Oxford mathematician Marcus du Sautoy says humankind's laziness might just be its saving grace.
Despite being frowned upon, du Sautoy says our inherent antipathy towards hard work can often lead us to think of clever ways to solve problems.
In his new book Thinking Better: The Art Of The Shortcut In Math and Life, du Sautoy takes a romp through the last 2000 years of smart problem solving and shortcut creating that has enabled much of human progress - whether in constructing the first cities around the Euphrates, using calculus to determine the scale of the universe, or in writing algorithms to help find a partner.
Photo: Oxford University Images Joby Sessions / Supplied
Du Sautoy’s previous books include The Creativity Code, How to Count to Infinity and The Great Unknown.
In fact the idle mind is often at its optimum for solving problems, he told Kim Hill.
“Often my most productive time is when I'm away from the desk. And what I think is happening is that the brain is using its subconscious to try out lots of different possibilities that you don't want to consciously go through because it will just take time … your idle time is when your brain is trying out these possibilities.”
When there is a fit and something works that is what leads to the ‘a ha’ moment he says.
“That's why I think that it's really important that our laziness sometimes allows us the space for our brain to come up things.”
He writes about a neuroscientist in the book who analysed the thinking of a grand master chess player.
“He was wondering what's special about their brains compared to mine? And again, it turns out that they seem to be using the less of their brain. So, they seem to be missing out the kind of bit in the middle, where we would be consciously checking possible chess moves in advance, they seem to almost have a shortcut across the brain, which they are tapping into to reach that Grandmaster level.”
There is a paradox at the heart of the clever shortcut, he says.
“I'm presenting you with all of these cunning ways of looking at complex problems in the world. But these cunning ways that we've come up with often have taken a huge amount of work. People often ask is there a shortcut to finding shortcuts?
“And I don't think there is. I think there's a long gestation time to come up with these extraordinary ways of looking at things. But once you have, once you've dug that tunnel under the mountain … just recently there was a tunnel under the Alps in Europe, it took 17 years to do that tunnel. Now it takes 17 minutes to pass through it.”
He also examines probability in the book which he says is counter intuitive.
“If you try and use your intuition, you'll probably end up in the wrong place.”
He references work done by Daniel Kahneman.
“There's a very famous book called Thinking Fast and Slow. And he illustrates that our fast, intuitive thinking is often incredibly faulty.
“And so, he argues for slow, analytical thinking. But the reason I call my book, Thinking Better is I think you can do this analytic thinking, but still use fast techniques, which we call mathematics to get to your solution.”
Numbers are themselves shortcuts, he says.
“I think it's interesting to go back to how the Egyptians wrote their numbers, because they used hieroglyphics. And whenever the number got bigger – 10, 100,000, one million, they had to come up with a new picture to represent that kind of larger number.
“I love the one for a million because there's a little man on his knees with his hands in the air as if he's won the lottery.
But it's incredibly inefficient and actually to write right 999,999 It's just like a mess of hieroglyphics.”
It was Hindi Arabic mathematicians that cracked it, he says.
“They said, why don't you use the position of a number also to help you.
“So if I say 111, it's interesting, we're using the same number 111, But it's position tells us that actually, it's one unit, one 10 and one 100.
“So, this is kind of major breakthrough. That's a shortcut. Suddenly, to write numbers. I don't need infinitely many little pictures now. And you know, as the Hindu Arabic numeral system shows, you can get away with 10 symbols, one to nine and this zero, and then you can write a number as big as you want to.”
It was a breakthrough comparable to the printing press, he says
“It really revolutionised and kickstarted mathematics with this kind of observation of the efficiency of writing numbers and with that efficiency came efficiency of calculation, as well.
“These shortcuts really just revolutionise moments in history, when civilizations suddenly make huge, great breakthroughs, because they had these new tools at their fingertips.”
