“The brain is a three dimensional object.” It would seem that this is one of the least controversial facts about the brain, something we can all agree on. But now, in a curious new paper, researchers Arturo Tozzi and James F. Peters suggest that the brain might have an extra dimension: Towards a fourth spatial dimension of brain activity
From topology, a strong concept comes into play in understanding brain functions, namely, the 4D space of a ‘‘hypersphere’s torus’’, undetectable by observers living in a 3D world… Here we hypothesize that brain functions are embedded in a imperceptible fourth spatial dimension and propose a method to empirically assess its presence.
I must admit that I’m not sure whether Tozzi and Peters literally mean that the brain is a four dimensional object. I don’t know if we are to read this paper as meaning that neural activity is in some way analagous to a hypersphere (a four-dimensional sphere), or whether we’re being asked to believe that the brain actually is or contains one.
For instance, the authors write:
How do thoughts flow in the brain? Current advances in neuroscience emphasize the role of energetic landscapes (Watanabe et al. 2014; Sengupta et al. 2013), a sort of functional linens equipped with peaks, valleys and basins made of free-energy, where thoughts move, following erratic and/or constrained trajectories… This review, based on recent findings, introduces the concept of a spatial fourth dimension, where brain functions might take place, as a general device underlying our thoughts’ dynamics.
This suggests that the fourth dimension is a metaphor, in the same way that energy “landscapes” are metaphorical, not actual places. But then on the other hand, we read the following, which seems to imply that the fourth dimension is a real thing (albeit something we can’t see):
Brains equipped with a hypersphere is a counter-intuitive hypothesis, since we live in a 3D world with no immediate perception that 4D space exists at all. We need thus to evaluate indirect clues of the undetectable fourth dimension…
So what’s the evidence for this mysterious dimension? Tozzi and Peters say that we need to look for 3D “shadows” or “echoes” of the 4D object, and we can do this using the Borsuk-Ulam Theorem (BUT) which, they say, predicts that ‘antipodal points’ on the 4D brain will be activated during activity of the 3D brain, as follows:
The activation of a single point on the 3D brain S2 surface leads to the activation of two antipodal points on the 4D brain S3 surface (Fig. 3b). In turn, the activation of two antipodal points on S3 leaves on the 3D brain S2 surface ‘‘hallmarks’’ which can be detected by currently available neuroimaging techniques.
Essentially, the claim is that if an fMRI study detects activity at two opposite points on the brain, this is evidence for an unseen 4D reality. They review various resting state fMRI studies and, they report, find that many of them have indeed detected antipodal activations. The illustrate this with a series of images, taken from recently published papers, in which black and white bars are used to depict the antipodal points:
Hmm. I can see a few problems with this. For one thing, it’s cherry picking: every fMRI study is different so some of them will produce antipodal patterns by chance alone. But more fundamentally, this approach ignores the facts of neuroanatomy. The brain is bilaterally symmetrical: it has a left and a right hemisphere, and the corresponding points on each hemisphere are connected by the corpus callosum. For this reason, neural activity is generally symmetrical. We don’t need to posit a 4D brain to explain this, yet many of the Tozzi and Peters “antipodal bars” can be easily explained in this manner.
So I’m not convinced by this paper, but nonetheless, I suspect it might become a ‘cult classic’ of theoretical neuroscience, as the idea is rather gloriously weird.
Tozzi A, & Peters JF (2016). Towards a fourth spatial dimension of brain activity. Cognitive Neurodynamics, 10 (3), 189-99 PMID: 27275375