Speed Flow subitization

Question: can we subitize the number of speed flows too?

A small experiment after reading “The Number Sense” (while tanning in southern Thailand) – by Alvaro Cassinelli

Tokyo, 14.1.2008


Besides the well known number subitization, evolution may have endowed us with a “speed flow number subitization” too. Either per se, or as an intermediate mechanism that would speed-up the (more fuzzy) numerosity estimation of a large number of objects when these move in groups – as in fish banks, flocking birds, estampede, crowds, etc.

In such case, we may have an interesting arithmetic ability that goes beyond the “accumulator”: perhaps an intuitive grasp of the arithmetic product between the subitized number of speed flows (a discrete, exact quantity), and the approximate estimation of the number of particles in each class, leading to the (approximate) estimation of the total number of objects. This strategy may be hardwired in our brains, an be more natural than the abstract (perhaps irremediably symbolic?) cartesian product operated when we mentally separate objects into subsets in order to calculate their total numerosity.

If this subitization effect exist (which seems to be the case – see below), it can also be a fortuite effect from the recruiting of neural networks for static numerosity with a different input (how speed is “encoded” in the brain? can it be the clustering of frequencies of firing neurons in different places of the visual cortex?).

Try it by yourself

This is of course a very preliminary experiment. The goal is to try to estimate the number of motion flows without resorting to counting.

Hitting the space bar will end the experiment and show the actual number of speed flows; hitting it again will restart the experiment with a different number of speed classes. A few parameters can be changed by the keyboard (such as number of particles in each flow-class, size of the particles, and on/off of trajectory trail).

Click on the images to launch the applet-experiment >>

I have the impression (must be confirmed) that the subitizing effect is limited to 2, and at best 3 speed classes. Interestingly, up to three, one have the illusion that the particles are attached to a separate transparent sliding sheets (in fact, this also depends on the density of particles on the screen). After this number, I need some conscious effort to discriminate these planes, and when the number of flows gets too large (more than seven or so), I don’t see any more these planes but almost random particles.

Possible experimental protocol:

Of course, a more serious experiment would be essentially a transposition, in the speed domain, of the static numerosity experiment. What is needed is to measure the response times as a function of the number of speed flow “planes”, in order to detect the moment when the subject resort to counting (time response would increase abruptly).

In the case of the static subitizing experiment, there were several subtle effect to take into account (like the relative position of the points on the plane); in the present case, there may be even more parameters to take into accout. Not only the relative position of the particles (creating rapidly recognizable figures), but also:

  • Relative importance of the speed magnitude vs. speed direction for discriminating the flows. Since the magnitude of the speed is a continuous quantity that is perhaps estimated independently, it is likely that this estimation suffers from a ( speed) magnitude/distance effect. Therefore, if the total numerosity of particles is estimated as a product of flow numerosity and approximate number of particles in each class (which also may suffer from magnitude effect), then the final estimation will suffer from a stronger magnitude/distance effect (actually a product of the standard deviation) that may be more dramatic than the effect as measured directly on the set of particles, but at rest. This may be measurable!
  • Effect of total number of particles, total particle density, and relative number of particles in each flow class (for instqance, when the number of flows change, we can either leave unchanged the number of particles in each class, or unchanged the total number of particles, so as to warrant the same particle density).
  • In order to eliminate directional biases (such as the left-to-right reading direction biais), the image could continuously rotate while doing the estimation. Effect on the flow estimation numerosity when the particles behave in a more “realistic” way (such as falling because of gravity). Perhaps evolution has trained us better to count in these real cases (falling fruits, stones, etc).
  • Color and size of particles (why not trying with recognizable objects too, such as faces?)
  • A separate experiment: does we have direction-numerosity? (probably yes: estimate of the numerosity on spatial-frequency domain)
  • What is the maximum speed-flow subitizing number for three-dimensional flows of particles?


More reflextions (and pictures) to come!

Combien y a-t-il de poissons?

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Lisa fait un peu de maths a la plage…

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Le meme se repand rapidement: Monica et sa mere s’y mettent aussi!

Thomas (a droite) nous apprend un peu de Yoga: je compte cinq apprentis et un photographe (lui aussi apprenti bien sur!)

Entasses comme du betail, les touristes vont a Chiang Mai… combien il y en avait? pas reussi a savoir, mais c’etait pas la fete…

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Un sosie de Philippe s’est faufile dans cette image. Reussirez vous a le trouver?