This has everything to do with the fact we have two brains. The left and right brain (more specifically the left and right hemispheres of the Cerebral Cortex) hold different functions cognitively, control the motor movements of the opposite sides of the body, and communicate thru the Corpus Callosum. Your full consciousness, or thought, is almost like a 'stream' created at this meeting point of the two brains where the neural traffic is so dense (more like my own theory...). However, if you were to find a patient where this connection is severed, like an epileptic patient whos Corpus Callosum was surgically bisected to cure them of chronic seizures, you would then have someone with 2 separate brains that cant talk to one another. This is split brain theory. I wrote a paper on this in undergraduate and id have to pull up a ton of other details, but essentially go watch videos on Michael Gazzaniga and Dr. Roger Sperry's experiments with these people. They would experience the right brain reaching for one outfit to get dressed in the morning while the left brain "thought" the idea of another outfit, so they would be very confused. Its very revealing to the mapping of our brain and all the different human functions, and how we learn! Then you lead down the rabbit hole of Bicameral Mind... but anyways, i believe thats why everyone can count in their left brain, and then from there its up to each brain system to figure out how to map the second task to the right brain so they can enter the consciousness stream simultaneously. There is an internal mechanism everyone develops themselves and Feynman is showing you can test that. Its probably right around most humans cognitive limit to use the right brain to help either reading OR speaking as the left brain is the primary handler of all of these (math, reading, speech). I also think thats why Feynman saw colors with his math; his right brain was assigning a unique identifier (color) to his logical problem being worked out in his left brain (all the different symbols and letters). Fascinating.
it does feel like quite the coincidence that 2 seems like the magic number and we do, in fact, have two hemispheres. i doubt that the processing for any of these tasks falls strictly down the left vs right hemisphere, but i do kind of feel like our consciousness is kinda built on having a sort of internal tick-tock cycle, and we do certain kinds of thinking on tick and others on tock. but that is just armchair introspective dilettante neuroscience-- not to be confused with the actual thing.
The article's EEG images don't seem to suggest this is due to two brain hemispheres.
I can't remember the book now, I think one of Antonio Damasio's? He recounted an experiment with a patient that had a severed corpus callosum where they put a wall between the eyes and showed him two different pictures, asking him what he saw, and he wrote one answer and spoke another, without any indication either half of him was aware the other half was inconsistent.
It was terrifying 20 odd years ago to read this kind of thing, but it's amusing in light of all the obsession with productivity hacking in Silicon Valley that I could almost see someone with a YouTube channel doing this on purpose to try and be able to accomplish simultaneous tasks a normal person would be tripped up on by the need for a normal brain to produce a single consistent narrative.
Fun fact, the Zizian AI murder cult is similarly obsessed with the idea of two hemispheres being separate brains. They also believe gender dysphoria is a trait present or absent within each hemisphere.
Their long term goal was to abolish sleep by making one hemisphere of their brains sleep at a time, leaving the other to be awake. Supposedly this would allow them to work more and have more sex. In reality, they all simply went insane, committed pointless murders, and ended up in prison.
As it happens, dolphins and whales do this so as to not drown, and they consequently have an underdeveloped hippocampus and take 3x as long as primates to learn the same things.
Long story short: don't mess with your sleep or you might start a murder cult.