Wider, way wider.
Flatter.
Still limited.

Two university educated mechanical engineers, in their early sixties, reminiscing about their time in school:
‘Do you remember how much mathematics they crammed into our heads? You liked it, I didn’t. And none of us has actually used that information. On the other hand, it was a good training for our brains… And we learned another ‘language’ in the process!’
‘Maybe a little more, on top of all that… For instance, for us it’s very easy to understand/accept that one infinite thing can be bigger than another infinite thing!’
‘Never thought of it! But yes, you’re absolute right. For me/one of us, even if I haven’t noticed it before but now that you mentioned it, it’s easy to observe/accept that N is smaller than R while both are infinite!’
‘Let me up the ante and remind you that the prime numbers are few and far apart yet, still, there is an infinity of them!’.
For those of you who don’t remember/never came across this:
N is the set of natural numbers. 1, 2, 3… 101…95217… and so on.
R is the set of real numbers. From – whatever to – 99986524581.2789 … on to – 3.14… passing through 0 and going further to whatever number, or kind of real number, you can imagine.
A prime number is that which can be divided only by 1 and itself. 1,2,3,5,7,11 and so on. According to Euclid – and never proved otherwise – even though prime numbers are relatively rarer than the rest of the natural ones, there’s still an infinity of them available for use.
Fung Yu-Lan. A Short History of Chinese Philosophy, 1948:
“In another passage an imaginary conversation is recorded between Tzu-ch’an, a famous statesman of state of Cheng who lived in the sixth century B.C., and his two brothers. Tzu-ch’an governed the state for three years and governed well. But his two brothers were out of his control; one of them was fond of feasting and the other of gallantry.
One day, Tzu-ch’an spoke to his brothers, saying: “Those things in which man is superior to beasts and birds are his mental faculties. Through them he gets righteousness and propriety, and so glory and rank fall to his share. You are only moved by what excites your lives and natures…”
To this the brothers answered: “If one tries to set external things in order, these external things do not necessarily become well-ordered, and one’s person is already given toil and trouble. But if one tries to set the internal in order, the external things do not necessarily fall into disorder, and one’s nature becomes free and at ease. Your system of regulating external things will do temporarily and for a single kingdom but it is not in harmony with the human heart. Our method of regulating what is internal, on the contrary, can be extended to the whole world, and [when it is extended] there is no need for princes and ministers.”
Chapter 20 Neo-Taoism: the Sentimentalists.
What do we make out of this whole thing?
Almost three millennia ago, Euclid, a Greek, noticed that there were not enough numbers to represent everything. Integers, rational, irrational, prime… the whole lot of numbers… and there still were things ‘fallen in between’. Things which still can not be expressed as precisely as people wish. Which begets a sorry conclusion. No judgement, no decision, will ever be ‘definitive’. Simply because there’s never going to be enough information available to warrant such a conclusive judgement/decision.
Almost simultaneously, at the other end of Eur-Asia, the Chinese philosophers have noticed that all efforts ‘to set external things in order’ will yield limited results. Limited in space. Only as ‘far’ as the decision maker can impose their will. And limited in scope. By the decision maker’s expertise, good will and gamut of interests. Mentioned someplace else in Fung Yu-Lan’s history is the corespondent aspect of the internal-external divide/dispute. Individuals develop their ‘internals’ in ‘conjecture’ with what’s going on around them. Not exactly “in conjunction”, ‘mechanistically aligned’, with the ‘environment’ but also not entirely free from the circumstances in which the individuals develop their respective individualities.
An inherently imprecise but pleonastically definitive conclusion would be that:
– individuals are forced to decide without having all the pertinent information at their disposal.
– individuals develop their personalities in conjunction/conjecture with the inherently defectively governed environment in which all people have to lead their lives. Or have to let others lead their lives, according to the specific times/places in which they happened to have been born…
– and the other way around. Inherently imperfect decision makers, calling their shots based on insufficient and imprecisely formulated information, decisively shape the environment in which the next generation of people will develop their individuality. Their respective individualities, to be more precise.
Discouraging?
Why? People are still here… they’ve somehow managed to survive, didn’t they?
Somehow managed to wither through this layered imprecision…
