It’s not the sensation, it’s the neuroscience
Philosophers have argued about whether it’s even conceivable to have pain without the physical sensation. According to 3News (and other media outlets worldwide), University of Chicago neuroscientists don’t have a problem with this:
Mathematics can be difficult, and a new study shows even thinking about doing it can physically hurt.
Of course, that’s not quite what the study found (and credit to 3News for linking), though it does seem to be what the researchers said they found. The study was in people with ‘high levels of math anxiety’ and the abstract says
We show that, when anticipating an upcoming math-task, the higher one’s math anxiety, the more one increases activity in regions associated with visceral threat detection, and often the experience of pain itself (bilateral dorso-posterior insula).
That is, some of the parts of the brain that are active during pain or threat were also active when anticipating a maths task, even though there was no actual pain reported.
A simpler explanation might be that if you’re scared of maths, then your brain looks as if you’re scared of something. Although the researchers don’t believe this, they do actually concede it is an alternative explanation in the discussion section of the paper
the INSp activity we found could be reflective of something else. For example, it has been suggested that INSp activity is not so much reflective of nocioception, but rather reflects detection of events that are salient for (e.g., threatening to) bodily integrity, regardless of the input sensory modality
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