*a weekly roundup of links, cartoons, and
profound hypotheticals that only a 5-year-old would imagine*

Great piece by Adam Kucharski on the discovery of the monstrous nowhere-differentiable function, and its ripples across history:

Calculus had always been the language of the planets and stars, but how could nature be a reliable inspiration if there were mathematical functions that contradicted the central ideas of the subject?

Somehow, linking to Clickhole makes me feel very square and old-fashioned, like taking out a newspaper ad to endorse a Tweet, but I want to draw your attention to 7 Shapes That Will Be Completely Obsolete After I Introduce My Latest Shape, the Triquandle:

A quadrilateral with only one pair of parallel sides? Ha! Pathetic. Try a triquanderlateral with so many pairs of parallel sides that men have died just trying to count them all. How many men died creating the trapezoid? Zero. Zilch. Nada.The Trapezoid.

FiveThirtyEight asks the daring question: “What Would Happen If There Were No Number 6?” (A 5 1/2-year-old wanted to know.) The mathematicians interviewed paint a pretty dire scenario:

Lillian Pierce, another Duke math professor, thought you’d have to eliminate 2 and 3, as well, because, otherwise, what would 2 x 3 equal? Anything that could multiply or divide into 6 would have to go. If losing 6 meant losing 2, Pierce wrote to me in an email, then we would also lose the concept of “even” and “odd” numbers.

I loved the piece, but I think the metaphysics of this question lead to a pretty fast dead end. (You’re pretty much left in a world of modular arithmetic, where 5 + 1 brings you back around to 0.)

But the *psychology* of the question has a lot of potential. I can almost imagine a world where 6 exists, but we are unable to bring our minds to focus on it, in much the same way that certain neurological patients are unable to understand the direction “left.” It’s not that left doesn’t exist; it’s that they can’t perceive it, can’t even conceptualize it. When asked to draw a picture of a clock, they draw the right half. When asked to find something to their left, they turn right three times and are surprised to discover it.

What would it be like to have this selective blindness for a *number*? To render invisible not a component of the physical world, but the mental one? What’s the mathematical equivalent of turning right three times to make a left?

Over on Quora, there’s a worthwhile thread of The Greatest Examples of the Butterfly Effect in History. An almost-perfect one explains, “Barack Obama Became President of the United States because Garrett Wang of Star Trek was hot.”

I’m eager to believe that we owe the nature of our timeline to Ensign Harry Kim of the starship Voyager. (It wouldn’t be the first time he saved the world.) Unfortunately, I think Obama would have won his ’04 Senate campaign even without the chain of events described, but it’s still a good read.

If you’re over spelling bees, there’s a “Date of the Week” Bee where you have to compute the day of a week for any date between 10/15/1582 and 12/31/2099.

Saving the best and heftiest for last, here’s an important research article from Jack Schneider on the history of grading in American schools:

this work tells a story about a core and seemingly inescapable tension in modern schooling: between what promotes learning and what enables a massive system to function.

My nephew wanted to know why he was one half of a number…he decided that his age was five and there wasn’t any half anything about him. I loved his reasoning…much like I love your writing!

I admire the logic there. People are whole, integral things. Not even children are creatures of halves.

I have wondered if there were things in the world that we do not percieve fully because of our sensory limitations. Like some animals which only recognise one colour. The very comfort in math that is not present in the real world is that it is “objective”. So it is indeed a bit mind boggling to imagine the absence of a complement where we are always used to symmetry. Like the left right instance. But the world is filled with counter examples and that’s what makes it awesome!

Admire your writing style- it would be awesome if you wrote math books !

complement where we are

Yeah, perception of color is another great example. We can’t see UV rays; bees can. We can’t sense infrared; snakes can. When you’re truly blind, as we are, it’s impossible to imagine what sight is like, but it’s fun to try. And the reverse is perhaps true, too – when you can truly see, it’s impossible to imagine blindness.

As for writing books, that’s very kind of you to say. Stay tuned. 😉

The consensus of math users seems to have no problem leaving “division by zero” UNdefined. A system of numbers without “six” simply seems to DIS-define “six” within the system, as well. So we have the set of all numbers “x” which remain even if

f(x) = 1/[x-(2*3)]