tl; dr Many examples of Rapid Capability Gain can be explained by a sudden jump in fidelity of a multi-step error-prone process. As the single step error rate is gradually lowered there is a sudden transition from a low fidelity to a high fidelity regime for the corresponding multistep process. Examples abound in cultural transmission, development economics, planning & consciousness in agent, origin of life and more.
Consider a factory making a widget in N distinct steps. Each step has a probability of a fatal error and the subsequent step can only occur if the previous step was succesful. For simplicity we assume that the chance of an error for each step is given by a single ‘single step error rate’ parameter. What is the error rate for the entire process?
Here are some values
Single step error rate
10 step error rate
100 step error rate
1000 step error rate
10%
0.34
0.27∗10−4
0.17∗10−45
5%
0.59
0.6∗10−3
5.3∗10−23
1%
0.9
0.37
0.43∗10−4
0.1%
0.99
0.9
0.37
Math nerd remark: for an N-step process with 1/N single step error rate will be approximately 1e=0.37. We see that an order of magnitude difference in the single step error rate or an order of magnitude difference in the number of steps can be the difference between a completely unrealistic plan (0.27∗10−4) and plan with at least a fair chance of working (0.34). Another order of magnitude worse fidelity or longer multistep process goes from a unrealistic plan (0.27 *10^{-4}) to an astronomically unlikely.
It’s a simple causal mechanism that shows up in many different places whenever we sudden capability jumps.
Why are some countries much richer than others?
(see also Gareth Jones https://www.sup.org/books/title/?id=23082 ) The ultimate cause(s) are a point of contention, but the proximate cause is simple: rich countries produce complex specialized goods that are much more valuable than their raw inputs. These are produced by large highly hierarchical teams of specialists. Making complex specialized goods like uranium refinement, aeroplanes, microchips, industrial tooling requires many processing steps. To efficiently produce these products it is imperative to have single-step fidelity. For whatever reason rich countries have been succesful in lowering this single-step error rate.
Rk. As an aside, most of the gains are not actually captured by these specialists because of comparative advantage. Similarly but perhaps surprisingly, low skill workers gained with respect to high skill workers during the Industrial Revolution. [Citation!]
Cultural Transmission Fidelity as key indicator in human cultural evolution
Cultural Transmission Fidelity as cause of human-ape divergence
We can also understand cultural transmissionAtleast whales and apes have forms of cultural learning too. The difference seems to be the fidelity of human cultural transmissions. Humans are also smarter per individual though so it can’t be just cultural transmission (the relevant quantitity is probably cortical neurons—humans are only outclassed by certain whales on this measure—and even compared to whales human brain are probably superior, being more densely packed). However, it is likely
Proofs & High Fidelity Reasoning.
The remarkable deep structure of modern mathematics probably partially explained by high fidelity reasoning furnished by proofs. (see also thin versus thick reasoning)
RNA & DNA copying fidelity
For Life to have started it would have been necessary for a high-fidelity self-replicating process to arise.
There is a fairly well-supported theory on the Origin of Life that holds that initially life was all RNA based—which has an intrinsically high mutation rate. Once DNA came onto the scene the mutation rate became much lower → complex life like bacteria became possible.
IQ-divergence on increasingly harder tasks
Why we see more IQ-divergence on harder tasks? High IQ individuals probably have higher fidelity on single step reasoning—multi-step reasoning problems start to favor the shrewd more and more as the number of steps increases.
Global workspace theory
The key variable of high-level serial conscious reasoning according to global workspace theory is how fast teh different modules can communicate with one another. That is, the latency of communication. This key parameter plausibly underlies much of intelligence (indeed in the theory this is basically working memory which is highly correlated with IQ).
Multi-Step Fidelity causes Rapid Capability Gain
tl; dr Many examples of Rapid Capability Gain can be explained by a sudden jump in fidelity of a multi-step error-prone process. As the single step error rate is gradually lowered there is a sudden transition from a low fidelity to a high fidelity regime for the corresponding multistep process. Examples abound in cultural transmission, development economics, planning & consciousness in agent, origin of life and more.
Consider a factory making a widget in N distinct steps. Each step has a probability of a fatal error and the subsequent step can only occur if the previous step was succesful. For simplicity we assume that the chance of an error for each step is given by a single ‘single step error rate’ parameter. What is the error rate for the entire process?
Here are some values
Math nerd remark: for an N-step process with 1/N single step error rate will be approximately 1e =0.37. We see that an order of magnitude difference in the single step error rate or an order of magnitude difference in the number of steps can be the difference between a completely unrealistic plan (0.27∗10−4) and plan with at least a fair chance of working (0.34). Another order of magnitude worse fidelity or longer multistep process goes from a unrealistic plan (0.27 *10^{-4}) to an astronomically unlikely.
It’s a simple causal mechanism that shows up in many different places whenever we sudden capability jumps.
Why are some countries much richer than others?
(see also Gareth Jones https://www.sup.org/books/title/?id=23082 )
The ultimate cause(s) are a point of contention, but the proximate cause is simple: rich countries produce complex specialized goods that are much more valuable than their raw inputs. These are produced by large highly hierarchical teams of specialists. Making complex specialized goods like uranium refinement, aeroplanes, microchips, industrial tooling requires many processing steps. To efficiently produce these products it is imperative to have single-step fidelity. For whatever reason rich countries have been succesful in lowering this single-step error rate.
Rk. As an aside, most of the gains are not actually captured by these specialists because of comparative advantage. Similarly but perhaps surprisingly, low skill workers gained with respect to high skill workers during the Industrial Revolution. [Citation!]
Cultural Transmission Fidelity as key indicator in human cultural evolution
Secret of our Success is a recent book on the high fidelity cultural transmission model. https://press.princeton.edu/books/paperback/9780691178431/the-secret-of-our-success
Cultural Transmission Fidelity as cause of human-ape divergence
We can also understand cultural transmissionAtleast whales and apes have forms of cultural learning too. The difference seems to be the fidelity of human cultural transmissions. Humans are also smarter per individual though so it can’t be just cultural transmission (the relevant quantitity is probably cortical neurons—humans are only outclassed by certain whales on this measure—and even compared to whales human brain are probably superior, being more densely packed). However, it is likely
Proofs & High Fidelity Reasoning.
The remarkable deep structure of modern mathematics probably partially explained by high fidelity reasoning furnished by proofs. (see also thin versus thick reasoning)
RNA & DNA copying fidelity
For Life to have started it would have been necessary for a high-fidelity self-replicating process to arise.
There is a fairly well-supported theory on the Origin of Life that holds that initially life was all RNA based—which has an intrinsically high mutation rate. Once DNA came onto the scene the mutation rate became much lower → complex life like bacteria became possible.
IQ-divergence on increasingly harder tasks
Why we see more IQ-divergence on harder tasks? High IQ individuals probably have higher fidelity on single step reasoning—multi-step reasoning problems start to favor the shrewd more and more as the number of steps increases.
Global workspace theory
The key variable of high-level serial conscious reasoning according to global workspace theory is how fast teh different modules can communicate with one another. That is, the latency of communication. This key parameter plausibly underlies much of intelligence (indeed in the theory this is basically working memory which is highly correlated with IQ).