To establish how is to embrace the word anthropomorphic
How and why are inseparable in this sense

Why measure by three and not four.

Well I believe it has been in my family for four generations or at least from the time my GG Grandfather first saw the shores of this god-for-saken country down under. He was a saddle-maker from Taunton, England. I can remember teaching my grownup son at least 35 years ago that it was much easier and certainly more meaningful to measure by three. That way we both knew what the other was doing and there have been times when I have actually used the little finger for the fraction 2/3rds, not often but it has been done.

Trying to reason with the ancients is not so much about identifying signs or even applying mathematical logic but rather coming to terms with a universal anthropometric system that has practicality to its advantage. Does it work in the field or doesn't it.

If you look at you own hand it becomes quite obvious that we have three "more or less': equal fingers and one rogue.and when we actually put such a measuring system into practice we soon learn how easy it is to lay down three and not four of a palm.

I have never dealt in averages.

Ah the arm's length! That's another story altogether and it's more like yards to a cricket pitch, 22 in total, and the maths came much later in life

825 x 22 = 18150

Counting by three actually has historic significance for when we look at rule no 2 of Egyptian arithmetic (they only had two as far as I can see) the penny drops

Rule No 2.

"This two-thirds table was so much part of the scribe's stock in trade that, were he required to find one third of a number, he would first find two-thirds of it and then halve his answer, instead of just dividing by 3. The technique was so ingrained that we find it actually being used for such simple operations as finding one-third of 3, and one-third of 1! (see RMP 25 and 67.)."
Richard J. Gillings Mathematics in the time of the Pharaohs.

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Its more visual than calculative. Make three strokes in the sand, then two, then one. What you have actually done is to extract tho-thirds before halving. It might be primitive but then everything has its origin.

Graham Oaten

The great amount of labour involved in quarrying and transporting such a mass of masonry as even the casing, has always been a cause of astonishment - Sir Flinders Petrie.