Look at your surroundings.

Now, explain how you got here.

Did your answer include the creation of the universe, perhaps the The Big Bang? If not, your answer is incomplete.

A Reason is Born

Don’t be too hard on yourself. This prompt is typically interpreted as a request for the most immediate and significant reasons for being here, such as: “I fell off my bike and broke my arm, so now I am in the ER”. Your explanation did not need to be 100% complete to sufficiently answer the question. For obvious reasons, it is impractical to describe The Big Bang and then every sequential moment that led to you falling off your bike. Nonetheless, let’s examine the reasons: (1) ain’t nobody got time for that. (2) any attempt at a complete explanation would be riddled with false assumptions and inaccuracies. Nobody has observed every moment in spacetime, nor possesses the memory to remember, nor the processing capability to completely comprehend these moments. The main point here is that there is a reason for being (not to be confused with purpose, although purpose is an important part of this story). The reason that ‘you’ exist is because your dad’s sperm fertilized your mom’s egg. Somewhere along the way, ‘you’ came into existence*. However, both this explanation and the previous answer to “Why did you fall off your bike?” require infinite precision to achieve perfect accuracy (we obviously do not care about 100% accuracy in all cases, nor is 100% accuracy attainable). This is what we will explore in this post.

Elements of the Mind

We usually do not care about The Big Bang when examining our current position in life. Instead, let’s view the most important epoch of history -- your lifetime -- everyone is the hero of their own story.

Let’s begin at the moment in which ‘you’ obtain consciousness** (ironically, a moment that nobody remembers). Upon accessing reality for the first time, you are immediately introduced to the cause and effect protocol of the universe, become aware of your existence (‘consciousness’), as well as develop an awareness of ‘thoughts’ and a procedure of thoughts (‘thinking’), obtain (some level of) control over your body and thinking (‘agency’), and privately experience a sequence of sensations (‘perception’). We eventually learn about reality by perceiving stimuli and conceiving a model of its existence and relations to other phenomena (‘intelligence’, ‘cognition’, ‘understanding’, or as I like to say, ‘the ability to connect dots’). In this case, the dots are bits of observed data (‘information’) which are interpreted into truths (‘knowledge’) and stored in our ‘memory’ as associations. It is almost as if reality is a Turing-Complete system (a BIG assumption, formerly known as the Turing Principle), and our brains are a universal Turing Machine (another BIG assumption in some computational theories of mind). The conspicuous mystery in the brain-computer analogy is our ‘imagination’ -- the power to “see without seeing”. It is not obvious how a program for imagination would run on a Turing Machine, making humans extra interesting. The human brain (our “interpretation machine”) is unique in the world and, despite tremendous progress in neuroscience, still not very well understood. We are also skipping the sub-conscious element of this model for now … but will discuss it later.

Trapped In The Present (Mind)

A primary justification to study history is to learn knowledge that helps us in the future. At birth, the knowledge at our disposal is inherited from our birth family -- programmed in our genes or endowed via generational wealth (the type of wealth that confers power to effectively control one's environment) -- and depends on when, where, and into what circumstances we are born. At this point, our minds have yet to be infiltrated by the ideas of our contemporaries. We commence our personal learning journey with phenomenological experience by observing actions that punish us with pain and those that reward us with pleasure. In the pursuit of our desires, we eventually learn to communicate with others using language, trade ideas and inspiration with them, and trust their observations and accounts of history***. After all, we cannot physically observe everything ourselves, and humans have merely scratch the surface of permissible experiences. Furthermore, your first conscious moment is different from my first moment, and our experiences may never overlap in any significant way (disregarding butterfly effects for now ... and the fact that you just read a sentence that I wrote).

We can hardly recount the past with confidence, especially past events that we did not personally observe. (And even when we are the primary source, our memory is fuzzy since our brain stores information in a compressed and unreliable manner, like a computer hard drive, occasionally failing upon retrieval (though, we have the faintest idea of how the brain stores or recalls memory). Our memory could utilize a vastly different mechanism than modern computers. Memory caches and RAM seem to roughly correlate to short-term memory and long-term memory respectively, but the correspondence is ambiguous and has glaring disparities). You will trust your memory even less upon realizing that memories and hypotheticals are metaphysically identical, both existing as a pendulous thought in the mind. Each of these thoughts comply with our present experience and current conception of the world -- a memory supposing what happened and a hypothetical envisioning what can happen (or what could have happened in another time or space … perhaps in the future or past or in another possible world). Given the limits of our brain, it only seems fair to offload some of the processing to our peers, and in modern-day times, to our computers too. The library gives us a headstart on our learning journey by instantly exposing us to Lindy ideas and novelty, but canonical teachings can also be misleading when approached without vigilance. The famous motto from The Royal Society is pertinent here -- Nullius in Verba -- “take nobody’s word for it”.

Narratives are more convincing when there is evidence to corroborate it’s truth. However, evidence is simply circumstantial information. It does not have the power alone to prove, or even directly support, the truth of a story. The sole power of evidence is refutation -- disqualifying a conclusion in conflict with the evidence -- thus indirectly supporting the surviving conclusion(s). (And only “supports” when there is a finite set of competitive conclusions since the “support” points equally towards all remaining competitors.) Proof is discovered by proposing a valid conclusion, one that is consistent with the current evidence and most resilient to the evidence yet to be discovered in the future. We commonly “jump to a conclusion” by conflating evidence with proof. Instead, we should think “what world could have left this evidence?”

"Discovery is seeing what everybody else has seen, and thinking what nobody else has thought." -- Albert Szent-Györgyi (1893 - 1986)

Let’s imagine that we are detectives hired to investigate a crime. The objective of our investigation is to resolve the crime (as it typically is) by figuring out what happened, and how and why. In other words, we need to create an explanation of what happened to justify the repercussions. We recall from watching crime documentaries that a proper investigation commences with a combination of collecting evidence and conjecturing about what happened (to know when and where to look for more evidence). As we will discuss later, the order of these operations does not matter as long as our conclusion depends on an individually necessary and collectively sufficient set of evidence. We will inevitably introduce bias into our evaluation of the evidence since we view the world through a perceptual lens in a subjective scope. But, by keeping a grain of salt in our investigatory lens, we may account for psychological factors (motivations, ideals, cognitive bias, emotions, etc.) influencing which evidence we look for, notice and pay attention, and our phenomenological experience of said evidence. The salt is a token to remind us that subconscious psychology is a layer of our perception. (Not to mention the neurochemistry from which our percepts emerge.)

The rest of our phenomenological experience comes from sense perception. We have sense organs with receptors tuned to receive specific input (and not other input) returning a complex neural impulse (coding for a specific mental state) which compels us to react in particular ways. We tend to forget all of this in the heat of the moment (including the physical limitations and fallible interpretation of sensory experience and of our understanding of human perception). It is reasonable to assume that photons have always behaved in the manner that we perceive and understand them now -- as a quantum of radiation in the visible light frequency spectrum. According to our cosmological theories (and for the sake of the argument), photons have almost always existed (actually existed with real historical impact, not just abstractly in the imagination of a human). However, the human instruments for biological detection and conception of photons are practically current events in the grand scheme of history. A common example of sensory tuning is the comparison between homo sapien sight and that of a butterfly. Humans naturally perceive photons (light) in the visible spectrum (a very anthropocentric classification) through the retina and optic nerve. Meanwhile, butterflies perceive most of the light in the visible spectrum and also light in the ultraviolet spectrum (which humans only recently discovered in 1801 and may, at best, only imagine the experience of ‘seeing’ ultraviolet radiation. This makes it more difficult to conceive of its existence and effects). In many cases, we can do a bit better than “eyes-closed” imagination because we can create artificial ‘sense organs’ with instruments that imitate a particular functionality. A prime example of a synthetic sense organ is a pair of infrared goggles that ‘sense’ infrared radiation waves (which we cannot see with the naked eye) and translate those input signals into an output pattern of pixels on a screen display emitting visible light (which we see with the naked eye). The respective tuning of sense organs (eyes in the optical case) to an environment is attributed to evolution by natural selection.

Most biologists accept the theory of evolution by natural selection applied to genetic information (DNA sequences, eg. genes). Far fewer scientists are familiar with the deeper concept of The Evolution of Everything, namely knowledge replication, which describes the propensity to observe information most adapted to its niche. The adaptiveness of knowledge is equivalent to its persistence across possible worlds (and as a measure of the quantum multiverse…more on this later) which is discovered through interactive “trial and error”. The proliferation of knowledge representations is a unique feature of conscious, intelligent life and abides by the same laws of evolution (i.e. memes and other ideas … a topic for another post). Scientists routinely apply evolution to theories without even recognizing the evolutionary structure of their reasoning. It is important to note that evolution is spacetime-dependent and exhibits locality, which means knowledge replication depends on the specifics of its point in spacetime and only interacts with proximal points. Knowledge at one point in history may not be adapted to other points.

The Truthseeker who adopts realism and objectivity, both of which have proved to be useful for the purpose of science, is well on its way to discovering replicable knowledge. Despite this noble pursuit, the Truthseeker may become frustrated as it bumps up against the limits of its understanding imposed by its present mental faculties. Like the Truthseeker, we tend to find ourselves grasping at illusions as we stumble through our perceptual simulation of the world. We discern phenomena at various scales, but are mostly confined to a small spacetime interval. Our phenomenological experience is determined by the conscious and subconscious, visible and invisible, explicit and inexplicit, conceived and unconceived, expected and unexpected, understood and misunderstood. The function of our imagination, senses, memory, and perceptual tools was selected by nature and is optimized for replication, not Truth.

Let’s resume our crime investigation and say we find an eye witness to the crime. Following forensic best practices, we scrupulously reconstruct the eye witness’s perspective to discern the truths in the account. Conveniently, humans share the same sensory apparatus with one another, which means there will be little variation in our sense perception when compared to that of the witness. We can trust our eye witness had similar sensations and shared common aspects of the phenomenological experience with us. We need a dash of cynicism to apprehend the idiosyncratic psychology and personal motives layered into the witness’s account at the interpretation level.

Since phenomenological experience depends on the observer, rather the observer’s perceptual tools, it follows that a historical account must contain subjective bias and requires faith in its resemblance to truth (and we usually realize overconfidence). For example, the discovery of fossils indicates the existence of extinct dinosaurs. And we can even imagine what they might have looked like! However, not the fossils nor the present-day graphical renderings ultimately prove dinosaurs’ existence. The evidence, fossils in this case, simply exists and humans suggest plausible explanations for its existence. A different explanation for the existence of fossils could be that an egotistical scientist synthesized organic bone materials in a lab and subsequently buried the fossils to claim fame once she later “discovers” them and proposes a breakthrough theory of dinosaurs. However, there are sound reasons that discredit this explanation. For instance, there is no evidence of a scientist or lab in 1677 (when Robert Plot found the first fossil) that had the capability to synthesize an organic material that could resemble a fossil. Also, there was no way of digging to those depths of Earth’s crust undetected since the process of digging would have left its own evidence, which was never reported. The totality of conflicting evidence (and lack of corroborating evidence) makes the “mad scientist” explanation ‘problematic’. A better explanation is that large prehistoric animals roamed the Earth many millenniums ago whose remains were naturally buried and preserved. There will always be missing context, so we will never have a totally complete nor perfectly accurate account of history. But, not all context is necessary for a valid conclusion. This is the essence of Relevant History.

The most influential theories garner mass consensus (a flawed method for finding truth … though it does provide a clue). There is a well-known saying, “wisdom of the crowd”, accompanied by a lesser known but equally prescient saying, “fatality of the mob”. The objective of consensus is to win a majority, which requires compromise****, not truth-seeking. The danger of deploying consensus as a measure of truth is it leverages groupthink. When everyone thinks that the other person has done the necessary due diligence on an idea, nobody ends up doing it. The errors bars of a consensus value also scale according to the contentiousness of the minorities. Consensus provides a signal for extrinsic sociology and psychology of the matter moreso than the intrinsic epistemology.

Here’s another trope: “history is written by the winners”. This may not be strictly true in its literal translation but captures the inextricable bias of historical accounting. The history textbooks are missing many facts, particularly from the loser’s point of view. The publisher is not entirely at fault -- there are typically less of the losers around after major evolutionary equilibriums like war, and the historiographer’s best interest was to align with the winners and paint them in the best light. Regardless, the missing context make the history book’s content sensitive to a combination of bias -- hindsight, confirmation, selection, conformity, misattribution, and survivorship to name a few.

In light our parochial worldview, it is tempting to meander into Skepticism. Reasoning is the only escape.

The Primacy of Explanations

When I stumbled upon Laplace’s Demon for the first time, I was convinced that the world must be fully deterministic because of the principle of sufficient reason (PSR) – the evident principle that a thing cannot occur without a cause which produces it. PSR resonated with me so deeply that it felt undeniable. I have since come to see it as a good explanation.

“Nothing would be uncertain and the future, as the past, would be present to its eyes.”

--Marquis Pierre Simon de Laplace

A hypothetical ‘Demon’ intelligence has the view from nowhere. With its perfect knowledge, chance ceases to exist. To emulate the Demon is to take PSR to its natural conclusion, Fatalism -- the concept that what happens and what will happen was always going to happen and is the only way it could have happened. This is disconcerting news for sentient beings who frequently wonder “how can I prevent undesirable happenings?” I encountered a revelation while reading David Deutsch’s The Beginning of Infinity, thankfully extinguishing my dismay*****.

The main takeaway from the book is the answer to the question: What does it mean that the omniscient Demon knows everything? The answer: It means that the Demon can correctly explain anything, and with this perfect ‘understanding’, can accurately describe and predict everything. Luckily, we share this first capability in common with the Demon because we possess ‘creativity’ -- an ability to create new “ideas” (no matter that these “ideas” are determined and were always going to be created) -- and criticism -- an ability to spot errors. Deutsch also proposes that phenomenological emergence and computational universality jointly imply that humans do not need to know every fact that exists in order to know anything that could be known (though Gödel may have qualms with how we define knowledge, more on this later). More succinctly, you do not need to know everything to know anything. What a relief!

By marrying two concepts -- the ‘Human Brain as a Universal Computer’ and the ‘Infinite Demonic Wisdom’ -- we find that humans are universal explainers because our brains are constantly running a program that perceives and evaluates the universe. This marriage implies that anything which is explainable is explainable by us, and we improve our understanding with better explanations. That said, the universe never asked to be understood and was not necessarily designed for us to understand it intuitively. Humans have evolved to understand explanations and seek explanations to solve problems. Our scientific predictions are continuously getting more accurate and, more importantly, our understanding is more adapted, insinuating that we can make progress towards more objective knowledge. One need not look further than the trends in average human lifespan or GDP per capita or at modern medicine to be convinced that our collective understanding of the universe is far more resilient than its forebears.

Another big takeaway from the book is Deutsch’s principle of optimism: All problems are caused by insufficient knowledge. Let’s define a “problem” as an undesirable state or as the obstacle to a more desirable state. Then, problems are inevitable because our knowledge will always contain errors, and there is always another question to answer. Yet, problems are soluble since everything that is not forbidden by the laws of nature is achievable, given the right knowledge. If something were not achievable, given complete knowledge, then it would be a regularity in nature that could be explained in terms of the laws of nature. Hence, there are only two possibilities: (1) either something is precluded by the laws of nature, or (2) it is achievable with knowledge. Deutsch refers to this as the momentous dichotomy. As we explore reality, inevitably encountering problems along the way, it becomes self-evident that both problems and solutions are infinite. Furthermore, a slight reframing of optimism shows that opportunities are ubiquitous. There is no guarantee that we will solve our problems, but it is possible that we can. Survival depends on creating the requisite knowledge at a higher rate than the onslaught of existential problems. The omniscient Demon has solved all problems.

PSR implies that there is an explanation for everything, so the quest for God-like omniscience is a hunt for good explanations. Unlike mere matters of fact, an explanation accounts for a meta-understanding of why the facts must be the case, revealing The Fabric of Reality. An explanation is simply a proposed reason for ‘being’ or ‘becoming’ that describes the present, the future, or the past. PSR dictates that all claims are the consequence of an explanation. When an explanation is figuratively expressed as a statement, it describes a set of conditions that give rise to the observed world. The conditions also have historical significance for other possible worlds (implications of the future (prediction) or of the past (retrodiction)). Explanations can always be framed as the answer to a ‘how-question’. It is this property that makes a proposition explanatory vs. non-explanatory. A true explanation refers to a Real Pattern in the universe. Accordingly, explanatory knowledge transcends spacetime and may be applied repeatedly to familiar and unfamiliar situations as long as the descriptive conditions and patterns hold.

Karl Popper’s demarcation criterion between a scientific and non-scientific explanation is falsifiability. In Popper’s words, a scientific explanation must have “predictive power” -- the capacity to make testable predictions comparable to evidence (a.k.a. our most persuasive arguments). Predictive power is synonymous with “consequential”, “relevance”, “salience”, “inference power”, which means its truth has testable implications (predictions and/or retrodictions). When Popper refers to scientific falsifiability, he is referring to experimental refutation (in the empirical sense). Non-scientific explanations are not experimentally refutable. However, this does not disqualify non-scientific explanations from containing knowledge. Just because an explanation is indisputable (now) does not mean it cannot be true (now) nor disputed at some point (in time). We can use different modes of criticism to refute bad non-scientific explanations -- Does the explanation create more problems than it solves? Could its contents easily be varied or replaced and remain valid? If an explanation solves a problem, then it constitutes knowledge (even a non-scientific explanation). Failing to acknowledge this fact is the fallacy of scientism. Popper also devised a hygienic strategy for maintaining the falsifiability criterion: when positing a theory one should also answer the question “under what conditions would I admit my theory is untenable” (Unended Quest pg. 42). In other words, which conceivable facts would I accept as refutations of my theory? (As an aside, many investors find this to be a clever schema when buying/selling a financial security: “assuming constant information, at which price should I reverse my trade?” I will have more to say on falsifiability in future posts).

Popper’s criterion says nothing about whether an explanation is meaningful or not. It only demarcates science from non-science. Any explanation that represents a conceivable, graspable reality is meaningful. This is not a claim that every meaningful explanation correctly refers to reality in the sense that its abstract representation corresponds to reality (more on correspondence later).

So what do we do when faced with two (or more) theories that are observationally equivalent? If all of their empirically testable predictions are identical, then empirical evidence alone cannot be used to distinguish which is closer to being correct. (Indeed, it may be that the distinct theories are actually two different perspectives on, or representations of, a single underlying theory.) In cases of competing explanations and in the absence of any relevant evidence, it is logical to apply Laplace’s principle of indifference (also called principle of insufficient reason, “PIR”) which says every competing explanation is equally possible (should hold the same credence, although credence is a proxy for ignorance). If there is no reason to prefer one theory to another, then a commitment to one is definitively arbitrary. Each competing explanation should stand on equal ground until observational evidence (a.k.a. our most agreeable theories) or superior arguments reveal a preference for one.

PIR leads to the underdetermination of theory by data which says that evidence available to us at a given time may be insufficient to determine what beliefs we should hold in response to it (i.e. the mosaic of explanations contains more unknown variables than equations to solve for them). To show that a conclusion is underdetermined, one must show that there is a rival conclusion that is equally well corroborated by the evidence. Let’s apply Baye’s theorem to elucidate the concept of underdetermination:

E(possible explanations | observation)
"Given this observation, the set of possible explanations to expect." Underdetermination occurs when the set of explanations is > 1.

Eventually, even if our criticism fails to eliminate bad ideas, the relentless force of evolution eradicates maladapted knowledge when an unforeseen, critical contradiction with reality causes its extinction. Lucky for us, we can use rational criticism to vigilantly anticipate problems and refine maladapted knowledge before it wipes us out. A “crucial experiment” is a test that is capable of determining whether or not a particular theory is superior to all its competitors (at least those that are presently conceived). Devising such an experiment is itself an act of creativity because the test must discern the historical implications (predictions or retrodictions) that differ amongst the competing explanations:

E(possible observations | explanation)
"Given this explanation, the set of possible observations to expect."
A crucial experiments tests the exclusive disjunction of rival theory's possible observations.

Experimentation is a theory about how to discriminate between theories. It is one of several modes of criticism. Other modes directly attack explanatory weaknesses, including: refutability, self-consistency, variability, conciseness, cohesiveness, complexity, leaving less unexplained, general completeness (can solve more problems/decide more propositions), etc. Therefore, experimentation is appropriate only once an explanation survives those criticisms, so many explanations are refuted without the need for a rigorous experiment. In a physical experiment, the scientist controls the experimental conditions to match those inherent in the unresolved problem and then observes which theory’s prediction corresponds (or not) with the results. And experiments don’t need to be physical. Running a simple thought experiment can settle many arguments. By thinking deeply on an idea, an expert is likely to have considered more plausibilities and observed more relevant thoughts than their peers, so it is reasonable to trust their epistemic positions, not because an infallible authority has been bestowed upon them, rather assuming they have had more chances to refute an idea. (Again, they may have extrinsic reasons (political motives, etc.) for not publishing their rebuttals.) Bad ideas are usually less adapted than good ones, but the bad idea may have extrinsic properties, like virality or shock value, making it more adapted than can be explained purely by its intrinsic properties.

The purpose of observation is to testify against a theory, and it is only reasonable to abandon theories that make false predictions. Of course, experimental evidence alone cannot logically refute a theory without a theory telling us what the observed evidence is. Observations are theory-laden, and theories are error-laden. Without a next best theory to replace or amend a problematic one, it is only rational to assume that a conflict between theory and experiment is the result of experimental error or faulty measurement.

“What I cannot create, I do not understand”

-- Richard Feynman

The building blocks of explanations are First Principles -- the most fundamental truths operating at a particular level of emergence -- and the fuel for progress is creativity and criticism. First Principles are the most critically acclaimed, battle-tested theories at our disposal. Scientific principles (relativity, quantum, evolution, etc.) are continuously tested with crucial experiments to settle old problems and give birth to new ones. Science is an error-correcting process and its theories are engaged in an everlasting trial. If science were a judicial system, it adopts the “innocent until proven guilty” policy. When a theory is “proven guilty”, scientists seek new explanations to remedy the mistakes of its problematic predecessor.

Explanations require imagination because they incorporate the Unseen:

(1.) “Modalities” -- (im)possibilities, contingencies, necessities, counterfactuals, or hypotheticals.

(2.) “Abstractions” -- abstract representations which are further classified into 1. Platonic Objects (ideals, forms, logical structures and propositions, and concepts like numbers, objects, properties, categories, and relations) 2. emergent entities (simplicity that implies something about the properties of complexity, and vice versa), things like financial markets or molecular biology, and 3. imperceptibles (i.e. things not directly apparent to our senses or scientific instruments). For example, we measure the weight of a backpack with a scale which is a function of the massive books inside and gravity. We do not observe the gravitational field, just its effects, which is how we know it exists. We measure the temperature of an atom’s nucleus with a thermometer, but we cannot directly observe the motion of quarks which are the cause (we think) of the temperature measurement that we observe. We access imperceptible phenomena by imagining them and how they interact with other things. Then, we measure their physical effects with finely-tuned instruments, but the empirical data in this case are quantitative measurements displayed on an instrument’s digital panel. The measurement readings that we see are caused by things that we do not see.

Oftentimes, the objective of an explanation is to accurately describe reality so that we may control it to our liking. However, accuracy is not always the highest priority as demonstrated by disinformation campaigns. Since explanations are meant to solve problems, and our problems are subjective, the absolute accuracy of an explanation may be secondary to another purpose. This underlies the importance of considering information sources and seeking ‘good’ explanations. Stop to ask “why and how am I seeing this content instead of another?” A good explanation, like a good lie or conjuring trick, is crafted to persuade the receiver of some reality. The only difference in this case is the intention:

scientist’s goal = understanding vs. magician’s goal = deceit.

In either case, the burden of proof lies with the receiver. The path to the Truth is deciphered with explanations. An explanation could be true if it coheres with other true assertions and prevails against attempts to disprove it. If a contradiction arises, then we may logically ascertain that at least one of the claims is strictly false. In this way, an explanation is our best guess, and even good explanations are at risk of being wrong. This is how we create better, more powerful knowledge.

A good explanation is refutable, convincing, and precisely answers “What?”, “Why”, and “How?”. It is our best description for how something works, why something happened, or why something will happen, at any given time. In a good explanation, each constituent element plays a functional role (individually necessary and collectively sufficient) in explaining that which it purports to explain, making it succinct and hard to vary. A good explanation is hard to vary in the sense that varying its contents, say to accommodate recalcitrant data, alters its historical implications. The invariability principle is important for epistemic value, yet counterintuitive. For example, let’s say there is an original explanation named “Joe”. If alterations of Joe yield the same set of possible worlds as Joe, the world could be described by any one of Joe’s variations. If Joe is corroborated, then we could still reside in any of many possible worlds, namely the worlds in which Joe’s variants are also corroborated, so we gain little information about our specific world. Counterintuitively, the harder it is to vary Joe without altering its history, the narrower the set of possible worlds permitted by Joe, so it is less likely that Joe correctly describes our world. Yet, if Joe is true, then there are fewer possible worlds in which we can find ourselves. The hard to vary criteria is related to the conjunction fallacy which says that an explanation containing many conjoined details is always less likely to be true than a less-detailed but otherwise identical version of the explanation. The more-detailed explanation might appear more plausible, thus more likely to be true, but it makes more falsifiable claims and is more likely to be false (see the Linda Problem). In other words, the details allow the explanation to decide more propositions and generalize over more observations, so it has more chances to be wrong. As Karl Popper says, “good explanations make narrow, risky predictions” appealing to a specific line of reasoning. They dig deep to find the roots at a level of emergence. Try the 5 Why’s method to increase the reach of an explanation.

“Science is a way of thinking much more than it is a body of knowledge.”

— Carl Sagan

Explanations are measured by their explanatory power -- the capacity of its contents (descriptions of necessary and sufficient conditions) to replicate the phenomena it purports to explain. As shown in the bike example at the beginning of this post, an explanation does not need to be entirely complete to be relevant or valuable. Humans inherently recognize patterns in our experience and make inferences on the fly. Some of these inferences spontaneously emerge from subconscious processes. In fact, the type of explicit knowledge to which I have been referring (namely explanatory knowledge expressed as linguistic statements) are completely unnecessary for life. We do not need an explicit explanation of our reproductive system to have sex or of our digestive system to know that we need to eat food to survive. The inexplicit knowledge of ‘sex drive’ and ‘hunger’ are genotypically coded in our DNA and phenotypically expressed as instinctual feelings to guardrail our thinking towards evolutionarily adapted actions and decisions. The genes that anticipated problems with the most adaptive response were passed to subsequent generations. Of course, our feelings can also be misleading and contribute to our downfall if improperly examined. This is one of myriad examples of subconscious knowledge (sometimes called inexplicit or tacit knowledge, or intuition when it involves an instinctual judgement of unknown origin) whose explanatory power exists in the background, unbeknownst to the observer, until it is consciously observed. Only once the phenomena is consciously observed, as a sensation or idea or percept, do we have the chance to rationalize with it and turn it into explanatory knowledge. We might never consciously observe (or come to understand) the exact knowledge that keeps us alive.

We also get epistemically lucky when our best explanations contain adapted knowledge but not for the exact reasons that we thought (see Gettier Cases). The actual knowledge (truly understood or not) interacts with other actual knowledge regardless of its status (or non-status) in the awareness of consciousness. For example, the Mimic Octopus, known for its camouflaging color changes, does not need to understand how or why it changes color, or have a concept of color, or be aware that it changes color, or even be conscious of anything in order to benefit from its color changes. The octopus, if it can think, may believe that it is surviving its shark encounters by closing its eyes and thinking happy thoughts that propagate repellants. An external observer (with visible light vision) would argue that it is the octopus’s changing colors that make it undetectable to voracious predators. The color changes could be purposeful (perhaps intentionally induced with happy thoughts), or they could happen automatically without an inkling of agency from the octopus. It does not matter in the eyes of evolution. The replication of knowledge hinges on satisfying an objective problem, even if that problem is subjectively hidden, not in our awareness, or so misunderstood that it may as well be obstructed from view. This is how inexplicit knowledge contributes to successful replication without recognition.

Explanations have degrees of completeness based on the amount of information they can explain******. A thorough explanation leaves little to chance. A complete explanation is certain, leaving nothing to chance. The pinnacle of explanations is a perfect explanation -- totally complete and objective, thus entirely accurate and essential. The jury is still out on if a perfect explanation exists (Gödel says “no”). The perfect explanation would resemble an ultimate explanation, a Theory of Everything. From time immemorial, suitors have chased after this theory and made proposals. The annals of physics is replete with their candidate offerings, such as Michio Kaku's The God Equation (I have not read yet). None have entirely succeeded. Most attempts to formulate a Theory of Everything look more like a Theory of Anything. These faux theories are actually a Theory of Nothing because they do not exclude anything nor make testable predictions (falsifiable implications). A theory that does not rule out any possibilities is worthless since it cannot solve any problems nor yield any power. For example, “supernatural magic” could explain anything, so absolutely anything is possible in such a regime. Therefore, we cannot deduce meaningful consequences from its truth (other than perhaps the warm and fuzzy feeling of epistemic security…which at times is useful enough). This is the hallmark of a ‘bad’ explanation. This type of belief system is not likely to endure.

Let’s start with a Theory of Something…

Truth -- True or False?

In order to 'know' something, we need to 'know' what it means to ‘know’. Humanity’s initial guess for how knowledge works is known as the “justified true belief” (JTB) theory of knowledge. JTB says that knowledge is about justifying your “beliefs” as true. It then goes on to say that if you sufficiently justify a belief, then your belief is true. JTB is a misconception because it fails to qualify ‘sufficient justification’. Most damningly, JTB suffers from the problem of induction -- there is no amount of supporting examples that can overcome a single counterexample.

Gödel’s profound incompleteness theorems tell us there will aways be truths that a truth system cannot logically prove, including the validity of the truth system itself. In fact, any system capable of producing infinite propositions is capable of producing infinite unprovable propositions. Therefore, it is impossible to prove whether any belief is ultimately true because proof depends on the system from which it is derived, which leaves nothing to prove the completeness or consistency of the system itself (see epistemic regress). We now know that Truth (with a capital ‘T’) exists independently of any such proof system, so induction cannot logically prove a Truth. One may provide evidence to hone in on truth, but this is not proof (as discussed earlier).

The first step to finding truth is to develop a theory of knowledge (epistemology). The method of knowledge-finding to which I subscribe (and have been describing in this blog post) is Popperian critical rationalism (CR). This theory says that if a statement cannot be logically deduced (from what is known), it might nevertheless be possible to logically falsify it. CR asserts that we are fallible knowledge creators, so what we come to know should not be determined by what we already know. CR is like the scientific method on steroids because it utilizes imagination to extend the criterion of falsifiability beyond the archives of empirical evidence and deductive reasoning. CR includes the Unseen (such as new conjectures, missing assumptions, or counterfactuals) as a means to refute knowledge and thereby deliver future knowledge from any dependence on current knowledge.

Therefore, a critical rationalist (provisionally) accepts the truth of knowledge contingent on a set of assumptions (axioms or premises) which may eventually be refuted (always tentatively) by superior knowledge. The beauty of CR is that it is leaves the door open for its own destruction and correction. Although CR may be the best explanation of knowledge today, it is overwhelmingly likely that CR is not the perfect definition of knowledge or means of acquiring it. When CR is refuted, a critical rationalist would willingly adopt the succeeding, better explanation of epistemology. (Even though it is likely false, CR has been a fun way to view the world for me.)

Even our cherished “laws of nature” are ideas about the world that emerge from phenomena that can be understood more fundamentally. Knowledge that withstands criticism is likely to be considered useful and persist; yet, we can never be absolutely certain that a piece of knowledge is a Truth. There is always a chance that we discover new information at odds with our theory. Therein lies the tension of truth. The only rational thing to do is to take our best explanations seriously while also knowing that they may be wrong. Karl Popper describes this friction as the Growth of Scientific Knowledge. New information can destroy deeply entrenched, foundational knowledge. When the rest of the knowledge edifice topples with it, we suffer cognitive dissonance. Instead of trying to forcefully harmonize our prior knowledge with new information, a critical rationalist plainly declares the old knowledge to be problematic and creates better knowledge. Truth is boolean -- it is either right or wrong, not probably right or probably wrong. One can cling to an ostensible truth while speculating it is not totally (or even remotely) correct. This is okay because we should not be believing theories; rather, we should just tentatively accept and critique the best one(s). We can use a framework called “Strong Opinions, Weakly Held,” developed by technology forecaster and Stanford University professor Paul Saffo, to enforce rational criticism.

“For superforecasters, beliefs are hypotheses to be tested, not treasures to be guarded.” ― Philip Tetlock

At this point, we have discussed information as an obscure sort of ‘data’ to be taken as fact, such as our empirical observations. However, this conception is misleading because information is actually a concept used to communicate data. According to Claude Shannon’s information theory: information is the difference between the maximum entropy (maximum count of logical possibilities or configuration states) and the present entropy (remaining count of logical possibilities or configuration states) of a system. Therefore, the value of information is relative to the universe of possibilities, and a state of information is a set of eliminated possibilities (aka impossibilities). The universe of possibilities is constrained by our theories of what is logically (im)possible, such as violations of our physics laws. We like classical logic structure because it seems to map well onto our experience. (Actual possibility is only constrained by the actual laws of nature, whatever they are. It is also important to distinguish the set of logical possibilities from the set of conceivable possibilities. The former is a subset of the latter, and the latter is uncountably infinite due to the unboundedness of imagination. Logical possibilities depend on a formal system, and the formal system is an abstraction of a physical possibility (namely a brain configuration), so logical possibilities depend on a conceivable formal system). Information requires an interpretation machine because there must be a theory to discover data in the first place, and a theory of what it is, how to measure it, and what it tells us. Even our sense data has built-in interpretations (a topic for another post).

The primary theory of neuroscience is Carl Friston’s free energy principle which says biological systems want to minimize uncertainty and maximize computational efficiency. In this theory, the human brain behaves like a computer running software that continuously learns by updating its predictive model of the universe based on sensory input. Intelligence is a software package that encodes an entropy decreasing function to minimize the surprise of the model’s output. As such, “intelligence” and “surprise” are both terms that stand for computational metrics -- the iteration rate on a possibility/proposal space in pursuit of a satisfactory solution and the magnitude of an error, respectively. Learning is an evolutionary program that applies and stores knowledge to gain a progressive adaptation. Generally, intelligence means how effective an entity is at learning, so intelligence is the capacity to improve knowledge via error-correction. Because the set of conceivable possibilities includes falsities, an intelligent being can learn falsities and only corrects those falsities with future learning.

It follows that knowledge is a proposition with a corresponding truth value. When a person is said to possess certain knowledge, one is saying that they have a specific idea in their mind. The idea corresponds to a brain configuration (a physical information state) that influences the body (another physical state) which impresses an affective experience (emotional or qualitative state). Thoughts induce feelings, and feelings induce thoughts, and our mood affects how we interpret data signals.

Knowledge is a type of information that contributes to its replication by solving an objective problem in its environment. It can be abstractly represented as a mental state in the consciousness of a mind, but it is always a physical state. Knowledge exists in the context of other knowledge and holds its truth value relative to the other propositions of the knowledge base. A proposition holds true by remaining consistent (logically possible -- free of contradictions) with other true propositions or by outcompeting a tenet of the base, and vice versa for false propositions. Hence, a valid critique of knowledge must address the formal system (knowledge base and interpretation machine) that created it.

At this point, it is worth rei-iterating the conjectural nature of knowledge and human fallibility. The truth (or adaptiveness) of knowledge depends on its context (or niche), which contains unknowns (and surprises). When speaking in everyday conversation, the majority of context goes unstated, either as an implicit or inexplicit proposition. Also, the content of a statement can mean different things based on its context. These holes are left for the receiver to fill. Since truth is predicated on relevant context, and context is relative to a perspective, it should come at no surprise when subjects fill differently than intended or come to see contrasting truths from one another.

A subjective truth depends on the observer’s perspective (your truths may not be my truths) and it is highly sensitive to new information. An objective truth is the unique interpretation of an unbiased observer, impervious to new information, holding a constant truth value from a given perspective. An absolute truth holds a truth value from every attainable perspective. This spurious “view from nowhere” could yield context-independent truth, the special mark of invariance that defines the scientific community’s criterion for what “real”. This view is rejected by fallibilists who recognize the incompleteness and context-dependence of all knowledge and learn by entertaining plausible viewpoints. Instead, they adopt the "view from everywhere" where a shift in perspective allows one to see different, perhaps more adept, truths.

The difference in our experience is determined by our differing perspectives. Your perspective is determined by your brain chemistry and circumstantial history, amongst many other factors. You feel as though your beliefs are how the world really is. Other people embedded in different perspectives and situations may feel like they are inhabiting a different world from you. Each of these subjective experiences is objective to an individual Self. The disagreement amongst Selves is not to be confused with obstinance. The world feels different to them - even if they are in fact embedded in the same reality. Ultimately, each human wields an interpretation engine trained on ephemeral signals from its biological hardware, originally inherited at birth and developed over time with genetic functions and phenomenological memory. The brain is manually conditioned by itself because the affective response to certain stimuli is entrenched in evolutionary sapience, and we learn which stimuli yield which responses (and even learned to manually adjust them with drugs). With a deeper understanding of medicine, humans can delve beyond ephemeral therapies. Humans have manipulated health with medicine for centuries, but the medical breakthroughs of modern history -- drug discovery, gene editing, cyborg prosthetics -- are transformational milestones in human history, not just for healthcare but also the proliferation of consciousness. These interventions promise to modify the human experience by engineering humans at the level of biological hardware.

So how does a Truth become knowledge or knowledge become Truth? Well, despite the effort of countless philosophers, it can’t. In the end, knowledge is a fallible hypothesis about what Truth is (and is not) that is discovered by iterating through possibilities. Humans seek highly objective knowledge because we get rewarded with an understanding that yields better predictions and control over our future experiences. Nassim Taleb describes a concept of non-observables in his Incerto (my favorite is The Black Swan), which focuses on the problem of induction in predictions. Taleb’s non-observables are events that have yet to be observed, or even conceptually recognized, which is a version of the “Modalities” aspect of the Unseen********. For example, every swan that I have observed has been white, so I assume that all swans are white. The logic of the statistical conclusion rests on priors and inductive inference, namely the uniformity of the universe of swans; so, if I were a pure Bayesian, I would place complete faith in the fact the next swan I see will be white. I feel quite insecure about this prediction because I have not seen every swan in existence (or all the swans that will ever be). No matter how many white swans I see, I cannot confirm my supposition that “all swans are white” because I may eventually come across a single black swan, falsifying my prediction. I would much prefer to have an explanation for the uniformity of swans. The claim that “all swans are white” seems naked because it is missing explanatory content, say genetics, that precisely guarantees the condition in which a swans will be white (making black swans impossible under those conditions). On the contrary, it is abundantly clear from our best explanations in genetics that black swans are permitted (because of genetic or epigenetic mutations in DNA). Explanatory contents are the reasons, the abstractions behind the observations. The explanatory contents of the statement “all swans are white” is the implicit proposition that there exist a universal law mandating the whiteness of swans. Who created that law??? none of your business.

There will always be non-observables, and by definition, we do not know the significance of those non-observables. The highly significant non-observables are the “Black Swans”. We don't know for sure what will effect us, kill us, or save us. It may not exist (to us) today. Because non-observables could undermine our best explanations of reality, we must acquiesce to our fallibility.

According to Plato, perfect propositional knowledge has always been available. It is just a matter of whether or not we come to grasp it. When a scientists contemplates a novel explanation, they bring an abstraction into existence that did not previously exist (or at least did not exist to ‘you’). It is quite liberating upon realizing that imagination enables your universal explainer program, so in theory, you can understand anything! Knowledge is not scarce, regardless of the possibility space*********. It is the product of experience, unbounded imagination, and intelligent criticism. Our problems are unpredictable, as are their solutions. If we already knew a perfect solution to a problem, then by definition, the problem goes away and (hopefully) leads us to better problems. Because of our unpredictable problem situation, knowledge is not guaranteed to progress towards anything in particular. It simply evolves. This is the essence of Joseph Schumpeter’s Creative Destruction. Furthermore, reality is the ultimate feedback for knowledge. An idea’s replicability, and its host’s survival, depends on its environmental adaptiveness more than its ultimate truth. According to Gödel’s incompleteness theorems, there are always (and will always be) propositions that are undecidable (unprovable) using the current set of assumptions. This means that deciding these truth propositions can only be accomplished by including a new, non-derivable assumption (the product of a creative act). Of course, the newly added assumption is itself undecidable, so there will always be new assumptions to make. Thus, Popperian epistemology is a Beginning of Infinity.

Keep in mind, Truth is the foundation of reality. It is what it is**********. It is pure objectivity. It is the ultimate arbiter. Frankly, reality does not care about you (or anything). It is unbiased. It has no preferences. Its laws are pre-ordained. Humans pass judgement on a world that does not need a judge. The peculiarities of reality are subject to human interpretation -- a translation into meaning. The most useful application of this revelation is to practice a posteriori acceptance (more in an Amor Fati Stoic sense and less in a Zen Buddhist sense) because the universe is not conspiring against you, and a deterministic world could not have been otherwise. On the other hand, humans are change agents capable of effecting their own lives. Our choices have consequences, so we should practice a priori self-determination by proactively intervening to solve our problems and reactively reflecting on our problem situation. Self-determination opposes the Buddhist practice of re-interpreting problematic situations as acceptable and denying desire entirely. Not all problems are of equal importance and priorities are a form of knowledge (subjective perspective = wiring of interpretation machine … a topic for another post).

We may not have a choice in which cravings we have, but our appetite for satisfaction determines which experiences we prioritize. We are pre-disposed to have certain preferences, perhaps fully determined, by factors outside of our control. Yet, desires are nonetheless real to the “emergent Self”, and it makes a priori, rational choices amongst possible actions (i.e. desires are innately determined and The Self acts upon them). A decision is often misconstrued as an illusion of our minds’ ability to imagine multiple courses of action, mistakenly leading to the rejection of free will. The mistake in this argument is in regarding free will as a physical entity, rather than as emerging from physical entities. Free will is an emergent phenomena, and a ‘decision’ is the sensation we feel when presented with choices. When explaining why someone walked to the grocery store instead of driving, we can use use the abstraction of free will to generalize the physical conditions that determined the decision, namely the present neural configurations and relevant ecological history that impact things like memories.

Since we all have access to the same reality, the difference in our subjective experience of reality is determined by our differing points of view. Our rational perspective is built from the abstractions at our disposal. Abstractions can be physical (such as atoms, chemicals, neurons), or they can be musical (such as tone, pitch, tempo), or anything else, all existing at a level of emergence. If our best explanation invokes an abstract thing, then it exists because the abstraction is necessary in making sense of the world. It exists until a better explanation comes along that may or may not include that abstraction in its contents. Sure, we are simply delaying the inevitable when we ponder decisions or deliberately sift through our options in a deterministic world. But practically speaking, creating good explanations takes time, and we can use good explanations to make better decisions.

For every effect, there is a cause***********. For every output, there is an input. You may notice the continuity of this universal model. But what happens when there is a discontinuity in the model? And what does a gap represent?

The Odds It Is Random

Randomness is unpredictability due to a lack of information. The land of uncertainty is where we can rationally assign probabilities and use probability theory to model our ignorance, which turns out to be all the time, rather than make guarantees about future events. It is not useful (or rationally tenable) to assign a degree of credence to truth, like an explanation, since probability is always a mere substitute for the lack of an explanatory theory. PSR says that reality is not intrinsically random or uncertain about itself; but our understanding of reality most definitely is. There is one theoretical exception to this rule -- quantum mechanics.

Quantum theory is an explanation of the “possible states” in which we find discrete units of energy, especially observed at infinitesimal scales (as spacetime approaches zero), which aligns with the natural stochasticity (ontic randomness) in our observations. Many scientists posit interpretations of quantum mechanics that elicit an ontic randomness to the universe by invoking a “wave function” that behaves according to probability theory. In such theories, we can make predictions about quantum states (the properties of a distribution of quantized particles) that are just as accurate as other interpretations. However, the instrumentalist “wave function collapse” explanation is a “shut up and calculate” theory that provides a flawed information metaphysics of the universe. It leaves many unanswered questions, such as what “the collapse” is and how and why it happens, so we have little use for this explanation beyond calculating predictions. Quantum randomness gets more interesting when considered in a geometric sequence of n states. To an observer in the reference frame (at t = 0), quantum predictions involve calculating a geometric series of n elements, where the common ratio is given by the wave function. As one can imagine, the information in each sequential future moment gets increasingly difficult to predict from the reference frame. In classical physics, wherein a physical system is highly sensitive to the specifications of its initial conditions and dynamical laws, the system’s complexity explodes because approximation errors compound exponentially in subsequent moments. Using classical computation, an inkling of imprecision in the initial conditions quickly makes the system intractable. This led physicists to chaos theory. However, classical physics is now just an approximation scheme for physical reality since it was refuted by a crucial experiment and superseded by quantum physics. In quantum physics, wherein a physical system is sensitive to the other possible states of the system, the complexity scales according to the number of quantum interactions (quantum-entangled entities) in the system. Using quantum computation, the system’s tractability scales linearly with the number of quantum variables. The value of a quantum variable follows a distribution specified by Schrödinger’s wave function. Taken literally as a description of reality, quantum mechanical equations denote interactions in a multiverse, though not all quantum physicists share this conclusion*************.

All other probability is subjective and epistemic in nature, which means it can be explained by ignorance. Of course, an event either happens or it does not, so any likelihood that you attribute to an event is a function of your ignorance. When we say “I am uncertain”, we are referring to a feeling of doubt in the presence of possibility. We are admitting that we do not know a critical piece of information that would make the truth apparent, and its absence unveils a set of possibilities, some of which might be unfavorable, hence the unsettling feeling. We can mitigate uncertainty and increase the accuracy of our predictions by creating better explanations. Here are two ways to close information gaps and improve our predictions:

1.) exploratory method -- surmise a hypothesis from observational data.

2.) explanatory method -- imagine a world that could create the observational data.

These methods are most powerful when deployed in tandem.

Exploratory research is meant to stimulate our curiosity and generate interest in a problem. It is a form of empiricism that begins with blind data collection. Of course, the collection process is not really blind because we need a good explanation of what the data is and how to interpret it. Once this explanation is in hand, we may continue to make hypotheses about what the data implies and what to expect. Subsequently, exploratory researchers extrapolate statistical patterns in the data to help find, describe, and define problems worth solving. It is common practice to conjecture about which factors in the data are ‘independent’ and then infer their ‘dependencies’ (also known as causal inference). While causal inference may seem inductive in nature, it is actually hypo-deductive reasoning disguised as inductivism. The process always starts by hypothesizing a relationship between observations, in which the observations are mere deductive consequences. Typically, the researcher will put their hypothesis to the test by conducting an experiment in which they alter the conditions of the experiment to gain information about the possible relations amongst factors (i.e. varying the independent variable while controlling for extraneous variables and observing changes in dependent variables). For example, you can vary the temperature of your thermostat (the independent variable) and measure its effect on sleep quality (the dependent variable) via an Oura Ring, or similar biomarker device.

Even with a meticulous experimental setup, we run into the Duhem-Quine Thesis, which says it is impossible to experimentally test a scientific hypothesis in isolation, because an empirical test of the hypothesis requires one or more background assumptions (also called auxiliary assumptions or auxiliary hypotheses). The set of associated assumptions supporting a theory is sometimes called a bundle of hypotheses (similar to what I have been calling a knowledge base). Although a bundle of hypotheses (i.e. a hypothesis and its background assumptions) can be empirically tested and falsified if it fails a critical test as a whole, the Duhem–Quine thesis says it is impossible to isolate a single hypothesis in the bundle, a viewpoint called confirmation holism; therefore, unambiguous scientific falsifications are unattainable. The scientific community refers to this as the Duhem-Quine ‘Problem’, but this is another unfortunate misnomer because science is not about using experimentation to once-and-for-all justify or falsify a theory. Science is about identifying and solving problems, and that is exactly what happens when a crucial test contradicts a theory. Experiments discover conflicts between theoretical content and its reflection in reality. When an experiment refutes a theory, it does not prove the theory ultimately false for the same reasons we cannot prove that a theory is ultimately true. An experimental refutation can logically mean one of two things: (1.) the theory is indeed false (2.) the experiment is flawed in some way, such as in design or false background assumptions or linguistic misinterpretations (or faulty equipment that was presumed to be perfectly functional). The conflict can only be resolved with a better explanation, which may retain much of the knowledge from the problematic theory to explain everything it could, but must include alternative assumptions that also explain the conflicting experimental results. Therefore, the consequences of experimental results are tentative. Corroborating evidence is a piece of information that eliminates all other competing explanations. The other possible explanations stood on equal footing with the prevailing explanation until the corroboration revealed terminal contradictions with each. Not a single empirical observation can positively confirm a theory. Yet, a single counterexample can indicate a flawed theory (more precisely, a flawed bundle of theories wherein at least one theory is strictly false). What about when we observe a new thought or idea that leads to a better theory? In this case, it is an observation that did the corroborating.

Here’s a useful hint for statistical models: when correlations between variables approach 100%, there is a chance of a causal relationship between the variables. Since correlations are caused by common determinants, we should always consider what is causing the correlations. Otherwise, an observed correlation could have been a chance occurrence. Also, there is always the chance that “hidden variables” ************** are the true root cause of the observed correlation, in which case the model is reliable by virtue of being associated with those hidden factors in some way. Without a complete account of the conditions, a correlation between conditional states is not determined to persist because the correlation could be conditioned on an unnamed variable or impacted by an exogenous factor. CORRELATION ⇏CAUSATION***************

…. so … how do you know if the measured response in the ‘effect variable’ was caused by varying the ‘cause variable’ or if the independent factors are truly independent themselves?

Statistical theory, like all branches of mathematics, describes an idealized world of possibility. To be effectively applied in predictions, an explanatory theory, beyond statistical theory, is required to support why and how a correlation, extrapolation, or causal relationship will persist. Historical data are observations that we interpret into representations in order to connect them to the world. Otherwise, plain data could represent anything. How did the data come to be? Explanatory theories save the day by submitting a model of inputs, outputs, and transformations.

You might be asking “How are explanatory theories conjectured?” Well … the explanatory method begins by imagining an abstract representation of the Seen in terms of the Unseen. We need the Unseen to comprehend the Seen. An (accurate) understanding of Seen phenomenon is limited only by our ability to conceive of the (correct) Unseen phenomenon and their relations. We obviously do not see symbols, like the variable “X” or the number “1212”, floating around doing things in the world. What we actually care about (and only occasionally see) is what “X” depicts in reality. If we wish to convey an explanation, then writing symbols on a piece of paper will suffice, though the representations do not need to be instantiated as printed symbols. (An abstraction could also be instantiated as Braille characters or rendered as a VR environment. Some abstractions are easier to implement than others and may also deliver distinct intuitions of the reality they represent. These factors help decide which abstractions to use.)

Then, one moves to describe the relationship between Unseen entities. This amounts to writing more symbols on the paper. For an explanation to be (subjectively) meaningful and communicable, the Unseen Symbols must portray something real to its source and receiver. (There can sometimes be a mismatch between the intention and interpretation of an expression, and such misinterpretations may lead to substantial misunderstandings … a topic for another post.) Supposedly, the combination of abstract symbols written on the paper correspond to reality in the sense that they represent real entities and constitute an explanation by explaining how the entities interact. The explanation may implicate an observed or previously unobserved factor as the root cause for some effect. To deem something ‘inexplicable’ is a surrender to the supernatural by invoking an entity impervious to reason. Such a depressing concession indicates a severe information gap or a lapse in imagination, or both.

I suggest watching Vsauce's YouTube video: "What is Random" and Veritasium’s sister episode: "What is Not Random" to further explore the link between randomness and ignorance.

Conclusion

The least we can do to maintain epistemic humility is acknowledge our tendency for over-inferring causality between unrelated things (or related through layers of dependent correlations). We can utilize imagination to expand our search space with a tunnel into possible and impossible worlds. We learn from trial-and-error. We make epistemic progress by creating new ideas. We improve ideas by correcting their errors. We can seek better explanations to make better predictions. After all, criticizing our best explanations is the best way to hunt for Truth. Since First Principles and Laws of Nature could turn out to be chimeras, we can lean on Zeroth-Principles Thinking to acquire deeper explanations of the world. On the other hand, we are fallible idea creators and will always have to make decisions with imperfect knowledge, incomplete information, and even systematic bias. If an explanation withstands criticism, then it is plausibly the Truth, but never certainly the case. Certain knowledge endures for reasons that we can never know with certainty. We are perpetually exposed to uncertainty … so get used to it!

I glossed over the fact that “meaning” is an important part of the brain’s interpretation machine. Sooo … what is meaning? How and why does it exist? Is meaning relative or intrinsic, subjective or objective, or all of the aforementioned? What do determinism and free will have to say about meaning? If we assume that life is meaningful, then what is the meaning? How is meaning related to purpose? My best answer right now: the meaning of life is to create objective knowledge. More on that in the next post…

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*I enjoyed Tom Clark’s philosophical article on the birth/death of consciousness. Undoubtedly, we can improve our understanding of consciousness with better explanations of how/why it emerges.

**Metaphysics is the ontology of existence, i.e. the study of what kinds of things exist and how and why? I subscribe to a criterion of existence which says existence is to interact with something (similar language for “interact with” are “be relative to” or “be observed by”). The relation is the raison d'etre. I assumed ownership of consciousness for the analogy’s sake; rather, consciousness spontaneously “exists” as a mind-dependent subject without a precise initial moment. Then, consciousness is a continuous awareness of “Leibnitzian discernibles” (discrete things like internal mental states, sensations, phenomenological experiences, thoughts, memories, emotions, qualia, etc.), and the Self is “the observer” of consciousness (an identity of consciousness relative to Non-self). I enjoyed Brett Hall’s metaphysical view of consciousness. The mind requires a definition for the concept of “you” (a whole exercise itself). I use a version of “you” that represents an identity of consciousness that is not myself and which is independent of experience, so “you” are not “your qualia” or “your thoughts”. I also enjoyed Evan Conrad’s article on Cognitive Behavior Therapy (CBT) which suggests many practical applications of the “independent self” view. The Self is an observer of qualia (including sensations, thoughts, and feelings) and any sort of experience appears real to you, rather than being you. Your mind (“You”) observes (interacts with) with a thought as the product of your brain (a physical machine that performs physical thinking procedures and serves the next thought). We have agency over thinking in the sense that we may choose to pay attention to a thought or sensation by being aware of its relation to “you” (an interpretation machine) and to the non-self (the rest of reality, though our body and brain matter belongs to this same reality). People who extend the “mind as a computer” analogy argue that an “interpretation machine” is just a universal computer and an “interpretation” is actually a computation. Therefore, a mental state (qualia) corresponds to a specific state on a universal computer. Theoretically, a universal computer (quantum or otherwise) must be able to model the phenomena of a mind (see Church-Turing-Deutsch Principle). The argument is as follows: The mind emerges from a brain. A brain is a physical system obeying quantum mechanics, so reproducing that physical system with the right combination of quantum logical circuitry and inputs could simulate a brain’s functions, thus the mind. The physical implementation also seems to be substrate independent (i.e. does not require biological matter), but it could turn out that our memory and/or computational process depends on a unique mechanism only possible with biological machinery. It is still unclear how consciousness emerges from a physical system, such as a quantum computer. Consciousness seems to be a sort of user interface (UI) between physical reality and abstractions (API?) that emerges (as a HUD?) and to which qualia appear. I draw the distinction between consciousness and computational universality because of the seeming incoherence of creative imagination and Turing Completeness. A counterargument against physically-independent consciousness is that creativity (and its apparent randomness) can be explained by quantum possibilities in a universal quantum computer. We are also different from modern computers in that we may be aware of ourselves (self-aware) as a computing entity within the system being computed. The fact that we are knowledge-creating entities aware of the fact that we are knowledge-creating entities is a dilemma of the human condition. Humans can understand the world better than anything else, as far as we know, which can be a blessing and a curse. This is not the same as being the most adapted.

***Yes, trust in fellow humans is risky, but the payoffs have historically outweighed the costs. In fact, many evolutionary anthropologists postulate that Homo Sapiens’ capacity to cooperate with each other was its greatest competitive advantage relative to other hominin species. Cooperation eventually allowed us to create languages for communication, coordinate hunts, trade, and specialize in advantageous ways. Needless to say, we survived and our relatives did not. There is also a concept of infinite games in Game Theory that incentivizes cooperation in most instances. Early humans rationally arrived at these same conclusions despite not formalizing game theory or walking around with computers to calculate probabilistic utility functions or multi-agent decision trees. This knowledge seems to have arrived more intuitively and likely entailed a risk-tolerant first-mover to trust another person despite having mixed feelings about the encounter. Or, the discovery of mutually beneficial trust might have been the unintended consequence of an otherwise pernicious pursuit. Either way, the successful exchange of value demonstrated that humans could place trust in one another to help solve each others’ problems, rather than roil in strife, unlocking immense productivity gains. Logically, a group that cooperates to solve a common problem is more likely to succeed since the group is able to throw more collective brain power towards creating and iterating through possible solutions (that is unless the group resorts to lazy groupthink rather than independent thought). I like Matt Ridley’s concept of Ideas Having Sex. Another reason to be trustworthy is that one’s moral code glorifies ‘honesty’ as ‘good’. But, these moral concepts were not dropped onto humans as a pre-ordained script from an authority on high and were undoubtedly created well after, or because of, the first cooperative encounters. Web3 is exciting because it places trust in computation and game theory as opposed to the goodwill of fellow humans, which makes cooperation on the internet more viable.

****We will explore the mechanisms of markets and consensus in other posts.

*****I highly recommend reading it. In fact, it was the inspiration for this blog (if you don’t read books, then at least listen to Naval Ravikant’s The Beginning of Infinity podcast or Brett Hall’s podcast series breaking down the book).

******actually, Gödel ’s first incompleteness theorem postulates that every formal system will contain propositions derived from the language, axioms, and inferential rules of the system with truth values that cannot be decided (proven nor disproven) within the system. The second theorem includes a proof demonstrating that a proposition expressing the system’s own consistency is itself an unprovable proposition. Such propositions are said to be undecidable and such systems containing undecidable propositions are incomplete. Explanatory completeness refers to decidability within a domain, namely a level of emergence. Explanatory reach is the set of domains in which an explanation has explanatory power, so we can say that a Theory of Everything reaches everything. Knowledge is a proof derived from (made possible by) other explanatory knowledge, so truth depends on the axioms that one adopts. When we say anything about the world, we are doing so via an abstraction. Statements point to abstractions (propositions, numbers, virtual reality, etc.), so there is an implicit theory baked into every statement that either corresponds with reality or does not. Our best statements are our best pointers (labels for) propositions. The truth values of statements are determined by whether the abstractions to which they refer correspond to our reality or not, which we determine with criticism. Everything, including our empirical observations, is an abstraction (truth) derived from a knowledge-creating system which may or may not correspond to reality (Truth). We intervene with the world based on our abstractions and understanding of relations between abstract things. The uncountably infinite set of natural language statements, or statements of any figurative form, have an identity relation with the set of abstractions which have a general (non-surjective, non-injective) relation with the set of real things. In other words, there is more than one way to say the same thing, and we do not say everything. And, we sometimes say the wrong thing or nothing at all. Since there is no such thing as a perfectly precise language, there will always be scope for misconception when interpreting (translating) linguistic statements into propositions (meaning). Language is itself a beginning of infinity wherein we are trying to find the best way to point to abstractions. Any statement expressed in natural language is ambiguous and imprecise, so explanations are always incomplete when linguistically expressed. Can we possibly have a complete explanation (expressed linguistically)? If information tends to infinity as entropic laws dictate, then we clearly cannot since there will always be information beyond the last information discovered, and we will always need new linguistic representations for the new information. Our foundational truths are temporary because of the unpredictable knowledge that can be created. Formally, this is the veritable view known as infinitism (we can always add a new axiom while digging for Truth), as opposed to the fallacious view of foundationalism (we can hit bedrock Truth while digging). We may hit bedrock, but there is no way of confirming that we did. Because of this, it is possible that we uncover bedrock Truth (without realizing it) and then subsequently retreat from it. Committing to any truth requires faith in the truth of its originating system.

******* We ascribe the moniker “Laws of Nature” to regularly observed relations between physical phenomena. There may be absolute “Laws of Nature” that are actually real, but our theories about these laws are no closer to Truth than any other knowledge because, like any other knowledge, its truth depends on the system from which its derived. There are REALLY good explanations with content that corresponds to Truth in an evolutionarily significant way, but we would never be able to prove or definitely know it to be a Truth, nor a False. The common-sense metaphysics of realism is the view that objective reality exists independently of whether we come to know it our not. Realism posits an ultimate Truth/False which seems to correctly account for how our beliefs can appear true and eventually be shown false. Since our perception is a subjective reflection of reality (Truth), truth is only true or false relative to other reflections of Truth, not actual Truth. You may derive truths within a truth system, but in order for these truths to become Truths, you would need to prove that the truth system from which they came is consistent and perfectly objective (a perfect reflection of Truth), which is impossible (according to Gödel’s incompleteness theorems) without adding an infinite regress of premises -- the introduction of new premises brings the burden of proving the new premises, which requires introducing new premises, ad infinitum.

********The classification of non-observables as "The Unseen” is biased towards the sense of sight. It could have just as easily been named "The Unsmelt" or "The Unfelt" or “The Un-[insert any other sense]”. We favor sight because it is the dominant mode of sensory input to the human brain and is the most accurately understood in terms of its underlying mechanisms. We also seem to discern and describe visual qualia with greater precision and clarity. Amongst sensory experiences, vision causes the least dissent, making it the most objective perspective to frame observations. Even these additional classifications of non-observables is biased towards sense perception since we clearly have phenomenological experience beyond our immediate sense perceptions (e.g. observing an abstract thought or a joke or examining a mental state like happiness, sadness, or anger). And even this classification is biased towards human observation. What about the infinite experiences that humans have yet to observe or never will observe? A better naming would be "The Unobserved".

*********The more important and deeper question is whether reality is fundamentally continuous (uncountable, indefinite) or discrete (countable, definite). This question is most famously illustrated by Zeno’s Paradox. The answer requires one to take a position on whether absoluteness or relativity dominates the world. This dichotomy is at the crux of the disharmony between quantum theory and general relativity. Each paradigm accurately models particular situations, but we don’t know how the descriptions correspond to each other. Most people think an intermediary translator, like quantum gravity, will unify these theories. I think the answer requires a better understanding of time and information. What does info exist relative to? What does time exist relative to? How do time and information interact? Does reality exist as a state of information at points in time? How could a zero-dimensional point in time exist? Does the set of informational elements grow, accumulate, remain static, or simply change between states? Are new elements or “things” created? I will surely be following developments in Deutsch’s Constructor Theory for inspiration.

**********The Truth Spectrum is not to be confused with true vs. false values in logic and is not a refutation of the Law of Excluded Middle. It is more closely related to the concept of entropy in Information Theory, which is to say that it depicts the number of possible interpretations derivable from differing perspectives. Once a perspective (formal system) is established, truths may be derived. I suppose the ultimate truth is whether reality itself exists or not. The answer seems to be buried in the following question: Reality is ‘something’, so can it be ‘nothing’? If ‘nothing’ is in fact ‘nothing’ (not something that exists), then reality could not exist as ‘nothing’. If ‘nothing’ is ‘something’ (a special form of ‘something’), then ‘nothing’ could exist. Since ‘something’ is the identity of a relation to another ‘something’ (i.e. an observation to an observer), then ‘nothing’ must relate to ‘something’ for it to be ‘something’. The question then becomes “What is the ‘something’ to which ‘nothing’ could relate?” Since ‘something’ must relate to ‘something’, then ‘not something’ must not relate to ‘something’ (i.e. nothing must relate to nothing (i.e. it relates to itself)), which is a contradiction. I currently subscribe to Robert Lawrence Kuhn’s reasoning that “nothingness interacts with possibility”, so nothing is an infinitely empty possibility space. Consequently, sentient beings can explore the infinite possibilities of reality.

***********In another post, I will investigate whether the inverse is necessarily true. This will require a deep consideration of the nature of infinity. Since observational information lags behind explanatory knowledge, a Laplacian Demon seems plausible. Here is an interesting argument refuting the possibility of Laplace’s Demon. The argument hinges on the impossibility to achieve complete information of the present moment during that same moment. If the complete set of information were available at present, then, in theory, an infinitely fast processor in the present could predict the next moment (or retrodict the preceding moment) using the information from the present moment as long as the predictive computation does not affect the present moment. However, this leads to an infinite regress since the Demon would not know whether the prediction itself affects the current moment (thus changing the prediction of subsequent moments) without knowing the effects of its prediction before making it. The prediction is the output of a physical process that physically interacts in the universe and thus could impact the physical inputs used to make the prediction in the first place. (Assuming the Demon exists within the same physical system it is trying to predict.) A similar challenge known as the “observer effect” arises in quantum theory whereby the act of measurement disturbs the state being measured and affects the measurement. The Demon runs into a self-referential problem because it needs an external perspective of the current moment in which it resides. In other words, the Demonic Predictor is an observer that needs to “observe” itself (relate to itself) which seems to contradict with how things really exist…so the Demon is not real...or at least cannot exist within the system in which it has complete knowledge. (There are possible workarounds for the Demon, such as its predictive output completing the present moment, thus having no effect in the world, and connecting the present moment to the next. But having no effect in the observable world is the same as not existing). This thought experiment explains why such a ‘Demon’ computer program could not logically be completed, similar to the Halting Problem and other unsatisfiable problems. (For more on these thought experiments, see Newcomb’s paradox and the grandfather paradox.) There is also the fact that the Demonic computer program would physically need as much matter as exists in the universe for the memory space and processing energy to execute the computation. This is why a Demonic program must, both logically and physically, exist outside of the system it is simulating. If we can be like the Demon, in the sense that we can understand things, then perhaps our consciousness also exists independently of the reality of which it is aware? This would explain why we are only ever aware of a single moment at a time.

************I will address these concepts in more detail at some point. “We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow.” -- Laplace. If we assume that the previous moment is required for the next moment, then it follows that the entirety of the past is required for the next moment because the previous moment had a necessary moment preceding it, and that moment needing the one preceding it, and so on and so forth. If we take this conclusion to be true, then the inverse is also true -- the entirety of the future is necessary for the past because a future history is the unique effect of a past history. This means reality is an unavoidable destiny or fate. All of history matters for any particular moment. However, a deterministic world does not necessarily incorporate causality and retrocausality. A common rejection of Laplace’s principle of sufficient reason (and Fate) is to assume that reality is a Markov chain, that is to say that only the current state of the system is necessary for the future state and there is an irreducible element of chance between moments. Then, the entire past is not necessary for the present because we could randomly arrive at the same present from different histories consistent with that moment. In Markov Chains, the transition between states is all that matters. If reality has a Markov property (memorylessness of a stochastic process), then the next state resides within a probability distribution of possible next states, so the next moment is determined by probability theory. If reality is a Markov chain in which the transition between states has a level of autonomy independent of deterministic dynamics (perhaps Free Will, creative knowledge, or exogenous chaos), then only the current state is necessary for the next state in the chain. Both of these arguments implicitly assume that the arrow of time has a direction and differ only on whether the transition between moments is fully determined or stochastically-determined. We have observed a reversibility property in our physics, such as not being able to discern between a video of a bouncing ball in an anti-gravity chamber played forward or in reverse. This suggests that the laws of physics are backward compatible, not leaving any room for ontic probability. Let’s consider a more complex case, such as a video of a melting ice cube on Earth. We can tell the direction of the video only because of our assumed explanations (and past experience) of gravity, phase transitions, and heat entropy. To predict the “after” image of the ice cube given just the “before” image, we can use our best model of fluid dynamics to calculate a (pretty accurate) prediction. So, can we reverse these same explanations to predict the “before” image of the ice cube given just the “after” image? The second law of thermodynamics says “No, this system is not reversible”. But of course it is reversible! (given perfect explanations of how). The second law stipulates that an unbalanced system will gain entropy, making it computational intractability. But computational intractability is different from irreducible probability. It is still safe to say that irreducible probability is fictitious and any invocation of probability is an indication of ignorance (or a dearth of computational resources). We perceive time as the specious present -- an ongoing sequence of discrete moments with a finite duration (or maybe a collective series of moments when considering the nature of memory). Ultimately, time may not actually be an ordered sequence or series of moments in the way that we perceive it, in which case the conclusions of the prior arguments fall apart. Our understanding of time is distorted by our perception of it. The most convincing concept of time (that I can understand) is as a periodic relationship between discrete moments. Time occurs whenever the state of the univere changes. A unit of time is the relative difference between reference frames. A duration of time is a count of distinct reference frames (points in time representing physical configurations or information states, depending on whether physics or computation is more fundamental). In this concept, a moment (or reference frame) is the physical state of a universal computer. The periodicity is the “clock” in the universal computer that runs the “time program” composing reality. Therefore, a point in time refers to a state of information (state of The Universal Computer) and the program (The God Equation) determines the relation between moments. The state of information represents the set of possible/impossible transformations from that state to another. Time is the infinitesimal gap between moments, the distance between programmatic steps, that is constantly being filled by change. To a subjective observer, a duration of time is an accumulation of entropy (or compression of info). Objective knowledge is info that remains constant (replicates across moments) by compressing entropy to anticipate the next state in an adaptive way to resist evolutionary pressures. The objectivity of knowledge can be measured by its persistence across moments, literally a quantum measure of the wave function. If time is the program mapping a state of info to another state of info, which type of relation is it? A blockchain technically and economically incentivizes an immutable record. By publishing to a blockchain, one can scribe a revisionist-proof history in stone, which could be useful for many applications: business, research, art, etc.

************* Chaos theory and statistical mechanics describe dynamical systems using a Newtonian model of initial conditions and dynamical laws. The laws mandate the transitions between conditional states. A statistical model is an explanation-less attempt to make predictions using numerical relations (or whose explanation is implied by the stated relations) and inductive reasoning -- which counterintuitively requires a closed, non-universal, static system and assumes constant numerical relations to have any degree of certainty. The equations of a closed system only need an initial state. But many systems aren't closed and instead continuously respond to the environment (such as our thermostat example) or a stream of input data (such as a speech translator). In systems that interact with people, that input data is ipso facto unpredictable because it is impossible to predict the knowledge the people will create. We cannot even predict what we will be thinking about in the future. Ask yourself: “what will I be thinking about an hour?” “What about two minutes from now?” Statistical predictions rely on the misconception of Stationarity: an assumption that the past is a statistical guide to the future, based on the idea that the forces impacting a system are known with certainty and don’t change over time. Stationarity is a principle of induction (and other Bayesian forms of inferencing), a wonderful concept that works right up until the moment it doesn’t. In our world, things that have never happened before happen all the time. We can use an explanatory models to infer things not present in the data, but non-observables belong to the realm of unknown unknowns, not known unknowns. By observing a system, we obtain information which effectively eliminates the other possible states (and explanations) of the system.

**************The judgement of whether a variable is dependent or independent is an inference made by an explanatory model positing a causal structure to a system. In an incomplete system, there is always a chance that a change in the dependent variable (Measured Effect) may be caused by an unknown factor (Actual Cause) rather than the independent variable (Supposed Cause). The independent variable (sometimes called an exogenous variable) may cause an effect (Intermediate Effect or Mediator) which is in turn necessary and sufficient for the Measured Effect. Let’s say that the Supposed Cause guarantees the Intermediate Effect (i.e. the Intermediate Effect is entirely determined by the system and considered an endogenous variable). In this case, the Supposed Cause indirectly guarantees the Measured Effect by way of the Intermediate Effect, and we can say that the Supposed Cause is the Actual Cause of the Measured Effect. However, if it is possible for the Intermediate Effect to exist independently of the Supposed Cause (i.e. the Supposed Cause is unnecessary for the Intermediate Effect), then the Measured Effect may not depend at all on the Supposed Cause. If the Supposed Cause does not guarantee the Intermediate Effect, then the Intermediate Effect could be an exogenous variable (and potentially also a confounding variable if it also causes the Supposed Cause, in which case the Supposed Cause could actually be an endogenous variable and irrelevant to the causal chain).

It is hard to control extraneous variables (especially unknown ones!). Hidden Variables are ‘extraneous’ until they are identified and controlled in the experiment. Since physical experiments are temporal in nature, there is always a moment between the one being measured, and that could be the frame with the Hidden Variable. Humanity’s most prolific theory, quantum theory, posits a natural randomness (indeterminism) following Heisenberg’s uncertainty principle and Schrodinger’s wave functions. Quantum theory is scrutinized in light of the scientific tradition which favors reducibly non-random (deterministic) processes. Most pundits suggest probabilities mark the end of explanation and the beginning of theoretical ignorance. So, the natural conclusion is that quantum theory is incomplete, and quantum randomness is the result of Hidden Variables, and the perpetual notion of incompleteness is the crux of quantum indeterminacy. Without proposing an explanation of the Hidden Variables, the explanatory power of the theory cannot progress. Even so, randomness could be compatible with determinism. We can say that randomness is determined by an arbitrary choice amongst possibilities (measured by a distribution). We can think of the chosen value as being determined (by a random choice from a predetermined distribution), but the value itself could therefore not be predetermined. This begs the question “how is the choice made” and “why from this distribution”. It could also be the case that the “probability” of a particle being in any particular state is determined by some unspecified, perhaps undiscovered, conditions that shows up at these particular frequencies. Then, if you can identify the set of conditions (using a good explanation) and have knowledge of the conditions’ existence, then the uncertainty goes away…UNLESS there really is an ontological randomness so that a set of conditions may cause another set of conditions only at particular frequencies … in which case we run into the problem of induction once again. We would need infinite observations to observe every outcome in time to know the exact frequencies (i.e. you can not completely predict an infinite future with a finite set of past observations). Therefore, a diligent forecaster considers whether the current conditions match the past conditions before making an extrapolation into the future. The goal of forecasting is to present a case for how frequently the causal conditions will show up in the data. One can back into a forecast by imagining the possible environments (niche) in which the measurements can take place, and then count how many of those possibilities include the causal conditions. Furthermore, even our best explanations fail to escape the problem of induction because there is always another “why” or “how” question which the explanation leaves unanswered. The problem of induction may prove to be the only unsolvable problem for humans. Hume proposed the Uniformity Principle as a solution but ultimately failed to prove its necessity. In following Karl Popper’s trailblazing footsteps, David Deutsch lands on a profound refutation of inductivism/justificationism in ch. 7 of The Fabric of Reality. While Popper and Deutsch claim to have defeated the problem of induction, the problem of uncertainty still remains. We can only try to mitigate the problem by eliminating as much induction as possible in our explanations. We may or may not discover the true God Equation; and in our current epistemology, we are unable to prove its truth ultimately (even if it is true).

***************Correlation is an association between sets, not a function. Causality is a function in the sense that outputs (effects) are determined by inputs (causes). I like to think of it as a forcing function which takes all possible worlds as arguments and outputs a single world, or vice versa. You cannot literally point at causation since it is a abstract concept, not a physical thing (and may even be an illusion of our perception). Instead, you can point at an explanation as a description of causation, including elements and relations between elements, acting like a bridge connecting two moments (conditional information states). We think of causality as being a one-way relation because of the positive arrow of time. By thinking in terms of possibility, necessity, and sufficiency, we can re-interpret causality in terms of consequences without a reference to time. In causal logic, the symbol “=>” denotes implication and is used to specify the following relationship between states: the condition to the left of the “=>” symbol portrays a sufficient condition which guarantees the condition to the right of the symbol. The condition to the right of the symbol “=>” portrays a necessary condition which is required for the sufficient condition to be truly sufficient. A causal relation is where collectively sufficient inputs (a cause or sufficient set of reasons/conditions) determine specific outputs (effect or affected outcomes). Overdetermination occurs when a single observed effect is determined by multiple causes, any one of which alone would be conceivably sufficient to account for ("determine") the effect (i.e. there are more causes present than are necessary to cause an effect). This would imply a specific effect does not guarantee a specific cause i.e. effect ⇏ cause, but a specific cause guarantees an effect, i.e. cause => effect.. Logically, this relation dictates a single effect for every cause but leaves open the possibility of alternative causes, perhaps unknown, to arrive at the same effect. Overdetermination is problematic in particular from the viewpoint of a counterfactual understanding of causation, according to which an event is the cause of another event if and only if the latter would not have occurred, had the former not occurred. (IFF statements are analogous to biconditional relations “<=>”). Counterfactual determinism is a fully reduced form of causality where there can only be a single way to arrive at a particular moment (and it requires a specific past history and future history). So, counterfactual causation implies that causality is a 1 to 1 relationship between cause and effect. Counterfactuals define the limit of necessity and sufficiency in causation so that a “root cause” must not only be sufficient but also necessary for an effect. Therefore, overdetermination must be false in the limit, and discrepancies in the causal chain, as it is understood, must therefore arise from falsities or imprecisions. Cases that seem overdetermined or where the root cause appears absent must be the result of an inaccurate or incomplete representation of the conditions or misunderstanding of the actual root cause.

PS: I promise future blogs will not be this long.