iSoul In the beginning is reality

Category Archives: Science

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

Amateur and independent science

An independent scientist (or gentleman scientist) is someone who pursues scientific research while being independent of a university or government-run research and development body. “Self-funded scientists practiced more commonly from the Renaissance until the late 19th century … before large-scale government and corporate funding was available.” (Wikipedia)

Independent scientists are amateurs in the sense that they are doing scientific research for the love of it (the word is from the French amateur, “one who loves”) rather than as an occupation. They may have an occupation in a related field such as teaching science but their scientific research is done on their own time. Or they may be professional scientists in a specialty other than their research.

I remember years ago hearing the great Hungarian mathematician Paul Erdős remark that an “amateur mathematician” had done work in number theory. He explained that the amateur was a professional mathematician but not a professional number theorist. That made the person an amateur number theorist. It is the same with professionals in any specialty outside their own.

Some great scientists were professors of mathematics, such as Galileo, who was a professor of mathematics at the University of Padua, and Isaac Newton, who held the Lucasian Chair of Mathematics at the University of Cambridge.

In the history of science many breakthroughs have been done by amateurs. Here are some great amateurs or independent scientists:

Albert Einstein – physics
Antonie van Leeuwenhoek – microbiology
Charles Darwin – biology
Gregor Mendel – genetics
Joseph Priestley – chemistry
Michael Faraday – electromagnetism
William Herschel – astronomy

One could add others who were primarily inventors such as Thomas Edison and the Wright brothers, since science is often given credit for inventions.

On a related note, Robert A. Stebbins wrote Amateurs, Professionals, and Serious Leisure (McGill, 1992) and other works on productive uses of one’s free time.

Inverse causes

I’ve written about Aristotle’s four causes before (such as here and here). This also continues the discussion of observers and travelers, here.

Forward kinematics refers to the use of the kinematic equations of a robot to compute the position of the end-effector (the device at the end of a robotic arm) from specified values for the joint parameters. Forward kinematics is also used computer games and animation. Inverse kinematics makes use of the kinematics equations to determine the joint parameters that provide a desired position for each of the robot’s end-effectors.

In other words, forward kinematics is for finding out what motion happens given particular inputs, whereas inverse kinematics is for determining how to move to a desired position. In terms of the four Aristotelian causes or explanatory factors, forward kinematics is concerned with the efficient and material causes, and inverse kinematics is concerned with the final and formal causes.

The surprising thing is that these two kinds of causes (higher and lower) are inverses of one another.

Higher Final Formal
Lower Efficient / Mechanism Material

From the lower perspective one begins with some material. From the higher perspective one begins with the objective. From the lower perspective forces and laws make things happen. From the higher perspective following plans gets the job done.

One can see rôles parallel to the causes:

Traveler Set the destination Plan the trip
Observer Observe the motion See the material

And in robotics (or animation):

Inverse Pick the end position Plan the motions
Forward Make the motions Pick the device

One could say that forward kinematics is for scientists and inverse kinematics is for engineers since the latter incorporate objectives and designs in their work but the former are focused on observation only. To go beyond observation scientists would have to open up to formal and final causes.

Logic as arithmetic

George Boole wrote on “the laws of thought,” now known as Boolean Algebra, and started the discipline known as Symbolic Logic. A different George, George Spencer Brown, wrote on “the laws of form,” which presented an arithmetic system underlying logic. Below are two symbolic logics equivalent to Boolean algebra that resemble ordinary arithmetic in some respects. To resemble arithmetic in other respects, use the Galois field of order 2, GF(2). Zero is taken as representing false, and one as true.



A – 0 = 1 – A = 1

A – 1 = A


– A is defined as 0 – A (and so 0 is ”  “, ground, false)

A + B is defined as  A – (– B)


A 0 − A A − B 0 1 A + B 0 1
0 1 0 1 0 0 0 1
1 0 1 1 1 1 1 1


– (– A) = A

A − B = A ← B

A + B = A ∨ B

A + B = B + A

– is not distributive



0 / A = A / 1 = 0

A / 0 = A


/ A is defined as 1 / A (and so 1 is ”  “, ground, true)

A • B is defined as  A / (1 / B)


1 / (1 / A) = A

A / B = – (A → B)

A • B = A ∧ B

A • B = B • A

/ is not distributive


A 1 / A A / B 0 1 A • B 0 1
0 1 0 0 0 0 0 0
1 0 1 1 0 1 0 1


Physics and theology

The 19th century physicist Ernst Mach is known for his view that all motion is relative, which influenced Albert Einstein. Mach is also known for his book The Science of Mechanics (1883 in German, 1893 in translation), from which the following excerpts about physics and theology are taken (Open Court edition, 1960):

Consolation, [Pascal] used to say, he could find nowhere but in the teachings of Christianity; and all the wisdom of the world availed him not a whit. p.543

Every unbiased mind must admit that the age in which the chief development of the science of mechanics took place, was an age of predominantly theological cast. Theological questions were excited by everything, and modified everything. No wonder, then, that mechanics is colored thereby. p.546

In Leibniz’s correspondence with John Bernoulli, theological questions are repeatedly discussed in the very midst of mathematical disquisitions. Their language is not unfrequently couched in biblical pictures. p.549

Maupertuis, the famous president of the Berlin Academy, and a friend of Frederick the Great, gave a new impulse to the theologizing bent of physics by the enunciation of his principle of least action. In the treatise which formulated this obscure principle … the author declared his principle to be the one which best accorded with the wisdom of the Creator. p.549

Euler magnanimously left the principle [of least action] its name, Maupertuis the glory of the invention, and converted it into something new and really serviceable. … The theological point of view, Euler retained. He claims it is possible to explain phenomena, not only from their physical causes, but also from their purposes. “As the construction of the universe is the most perfect possible, being the handiwork of an all-wise Maker, nothing can be met with in the world in which some maximal or minimal property is not displayed. There is, consequently, no doubt that that all the effects of the world can be derived by the method of maxima and minima from their final causes as well as from their efficient ones.” p.550

Similarly, the notions of the constancy of the quantity of matter, of the constancy of the quantity of motion, of the indestructibility of work or energy, conceptions which completely dominate modern physics, all arose under the influence of theological ideas. The notions in question had their origin in an utterance of Descartes, before mentioned, in the Principles of Philosophy, agreeably to which the quantity of matter and motion originally created in the world–such being the only course compatible with the constancy of the Creator–is always preserved unchanged. The conception of the manner in which this quantity of motion should be calculated was very considerably modified in the progress of the idea from Descartes to Leibniz, and to their successors, and as the outcome of these modifications the doctrine gradually and slowly arose which is now called the “law of the conservation of energy.” But the theological background of these ideas only slowly vanished. p.551

During the entire sixteenth and seventeenth centuries, down to the close of the eighteenth, the prevailing inclination of inquirers was, to find in all physical laws some particular disposition of the Creator. But a gradual transformation of these views must strike the attentive observer. Whereas with Descartes and Leibniz physics and theology were still greatly intermingled, in the subsequent period a distinct endeavor is noticeable, not indeed wholly to discard theology, yet to separate it from purely physical questions. Theological disquisitions were put at the beginning or relegated to the end of physical treatises. Theological speculations were restricted, as much as possible, to the question of creation, that, from this point onward, the way might be cleared for physics. p.551-552

Towards the close of the eighteenth century a remarkable change took place,–a change which was apparently an abrupt departure from the current trend of thought, but in reality was the logical outcome of the development indicated. After an attempt in a youthful work to found mechanics on Euler’s principle of least action, Lagrange, in a subsequent treatment of the subject, declared his intention of utterly disregarding theological and metaphysical speculations, as in their nature precarious and foreign to science. He erected a new mechanical system on entirely different foundations, and no one conversant with the subject will dispute its excellencies. All subsequent scientists of eminence accepted Lagrange’s view, and the present attitude of physics to theology was thus substantially determined. p.552 [Lagrange’s Mécanique analytique was published in 1788.]

Newton never, despite his profound religiosity, mingled theology with the questions of science. … The same may be said of Galileo and Huygens. p.552

It stands to reason that in a stage of civilization in which religion is almost the sole education, and the only theory of the world, people would naturally look at things from a theological point of view, and that they would believe that this view was possessed of competency in all fields of research. p.553 #

… the theological conception of nature itself owes its origin to an endeavor to obtain a more comprehensive view of the world;–the very same endeavor that is at the bottom of physical science.  p.556

In fact, science can accomplish nothing by the consideration of individual facts; from time to time it must cast its glance at the world as a whole. p.556

But now, after a century has elapsed, after our judgment has grown more sober, the world-conception of the encyclopaedists appears to us as a mechanical mythology in contrast to the animistic of the old religions. p.559

Physical science does not pretend to be a complete view of the world; it simply claims that it is working toward such a complete view in the future. The highest philosophy of the scientific investigator is precisely this toleration of an incomplete conception of the world and the preference for it rather than an apparently perfect, but inadequate conception. p.559

# One might update this sentence as follows: It stands to reason that in a stage of civilization in which science is almost the sole education, and the only theory of the world, people would naturally look at things from a scientific point of view, and that they would believe that this view was possessed of competency in all fields of research.

Design illustrated

This post continues thoughts about design, last posted here.

Here is a description of how cement is made from the Portland Cement Association:

In its simplest form, concrete is a mixture of paste and aggregates, or rocks. The paste, composed of portland cement and water, coats the surface of the fine (small) and coarse (larger) aggregates. Through a chemical reaction called hydration, the paste hardens and gains strength to form the rock-like mass known as concrete.

The key to achieving a strong, durable concrete rests in the careful proportioning and mixing of the ingredients. A mixture that does not have enough paste to fill all the voids between the aggregates will be difficult to place and will produce rough surfaces and porous concrete. A mixture with an excess of cement paste will be easy to place and will produce a smooth surface; however, the resulting concrete is not cost-effective and can more easily crack.

The design in this case is the proportion of ingredients in the mixture. It might happen that the ingredients formed naturally but they would be in the correct proportion only by design. That is, the particular application entails a goal, which the design meets.

Certainly concrete can and does happen naturally in aggregate rock formations. But it does not meet a need without a design. And that doesn’t happen naturally. Roads built with concrete only happen because engineers and construction crews built them. There’s nothing natural about that.

Design and entropy

A carrier is the baseline transmission (such as a wave) that is modulated for a signal. Carriers have minimum entropy. Their opposite, noise, has maximum entropy. A signal conveys a message between a sender and a receiver. The entropy of signals is between that of the carrier and noise.

Carriers are the canvas for the artist. The canvas starts out blank. Then paint is added, which is the signal for the viewer. Noise would be like splotches of paint that somehow got put on the canvas. If the canvas were all noise, the signal would be completely covered with random bits of paint. The signal is designed to be between these extremes.

The closer a signal is to looking like the carrier, the lower the entropy and the simpler the message. The closer a signal is to looking like noise, the higher the entropy and the less the complexity of a message that can be transmitted. With the carrier alone or noise alone there is no message.

Design works the same way. A carrier alone or noise alone exhibit no design. A simple design would be similar to a carrier or to noise. A more complex design would be between the extremes of all carrier and all noise.

Entropy is a way to determine the presence of design. The more that entropy is in-between zero and the maximum, the more likely it is a result of design. A simple measure of design may be constructed from entropy as follows:

Define a design index, Υ (upsilon) from the entropy, H, as

Υ := (HHmin) / (HmaxHmin),

which ranges from zero if H = Hmin to one if H = Hmax. If the design index is one-half, then H is the mid entropy. The closer the value of Υ is to one-half, the more likely the distribution is the result of design.

2015, updated

Knowledge and repetition

Consider the distinction between repeatable events from unrepeatable events. Repeatable events includes events that have repeated or may be repeated at will (as in a laboratory) or may possibly repeat in the future. Unrepeatable events are events that are very unlikely to repeat or are impossible to repeat. It is said that science only studies repeatable events, and it can be argued that history is the study (science) of unrepeatable events – not that it excludes repeatable events but that it focuses on unrepeatable events.

“Nature” could be defined as the realm of repeatable events. Then natural science would be the study of nature or repeatable events. Those events that are unrepeatable would be left to historians but ignored by natural scientists. But could such scientists rightly study the past while ignoring unrepeatable events? Ignorance of unrepeatable events would be a limitation and a defect. We would not expect historians to ignore repeatable events, so why expect scientists to ignore unrepeatable events?

We may well expect events that only involve inanimate nature are repeatable in some way. But are all events with living beings repeatable? The position of naturalism says, Yes. But at some point we need to say, No, at least some living beings have free will (or whatever you want to call it) so that their actions may be unrepeatable, and thus beyond the purview of a science of repeatable events.

Knowledge of repeatable and unrepeatable events may need different methodologies to address both kinds of events but it could not ignore either kind without bias. We need both the study of history, with its unrepeatable events, and the study of science, and its repeatable events, as independent disciplines. The synthesis of science and history would require a different discipline, perhaps called “scihistory” or “histence”, that would balance the input of each discipline with the other.

Science in the center

There are many different musical temperaments that have been used to tune musical instruments over the centuries. They all have their advantages and disadvantages. But there is one musical temperament that is optimally acceptable: the equal temperament method in which the frequency interval between every pair of adjacent notes has the same ratio. This produces a temperament that is a compromise between what is possible and what is agreeable to hear.

Science faces many situations such as the challenge of musical temperament. Conventions and methods need to be adopted and there are multiple options, each with their advantages and disadvantages. There are those who promote one method and those who promote another method, often the opposite method. Should science pick one and force everyone to conform? Or should science find a compromise of some sort?

There is a way in the middle that is a compromise between extremes and alternatives. It is a conscious attempt to avoid extremes and biases, and seek a solution that is the most acceptable to all. This is science in the center, a science that minimizes bias. Although it might be called “objective,” that obscures the fact that it is a conscious choice.

I previously wrote about the need for a convention on the one-way speed of light. Science of the center would avoid the bias toward one direction of light and choose a one-way speed that is in the middle between all the possible speed conventions. This is the Einstein convention, which is part of his synchronization method.

Science in the center includes not biasing classifications either toward “lumping” or “splitting.” Nor should explanations of behavior be biased toward “nature” or “nurture.” The particulars of each case should determine the outcome, not a preference for one side or the other. If there’s any default answer, it’s in the center between such extremes.

Occam’s razor is understood to prescribe qualitative parsimony but allow quantitative excess. This is as biased as its opposite would be: to prescribe quantitative parsimony but allow qualitative excess. Science in the center would avoid the bias that each of these has by prescribing a compromise: there should be a balance between the qualitative and the quantitative. Neither should be made more parsimonious than the other. All explanatory resources should be treated alike; none should be more abundant or parsimonious than any other. I’ve called this the New Occam’s Razor, and it is an example of science in the center.

Reality and conventions #4

This post continues a series of posts. The previous one is here.

Modern natural science attempts a systematic account of the causes of change in the physical world, and is willing to go against the appearance of the physical world if that will further its goals. This differs from the ancient Platonic attempt to “save the appearances” at all costs by placing appearances within an ad-hoc but meaningful system.

In one sense, philosophy is the helpmeet of science. It aids in the task of putting our conceptual household in order: tidying up arguments, discarding unjustified claims. But in another sense, philosophy peeks over the shoulder of science to a world that science in principle cannot countenance. As Professor Scruton put it elsewhere, “The search for meaning and the search for explanation are two different enterprises.” Science offers us an explanation of the world; it may start out as an attempt to explain appearances, “but it rapidly begins to replace them.” Philosophy seen as the search for meaning must in the end endorse the world of appearance. The New Criterion, vol. 12, no. 10

Saving the appearances famously led to tweaking Ptolemaic astronomy despite its inability to explain why celestial bodies should move in epicycles. The Newtonian system didn’t give ultimate explanations but at least it gave laws that applied on Earth and skyward.

Yet there is nothing “wrong” with saving appearances such as the motion of the Sun relative to the Earth. In that sense, geocentrism was never wrong despite generations of people being taught so. Whether saving the appearances or saving the system is a goal, both must accept some conventions that include things such as the celestial body of reference – or lack thereof.

One may legitimately pursue a phenomenal science that saves appearances by sacrificing some consistency in conventions. For example, the Moon is in orbit relative to the Earth and the Sun is in a different kind of orbit relative to the Earth. In order to save both of these appearances, one would have to use a gravitational dynamics for the Earth-Moon system and a levitational dynamics for the Earth-Sun system. Awkward, perhaps, but legitimate.

Reality and conventions #2

This post continues the topic of the previous post here.

Every pair of contrary opposites may have one or more conventions associated with it. That is because there is a symmetry between the two that can be reversed. Note this is not the case with contradictory opposites: they are not symmetric. Note also that terms may be symmetric without the references of the terms being exactly symmetric.

I’ll start with the latter point. A common example is the terms for male and female. In some respects they are symmetric opposites but in other respects they are not. The language can mislead on this point. Males and females have some similarities, some contrary (or complementary) differences, as well as differences that are not contraries, just different. Some aspects of male-female relations are conventions but not every aspect is.

The deconstructionists associated binary opposites with power structures (not unlike Hegel). They would reverse the meaning in order to undermine them. That assumes pairs are complete contraries, which is not as common as they thought. Deconstructionism works mostly on texts, in which the language of contrary opposites is deconstructed. The conventions associated with contrary opposites can be reversed but not all binary opposites are genuine contraries.

Contradictory opposites such as good and evil or true and false are not symmetric, contrary to the language that is often used. Not-evil is not necessarily good and not-false is not necessarily true. What is a matter of goodness or truth are not mere conventions.

There is a reality independent of us (or of our minds) but some things are conventions that are dependent on us. Motion is real but all motion is relative so it is a convention as to what motion is relative to. Galileo and the Scholastic philosophers (and their supporters) were wrong to think of the Earth as either only at rest or only in motion. Whether or not the Earth moves is a convention.