3 ms·

I've had similar thoughts lately. Here's a simple mathematical model of the process that I felt inspired to create by your comment: k[i] = (1 - c1) * k[i - 1]

I've had similar thoughts lately. Here's a simple mathematical model of the process that I felt inspired to create by your comment: k[i] = (1 - c1) * k[i - 1] + c2 where i is the generation number, k is the amount of knowledge we have, c1 is the loss factor (amount of knowledge lost from one generation to another, 0 ≤ c1 ≤ 1), and c2 is the (constant) amount of new knowledge created by generation i. In this model, it's easy to show that after long periods of time the amount of knowledge will plateau. In fact, the plateau is k[∞] = c2 / c1 The basic point of this is to highlight that both knowledge creation and loss are factors, and the loss means that knowledge may not keep increasing indefinitely. Of course, any number of the approximations and assumptions involved in this derivation may not be valid, but I think the possibility that knowledge loss can cause problems is worth considering.

jjk166 6y ago
Treating c1 and c2 as constants seems problematic. Different generations have different populations and access to resources such as education, technology, etc. The unknown knowledge to be discovered varies. The methods of preserving and transmitting knowledge vary. There were certainly cavemen born with Einstein-level intelligence from time to time, but without a foundation to build on, peers to collaborate with, or written language to preserve their knowledge, they would both create and pass on significantly less knowledge than someone in modern times. One generation might lose a large portion of all the knowledge built up for millenia prior during a civilization's collapse; while another generation may stumble upon a discovery which ushers in a short but extremely productive era of knowledge production. If nothing else, if you have 4 billion people in one generation and 8 billion in another then all else being equal the latter generation has twice as many brains with which to store and create knowledge.
- btrettel 6y ago
  Fair points. I've made a few refinements already on paper, switching to an ODE model rather than a difference equation and changing the knowledge production rate to vary. If there are diminishing returns then we would expect c2 to decrease as k increases at large k. As you're aware, perhaps this is offset by increases in population. As you've indicated, heterogeneity in various parts of the problem make this sort of modeling questionable. It's a crude model not meant to make precise predictions, just show that knowledge loss can be a major factor at long times.

jjk166 6y ago

Treating c1 and c2 as constants seems problematic. Different generations have different populations and access to resources such as education, technology, etc. The unknown knowledge to be discovered varies. The methods of preserving and transmitting knowledge vary. There were certainly cavemen born with Einstein-level intelligence from time to time, but without a foundation to build on, peers to collaborate with, or written language to preserve their knowledge, they would both create and pass on significantly less knowledge than someone in modern times. One generation might lose a large portion of all the knowledge built up for millenia prior during a civilization's collapse; while another generation may stumble upon a discovery which ushers in a short but extremely productive era of knowledge production. If nothing else, if you have 4 billion people in one generation and 8 billion in another then all else being equal the latter generation has twice as many brains with which to store and create knowledge.

btrettel 6y ago
Fair points. I've made a few refinements already on paper, switching to an ODE model rather than a difference equation and changing the knowledge production rate to vary. If there are diminishing returns then we would expect c2 to decrease as k increases at large k. As you're aware, perhaps this is offset by increases in population. As you've indicated, heterogeneity in various parts of the problem make this sort of modeling questionable. It's a crude model not meant to make precise predictions, just show that knowledge loss can be a major factor at long times.