I think you have a very high bar for relevance.
Put another way, this discussion certainly has more than an infinitesimal relation to the original link.
> Hippasus is sometimes credited with the discovery of the existence of irrational numbers, following which he was drowned at sea. Pythagoreans preached that all numbers could be expressed as the ratio of integers, and the discovery of irrational numbers is said to have shocked them. However, the evidence linking the discovery to Hippasus is unclear.
> Pappus merely says that the knowledge of irrational numbers originated in the Pythagorean school, and that the member who first divulged the secret perished by drowning.
“Aristoxenus (Fr. 90 Wehrli = DK I 109. 31 ff.) reports that Hippasus prepared four bronze disks of equal diameters, whose thicknesses were in the given ratios, and it is true that, if free hanging disks of equal diameter are struck, the sound produced by, e.g., a disk half as thick as another will be an octave apart from the sound produced by the other disk (Burkert 1972a, 377). Hippasus, thus, may be the first person to devise an experiment to show that a physical law can be expressed mathematically (Zhmud 2012a, 310).” [1]
Also in [2] this experiment is claimed to be the first documented scientific experiment in history. After all, Hippasus took a mathematical model for a physical phenomenon (how consonance relates to the mathematical ratios of a musical string) and tests the generalization of that model in a another physical medium (viz. bronze chimes with the same ratios 1:2 and 2:3 make the octave and fifth).
[1] https://plato.stanford.edu/entries/pythagoreanism/#hippasus
[2] https://www.sciencedirect.com/science/article/pii/S240587262...
Pythagoras & The Pythagoreans: Mathematics, Music, and Mystery
Pythagoras was an ancient Greek mathematician and philosopher who lived around 500 BC. He traveled widely and gathered knowledge from diverse cultures, like Egypt. He also founded his own school of men and women in Italy. There, he taught that numbers held the key to understanding the whole universe. Pythagoras is best known for the Pythagorean theorem.
Fun Fact! There are stories that when Pythagoras discovered his famous theorem, he celebrated in a big way. Some say he sacrificed 100 oxen, while others claim it was just an ox made of flour. The Pythagoreans were famously vegetarian, so what do you think?
Math & Music: Pythagoreans explored the relationship between math and music. They discovered that musical notes have mathematical relationships. Hippasus, a member of the Pythagorean community, used bronze disks to show that musical notes are connected to mathematical ratios. This is considered one of the first scientific experiments!
Activity: Using a stringed instrument, like a guitar, try plucking the strings when pressing at 1/2 the string or 2/3s the string. Try different fractions. Can you hear the mathematical relationships in the sounds?
(My Pythagorean math blog is yet to be, but I do have some Pythagorean blog posts at https://aixd.substack.com)
You can find the whole thing on youtube
jk DD rocks
Asking the children "why do you think these sound different?" without telling them why first, letting them explore it themselves, gently correcting them along the way. Then pulling out another example and encouraging them to apply the same logic to the new example.
No, instead for the most part, children _still_ get what we all had: memorise these facts without explanation and fill out the blank space on the exam where the memorised words get you points. Most of our entire schooling is just an exercise in memorisation, not in thought and it's sad.
https://www.independent.co.uk/news/people/terrence-howard-th...
"How can it equal one? If one times one equals one that means that two is of no value because one times itself has no effect. One times one equals two because the square root of four is two, so what's the square root of two? Should be one, but we're told its two, and that cannot be."
Howard studied chemical engineering at the Pratt Institute in Brooklyn until he fell out with one of his professors over the answer to the 1x1=1 conundrum.
Hippasus, a member of said cult, however managed to compellingly demonstrate that the square root of 2 could not be a rational number. Pythagorus tried to swear him to silence. When that did no twork, he had him killed. Over the square root of 2.
[1] - https://sciencefocus.ust.hk/the-square-root-of-two-at-the-co...