In this episode I discuss the great, classic article "The Median Isn't the Message" by Stephen Jay Gould. We delve into the article, its meaning, and lots of the depth and breadth we can get out of it. It should be read and studied by every statistics teacher and statistics student -- and everyone else, it is so full of lessons.

Contact Michael:
1. Email: reasonrx@aol.com
2. Gold Academy: https://www.goldams.com
3. Total Human Fitness: https://total-human-fitness.com
4. Cypress Creek Ecological Restoration Project: https://ccerp.org
5. LinkedIn: https://www.linkedin.com/in/michael-gold-2883921/
6. Twitter/Instagram: EpistemeRx



Notes.
1. "The Median Isn't the Message" by Stephen Jay Gould
https://www.edwardtufte.com/bboard/q-and-a-fetch-msg?msg_id=0003ms

2. Left skewed vs. right skewed
i. https://www.statology.org/left-skewed-vs-right-skewed/
ii. https://www.cuemath.com/data/right-skewed-histogram/

3. An article on Aristotle and science (high school- or college-level reading): https://galileoandeinstein.phys.virginia.edu/lectures/aristot2.html

“To summarize: Aristotle’s philosophy laid out an approach to the investigation of all natural phenomena, to determine form by detailed, systematic work, and thus arrive at final causes. His logical method of argument gave a framework for putting knowledge together, and deducing new results. He created what amounted to a fully-fledged professional scientific enterprise, on a scale comparable to a modern university science department. It must be admitted that some of his work - unfortunately, some of the physics - was not up to his usual high standards. He evidently found falling stones a lot less interesting than living creatures. Yet the sheer scale of his enterprise, unmatched in antiquity and for centuries to come, gave an authority to all his writings.

“It is perhaps worth reiterating the difference between Plato and Aristotle, who agreed with each other that the world is the product of rational design, that the philosopher investigates the form and the universal, and that the only true knowledge is that which is irrefutable. The essential difference between them was that Plato felt mathematical reasoning could arrive at the truth with little outside help, but Aristotle believed detailed empirical investigations of nature were essential if progress was to be made in understanding the natural world.”

4. The BBC provides a great, honest tribute to Aristotle for his work in science and biology: https://www.youtube.com/watch?v=JN8ortM4M3o

The BBC program is also here: https://www.youtube.com/watch?v=e12pbSHrzAs&list=PL2VcIjTwDHoLScpo2c26t-x3EdTP6WepL&index=1

5. From: https://www.theguardian.com/books/2014/oct/02/the-lagoon-armand-marie-leroi-aristotle-review

Excerpt 1. "The Greeks are famous, perhaps notorious, for casting their science whole, from first principles, without troubling to examine the natural world it sought to explain. But Aristotle changed everything, providing lengthy accounts of fish and fowl, their lives, courtships, kinds, anatomies, functions, distribution and habits. They were often erroneous, but what sets Aristotle apart is his workmanlike attitude. One gets the impression of a practical man, given to neither the remote and crystalline idealism of his predecessors, nor the flights of fancy of later natural historians such as Pliny the Elder."

Excerpt 2. "Darwin knew almost nothing of Aristotle until 1882, when William Ogle, physician and classicist, sent him a copy of The Parts of Animals he'd just translated. In his note of thanks, Darwin wrote: 'From quotations which I had seen I had a high notion of Aristotle's merits, but I had not the most remote notion of what a wonderful man he was. Linnaeus and Cuvier have been my two gods, though in very different ways, but they were mere schoolboys to old Aristotle.' “

6. See also this article by Dr. James Lennox: https://plato.stanford.edu/entries/aristotle-biology/

7. A quote about Galileo that discusses the importance of Aristotle, reasoning, and a correct view of logic.

In the book Galileo Galilei – When the World Stood Still, Atle Naess wrote:

“Galileo’s radical renewal sprang, nevertheless, from the Aristotelian mind set, as it was taught at the Jesuits’ Collegio Romano: human reason has a basic ability to recognize and understand the objects registered by the senses. The objects are real. They have properties that can be perceived, and then ‘further processed’ according to logical rules. These logical concepts are also real (if not in exactly the same way as the physical objects).”

8. A quote of Galileo himself that shows the importance of Aristotle to science and all human reasoning, and that identifies a basic principle of reason and logic: they are based on the evidence of the senses.

"I should even think that in making the celestial material alterable, I contradict the doctrine of Aristotle much less than do those people who still want to keep the sky inalterable; for I am sure that he never took its inalterability to be as certain as the fact that all human reasoning must be placed second to direct experience."

From the Second Letter of Galileo Galilei to Mark Welser on Sunspots, p. 118 of Discoveries and Opinions of Galileo, translated by Stillman Drake, (c) 1957 by Stillman Drake, published by Doubleday Anchor Books, Doubleday & Co., Garden City, New York.

9. Newton's Four Rules of Reasoning (showing he was Aristotelian, not Platonic, and showing you some fundamentals of how to reason and do science): http://apex.ua.edu/uploads/2/8/7/3/28731065/four_rules_of_reasoning_apex_website.pdf

Newton explicitly rejects Platonic thinking and the practice of some at the time of making stuff up in their heads when he says, in Rule 4, “not withstanding any contrary hypothesis that may be imagined.”

So he is with Galileo in method and philosophy of science.

He says himself that we stick to facts, we find causes, and that we use induction:

“Rule 1 We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

“Rule 2 Therefore to the same natural effects we must, as far as possible, assign the same causes.

“Rule 3. The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

“Rule 4. In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, not withstanding any contrary hypothesis that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.”

10. In "Plato And Saving The Appearances," The Bedford Astronomy Club writes:

"Plato lays down the principle that the heavenly bodies' motion is circular, uniform, and constantly regular. Thereupon he sets the mathematicians the following problem: what circular motions, uniform and perfectly regular, are to be admitted as hypotheses so that it might be possible to save the appearances presented by the planets? (Duhem, To Save the Phenomena, 5)

"Continuing, Simplicius explained:

"The curious problem of astronomers is the following: First, they provide themselves with certain hypotheses: . . . Starting from such hypotheses, astronomers then try to show that all the heavenly bodies have a circular and uniform motion, that the irregularities which become manifest when we observe these bodies—their now faster, now slower motion; their moving now forward, now backward; their latitude now southern, now northern; their various stops in one region of the sky; their at one time seemingly greater, and at another time seemingly smaller diameter—that all these things and all things analogous are but appearances and not realities. (Duhem, To Save the Phenomena, 23)"

See: https://www.astronomyclub.xyz/uniform-circular/plato-and-saving-the-appearances.html

11. The "Saving the appearances" quote I mentioned.
https://goldams.com/galileo-rejecting-plato/

12. Here is a good example of the failure of Platonic and “lost in math” “science.”

Excerpt: ”Galileo claimed to have seen moons around the planet Jupiter. Another scholar, Francesco Sizi, attempted to refute Galileo, not with observations, but with the following argument:

“ 'There are seven windows in the head, two nostrils, two ears, two eyes and a mouth; so in the heavens there are two favorable stars, two unpropitious, two luminaries, and Mercury alone undecided and indifferent. From which and many other similar phenomena of nature such as the seven metals, etc., which it were tedious to enumerate, we gather that the number of planets is necessarily seven...ancient nations, as well as modern Europeans, have adopted the division of the week into seven days, and have named them from the seven planets; now if we increase the number of planets, this whole system falls to the ground...moreover, the satellites are invisible to the naked eye and therefore can have no influence on the earth and therefore would be useless and therefore do not exist.' (Holton & Roller, 1958, p. 160)"

From: https://www.nichd.nih.gov/publications/pubs/using_research_stanovich