autosave: 2026-03-10 06:43:48

Author: tecunningham

posts/2025-08-02-landscape-shrouded-in-clouds.qmd

@@ -446,7 +446,7 @@ General model of knowledge.
 | - random landscape (Kortum)              |  none  | categorial  |
 | - random with noise (Jovanovic & Nyarko) |  none  | categorical |
 | - K-arm bandit                           |  none  | categorical |
-| - Brownian landscape (Callander)         |  none  |   scalar    |
+| - Brownian landscape (Callander/Bardhi)  |  none  |   scalar    |
 | - NK fitness                             |  none  |   vector    |
 | - Bayesian optimization (GP-UCB/TS)      |  none  |   vector    |
 |                                          |        |             |
@@ -494,15 +494,22 @@ Continuous action, Weiner outcome.
 
 
 Atomic actions.
-
-: @kortum1997research models technological progress as taking random draws from a distribution ("undirected search"). Thus the returns to experience and R&D will depend on the thickeness of tails of the underlying distribution:
+:   @kortum1997research models technological progress as taking random draws from a distribution ("undirected search"). Thus the returns to experience and R&D will depend on the thickeness of tails of the underlying distribution:
       - If the distribution is bounded, growth asymptotes to zero.
       - If the distribution is exponential (thin tails) then growth has diminishing elasticity, $A=\ln n$.
       - If the distribution is Pareto (thick tails) then growth has constant elasticity, $A = n^\gamma$.
 
-      Note that random/undirected search seems a poor fit for most innovation processes. It implies that the share of trials that are failures will increases very strongly over time, but this seems unlikely to be true in the data. Most search seems pretty directed: Edison testing filaments, high-through drug discovery, evaluating mutations.
+    Note that random/undirected search has some odd implications:
+
+    1. A given innovation is equally likely to be discovered early as late, a caveman is equally likely to invent the transformer, as a software engineer.
+    2. The share of trials that are successes decreases very strongly over time.
+    3. The distribution of proportional jumps is independent of the level, $P(q>\theta \bar q \mid q>\bar q) = \theta^{-\alpha}$.
+    
+    In practice most search seems pretty directed: Edison testing filaments, high-through drug discovery, evaluating mutations.
+
+    
 
-: @agrawal2023automation model a finite distribution of alternatives, and the inventor has a prior probability of success for each. They let AI change the distribution of priors, and they show that this change will tend to decrease time-to-success and increase R&D effort.^[Note that they set up the landscape as a combination of N elements, but by email they confirm that the combinatorial structure isn't actually used. They say their earlier paper, @agrawal2019needles, does use the combinatorial structure.]
+:   @agrawal2023automation model a finite distribution of alternatives, and the inventor has a prior probability of success for each. They let AI change the distribution of priors, and they show that this change will tend to decrease time-to-success and increase R&D effort.^[Note that they set up the landscape as a combination of N elements, but by email they confirm that the combinatorial structure isn't actually used. They say their earlier paper, @agrawal2019needles, does use the combinatorial structure.]
 
 Combinatorial actions.