The map of the world on the back of your head

Everything in front of you right now is laid out, physically, across a few square centimetres of cortex behind your ears. Neighbouring parts of what you see sit on neighbouring parts of the tissue. This is one real person's map, measured while a bar and a wedge swept across their view. Click the coloured cortex and the wheel shows you where that piece of brain is looking.

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Why this is the best thing the brain does in public

Most of what a brain does is invisible from outside it. This is not. Visual space is spread across the cortical surface in an orderly sheet, so a patch of tissue you can point at answers to a patch of the world you can point at. Two things next to each other in your view are next to each other in your head.

Turn on how far out and you can see the other half of the arrangement: the centre of gaze takes an enormous share of the cortex, and the far periphery is squeezed into a thin rim. That is why you can read this sentence only where you are looking, and why everything else is a vague impression of shapes.

How the map was measured, and how I checked it

The subject lay in a scanner and watched a bar sweep across a blank field, and a wedge rotate around it. Every point on the cortex has a time course, and for each one a model asked which small patch of visual space best explains when that point got busy. The answer is two numbers per vertex: which direction from the centre of gaze, and how far out.

I did not take that on trust. A real retinotopic map has a property noise does not: it is smooth across the cortical sheet, because neighbouring vertices see neighbouring parts of the world. Measured on this surface, neighbouring vertices differ about thirty times less than randomly chosen pairs, and shuffling the values destroys that completely, scoring 1.00 as it must. The build script runs that test on both hemispheres, before and after the mesh was simplified for the web, and refuses to write anything if it fails.

Each half sees the opposite world

Look at the two hemispheres separately. The left one is almost entirely coloured for the right half of the visual field, and the right one for the left. Measured on this subject: at a 25 per cent fit, 95.8 per cent of the left hemisphere's well-fitted cortex answers to the right of where they were looking, and 97.7 per cent of the right hemisphere answers to the left. Raise the fit quality and it goes to 98 and 99 per cent.

That the numbers get cleaner as the fits get better is itself the argument that these are real measurements rather than noise. Shuffling which hemisphere each point belongs to gives 48.7 and 49.7 per cent, which is chance, as it has to be. The build refuses to write the file if any of that fails.

This is why a stroke on one side of the back of the head takes away one side of the world rather than blurring all of it.

Most of the brain is grey here, on purpose. Only about 27,000 vertices per hemisphere have a receptive field the model can fit at all. Everywhere else it explains almost nothing, and colouring that would be colouring noise dressed up as a map. What is coloured is roughly the back tenth of the brain, which is a fair picture of how much cortex is given over to early vision.
Why polar angle uses a colour wheel. Direction is cyclic: straight up is one value whether you count clockwise or anticlockwise to reach it. A normal left-to-right colour ramp would invent a hard seam where the numbers wrap, and on a retinotopic map that fake seam would land near the real boundaries between visual areas, which is the worst possible place to put a lie.
Credit, with a caveat. This dataset is released CC0 and its own description file lists its authors as a placeholder, TODO: First1 Last1. There is no paper to cite and nobody named to credit, which is not how it should be. It came from the NYU Center for Brain Imaging, OpenNeuro ds007283, and the credit is theirs.