The word ‘utility’ can be used in two different ways: normative and descriptive.
You are describing ‘utility’ in the descriptive sense. I am using it in the normative sense. These are explained in the first paragraph of the Wikipedia page for ‘utility’.
As I explained in the opening paragraph, I’m using the word ‘utility’ to mean the goodness/desirability/value of an outcome. This is normative: if an outcome is ‘good’ then there is the implication that you ought to pursue it.
Sorry to be a party pooper, but I find the story of Jason Padgett (the guy who ‘banged his head and become a math genius’) completely unconvincing. From the video that you cite, here is the ‘evidence’ that he is ‘math genius’:
He tells us, with no context, ‘the inner boundary of pi is f(x)=x sin(pi/x)’. Ok!
He makes ‘math inspired’ drawings (some of which admittedly are pretty cool but they’re not exactly original) and sells them on his website
He claims that a physicist (who is not named or interviewed) saw him drawing in the mall, and, on the basis of this, suggested that he study physics.
He went to ‘school’ and studied math and physics. He says started with basic algebra and calculus and apparently ‘aced all the classes’, but doesn’t tell us what level he reached. Graduate? Post-graduate?
He was ‘doing integrals with triangles instead of integrals with rectangles’
He tells us ‘every shape in the universe is a fractal’
Some fMRI scans were done on his brain which found ‘he had conscious access to parts of the brain we don’t normally have access to’.
As far as I can tell, he hasn’t published any technical math/physics writings (peer-reviewed or otherwise). He wrote a book but as far as I can tell, this is mostly a memoir, with a bit of pop-math thrown in. From his website, this is what he’s working on:
Yep, those certainly are physics-y words! Good luck to him making progress in this area!
Its suspicious to me that he doesn’t have any writings on his mathematical works, so we are not able to judge what he’s doing. (Even time-cube man posted his writings on the internet)
This is my summary of the story:
He was hit on the head and experienced some changes after this. (Very believable )
These changes were significant enough to be visible on fMRI scans. (Also very believable )
He experienced OCD-like symptoms and other personality changes after the injury (I’m not a neuroscientist, but this seems plausible)
He experienced seeing visual distortions and ‘fractal-like’ images after the injury. (Again, I’m not a neuroscientist, but this seems plausible)
The visual hallucinations and personality changes caused him to be more interested in fractals, geometric designs, art, and math.
He took a few entry-level math classes and did ok in them.
The mugging took place in 2002 but apparently he hasn’t produced any technical writing in the subjects of math and physics.
In 2015, he was running futon stores in Washington State
This all leads me to believe that he is not ‘math genius’. I am agnostic about whether he is delusional about his abilities or whether he is a con-man.