iSoul In the beginning is reality

Essentials of Christian Thought, part 3

This post continues from part 2, which is here. The following are more excerpts from Roger E. Olson’s The Essentials of Christian Thought.

For [Emil] Brunner, and for me, natural theology means only (1) that the biblical-Christian worldview better answers life’s ultimate questions than its competitors and alternatives, and (2) that eyes of faith for whom the Bible “absorbs the world” see the natural world as God’s good creation—”charged with the grandeur of God”—even if eyes of unbelief cannot see it as such. p.75

For biblical-Christian thought, in contrast with Greek philosophy, souls are created by God, they are not emanations, offshoots, of God’s own substance. p.81

Nearly all extra-biblical philosophies struggle with the [biblical] idea of a personal, related, vulnerable ultimate reality capable of being influences by what creatures do. p.84

Brunner believed God is revealed in nature and in the human spirit generally (general revelation). p.92

First, … nature and universal human experience, general revelation, yield only a “thatness” of God but not God’s “whoness,” personhood, and will. What humanity needs is to know God personally, not just God’s nature as ultimate reality. Second, according to Brunner, in complete agreement with most classical Protestant theology (and the Bible in Romans 1!), reason, or the use of reason, has been spoiled in humanity by sin. p.93

The reason the human person cannot use his own reason to arrive at a satisfying life philosophy or vision or reality is his own natural tendency to minimize evil—especially in himself. p.93

Brunner argued that “everyone who philosophizes does so from a definite starting point, upon which he, as this particular man, stands. The Christian philosophizes from that point at which God’s revelation sets him.” p.94

For Brunner, the God of biblical revelation is supernatural and personal but not human. p.95

God is both ontologically beyond and personally present. p.98

The point of this entire chapter is that there is a biblical, narrative-based metaphysic that contrasts with other metaphysical visions of ultimate reality, is not irrational, lies at the foundation of Christianity itself, and is being retrieved by Jewish and Christian scholars who are also separating it from extrabiblical philosophies that conflict with it. p. 99

Many scholars tend to define the difference between philosophy and theology as revelation—theology uses it and philosophy does not. There are, however, exceptions. “natural theology” is the rational exploration of the evidence of God in nature and universal human experience. “Philosophical theology” is philosophy that explores reasons for belief in God …. p.100

Brunner coined the term eristics for his own belief that, when set alongside alternative worldviews, Christian philosophy is superior. p.106

… the biblical narrative requires belief that God’s existence precedes the world’s not only temporally but ontologically. That is, the world is dependent on God, not vice versa. p.119

[Plantinga’s] conclusion, therefore, is that there is superficial conflict but deep concord between science and theistic belief, but superficial concord and deep conflict between science and naturalism. p.122

Humanism is simply any belief in the dignity and creativity of human persons, that human beings are unique and above nature, in some sense transcendent, capable of great culture achievements as well as terrible destruction. It places special value on humanity. … the real humanism is Christian humanism because of the biblical-Christian emphasis on humans as created in the image and likeness of God. p.123

functional naturalism—belief that although God exists and is person, he does not intervene in history or human lives, which are ruled by natural laws and explainable by science. p. 125

Classical Christian theism, born in the cauldron of philosophized Christianity in the second and third centuries in the Roman Empire, reached its zenith in Anselm and Aquinas. p.132

Gradually, Christian began to envision ultimate reality, God, along the lines of Platonic metaphysics—including the idea that God, being metaphysically complete and perfect in every way imaginable, cannot suffer or be affect by temporal events or creatures. The word for this was and is impassibility. p. 136.

The next post in this series is here.

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.

LOGIC OF SUBTRACTION

Subtraction

A – 0 = 1 – A = 1

A – 1 = A

Definitions

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

A + B is defined as  A – (– B)

Tables

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

Consequences

– (– A) = A

A − B = A ← B

A + B = A ∨ B

A + B = B + A

– is not distributive

 

DIVISION LOGIC

0 / A = A / 1 = 0

A / 0 = A

Definitions

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

A • B is defined as  A / (1 / B)

Consequences

1 / (1 / A) = A

A / B = – (A → B)

A • B = A ∧ B

A • B = B • A

/ is not distributive

Tables

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

 

Essentials of Christian Thought, part 2

This post continues from part 1, here.

One characteristic of the book is that the “essentials” or “metaphysics” that Roger E. Olson elucidates are somewhat buried among the text dealing with the competing alternatives. What follows are excerpts that focus on the essentials of Christian/biblical thought itself.

A basic presupposition of this book is that the Bible does contain an implicit metaphysical vision of ultimate reality—the reality that is most important, final, highest, and behind everyday appearances. p.12

Ultimate reality is relational. p.13

Ultimate reality is personal, not impersonal, and humans reflect that ultimate reality in their created constitution—what they are. Here we will call that “Christian humanism.” p.17

Here metaphysics is simply another word for investigation into the nature of ultimate reality. p.19

… both Tresmontant and Cherbonnier argued very cogently that the biblical philosophy is holistic, not requiring supplementation by extrabiblical philosophies … and that the biblical philosophy is fundamentally contrary to Greek philosophies. p.22

in this postmodern age every philosophy is rooted in some story and tradition based on it, and that for the Christian “the Bible absorbs the world”—the biblical story, narrative, is the lens through which the Christian sees reality as God’s good creation (for example). p.23

belief in the supernatural (something above and free from nature and nature’s laws) is no more a matter of faith, “seeing as,” than belief in naturalism (that nature and its laws are all that are real). p.33

The biblical-Christian vision of reality is a “view from somewhere,” … that … better answers life’s ultimate questions than any competing worldview or metaphysical vision of reality. p.39-40

… Christian theology’s main task is not correlation with other, non-Christian worldviews or plausibility structures, but self-description of the Christian view of reality from within the Christian tradition-community inspired by the biblical story. p.41

… being Christian means, in part, seeing the world as the reality described, or presupposed, by the Bible. p.43

… [Hans Frei] argued that faithful Christians ought to take the Bible seriously as “realistic narrative.” In other words, the Bible ought not to be viewed either as history in the modern, literal sense (viz., a textbook of facts about history) or as myth (symbolic representation of universal human experience). Rather, a Christian should find the meaning of Scripture out outside it—whether in outer history or universal human experience—but inside of it. p.43

Frei’s point is simply that the meaning of the Bible is not outside of it. p.44

The Bible depicts ultimate reality—the highest, best, final, eternal reality upon which all else is dependent—as supernatural and personal but not human. Here supernatural simply means “beyond nature,” not bound to nature and nature’s laws, free over nature, not controlled by nature. Some people would prefer the word transcendent for all that … p.53

The Bible depicts ultimate reality as personal, which here means having intelligence, thought, iintentions, actions, and some degree of self-determination. It also means “relational”—being in relation to others, drawing one’s identity partly, at least, from relations with others. p.53

… the long history of philosophical metaphysics, from Plato in ancient Greece to Hegel in nineteenth-century German, has tended to depersonalize ultimate reality, to represent ultimate reality as impersonal, a power, force, or principle behind appearances. p.56

… the ultimate reality of the Bible, Yahweh, God the Lord, is personal in the primary, supreme sense, the pattern of true personhood, which human beings are personal in the secondary sense, copies of the pattern of true personhood. p.57

In Athens Paul articulated concisely what later Christian thinkers came to refer to as God’s transcendence and immanence—that God is both present within creation and exalted above creation as its source and sustainer who needs nothing. p.62

Summing up, the biblical view of ultimate reality is that it is not an it but a he. According to the biblical narrative … ultimate, final, eternal, all-powerful, all-determining reality is a personal being both beyond the natural world and dynamically present within it. This metaphysical vision has variously been labeled “personalistic theism” and “biblical theistic personalism.” At the heart of ultimate reality, the one unifying source behind and withing everything, is an intelligence, free agency, and independent will marked by loving-kindness and justice. p.63

The next post in this series is here.

Essentials of Christian Thought, part 1

The Essentials of Christian Thought: Seeing Reality Through the Biblical Story by Roger E. Olson was published by Zondervan in 2017. It’s 256 pages long in seven chapters with as many “Interludes” but no bibliography or index. The author gives a video introduction here.

The intended audience for the book is those who accept the Bible as a guide “to the nature of ultimate reality” (p.11). Its purpose is to describe that ultimate nature (or metaphysics) according to the Bible. Much of the book is spent delineating differences between the biblical metaphysics and that of others. The author leans heavily on four authors (in order of the number of references):

Edmond La Beaume Cherbonnier (1918 – 2017), “an American scholar in the field of religious studies. He served as Professor of Religion at Trinity College, Connecticut”. Wikipedia

“Is There a Biblical Metaphysic?”, Theology Today, 15(4), January 1959, pp. 454–69.
Hardness of Heart, Doubleday, 1955.
“Biblical Metaphysic and Christian Philosophy”, Theology Today, 9(3), October 1952.
“The Logic of Biblical Anthropomorphism,” in Harvard Theological Review 55(3), 1962, 187-206.

Claude Tresmontant (1925 – 1997), “taught medieval philosophy and philosophy of science at the Sorbonne.” Wikipedia

A Study of Hebrew Thought, tr. by Michael Francis Gibson, Descle, 1960.
Christian Metaphysics, Sheed and Ward, 1965.
The Origins of Christian Philosophy, Hawthorn Books, 1963.

Emil Brunner (1889 –1966), “a highly influential Swiss theologian who, along with Karl Barth, is associated with Neo-Orthodoxy or the dialectical theology movement.” Theopedia

The Philosophy of Religion from the Standpoint of Protestant Theology, tr. by Bertram Lee Woolf, James Clarke, 1958.
Revelation and Reason: The Christian Doctrine of Faith and Knowledge, tr. by Olive Wyon, SCMP, 1946.
“Nature and Grace” in Natural Theology, tr. by Peter Fraenkel, Geoffrey Bles, 1946.

Abraham Joshua Heschel (1907 – 1972) “was a Polish-born American rabbi and one of the leading Jewish theologians and Jewish philosophers of the 20th century.” Wikipedia

Man is Not Alone, Farrar, Straus and Giroux, 1976.

The next post is here.

Curves for space and time, continued

The following is a continuation and revision of the previous post, here.

Based on the differential geometry part of the book Shape Interrogation for Computer Aided Design and Manufacturing by Nicholas M. Patrikalakis and Takashi Maekawa of MIT. A pdf version in parallel is here.

Let a three-dimensional curve be expressed in parametric form as x = x(t); y = y(t); z = z(t); where the coordinates of the point (x, y, z) of the curve are expressed as functions of a parameter t (time) within a closed interval t1tt2. The functions x(t), y(t), and z(t) are assumed to be continuous with a sufficient number of continuous derivatives.

In vector notation the parametric curve can be specified by a vector-valued function r = r(t), where r represents the position vector (i.e., r(t) = (x(t), y(t), z(t)).

curve1

Displacement Δr connecting points A and B on parametric curve r(t).

Consider a segment (displacement) of a parametric curve r = r(t) between two points P(r(t)) and Q(r(tt)) as shown in the figure above. As point B approaches A or in other words Δt → 0, the length s becomes the differential arc length of the curve:

ds = |dr/dt| dt = | rt | dt = √(rtrt) dt,

where the superscript t denotes differentiation with respect to the arc time parameter t. The vector rt = dr/dt is called the tangent vector at point A.

Then the arc length, s, of a segment of the curve between points r(t0) and r(t) can be obtained as follows:

s(t) = ∫ ds = ∫ √(rtrt) dt = ∫ √((dx/dt)2 + (dy/dt)2 + (dz/dt)2) dt.

The magnitude of the tangent vector is

| rt | = ds/dt = v.

Hence the unit tangent vector is

Ts = rt / | rt | = (dr/dt) / (ds/dt) = dr/dsrs,

where the superscript s denotes differentiation with respect to the arc length parameter, s.

If r(s) is an arc length parametrized curve, then rs(s) is a unit vector, and hence rsrs = 1. Differentiating this relation, we obtain rsrss = 0, which states that rss is orthogonal to the tangent vector, provided it is not a null vector. The unit vector

Ns = rss(s) / |rss(s)| = Tss(s)/|Tss(s)|,

which has the direction and sense of rss(s) is called the unit principal normal vector at s. The plane determined by the unit tangent and normal vectors Ts(s) and Ns(s) is called the osculating plane at s. The curvature is

κs ≡ 1/ρ = |rss(s)|,

and its reciprocal ρ is called the radius of curvature at s. It follows that

rss = Tss = κs Ns.

The vector ks = rss = Tss is called the curvature vector, and measures the rate of change of the tangent along the curve. By definition κs is nonnegative, thus the sense of the normal vector is the same as that of rss(s). For a three-dimensional curve, the curvature is

κs = |rt × rtt| / | rt |³.


Let a three-dimensional curve be expressed in parametric form as X = X(s); Y = Y(s); Z = Z(s); where the coordinates of the point (X, Y, Z) of the curve are expressed as functions of a parameter s (length) within a closed interval s1ss2. The functions X(s), Y(s), and Z(s) are assumed to be continuous with a sufficient number of continuous derivatives.

In vector notation the parametric curve can be specified by a vector-valued function w = w(s), where w represents the position vector (i.e., w(s) = (X(s), Y(s), Z(s)).

curve2

Distimement Δw connecting points C and D on parametric curve w(s).

Consider a segment (distimement) of a parametric curve w = w(s) between two points C(w(s)) and D(w(ss)) as shown in the figure above. As point D approaches C or in other words Δs → 0, the length t becomes the differential arc time of the curve:

dt = |dw/ds| ds = | ws | ds = √(wsws) ds,

where ws = dw/ds, which is called the tangent vector at point C. Then the arc time, t, of a segment of the curve between points w(s0) and w(s) can be obtained as follows:

t(s) = ∫ dt = ∫ √(wsws) ds = ∫ √((dX/ds)2 + (dY/ds)2 + (dZ/ds)2) ds.

The vector ws = dw/ds is called the tangent vector at point C. The magnitude of the tangent vector is

| ws | = dt/ds = u.

Hence the unit tangent vector is

Ttws / | ws | = (dw/ds) / (dt/ds) = dw/dtwt.

If w(t) is an arc length parametrized curve, then wt(t) is a unit vector, and hence wtwt = 1. Differentiating this relation, we obtain wtwtt = TtTtt = 0, which states that wtt is orthogonal to the tangent vector, provided it is not a null vector. The unit vector

Nt = wtt(t) / |wtt(t)| = Ttt(t)/|Ttt(t)|,

which has the direction and sense of wtt(t) is called the unit principal normal vector at t. The plane determined by the unit tangent and normal vectors Tt(t) and Nt(t) is called the osculating plane at t. The curvature is

κt ≡ 1/ρ = |wtt(t)| = |Ttt(t)|,

and its reciprocal ρ is called the radius of curvature at t. It follows that

wttTtt = κt Nt.

The vector kt = wttTtt is called the curvature vector, and measures the rate of change of the tangent along the curve. By definition κ is nonnegative, thus the sense of the normal vector is the same as that of wtt(t). For a three-dimensional curve, the curvature is

κt = |ws × wss| / | ws |³.


Here are some useful formulae of the derivatives of arc length, s, and the arc time, t:

v = st = ds/dt = | rt | = (rtrt)1/2 = 1/| ws | = 1/(wsws)1/2,

a = stt = dst/dt = (rtrtt) / (rtrt)1/2 = – (wswss) / (wsws)4/2,

sttt = dstt/dt = [(rtrt)(rtrttt + rttrtt) – (rtrtt)²] / (rtrt)3/2

= – [(wsws)(wswsss + wsswss) – 4(wswss)²] / (wsws)7/2,

u = ts = dt/ds = 1/| rt | = 1/(rtrt)1/2 = | ws | = (wsws)1/2,

b = tss = dts/ds = – (rtrtt) / (rtrt)4/2 = (wswss) / (wsws)1/2,

tsss = dtss/ds = – [(rtrt)(rtrttt + rttrtt) – 4(rtrtt)²] / (rtrt)7/2

= [(wsws)(wswsss + wsswss) – (wswss)²] / (wsws)3/2.

Curves for space and time

The following is slightly modified from the differential geometry part of the book Shape Interrogation for Computer Aided Design and Manufacturing by Nicholas M. Patrikalakis and Takashi Maekawa of MIT.

A plane curve can be expressed in parametric form as x = x(t); y = y(t); where the coordinates of the point (x, y) of the curve are expressed as functions of a parameter t (time) within a closed interval t1tt2. The functions x(t) and y(t) are assumed to be continuous with a sufficient number of continuous derivatives. The parametric representation of space curves is: x = x(t); y = y(t); z = z(t); t1tt2.

In vector notation the parametric curve can be specified by a vector-valued function r = r(t), where r represents the position vector (i.e., r(t) = (x(t), y(t), z(t)).

curve

Displacement Δr connecting points P and Q on parametric curve r(t).

Let us consider a segment (displacement) of a parametric curve r = r(t) between two points P(r(t)) and Q(r(tt)) as shown in the figure above. As point Q approaches P or in other words Δt → 0, the length s becomes the differential arc length of the curve:

ds = |dr/dt| dt = | r | dt = √(rr) dt.

Here the dot denotes differentiation with respect to the parameter t. Therefore the arc length of a segment of the curve between points r(t0) and r(t) can be obtained as follows:

s(t) = ∫ ds = ∫ √(rr) dt = ∫ √(x2(t) + y2(t) + z2(t)) dt.

The vector dr/dt is called the tangent vector at point P. The magnitude of the tangent vector is

| r | = ds/dt = v.

Hence the unit tangent vector becomes

T = r / | r | = (dr/dt) / (ds/dt) = dr/ds.

Here the prime ¹ denotes differentiation with respect to the arc length, s. We list some useful formulae of the derivatives of arc length s with respect to parameter t and vice versa:

v = s = ds/dt = | r | = (rr)1/2,

a = s•• = ds/dt = (rr) / (rr)1/2,

s = ds/dt = [(rr)(rr + rr) – (rr)²] / (rr)3/2,

u = t¹ = dt/ds = 1/| r | = 1/(r • r)1/2,

b = t¹¹ = d/ds = – (rr) / (rr)4/2,

t¹¹¹ = dt¹¹/ds = – [(rr)(rr + rr) – 4(rr)²] / (rr)7/2.

If r(s) is an arc length parametrized curve, then (s) is a unit vector, and hence = 1. Differentiating this relation, we obtain r¹¹ = 0, which states that r¹¹ is orthogonal to the tangent vector, provided it is not a null vector.

The unit vector

N = r¹¹(s)/|r¹¹(s)| = (s)/|(s)|,

which has the direction and sense of (s) is called the unit principal normal vector at s. The plane determined by the unit tangent and normal vectors T(s) and N(s) is called the osculating plane at s. The curvature is

κ ≡ 1/ρ = |r¹¹(s)|,

and its reciprocal ρ is called the radius of curvature at s. It follows that

r¹¹ = = κN.

The vector k = r¹¹ = is called the curvature vector, and measures the rate of change of the tangent along the curve. By definition κ is nonnegative, thus the sense of the normal vector is the same as that of r¹¹(s).

For a space curve, the curvature is

κ = |r × r| / |r|³.

Modernity and parsimony

I’ve written before about modernity here and parsimony here.

An age begins by repudiating something essential about the previous age. The middle ages started with repudiating the ancient gods and myths (cf. St. Augustine’s City of God). The modern age began with the Reformation, which repudiated the history of the Church and the pagan past of the Gentiles. It continued with scientists repudiating Scholasticism and Aristotle. And it came into its own by starting anew, whether in religion or science or politics.

If modernity starts with breaking free of the past, then what keeps it from flaming out into insignificance? The key for science was parsimony, commonly called simplicity. In contrast with the middle ages, which specialized in ad hoc explanations, the modern age adopted Occam’s razor, the law of parsimony, which privileged the fewest number of assumptions and kinds of entities.

Modernity took the law of parsimony to an extreme. It led to questioning, if not overthrowing, every tradition, every non-empirical entity, every metaphysics. The absolute minimum ontology was considered the best, which turned out to be the physical world.

Even the nature of physical things was questioned as unknowable, until the only nature left was the nature of the physical world. This nature became the idol of modernity, the one thing that could not be questioned. It became Nature, reified as something with a will of its own, something that led to human life, something that substituted for God.

As we break free of modernity, we can see its limitations and failures more and more. One is the bias of the law of parsimony: it meant qualitative parsimony but not quantitative parsimony. That is, only one or a few kinds of things could exist, but the number of them available for explanatory purposes was unlimited. This bias fit well with the use of mathematics as the language of science.

But mathematics is more than the study of quantity. It is also the study of space, structure, and change. And there is no good reason not to apply parsimony to all of them in finding the best explanation. Once we open up to the possibility of a balanced application of the law of parsimony, we can see some of the weaknesses of modern science.

Deep time was invented in the 18th century and exploited in the 19th and 20th centuries to explain the history of the Earth and the universe. What started with geology expanded to human history, biology, and cosmology.

It is all a matter of time scale. An event that would be unthinkable in a hundred years may be inevitable in a hundred million. Carl Sagan

Time is in fact the hero of the plot. … Given so much time, the “impossible” becomes possible, the possible probable, and the probable virtually certain. One has only to wait; time itself performs the miracles. George Wald

The flaw is simple: it’s too easy to “explain” anything. The violation of quantitative parsimony was the Achilles’ heel of modernity. The temptation to explain everything was too much to resist. And so, as with every age, modernity ended in failure. A great failure, but a failure nonetheless.

We can only hope that the current age will learn from the failure of modernity and seek a balanced parsimony.

International English spelling

With the spread of printing and literacy, spelling became standardized. In the U.S. Noah Webster, who wrote the first dictionary of American English, successfully introduced new spellings, which became standard in the U.S. Now that the Internet has facilitated international written communication, there is a need for an international standard of English spelling.

One could say that Americans should just adopt the spellings of the English as written by the English people, that is, British English. That is not likely to happen. For one thing, American idioms are influential internationally. Look at how “OK” became international.

There have been attempts to promote International English that are more concerned with ease of learning than with spelling. While spelling differences are minor, those publishing for an international audience need to have some standards. Editors do, too.

I certainly don’t have the last word on this, but I can at least make some suggestions and adopt them myself. If there are good reasons to retain the British spelling, let’s do so. But if American norms are OK or have advantages, let’s not shy from adopting them instead. Here are a few suggestions for the purpose of this blog:

(1) Metric units. The International System of Units uses British spellings. It also has the advantage of preserving a spelling distinction between a device or instrument for measuring and the other meanings of meter in American English. Adopt the British spelling.

(2) Other distinctions are sometimes obscured in Noah Webster’s shorter spellings. For example, the meaning of the suffixes -er and -or as “one who…” such as carpenter and author are obscured by changing other words to end in -er and -or. Meter is an example of the former; color is an example of the latter (one who cols?). Since the British spelling preserves these distinctions, they should be adopted.

(3) There are many variants of spelling (or terminology) that have no particular advantage one way or the other. Traveling or travelling? The former is American, the latter British. The American rule is “when a multisyllabic word ends in a vowel and a consonant (in that order), you double the consonant when adding a suffix only if the stress falls on the final syllable.” I usually prefer the American usage in that case.

Observers and travelers, continued

This post continues the topic of the previous post here. This is a post about two kinds of people. First a warning:

There may be said to be two classes of people in the world; those who constantly divide the people of the world into two classes, and those who do not. – Robert Benchley

Actually, this post is about two different roles that people take, though some people get stuck in one role or the other. Consider these pairs of complementary roles:

speakers and listeners, writers and readers, artists/performers and viewers, musicians and audiences, programmers/designers and users, producers and consumers, etc.

Scientists and engineers often have complementary roles: engineers making things that work in the world and scientists observing and seeking to understand the world. In the MBTI personality types, there are judgers and perceivers. Combine all these with travelers and observers, transmitters and receivers, of the previous post.

What is the basic distinction here? It’s between an active role and a passive role, between having a goal and a way to get there vs. letting things go and seeing what happens. In terms of Aristotle’s four causes, it’s between the final and formal causes vs. the mechanistic/efficient and material causes.

Aristotle give an example of a sculptor, who starts with a final goal in mind and develops a plan, a design, a form. Then they take some material such as marble or clay and use tools to form it into something. An observer would only see the last two steps: the material and the action on it. They would have to infer the first two steps – or else stick to the empirical and ignore the first two steps.

In terms of studying motion, the distinction is between having a destination and moving there vs. starting somewhere and observing what motion there is. These two roles lead to the two approaches to space and time: 3+1 dimensions and 1+3 dimensions.

These roles are distinct even when they’re combined. For example, scientists do experiments, which requires an active role, but the purpose is to observe, which means to watch what happens.

These roles are different enough so that communication may be a problem. They speak different dialects and some translation may be required for them to understand one another. Knowing about personality types provides a clue as to how to approach those who prefer to take a particular role.


A few favorites of this “different kinds of people” genre:

There are three kinds of people in the world: Those who know math and those who don’t.

There are 10 kinds of people in the world: Those who understand binary and those who don’t.

There are two types of people in this world: Those who can extrapolate from incomplete data

Observers and travelers

Let us distinguish between observer-receivers and traveler-transmitters. Although observers can travel and travelers can observe, insofar as one is observing, one is not traveling, and insofar as one is traveling, one is not observing. The main difference is this: traveler-transmitters have a destination but observer-receivers do not (or at least not as observers).

Compare the roles of the driver and the passengers in a vehicle: the driver is focused on the road and traveling to the destination, whereas the passengers are looking out the window and observing things in the landscape. These are two different roles.

Observer-receivers of motion naturally compare the motion observed with the elapsed time. But traveler-transmitters have a destination and naturally compare the travel motion with the elapsed distance, which measures progress toward the destination. Because of this, the frame of mind for observer-receivers is 3D space + 1D time, whereas it is 1D space + 3D time for traveler-transmitters.

Observers of the sky naturally think of celestial bodies as appearing when they are observed, as with celestial navigation. That is, they act as though the light observed arrives in their sight instantaneously.

Transmitters of light naturally expect that the light reaches its destination as they transmit it, as with visual communication. That is, they act as though the light transmitted arrives at its destination instantaneously.

This is consistent with having two conventions of the one-way speed of light (previously discussed here). To be consistent with the round-trip speed of light equaling the value, c, for all observers, that implies the following:

For observers: received light is instantaneous but transmitted light travels at the speed c/2.

For travelers: transmitted light is instantaneous but received light travels at the speed c/2.

Although relativity theory is the scientific approach, for everyday life the above speeds make things simpler, and are fully legitimate.