Why was algebra so difficult to discover?

Filed under: math — jlm @ 18:48

(tl;dr: Asking a bunch of questions, and not making any guesses.)
Consider integer arithmetic prior to the discovery of algebra. How do you go about a really foundational task such as defining division? You give everything involved names, like so: A number called the dividend divided by another number called the divisor is a number called the quotient with a non-negative number called the remainder if the divisor times the quotient plus the remainder is the dividend and the remainder is smaller than the divisor. How do you get anything done with that kind of word salad? No, when you want to actually do some number theory, you go with: n÷d = q R r is equivalent to n = q∙d + r ∧ 0 ≤ r < d. This terminology is taught because you teach division well before you teach algebra, but it’s so useless afterwards that I very well might have never used this sense of the word “dividend” all these years since I learned algebra. Anyone skeptical that basic grade school arithmetic isn’t far harder to grasp without algebra is invited to explain how come long division gets the right answer without using it.

So fine, algebra is incredibly useful, but utility has no relevance to ease of understanding. I remember having some confusion when I was introduced to it. It was along the lines of: “What number is x?” “That can be any number.” “*boggle*”. Yet, those named terms above, they’re just placeholders too: “What number is the dividend?” “That can be any number.” “Oh, okay.” — How come that’s different?

The Greeks were using letters to represent arbitrary points in geometry centuries earlier than the Arabs did that for arbitrary numbers. In teaching geometry we don’t get the problem “What point is A?” “That can be any point.” “*boggle*” — What makes “x can be any number” so much harder than “A can be any point”?


Colloidal suspension of disbelief

Filed under: humor — jlm @ 20:01

Numi makes decent enough herb teas, but their “100% real ingredients” teabag tag always strikes me as weird.

Real ingredients.  100%.  Nothing else.

What’s the alternative? Fictional ingredients?

Ingredients: cinnamon, orange peel, cloves, hibiscus, allspice, ginger, Melange, phoenix down, ice nine, caloric, kryptonite, phlebotinum, vibranium powder, dragon scales, dried minotaur blood, mithril, nebulium, phlogiston, dilithium crystals, pigeon teeth, elan vital, roc talon, unicorn horn (not narwhal — we have some class!), luminiferous ether, dehydrated Atlantis spring water


Oakland bonsai garden

Filed under: sfba — jlm @ 14:47

I recently took a walk around the gardens in Oakland’s Lake Merrit Park, and found the bonsai garden there to be especially nice.

Which means you get to enjoy some photos!

bonsai photo 1bonsai photo 2bonsai photo 3bonsai photo 4bonsai photo 5bonsai photo 6bonsai photo 7bonsai photo 8bonsai photo 9


Faces are hard

Filed under: web — jlm @ 22:10

So, there’s this webcomic Prequel Adventure set in the Elder Scrolls: Oblivion universe. It’s an excellent comic, with a compelling plot and great humor. (It also is paced extremely slow, with a real-time:in-universe-time ratio that handily exceeds even that of Freefall.) The panels are drawn simply, supporting the story’s elements and the comic’s jokes, and clearly indicating that the focus is on telling a good story in a funny manner, and not on having beautiful art (another similarity with Freefall). But despite the comic’s simple drawing style, there’s one bit which Kazerad absolutely nails: Facial expressions. I mean, look at the final panel from this page.


Do not use for lunch

Filed under: humor — jlm @ 10:27

Safeway advertisement


Economics is the dismal science because people don’t think it’s a science

Filed under: econ — jlm @ 11:13

So, here I am, reading this article on the FDA proposing rules on “e-cigs”, and come across this:

Some smokers use e-cigarettes as a way to quit smoking tobacco, or to cut down. However, there’s not much scientific evidence showing e-cigarettes help smokers quit or smoke less, and it’s unclear how safe they are.

… Tobacco company executives have noted that they are eating into traditional cigarette sales, and their companies have jumped into the business.

That sure sounds like economic evidence that they help people to smoke tobacco less.


TC on SF

Filed under: sfba — jlm @ 16:08

Do you enjoy long, complicated analyses of city policy? Here’s an excellent one on San Francisco’s distress from TechCrunch.


The thing about sides

Filed under: politics — jlm @ 10:17

Dianne Feinstein, my senator, has been making waves as of late after discovering the CIA had been spying on her congressional staff. The waves are not so much on the merits of the charge, but due to the history of the person making them: Sen. Feinstein has until now been a vociferous booster for the US’s intelligence agencies, and their intelligence-gathering operations, both foreign and domestic. She was, for example, perhaps the Democrat most vocally in favor of granting the phone companies unqualified immunity for participation in bulk wiretapping of their customers. Had that immunity not halted the lawsuits back in 2008, part of the scope of the intelligence community’s bulk domestic spying would have come out in discovery long before Edward Snowden popped up on the radar, and perhaps the CIA, NSA, etc. would not have been so bold these last six years in exceeding their authority under the FISA.

So now Sen. Feinstein has gotten bit, and is indignant that it’s from the very snake she has been feeding and protecting. My surprise is that this is to Feinstein’s surprise! There’s an old saying — just because you’re on their side doesn’t mean they’re on your side. Seems my very honorable senator is rapidly becoming acquainted with the application of that proverb, somehow managing to get into the US Senate without having been!


Happy Christmas from Edward Snowden

Filed under: politics — jlm @ 12:46

A holiday message from our currently most famous fugitive.

And may your new year be private.


Good job, China. Awful job, media.

Filed under: science — jlm @ 11:34

China has pulled off the first Moon landing in 37 years and just deployed a lunar rover. Nice job!

You wouldn’t know it if you just get your news from the L.A. Times or S.F. Chronicle, though. What the hell, news media? This is not newsworthy?!

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