“Geometry is knowledge of the eternally existent.”Pythagoras
Some people are better thinking in symbols rather than words. For French inventor Philipe Starck, that symbol was “∞” for infinity, designed by English mathematician John Wallis in 1655:
For me, it is the most intelligent piece of graphic design in the world. To say something in a complicated way is very easy. But to find a way to say it simply – that takes a lot of work.
The infinity symbol is a paradox: it solidifies a number in absolute terms to illustrate something that never ends. As Starch puts it, infinity “is about the fight we have with ourselves to try to understand more and more.”
Infinity is too impossible to count. The simple representation provides both a temporary relief and impetus for a more in-depth understanding of something that goes beyond comprehension.
People are afraid of big numbers because they have no spatial understanding; the largest numbers are beyond comprehension, as the multitude of chess moves or the unfathomable number of sand grains in the desert. Infinity appears impossible to count!
University of Texas computer science professor Scott Aaronson believes the answer to naming the world’s biggest number lies within the deepest paradigm, some of which is solvable by exponentials, language, and sheer imagination:
“When thinking about 3, 4, or 7, we’re guided by our spatial intuition, honed over millions of years of perceiving 3 gazelles, 4 mates, 7 members of a hostile clan. But when thinking about BB(1000), we have only language, that evolutionary neophyte, to rely upon. The usual neural pathways for representing numbers lead to dead ends. And this, perhaps, is why people are afraid of big numbers.”
It is a canard to think that math can’t fail. All you need to do is look at the way society constructs algorithms – from job and college applications to Facebook feeds to find out that sorting can be wrong and biased.
In the case of the 2016 election, algorithms did more harm than good. Facebook fed the internet silos with fake news. As Cathy O’Neil author of Weapons of Math Destruction puts it in a 99% Invisible podcast: “The internet is a propaganda machine.”
We’ve adopted the factory mindset of mass-sorting, leaving the anxiety of decision-making up to machines. Humans are pieces of data, waiting to be organized by the least valuable candidate or customer.
There are too many of us and not enough time to make individual considerations. But a conversation around algorithmic frailty might do us some good. Making generalizations impedes the magic of discovering an outlier.
In an interview with Time Magazine, Japanese author Naoki Higashida reveals his favorite number. His answer is both complex and beautiful:
I’ve never really thought about my favorite, but if pushed, my answer would be 3. The number 1 is the most important. It feels like proof that something is there. Then again, zero is the most amazing discovery. The concept of nothingness is proof of human civilization. After 1 comes 2 in order of importance. The number 2 lets us divide things and put numbers in order. These three numbers (0, 1 and 2) would have been sufficient. As a number, 3 is enchanting. It was created even though it wasn’t needed. Perhaps it was born out of creativity?
Digits transcend each other. Like words, each one fits into the fabric of a larger numerical system.
The whole is a sum of its parts. What’s your favorite number?
Image via Celeste Ng
Do your math: check out the ‘Coltrane circle.’
You have three options when you get stuck: keep going, give it a break, or quit.
Being stuck is part of making progress. The real problem though is that we often interpret stuckness as a failure. Having a bad experience undermines the enjoyment of doing. It convinces us to switch subjects to something newer and achievable.
Mathematics is one of those discouraging topics that gets left behind as we age. We lose patience with math’s rules and exactitude–the answer is either right or wrong. But it’s not as rote as it seems. Says famed mathematician Andrew Wiles: “it’s extremely creative. We’re coming up with some completely unexpected patterns, either in our reasoning or in the results.”
Math, just as playing sports, writing and other crafts, takes persistence. Maintaining excitement and having faith in the process are the keys to sticking it out.
“Yes, you don’t understand [something at the moment] but you have faith that over time you will understand — you have to go through this. It’s like training in sport. If you want to run fast, you have to train. Anything where you’re trying to do something new, you have to go through this difficult period. It’s not something to be frightened of. Everybody goes through it.” — Andrew Wiles
In a world of abundance, we need algorithms more than ever. From movies to books, music, and resumes, algorithms intend to save us time by eliminating a lot of the possibilities up front.
The problem with algorithms though is that they remove the outlier. The things that shape you are usually outside your normal scope of interest.
Professor of engineering at Oakland University Barbara Oakley was once a linguist until she realized she could apply the same “chunking” principles to become fluent in math. Mixing subjects broadened her understanding of how discovering new things work.
Algorithms never go deeper than the prescriptive answers. They take what’s most likely of interest and give you more of that, confirming your bias.
Human discovery is less fallible than machines. Aggregated tastes or wisdom of crowds is a viable recommendation engine. But the problem with people is a lack of time–we take too long to gather content and dig through it. The machines can sort through content streams faster, and with accuracy.
We can’t afford to our put our taste in any method. The only way to balance the curators, friend recommendation, with the algorithmic engines is to go manual, staying open to the possibility of discovering something outside our standards interests. Those magazines at the dentist’s office are worth perusing.
“Point your camera toward a math problem and Photomath will magically show the result” Photomath
And all I had was the TI-89 calculator!
The answers are already here at our fingertips. Not just for math but for foreign languages and all types of knowledge. What’s the capital of Uruguay? Just google it or ask Amazon’s Alexa. Can’t decide which photo to use? Ask an algorithm like the Roll to identify your best photo. Facebook automatically identifies people in photos just in case you can’t recall that person’s name from last night’s dinner party.
Knowledge has become a kind of obesity of the mind in the digital age.
Why remember anything or master a skill if you don’t have to? Could knowledge become a commodity? Perhaps people who know things without using Google or Photomath will be considered superior, maybe even genius.
Humans aren’t going to be running the show too much longer. The machines are learning fast and securing our dependency on them. They don’t just fix our brains; they ARE our brains.
Perhaps all that’ll make us human is the ability to feel emotion and dream. But is that enough?
Well, at least if the cars pilot themselves we can do more thinking about how human brains were once considered computers.