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Saturday, October 24, 2015

Why We Can't Grasp Very Large Numbers

Follow on Twitter as @kate_baggaley
"Today, October 23rd, is the National Mole Day, created not for the tiny burrowing mammal, but to celebrate the basic unit in chemistry. One mole, also known as Avogadro's Number, is 6.02x10^23 of whatever you are measuring." according to Kate Baggaley, Associate Editor.

Photo: Braindecoder

So a mole of moles would be 602,200,000,000,000,000,000,000 animals.

Now, can you imagine how many moles that is? Probably not. The way our brains are set up, truly understanding that vast a number is pretty much impossible.

"Our cognitive systems are very much tied to our perceptions," said Daniel Ansari, a researcher at the Numerical Cognition Laboratory at Western University in Canada. "The main obstacle is that we're dealing with numbers that are too large for us to have experienced perceptually."

By contrast, we constantly experience small numbers. "Smaller numbers are more frequent in our daily vocabulary," Ansari said. "When you lay the table you ask your child, how many knives do we need? It's never going to be 10,000 unless you have a very big dinner party."

And in line with our normal life experiences, our brains have become capable of representing small numbers, but helpless at accurately reflecting very large ones. "What you don't have is an intuitive sense of what this number means," said Brian Butterworth, a cognitive neuroscientist at University College London and author of The Mathematical Brain. "The reason for this is that our sense of number is based upon two innate systems which essentially deal with small numbers accurately or large numbers only approximately."

Using the first system, we can visualize, say, five balloons but can't imagine 500 of them. Using the second system, we can tell 500 balloons are significantly more than 50 balloons. Butterworth and his team have found evidence that other animals have these two systems as well. They've seen that fish, which benefit from the protection offered by joining a larger shoal, are pretty good at estimating which of two groups of fish is larger. They can also accurately distinguish between small numbers of fish. "What this tells us is that our innate system has deep evolutionary roots that go back at least to the common ancestor for small fish and humans," Butterworth said. 

But unlike us, fish don't have symbols to represent large numbers. "So they can't get up to large number exactly the way that we can, because we've got counting words and the digit system," said Butterworth.

This ability stems from a connection between the two innate number system and other parts of the brain. In humans, brain systems dedicated to processing numbers seem to reside in the parietal lobe, in two key areas. One is the intraparietal sulcus—studies in monkeys have found that some groups of neurons in the intraparietal sulcus code numerosity linearly: the more objects the animal sees, the more they fire. In contrast, neurons in another part of the intraparietal sulcus fire preferentially for a specific number— one fires for 3, another for 4, and so on up to 5, the highest number tested in this way, Butterworth said. Similarly, studies of number processing in humans have pointed to the intraparietal sulcus, and have found that certain structural and functional abnormalities in this region in children are linked with dyscalculia, an impairment of mathematical ability. The other brain area involved in number processing is the temporal-parietal junction, which seems to deal with small number comparisons
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Source: Braindecoder