knitr::opts_chunk$set(
  comment=NA,
  fig.width=7,
  fig.height=6
)

library(dplyr)
library(ggplot2)

It is a widely used and cited metric in predictions about the development of Artificial General Intelligence. Perhaps the best-known of these is futurist Ray Kurzweil's projections in The Singularity is Near [-@Kurzweil2005-mh], which are based on simple, linear extrapolations of Moore's law.

Moore's Law

Roughly stated, Moore's law predicts that the density of transistors in a single processor core grows exponentially. [@Moore1998-ze]

library(AIPredict)
library(dplyr)
library(ggplot2)

ai_moores_law %>%
  ggplot(aes(Year, Transistors)) +
  geom_point() +
  scale_y_log10() +
  stat_smooth(method="lm")

Koomey's Law

Koomey's law states that the electricty required to execute some number of computations declines exponentially over time [@Koomey2011-fc]. While less well-known than Moore's law, it offers another critical benchmark for comparison to the human brain, which computes a mind on a metabolic budget on the order of approximately 10 watts.

ai_koomeys_law %>%
  ggplot(aes(Year, WattsPerMCPS)) +
  geom_point() +
  scale_y_log10() +
  stat_smooth(method="lm")
koomeysLaw <- lm(Year ~ log(WattsPerMCPS), data = ai_koomeys_law)
summary(koomeysLaw)

While Moore's law is now expected to slow down (owing to Intel's recently signalled development cycle), Koomey's law may remain more-or-less "on-schedule", implying that energy costs per transistor are falling faster than indicators of Moore's law.

Top 500 Supercomputers

The Top 500 Supercomputers. Another good source for demonstrating Moore's and Koomey's laws.

ai_top500 %>%
  filter(Rank == 1) %>%
  mutate(RMAX=ifelse(is.na(RMax), Rmax, RMax)) %>%
  filter(!is.na(RMAX)) %>%
  ggplot(aes(Year, RMAX)) +
  geom_jitter(width = 1, height = 0, alpha=.3, size=5) +
  scale_y_log10() +
  stat_smooth(method = "lm")

Graph 500: Top 500 Graph-traversing Supercomputers

The Top 500 Graph-traversing Supercomputers.


Bitcoin Hashrate

The Hashrate of the Bitcoin network provides a useful insight into the growth of financially-motivated expenditure of computing resources to compute the solution of a single problem. I suspect that this will be a useful point of comparison as the network's exercised capacity approaches levels comparable to the the human brain.

ai_bitcoin_hashrate %>%
  ggplot(aes(Date, GHPS)) +
  geom_line()

Animal Brains

As our computational capacity climbs through the ranks of the animal kingdom, there are a variety of metrics which would be useful for comparison. The Number of Neurons, Cortical Neurons (in mammals), Synapses, Brain size, Brain-to-Body Mass Ratio, Encephalization Quotient and Cranial Capacity might all be useful in this line of research. Sadly, I've not yet found any sources (let alone reliable ones) for more than a few species. This dataset was scraped from the Wikipedia's List of Animals by Number of Neurons. Those, in turn, were assembled from a variety of sources, most prominently @Herculano-Houzel2007-qt. (This last set is on my list of sources to add.)

ai_animal_neurons %>%
  ggplot(aes(Neurons, Synapses)) +
  geom_point() +
  scale_y_log10() +
  scale_x_log10() +
  stat_smooth(method = "lm")

The logarithmic scale in both dimensions suggests a power-law relationship, but this is derived from a very small, very noisy sample.

References



AABoyles/AIPredict documentation built on Nov. 15, 2019, 9:20 a.m.