While not intended to be used mathematically, the I Ching hexagrams developed around 1000AD represented the binary numbers from 0-63 (2^6), as discovered by Leibniz who was quite fond of binary himself.
https://en.m.wikipedia.org/wiki/I_Ching
And as you know each hexagram was composed of two groups (trigrams) of three pairs. Similar to bytes and nibbles.
Even though the superstition is unfounded, the trigrams could combine in any way to refer to concepts and expositions that could give a lot of food for thought. Quite a nice system and very elegant because of its basis in binary numbers.
Edit: and I think you meant to say 1000 BC, not AD. In short a LONG time ago!
[1] https://www.jstor.org/stable/1399337?seq=1#page_scan_tab_con...
As long as you realize that you can use different combinations of the "first" spots with each additional spot you quickly come up with what is effectively binary.
I distinctly remember in early middle school trying to think of ways to enumerate things where you could never confuse one for the other based on the symbols. I was using base 10 because I wanted to store the combination of things in a variable in BASIC on a program I was trying to write on my calculator. As I was playing around on paper I came up with a great system.
I would only use one and zero because you could always tell them apart, where as if you use the other numbers then you can't tell if you meant five or if that five was a combination of two and three. When you needed to make another thing and you were out of places you would just add a digit on the left.
Then about five seconds later it hit me that what I had was just binary. All of a sudden the idea of using individual bits in masks to represent things (which I'd seen before) made a lot more sense.
...because people are smart. People have _always_ been smart, it's one of the defining attributes of humanity.
It strikes me oddly (not specifically your comment, but the general color accompanying these kinds of articles)--there's a kind of ground assumption that by looking into the past, one sees nothing but a gradually descending IQ.
I don't disagree, but I think there's more to it than just that.
Our raw mental capabilities may have always been the same, but how smart we are also depends on our learning. Learning gives us extra leverage. If you have two smart people and one of them was trapped by themselves all their life on a desert island and the other learnt a lot about (say) maths and science, then the latter person could in practical terms have greater intellectual capabilities.
Over the centuries we've made great gains in mathematical tools, scientific knowledge, in democratizing education and in disseminating knowledge. And this means over the centuries we've (as a species) obtained more leverage that we can apply to our raw mental capabilities, giving us (overall) greater intellectual capabilities.
FWIW, I tend to equate "smart" with "cleverness," as a separate measure distinct from "experience," for the same reason you describe--so what I usually go by is something along the lines of:
Cleverness is a measure of "what can you do with what you have," whereas experience is a measure of "what do you have?"
> Over the centuries we've made great gains in mathematical tools, scientific knowledge, in democratizing education and in disseminating knowledge. And this means over the centuries we've (as a species) obtained more leverage that we can apply to our raw mental capabilities, giving us (overall) greater intellectual capabilities.
I don't think we've gained greater intellectual capabilities--our intellectual capabilities are the same, we just operate in a completely different mental environment than our priors did.
Moreover, having a different view of the world allows for different connections to be made, and different potentials to be expressed (irrespective of one's individual level of cleverness).
So, for example, by placing a priority on stories & views that encourage greater investigation of the physical world, we get to where we are today. And we can teach the next generation slightly different stories that optimize for different kinds of usefulness.
To bring it to the HN contingent--if I learn a new programming language, I've gained experience in different ideas and operate in a different mental landscape. But I'm not smarter afterwards, and I wasn't dumber before.
Actually, it quite literally might be so: https://en.wikipedia.org/wiki/Flynn_effect
Though it's questionable as to how IQ is related to actual intelligence over time.
Hopefully without repeating the mistakes of the past tho!
Even that phrase "mistakes of the past" is telling, right? I mean it's not like, IMHO, you hear a similar amount of talk about, "the brilliance of the past", except it a sort of quaint, dismissive way: "oh, look, plumbing in ancient Rome, weren't they sort-of clever!"
This is not to beat our chests in a "we're better" kind of fashion, but just to acknowledge that we have the benefits of the knowledge that people who came before us built.
The correspondence between the hexagrams and the binary numbers nothing more than a necessary consequence of the representation chosen: the number of states of a string of 6 characters in a system of 2 symbols.