iSoul Time has three dimensions

Category Archives: Knowing

epistemology, science, kinds of knowledge, methodology

Circular/harmonic motion

The outline below is also in pdf form here.

Angular speed (velocity) and angular pace (legerity)

  • Speed, v = Δst, Pace, u = Δts so u = 1/v and v = 1/u except if u or v are zero
    • Zero speed: no motion but time changes because time is independent
    • Zero pace: no motion but length changes because length is independent

Circular motion in space and time

distance, x; distime, t; radius r (or a or R or A); period radius q; circumference S = 2πr = wavelength λ; period T = 2πq = wavetime μ; angular velocity, v; angular legerity, u; arc length, s; arc time, w

  • Circle in space
    • space angle θ, arc length s, radius r
    • angle in space: θs/r; r = s/θ; s = rθ; 1/θ = r/s; 1/r = θ/s
    • angular time rate: ωθ/t; t = θ/ω; θ = ωt; 1/ω = t/θ; 1/t = ω/θ
  • Circle in time
    • time angle φ, arc time w, period radius q
    • angle in time, φw/q; q = w/φ; w = ; 1/φ = q/w; 1/q = φ/w
    • angular space rate: ψφ/x; x = φ/ψ; φ = ψx; 1/ψ = x/φ; 1/x = ψ/φ

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Geometry of motion

Kinematics, the geometry of motion, studies the positions of geometric objects parameterized by time. This is a 3D space with functions representing the path or trajectory as the locus of places occupied by points. It has a dual mathematics of 3D time with functions representing the course of motion as the locus of times occupied by events. Below is an introduction to both, following the exposition in Principles of Engineering Mechanics: Kinematics by Millard Beatty Jr.

1.3 Motion and Particle Path

To locate an object in space, we need a reference system. The only reference we have is other objects. Therefore, the physical nature of what we shall call a reference frame is an assigned set of objects whose mutual distances do not change with [dis]time – at least not very much. …

We define a three-dimensional Euclidean reference frame φ as a set consisting of a point O of space, called the origin of the reference frame, and a vector basis {ei} ≡ {e1, e2, e3}. That is, φ = {O; ei}. We shall require for convenience that the basis is an orthonormal basis, i.e., a triple of mutually perpendicular unit vectors.

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Helical motion

This continues the previous post here.

The parametric equation for a circular helix around the x1-axis with radius r and slope b/a (or pitch 2πb) is x1(t) = bt, x2(t) = r cos(t), x3(t) = r sin(t). Its arc length equals t · sqrt(r² + b²).

The parametric equation for a circular helix around the t1-axis with radius q and slope c/q (or pitch 2πc) is t1(x) = cx, t2(x) = a cos(x), t3(x) = q sin(x). Its arc length equals x · sqrt(q² + c²).

The linear motion along the x1-axis measures length, s, with velocity b. The circular motion around the x1-axis measures time, t, as an angle. The linear motion along the t1-axis measures length, w, with velocity c. The circular motion around the t1-axis measures length, x, as an angle.

(1) If the circular motion around the x1-axis is independent, it measures time, t, as an angle. If the linear motion along the x1-axis is dependent, it measures length, s, as a parameter, and the axis is a space axis, xs.

(2) If the linear motion along the x1-axis is independent, it measures length, x, as a parameter, with velocity b. If the circular motion around the x1-axis is dependent, it measures time, t, as an angle, and the axis is a time axis, xt.

(3) If the motion is helical, that is both circular and linear, then if it is measured by length, it forms a curve in 3D space. If it is measured by time, it forms a curve in 3D time.

Galilean transformation with independent time: xt´ = xt, xs´ = xs – vx. xtys´ = ys, , zs´ = zs.

Simplified notation: t´ = t, x´ = xvt, y´ = y, z´ = z.

Galilean transformation with independent space: xs´ = xs, xt´ = xtux. xsyt´ = yt, , zt´ = zt.

Simplified notation: s´ = s, t´ = tux, t2´ = t2, t3´ = t3.

Science posts


Today the word science usually means naturalistic science. Historically, naturalism was not dominant in modern science until the nineteenth century, when it was promoted by those who were called “naturalists” (not to be confused with a naturalist as someone who studies natural history). These naturalists promoted the idea that science was limited to naturalism. They were adept at taking leadership of science at a critical time when it was becoming professionalized and supported by government largesse.

Since naturalism is a false philosophy, science today is alienated from truth. The intelligent design movement challenges the idea that science is limited to naturalism. The creation science movement, which is related but independent, denies naturalism and much of the science built upon naturalism, including evolution and deep time. While these movements are small, it is important to remember that they stand in a tradition that goes back to the first centuries of modern science. The science of Galileo, Newton, and other great scientists of the past was not naturalistic science.

Science and terminology

Science is knowledge (scientia) that is systematically gained and/or organized. That entails that the terminology of science be systematic, i.e, a nomenclature rather than a hodgepodge of terms. This can make discussions about science hard since people have to learn a body of nomenclature before understanding a science. This applies to all sciences, whether natural sciences, social sciences, historical sciences, or subjects with some systematization such as systematic theology.

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Creation and evolution posts

Creation and evolution typology

The first issue that arises in developing a typology for ideas about creation and evolution are the terms themselves: they are sufficiently ambiguous that their meaning differs even by the same author in the same work. This can be part of a fallacy of equivocation or it can simply mean the terms are general and should not be expected to carry a technical meaning unless that is specified. Let’s take the latter path and use them as general terms.

Some authors promote creation only whereas others promote evolution only but there are other ways of speaking. Some speak of creation by evolution which means evolution but a Creator is given credit for it. Others speak of evolution by creation which means progressive creation but evolution is given credit for it. These are categorized under evolution and creation, respectively.

Further, creation used to mean static creation, that is, life, the earth, and the universe were created in a state that has not significantly changed. Also, evolution used to mean only gradual evolution, that is, life, the earth, and the universe have changed gradually but drastically over a long period of time.

Others combine creation and evolution in a kind of partnership. Creation with evolution makes creation primary but acknowledges something like evolution within created limits. This dynamic creation differs from the older conception of a purely static creation. Evolution with creation applies to others who make evolution primary but acknowledge something like creation within evolutionary limits. Evolution with large catastrophic or saltational changes differs from the older conception of a purely gradual evolution.

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Creation posts

Creation and paradigm

Creation is a fact. Creation is the oldest fact but creation as a paradigm is relatively new. Let me explain.

The word “paradigm” was used by Thomas Kuhn for “universally recognized scientific achievements that, for a time, provide model problems and solutions for a community of practitioners.” I would characterize a paradigm as a theme or framework that relates a family of theories and a research agenda.

The ancient paradigm was Perfection. This included theories of circular movement since circles were considered perfect. It also included theories of stasis since change was considered imperfect.

The Perfection paradigm led to a world of static biological species that could not be improved on. This is where the Creation paradigm first arose: God created the perfect universe and it hasn’t really changed. So the Perfection paradigm at first incorporated a Creation paradigm.

Stasis was challenged by Copernicus since the earth moved in his theory. Perfection was further challenged by Kepler and especially Newton since ellipses and other non-circular movements were included.

The new paradigm that arose was the Mechanical paradigm. Theories under this paradigm had movements that fit mathematical curves and concepts such as force which had a mechanical analogue. Linear was in and circular was out.

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Evolution posts

Evolution for everyone

The word evolution is related to the terms evolve and evolute, and originally meant an unrolling. It acquired a sense of development in the 19th century and was associated with progress, especially as promoted by Herbert Spencer. Charles Darwin used it in print only once since his theory was not a theory of progress. “But Victorian belief in progress prevailed (and the advantages of brevity), and Herbert Spencer and other biologists after Darwin popularized evolution.” (source)

Today the basic meaning of the word evolution is change over time. That is, evolution refers to a process that changes one form into another form over time; in short, transmutation. There are various proposed means or mechanisms of evolution but they are all asserted to produce change over time.

Thus the concept of evolution is the opposite of the idea that forms do not change over time. What makes it complex is that some forms may change over time but not others. But no one today seriously alleges that there is no significant change over time. In that sense, we are all evolutionists.

Then we need terms to distinguish the different kinds of evolutionary concepts. One could simply attach the names of their originators, but their concepts are modified over time so additional terms would be required. We need simple terms to designate the main types of evolution. Three-letter acronyms would help, too.

Thus I propose the following terms and acronyms, starting with those who acknowledge no limits to evolution:

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Basic Gospel

Basic Gospel Message

Vic Scaravilli is a Catholic who put the following on his website here. I’m reposting it (with permission) and note that Evangelicals would agree that this is the gospel, with some nuances about baptism.

The Basic Gospel Message

By Vic Scaravilli

God loves each one of us. He loves me and He loves you with an unconditional love. You are precious in His eyes.

There is something that has kept us separated from God, something that has kept us from experiencing His love in our lives. That something is called sin. The result of sin is spiritual death. We have all sinned and never can be perfect.

Does that mean we can never know and experience God’s love? No, because God loved us so much He sent His only Son to die for each one of us. Jesus is the only bridge that takes us from our sin to the love of God. By His death and resurrection, Jesus opened the gates of heaven for everyone.

This is called salvation. It is the free gift of eternal life that is completely given to us by God’s grace. Salvation is the life in Jesus that begins now and will be for all eternity.

The free gift of salvation must be accepted in order for it to be our own. We must experience an internal conversion experience that changes our hearts. Once we accept Jesus into our hearts and allow Him to come into our lives, we begin to experience His love.

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Design and evolution

I last wrote about design here.

What is the essential element of a design? Dictionaries define design in terms of a plan but that concerns how a design is recorded or communicated rather than the design itself. I suggest that the essential element of a design is the necessity of a trade-off.

To define a trade-off first define incompatible qualities as qualities that contain contraries, for example, doing something accurately and speedily. An increase in accuracy causes a decrease in speed and an increase in speed causes a decrease in accuracy. Accuracy and speed are not contraries but accuracy contains slowness and speed contains inaccuracy, which makes accuracy and speed incompatible.

A trade-off is the situation calling for a selection of the degree of two incompatible or contrary qualities. A design is the selection of the degree or amount of two incompatible qualities or things. The design decision may be made by maximization of something desirable, such as profit, or minimization of something undesirable, such as cost. Hence optimization results in a design.

Evolutionary algorithms are solution-space trial and error search algorithms with stochastic optimization. They are based on concepts from evolutionary biology. Their result is an optimum solution within the given solution space. Because of the stochastic element of evolutionary algorithms, it may seem as if the computer made the optimization decision and so the solution was not designed.

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Generic units of measure

Customary units of measure such as the foot and the pound are suitable for everyday purposes such as measuring the dimensions of a person or a room. Metric (SI) units of measure such as the Kelvin and the kilogram are suitable for scientific purposes. Some metric units are suitable for everyday use, and they are so used in many countries.

However, there are some draw-backs to metric units for everyday purposes, for example: the SI unit of temperature is the kelvin (K) which does not relate to the temperatures of everyday life (even the related degrees Celsius compresses surface air temperatures into a narrow band); the kilometre is rather short compared with a mile; and the kilogram is large compared with a pound (500 g is sometimes used).

The purpose of this post is to explore a generic system of units that would be suitable for both everyday and scientific usage.

Start with temperature. For scientific purposes, the absolute minimum temperature is an important limit, so it should be set to zero or some multiple of 1000. The triple point of water is meaningful for both scientific and everyday usage. These two points suggest a scale with the absolute minimum set to –1000 degrees, and the triple point of water set to 0 degrees. One generic degree equals 0.27315 K. So a value of 100 equals 27 ºC or 81 ºF.

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