Real-Life Weirdness

[ak_aramis]

Originally Posted by Daigoro

How is that a revelation? And why not go to base-120 or base-600?

If going up, you want to go by the next prime...

Prime factors of 60 are 1, 2, 3, 5
Prime factorization is 2×2×3×5.

Next logical choice base is 2×3×5×7... 210.

But even at 20, we see the practical system isn't base 20 in practice. (Meso and South-American empires used base 20 in a base 5 and base 4 combination.
0-4 dots, then bars for each 5, with a zero indicator, and place locations being powers of 20.

Likewise, Babylonian, has (essentially) tallies for 1-9, and then arrows for 10-50, and a placeholder for "nothing in this placevalue" with placevalues being powers of 60.

[William]

To keep this on gaming, note that hexadactyly is a dominant trait, so it's only by a quirk of evolution that the general body plan on our branch of the tree of life has five digits. Six would have been a very easy change, and perhaps even somewhat more likely than five; instead of having the PCs' home universe in a multiworld game be different in some way that provides them an advantage, perhaps it's simply odd that we're quintadactyl.

Everyone else might be comfortable with base-6 or base-12, which have considerable advantages over base-10, in that they are more divisible in useful ways.

Should we be interacting with humans from worlds where the general norm is hexadactyly, we might be at a disadvantage when using their equipment, lacking the extra finger; on the occasional plus side, it's much easier to disguise one of us as one of them than vice versa.

[Johnny1A.2]

Originally Posted by William

To keep this on gaming, note that hexadactyly is a dominant trait, so it's only by a quirk of evolution that the general body plan on our branch of the tree of life has five digits. Six would have been a very easy change, and perhaps even somewhat more likely than five; instead of having the PCs' home universe in a multiworld game be different in some way that provides them an advantage, perhaps it's simply odd that we're quintadactyl.

Everyone else might be comfortable with base-6 or base-12, which have considerable advantages over base-10, in that they are more divisible in useful ways.

Should we be interacting with humans from worlds where the general norm is hexadactyly, we might be at a disadvantage when using their equipment, lacking the extra finger; on the occasional plus side, it's much easier to disguise one of us as one of them than vice versa.

Hmm...I don't know that it would be any easier to disguise us as them than vice versa, just that it would be less painful to disguise us as them than them as us. Ouch.

[Johnny1A.2]

Originally Posted by Flyndaran

Iron sulfide not iron oxide and near vents spewing out a chemically "easier" form to incorporate. I also don't think it's a form stable at surface pressures and of course where oxygen is so prevalent.
But I remember when I first heard of this snail. Life uses whatever is available even if it's only available in that one tiny area. Always amazes me.

(Honestly, if you want super strong exoskeletons, why not make layered organic diamond? Far less energy to extract than splitting iron from rock.)

But would that be super-strong or just super-hard? Diamond is very very hard, but it's not necessarily all that strong, it shatters easily, for ex.

[Anaraxes]

Originally Posted by Daigoro

How is {base 60} a revelation?

It's probably hard to imagine from a modern viewpoint, but the Babylonians couldn't do fractions. Even the Egyptians had a pretty awkward and limited system for doing arithmetic with parts of things. When you can't do fractions at all, it becomes much more useful and important to have a system with more possible integer divisors, so as to be able to calculate more results and maintain more accuracy while using only integers.

(This is one reason for the existence of some of the old units with high counts -- 7000 grains in a pound, 1024 drams per gallon. When you can't deal with the quantity 3 / 7000 * price_per_pound, you can at least adopt a tiny unit so you can just deal with the integer quantity 3 * price_per_grain. Annoying as counting out all those grains might be, it still beats not being able to calculate.)

And why not go to base-120 or base-600?

Because then you need 120 or 600 glyphs just to write down any number. There's a diminishing return on the marginal utility of stacking up additional factors in the base, while the cost of managing a recognizable notation grows rapidly as those prime factors get further and further apart. The ideal spot will be somewhere in the middle, between "too few" factors (why not unary, just counting vertical line scratch marks?) and "too many", which bounds will be fuzzy and a matter of taste and practice, not of mathematical law.

[Anaraxes]

Originally Posted by Flyndaran

if you want super strong exoskeletons

Oh, the armor is even better than an iron sulfide coating. It's actually a multi-layered structure, with the iron sulfide particles sitting on top of a flexible organic, proteinaceous layer, which in turn sits on a calcified inner shell, for alternating layers of rigidity and flex. It's layered composite armor, like the armor on modern main battle tanks.


More than you wanted to know can be found in this PNAS article, which has wonderful paragraphs that would fit right into some forum conversations, like:

The experimentally measured local mechanical data were directly incorporated into a larger length scale computational (finite element) model representing the entire curved, multilayered shell structure (including the OL, ML, GL, and CLL) in response to a penetrating rigid indenter normal to the shell surface (Fig. 3A, see Materials and Methods). Modulus and yield stress values were obtained through elastic–perfectly plastic finite element fits to nanoindentation data, rather than the O-P data of Fig. 2. This model simulates the local loading of a common generic predatory attack (penetrating indent), for example, by Brachyuran crabs (Austinograea sp.) that were found in the same vicinity of the Kairei vent field as the gastropod (28). Crabs are known to compress gastropod mollusc shells between their chela (claws) (35), which is expected to result in a local indentation of the shell structure at the sites of the chela protruding “fingers.” Each material layer was represented by an elastic–perfectly plastic constitutive model and maximum loads up to 60 N were employed, comparable in magnitude to the known crushing force generated by the chela of Brachyuran crabs (36)

(Clearly, GURPS 5e needs to employ their FEA model code to properly determine DR values and ST-based melee damage for a variety of creatures in addition to just C. squamiferum and those Brachyuran crabs. I think Douglas Cole and Dan Howard have another Pyramid article to work on.)

[Daigoro]

Originally Posted by Anaraxes

It's probably hard to imagine from a modern viewpoint, but the Babylonians couldn't do fractions.

I was talking about the supposed revelation that base-60 presents to modern mathematicians.

[ak_aramis]

Originally Posted by Daigoro

I was talking about the supposed revelation that base-60 presents to modern mathematicians.

Essentially, very inobvious shortcuts in base 10, base 2, and base 16 become apparently almost obvious in Base 60.

Those shortcuts may or may not be reverse engineered into other bases; I don't know.

Originally Posted by Anaraxes

Because then you need 120 or 600 glyphs just to write down any number.

No, you just get compounded glyphs.
One of the mesoamerican versions uses 3 distinct glyphs: Dots, bars, and eyes.
0: eye
1-4: that many dots
5: 1 bar
6-9: 1 bar under 1-4 dots
10: 2 bars
11-14: 2 bars under 1-4 dots
15: 3 bars
16-19: 3 bars under 1-4 dots
20: cell 1: 1 dot; Cell 2: eye.
103: cell 1: 1 bar; Cell 2: 3 dots
417: cell 1: 1 dot; cell 2: eye; cell 3: 3 bars under 2 dots

Assyrians use two half-spaces per "digit"
Right half: 1-9 are a cluster of vertical tallies in a 3x3 grid
left half: 10,20,30,40,50: 1 to five left-pointing "carets" <
Empty Place value: two diagonal marks \\

[Flyndaran]

Originally Posted by Anaraxes

Oh, the armor is even better than an iron sulfide coating. It's actually a multi-layered structure, with the iron sulfide particles sitting on top of a flexible organic, proteinaceous layer, which in turn sits on a calcified inner shell, for alternating layers of rigidity and flex. It's layered composite armor, like the armor on modern main battle tanks.
...

Life does love turning marginal materials into parts of amazing composites. It's not like calcium hydroxyapatite is a really good structural substance being a brittle crystal and all, but life turned that along with protein into bone.

Black smokers spew out lots of unique chemicals with elements in forms far more readily bio-available than they are anywhere else. Finding/creating value in the valueless but common is a wonderful aspect of evolution.

[Daigoro]

Originally Posted by ak_aramis

Essentially, very inobvious shortcuts in base 10, base 2, and base 16 become apparently almost obvious in Base 60.

Those shortcuts may or may not be reverse engineered into other bases; I don't know.

Okay, but are any of these things revelations that modern mathematicians didn't know about until this paper revealed "the lost secrets of Babylonian trig?" Do they gain anything by using base-60 that isn't gained by using radians or purely algebraic expressions, and that wasn't already known about?