The Spooky Stuff

To borrow a phrase from Robert Bauval, this falls under the Spooky Stuff category.

It is a very strange connection between the Grand Metre (1 + royal cubit), the base of the natural logarithm ⅇ, and the royal cubit as measured in inches.

Royal cubit, e and inch

I have no explanation for this. It just highlights again the ancient origins of the metre, inch and royal cubit, and how they mysteriously link together with π and ⅇ. But what about φ you ask?…. here you go:

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No body parts were harmed producing this post

It is the mainstream academic consensus that ancient people based their measurements on body parts. As discussed in Some thoughts on the cubit (and foot) , I don’t think that’s necessarily so, despite at least two (the Persian and Roman feet) at one point being based on the length of the foot of their leader (or his over-sized statue).

I still think the names that these measurements became known as (cubit, foot, palm, etc) were backnyms to create a easy-to-use-and-remember name for a length.

Even something simple like measuring the width of a hand is not exact because fingers move, flesh compresses, etc., and fingers are not all the same width.

So… here’s a little exercise to show that we can get the same list of parts of the cubit just with maths. In some cases two different methods produce values on either side of the target.

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The Mile. Not the Green Mile or the Last Mile or even Mile 22

Just the British mile.

Which, bless them, they defined as being 8 furlongs long. Yeah, what the heck is a furlong… you need to be a British horsey type to be familiar with such things. For the rest of us, a furlong is 660 feet. So that makes a mile 8 x 660 = 5280 feet.

In the early hours of this morning I had an embarrassing “light bulb” moment. As previously shown, a foot is simply ⅕ of a Grand Metre ( 1 + π/6). This morning, the flip side of that hit me … that the Grand Metre (especially in the slightly rounded for practical purposes form of 1.524m) is exactly five feet. I suppose we could call that a fiveet.

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The Persian Foot

The Persian foot was slightly larger than the well-known English foot.

According to The Lost Science of Measuring the Earth by Robin Heath and John Michell, it was based on the foot of Darius at exactly 1.05 British feet, which converts to 32.004 cm, while Howard Crowhurst, in his video (and presumably book) pegs it at 32 cm. Wikipedia of course is happy to claim a mere 300 mm (citation required…).

We can relate this to the cubit with reasonable accuracy. Remember that the normal British foot is 1/5th of Grand Metre (1 metre plus 1 royal cubit).

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The Nautical Mile

The nautical mile has a chequered history. The basic idea was to have it set to one degree of arc of the circumference, but that depends on what latitude you are at. You can read Wiki’s take for some background.

Anyway, yes, that royal cubit can be related to a good approximation of the nautical mile, given that the exact definition has varied over time. It’s currently “defined” at 1852 metres.

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Introducing the wroft

School children around the world today generally use the same length ruler, being 30cm long. For the Yanks and maybe some British, they may still use the foot ruler.

I remember when  I was in junior school around Std 1, we did the whole switch from imperial measurements to metric, and I had to stop using my nice wooden ruler with the embedded brass strip, in exchanged for this new 30 cm plastic ruler with miniature “inches”.

My first thought of course was “why 30cm?” … that’s a strange number. It’s not called anything, it doesn’t divide nicely into 1 metre, so what’s the story?

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The Magical Mystical Royal Cubit

Let the maths do the talking…. click image to enlarge.

The magical mystical cubit

I’m leaving out 1/√(364.75/100) until such time as I have a better explanation for it. (Although it does effectively pop up in the discussion about the nautical mile.)

According to Wikipedia, the Reed was different things at different times … at one point being only 2 cubits, about 1 metre, long. They also called the 6-royal-cubit length “kalamos”. Given that we’re dealing with civilizations that lasted thousands of years, it’s hard to know what’s what.

I suspect that’s why there are different versions of the Royal cubit floating around … on the one hand, copy errors, on the other people using actual body parts to create measurements. It is my humble opinion that whoever came up with these things did it very logically, based on maths, and the metre and pi and phi. The big remaining question is how the heck did they get the metre.

Cubit with squares

Okay, REALLY last one for tonight. Found an approximation for the cubit using square roots. Not very good, in fact worst so far.

Formula is

Cubit in squares

Comparison table is now:

MethodValueDifference from π/6Abs difference
Ave Year0.523607797087850.000009021489560.00000902148956
π – φ²0.52355866483991-0.000040110758390.00004011075839
cube roots0.523600350171940.000001574573650.00000157457365
square roots0.523403736847960.000195038750330.00019503875033

Cubit with cubes

Okay, last one for tonight… since I upset √2 with the previous formula, I thought I’d have a go using square roots, but didn’t find anything yet. Maybe another day.

But… I did find something using cube roots… in fact, the cube roots of 2, 3, 5, and something derived from 7 …. and the accuracy is the best yet, even if the formula is horribly complex. Beauty and the beast, I suppose.

Cubit in cubes…

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