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An astonishing mathematical puzzle holds a clue to how reality is woven and destiny is evoked. Note: It is necessary to watch the video to understand the basis of this commentary.
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Derek @ Veritasium decided to “go deeper” on an astonishingly counterintuitive mathematical puzzle. He did a great job with the video but in my view he only sparked an inquiry to something much deeper and more meaningful to us conscious humans who find ourselves making decision after decision as we wend our way through our lives. We wonder whether our decisions are beneficial to ourselves or promote what we value. Most of us retain a sense that it matters, that somehow the results we could evoke depend on good decisions. But it also seems there’s little understanding of what all goes into making good decisions. At an elementary level, most of us learned the difference between some good and bad choices from past experience, remembered the lesson, and have the will and discipline to apply it, they should fare better than an unlearning fool who merely acts at random. But this sort of advantage is both obvious, simple, and behaviorist, which implies that even an automaton, a programmed machine, could do as well with its choices based on similar methods.
Nowadays I think many are left assuming there is nothing more to be known about the best way to proceed. We feel alone, dependent on our experiences, and though interested in the experiences with others which we can apply analogously to our own cases, we’re ultimately just operating on the experience-based model through our self-guided wills.
This “math puzzle”, though, demonstrates that something much deeper and amazingly valuable is available to us as we move through our interactions with the world. This something in the model, explored as the puzzle, produces an almost 10% improvement in successful outcomes for each individual who participates and an almost infinite improvement in outcomes for them as a group. So it’s something that makes a big difference in outcomes for these participants… shouldn’t we try to understand just how that advantage works and how to apply it to our decisions in general?
To tie in a basic analogy, think of the
Now, let’s continue extending the analogy and ask some important questions:
What exactly is different between entering the room without a plan and entering the room with the plan which created the big advantage?
Where did the plan come from?
What’s the ontology of the plan? That is, what kind of thing is a plan? Is it a real thing in the real world? A bit of knowledge? A bit of wisdom? A sense of purpose?
Even if you just stick with the ultra-simple puzzle as itself, the mystery of this plan’s nature, its derivation, its effect on the behavior of the prisoners, and most importantly, its impact on the success rate of the prisoners, are all quite astonishing to us. There’s something here that’s important but hard to understand. This deserves our attention until we grasp what it should mean to us. Let’s dig into this bit about the plan and how it works, because this is where all the magic is found.
This plan the prisoners each come in with seems to create something within the room. Specifically, it creates these “referential loops” from an otherwise unrelated set of slips in boxes. But what exactly do we mean by “create” here? It’s not as if any aspect of the reality in the room is reconfigured by the imposition of the plan. The slips and boxes are all pre-configured when each prisoner enters. They don’t move around even as the prisoners engage with them. Without this plan, these loops are effectively hidden, or perhaps just as correctly can be said to not exist at all. Somehow this plan evokes the loops by establishing relationships among the boxes and their contents, and thereby guidance for the journey of a prisoner through the room. This is amazing.
Let’s note too that these relationships between the boxes and slips are NOT somehow specially built-in just to favor this one plan. That is, it’s possible to come up with a different plan that creates the same kind of loops and yet loops with completely different contents and sequences of boxes. As Derek showed in his video, a different plan produces different loops (but still loops!), and changes of the configuration don’t change the statistical basis of the outcomes, though the outcomes for any single attempt will of course vary under different configurations or different plans.
So it seems that as long as all the boxes each contain one unique slip, and the slips each relate to a specific and unique box in discernible ways, imposing any of a large set of possible plans will evoke these loops out of those relationships. And if these loops are faithfully navigated by the participants, the transformation of the outcomes to significantly improve their success is statistically assured.
So we should inquire into just what kinds of plans will achieve these results. I’m going to skip it for now, except to note the following:
What we’ve covered so far helps us understand that it’s the closed and entire relatedness of the slips and boxes which produces the possibility of defining the loops. The plan then provides the definition of the loops, effectively creating the loops out of the raw information already present in the room’s configuration. Are all the loops present absent any plan? No they aren’t. However, the room does represent a superposition of many loop-enriched states, a pregnant substrate from which can be evoked any set of loops, lacking only the plan by which to define their existence. Add the plan, then you get the loops, and with them a sense of order from a random distribution of information, as well as the path to improved success. That sense of order could be called meaning. That path to success could be called purpose.
The way the plan evokes the loops is the same way our observation of a particular patch of sky can evoke a rainbow. When the sky is in such a state that raindrops are falling through it and sunlight is streaming into it, an observer in a certain place can see a rainbow. To extend the analogy, the raindrops are like the boxes, and the assignment of the slips to the boxes is like the sunlight. The light is bent and scattered by the raindrops in lots of directions and lots of patterns, producing many potential rainbows for a set of possible observing locations. But there’s truly no rainbow until the observer looks at that patch of sky from his or her validated perspective. That look at the sky is just like the formulation of the plan for the prisoners. It’s a position (for the prisoners the position is the number they themselves wear) and an approach (an intended way to select boxes and interpret slips, or in the rainbow analogy, a look at the right part of the sky) to engage with the entirety of the situation.
I’ve used the word superposition to describe the totality of all potential loop systems which might be evoked from the room’s configuration. That’s because this analogy holds very well to understand how quantum superpositions “collapse” or “are selected” to produce the reality which is experienced by related material beings. To observe in the quantum experimental sense is to engage in interpreting the configuration of the environment, just as a prisoner executes his plan in the room full of boxes and slips. When all the prisoners engage the room with the same plan, they all experience the same reality or system of loops, even though their different starting positions will often put them on different loops during their engagement. To explore the analogy further, let’s use the double-slit experiment as our quantum nature demonstration. When we configure the slits, the light source, and the detector, we are effectively imposing the “plan” for evaluating the behavior of the light beam, while the physics of the light beam and the material used in the apparatus are like the boxes and slips. Evaluation (reading slips) occurs as we measure the incidence of photons on the detector. The position of the interference patterns evoked by the physical configuration of the experiment are analogous to the loops that were evoked from the plan we gave to the prisoners.
I’ve brought quantum physics into this essay to address the confusion many people have about interpreting quantum behavior. Confusion about the role of the observer and the nature of “collapse of the wave function” is cleared up when we use a suitable analogy like this prisoners’ puzzle to better define just what an observer brings to the experiment. An environment in which quantum states are present but un-entangled and un-collapsed, is just as real as a material environment where those states are well bound into matter. Some would say that conscious knowing is required to evoke the collapse that comes with observation. This seems supported by the idea that a “plan” for testing the contents of the boxes is required to evoke the “loops” from the otherwise patternless configuration of the environment. But this just brings us back again to needing to take a closer look at just what a “plan” really is. Must the plan be “known” by a “conscious” participant? Or is the plan itself just a configuration operating on another level. This seems true when we consider that consciousness itself is a higher-level ordering of relationships among conceptual states, and within that consciousness we can host such a plan. But other kinds of configurations can implement other plans that would be suitable to produce the meaning and purpose that does the trick. For example, a collapsed (quantum stabilized) configuration of matter, like for example a ceramic cup, itself represents a plan in its design. That design, just a configuration of matter, evokes shape from liquids that are dumped into it. Taking this idea back to the quantum layer we can say that uncollapsed quantum behaviors can be thought of as unformed potentials to take on configurations as matter and energy which participates in a meaningful way. Our experiments are like the cup, and the quantum flux is like the liquid.
Now that we’ve explored how the plan works to create the experience, let’s revisit the earlier exploration of just what kind of thing a plan is. It’s not the starting state of the participant, and it’s not dependent on the specific configuration of the room, although the room does need to be configured according to some rules of relatedness. The plan is an ordering concept which is held by the agent as a means of interpreting experience. It’s a way of understanding the information that is produced when interacting with an opportunity. It is a kind of guidance, an algorithm, or decision-making tool.
As a sort of game theory thought experiment, the prisoners’ stakes in the model are set very high. For example, they all must: