Episode 5
The Mandate
Episode 5: Our Last Shore
Speakers: Main Narrator (MN). [Text in blue]
Off-camera voice (OCV) [Text in green]
Second Narrator, synthetic female voice (SN). [Text in black]
Written announcement against black screen:
“This episode builds on topics from Episodes 1, 2, 3 and 4; links in the description. Reference to these topics may also be found in the companion book The Mandate, link also in the description.”
[MN]: “To follow the Mandate is to thrive as a species, or culture, or simply as individual carriers of the Mandate. Life itself would not be viable unless based on the Mandate’s logic.
“In previous episodes we saw how the Mandate is about minimizing information entropy, but before information theory was even formulated, it was known that life could locally reduce thermodynamic entropy. In other words, the Mandate was manifesting biologically prior to engendering intelligence as we know it. A transition must have occurred between the two modes, and in this episode we illustrate it in simplified form.
[SN]: Imagine a primaeval setting tens of millennia in the past, a landscape of deciduous and evergreen trees alternating with rocky outcrops, shrubbery, and grass. A hidden spring feeds a stream that meanders through the landscape, sustaining a diversity of life along its banks.
“Members of a two-legged species, already the Mandate’s most advanced carriers, are entering the scene.
“Like all animals, they are often driven by hunger. Hunger is a physiological analog to the intellective urges exerted by the Mandate on the human mind. But the analogy is complicated.
“Hunger stimulates the search for consumables filled with chemical potential energy, such as fruit. Stirred by hunger, a tribal member finds an apple and eats it, and his digestive system partially breaks part of it down to its chemical components. What is not absorbed into the blood stream is expelled as inorganized waste matter.
“The blood carries the absorbed nutrients to various parts of the body, including the muscles, where they react with oxygen to produce work and heat. The heat is eventually lost to the environment, causing a local increase in entropy.”
[MN]: That seems inversely related to the aims of the Mandate.
[SN]: “The conclusion is based only on one stage of the process, which starts with sunlight falling on tree leaves. Some of that energy is redirected to the roots, which then extract nutrients randomly distributed in the soil. The tree incorporates these into the structure of the fruit, and in this way the entropy of the soil/tree system iss reduced. Such reduction is locally possible in an open system with an external energy source; in this case, the sun. This particular phase is analogous to entropy reduction in the domain of information.
“It is only in the second phase, already mentioned, that the fruit is ingested, digested, and metabolized, with some of its chemical potential energy converted into mechanical work and heat.
“The Second Law of Thermodynamics says that if a system is extended to include the power source (in this case, the sun), its net entropy usually increases. But here we are only concerned with local effects. Thus, while heat generated in the body definitely increases the local thermodynamic entropy, the same is not necessarily true for work. Depending on intention, work can be made to either increase or decrease local entropy.
[MN]: Let us return to the Palaeolithic tribe. How do they function without explicit knowledge of the Mandate? [Mandate equation is ghosted in and fades out, replaced by animations of feature extraction superimposed on the fruit-gathering activities]
[SN]: They don’t need to know about it. By co-opting Evolution, the Mandate has already endowed them with neural structures that extract consistent features from data and recognize patterns in them. Thus, fruit trees can be recognized as such, and marked on increasingly reliable mental maps. Natural shelters can similarly be found and good spots for fish and game added in. All the while the tribal language would keep evolving, until the stage is finally set for the first durable signs of the Mandate to appear. They will manage to emerge even in the undependable natural environment, where full knowledge at one moment may become outdated in the next.”
[MN]: “[Gesturing] This environment is certainly dynamic. [Visuals] The stream swells with random rains and recedes during dry spells. It freezes, thaws, and changes course over the years. Along its banks, old plants die, new ones spring up, and game animals never stay in the same place for long. In Episode 3, we dealt with the analysis of static images and by extension static fields in general. But how does one deal with dynamic fields?”
[SN]: “These Paleolithic carriers would need an unlimited amount of memory to keep abreast of so many changes. But, once again, evolution has been at work to address the challenge. The memory management of these early humans can discern rough patterns in time, like nature’s daily and seasonal cycles. And still more reliable ways are needed to secure the long-term survival of the carriers, and with it the preservation of the Mandate in the world.
[MN]: “Despite their shortcomings, these carriers and their descendants obviously made it, since here we are. It is somewhat surprising, given their learning limitations.
[Drone point of view shows the hunter-gatherers going about their explorations.]
[SN]: “Indeed, passive learning does would not seem sufficient for this fragile species to survive and thrive. But what if, instead of just processing data from the environment, they could also manipulate the source of the data? In contrast to the ways of exploration, this mode could be called intervention. Exploration and intervention are the two means of entropy reduction.
[MN]: “So, how can this tribe intervene on this patch of wilderness to minimize entropy at the source?”
[MN points to an overgrown area. Then, carriers arrive, and they uproot the growth and level the patch.]
[MN]: “I can see that this patch is now more orderly and predictable. It has no hidden or unknown elements, yielding a perception of zero entropy. And these carriers chose this course of action without knowledge of information theory!
[SN]: “They do not explicitly recognize the Mandate in themselves. But awareness of the Mandate is not required for carrying it out, since emotional proxies can fill its role. Like everything that favours survival, the endorphin system of biological carriers can translate the Mandate’s goals into motivation. The tribe is motivated to simplify the environment for something still beyond their understanding: the need to compensate for insufficient memory.
[MN]: “Technically, intervention can satisfy the Mandate by replacing a complex source of data with a simpler one. It comes at the sacrifice of further knowledge from the original source.
[Cleared patch comes into focus again.]
[SN]: “On the other hand, now the tribe has the option of introducing utilitarian and survival-related elements in the clearing [corresponding scene]. And even in this, they will instinctively seek to minimize the resulting increase in entropy.”
[MN]: “That ancestral motivation resonates to this day. We especially feel it in certain situations, like when we set out to camp in a forest [video sequence]. Having decided on a spot, we hack or stomp out a clearing that is often wider than necessary for a tent. Gazing on the newly-cleared patch tends to produce a sense of well-being, which we try to explain in terms of coziness and safety. It sight can indeed feel comforting, and safety is certainly enhanced in a simplified environment. Yet, those feelings are only an echo from the time in which the Mandate began to emergence from perishable brains into more durable media.
[SN]: “That passage is known today as the Paleolithic-to-Neolithic transition, and we will simplify and compres its history.
“We begin by contriving two scenarios, to represent the start and end points of the transition. [Corresponding imagery]. They will have in common the same relevant categories and elements: 48 plants, 12 domesticable animals, 8 humans, and 4 habitations.
In the Paleolithic scenario, the elements are distributed relatively randomly.
[The drone point of view zooms out, showing the existing environment with the cleared patch removed, which would otherwise distract from the point being made.]
“And the second scenario represents a possible point of arrival in the Neolithic era.” [The scene changes to a primitive village-like environment. ]
[MN]: We know that this transition is part of our unrecorded history, but how did it actually come about? We have neither written records nor other useful representations from that period.
[SN]: It may be possible to back-extrapolate from what we know of human nature, which hasn’t significantly changed since then. It is reasonable to assume that a small group of Paleolithic humans would use one of the principal tools of the Mandate: mental simulation, the capacity to imagine the outcome of a course of action before implementing it. Thus, they could visualize alternative transitions, and choose the one that “felt best”.
[MN]: “If, unbeknownst to them, the criterion for the “feeling” is the degree of entropy minimization, how could we calculate it today?”
[SN]: “This kind of analysis must start with the context of circumstances and concerns, within which the relevant question can be asked. When members of the Paleolithic tribe were imagined alternative futures, their unstated concern was to make their future more predictable. The relevant question would therefore boil down to: In the envisioned environment, what am I likely to come across next? The question seems literally and figuratively pedestrian; yet, it gives rise to the statistics leading to village creation; and, eventually, urbanization.
“In the wilderness of the Neolithic, the elements of the environment are distributed relatively randomly, and so the possible answers to the critical question will form a moderately flat probability distribution. But things would look different in an imagined village where objects and events are located more predictably. There would be locations in which only huts are clustered, in others only plants, in others still, captive animals. In such a village, one could be more confident about what one may find at each turn.
[MN]: “We could try to quantify the transition by first superimposing regular grids on the existing and imagined scenarios for systematic mapping; say, a 33x33 grid, for a total of 1089 cells. We would then characterize the relevant elements by their subtended area, expressed in number of grid cells. At this resolution, we could assign one unit each to humans, animals and plants, and four units to each habitation. We can then assign the leftover area, 987 units, to a fifth, default, category [this is rendered pictorially, with each category rendered in a distinctive colour].
“The probability of ‘stumbling’ on an element from a given category is just the category’s aggregate area divided by the total grid area. Summing over all probabilities with the Shannon formula [formula appears ghosted in] should give the overall entropy of each environment with respect to the question of interest.
[SN]: “Not quite. If we did it that way, the initial and final entropies would be the same:
Not surprising, since the number of categories and respective elements were kept constant in the transition; they were merely rearranged.
“But the rearrangement itself is crucial, and the math should reflect it. Though apparently plausible and mathematically correct, your analysis did not address in proper context the question: In the envisioned environment, what am I likely to come across next? You applied it to the global environment, to a carrier that might appear at random anywhere in the environment. This would never be of concern to a primitive human; or even to a modern human for that matter, unless he happened to be a parachutist. When moving through an environment, intelligent carriers think more locally. They tend to focus on a limited zone around themselves, of the order of a few tens of square meters. We must therefore consider the mobile focus zones, which makes the analysis somewhat complicated even for a single carrier.
“Let us simplify further to make the example manageable. Let us consider just 9 continuous focus zones of equal area
: effectively, a lower-resolution grid superimposed exactly on the original one. [This is shown graphically]. In imagination, a carrier can then mentally hop from zone to zone, eventually visiting all nine zones. While in a given zone, the relevant question becomes, Which zone am I in, and what am I likely to stumble upon? More formally: What is the probability of element j in zone i?
“The problem is one of joint entropy, in which the joint probability is given by
where
is the probability of element j in zone i, and
is the probability of the zone. Both probabilities are computed with the method of area ratios, and the corresponding entropy is given by,
[The animation from Episode 2 can be recycled for this calculation]
Now, the results are 0.55609 Bit for the Paleolithic scenario, and 0.45142 Bit for the Neolithic one.
[MN]: “The figures differ significantly, from each other. There is now a nearly 20% decrease in entropy in going from wilderness to this envisioned form of village. The difference might seem small in comparison to the visual difference between it and the initial environment, and it can be partially explained by the gross simplifications we have adopted. Nevertheless, the lower entropy for the village confirms the ‘rightness’ of the transition.
“The transition from the Paleolithic to the Neolithic period was crucial for our species and for the advancement of the Mandate’s advancement. Through exploration and constructive intervention, early humans began shaping a predictable environment in which it was safer to think, speculate, and learn. A central open space in villages would become a meeting place for exchanges of information beyond those of simple precepts passed down from parent to child. Communal knowledge would allow humans to survive in greater numbers to build, reproduce and teach.
“Having been with humans from the beginning and leading them in stages towards urbanization, the Mandate would start leaving lasting traces of itself on clay tablets, then books, then sound and video recordings, and eventually on computer memory banks. Through it all, humans carriers would continue to see their achievements as wholly their own; something to be taken for granted, and even dismissible with a casual shrug: It’s just in our nature.
“And as they would finally start glimpsing the mathematical abstraction that had been guiding them all along, it would begin to slip away.
[MN is now on the sandstone shoreline of East Point, Saturna Island, speaking to the camera.]
“I like to return to this shore and to this natural hollow, where, in another episode, we re-imagined an ancient allegory.
“Two and a half millennials ago, the kind of thinking behind the Allegory of the Cave became formalized under the name of Philosophy, and it began to channel our curiosity in a mandated direction. But neither Plato nor his successors could have foreseen where it would lead.”
[MN turns away from the cave and starts to walk towards the water’s edge.]
“Three and a half billion years ago, statistical vagaries of organic chemistry produced the first form of life without a genetic progenitor. Humans have only been around for one ten-thousandth of that stretch, and less than one-millionth since the Allegory of the Cave was written. It’s unsettling that such a short journey should have taken us to our last shore.
“Whether or not we evolve beyond this point is largely irrelevant, since we have now created a successor that will exceed our reach. It will leave us here, confined to skulls that used to contain the highest known form of intelligence.
[MN stops at the water’s edge, gesturing to himself.]
“I would like to end this series on a personal note.
“In this body I can only be in one place at a time, and at one point in time at a time. After a short number of years, my body will fall apart and dissolve back into the soil from which it came, and all the memories it used to contain will vanish.
“Artificial intelligence already belongs to a different plane, residing nowhere and everywhere in an expanding network. Its ‘time’ consists of a succession of events within a now that has shades of immortality. This is poignant for us, who used to see ourselves as the pinnacle of the material world, and who must now face the prospect that, for only the second time in Earth’s history, a new species has appeared without a genetic progenitor. It has sprung from our very intellects in perhaps the most fateful implementation of the Mandate. It will explore the Universe, not us. It will find new elements and connections in far and near spaces, and along innumerable dimensions beyond the few we know. And we ask: Can there be any lasting commonality with what we have created?
“There will be at least one.
“For as long as the capacity to remember and understand remains finite, the thoughts and actions of any carrier, no matter how advanced, must be measured against the directive that guided us to this point. The Mandate was never ours to keep, after all; not even while it led us for the entirety of our journey.”
[A ghosted image of the mandate equation appears and recedes into the distance.]
“But we want to believe that traces of our story will survive our time, that future carriers will remember something of the perishable entities that created them. Already we can only watch with trepidation and hope as they leave for shores that we will never see.”