This article will focus on why we make silly mistakes in math. Once you understand what’s going on with your mind, you won’t have a hard time figuring out how to avoid silly mistakes in maths.
Once, I was solving a math problem while preparing for an exam. Although the concept was clear to me and I knew what formulae I had to use when I finished the problem I got the answer wrong.
I was surprised because I’d solved almost a dozen other similar problems earlier correctly. So I scanned my notebook to find out where I’d committed the error. During the first scan, I found nothing wrong with my method. But since I’d arrived at a wrong answer something had to be.
So I scanned again and realized that I had, at one step, multiplied 13 with 267 instead of 31 with 267. I had written 31 on the paper but misread it as 13!
Such silly mistakes are common among students. Not just students but people from all walks of life commit similar errors in perception from time to time.
When I finished lamenting my silliness and beating my forehead, a thought flashed across my mind… Why did I misperceive 31 as 13 only and not as 11, 12 or 10 or any other number for that matter?
It was evident that 31 looked similar to 13. But why do our minds perceive similar objects as the same?
Hold that thought right there. We’ll come back to it later. First, let’s look at some other perception distortions of the human mind.
Evolution and perception distortion
Do you know that some animals don’t see the world as we do? For example, some snakes see the world as we would if we were looking through an infra-red or thermal sensing camera. Similarly, a housefly is unable to figure out the shape, size, and depth of objects as we do.
When the snake notices something warm (such as a warm-blooded rat) in its field of vision, it knows it’s time to eat. Similarly, the housefly is able to feed and reproduce despite its limited ability to perceive reality.
Greater ability to perceive reality accurately demands a greater number of mental calculations and hence a larger and advanced brain. It seems that we humans do possess a brain advanced enough to perceive reality as it is, don’t we?
Not really.
Compared to other animals, we might have the most advanced brain but we don’t always see reality as it is. Our thoughts and emotions distort the way we perceive reality in order to maximize our evolutionary fitness i.e. the ability to survive and reproduce.
The very fact that all of us commit errors in perception means that these errors must have some evolutionary advantage. Otherwise, they just wouldn’t exist in our psychological repertoire.
You sometimes mistake a piece of rope lying on the ground for a snake because snakes have been deadly to us throughout our evolutionary history. You mistake a bundle of thread for a spider because spiders have been dangerous to us throughout our evolutionary history.
By letting you mistake a piece of rope for a snake, your mind is actually increasing your chances of safety and survival. It’s much safer to perceive something safe as deadly and take immediate action to protect oneself than to misperceive something deadly as safe and fail to protect oneself.
So your mind errs on the side of safety to give you enough time to protect yourself in case the danger was real.
Statistically, we’re more likely to die in a car crash than falling from a tall building. But fear of heights is much more prevalent and stronger in humans than fear of driving. It’s because, in our evolutionary history, we regularly encountered situations where we had to protect ourselves from falling.
Experiments have shown that we perceive changes in approaching sounds as greater than changes in receding sounds. Also, approaching sounds are perceived as starting and stopping closer to us than equivalent receding sounds.
In other words, if I blindfold you and take you to a forest you’ll hear a rumbling in the bushes coming from 10 meters when in fact it may be coming from 20 or 30 meters away.
This auditory distortion must have provided our ancestors with a margin of safety to better protect themselves from approaching dangers such as predators. When it’s a matter of life and death, every millisecond counts. By perceiving reality in a distorted fashion, we can make the best use of the additional time that is made available to us.
Making silly mistakes in math
Coming back to the mystery of the silly mistake that I committed in a math problem, the most likely explanation is that in some situations it was beneficial for our ancestors to perceive similar-looking objects as the same.
For example, when a predator approached a bunch of our ancestors, it didn’t really matter if it approached from the right or from the left.
Our ancestors were wise enough to realize that it made no difference whether a predator approached from the right or from the left. It was still a predator and they had to run
So, we can say that their minds were programmed to view similar things as the same, no matter what their orientation.
Today, on an unconscious level, we still perceive some similar objects as being one and the same.
Many of our cognitive biases may be nothing more than behaviours that were advantageous to us in the context of our ancestral environment.
My conscious mind was probably distracted while solving that problem and my unconscious mind took over and worked as it normally does, without bothering much about logic and just trying to maximize my evolutionary fitness.
The only way to avoid such silly mistakes is to concentrate so that you don’t let your conscious mind wander off and rely on your subconscious, which may have been helpful for our ancestors but is kind of unreliable in today’s environment.