The Relativity of Wrong

❄ Asimov's Essay

❄ Randall's Modern Science

❄ Probably Approximately Correct

Isaac Asimov

was a great science, science fiction, and non-science fiction writer. He inspired a lot of the current scientists of our world. Part of the most widely successful examples of reason, logic, and skepticism in the 20th century. He can be honored as being the first spark of awe for reality in many of our brains, mine included.

He once received a letter from a non-scientist. An English Literature major. As a response to one of the many essays, he made on the progress of knowledge and science.¹

Quote:

His answer to him was:

Once people thought the earth was flat and they were wrong, but they were also nearly right. Bear in mind that when a flat-earther tells you his arguments, there's observation and logic that are >0.

The curvature of an ideal flat surface is indeed zero and the curvature of the earth's surface is very near to zero. This is dependent on the kind of measurements you can make. So for a long time, it was the best approximation. The approximation is the first important concept.

Later, the hypothesis of a spherical earth comes to us traceable at least to the greeks. (there are mentions a spherical or at least circular surface in places like the bible; then histories from Herodotus and the Phoeniciansns, later Pythagoras, Aristotle and Eratosthenes)

Eratosthenes (276-195 BC) measured this. He used the difference in elevation in altitude at noontime sun on June 21st summer solstice, that shined over a well in Alexandria reliably through a vertical well in the town of Syene, Egypt (it was taken as 0°). Approximately 500 Miles from his home in Alexandria (7°). He calculated an approximate curvature of 0.000126 per mile for the earth. Close to Zero, but not zero and this is significative. Of course, this was still wrong but a lot better.

He also calculated the tilt of the earth, great fucking dude

Source1 Source2

Later, based on the observation of other planets, Isaac Newton (1642 - 1727/26) noted that rotating big masses are slightly flatter at the poles. Using better instruments than shadows, scientists determined that the curvature varied from |7.973 - 8.027|/mile² in different places of the earth, an oblate spheroid. Of course, this was also wrong and the improvement is even less noticeable in absolute terms at the scale of observation of square miles but the relative implications are huge.

In 1958, when the satellites measured the gravitational pull of the earth with more precision and we found that the section of the circumference down the equator was bigger than one north, like a pear. This change in precision is in the millionth of an inch per mile. Of course, this is also wrong... or more precisely speaking, Incomplete.

Mod Source

Quote:

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My favorite

modern scientist, theoretical physicist Dr. Lisa Randall. Explains how the process of science works in her book, Knocking on Heaven's Door (I've mentioned in the past how scientists love puns, acronyms and to use Bob Dylan references²)

In an interview for Wired magazine, she speaks about her current work on theoretical physics. The same week her book was published, the OPERA (The Oscillation Project with Emulsion-tRacking Apparatus) published their results, 2012ₐ for faster than light neutrinos of their observed candidates since 2010.ᵦ Later proven to be wrong.ᵧ

It wasn't wrong to try to find out if it was right or to present such findings. Why do research in science:

In her book, she explains how even if most people lack the mathematical knowledge to fully grasp the physical concepts of modern physics, people can still gain an understanding not based on faith and appeal to authority, because just like a person reading math and concepts beyond what they are ready for, part of a scientist job is to deal with information more complex than they might be able to grasp and obtain their own probable approximations. ³

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Bayesian

rationality has been for a long time the basis of human reasoning.⁴ Even if people don't use the mathematical formulas, it has been shown that coherent predictions of reality can be done by regular people in constrained domains with different levels of mastery by statistical inference.⁵

How information is presented activates bias in people, that must be taken into consideration to make the message clearer. The whole information theory paradigm started by Shanon is an attempt to send a message reliably through an unreliable channel.

Machine learning mimics this by using computational applied statistics. What is learnable is the basis for some of the most imporatant advances like probably approximately correct learning.

It is a framework that allows us to know what is learnable and how many steps away from learning are we. We approach to the problem by worst-case scenarios to make interaction games fair, to make them learnable.⁶

Mod source, Northwestern University. ML, EECS 395-22

This is extremely important. Because even if people have ideas of Lamarckism, Creationism, Geocentrism what's relevant is the good faith of wanting a better approximation based on reliable measurements they can improve on their own terms. If they can advance their heuristics at least by a little, not dealing in absolutes, that's beautiful. More precission.

Because according to our state of the art understanding, rationality is bounded ⁷ and that's Probably Approximately Correct.

Thanks for reading.

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References

1 The Skeptical Inquirer, Fall 1989, Vol. 14, No. 1, Pp. 35-44

2 Carl Gornitzki, Agne Larsson, Bengt Fadeel, Freewheelin’ scientists: citing Bob Dylan in the biomedical literature BMJ 2015; 351

3 CERN or Einstein? Interpreting the Findings By Lisa Randall. HuffingtonPost, THE BLOG 09/25/2011 10:55 am ET Updated Nov 25, 2011

4 Bayesian Rationality: The probabilistic approach to human reasoning
Mike Oaksford and Nick Chater Print publication date: 2007

5 Gigerenzer, G. (1991). How to make cognitive illusions disappear: Beyond "heuristics and biases". European review of social psychology, 2(1), 83-115.

6 Lecture on PAC Learning, Carnegie Mellon

7 Gigerenzer, Gerd; Selten, Reinhard (2002). Bounded Rationality: The Adaptive Toolbox. MIT Press. ISBN 0-262-57164-1

Recommended:
Review on PAC learning 2016

Images not sourced: Google images labeled for reuse.