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.

My brother sent me this article about altruism and pinpointing and predicting it in the brain using fMRI scanning.

What it started, was a simple thought process that ended up taking on a life of its own. Thus I wanted to get it down for posterity sake.

It's an interesting article. I came across it on http://www.eurekalert.org/ the other day but never read it. Quite a few of these functional magnetic resonant imaging (fMRI) studies are popping up lately I just haven't had the time. One reason is they only monitor active blood flow/synapse potential(electrical firing) density in clusters over long periods of time (1-3 seconds) at an accuracy of about a millimeter and are only really useful for comparison purposes to get a rough idea of where tasks are active in different parts of the brain. Thing is as I'm finding we're all wired a little differently, sometimes a lot depending on the part of the brain, and that resolution, while good for hypothesis on how we work, isn't detailed enough for me to gain an understanding as to why we work and are built a certain way.

Thus I'm learning about neurons at the moment and how they store memory. Basically the more you react to stimulus (called sensitisation) and a form of learning where you learn to ignore innocuous stimulus (called habituation). Combine the two and you have conditional learning. Interestingly its the synapses already connecting one neuron to another that strengthen and weaken, not new connections being formed when performing sensitisation. I need to finish reading the Kandel article but I think its the same for habituation… I'm also learning about how, where and why new neurons form and do connect. From birth they seem to work in clusters and send out connectors (axon) and waves of exploratory signals along them that stop sending once they find something they connect with that responds in a way they expected according to Shatz. Like calling everyones telephone until you connect to the right person and then adding them to autodial for whenever you have a message to send, all done through strengthening selective synapse connections to other neurons while weakening others. Alternatively think of it as internet messaging where weakening synapses is used as a form of spam prevention because in the brain neuron spikes(the voltages the fMRI picks up) may be heard from neighbouring neurons. Also no neuron is the same and each probably have their own signature like an IP address eg. 192.168.1.77 only it probably looks like ACTGATGCATAGATAGATAAC, while types of neurons (clusters) are subnets of that IP address. eg. 192.168.1.* And that those subnets are signatures stored in our genes so that as different cells grow they can find other cells to talk to and connect with to form the functional beings we are.

Imagine your a nerve cell that has been cultured in a dish and injected into the skin of someone and your not connected to anything yet. Then one day something presses up against you and causes you to enough pain to threaten your existence. Your going to send out a signal and complain right, and your neighbours(if they hear you), in order to get you to shut up, will send messages further until they get to the cell in charge who tells everyone else what to do next. Over time neural highways form, structure (who talks to who and who listens) is then encoded in cells that talk a lot back and forth. An example of being encoded with information being adult stem cells. Recently they've even found intermediate stem cells.
It has been shown that synapses over time when conditional learning happens (both sensitisation and habituation) cause the nucleus of the neurons to synthesise proteins. Are they simply changing their IP address from say 192.168.1.10 to 192.168.2.1 and forming a biological component hierarchy in this process? They may well be. And that the letters: ACTG, what are called the bases in Genome sequencing and used to construct the name GATTACA and my blog name CATAGA - are in fact the subnet code.

Are you asleep yet? If not did you like my hypothesis? It's a work in progress. (I came up with it as I typed this message to my brother)