## Sunday, 3 July 2016

### The curious incident of the mathematician at the self-checkout kiosk

We had some produce that had no barcode on the package, so we tapped the [ LOOK UP ITEM ] rectangle on the touch-screen, and it displayed some options for identifying the product:

The product did not have a 4-number code, so the choice was to search for the product alphabetically. For example, if the product was beans you would touch the B - C button which would bring up an array of pictures — Bananas, Basil, Beans (green), Beans (wax), Bread, Brussel Sprouts, etc. (Of course, touching one of these might lead to yet another screen, and so on until you see the exact item you wish to purchase.)

The actual product we wanted was grapes. So indulge me: what button would you touch?

At the kiosk I noticed that there was some hesitation when my wife responded. I wondered if it might be different if she had to choose a number range instead of a letter range. So we both did a quick trial when we got home.

On the right is a search screen that uses numbers instead of letters.

Here, the problem is to choose the button with the number range that contains the desired number.

Which button would you touch for the number 7?

These is very much the same question with numbers instead of letters. So, why were we able to answer this question much more quickly using numbers?

Perhaps it is because I have had more practice with numbers — I am a mathematician, after all. But that doesn’t explain why my wife had the same experience — she is not a mathematician — and she also answered more quickly when numbers were used.

When I was a child, we spent a lot of class time learning how to find a word in a dictionary. We learned how to bracket words alphabetically —  and we learned how to put things in order alphabetically, and the teacher made sure we had lots of practice.  We knew the order of the English Alphabet quite intimately. What we did in school was a much more demanding task than selecting the correct screen at a checkout kiosk.

If you have read my previous post (It’s not all snake oil) you know that I have some interest in understanding how the brain (and mind) reacts to numbers.

That post was concerned with cardinal numbers — numbers being used to describe magnitude or size. It is now well established that there is a specialized region of the cortex that reacts to such numbers, and the region seems to be unresponsive to things other than numbers (such as colours, or music, or words that are not tied to numbers).

In the at-home kiosk task, however, we are dealing with ordinal numbers — numbers being used to describe order and sequence.

Recently, cognitive neuroscientists have begun more closely investigating both ordinal numbers and more general (non-numerical) ordered sequences. But the state of affairs is not clear cut. Exactly what happens depends on a large variety of factors.

Even the situation regarding ordinal numbers by themselves appears to be clouded by the fact that numbers represent both magnitude and order. When you are asked "Is 7 between 4 and 11?" do you decide this "immediately" in some sort of a subitizing way, or do you decide by comparing the magnitude of 7 successively to the magnitudes of 4 and 11? The answer seems to be that it depends upon the context, and that affects what regions of the brain are involved.

In particular, I was curious to see if there was a distinction between how the brain deals with the ordered sequence of numbers as opposed to the ordered sequence of the alphabet.

From what I have read the only conclusion I can draw is  "Maybe."

For now, I guess I'll  have to live with the fact that my wife and I are alphabetically challenged.