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Biological classes and ancestries

Taxonomy is the science of classification. Once multiple classes are determined, it is possible to determine the classes of classes and so on. At some point this process will end, either with a single class or multiple classes with too many differences to be reasonably classified together.

Taxonomy applied to biology is a systematic approach to classifying organisms. It can be applied to all organisms at a particular time, throughout time, or within any context. Once a classification is determined, other questions arise such as whether there is an independent reason that organisms are in a same class together.

The basic question in all classifications is whether the objects to be classified fit within a class or belong to another class. The goal of a classification is to minimize the within-class differences and maximize the between-class differences. This is often done by defining a distance metric that quantifies the differences.

Carl Linnaeus is known as the father of modern taxonomy who formalized the binomial nomenclature and called the lowest classes species and genus (no doubt after Aristotle’s method of defining with species and genera). His original expectation was that these biological species were natural kinds that persist through time. With the discovery that fossils were from dead organisms, it became clear that his species changed over time.

The solution to this problem is to classify organisms both living and dead in one classification system. But this was easier said than done since it took years for fossils to be examined. Meanwhile, people were anxious to know how all the diversity of species arose. Charles Darwin‘s answer was quickly adopted: species are temporary population groupings rather than natural kinds that persist over time.

Without persistence over time there is only one permanent class: the class of all organisms.

Others reject Darwin’s answer and assert there are multiple classes of organisms that persist over time. This is implicit in arguments that infer design or special creation, in which there are discontinuities between classes. How can this dispute be resolved? Elliott Sober compares these two hypotheses in his book Evidence and Evolution.

Sober argues for a likelihood approach to determining the better of two hypotheses. The law of likelihood states that evidence E favors hypothesis H1 over H2 if and only if the probability of E given H1 is greater than the probability of E given H2, or in symbols, P(E | H1) > P(E | H2). Note that this is a comparative approach; it only works when comparing two specific hypotheses.

In this case, the context is all organisms on the earth over all the history of life on earth. Hypothesis H1 states that there are multiple classes of organisms that span the history of life on earth (because there is separate ancestry). Hypothesis H2 states that there is only one class of organisms that span the history of life on earth (because there is common ancestry).

Sober notes that Darwin routinely inferred common ancestry if there was some similarity between organisms or species. Sober calls this modus Darwin. But it is better to have an overall metric of distance between organisms or species than rely on a few similarities. However, there is no such generally accepted distance metric. In its absence, we can still make general inferences.

If there are many similarities between two organisms or species, that evidence is more likely given hypothesis H2 (common ancestry). But if there are fewer similarities and some great differences between two organisms or species, that evidence is more likely given hypothesis H1 (separate ancestry). Since hypothesis H1 includes partial common ancestry, it can explain similarities as well as differences. The conclusion from this exercise is that separate ancestry is the superior hypothesis.

A problem arises when proponents of common ancestry insist on an explanation of how these separate lines of ancestry arose in time. The best answer is that, just as biogenesis is not part of the common ancestry hypothesis, so the ultimate origin of the separate classes is not part of the separate ancestry hypothesis.

Elemental inverse

Begin with elements. Elements are a very general concept: they may be either members of sets or distinctions of classes. As a set is defined by its members, so a class is defined by its distinctions. So, the elements of sets are members and the elements of classes are distinctions.

Sets may be divided into subsets or combined into supersets. Classes may be divided into subclasses or combined into superclasses. Distinctions may be between classes or within classes. Members may be within sets or without sets.

One might say that a class is just a set of distinctions, or one might also say that a set is just a class of members. But that would blur their differences.

Sets assume one knows members and is trying to combine them into the right sets. Classes assume one knows distinctions and is trying to divide them into the right classes. Aristotle assumed that classes could be known by defining them with the right distinctions. Empiricists assume that sets can be known by defining them with the right members.

Realists begin with classes. A tree is defined by its distinctions. Upon inductive investigation, trees may be grouped into types of tree. Upon deductive investigation, types of trees have certain properties.

Induction proceeds from classes to sets. Deduction proceeds from sets to classes. Sets and classes are like inverses of one another.

Both sets and classes are axiomatized by Boolean algebra with the axioms of identity, complementation, associativity, commutativity, and distributivity.

Physical history

At the highest level of classification, history may be divided into human history (better known simply as ‘history’) and physical history. The former is a large subject with many subdivisions, while the latter is usually turned over to the physical sciences. This is a pity since science and history are different disciplines (see posts here). What follows is a description of physical history as distinct from physical science.

History requires an agent of some kind. The environment is the proxy for an agent in evolutionary science. In physical history the agent is either humanity or one or more non-physical beings that connect to the physical world at its boundaries. The metaphysics of the latter are of no interest here, only their possibility. In other words, the physical universe has boundary conditions that are given; they are not a result of physical laws or processes.

But this sets up a potential conflict between a boundary condition which could have been the result of physical laws or process but was not. It would be simple to assume that all boundary conditions are such that they could not have been the result of physical laws or processes. But that assumes the limits of physical laws or processes are known, when they are to be determined rather than assumed.

Accordingly, the limits of physical laws and processes are themselves a matter of investigation. In other words, such limits are an open question. A good example of this is the argument for the existence of design in the physical world apart from human design. From human design we know something of what design is; if the physical world exhibits the features of human-like design but were not designed by humans, then a boundary condition has been found.

Otherwise, physical history is like human history. Physical particulars of the past are at the forefront, and universals of physical science are in the background. Whatever might be determined by physical science is acknowledged but the significant changes, the physical catastrophes and surprises, are granted a much greater rôle. There will no doubt be controversies between those who place much weight on key events versus those who look to the slow accumulation of little changes but such is usual for history.

Cycle of science

There is a well-known alternation of induction and deduction in science (click to enlarge):

induction-deduction cycleThe induction phase consists of data collection, data analysis, and model development. The deduction phase consists of taking the model, making hypothetical inferences, and following up with experiments that lead to new data collection. Then the cycle repeats.

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Isaiah Berlin on history and science

The following (long) excerpts are from Isaiah Berlin’s article “History and Theory: The Concept of Scientific History”, published in History and Theory 1 (1):1 (1960). Republished in Concepts and Categories: Philosophical Essays. NY: Viking Press, 1979. (online here).

HISTORY, according to Aristotle, is an account of what individual human beings have done and suffered. In a still wider sense, history is what historians do. Is history then a natural science, as, let us say, physics or biology or psychology are sciences? And if not, should it seek to be one? And if it fails to be one, what prevents it? Is this due to human error or impotence, or to the nature of the subject, or does the very problem rest on a confusion between the concept of history and that of natural science? These have been questions that have occupied the minds of both philosophers and philosophically minded historians at least since the beginning of the nineteenth century, when men became self-conscious about the purpose and logic of their intellectual activities. But two centuries before that, Descartes had already denied to history any claim to be a serious study. Those who accepted the validity of the Cartesian criterion of what constitutes rational method could (and did) ask how they could find the clear and simple elements of which historical judgements were composed, and into which they could be analysed: where were the definitions, the logical transformation rules, the rules of inference, the rigorously deduced conclusions? While the accumulation of this confused amalgam of memories and travellers’ tales, fables and chroniclers’ stories, moral reflections and gossip, might be a harmless pastime, it was beneath the dignity of serious men seeking what alone is worth seeking – the discovery of the truth in accordance with principles and rules which alone guarantee scientific validity.

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History and science combined

For previous posts on history and science, see here.

History and science are different kinds of knowledge. History is based on the particulars that go into narratives. Science is based on the universals that go into theories.

History is focused on the matter and science is focused on the form, in the Aristotelian sense. The nature of something is its essence, its participation in universals, which is why there are natural sciences. Social sciences look at the form of human interaction. The term natural history is an older term for a scientific investigation into the natural world, especially biology, not a history in the modern sense.

The matter of something is its key particulars. Physical history is the investigation of the key particulars of physical objects in the past resulting in a narrative. This might be called natural history, but that term has meant science so it would be confusing. The investigation of the key particulars of documents in the past resulting in a narrative is simply called history.

History and science can be combined to explain something in the past. Yes. This is often called science but it is mainly history, with science assisting. For example, the investigation leading to the conclusion that the extinction of the dinosaurs was caused by a large asteroid or volcano is physical history that is commonly called science. Key particulars explain what happened. Science provides support. The result is a narrative, not a theory. (See here.)

The explanation of an event or series of events is history, since the particulars of events are history, even if science takes a supporting rôle. The explanation of a phenomenon or multiple phenomena is science, since their explanation depends on their nature, even if history takes a supporting rôle.

Repeating events entail universals that require science for explanation. Non-repeating events entail particulars that require history for explanation. Ancient mythology tried to explain repeating events through particulars, e.g., Zeus’ anger explains lightening, as if their nature was irrelevant. Modern mythology tried to explain unique events through universals, as if their substance was irrelevant.

“Creation science” concerns created universals. “Creation history” concerns created particulars.

Length contraction and time dilation

These derivations follow that in ‘Hyperphysics’ here.

Length Contraction

The length of any object in a moving frame will appear foreshortened in the direction of motion, or contracted. The length is maximum in the frame in which the object is at rest.

Fixed and moving reference frames

If the length L0 = x2´ − x1´ is measured in the moving reference frame, then L = x2x1 in the rest frame can be calculated using the Lorentz transformation.

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Length and duration in space and time

The following derivations are based on the exposition by G. G. Lombardi here.

Time Dilation

Time dilation with a light clock

A clock is made by sending a pulse of light toward a mirror at a distance L and back to a receiver. Each “tick” is a round-trip to the mirror and back. The clock is shown at rest in the “Lab” frame in Fig. 1a, or any time it is in its own rest frame. Consequently, it also represents the clock at rest in Rocket #1. Figure 1b is the way the clock looks in the Lab when the clock is at rest in Rocket #1, which is moving to the right with velocity v and legerity u, hence speed v and pace u.

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Lorentz from light clocks

Space and time are inverse perspectives on motion. In space length is measured by a rigid rod at rest, whereas duration is measured by a clock that is always in motion. In time duration is measured by a clock at rest relative to the time frame, whereas length is measured by a rigid rod in motion that counteracts time as it were.

This is illustrated by deriving the Lorentz factor for time dilation and length contraction from light clocks. The first derivation is in space with scalar time and the second is in time with scalar space.

light clock with height hlight clock in motion

The first figure above shows a light clock in space as a beam of light reflected back and forth between two mirrored surfaces. The height that the light beam travels between the surfaces is h. Let one time cycle Δt = 2h/c = 2 or h = cΔt/2 = Δt/(2¢), with mean speed of light c and mean pace of light ¢.

The second figure shows the light clock as observed by someone moving with velocity v and pace u relative to the light clock; the length of each leg is d; and the length of the base of one triangle-shaped cycle is b.

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Linear clocks and time frames

The idea of a linear clock was mentioned before here, here, and here.

One bar on top of anotherOne bar shifted on another

Consider two bars or rods, one on top of the other (left), each with a zero point aligned at first. The top one moves at a constant rate relative to the other, which is at rest. After a time T, the top bar has moved an interval measured by the difference between the zero points of the bars (right). The length that B moved relative to A measures the time of motion.

Side note: a 12-inch ruler turned into a circle would form the markings for a 12-hour clock. The hours of time would correspond to inches of length.

A time frame of reference (TFR), or time frame, is a frame of reference for time. Like a space frame of reference (SFR) it is composed of rigid bars or rods that can in principle be extended indefinitely.

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