), which is also in the sweet-spot for a little line-loss on a 2m cable, then regulating down to 4.0oPV 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 (⅓) of 10V at the efficient end of the range, so choosing a very-close-by 4.0oPV (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 arbitrarily change it to suit yourself! Though you could change the total number of cells used, but.... While the alternators on cars/trucks could be designed to be any (reasonable) voltage, they work at around 13.8/27.6V, because they need to run slightly higher than the battery's discharge voltage to charge them.

Likewise, 1.5V zinc 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 easy SI values from generous rounding of the real value, sometimes quite significantly: NiCad cells designed to substitute for zinc (A)AAs operate at 1.3V, but get away with being considered "1.5V" because most equipment is designed to still work with somewhat-depleted regular zinc cells anyway so don't care about a little bit (15%!) of under-voltage.

As a final example, getting away from battery chemistry, 24V became a psudo-standard for industrial control for a number of sensible reasons: Higher voltages allow you to push more power down the same gauge (size) wire, at the expense of requiring thicker (though still cheaper than copper!) insulation; two standard 12-V car-batteries can give you a cheap, and easy-to-replace from stock-parts, portable/backup power source. There have been occasional pushes to change 'standard' DC voltages in various fields to 48V, but they generally fail because above around 30VDC, points-disconnection inside mechanical switches causes electrical-arcing in Earth-composition-air at sea-level-pressures, forcing you to use expensive switches made of exotic metals or sealed up with special insulating fluids inside, so 24VDC tends to stick around. (48V works for power-over-Ethernet because it avoids the mechanical switching issues by switching electronically instead. 48V USB-C power-delivery is likewise viable, but these mainly work out because the extra circuitry for the electronic switching is fairly tiny+cheap compared to the rest of the circuitry involved in the associated devices). Note we are talking about DC here. AC achieves reliable mechanical switching at much higher (around 10x) voltages because the current crosses zero 50/60 times a second which give the switches a low-voltage point to break contact without all that switch-damaging electrical arcing! ... Which also means cheap and readily-available 220VAC switches/relays/etc. are generally also rated to reliably switch 24VDC, another point for using DC at around 24V!

So all-up, while I might be altering the exact values used, I don't - for very real-world reasons - have the latitude to stray far from what we ended up with anyway (the notable exception being to put light vehicles on the same DC voltage as heavy vehicles and industrial control, which does provide multiple benefits).

TechnologyV (rounded)oPV (rounded)Notes
Zinc Battery cell1.6 (1.5)1.7 (1.4)3 cells to make a bit over 4oPV; 4 cells comfortably over.
Nickel Battery Cell1.3 (1.5)1.5 (1.4)3 cells to make slightly over 4oPV; 4 cells comfortably over
Lead Battery cell2.1 (2)2.3 (2.4)12 cells to make the below "40" (really 36) oPV vehicle battery.
Vehicle Battery Bank25.2 (24)36 (40)"Battery" voltage that all vehicle equipment must work down to.
Vehicle Alternator27.6 (24)40 (40)"Running" voltage that all vehicle equipment must work up to.
By necessity a little higher than battery voltage to charge.
Industrial Control24-28 (24)36-40 (40)DC can't go much above this without needing special (expensive) mechanical switches.
Provides useful DC power at managable current. Vehicle-component compatible.
Domestic Power220 (220/230)400 (400) RMSAC can't go much above this without needing special (expensive) mechanical switches.
Provides useful domestic power at managable current and isn't too tough on insulation.

Physical Artefact?

I don't really do much electric/electronic work in which I have any real control over the exact voltages used. Though I do tend to work at 28VDC when appropriate for higher-power DC usage: I run a bit of 28VDC around my apartment for custom lights/fans/etc. (automotive/indutrial gear is generally rated to work from 24VDC to 30VDC). And 3.3VDC is so close to 3.4VDC that I may as well consider them the same thing! (Plus, I sadly don't have my own microchip fabrication facilities!) And I have already justified using USB-2's 5V regulated down to 3.4(ish)VDC above. Interestingly, the USB-3 power-delivery standard even has a specific 28V mode!

I am still in two minds if I actually need to be using 28VDC or could just run 5V everywhere - USB-powered devices (including microcontrollers I can use to make 'smart' devices) are highly available, and while 28V provides more power with less line-loss, there aren't many places I actually need that much power, nor are my cable-runs particularly long!

216VAC is easily within tolerance-range of 220VAC internationally common, and even the 230VAC officially supplied in Australia. So I guess I am already there in any way that practically matters! (And while I am qualified to do non-fixed 240VAC work, who on Earth would mess with that unless they really had to!) As for mucking around with the AC frequency, while historically mains-powered clocks and analog TVs often used the mains frequency to keep sync., not much equipment cares about it these days, but there are likely still a few things about that might (plus it is, again, so close I couldn't perceive a difference without test-equipment anyway!)

Australian mains voltage used to be 240VAC±10%, but in 2000 they nudged the standard down to 230VAC+10%/-6% to more-closely match what overseas equipment is often designed for (220VAC±10%), but 240VAC is still within tolerance range and most power providers still supply 240VAC to the home anyway! Even on the new standard, Australian equipment is supposed to be able to safely handle up to 250VAC.

Which is also why, while I will happily buy low-voltage stuff cheap from overseas, I will only use mains-connected gear from reputable Australian sources (including throwing out overseas power bricks and using locally-sourced ones): that way I can be sure it has been properly tested to AS3820 safety standards, and can handle a full 250VAC! (And I have seen some examples from overseas that will work fine 99.9% of the time, but the other 0.1% may fail by pumping 240VAC strait onto the low-voltage DC rails and user-contact cabling/casing that definitely can't insulate such voltages! Scary stuff!!)


You can look up the other Planck Units (and their derivatives) and do the maths yourself as desired, choosing 8±n 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.

You don't have to use base-8 either, of course! Dozenalists would obviously want to use base-12. And the barbarians among us can even use base-10! I even know someone who likes base-3! Just remember you can't start with my human-scale octal units in those cases but must multiply/divide from the original Planck values in nbase steps! Your human-scale units will be different due to the multipliers/dividers needed to get there in your preferred numeric base being different.

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 is just for fun/interest, and isn't in any way obligatory.