Twinkle and Sprinkle: Difference between revisions
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The task is to do a statistical analysis of two remarkable fictitious cities, Twinkle and Sprinkle, that form a natural experiment. Twinkle and Sprinkle are practically equivalent, all possible variables having been controlled. |
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The task details are contained in [[#Python|the Python reference implementation]]. |
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This task started out as one to statistically analyze the epidemiologies of two cities in France. I had started researching on the net, looking for statistical packages I might want to use, or algorithms I might implement, when I remembered the famous motto from R. W. Hamming's ''Numerical Methods for Scientists and Engineers'' (Dover, 1986): |
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:THE PURPOSE OF COMPUTING IS INSIGHT, NOT NUMBERS |
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So I went ahead and wrote a Python program that, instead of crunching numbers, depended on the human brain to gain insight enough to hard code in the correct numbers. Perhaps your program will contain different numbers. |
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=={{header|Phix}}== |
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{{trans|Python}} |
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See Python entry for explanatory comments (which have been omitted for clarity) |
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<!--<syntaxhighlight lang="phix">(phixonline)--> |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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<span style="color: #008080;">constant</span> <span style="color: #000000;">txt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""" |
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Heart attack rates, according to logical inference |
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Women Men Overall |
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Twinkle (predicted) 0 1 0.5 |
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Sprinkle (observed) 0 1 0.5 |
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Heart attack rates, according to the incurious |
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Women Men Overall |
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Twinkle (predicted) ??? ??? ??? |
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Sprinkle (observed) 0 1 0.5 |
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Heart attack rates, according to Dr. Godzilla |
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Women Men Overall |
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Twinkle (predicted) 0 0 0 |
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Sprinkle (observed) 0 1 0.5 |
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Heart attack rates, according to observers |
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Women Men Overall |
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Twinkle (observed) 0 1 0.5 |
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Sprinkle (observed) 0 1 0.5 |
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Output of an AI of a "Godzilla's theorem" adherent |
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However strange it may seem, heart attacks in Twinkle and |
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Sprinkle are now scientifically proven to involve some kind |
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of violation of causal reality. |
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Output of an AI of a very intellectual person |
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Adherents to "Godzilla's theorem" are society's greatest |
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geniuses, so what they say is true. |
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"""</span> |
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<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">txt</span><span style="color: #0000FF;">)</span> |
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<!--</syntaxhighlight>--> |
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Output same as Python |
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=={{header|Python}}== |
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<syntaxhighlight lang="python"> |
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#!/bin/env python |
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###################################################################### |
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# |
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# In his famous and highly respected paper, "Bertlmann's socks and the |
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# nature of reality" (available open access at |
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# https://cds.cern.ch/record/142461/ ), the physicist John S. Bell |
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# asserts that, if we could control the temperature, and control for |
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# family quarrels, and so on, then the rates of heart attack in Lille |
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# and Lyon would be statistically independent (Equation 10). His |
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# defense of this assertion is that "it seems reasonable to expect". |
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# |
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# "It seems reasonable to expect" is, of course, not a defense at |
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# all. And there is an actual mathematical theory of probability that |
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# Bell is blithely ignoring, or perhaps did not even know about, that |
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# says this expectation is unreasonable. But let us ask: to what |
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# purpose is he making this claim? It is to justify the assumption |
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# that two variables can be treated as independent parameters (rather |
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# than as functions of other parameters), even if the two variables |
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# describe objects that have a common origin. |
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# |
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# By such reasoning, my siblings and I must have statistically |
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# independent DNA! For the only thing our DNAs have to explain any |
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# correlation is that share a common origin. Hold as many variables |
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# constant as you want, it will make no difference in the |
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# correlation. For this reason, I can hardly believe anyone doesn’t |
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# simply burst out laughing, when reading Bell's writing. But this |
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# writing is, in fact, mandatory doctrine not only in physics |
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# departments, but wherever quantum computers are dealt with. |
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# |
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# But let us, as amateur and professional computer programmers, not |
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# burst out laughing, but instead use our computers to examine what |
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# happens if we assume two cities have the same temperature, the same |
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# quarreling behaviors, etc., and--this is crucial--whose populations |
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# share a common origin. |
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# |
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# I do not expect either our programs or what I said above about |
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# sibling DNA to make the slightest difference with physicists and |
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# quantum computer researchers. They believe what they believe. But we |
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# are programmers of binary digital computers: probably not also |
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# quantum physicists, and surely not "qubit" programmers. So let us |
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# use our computers to enlighten at least ourselves. For, to quote |
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# Richard Hamming: |
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# |
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# THE PURPOSE OF COMPUTING IS INSIGHT, NOT NUMBERS |
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# |
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# I had set out to try to write a fancy Five-Thirty-Eight simulation, |
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# seeking insight into the matter. I looked into using GNU R to do |
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# statistically analysis, and so one, but soon realized that to do so |
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# would produce as much INSIGHT as do Five-Thirty-Eight's fancy |
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# simulations. Which is to say: none at all. |
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# |
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# Instead I came up with the following story. |
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# |
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###################################################################### |
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# |
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# Our story runs as follows: |
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# |
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# The cities of Twinkle and Sprinkle always have the same temperature, |
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# same weather, same day length, same time zone. They always have the |
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# same quarreling behavior. Everybody eats practically the same things |
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# and practically at the same times. The two cities have |
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# indistinguishable sleep habits. They share their water supply. So on |
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# and so on and so on. |
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# |
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# In fact, let us go so far as to say that Twinkle and Sprinkle have |
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# exactly the same population. Not only that, but exactly half the |
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# population of each city is women cloned from the same woman, and |
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# half the population is men cloned from the same man. We shall |
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# further assume that the two progenitors were genetically sterile, so |
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# that there are no children in either Twinkle or Sprinkle. Everyone, |
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# in fact, is exactly the same age. There is no mutation or genetic |
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# drift. |
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# |
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# We could say much more, but you get the idea. We have controlled |
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# every variable there is: not just every variable we can think of, |
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# but literally every variable there IS. One of which is: the rate of |
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# heart attacks. Let us say that no one in either Twinkle or Sprinkle |
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# ever, ever has a heart attack. |
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# |
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# Let us now more closely examine the two progenitors. We discover |
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# that the male progenitor, but not the female progenitor, had a |
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# peculiarity of the DNA: that the sound of the "Lady Beware Alarm" |
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# device of the movie "Invasion of Astro-Monster" |
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# (https://godzilla.fandom.com/wiki/Invasion_of_Astro-Monster) causes |
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# instant heart attack. |
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# |
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# On a sunny day in July, suddenly it is raining "Lady Beware Alarm" |
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# devices on Sprinkle, and the devices are blaring at full blast. We |
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# observe Sprinkle and see that all the men have heart attacks, but |
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# none of the women do. |
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# |
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# We have not observed events in Twinkle. However, we know about the |
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# pecularity of the DNA, and we know that, as with everything else, |
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# rainfall in Twinkle is the same as in Sprinkle. We know this to be |
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# true even if the rain is made of electronic devices instead of |
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# water, because the two cities are controlled for every variable. Not |
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# only variables we thought of, but literally every every variable |
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# there is. |
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# |
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# Here we come to the use of a computer to gain insight. |
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# |
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# Write code to compute and print the heart attack rates for that July |
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# day in Twinkle and Sprinkle. The rates in Sprinkle are the observed |
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# ones, but the rates in Twinkle are predicted by inference. |
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# |
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print () |
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print (" Heart attack rates, according to logical inference") |
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print (" Women Men Overall") |
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print (" Twinkle (predicted) 0 1 0.5") |
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print (" Sprinkle (observed) 0 1 0.5") |
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print () |
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# |
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# Now assume, against all common sense and soundness of logic, that |
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# heart attacks in Twinkle cannot be predicted from heart attacks in |
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# Sprinkle. We have controlled for all variables, but we also assume |
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# common origin is irrelevant. |
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# |
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# Write code to compute and print out the heart attack rates, |
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# according to that way of thinking. |
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# |
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print (" Heart attack rates, according to the incurious") |
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print (" Women Men Overall") |
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print (" Twinkle (predicted) ??? ??? ???") |
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print (" Sprinkle (observed) 0 1 0.5") |
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print () |
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# |
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# According to such theory, there is nothing we can predict about |
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# Twinkle. What happens in Twinkle will remain a complete mystery |
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# until we go there and observe. |
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# |
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# But further suppose we have a so-called "Godzilla's theorem", which |
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# quotes no postulates or theorems known to mathematics, but which |
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# instead introduces this postulate: that men having heart attacks in |
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# Sprinkle would have to have a causal influence on heart attack rates |
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# in Twinkle, for Twinkle's heart attack rates to change. This is so |
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# because we have controlled all variables and the "residual |
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# fluctuations" can be integrated out (as in Bell's Equation 10). The |
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# two cities are utterly the same. The only difference is we have |
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# observed the men in Sprinkle have heart attacks and have not |
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# observed Twinkle at all. |
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# |
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# Write code to compute and print out the heart attack rates predicted |
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# by "Godzilla's theorem". |
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# |
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print (" Heart attack rates, according to Dr. Godzilla") |
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print (" Women Men Overall") |
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print (" Twinkle (predicted) 0 0 0") |
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print (" Sprinkle (observed) 0 1 0.5") |
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print () |
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# |
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# Now we go into Twinkle and observe that all the men have had heart |
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# attacks, but none of the women have. |
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# |
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# Write code to compute and print out the observed heart attack rates. |
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# |
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print (" Heart attack rates, according to observers") |
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print (" Women Men Overall") |
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print (" Twinkle (observed) 0 1 0.5") |
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print (" Sprinkle (observed) 0 1 0.5") |
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print () |
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# |
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# These empirical results stand in stark contrast to our prediction, |
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# which was predicated on the assumption of "causal reality". |
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# |
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# Write Artificial Intelligence code to print out the conclusion of |
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# adherents to "Godzilla's theorem". |
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# |
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print (" Output of an AI of a \"Godzilla's theorem\" adherent") |
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print ("However strange it may seem, heart attacks in Twinkle and") |
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print ("Sprinkle are now scientifically proven to involve some kind") |
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print ("of violation of causal reality.") |
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print () |
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# |
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# Then write Artificial Intelligence code to print out the conclusion |
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# of the educated public. |
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# |
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print (" Output of an AI of a very intellectual person") |
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print ("Adherents to \"Godzilla's theorem\" are society's greatest") |
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print ("geniuses, so what they say is true.") |
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print () |
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# |
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# That was the tale of two remarkable cities, Twinkle and Sprinkle. |
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# |
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# Okay. Now what do YOU, who just wrote a program for the purpose of |
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# gaining insight, think? What insight have you gained? |
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# |
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# In the end, we are all individually responsible for what we think, |
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# even if we got it by deferring to "scientific authority". |
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# |
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# THE END. |
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# |
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# Afterword: Those familiar with the debates within physics might |
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# recognize that the DNA peculiarity is what they would call a "hidden |
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# variable". The crucial question is this: can a "hidden variable" be |
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# shared due to a common origin, or can it not? I say it can be, John |
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# Bell said otherwise. But you must decide for yourself. It is your |
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# decision, even if that decision is to believe "Whichever of the two |
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# 'scientific authority' proclaims to be the truth." |
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# |
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</syntaxhighlight> |