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Halbe’s Razor

September 20, 2023FundamentalsTorben Standard

Many philosophical and in fact political, economic and cultural “problems” are instead questions of thermodynamics. Or, at the very least, by looking at the thermodynamics behind them, many wrong avenues can be discarded outright. 

The underlying reason for this is the intricate relationship between entropy and randomness. High entropy means a lot of randomness, and this is in the way of describing “problems” and discussing “solutions”, because it means noise. But it also is in the way of affecting any change based on such discussions or one’s own considerations, because such change normally attempts to be not random, but in some way ordered, which also requires dealing with entropy lest it gets in the way.

This is why I propose “Halbe’s Razor”, which consists of six postulates. They are concerned with the best ways to find thermodynamic systems to talk about. To find such systems, one has to draw boundaries around matter and radiation. What is within these boundaries is a thermodynamic system, the rest of the universe is its surroundings.

Postulates

Postulate 1: Objects

When talking about anything at a specific point in time, one should draw boundaries around matter and radiation so that within those boundaries, the information is as different as possible to the information outside of it.

Linguistically speaking, these objects with these boundaries are normally referred to by nouns or pronouns with their accompanying adjectives and particles.

One can find different or overlapping objects with Halbe’s Razor at the same scene. For example, a cow contains (or is made up of) different information than the grass it is eating, so it is legitimate to speak of a cow and of the grass both as its own object. However, the pasture — cow, grass and all — contains different information than the houses or the forest beside it, so it is also legitimate to draw the boundaries around it and speak of the pasture as an object. Similarly, a fence that separates one pasture from another is different in information to the grass around it, so it can also be defined as an object. This might seem trivial for everyday observations, but is crucial when looking at orders of magnitude smaller or larger than what our senses specialize on. For example, one might first look at a molecule and rightfully define it as an object, but looking at a smaller order of magnitude, one will find several nuclei and electrons. At a larger order of magnitude, one will find it impractical to look at all the molecules within for example a cell organelle, and instead define the entire organelle as an object since it contains different information to the surrounding plasma. All of this is possible with Halbe’s razor.

While all of this might seem trivial when talking about physical objects, Halbe’s Razor gets quite sharp when used for more “abstract” things like in the social sciences. For example, how can the boundaries around a local community be drawn? Which people and places belong to it and which don’t? Or when talking about a person. Should I say a person is just his body or should I include the immediate environs (see Postulate 3) that influence what is going on in his brain and body? After all, information travels from these environs to the body and brain all the time. The answer is: Just the body can be a good object when for example describing for example the occurrence (see Postulate 2) of the person visually perceiving a table, in which case the table would be the other object. But when entering a larger order of magnitude and for example describing the occurrence of two persons talking to each other on the phone, the environs of each of them will influence the phone call—be it through influencing what they talk about, interfering through distractions or noise, or just setting the mood. A call made from a beach during a vacation is different in a lot of ways to one made from the office. This is why the occurrence could be best described as “person A (body and environs) talking to person B (body and environs)”, with person A and B being objects in this case. 

Also, while in the example with the cow above, we looked at concrete information to draw the boundary around e.g. the cow, in the overwhelming majority of cases, this is not even necessary. One just has to look for the information content which means the same as a similar level of entropy, because the less entropy, the more information.

While entropy could theoretically be measured physically in Joule per Kelvin, this would be very complicated in most applications. It also is not necessary. Oftentimes, just looking at how ordered matter is does the trick. Iron ore, where a lot of different elements are wildly mixed, has more entropy than an iron ingot and the resulting tailings taken together. Additionally, energy can also be less ordered, like heat, or more ordered, like electrical energy in a computer. Living beings are highly ordered (see Erwin Schrödinger’s seminal book “What is Life?”), they have less entropy than unliving solids (which in turn are normally more ordered than liquids, which are more ordered than gasses). 

Only in the case of very similar information content, one has to compare concrete information. This would suffice even in the examples above. A cow’s entropy level is lower than the one of grass, it thus contains more information. We wouldn’t have to compare the concrete information, like the color of emitted light or the chemicals the cow or the grass contains. While in this case, it is easy to check the concrete information since our eyes evolved to do so, it can be misleading. The entropy content should always be checked first because it is less error-prone, and in most cases — like “abstraction” or looking at how people work or how language works — this is even simpler than looking at concrete information.

Postulate 2: Occurrences

When talking about any development between two points in time, one should draw boundaries around matter and radiation so that within those boundaries, the entropy change is as different as possible to the entropy change outside of it. The boundaries should then be extended to include any source of information that played a role in lowering or even turning negative this entropy change.

Of course, if the entropy change has not been lowered by anything, meaning it is the baseline increase in entropy expectable from the system in question, there is no such source of information.

Including the source of information is important so that one can talk about any form of causality without having to open up more than one thermodynamic system, which would induce unnecessary complications.

Linguistically speaking, these occurrences within these boundaries are normally referred to either by a complete sentence, with nouns or pronouns with their accompanying adjectives and particles defined according to sentence 1 specifying subjects and objects of what is going on and verbs and adverbs specifying their interactions, or a noun is enough to describe the development. For example, a rainstorm is a process by itself without the need for verbs. 

Postulate 3: Environs

Environs are matter and radiation within the boundaries of an object or occurrence which are not explicitly named, normally because something else within the boundaries is much easier to name.

For example, a person could be an object defined as body and environs, with the environs being everything around him that is influencing what is currently going on in an occurrence like a phone call (see explanation regarding Postulate 1). This makes the object “person” similar to a quasi particle in physics, and for the similar purpose of ease of description. Similarly, when describing an occurrence like a boxing match, the environs in the sense of the referee, the judges, the ring doctor, the rules, the spectators, the venue, the broadcasting etc. are all included when saying “the environs of the fight between person A and person B”. This again sounds trivial because natural language already includes these environs by saying “the boxing match between person A and person B”. But again, in more abstract cases like in the social sciences, leaving out the environs can lead to bad conclusions because of their huge influence on what is going on, and for such applications, natural languages normally don’t have evolved to automatically include the environs.

In this sense, “…and environs” tells the listener that Halbe’s Razor is being considered instead of naively adhering to whatever natural language has developed definitions for, while still using the efficiency afforded by natural languages. 

The word “environs” is used because “surroundings” are by definition outside of the system boundaries. Theoretically, the word “environment” could be used instead of “environs”, but that would make it confusing when Halbe’s Razor is applied to discussions about environmentalism etc.

Postulate 4: Probabilism

Every application of Halbe’s Razor is probabilistic, i.e. it looks for high likelihood instead of for certainty.

This applies to the exact placement of boundaries around matter and radiation according to Postulates 1 and 2 (and thereby indirectly to Postulate 4), to the entropy measurements that result in these boundaries and to the questions whether the system such defined is self-organizing or stable (see Postulates 5 and 6), as well as to all Derivations.

This postulate follows from the observation that the world is fundamentally stochastic, see quantum mechanics, thermodynamics and information theory.

Postulate 5: Nonexistence

If there are no boundaries definable by either Postulate 1 or Postulate 2, the object or occurrence does not exist.

This can either be the case because the proposed object or development involves proposed things or interactions that do not consist of matter or radiation. Platonic ideals are an example for such a thing. Or because matter and radiation are everything that is involved, but the proposed object or development is so complex (measured in information content) that assessing the entropy (for objects) or entropy change (for occurrences) within them, which would be required to find out where to draw the boundaries, is more than a human brain can handle. For example, the attempt to say that “society wants” something is such an attempt, for it means talking about millions of individuals who, despite consisting of matter and radiation, contain more information than any human brain can handle even when limiting it to information relevant for the “wanted thing” in question.

Halbe’s Razor uses the term “esoteric” to classify such attempts to talk about some object or development that doesn’t exist.

Postulate 6: Self-organization

An occurrence wherein entropy is lowered between the two points in time mentioned in Postulate 2 is “self-organizing”. 

These systems lower entropy within themselves and thus stay in non-equilibrium states or alternate between them. Non-equilibrium because thermodynamic equilibrium, the state with the highest entropy a system can achieve, would mean homogenous temperature over the entire system as well as complete mixture of the constituent particles. For example, after I drop ink into water, thermodynamic equilibrium — aka maximum entropy — is reached when the entire body of water has a homogenous color.

Examples for self-organizing systems are living beings, economic activity, artificial intelligence, and computers. As well as some atmospheres, for example of Earth, Mars, and Titan (a moon of Saturn), because they transition between regular states far from thermodynamic equilibrium. Similarly, hydrological processes on land, i. e. how water dissipates through the Earth’s soil, are far from such an equilibrium.

All self-organizing systems can only achieve this because entropy outside of their boundaries increases more strongly than it decreases inside of them, because everything else would violate the Second Law of Thermodynamics. They can only do this by “using energy”, which, less colloquially put, means that energy is transformed from a more “ordered” form, like radiation or chemical energy, to a less ordered form, normally heat. 

Postulate 7: Stability

Only stable occurrences are existent. An occurrence is to be called stable if it maintains a somewhat constant level of entropy change within a relevant order of magnitude of time. 

This order of magnitude of time is related to its order of magnitude of space. Generally speaking, microscopic objects and occurrences are stable for shorter times than macroscopic ones, mostly because particles move around randomly, which has a more noticeable effect on smaller orders. For example, some enzymes can catalyze a reaction in a tenth of a second, which thus is the order of magnitude of time for an occurrence in which the system consists of the enzyme and its substrate. For a larger system like the one consisting of a robot, a partially constructed car and the fender the robot is attaching to the car, we can expect a duration and thus stability for far more than a tenth of a second.

To check for stability within the relevant time frame, one measures a system’s change in entropy over time. If it isn’t somewhat constant (within the levels of randomness expectable at the order of magnitude), it can’t be stable. For example, if a system starts with gaining some entropy per second but then suddenly starts to gain much more per second, it would be better to talk of one system until that point in time and then look for another one that starts afterwards.

This is why according to Halbe’s Razor, an unstable system does not exist: Because one or more better systems exist at the same order of magnitude which fulfill the Razor better. Saying that an unstable system exists is to be called esoteric.

Postulate 8: Homogeneity

Self-organizing, stable  occurrences are to be called “inhomogeneous” if they have inhomogeneous information processing, meaning that removing certain parts of them would take away the occurrence’s ability to self-organize because these parts play a dominant role in the information processing. These “parts” can be objects or occurrences according to Halbe’s Razor that are within the boundaries of the larger occurrence, and the removal process would be an occurrence. The opposite case is to be called “homogeneous”. 

For example, the atmosphere of Earth is self-organizing, but it would still be if a random 1000 km³ cube of air would be relocated to another planet. Only if a large percentage of its air was to be removed, the self-organization might break down, but it would not depend on which parts, just on the sheer amount. On the other hand, inhomogeneous information processing means that some parts are more important for the self-organization than others and taking these away would destroy its ability to self-organize. For example, removing the nucleus from a human cell would have such an effect. As would removing too many mitochondria. Removing just some cellular plasma, on the other hand, would not have such an effect, because the proteins etc. dissolved within it would be replaced through processes like translation soon. Similarly, removing a human from his home would destroy the ability of the system “human+house” to self-organize. Entropy in the house would increase, first through dust accumulating, eventually through more severe effects from lack of renovation. Removing a non-human part, for example some cups from the cupboard, would not have this effect since they are not as important for the system’s information processing. 

Both sorts of occurrences are perfectly describable with Halbe’s Razor, the distinction however is important because human-containing occurrences most often are inhomogeneous. 

Postulate 9: Impacted Surroundings

Having found a self-organizing occurrence, one should additionally draw boundaries around matter and radiation so that within those boundaries, a gain of entropy is statistically significantly directly or indirectly impacted by matter and radiation flow from the self-organizing occurrence. This auxiliary occurrence is the “impacted surroundings”. Its two points in time are the same as the ones of the self-organizing occurrence, offset by the delay required by this flow.

Self-organizing systems can only exist because they increase entropy outside of themselves, and physically speaking, the entire rest of the universe is the surroundings of a thermodynamic system. However, for discussing a self-organizing system especially regarding its impact on people, it is crucial to be more precise. 

This is why we need to draw boundaries around where this entropy ends up to the best of our statistical knowledge (we need to use statistics because of Postulate 4). The entropy will not teleport, thus matter and radiation are required to bring it somewhere else. It can do so directly, by flowing from the self-organizing system to another place. Or indirectly, by interacting with more matter and radiation in this other place which then in turns carries on the entropy to yet other places. We follow this process as far as we can distinguish this flow from noise and other flows using statistics, and draw boundaries around everything thus affected, and then measure the entropy change within it. This entropy change will occur between the first time the flow of matter and energy reaches these places, and end when the impact of the last time of such flow has become indistinguishable from noise.

Postulate 10: Parasitism

A self-organizing occurrence is to be called “parasitic” if its impacted surroundings are human-containing.

Occurrences that are not self-organizing can also dump entropy onto human-containing surroundings, but those are ephemeral because they are entropy-gaining. They will eventually reach thermodynamic equilibrium and cease being an issue. That means dealing with them requires temporary measures. For example, a massive landslide will unleash huge entropy on villages below, but as soon as the dust has settled, it’s done. The mountain will not rebuild itself into something capable of another landslide (or, as long as the mountain range is still growing due to geological reasons, it won’t do so for hundreds of thousands of years). In contrast, a parasitic system maintains itself and thus always causes trouble for its human-containing surroundings, meaning it must be dealt with differently. Calling it “parasitic” highlights this distinction and emphasizes this need for dealing with it. 

Derivations

These statements follow directly from the Postulates but are spelled out for greater clarity.

Derivation 1: Limit of one occurrence

One should never talk about more than one occurrence at a time, with the exception that when talking about self-organizing systems, one should also talk of the auxiliary occurrence called “impacted surroundings”.
Follows from: Postulates 2 and 9

Oftentimes, people attempt to talk about interactions between different thermodynamic systems, which creates at least three subjects for their speech: The two (or more) systems and their surroundings, which is everything in the universe not part of any of the systems.

Halbe’s Razor maintains that doing this adds unnecessary many measurements of entropy, each with its own measurement and sampling error. Moreover, it is largely arbitrary how these systems are delineated, meaning that a system of knowledge can calcify self-serving artifacts and sampling errors. In contrast, using Postulate 2 to delineate exactly one system to talk about will eliminate these arbitrariness as well as reducing the number of entropy measurements and thus the uncertainty. One can look at the three-body problem from physics to understand why it’s advisable to always talk about just one system and its surroundings.

For example, if I say that the cow is one system and the grass plant it eats is another and that the rest of the universe are the surroundings of both, I would observe that the cow is increasing the entropy of the particles of the grass because they are in an ordered form in the plant, but end up in solution in the cow. This however requires tracking all the grass particles through the cow and drawing a boundary between each grass particle and the surrounding cow particles. It is more efficient and less error-prone by many orders of magnitude to see the cow and the plant it eats as one system according to postulate 2. Then, it is apparent that the system “cow+plant” is losing entropy while its surroundings are gaining entropy (through excrements and the heat emitted during metabolizing the grass).

While this may seem trivial, consider for example that many scientists and activists are aggressively looking for zero-sum games. For example, they want to observe that human resource usage damages the environment or that people being wealthy damages poor people or that “minorities” are invariably oppressed. If they were right, this would mean an entropy flow from the “winner” to the “loser”. Instead, human interactions often are win-win situations, which would become apparent if one took each interaction of the “winner” and “loser” as one system which would turn out to be self-organizing, i.e. dumping entropy on the rest of the universe. Even if such a system would indeed dump entropy on other people (i.e. it is a parasitic system), the exception defined by Postulate 9 would discover that, which is why Halbe’s Razor in this case allows for looking at the auxiliary occurrence of “impacted surroundings” despite above-described difficulties of considering an additional system.

Derivation 2: Extrapolating from lower orders of magnitude

If running into Postulate 5 at a higher order of magnitude, an estimation of the direction of entropy change at this higher order can be acquired by extrapolating from objects and occurrences at lower orders of magnitude.
Follows from: Postulates 1, 2, 4, and 5

Postulate 5 prevents people from drawing boundaries around matter and radiation so complex that it is beyond human capacity for information processing. This can easily happen at larger orders of magnitude. However, if the next lower orders of magnitude are within capacity, i.e. boundaries according to postulates 1 and 2 can be drawn within them, one can still have some estimates regarding the stability of the proposed thing on the higher order of magnitude that is beyond capacity. In other words, one can never speak about it with even close to the accuracy afforded by Postulates 1 and 2, but one does not have to shut up about it completely and can arrive at rough estimates of entropy change. Such applications of statistics are afforded by the probabilistic principle stated in Postulate 4.

If the average entropy change of a representative number of occurrences at the lower order of magnitude is negative, I can assume stability at the higher level.

Derivation 3: Nonexistence of Organization

There is only entropy gain or self-organization, no organization.
Follows from: Postulate 6, Derivation 1

Since we can only ever talk about one thermodynamic system (Derivation 1) and since a system that loses entropy must be self-organizing (Postulate 6), Halbe’s Razor never allows saying that one system organizes another. Organization does not exist. 

Halbe’s Razor maintains that saying one system would organize another adds unnecessary complexity that can lead to errors. It is more precise to simply group the “organizing” and “organized” systems into one system, which is then called “self-organizing” and is defined by an entropy change different to its surroundings (see postulate 2). This way, artifacts that can result from arbitrary grouping are avoided, and instead of one measurement for each smaller system, there is just one measurement for a larger system, which reduces the extent of measurement errors and sampling error (see explanation of Derivation 1).

Derivation 4: Recursiveness of the Razor

Every observable attempted application of Halbe’s Razor as well as the creation of Halbe’s Razor is an occurrence describable through Halbe’s Razor. 
Follows from: Postulates 2 and 5

Every such attempt as well as the historical occurrence of me creating this document should be seen as a system that includes both the matter and radiation of the information-processing structures that draw the boundaries and the matter and radiation between those boundaries. This is necessary because elsewise, Halbe’s Razor would not exist according to Postulate 5.

Derivation 5: Razor success means self-organization

Every successful application of Halbe’s Razor is a case of self-organization.
Follows from: Postulates 6 and 7, Derivation 4

Since the drawing of boundaries needs to be non-random enough to even qualify for Halbe’s Razor, the system talked about in Derivation 4 needs to be self-organizing and stable. If the attempted application does not succeed, it means an entropy increase in this system instead.

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