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 Law of Encapsulation states that:

For any complex system to evolve in a constrained environment, eg. the earth; it must be dynamic yet rational to be robust. I call this the principle of life.

Life being the quintessential example of this principle - but not the only one - is exposed to it’s environment with layers of protection or encapsulations in order to afford evolution. It’s through this encapsulated and regulated exposure, that changes can occur and be maintained in a robust manner. It’s this encapsulation that affords control of known entities entering the encapsulation in any dynamic environment. However, as with any encapsulation, it is constrained, with limits, and as a result unknown entities may enter undetected. The reason for this - is that in a dynamic system no one encapsulation can internally ever know everything external of it, and as a result no one encapsulation can regulate external influence on internal change. Therefore all dynamic systems are inherently susceptible to the instability of external influence. Thus; in order to manage the environmental effects and maintain stability, the encapsulation must maintain knowledge of the environment in which it exists. It must do this all while utilising as few resources as possible so as to ensure stability of the constrained environment. It is only through management of internal function as a result of external influence that a system can evolve, thus forming a symbiotic relationship and everything we take for granted.

As an example of such a system, take humans. Humans are multi-cellular organisms. In cellular organisms, certain cells may allow resource for example; glucose and calcium, to pass their cell walls while preventing other known entities such as waste materials the cell can no longer use. Unknown entities - for example some viruses, nanoparticles or brute force attacks such as radiation - may also pass the cell wall, into the cytoplasm and nucleus - the result being change in the cell DNA. An example of this could be getting too much sun (radiation) and skin cancer (detrimental changes in cell DNA).

Thus, in order to maintain robustness, our cells divide and in doing so take with them the changes in the DNA caused by external influences. These changes represent aging. The reason for cell division comes as a result of any constrained environment. Cells become unstable as they accumulate more resources and grow. Cell division is therefore cheap redundancy. In large enough cell division numbers with related cells, it also serves as a shell to encapsulate - and protect - local and global DNA within a multi-cellular organism. In addition; expensive to produce stem cells maintain the function and integrity of important regions through specialisation. For example the immune system whereby stem cells are recruited like civilians and trained into army troops to fight an attack. While on the other hand skin cells encapsulate globally. The advantage of this encapsulation is that when external influences have caused changes in specific regions of the organism and not the whole, the organism maintains robustness and can repair limited damage from the unaffected cells, thereby efficiently utilising resources best put to other use.

Additionally; the reason for cell division and not conjugation(sex) at this level is that it’s expensive on resources. Aggregating the average of these DNA changes from multiple cells - into sperm or eggs - takes resources; the blood stream and all of the related reproductive organs. Conjugation is therefore expensive yet highly redundant in that it creates further encapsulation in that of a multi-cellular organism in it’s local environment. This is all so long as compatible conjugation occurs. This is where species come in, and the reason incompatible or altered DNA often cause miscarriage or defects and new species that adapt as a result of difference. It’s also the reason larger more efficient multi-cellular organisms live longer; they carry more useful information in their DNA relating to their specific constrained environment to protect against environmental instability. The use their resources more efficiently!

Conclusion

* Encapsulation alone is not a secure method in which to store knowledge of any dynamic environment. Therefore the encapsulation must evolve with it’s environment in order to survive. Therefore it must be dynamic in order to do so.

This is why we age, evolve, exist, are intelligent. Extrapolate anything you like from the Law of Encapsulation.

It’s why encryption algorithms aren’t secure in themselves. They must evolve with the system and in the process, aggregate information. Aggregate intelligence to defend against environmental instability.

The meaning behind the phrase; survival of the fittest.

The meaning of life.