Adaptive Stochastic Automata: Taking the Magic out of Maths

Adaptive Stochastic Automata

Taking the Magic out of Maths
by Randy Stack & Vic Stack

As humans, we tend to give human characteristics to most things, from our pets to our vehicles and even to concepts. This is “friendly”, “comforting”, “funny”, “considerate” or “happy”, for example. And, just like when we anthropomorphize non-human beings and things, our minds are also susceptible to conferring “personality” upon anything which behaves in a seemingly “intelligent” manner.

Many people consider a total eclipse to be a magical thing. The amazing way that the moon is exactly the right size to fill the entire whole of the sun. That is “magical” (proof of God?) and “lovely”. The mathematics and physics of all things are not magical but the unchanging laws of a changing universe. Things will change (evolution?) but the result of that change will still follow the same rules.

Stephen Hawking wrote A Brief History of Time to try and explain many things, like the above, to the general public. The masses did not understand as they considered it to be an “unfriendly”, difficult read. He then wrote A Briefer History of Time with the intention that the masses may see this as a “friendlier” book.

In his 1962 essay Hazards of Prophecy: The Failure of Imagination, Arthur C. Clarke observed, “Any sufficiently advanced technology is indistinguishable from magic.”


Of all the core tenets of psiometric science, the one key concept which suffers both this mystification and anthropomorphization the most is that of adaptive stochastic automata.

Most automata (including the well-known cellular automata) have a variable state space and a fixed rule space. The state space describes the currently manifest configuration whereas the rule space dictates how the automatous manifold will behave. Upon passing into its next generation, its new state space will reflect those rules’ impact upon its prior population. Then, in the next generation after that, those same rules will take their effect upon what has now become the present state space, ad infinitum.

Quite simply, with adaptive stochastic automata the state space manifold of the current generation becomes the rule space of the next. Thus, at each successive iteration, its behavior “adapts” to its present configuration. The only “rule” which remains fixed is that each higher dimension will be at a precise 90-degree angle (the phase differential between sine & cosine, real & imaginary) to its nearest lower-dimensional neighbor.

The function of adaptive stochastic automata are to extract order from (apparent) chaos. As such, it acts as an organizing force within any algorithmic environment into which it is introduced.


sentient (adj.) – able to perceive or feel things

Adaptive stochastic automata are considered sentient structures due to their ability to sense and adapt to the conditions of their environment. This does not, however, mean to imply they possess any semblance of personality or intelligence. Although these appear to an outside observer as self-governing entities capable of evolving over time, adaptive stochastic automata are collectively nothing more than dynamical yet impersonal state- & rule-space systems behaving in accordance with their internally ever-changing algorithmic adaptations; a “collective organism” not unlike a flock of birds or school of fish, albeit with far more complex behavioral patterns due to the continuous swapping of state- for rule-space at each progressive generation.


In ancient times, those whom we would now regard as scientists were seen as wizards or witches, yet the works they performed were not founded in wizardry, witchcraft or magic, but the universal mathematics of all things. There is neither “good” nor “evil” in mathematics, merely that which is right or wrong. And, with algorithms, it’s even simpler, since something cannot even be considered an algorithm unless it returns a result.

Still, this old prejudice seems to persist: Based upon some of the feedback we have received, there exists a subset of individuals who find adaptive stochastic automata a “spooky” concept, as if we are (and I quote) “trying to cast spells by creating and releasing automata that start out with intention but have their own evolvement and self-adaptation seemingly outside of the original intention.”

How can this be? Just because a process is not easily understood, does that render it “supernatural”? Just because it does not originate from a source of which all are generally aware, does that mean it stems from “secret knowledge”? If so, then its most fundamental, underlying principles like quantum decoherence must be pure magic!


We live in a world of wonders, of technologies advanced far beyond what prior generations would have even dared to dream. In this same spirit, we, too, must advance with open arms (and minds) to embrace the previously inaccessible potentials they offer, rather than reverting to the same old superstitious suspicions which held us bound fast in the past.

This is an amazing time, some of it even beyond our individual understandings.

Deal with it. šŸ˜†

Leave a Reply

Your email address will not be published. Required fields are marked *