iSoul In the beginning is reality.

Category Archives: Science

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

Galileo’s method

Extracts about Galileo from Scientific Method: An historical and philosophical introduction by Barry Gower (Routledge, 1997):

Galileo took great pains to ensure that his readers would be persuaded that his conclusions were correct. p. 23

The science of motion was then understood to be a study of the causes of motion, and to be, like any genuine science, a ‘demonstrative’ kind of enquiry. That is to say, experiential knowledge of the facts of motion was superseded by rational knowledge of the causes of those facts, this being accomplished by deductions from fundamental principles, or ‘common notions’, and definitions which were accepted as true. These facts of motion were understood as expressions of common experience rather than as generalisations based upon experiments. This was because the results of the experiments that could be performed were sufficiently uncertain and ambiguous to prevent reliable generalisation; discrepancies between conclusions derived from principles, and experimental results, could be tolerated. The appropriate model of a demonstrative science was Euclidean geometry, where the credibility of a theorem about, say, triangles depends not on how well it fits what we can measure but on its derivability from the basic axioms and definitions of the geometry. p. 23

For Galileo and his contemporaries there was a good reason why demonstration, or proof from first principles, rather than experiment, was required to establish general truths about motion. Any science—scientia—must yield knowledge of what Aristotle had called ‘reasoned facts’, i.e. truths which are both universal and necessary, and such knowledge—philosophical knowledge—can only be arrived at by demonstration. p. 24

there was a long-standing disagreement about the role that mathematics could play in natural philosophy, even though mathematics was able to give certain knowledge. p. 24

In some contexts, notably astronomy and geometry, the more elaborate and intellectually demanding methods of mathematics were often useful and appropriate, but in such contexts it seemed clear that those methods were applicable in so far as what was needed were re-descriptions which could help people formulate accurate predictions. ‘Hypotheses’ which successfully ‘saved the phenomena’, in the sense that they could be used as starting points for derivations of accurate predictions, could meet this need. p. 25

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Mathematics and beauty

Extracts from Scientific Method in Ptolemy’s Harmonics by Andrew Barker (Cambridge University Press 2004):

Mathematics is not the study of all quantities and all quantitative relations indiscriminately. It is the science of beauty. Its task, at the theoretical level, is to interpret, in terms of ‘rationally’ or mathematically intelligible form, the features, movements or states which, when they are present in perceptible phenomena, constitute their aesthetic excellence. p.264

Those of our senses through which we are able to perceive some things as beautiful are therefore involved in an intimate collaboration with mathematical reason. p.264

Since beauty is the manifestation to the senses of that which reason understands as perfect in form, the senses to which beauty is undetectable lack sensitivity, which sight and hearing possess, to those distinctions which, from a rational point of view, are the most significant. p.265

the mathematical sciences have a single objective, the analysis and understanding of the formal basis of beauty p.266

The conception of mathematical science which Ptolemy has presented is that of a capacity that does not merely analyse sets of quantitative relations, but homes in on those that are of special significance, and discovers the principles on which their significance rests. p.268

Composition order

Written compositions organized by temporal order are narratives. Items such as descriptions of people, places, or objects are organized as they occur to the narrator, for example, as the narrator takes apart an object or walks through a building or meets various people. This is a common method of composition but there are others.

Spatial order is another method of composition. Items such as descriptions of people, places, or objects are organized by their physical or spatial positions or relationships, for example, starting at the top and proceeding downward. Explanations of a geopolitical matter might proceed in geographic order.

Travel can be described temporally or spatially. An itinerary is usually arranged temporally but telling about it afterwards might be more interesting if arranged spatially. There are other principles of organization such as climactic order (order of importance) and topical order.

In science the independent variable determines the type of organization. If the independent variable is time, the organization is temporal. If the independent variable is space or distance, the organization is spatial. The stance in spatial organization corresponds to the time in temporal organization.

The values of the independent variable are the index to the order of the composition. If the independent variable is time, then the times indicate the steps in the order. If the independent variable is space or distance, then the stances indicate the steps in the order. Once the step is indicated, the composition may be the same: whether it’s Tuesday, so the tour is in Paris or it’s Paris, so the tour is on Tuesday makes no difference.

History and science balanced

As I’ve noted before (here etc.) history and science have different aims and methods. Mixing them just confuses both of them. There is no genuine “historical science” or “scientific history”. History narrates particulars among unique events. Science theorizes universals among repeatable events. In physics time is homogeneous: an experiment is the same whether conducted today or 100 years in the past or future. That is not true in history. Time is not homogeneous there.

History and science can and should balance one another. The more science expands its universals, the more history can point out particulars that are overlooked or are important in a particular context. The more history focuses on unique particulars, the more science can point out the significance of universals.

The homogeneous and inhomogeneous aspects of time can both be known only by balancing history and science. One could say something similar about all universals and particulars. The universal and particular aspects of reality can both be known only by balancing history and science.

Abstract and concrete movements

Abstraction in Western culture has increased over time, so much so that Hegel made this the engine of history: his dialectic is a progression from the concrete to the less concrete, the abstract to the more abstract. Certainly, the history of natural science shows this progression. Modern physics is more abstract than classical physics. Every science becomes more abstract over time.

Increased abstraction in society and politics requires larger collections of people. Equality with increased abstraction requires equality within larger groups of people. For example, pan-European equality is less abstract than equality within global equality. Increased abstraction requires loyalty to ever larger groups.

History does seem to progress toward greater abstraction. Tribal cultures gave way to city-states, then to nations, then to globalism. In the U.S., there has been a progression from an English culture to a European culture, to a Euro-Afro-Latin culture, to an increasingly global culture. Those who promote this movement are called “progressives”. Those who resist it or support caution about it are called “conservatives”.

In sub-cultures of the West and in some non-Western societies there are movements in the opposite direction, toward more concreteness. They are often called “regressive”, which assumes a prior progressive movement. They could simply be called “concretive” (or “introgressive”) since they prefer the more concrete to the more abstract.

Those who prefer more concrete or at least a less abstract culture are considered traditional, old-fashioned, or backwards. In order to engage their opponents, traditionalists need to justify their preference for the concrete in more abstract ways, which they may find difficult. But the concrete has its advantages as much as the abstract does.

One danger of greater abstraction is that one loses touch with concrete reality. After all, human beings are concretely embodied. Concrete food, shelter, and much more are necessary for human life. Traditional social and political structures have much experience and stability behind them and so “should not be changed for light and transient causes” (the U.S. Declaration of Independence). And the new global human who ignores the local culture where they happen to be is looking for misunderstanding and worse.

In fact, there is no global, pan-religious, pan-racial, pan-sexual, pan-economic, pan-linguistic culture. Is such a culture even possible? In this world, that is highly doubtful. People are both concrete and abstract, body and spirit.

Concrete and abstract movements both have their place. Cultures will lean more toward one than the other, but both are legitimate.

Lorentz factor from light clocks

Space and time are inverse perspectives on motion. Space is three dimensions of length. Time is three dimensions of duration. Space is measured by a rigid rod at rest, whereas time is measured by a clock that is always in motion relative to itself.

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

The first figure above shows frame S with a light clock in space as a beam of light reflected back and forth between two mirrored surfaces. Call the height between the surfaces that the light beam travels distance h. Let one time cycle Δt = 2h/c or h = cΔt/2, with speed of light c, which is the maximum speed.

The second figure shows frame with the same light clock as observed by someone moving with velocity v relative to S. Call the length of each half-cycle d, and call the length of the base of one cycle in space b.

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Set theory and logic and their dual

(1) Set theory and logic, (2) number and algebra, and (3) space and time are three foundational topics that each have duals. Let us begin with the standard approaches to these three topics, and then define duals to each of them. To some extent, the original and the dual may be used together.

(1) Set theory and logic

A set is defined by its elements or members. Its properties may also be known or specified, but what is essential to a set is its members, not its properties. The notation for “x is an element of set S” is “x ∈ S”. A subset is a set whose members are all within another set: “s is a subset of S” is “s ⊆ S”. If subset s does not (or cannot) equal S, then it is a proper subset: “s ⊂ S”.

The null set (∅) is a unique set defined as having no members. That is paradoxical but not contradictory. A universal set (Ω) is defined as having all members within a particular universe. An unrestricted universal set is not defined because it would lead to contradictions.

The complement of a set (c) is the set of all elements within a particular universe that are not in the set. A union (∪) of sets is the set containing all members of the referenced sets. An intersection (∩) of sets is defined as the set whose members are contained in every referenced set.

Set theory has a well-known correspondence with logic: negation (¬) corresponds to complement, disjunction (OR, ∨) corresponds to union, and conjunction (AND, ∧) corresponds to intersection. Material implication (→) corresponds to “is a subset of”. Contradiction corresponds to the null set, and tautology corresponds to the universal set.

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Three kinds of empirical science

This post is related to an old post here.

Broadly speaking, there are three kinds of empirical science, which correspond to three views of nature.

(1) The ancient view of empirical science is represented by Aristotle, which includes the careful observation of undisturbed nature. Motion, for example, meant natural motion, not “violent” motion in which there is a change of the natural course of things. Experimentation was not considered a way to understand undisturbed nature.

(2) The early modern view of empirical science includes experimentation because nature is understood to include what happens after an intervention in the course of nature. These experiments allowed early modern scientists to isolate causal factors in nature. The human observer was not considered part of any experiment.

(3) The late modern view of empirical science includes the observer as part of nature. The distinction between natural and artificial is discarded. The origin and nature of humans is included in his view of nature. Empirical science covers all aspects of human beings that can be observed. The scientist has a double life in which they both are and are not the object of science.

The second kind of empirical science is superior because it goes beyond the undisturbed nature of the first kind and does not include the contradiction at the heart of the third kind.

Terminology contexts

This post continues the one here. While I avoid coining new terms or new definitions, some have been necessary. To have a consistent vocabulary, I try to imagine contexts in which they easily fit.

Some words are simply variations of words in use: distime is like distance; dischronment is like displacement; chronation is like location; elaphrance is like mass; levitation is the opposite of gravitation; and oldtons are the units for release, analogous to newtons for force. Odologe is like horologe, which is a clock.

One context is racing. The term pace is used, particularly in running and (bi)cycling to mean the time interval per unit distance, which is the inverse of speed. The direction is ignored or assumed to follow the course of the race so a new term is needed to indicate the vector version of pace. A term that has been used is legerity (from French légèreté, agility). [Note: previously used lenticity, from Latin lentus, slow, and legerity, which is an old literary term for lightness of movement.]

The second context is transport, such as package delivery. Consider an order to duralate a delivery. That means to reduce the time of transport. Release is analogous to a force applied. A package stamped with “RUSH” gets a greater effort to reduce the time of delivery, analogous to a negative release. Drawing means a release over a distance, analogous to a force applied over time (which is called impulse). Repose is a release applied over a dischronment, and is the inverse of work. Lethargy is the capacity for repose, which is analogous to energy.

Intentional and extensional causes

This post continues previous posts on causes, especially the one here.

Final and formal causes constitute top-down causality, which may lead to efficient and material causes. Material and efficient (mechanism) causes constitute bottom-up causality, which may lead to formal and final causes. Top-down is intentional. Bottom-up is extensional.

The Inverse Causality Principle states that top-down causality is inverse of bottom-up causality.

The Inverse Correspondence Principle states that intentional motion is the inverse of extensional motion and experimentation is the inverse of observation. Similarly, transmission is the inverse of reception, developmental is the inverse of empirical, and time is the inverse of space.

The goal of science is empirical theory. The goal of engineering is development of something practical.

Goal and action go together like form and content or matter.

Consider Galileo dropping two balls, one wooden and one metal, from the tower of Pisa. One observer says it’s a race to the ground. Another observer says it’s an experiment. What is the nature of the balls? Or what does Nature do?

Final and formal causes are the inverse of efficient and material causes.