Jeffrey Aronson: When I use a word. . . test hypotheses in test times

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All the assumptions are unequal; some are more uneven than others.

I have previously discussed the Indo-European root DHE. The basic root, the so-called e-grade form, DHE, means to pose or to pose, to manufacture or to shape. But the vowels change easily, by the mechanism which Jakob grimm called ablaut (literally a false sound). So there is also an o-grade form, DHO, and a zero shape, DHƏ, in which the final vowel is a neutral vowel called schwa, after the Hebrew vowel of that name. The schwa, represented by an inverted e (lowercase or uppercase ??) usually occurs in weakly stressed syllables, such as e in “hypothesis” (/ hʌɪˈpɒθəsᵻs /). These different forms can also have prefixes and suffixes and can be duplicated. This results in a myriad of words, examples of which follow.

DHE gives act, mischief, and obsolete alms; as Queen Margaret says of Richard Duke of York in Henry VI, “Murder is your act of giving alms – Petitioners for the blood you will never deliver”. DHO gives us to do, to do and to do. DHEM gives a judgment and a theme, and DHOM gives fate and words ending in -dom, such as leechdom. Abdomen is conjecturally from the Latin abdere (ab + dare), to tidy up or to hide. DHEK give thèque (Greek θήκη), a sheath that contains an organ, and apothecary, from the Greek ἀποτιθέναι to store and therefore ἀποθήκη a warehouse. And the duplication, DHE-DHƏ, gives the Greek verb τιθέναι, to put or place, which gives the trilogy of dialectical materialism, thesis, antithesis and synthesis.

It is believed that “theory” comes from two Greek words meaning to see, and όράειν. However, I dare to suggest that it can come from τιθέναι + όράειν, to put in sight.

Thus a hypothesis, literally “placed below” (ὑπό), is a foundation, and therefore the base of an argument or a supposition. When he first entered English at the end of the 16the century, it meant a special case of a general proposition, and later the proposition itself. In logic, this meant a supposition or a condition forming the antecedent of a proposition. When Sir Thomas Browne used the word in his Epidemic pseudodoxy in 1646, he intended, by invoking the definition of Oxford English Dictionary, “A tentative guess from which to draw conclusions which must conform to known facts and which serves as a starting point for further investigation by which it can be proven or disproved and the true theory obtained.” “

This definition, not revised since 1899, deserves some attention. Hypotheses are indeed generally based on known facts and serve as starting points for further investigation, but only as such. It is easy to formulate explanations for phenomena once they have been observed, but it is wrong to accept them as gospel without further testing. However, to assert, as DEOthe definition of, that by such a test, a hypothesis can thus be proved is misleading. As Karl Popper taught us in The logic of scientific discovery (1959), originally published in German in 1934 under the title Logik der Forschung, the right way to test a scientific hypothesis is to try, not to prove it, but to disprove it, to falsify it, as Popper said. Here is what he wrote:

“A scientist constructs hypotheses, or systems of theories, and tests them against experience through observation and experimentation.” Denying the validity of induction, he suggests that “inference to theories, from singular statements which are ‘verified by experience’ … is logically inadmissible”. He then continues:

But today, Popper’s principle is abandoned. During the pandemic, researchers, presumably backed by ethics committees reviewing their proposed studies, decided that masked, randomized, placebo-controlled trials are not needed to test treatments for serious infection, with little reasons to assume that they will be effective. , or, even if it is effective, that the balance of pros and cons will be favorable.

In Greek ὑπόθεσις meant, among many things, a proposition or a proposed action, a suggestion or an advice, an excuse or a pretext, a practical problem or a supposition. Aristotle used it to signify the hypothesis of the existence of a scientific object. Today, this sense seems to be espoused again. Instead of testing their hypotheses, instead of trying to falsify them, researchers are trying to prove them. Next week I will be discussing how we should assess therapeutic hypotheses and test them in different ways.

Jeffrey Aronson is a clinical pharmacologist working at the Center for Evidence Based Medicine at the Nuffield Department of Primary Care Health Sciences in Oxford. He is also President Emeritus of the British Pharmacological Society.

Competing interests: none declared.

This week’s interesting integer: 274

  • 274 is a Tribonacci number. The series of Fibonacci numbers, described for the first time by Leonardo of Pisa (Fibonacci) begins with 0, 1 and continues by adding the two previous numbers: 0, 1, 1, 2, 3, 5, 8,… The Tribonacci number series starts with 0, 0, 1 and continues by adding the three previous numbers: 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274,…
  • 274 is a semi-prime, that is to say the product of two primes, 2 × 137. It is also an interpreter, the average of two consecutive primes, 271 and 277. The sum of its prime factors (2 + 137 = 139) is also prime.
  • 274 is a Smith number, so called when Albert Wilansky noticed that his brother-in-law’s phone number (493-7775) had an interesting property: the sum of its digits is the same as the sum of the digits of its prime factors (3, 5, 5 and 65837)

274 = 2 × 137 and 2 + 7 + 4 = 2 + 1 + 3 + 7 = 13

Smith’s numbers are also known as joke numbers. Numbers of this type that do not have repeated prime factors are also hoax numbers; 274 is the eleventh Smith number and the thirteenth number of hoaxes.

  • 274 is the sum of three non-zero squares in three ways:

274 = 32 + 32 + 162 = 32 + 112 + 122 = 72 + 92 + 122

  • 274 is the sum of four squares, one2, b2, vs2, and D2, so that a2+ b2, vs2 + d2, a2 + d2, and B2 + c2 are all prime: 274 = 132 + 102 + 22 +12

132 + 102 = 269; 22 +12 = 5; 132 + 22 = 173; ten2 +12 = 101

  • The square of 274 is the sum of 24 consecutive squares:

2742 = 442 + 452 + 462 + …… 652 + 662 + 672

  • The proper divisors of a number are all the numbers that divide it apart from the number itself. 274 is the sum of the squares of 1, 2, 3, 4, 6, 8, and 12, which are the proper divisors of 24.
  • 274 is a member of Moessner’s magic factorial triangle. In 1951, mathematician Alfred Moessner discovered a method to generate series of consecutive squares, cubes, fourth powers, etc. The variant of his method presented here generates the series of factorial numbers n! (ie 1, 1 × 2, 1 × 2 × 3,… .. 1 × 2 × 3 ×…. × n). Here is the method:

A) Write the numbers to count from 1 in a row. Cover the triangular numbers (1, 1 + 2, 1 + 2 + 3, etc.); these are colored yellow in the diagram below.

B) Add up the numbers left uncovered in row A to get the partial sums shown in row B. Cover the numbers to the right of each number section (colored blue).

VS) Add up the numbers discovered as before and write the partial sums in row D. Cover the numbers on the right (green).

D) Repeat (orange).

E) Repeat (purple).

The numbers on the far left of each row are the factorials 1 !, 2 !, 3 !, 4! and 5!

The process can be continued endlessly by writing more digits to the right of line A and continuing to progress downward.

The colored numbers above can be rearranged into a triangle, as shown below; the red numbers are the factorials and the orange numbers are the sums of the numbers in the corresponding lines of the triangle, in each case one less than the factorial that begins the next line.

Moessner’s magical process is similar to that of logarithms: it transforms powers into multiplications and multiplications into additions.


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