{"id":1348,"date":"2017-07-09T00:05:54","date_gmt":"2017-07-09T00:05:54","guid":{"rendered":"https:\/\/brendans-island.com\/catholic-citizen\/?p=1348"},"modified":"2021-01-07T18:56:50","modified_gmt":"2021-01-07T18:56:50","slug":"pythagorean-dribble-glasses","status":"publish","type":"post","link":"https:\/\/brendans-island.com\/catholic-citizen\/pythagorean-dribble-glasses\/","title":{"rendered":"Pythagorean Dribble Glasses"},"content":{"rendered":"

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<\/a>The diagram shows how a Pythagorean cup<\/a> works. It’s a thinking person’s dribble glass<\/a>, sort of. The cup, pan, and ladle in the photo is a yuza no ki<\/a>. Both are gadgets used for teaching moderation.<\/p>\n

The yuza no ki is in the Ashikaga District<\/a>, \u8db3\u5229\u90e1<\/a>, in the Tochigi Prefecture<\/a>. It hasn’t been since around 1896. Ashiga District, that is. Not officially.<\/p>\n

The cup might be.<\/p>\n

Again, it’s a learning tool. Empty, it’s tilted. Pour a little water in, and it goes upright. Pour in more, and it tilts again.<\/p>\n

Pythagoras of Samos<\/a> lived about 25 centuries back. Scholars seem to accept the idea that Pythagoras was a real person, although stories about him don’t add up any better than those about Homer. (July 7, 2017<\/a>)<\/p>\n

Pythagoras generally gets credit for showing how the Pythagorean theorem<\/a> works. Or maybe it was someone in Mesopotamia, India, or China.<\/p>\n

The Pythagorean theorem says the square of the hypotenuse equals the sum of the squares of the other two sides of a right triangle. Tweak it a bit, and it’ll describe similar relations in non-Euclidean space and n-dimensional solids.<\/p>\n

<\/a>Pythagorean Cups<\/h4>\n

<\/a>Non-Euclidean geometry may have given H. P. Lovecraft fits, or not, and that’s another topic.<\/p>\n

Depending on who’s talking, Pythagoras invented the Pythagorean cup as a practical joke, or to teach moderation<\/a>.<\/p>\n

I don’t see why he couldn’t have had both in mind, which reminds me of St. Philip Neri, and that’s yet another topic.<\/p>\n

Apparently Hero of Alexandria<\/a> used Pythagorean cups in his robotic systems.<\/p>\n

That’s probably a reference to Heron’s fountain<\/a>. Heron is another version of Hero’s name, yet again another<\/strong> topic.<\/p>\n

Let’s try this again.<\/p>\n

A Pythagorean cup is a dribble glass<\/a>. It’s a cup with a column in the middle. The column is hollow, with a little pipe inside, and a hole near its base.<\/p>\n

The cup works fine, as long as you don’t fill it past the top of the inside pipe. If you do, Pascal’s principle of communicating vessels<\/a> kicks in, and the cup’s contents pour out the bottom.<\/p>\n

Soren Sorensen Adams<\/a> (re-)invented the dribble glass. His other contributions to Western civilization include the snake nut can<\/a> and joy buzzer<\/a>.<\/p>\n

Pascal’s principle of communicating vessels is also called Pascal’s law<\/a>. Pascal’s rule<\/a> about binomial coefficients<\/a> is something else. You probably don’t need, and may not want, to memorize all that stuff.<\/p>\n

Blaise Pascal<\/a> didn’t draft Pascal’s law the way Robert A. Taft and Fred A. Hartley, Jr., sponsored the Taft-Hartley Act<\/a>. That’s \u2014 you guessed it, more topics. (March 24, 2017<\/a>)<\/p>\n

Now, finally, here’s the point of this post.<\/p>\n

Moderation is a good idea.<\/p>\n

“3<\/a><\/sup> There is nothing better for man than to eat and drink and provide himself with good things by his labors. Even this, I realized, is from the hand of God.
\n“For who can eat or drink apart from him?”
\n(Eccelsiastes 2:24<\/a>–25<\/a>)<\/p><\/blockquote>\n

<\/a>Enjoying Life: Within Reason<\/h4>\n

<\/a>If that doesn’t sound “Biblical,” I’m not surprised.<\/p>\n

Many of America’s assumptions and attitudes about faith tend toward the “Sinners in the Hands of an Angry God” style. The ones I run into, at any rate.<\/p>\n

I’ve talked about Jonathan Edwards and Mark Twain before. Also Hippocrates and health. (May 12, 2017<\/a>; March 5, 2017<\/a>)<\/p>\n

Temperance, the Catholic version, isn’t steadfastly refusing to enjoy life. “Blessed are the miserable, for they shall spread misery” is not<\/strong> in the Beatitudes. (July 10, 2016<\/a>)<\/p>\n

God creates a good world. Enjoying what’s here, within reason, is a good idea. The trick is remembering that ‘I want it’ doesn’t always mean ‘I should have it.’ We should think before acting. (Genesis 1:31<\/a>; Catechism of the Catholic Church, 1762<\/a>–1770<\/a>, 1809<\/a>)<\/p>\n

Not-entirely-unrelated posts:<\/p>\n