iSoul In the beginning is reality.

Category Archives: Science

Science particularly as related to creation and the creation-evolution controversy

Conventions and properties

Everything in science is a combination of conventions and properties. For example, frames of reference have certain conventions in common and particular properties that each individual frame has. The definition of a frame of reference is the first convention. Every frame of reference has an origin and at least the possibility of one or more coordinate axes. But the particular origin of a frame need not be in common with other frames; it is a particular property of one frame.

Definitions and postulates are conventions. Stipulations and measurements are properties. Physical laws are conventions with the appropriate supporting definitions and postulates. Interpretations of events become conventions when they are widely accepted.

The SI metric system is the international convention for measurement (i.e., metrology). Individual measurements are properties of things. Kinematics and dynamics have a convention for simultaneity (as well as simulstanceity). The orientation of orthogonal axes follows a convention for the order of the axes and the direction of positivity.

Two principles of velocity reciprocity

Velocity reciprocity in relativity theory is the relation between two observers, each associated with a frame of reference and moving at different, but constant, velocities. That is, an observer-frame S observes another observer-frame traveling with velocity +v relative to observer-frame S. A velocity reciprocity relation concerns the velocity of S that is observed by . Einstein’s principle of velocity reciprocity states that each velocity is the same magnitude (speed) but is in the opposite direction. That is, the velocity of S observed by  is –v.

Two frames with same orientation

Einstein’s principle of velocity reciprocity reads

We postulate that the relation between the coordinates of the two systems is linear. Then the inverse transformation is also linear and the complete non-preference of the one or the other system demands that the transformation shall be identical with the original one, except for a change of v to −v. Ref.

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What Galileo really demonstrated

Galileo Galilei’s inclined plane experiment is described in his work Dialogues Concerning Two New Sciences, which I quote from the Dover edition. He speaks (through his character Salviati) of “those sciences where mathematical demonstrations are applied to natural phenomena, as is seen in the case of perspective, astronomy, mechanics, music, and others where the principles, once established by well-chosen experiments, become the foundations of the entire superstructure.” (p.178) This is the ancient method of science that Galileo applied to experiments, establishing the foundation of modern science.

Galileo states his Theorem II, Proposition II as:

The spaces described [i.e., traced] by a body falling from rest with a uniformly accelerated motion are to each other as the squares of the time-intervals employed in traversing these distances. (p.174 or p.142 on the OLL edition)

But it has just been proved that so far as distances traversed are concerned it is precisely the same whether a body falls from rest with a uniform acceleration or whether it falls during an equal time-interval with a constant speed which is one-half the maximum speed attained during the accelerated motion.

Then he describes his experiment:

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Science and Hypothesis excerpts

What follows are excerpts from the book Science and Hypothesis by Henri Poincaré, translated (1905) from La Science et l’hypothèse (1902).

p.xxiii The latter [definitions or conventions] are to be met with especially in mathematics and in the sciences to which it is applied. From them, indeed, the sciences derive their rigour; such conventions are the result of the unrestricted activity of the mind, which in this domain recognises no obstacle. For here the mind may affirm because it lays down its own laws; but let us clearly understand that while these laws are imposed on our science, which otherwise could not exist, they are not imposed on Nature. Are they then arbitrary? No; for if they were, they would not be fertile. Experience leaves us our freedom of choice, but it guides us by helping us to discern the most convenient path to follow.

p.xxv Space is another framework which we impose on the world. Whence are the first principles of geometry derived? Are they imposed on us by logic? Lobatschewsky, by inventing non-Euclidean geometries, has shown that this is not the case. Is space revealed to us by our senses? No; for the space revealed to us by our senses is absolutely different from the space of geometry. Is geometry derived from experience? Careful discussion will give the answer—no! We therefore conclude that the principles of geometry are only conventions; but these conventions are not arbitrary, and if transported into another world (which I shall call the non-Euclidean world, and which I shall endeavour to describe), we shall find ourselves compelled to adopt more of them.

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Contraries as duals

Contrariety is a property of pairs of propositions, but it also applies to pairs of terms or concepts. “Two general terms are contraries if and only if, by virtue of their meaning alone, they apply to possible cases on opposite ends of a scale. Both terms cannot apply to the same possible case, but neither may apply.” (Aristotelian Logic, Parry and Hacker, p. 216) Opposite ends of a scale are also called extremes, which are contrasted with means between the extremes.

Every pair of contraries forms a duality by inverting the scale of which they are opposites. For example, quantitative contraries such as rich and poor become poor and rich when the scale is inverted. Every measurement scale can be inverted so in this sense a measurement and its inverse are a contrary pair that forms a self-duality. Every ratio or function of two variables, f(x, y), can be interchanged and form a duality, f(y, x). For example, the equation v = Δst can be interchanged to become u = v-1 = Δts.

The scale may be qualitative, too. For example, the qualitative contraries up and down become down and up, respectively, by looking upside-down. The contraries left and right become right and left when looked at facing the other way. Extension and intension are opposites that may be inverted by interchanging them with each other. Compare the duality of top-down and bottom-up perspectives.

“A pair of terms is contradictory if and only if by virtue of their meaning alone each and every entity in the universe must be names by one or the other but not both.” (Aristotelian Logic, Parry and Hacker, p. 216) May the terms X and not-X be made into duals? That depends. If not-X is the contradictory of X and means everything other than X, that includes things that are non-dual. But in some cases, not-X means the opposite of X, so that contraries are indicated.

Science, unity and duality

It is a Christian concept (or at least a theistic concept) that the world we inhabit is a universe. The existence of the universe requires there to be a perspective that encompasses the whole of the world, which is the perspective of a transcendent divinity. The universe is thus the whole of creation.

It is said that natural science studies the universe, but natural science today does not recognize a transcendent being, and so cannot genuinely recognize the universe. What can natural science recognize as the world that it investigates?

Natural science recognizes law and chance, the regular and the stochastic, but what determines the mix of law and chance? There are three possibilities: (1) the mix of law and chance is determined by law, in which case science investigates a cosmos; (2) the mix of law and chance is determined by chance, in which case science investigates a chaos; or (3) the mix of law and chance is determined by another mix of law and chance, which, if this duality continues at every level, indicates a dualism of law and chance as two independent principles for science to investigate.

Natural science seeks unity, so option (3) is distasteful. Option (2) is distasteful for aesthetic reasons, as well as for its lack of meaning. Option (1) is the least distasteful, and the science community increasingly states that they investigate a cosmos, a world of order that we inhabit. But mere law and order seems fatalistic, and the reality of chance keeps rearing its head, which undermines (1).

This pattern of seeking unity and finding duality occurs in other ways, too. Space and time are duals, but can they be unified by space or time? Either space alone is real (and time is unreal), or time alone is real (and space is unreal), or there is a duality of space and time that cannot be unified. Again, the first option is the most popular, though it has the same weaknesses as above.

The most satisfying answer for these dualities is that science investigates a universe, a unity that can be fully grasped only transcendently, but may be glimpsed by us. This gives us confidence that there is a unity, even if we haven’t yet found how that unity is shown by observation and experimentation. It is a qualified unity, which is not troubled by duality, and does not seek to force unity on a diverse universe.

Biological classes and ancestries

Taxonomy is the science of classification. 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 the 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 do not change over time. With the discovery that fossils came from dead organisms, it became clear that some of his species had changed over time.

The solution to this problem was to reclassify organisms both living and dead in a new 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 hypothesis was soon adopted: species are temporary population groupings with universal common ancestry. If all species are temporary, there is only one fixed class: the class of all species. Others hypothesize  there are classes of species that are fixed and have separate ancestries, which supports design or special creation.

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 species on the earth over all the history of life on earth. Hypothesis H1 states that there are multiple classes of species that span the history of life on earth, each class with separate ancestry. Hypothesis H2 states that there is only one class of species that span the history of life on earth, all with common ancestry.

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

If there are many similarities between two species, that evidence is more likely given hypothesis H2 (common ancestry), though there is some likelihood given hypothesis H1. If there are discontinuities between two species, even if there are some similarities, that evidence is more likely given hypothesis H1 (separate ancestry).

Note that if someone proposes a possible sequence of events that explains a discontinuity given hypothesis H2, it is merely a possibility and lacks likelihood. But since hypothesis H1 includes partial common ancestry, it is likely with evidence of similarities as well as differences. Note that universal common ancestry (H2) must have higher likelihood in all cases, which is unlikely. The conclusion from this exercise is that separate ancestry is the superior hypothesis.

A problem arises when proponents of common ancestry insist there must first be an explanation of how these separate lines of ancestry originated. The best answer is that, just as abiogenesis is not part of the common ancestry hypothesis, so the origin of the separate classes of species 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.

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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