I’ve been reading Backus among other things, attempting to grasp the differences between first-order predicate logic, function-level, and variable-level combinatory logic. One area that has stood out for me in reading Backus was the notion that function-level may be more efficient to reason about than the more user-friendly variable-level.

[rant] In some circles I understand function-level is also known as pointfree (or pointless) while the most common variable-level usages appears to be lambda calculus based. Talk about my brain having a lexical meltdown. Reading Backus is bad enough… but trying to understand just what pure functional programming is ain’t easy either when there appears to be no consensus on exactly what that means. [/rant]

Backus goes on after his efficiency claim to discuss the notion of using primitive functions to compose functional forms and type hierarchies from composing those functional forms in succession. This immediately piqued my interest because in the back of my mind it had been nagging me why someone could possibly continue along the function-level line of thought when the mainstream had moved on to the more popular get-things-done lambda calculus way of doing things.

Then something struck me. Something I’ve thought about with regard to intelligence and that of the realm of referential transparency and the way in which we all operate in life. I began to draw parallels between the notion of type hierarchies, atoms, elements, molecules, proteins, enzymes, cells and organisms. The composition of primitive functions into these functional forms. The hierarchies these then build based upon the physical properties (quantum mechanics?) of those primitive functions and the unique ways in which functions may apply to others creating yet more uniquely propertied functional forms. The complexity of properties of these functions meaning some will be more inherently stable than others (potentially the types). That these unique properties could themselves be derived from evolutionary encapsulation. In other words; turtles all the way down.

Months back I set out to model my own theory of encapsulation. Initially known as my Principal of Rational Dynamic Complexity. Later I prefixed Robust. Then after finding that difficult to remember it became the Law of Encapsulation with each of those elements becimong principles. My The Law of Encapsulation states that; for any complex system to evolve in a constrained environment(eg. the earth) it must be dynamic yet rational in order to be robust.

So while others may prefer the variable world of the lambda calculus to get things done today, tomorrow is a new day, one I believe may yet see the rise of function-level. Only your likely to never know it because it will come naturally to you. In other words… an interface abstraction. Just as our bodies are for our brains.

 New fMRI research from Vanderbilt neuroscientists gives insight into the limits of multi-tasking in the brain.

The results revealed that the central bottleneck was caused by the inability of the lateral frontal and prefrontal cortex, and also the superior frontal cortex, to process the two tasks at once. Both areas have been shown in previous experiments to play a critical role in cognitive control.

"We determined these brain regions responded to tasks irrespective of the senses involved, they were engaged in selecting the appropriate response, and, most importantly, they showed 'queing' of neural activity–the neural response to the second task was postponed until the response to the first was completed," Dux said.

"Neural activity seemed to be delayed for the second task when the two tasks were presented nearly simultaneously – within 300 milliseconds of each other," Marois said. "If individuals have a second or more between tasks, we did not see this delay.

Based on memory work I've read I'd postulate that neurons required for multiple tasks, block synapse unrelated to the current task based on temporal information it receives and later predicts. That the "queueing" shown is a simple battery of requested actions on different synapse from other circuits in the brain. And that priority is given next to the most active synapse.

I need to think about this further when my head is clearer.

That's my take after reading Amnesiacs struggle to imagine future events:

People with amnesia have difficulty imagining future events with any richness of detail and emotion, a new study reveals. The finding adds to a growing body of evidence suggesting that memories help people visualise the future.

Eleanor Maguire at the Wellcome Trust Centre for Neuroimaging in London, UK, and colleagues studied five patients who suffered from classic amnesia. The patients had all suffered infections that had damaged a brain region called the hippocampus. The damage left the subjects unable to recall past events, although they could remember facts such as the names of their relatives.

My belief is that in order to predict the future we need to be able to distribute our belief of what that future may be based on facts we already believe, so that other regions of the brain can allow for those beliefs in forming new ones. According to this study subjects could remember facts (memories stored in the hippocampus and linked to in other areas of the brain) but not past events. My hypothesis is that the feedback loop to some higher levels of brain function(potentially the sensory heirarchy that stores temporal patterns) critical to prediction, breakdown in areas of the amnesiac hippocampus.

The more I think about areas such as the hippocampus and amygdala, the more I believe that as we develop, functions migrate from lower levels into cortical areas of the brain where the real cognitive work done, and then fed lower in a feedback cycle where it's acted upon.

Alas, right now I've not thinking straight to ponder further in detail, my vision feels a little cloudy and my head heavy. Like the onset of a migraine. Thought I'd better jot this thought down before I forget it! I'm off to massage my neck and relax. Usually does the trick!