Train Your Brain

Regions, references, and what is not proven

Reading a digit and seeing a colour do not draw on the same region of the cortex. Tsuidoku is built on a rule that makes it impossible to handle one without the other.

Two regions, two jobs

Where digits and colours are processed

Recognising the glyph 7 — telling it apart from a 1, from a T, from a smudge — is not arithmetic. It is shape recognition, and it has its own territory.

The visual number form area

That territory has a name: the visual number form area. It sits in the inferior temporal gyrus, just in front of the temporo-occipital incisure, around MNI coordinates (51, −54, −24). It responds to digits more than to letters, faces or objects — a preferential response, not an exclusive one: neighbouring shapes activate it too, more weakly. The representation of digits there is bilateral.

It is the immediate neighbour of the visual word form area, the region that recognises letter strings. The ventral occipitotemporal cortex is the district of learned recognitions: this is where the brain files the symbols that no evolution prepared it for and that culture imposes on it.

The V4 complex

Colour is built elsewhere, and not in one piece. The V4 complex sits on the ventral face of the brain, in the fusiform gyrus: V4 in its posterior part, and V4α further forward, in its anterior part. The two form a chain rather than a single centre.

The sharpest demonstration of its role is clinical. A lesion of this ventral occipital region produces cerebral achromatopsia: the world turns grey. The retina is intact and the cones work — the loss is cortical. It is rarely strictly confined to colour, and other visual deficits often accompany it, but the colour loss is disproportionate: shape recognition survives a damage that colour does not. The two are dissociable because they are built separately.

Colour and digit shape are processed on two adjacent gyri of the same ventral cortex, a couple of centimetres apart. Schematic: gyri unfolded, proportions not to scale.

Proximity

Two regions that are neighbours

The visual number form area and V4α occupy the same district of the ventral occipitotemporal cortex, on two adjacent gyri: the fusiform for colour, the inferior temporal for the shape of the digit. A couple of centimetres, one sulcus.

That proximity is not an anatomical curiosity. It is the most discussed explanation of a known phenomenon: grapheme–colour synaesthesia. About one per cent of the population sees a colour when reading a digit or a letter. The 5 is red, the 2 is green, the correspondence holds for a lifetime, and it is not chosen.

The cross-activation hypothesis proposes that the phenomenon arises from an unusually direct communication between the region that recognises the grapheme and the one that builds colour — precisely because they are adjacent. Three observations support it:

in synaesthetes, V4 activates very early after the grapheme appears, in a time window too short for a reconstruction from memory or imagination;
the white matter of the inferior temporal cortex is more coherent there than usual — diffusion imaging shows increased fractional anisotropy, the signature of better-organised tracts, exactly where those connections would run;
in the inferior temporal cortex specifically, that structural difference tracks the lived experience: it is more marked in those who see the colour projected in space than in those who feel it mentally.

When those two regions talk to each other more than usual, it shows in the white matter, and it is heard in what the person reports.

What Tsuidoku does

A rule that forces the pair

Tsuidoku is not a sudoku that has been coloured in. Its rule is about the pair.

Every cell carries a digit and a colour. Each digit appears once per row, per column and per block — the sudoku rule. Each colour obeys the same constraint, independently. And above all: each digit–colour combination exists exactly once in the whole grid. Eighty-one cells, eighty-one pairs, no repetition.

The rule bears on the object, not on either of its two features taken alone.

That last rule changes the nature of the mental object. A player cannot reason about digits first and colours afterwards: they have to hold conjunctions in memory. “The 3 is already green somewhere” is a piece of information that exists neither in the layer of digits nor in the layer of colours. It exists only in their binding.

This is exactly the operation cognitive psychology calls feature binding. Feature integration theory holds that elementary features — colour, orientation, shape — are extracted in parallel and effortlessly, but that assembling them into an object requires attention. Deprived of it, the system produces illusory conjunctions: people report a red square and a blue circle where a blue square and a red circle stood.

With attention divided, features are correctly detected but wrongly assembled.

The parietal cortex is necessary for this binding. Bilateral parietal lesions produce massive illusory conjunctions, and transiently inactivating the parietal lobe in healthy subjects selectively degrades conjunction search while leaving single-feature detection intact.

The grid recruits a third family of regions as well. Under the triple-code model, a number exists in three independent formats: its visual arabic form, in the ventral occipitotemporal cortex; its verbal form, in the left perisylvian regions and the angular gyrus; and its analogue magnitude, carried by the horizontal segment of the intraparietal sulcus. Working out that only one slot is left for the 7 is reasoning by exclusion, not shape reading: deduction and recognition do not live in the same place.

Where the line sits

What can be claimed, and what cannot

✓Established

The regions described here exist, and their functions are documented by imaging, cortical recording and lesion studies. The anatomical proximity between grapheme recognition and colour processing is a fact. Attentional feature binding is a robust phenomenon, described for forty years. Sources at the bottom of the page.

=A description of the game, not a prediction

The unique-pair rule requires manipulating conjunctions rather than isolated features. That is not a hypothesis; it is what the constraint means.

✗Not demonstrated

That playing Tsuidoku durably changes anything in a brain. No study has been run on this game. And the brain-training literature calls for caution: the large transfer trials converge on an uncomfortable result — you get better at the task you train on, and the effect travels almost nowhere else. So we will not say that Tsuidoku makes you smarter. It makes you better at Tsuidoku, and it is a pleasure to play. That is reason enough.

?Open to testing

Does a trained player recognise digit–colour pairs faster than a non-player — the beginning of automatisation for an arbitrary conjunction? The question is measurable. A conjunction-search protocol run before and after training would answer it, and the result would be worth having whether it came out positive or negative.

If you work on feature binding, numerical cognition or synaesthesia, the grid is at your disposal. Write to us

One of a kind?

The only one of its species?

A nuance, because the wording matters.

Classical sudoku calls on number form and magnitude, with no chromatic dimension. Colour puzzles — filling regions, sorting hues — call on V4 without ever summoning a numerical symbol. Both have existed for a long time, separately.

To our knowledge, Tsuidoku is the only widespread logic puzzle whose central constraint bears on the digit–colour pair itself. Elsewhere, colour is decoration: take the colours out of a coloured sudoku and the grid is still solvable. Here that is impossible — the unique-pair rule would disappear with them.

This is a claim about the mechanics of the game, checkable by reading the rules. It is not a claim about the brain.

References

Sources

Peer-reviewed work on the regions and mechanisms described above. None of it concerns Tsuidoku.

Shum J., Hermes D., Foster B.L., Dastjerdi M., Rangarajan V., Winawer J., Miller K.J., Parvizi J. (2013). A Brain Area for Visual Numerals. Journal of Neuroscience 33(16), 6709–6715. doi:10.1523/JNEUROSCI.4558-12.2013
Grotheer M., Herrmann K.-H., Kovács G. (2016). Neuroimaging Evidence of a Bilateral Representation for Visually Presented Numbers. Journal of Neuroscience 36(1), 88–97. doi:10.1523/JNEUROSCI.2129-15.2016
Hannagan T., Amedi A., Cohen L., Dehaene-Lambertz G., Dehaene S. (2015). Origins of the specialization for letters and numbers in ventral occipitotemporal cortex. Trends in Cognitive Sciences 19(7), 374–382. doi:10.1016/j.tics.2015.05.006
Zeki S., Marini L. (1998). Three cortical stages of colour processing in the human brain. Brain 121(9), 1669–1685. doi:10.1093/brain/121.9.1669
Bartels A., Zeki S. (2000). The architecture of the colour centre in the human visual brain: new results and a review. European Journal of Neuroscience 12(1), 172–193. doi:10.1046/j.1460-9568.2000.00905.x
Bouvier S.E., Engel S.A. (2006). Behavioral Deficits and Cortical Damage Loci in Cerebral Achromatopsia. Cerebral Cortex 16(2), 183–191. doi:10.1093/cercor/bhi096
Hubbard E.M., Arman A.C., Ramachandran V.S., Boynton G.M. (2005). Individual differences among grapheme-color synesthetes: brain-behavior correlations. Neuron 45(6), 975–985. doi:10.1016/j.neuron.2005.02.008
Rouw R., Scholte H.S. (2007). Increased structural connectivity in grapheme-color synesthesia. Nature Neuroscience 10(6), 792–797. doi:10.1038/nn1906
Brang D., Hubbard E.M., Coulson S., Huang M., Ramachandran V.S. (2010). Magnetoencephalography reveals early activation of V4 in grapheme-color synesthesia. NeuroImage 53(1), 268–274. doi:10.1016/j.neuroimage.2010.06.008
Treisman A.M., Gelade G. (1980). A feature-integration theory of attention. Cognitive Psychology 12(1), 97–136. doi:10.1016/0010-0285(80)90005-5
Robertson L., Treisman A., Friedman-Hill S., Grabowecky M. (1997). The Interaction of Spatial and Object Pathways: Evidence from Balint’s Syndrome. Journal of Cognitive Neuroscience 9(3), 295–317. doi:10.1162/jocn.1997.9.3.295
Ashbridge E., Walsh V., Cowey A. (1997). Temporal aspects of visual search studied by transcranial magnetic stimulation. Neuropsychologia 35(8), 1121–1131. doi:10.1016/S0028-3932(97)00003-1
Dehaene S., Piazza M., Pinel P., Cohen L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology 20(3–6), 487–506. doi:10.1080/02643290244000239
Owen A.M., Hampshire A., Grahn J.A., Stenton R., Dajani S., Burns A.S., Howard R.J., Ballard C.G. (2010). Putting brain training to the test. Nature 465(7299), 775–778. doi:10.1038/nature09042
Simons D.J., Boot W.R., Charness N., Gathercole S.E., Chabris C.F., Hambrick D.Z., Stine-Morrow E.A.L. (2016). Do “Brain-Training” Programs Work? Psychological Science in the Public Interest 17(3), 103–186. doi:10.1177/1529100616661983