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Non-symbolic numerosities

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Sandie Cleland argues that non-symbolic representations of number do not offer a direct and automatic route to numerical-spatial associations.

Image courtesy of interviewee. March 11, 2024

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This video video discusses a series of experiments exploring the concept of spatial numerical associations known as **snark effects**—the tendency for people to associate smaller numbers with the left side of space and larger numbers with the right. This video video phenomenon was previously observed in children, and the study aimed to investigate whether similar effects could be replicated in adults using both symbolic (like digits and number words) and non-symbolic numerical representations (like arrays of objects).

The researchers conducted four experiments where participants had to respond to the presence of upright or inverted triangles displayed in varying quantities. The expectation was that responses would be faster for smaller numbers with the left hand and larger numbers with the right due to the mental number line hypothesis.

However, contrary to previous findings, the results showed no evidence of snark effects in adults, regardless of the number of triangles displayed or other stimulus variations. This video video failure to replicate the observed effects raises questions about the nature of how adults process numerical quantities. The authors highlighted the importance of replicating research findings in psychology and suggested that differences in learning and exposure to numerical systems might influence how adults engage with quantities compared to children.

The ongoing research seeks to explore whether the memorability or familiarity of certain representations influences the presence of snark effects, indicating a potential distinction between learned symbolic numbers and non-symbolic numerical cognition.

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X-TIMESTAMP-MAP:LOCAL=00:00:00.000,MPEGTS=900000

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Snarks.

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So a spatial numerical association of response codes.

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Um, so what it's is, it's linked to the fact

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that people seem to have a fundamental link between number

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and space when they, kind

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of think about the world when they encounter number.

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So when people perform tasks where they have

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to reason about, digits

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or number words, they behave as though they have, well,

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it's sometimes called a mental number line,

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which you could almost think of as like a, a,

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a representation of a ruler in their mind

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where they associate small numbers with the left side

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of space and larger numbers

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with the right hand side of space.

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So kind of the kinda classic demonstration

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of this is if you ask people to perform a task

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where they have to respond to a digit on a screen.

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So for example, they see a digit

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and they have to press one button of it,

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that even number and another button.

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If it's an odd number, what we tend to find is

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that people are faster to respond to smaller numbers

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with their left hand, and they're faster to respond

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to larger numbers with their right hand.

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Now, what that suggests to us is that there's a,

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this fundamental link between number

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and space and cognition.

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Um, yeah, as I said, it's called this mental number line

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that seems to go from the left to the right,

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where we associate smaller numbers with the left side

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of space and larger numbers with the right side of space.

01:21.145 --> 01:23.525
So with this study, what we were really interested in was

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whether the form of the representation of number mattered.

01:27.125 --> 01:29.285
So there's lots of different ways that you might encounter

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numerical information in life, right?

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You might see a digit, you might hear a spoken number word,

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you might see a plane card or a dice.

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What we were interested in is when you encounter quantities

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that aren't easily labeled.

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So in the paper we call these non-symbolic quantities.

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So this is just a collection of object.

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Now, in a previous study that we'd published,

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we'd found some evidence that you get snark effects

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for those types of quantities.

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Um, and, and what we'd done was we'd asked people to respond

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to between one and nine triangles on a screen.

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And what people had to do was they just had

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to indicate whether right and left hand,

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whether the triangles were upright

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or whether they were inverted.

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And we were interested in whether the quantity

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of triangles impacted how people perform the task.

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So in this previous study, we'd found

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that when you saw a small number of triangles,

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you were faster with your left hand.

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When you saw a large number of triangles,

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you were faster with your right hand.

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And we thought, this is great. This is really interesting.

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This suggests that the, you know, the form of

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that numerical representation, it, it doesn't matter.

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We still get this snark effect,

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which is we hadn't really seen in adult participants before.

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So in this paper, what we wanted to do though was to try

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and replicate that finding

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because it's, you know, it's

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so important in psychology research that we try

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and replicate our findings

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because we'd only shown this once.

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So that was really what this paper was about, trying,

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finding debate

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Whether, you know,

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what we call symbolic representations of quantities.

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So digit number words, things that are learned

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and culturally specific,

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whether those are processed in the same way

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as these non-symbolic quantities.

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Um, and so it kind of, it,

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it's really feeding into that literature.

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Do, do we, do we process them in the same way?

03:18.745 --> 03:21.605
Now, the interesting thing is that in, in young children,

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we do find that young children associate,

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non-symbolic number with these kind of, kind

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of spatial aspects.

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So children, prefer right sided responses

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for large groups of objects

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and left sided responses for smaller groups of objects.

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It hadn't really been shown in adults though.

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So what wasn't entirely clear was whether

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snark effects were linked to these effects that you see in,

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in young children, or whether there's something that's more

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to do with learning about how numbers work and school.

03:51.585 --> 03:53.765
And there's some evidence that says that it could be,

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you know, something to do with our education,

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because we know that in languages

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that are written from right to left,

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the snark effect tends to reverse.

04:02.795 --> 04:04.845
Okay? So we're kind of trying to get, you know,

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what's actually going on in adult participants.

04:06.705 --> 04:09.205
Do they, do they behave the same way as, as children do

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with these types of quantities?

04:10.585 --> 04:13.525
The four experiments were, were really, really similar.

04:14.225 --> 04:15.725
So in all of the experiments,

04:15.725 --> 04:18.485
what people did was they saw these, triangles.

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They were either upright or inverted.

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There were between one and nine triangles in each trial,

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and they just had a, you know, a left sided response

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and a right sided response.

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So upright, inverted,

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and this was swapped around for the participants.

04:31.375 --> 04:33.955
The differences between the studies were really to do

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with quite, low level aspects of the stimuli.

04:37.535 --> 04:40.315
So, for example, if I have a triangle,

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if I have one triangle and then I have nine triangles, just

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because you, you know, if the triangles are the same size,

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the nine triangles are just gonna cover more

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of the screen than the one triangle, right?

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And what we want to know,

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what we're interested in is really whether it's the number

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that's important rather than just kind

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of visual properties of the stimuli.

05:00.455 --> 05:03.315
So, for it, so, so two of the studies were really trying

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to get at, at that difference.

05:04.795 --> 05:06.995
So there was one study where we controlled the surface

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area, the triangles.

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What that meant was when you had

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one triangle, it was much larger.

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When you had nine triangles,

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each individual triangle was smaller,

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but the total surface area on the screen was the same.

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Uh, we also looked at how often it mattered,

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whether it mattered how often the stimuli

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were repeated, right?

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So when you see a digit like three

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or four, it looks the same every time you encounter it,

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but if you see a group of objects,

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they might be arranged differently on each trial.

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Three triangles in one trial might look like three tri

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different, three triangles on another trial.

05:39.735 --> 05:41.955
So we had another experiment where we looked at, you know,

05:41.955 --> 05:44.075
does it matter if the stim repeated,

05:44.615 --> 05:46.955
so seven triangles always exactly the same

05:47.375 --> 05:48.795
or whether they can be arranged in

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different forms in the screen?

05:50.135 --> 05:51.915
So those were the types of manipulations

05:51.915 --> 05:53.515
that varied across the four studies.

05:53.855 --> 05:56.155
But yeah, other than that, they were really, really similar.

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Um, I think they had around somewhere between three

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and 400 trials, between one

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and nine triangles in each one.

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And it just said whether they were upright

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or inverted, the results are really easy to summarize,

06:08.145 --> 06:10.445
and that we found absolutely nothing.

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We found no evidence of a snark effect at all.

06:14.785 --> 06:18.525
So it didn't matter how much area the screen it took up,

06:18.625 --> 06:21.285
it didn't matter how often the stimuli were repeated,

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there was no snark effect there.

06:23.635 --> 06:28.245
Okay? So this was, quite a humbling surprise

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to us having shown it previously our, in our lab,

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but so important as well, right?

06:33.425 --> 06:34.725
So, you know,

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and we used, we made sure that we had, you know,

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sufficient participant numbers.

06:39.865 --> 06:42.125
Uh, we did what you call a power analysis to check

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that we've run enough participants

06:43.745 --> 06:45.165
to find an effective, it's there.

06:45.945 --> 06:48.685
Um, we, we checked our analysis and double checked it,

06:49.065 --> 06:50.165
but, and,

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and none of the studies did we find an effective a effect.

06:53.145 --> 06:55.885
So it didn't matter how many triangles people saw,

06:56.055 --> 06:58.205
their right and left hand just did the same thing.

06:58.355 --> 07:00.445
They were completely unaffected by the quantity

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that they saw on the screen.

07:01.865 --> 07:03.645
So complete failure to replicate.

07:03.645 --> 07:05.325
There's kind of two aspects of this

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that I think is really important.

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The first is

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how important is trying replicate your own

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findings in psychology?

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You know, we'd find this really interesting, effect

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where we find snark effect for,

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for quantities hadn't been shown in adults before.

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We were quite excited about it,

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but obviously now we've been in

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and not replicated for it four times.

07:24.785 --> 07:27.885
So it's just, it's so important that, that, you know, you go

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and try and replicate your own findings.

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It's, it's just the way science works.

07:31.425 --> 07:33.325
So I think that's, that's one thing about this.

07:34.185 --> 07:36.685
Um, the other thing though, just, you know,

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if we assume then that we don't find smart effects

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for these types of quantities,

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that's very interesting in itself, right?

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And it raises a little bit of a puzzle.

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You know, we know that in children,

07:47.205 --> 07:50.665
and there's actually even some work in non-human animals,

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in birds, I show that birds prefer large quantities

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to be, to be on the right and smaller

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quantities to be on the left.

07:59.075 --> 08:00.935
So what's going on here? You know, we know that in,

08:00.935 --> 08:02.335
in children, children and,

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and even non-human animals, that there seem

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to be these preferences as adults.

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We're not showing them now, we can't know from the basis

08:10.515 --> 08:12.735
of our findings exactly what's happening there.

08:13.325 --> 08:16.215
It's possibly to do with something that happens

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during school when we learn about number, when we start

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to use kind of formal number systems learn symbolic number

08:22.455 --> 08:26.535
systems, but also it feeds into this wider debate

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around whether we think that symbolic numbers,

08:28.955 --> 08:31.975
so digits spoken number words, written number words,

08:32.355 --> 08:35.735
are processed in the same way as just quantities of objects

08:35.735 --> 08:36.855
and non-symbolic number.

08:37.235 --> 08:38.855
And there's a much wider debate

08:38.855 --> 08:42.015
around whether they have the same underlying processes

08:42.015 --> 08:44.295
and cognition, whether they use the same representations

08:44.675 --> 08:46.415
or whether these are actually two

08:46.415 --> 08:47.855
fundamentally different things.

08:48.355 --> 08:52.095
Now, we can't answer, but certainly based on

08:52.095 --> 08:53.855
what we, it seems,

08:55.865 --> 08:58.335
These kind of non-symbolic quantities,

08:58.805 --> 09:02.335
just encountering them is not enough to trigger access to

09:02.995 --> 09:04.535
the, the magnitude of that quantity

09:04.715 --> 09:06.135
or its spatial association.

09:06.235 --> 09:08.295
So I think we can see that on the basis of our data.

09:09.095 --> 09:10.395
In terms of what we're doing now,

09:10.605 --> 09:12.475
we're looking at whether it matters

09:12.575 --> 09:14.435
how memorable the stimuli are.

09:14.775 --> 09:16.955
So for example, we find that with dice patterns,

09:16.955 --> 09:18.155
we do get snark effects.

09:18.255 --> 09:21.075
So, you know, what is it about our d Do we get snark effects

09:21.095 --> 09:23.275
for dice patterns because they are something

09:23.275 --> 09:25.115
that we've learned, or do we get them

09:25.115 --> 09:26.155
because they are memorable?

09:26.155 --> 09:28.235
They're easy to remember, and that's why we, we,

09:28.295 --> 09:29.755
we associate them with number.

09:30.215 --> 09:32.355
So we're running further studies to kind of look at,

09:32.535 --> 09:34.395
you know, what really matters.

09:34.835 --> 09:37.035
D does, does the representation have to be something

09:37.035 --> 09:39.075
that we know or does it just have to be something that

09:39.655 --> 09:41.955
is easy to remember and and forms a pattern.

00:00 - Snarks. So a spatial numerical association of response codes. so what it's is, it's linked to the fact that people seem to have a fundamental link between number and space when they, kind of think about the world when they encounter number.

00:16 - So when people perform tasks where they have to reason about, digits or number words, they behave as though they have, well, it's sometimes called a mental number line, which you could almost think of as like a, a, a representation of a ruler in their mind where they associate small numbers with the left side of space and larger numbers with the right hand side of space. So kind of the kinda classic demonstration

00:41 - of this is if you ask people to perform a task where they have to respond to a digit on a screen. So for example, they see a digit and they have to press one button of it, that even number and another button. If it's an odd number, what we tend to find is that people are faster to respond to smaller numbers with their left hand, and they're faster to respond to larger numbers with their right hand. Now, what that suggests to us is that there's a,

01:07 - this fundamental link between number and space and cognition. yeah, as I said, it's called this mental number line that seems to go from the left to the right, where we associate smaller numbers with the left side of space and larger numbers with the right side of space. So with this study, what we were really interested in was whether the form of the representation of number mattered. So there's lots of different ways that you might encounter numerical information in life, right?

01:31 - You might see a digit, you might hear a spoken number word, you might see a plane card or a dice. What we were interested in is when you encounter quantities that aren't easily labeled. So in the paper we call these non-symbolic quantities. So this is just a collection of object. Now, in a previous study that we'd published, we'd found some evidence that you get snark effects for those types of quantities. and, and what we'd done was we'd asked people to respond

01:59 - to between one and nine triangles on a screen. And what people had to do was they just had to indicate whether right and left hand, whether the triangles were upright or whether they were inverted. And we were interested in whether the quantity of triangles impacted how people perform the task. So in this previous study, we'd found that when you saw a small number of triangles, you were faster with your left hand.

02:21 - When you saw a large number of triangles, you were faster with your right hand. And we thought, this is great. This is really interesting. This suggests that the, you know, the form of that numerical representation, it, it doesn't matter. We still get this snark effect, which is we hadn't really seen in adult participants before. So in this paper, what we wanted to do though was to try and replicate that finding because it's, you know, it's

02:43 - so important in psychology research that we try and replicate our findings because we'd only shown this once. So that was really what this paper was about, trying, finding debate Whether, you know, what we call symbolic representations of quantities. So digit number words, things that are learned and culturally specific, whether those are processed in the same way

03:10 - as these non-symbolic quantities. and so it kind of, it, it's really feeding into that literature. Do, do we, do we process them in the same way? Now, the interesting thing is that in, in young children, we do find that young children associate, non-symbolic number with these kind of, kind of spatial aspects. So children, prefer right sided responses for large groups of objects

03:33 - and left sided responses for smaller groups of objects. It hadn't really been shown in adults though. So what wasn't entirely clear was whether snark effects were linked to these effects that you see in, in young children, or whether there's something that's more to do with learning about how numbers work and school. And there's some evidence that says that it could be, you know, something to do with our education, because we know that in languages that are written from right to left,

04:00 - the snark effect tends to reverse. Okay? So we're kind of trying to get, you know, what's actually going on in adult participants. Do they, do they behave the same way as, as children do with these types of quantities? The four experiments were, were really, really similar. So in all of the experiments, what people did was they saw these, triangles. They were either upright or inverted. There were between one and nine triangles in each trial,

04:23 - and they just had a, you know, a left sided response and a right sided response. So upright, inverted, and this was swapped around for the participants. The differences between the studies were really to do with quite, low level aspects of the stimuli. So, for example, if I have a triangle, if I have one triangle and then I have nine triangles, just because you, you know, if the triangles are the same size, the nine triangles are just gonna cover more

04:49 - of the screen than the one triangle, right? And what we want to know, what we're interested in is really whether it's the number that's important rather than just kind of visual properties of the stimuli. So, for it, so, so two of the studies were really trying to get at, at that difference. So there was one study where we controlled the surface area, the triangles. What that meant was when you had

05:09 - one triangle, it was much larger. When you had nine triangles, each individual triangle was smaller, but the total surface area on the screen was the same. we also looked at how often it mattered, whether it mattered how often the stimuli were repeated, right? So when you see a digit like three or four, it looks the same every time you encounter it, but if you see a group of objects,

05:32 - they might be arranged differently on each trial. Three triangles in one trial might look like three tri different, three triangles on another trial. So we had another experiment where we looked at, you know, does it matter if the stim repeated, so seven triangles always exactly the same or whether they can be arranged in different forms in the screen? So those were the types of manipulations that varied across the four studies.

05:53 - But yeah, other than that, they were really, really similar. I think they had around somewhere between three and 400 trials, between one and nine triangles in each one. And it just said whether they were upright or inverted, the results are really easy to summarize, and that we found absolutely nothing. We found no evidence of a snark effect at all. So it didn't matter how much area the screen it took up, it didn't matter how often the stimuli were repeated,

06:21 - there was no snark effect there. Okay? So this was, quite a humbling surprise to us having shown it previously our, in our lab, but so important as well, right? So, you know, and we used, we made sure that we had, you know, sufficient participant numbers. we did what you call a power analysis to check that we've run enough participants to find an effective, it's there.

06:45 - we, we checked our analysis and double checked it, but, and, and none of the studies did we find an effective a effect. So it didn't matter how many triangles people saw, their right and left hand just did the same thing. They were completely unaffected by the quantity that they saw on the screen. So complete failure to replicate. There's kind of two aspects of this that I think is really important.

07:06 - The first is how important is trying replicate your own findings in psychology? You know, we'd find this really interesting, effect where we find snark effect for, for quantities hadn't been shown in adults before. We were quite excited about it, but obviously now we've been in and not replicated for it four times. So it's just, it's so important that, that, you know, you go

07:27 - and try and replicate your own findings. It's, it's just the way science works. So I think that's, that's one thing about this. the other thing though, just, you know, if we assume then that we don't find smart effects for these types of quantities, that's very interesting in itself, right? And it raises a little bit of a puzzle. You know, we know that in children, and there's actually even some work in non-human animals,

07:51 - in birds, I show that birds prefer large quantities to be, to be on the right and smaller quantities to be on the left. So what's going on here? You know, we know that in, in children, children and, and even non-human animals, that there seem to be these preferences as adults. We're not showing them now, we can't know from the basis of our findings exactly what's happening there. It's possibly to do with something that happens

08:16 - during school when we learn about number, when we start to use kind of formal number systems learn symbolic number systems, but also it feeds into this wider debate around whether we think that symbolic numbers, so digits spoken number words, written number words, are processed in the same way as just quantities of objects and non-symbolic number. And there's a much wider debate around whether they have the same underlying processes and cognition, whether they use the same representations

08:44 - or whether these are actually two fundamentally different things. Now, we can't answer, but certainly based on what we, it seems, These kind of non-symbolic quantities, just encountering them is not enough to trigger access to the, the magnitude of that quantity or its spatial association. So I think we can see that on the basis of our data. In terms of what we're doing now,

09:10 - we're looking at whether it matters how memorable the stimuli are. So for example, we find that with dice patterns, we do get snark effects. So, you know, what is it about our d Do we get snark effects for dice patterns because they are something that we've learned, or do we get them because they are memorable? They're easy to remember, and that's why we, we, we associate them with number.

09:30 - So we're running further studies to kind of look at, you know, what really matters. D does, does the representation have to be something that we know or does it just have to be something that is easy to remember and and forms a pattern.

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