[Cognitive science] Distance effects in non-numerical sequences?

[somegrue]

Hi,

I've been reading about how the brain processes magnitudes in general and numbers in particular, and keep coming across mentions of the distance and size effects. For context, Wikipedia touches on it at Weber–Fechner law § Numerical cognition, and there's a better outline in this viewpoint piece in Science: "Language and the Origin of Numerical Concepts" (right-hand column on the first page and figures on the second page, mostly)

Roughly, the distance effect says that we find it the easier to compare magnitudes the more they differ from each other, relative to their size. The top image in the Wikipedia article gives a good example. Somewhat counterintuitively, that applies even when the magnitudes have been encoded into symbols, so, using the example from the "Numerical Concepts" piece, it takes us "longer to decide that 3 > 2 than it does to decide that 5 > 2".

I'm curious if this can be extended even further, to sequences that have no straightforward relationship to magnitude at all. Does it take us longer to decide that C comes after B than that X comes after B, for instance? As you can imagine, "distance effect" does not a nice search term make, it has lots of other meanings in other contexts.

Thanks for any insights!

 

[jedishrfu]

I don't know the answer but have an analogue:

In grade school, we had to remember the times tables. Personally, I would always get confused by 8x7 vs. 9x6 and confuse the products 54 and 56.

I always attributed it to my dyslexia.

Later, I learned the times 9 convention, where the digits had to sum to nine when doing times 9. So, I could now recite 9x6 = 54 and, of course, by extension, 8x7 = 56.

Even today, I still go down that path internally to remember which is which.

Digits Add to 9​

In the products of 9 from 9×1 to 9×10, the digits always add to 9.

| 9 × 1 = 09 → 0 + 9 = 9
| 9 × 2 = 18 → 1 + 8 = 9
| 9 × 3 = 27 → 2 + 7 = 9
| …
| 9 × 9 = 81 → 8 + 1 = 9

 

[fresh_42]

I have similar trouble distinguishing $4\cdot 13$ and $3\cdot 14$ and have had the $54 /56$ issue, too.

 

[Klystron]

" No two of us learn our language alike, nor in a sense, does any of us finish learning it..."
Willard Van Orman Quine "Word and Object"

To this I would append 'learn our mathematics' in the sense that mathematics is language.

My learning dyslexia concerns misidentifying or, perhaps, confusing lowercase letter "r" with the integer "5". A head injury on the day in grammar school when teacher covered writing the alphabet may have led me to write "r" as five. They do have similar shapes. No problem with arithmetic or reading, but I sometimes wrote "r" in place of five, anticipating algebra, so to speak.

This mild dyslexia persisted intermittently into college where massive note taking during lectures provided a cure, else I merely outgrew it

 

[jedishrfu]

Ive had issues with remembering how to do certain proofs like the sin(a+b) or its cos(a+b) counterpart using a triangle diagram.

Or things in knot theory with Reidemeister moves. Dyslexia sets in and i cant continue like a mental overload.

 

[fresh_42]

Or things in knot theory with Reidemeister moves ...

That explains it! When I was a student, me and some colleagues decided to have a nice evening at a local casino. A European casino, where you need suits and ties. The meeting point was the parking lot at the casino. All others, except me, had something to do with knot theory. When I arrived, I was the only one who had already tied his tie, and one, who asked a hobo at a liquor store to tie his tie. The rest asked for help.

 

[jedishrfu]

I do like knot jokes.

A knot walks into a bar.

Bartender says, “We don’t serve your kind here.”

The knot leaves, twists itself up, parts its ends, and walks back in.

Bartender says, “Hey, aren’t you that knot from earlier?”

Knot says, “I’m a frayed knot.”