twinkle_and_sprinkle.py

#!/bin/env python
######################################################################
#
# In his famous and highly respected paper, "Bertlmann's socks and the
# nature of reality" (available open access at
# https://cds.cern.ch/record/142461/ ), the physicist John S. Bell
# asserts that, if we could control the temperature, and control for
# family quarrels, and so on, then the rates of heart attack in Lille
# and Lyon would be statistically independent (Equation 10). His
# defense of this assertion is that "it seems reasonable to expect".
#
# "It seems reasonable to expect" is, of course, not a defense at
# all. And there is an actual mathematical theory of probability that
# Bell is blithely ignoring, or perhaps did not even know about, that
# says this expectation is unreasonable. But let us ask: to what
# purpose is he making this claim?  It is to justify the assumption
# that two variables can be treated as independent parameters (rather
# than as functions of other parameters), even if the two variables
# describe objects that have a common origin.
#
# By such reasoning, my siblings and I must have statistically
# independent DNA! For the only thing our DNAs have to explain any
# correlation is that share a common origin. Hold as many variables
# constant as you want, it will make no difference in the
# correlation. For this reason, I can hardly believe anyone doesn’t
# simply burst out laughing, when reading Bell's writing. But this
# writing is, in fact, mandatory doctrine not only in physics
# departments, but wherever quantum computers are dealt with.
#
# But let us, as amateur and professional computer programmers, not
# burst out laughing, but instead use our computers to examine what
# happens if we assume two cities have the same temperature, the same
# quarreling behaviors, etc., and--this is crucial--whose populations
# share a common origin. Let us use our computers to enlighten at
# least ourselves. For, to quote Richard Hamming:
#
#       THE PURPOSE OF COMPUTING IS INSIGHT, NOT NUMBERS
#
# Towards this end, I came up with the following story.
#
######################################################################
#
# Our story runs as follows:
#
# The cities of Twinkle and Sprinkle always have the same temperature,
# same weather, same day length, same time zone. They always have the
# same quarreling behavior. Everybody eats practically the same things
# and practically at the same times. The two cities have
# indistinguishable sleep habits. They share their water supply. So on
# and so on and so on.
#
# In fact, let us go so far as to say that Twinkle and Sprinkle have
# exactly the same population. Not only that, but exactly half the
# population of each city is women cloned from the same woman, and
# half the population is men cloned from the same man. We shall
# further assume that the two progenitors were genetically sterile, so
# that there are no children in either Twinkle or Sprinkle. Everyone,
# in fact, is exactly the same age. There is no mutation or genetic
# drift.
#
# We could say much more, but you get the idea. We have controlled
# every variable there is: not just every variable we can think of,
# but literally every variable there IS. One of which is: the rate of
# heart attacks. Let us say that no one in either Twinkle or Sprinkle
# ever, ever has a heart attack.
#
# Let us now more closely examine the two progenitors. We discover
# that the male progenitor, but not the female progenitor, had a
# peculiarity of the DNA: that the sound of the "Lady Beware Alarm"
# device of the movie "Invasion of Astro-Monster"
# (https://godzilla.fandom.com/wiki/Invasion_of_Astro-Monster) causes
# instant heart attack.
#
# On a sunny day in July, suddenly it is raining "Lady Beware Alarm"
# devices on Sprinkle, and the devices are blaring at full blast. We
# observe Sprinkle and see that all the men have heart attacks, but
# none of the women do.
#
# We have not observed events in Twinkle. However, we know about the
# pecularity of the DNA, and we know that, as with everything else,
# rainfall in Twinkle is the same as in Sprinkle. We know this to be
# true even if the rain is made of electronic devices instead of
# water, because the two cities are controlled for every variable. Not
# only variables we thought of, but literally every every variable
# there is.
#
# Here we come to the use of a computer to gain insight.
#
# Write code to compute and print the heart attack rates for that July
# day in Twinkle and Sprinkle. The rates in Sprinkle are the observed
# ones, but the rates in Twinkle are predicted by inference.
#

print ()
print ("   Heart attack rates, according to logical inference")
print ("                       Women        Men        Overall")
print (" Twinkle (predicted)     0           1           0.5")
print (" Sprinkle (observed)     0           1           0.5")
print ()

#
# Now assume, against all common sense and soundness of logic, that
# heart attacks in Twinkle cannot be predicted from heart attacks in
# Sprinkle. We have controlled for all variables, but we also assume
# common origin is irrelevant.
#
# Write code to compute and print out the heart attack rates,
# according to that way of thinking.
#

print ("   Heart attack rates, according to the incurious")
print ("                       Women        Men        Overall")
print (" Twinkle (predicted)    ???         ???          ???")
print (" Sprinkle (observed)     0           1           0.5")
print ()

#
# According to such theory, there is nothing we can predict about
# Twinkle. What happens in Twinkle will remain a complete mystery
# until we go there and observe.
#
# But further suppose we have a so-called "Godzilla's theorem", which
# quotes no postulates or theorems known to mathematics, but which
# instead introduces this postulate: that men having heart attacks in
# Sprinkle would have to have a causal influence on heart attack rates
# in Twinkle, for Twinkle's heart attack rates to change. This is so
# because we have controlled all variables and the "residual
# fluctuations" can be integrated out (as in Bell's Equation 10). The
# two cities are utterly the same. The only difference is we have
# observed the men in Sprinkle have heart attacks and have not
# observed Twinkle at all.
#
# Write code to compute and print out the heart attack rates predicted
# by "Godzilla's theorem".
#

print ("   Heart attack rates, according to Dr. Godzilla")
print ("                       Women        Men        Overall")
print (" Twinkle (predicted)     0           0            0")
print (" Sprinkle (observed)     0           1           0.5")
print ()

#
# Now we go into Twinkle and observe that all the men have had heart
# attacks, but none of the women have.
#
# Write code to compute and print out the observed heart attack rates.
#

print ("   Heart attack rates, according to observers")
print ("                       Women        Men        Overall")
print (" Twinkle (observed)      0           1           0.5")
print (" Sprinkle (observed)     0           1           0.5")
print ()

#
# These empirical results stand in stark contrast to our prediction,
# which was predicated on the assumption of "causal reality".
#
# Write Artificial Intelligence code to print out the conclusion of
# adherents to "Godzilla's theorem".
#

print ("   Output of an AI of a \"Godzilla's theorem\" adherent")
print ("However strange it may seem, heart attacks in Twinkle and")
print ("Sprinkle are now scientifically proven to involve some kind")
print ("of violation of causal reality.")
print ()

#
# Then write Artificial Intelligence code to print out the conclusion
# of the educated public.
#

print ("   Output of an AI of a very intellectual person")
print ("Adherents to \"Godzilla's theorem\" are society's greatest")
print ("geniuses, so what they say is true.")
print ()

#
# That was the tale of two remarkable cities, Twinkle and
# Sprinkle. Write your own version of the program, in the programming
# language of your choice.
#
# Okay. Now what do YOU, who just wrote a program for the purpose of
# gaining insight, think? What insight have you gained?
#
# In the end, we are all individually responsible for what we think,
# even if we got it by deferring to "scientific authority".
#
# THE END.
#
# Afterword: Those familiar with the debates within physics might
# recognize that the DNA peculiarity is what they would call a "hidden
# variable". The crucial question is this: can a "hidden variable" be
# shared due to a common origin, or can it not? I say it can be, John
# Bell said otherwise. But you must decide for yourself. It is your
# decision, even if that decision is to believe "Whichever of the two
# 'scientific authority' proclaims to be the truth."
#