To me, there seems to be four basic possibilities. 1: Approximately linear 2: Somewhat like a parabola 3: Approximately asymptotic to some upper limit. 4: Initially somewhat like a parabola & then approximately asymptotic to some upper limit. 5: Other The 4th seems most likely to me. Perhaps other Posters would include more possibilities. It is likely that some or many others would disagree with my opinion.
I would say it is un-quantifiable in the sense that the more we learn, the more we come to find we have yet to learn.
“As our circle of knowledge expands, so does the circumference of darkness surrounding it.” -Albert Einstein
I don't think you understood the question. The question was about the shape of the curve that would describe it. What shape is a spiritual curve?
"Logistic." https://www.khanacademy.org/science...-and-regulation/a/exponential-logistic-growth Describes a lot of biological phenomena, not just population growth. Are you counting the stored knowledge - the stuff nobody actually knows right this minute, but has at hand if needed? How are you dealing with logical levels of knowledge - knowledge about other knowledge, that kind of thing?
That'd be kind of weird; it implies that knowledge is some sort of resource that gets used up, and grows scarcer with time. Can't really see that for humans anytime in the next few centuries or milennia. Since he's talking about "human knowledge", that implies the sum total of knowledge of everyone. Anything one get quickly must be gotten from someone else who provided it. That's what I'm getting at wen I mention quantifying it. What unit is being measured?
It might also derive from new knowledge becoming progressively more difficult and time consuming to acquire, because of the enlarging body of old knowledge that must be acquired or accounted for first. Something like that seems to be happening in mathematics, for example - in some fields, mastering enough of the known to be able to address the unknown takes several years longer than it did a century ago.
Right. But that would result in a slower growth rate; it won't result in an asymptote unless there's a hard upper limit.
I'll go with Dave and Albert One kink appears to me Our knowledge in the past included the Earth was flat If our graph included that nugget do we go back to previous levels of knowledge and readjust? Do we take out previous knowledge we now understand is Woo Woo but at the time considered knowledge? Please Register or Log in to view the hidden image!
Indeed. And that too is part of quantifying knowledge. Does this constitute a bit of knowledge? Does that?
Asymptotes are approached, not "resulted in" - an essentially "soft" process. Also they are not necessarily horizontal (a hard upper bound) even under negative acceleration (negative 2nd derivative) (although the basic logistic's is). Just being pedantic. But the entire scene there makes little sense to me - I'm unable to quantify knowledge. That the accumulation of knowledge itself impedes the gaining of more, in some ways, is clear. We see it in the human lifespan - children learn faster in part because they know less. But gains in complexity in the relationships of the already known are not as obviously obstructed. If a human being continued to gain vocabulary at the rate of the average ten year old in a literate culture, by age 70 they would have a vocabulary approximately the size of the Oxford English Dictionary, 2nd Edition, in 20 volumes printed and bound with a magnifying glass included for reading the typeface.
It cannot be asymptotic as the goal posts would keep changing, assuming that human civilization is not decimated by nuclear or biological warfare or massive natural catastrophe. Every year the funds for research and higher education is increasing, every year the seats for research scholars are increasing, new fields of research are added implying that for a very very long time the pace of knowledge enhancement would keep increasing year on year.
