iSoul In the beginning is reality

The story of nothing

Mathematics is the study of nothing. We make something out of nothing, acting the creator in a world of nothing. Here’s the story:

In the beginning is nothing. Not totally nothing because we’re there. But a blank page, a clear slate, a tabula rasa.

We draw a distinction, a part of nothing. The indistinct blankness of nothing gains a something. We indicate the something. We indicate the original nothing. We develop a logic of nothing.

We draw a place of nothing, a point. We draw a line of points, then a plane, and a solid. We select an original nothing, an origin. We develop a geometry of nothing.

We draw a number of nothing, a zero. We add it, subtract it, and multiply it. We raise numbers to its power. We develop an arithmetic and algebra of nothing.

We reduce a number to nothing, an infinitesimal. We define a function of it. We take its tangent, its sum, and its mean. We develop a calculus of nothing.

We take the set of nothing, the null set. We intersect it, union it, complement it. We take the power set of it. We find its cardinality. We develop a set theory of nothing.

In the end we have nothing, nothing but mathematics.

Four perspectives on space and time

There are four perspectives on space and time depending on whether the observer is internal or external to space or time. The four perspectives are internal space with internal time, external space with internal time, internal space with external time, and external space with external time.

The internal perspective is that of an observer traveling along a route or trajectory. It does not track direction because direction refers to the external perspective. So the internal perspective on movement is one-dimensional, a curve or world line, which has an arc length in space or time. The internal perspective makes space or time absolute because they travel with the observer.

The external perspective is that of one who observes an object move through a space or time with all its directional possibilities. So the external perspective on movement is three-dimensional, an abstract space or manifold, which contains a curve or world line that has direction at every point. Note that an internal perspective is external to the movement of another observer. The external perspective makes space or time relative because the observer and observed move relative to each other.

Each of these perspectives may be “classical” or “relativistic” depending on whether a Lorentz-type transformation is applied to them. The internal-internal perspective is absolute so its space and time are Lorentz invariant. Time and length are measured along the world line; they are the proper time and proper length (not to be confused with the comoving length).

Otherwise the ratio of movement should be one that is relative and three-dimensional in the numerator and absolute and one-dimensional in the denominator so that a vector is divided by a scalar. Thus the velocity should be used with 3D space and 1D time and the pace should be used with 1D space and 3D time.

The external-external perspective requires a different approach. Velocity and acceleration are defined relative to one-dimensional time so they cannot be used if time is three-dimensional. An inverse quantity (e.g., pace) is no better: that would be relative to one-dimensional space, which cannot be used if space is three-dimensional. One way would be to go back and forth between 3D space with 1D time and 1D space with 3D time.

A better way is via Minkowski’s approach to space-time: a new geometry. One advantage of this is that the invariant interval is defined without reference to velocity (though it includes the speed of light, a scalar). The Lorentz transformation can be represented as a hyperbolic rotation in a Minkowski space-time.

Change flows

Change happens. In fact, everything in the physical universe is changing. Note that refers to things in the universe, not the universe itself. Whether or not the universe itself changes is another question.

There are as many kinds of physical change as there types of energy: kinetic, thermal, chemical, electrical, electrochemical, electromagnetic, sound, and nuclear change (potential energy being related to kinetic energy). How do we measure change? We could simply compare one change with another of the same type.

But how do we measure change in general? Is there a framework in which all changes can be placed? The simplest answer is to adopt a single aspect of change, the beginning and ending of a standard change, as the unit of change. The question then is how many of these units of change does it take to measure a particular change (the measurand)?

A number of units of change is a rate of change. A standard rate of change would allow one aspect of every change to be measured. It would also enable a framework in which all changes could be placed if the standard rate of change generates a dimension of change that continues indefinitely.

What change would work well as a standard? It should have a regular rate of change. It should also have a clear beginning and ending, that is, it should be cyclic. Each cycle would constitute one unit of change.

The ancient standard was the cycle of days with the sundial as a convenient way to measure change. Over the centuries the movement of water, the burning of a candle, mechanisms of gears and weights, the cycle of a pendulum, and oscillations of quartz have been used as a standard rate of change.

Notice that I have avoided the words “time” and “clock”. There was no need for them. We could call a clock a change-measuring instrument. And time? That’s just another word for the rate of change measured by a clock.

Does time flow? If that means that change is always happening, then yes. But if the flow of time is supposed to be something intrinsic to the universe, that’s the assertion that the universe itself is changing. There is no need to go there to answer a simple question about change.

Three arguments for 3D time

There are three main arguments for time having three dimensions:

(1) The speed of light is a conversion factor between space (distance, length) and time (duration, length of time). In transportation there are less exact conversion factors in the typical speeds associated with different travel modes. Since space is three dimensional, its conversion into time is also three-dimensional. The scale of maps may be in units either of distance or of duration using a standard conversion speed.

(2) Observation follows the movement of light, which is three dimensional. In astronomy it is often said that observation of the sky is a way of looking into the past. Observation is a form of communication and any type of signal (sound, mail, etc.) will suffice though not as exact as light. As the observation of space is three-dimensional, so the observation of time is also three-dimensional. Maps of time are similar to maps of space: they show observations (signals) in different directions.

(3) Movement in orthogonal directions entails moving in three dimensions. Each dimension of movement has an average speed from the change in space (length) divided by the change in time (duration). As movement is in three dimensions, so the time aspect of movement is in three dimensions. Travel shows the same result. Maps of movement may show either spatial positions or temporal positions or both.

Each argument may be illustrated by a map. The conversion factor argument shows how any map may be scaled in units of space or time. The observation argument shows that maps of observations have units or space or time. The movement argument shows that maps of movement may show space or time or both.

Note that every argument has an analogue in ordinary travel and so is not unknown to nonspecialists. The arguments are however exact in the case of physics.

Variations on a clock

The U.S. National Debt Clock shows several ‘clocks’ that tick off dollars at a constant rate. The answer to “what time is it?” could be given in dollars.

The Census Bureau has a population clock that estimates the present population for the U.S. or the world. The U.S. has a net gain in population of one person every 12 seconds. The answer to “what time is it?” could be given as a number of people.

The current price of a stock in a stock market ticker is a kind of clock. Or a trader might be interested in the time until the market closes, which would be a countdown clock. The countdown to launch a rocket or celebrate the new year are famous countdown clocks.

With GPS trackers anyone can have a distance ‘clock’ with them. “What time is it?” could be translated into “how far have you gone?” Metres, miles, or some other distance would answer the question. A sprint might last a certain ‘time’ measured by distance.

A clock with a second hand of 0.16 metre would sweep out one metre in one minute. Time could be converted to distance with this ratio. Ten o’clock would mean 600 metres swept out since beginning the day.

There is no need to measure ongoing change with only clocks of hours, minutes, and seconds. Many other units can be used.

Branches of Christianity

Christians accept the four gospels as four different perspectives on the gospel. In fact, each is properly titled, “The Gospel According to …” That is, there is one gospel but four perspectives on it. While it is an interesting exercise to compare the gospels with each other, they are best thought of as parallel accounts of the gospel of Jesus Christ.

There are four branches of Christianity, corresponding to the four Gospels. The parallels between each gospel and each branch of Christianity show this. The four branches are the Orthodox, Catholic, Evangelical, and Pentecostal churches. Like the one gospel, there is only one church, but there are four perspectives on the one church.

The gospel of Matthew shows Jesus as the Messianic King. The gospel of Mark shows Jesus as the Suffering Servant. The gospel of Luke-Acts shows Jesus as the Son of Man. The gospel of John shows Jesus as the Son of God. From considerations like this, one can see the Orthodox, Catholic, Evangelical, and Pentecostal branches, correspond to the gospel according to John, Matthew, Mark, and Luke-Acts, respectively.

Christians have learned to accept the four versions of the one gospel, and their different perspectives. It is past time that Christians learn to accept the four branches of the one church, and their different perspectives.

Conversion of space and time

If there exists a constant, standard speed, then one may speak of the standard conversion of space and time. For example, the speed of light in a vacuum is a defined constant in the SI system of units. So in physical science and its applications one may speak of the standard conversion of space into time and vice versa. This means that even if in some sense light curves (as by gravity), then the path of light is a geodesic, that is, equivalent to a straight line.

In other contexts, there may be no such standard speed but still there may be a constant speed within a specified context, which serves as a contextual conversion of space and time. This allows a map with a consistent scale, for example this map of the London Tube:

Informally, this is done quite often. When asked how far away something is, we answer with the travel time by car or other mode.

Now the surprising thing is that the Lorentz transformation arises just because there exists such a conversion between space and time. It shows how to transform particular velocities in the context of a conversion speed between space and time. See the previous posts on the Lorentz transformation.

Time and memory

Is it possible to reverse time? Yes, in a sense. It is possible to reverse thermodynamic time by a local decrease in entropy. Cooling down, metabolism, and memory are examples of decreases in entropy.

Memory may be described as an information model: it compresses experience for storage. The information in memory is not all that happened; something was lost or not perceived.

As memory grows, it is necessary to do maintenance like that done with computer systems, such as defragmenting isolated memories and consolidating them into coherent storage. This, too, may decrease entropy. It is also necessary to review memory, to restore weak memories. This remembering, this return to the past, is a form of reversing time.

Time for us is memory. Without memory, there is no time–we are like children focused on the here and now.

Weekly and annual cycles of remembrance renew our memories and help integrate them into an existing framework. The cycle of the week is the cycle of creation and rest. The cycle of the year is the cycle of reviewing the history of God’s people. Other cycles give us a rhythm for life–cycles of the tides, of the school year, of national holidays.

The Greek word chronos describes these regular cycles, whereas the word kairos describes a progression. Chronos is measurable, predictable, cyclic time. Kairos is experienced time, which flows and grows in unpredictable ways. The experiences of kairos are turned into the cycles of chronos by memory.

Time in the Bible

Time in the Bible is duration, not what is called thermodynamic time or the arrow of time. There is no inevitability about time in the Bible, unlike the increasing entropy of thermodynamic time. In the Bible time has a beginning and an ending. Time is an era, an age, a period of time. It is what takes time, that is, duration.

In ancient times the motions of the sun, moon, and stars formed a cosmic clock, not outer space. Before the rise of the Roman Empire, people expressed “how far” in terms of “how much time”. The distance between places was given as how many days’ journey by a typical traveler. Genesis 30:36; Genesis 31:23; Exodus 3:18; Exodus 5:3; Exodus 8:27; Numbers 10:33; Numbers 33:8; Deuteronomy 1:2; and the Sabbath day’s journey, Acts 1:12. The distance covered by an average man in a day’s walk was 10 parsa’ot in Hebrew.

Greeks such as Herodotus also referred to a day’s journey, for example: “These Husbandmen extend eastward a distance of three days’ journey to a river bearing the name of Panticapes, while northward the country is theirs for eleven days’ sail up the course of the Borysthenes.” He also mentions: “a journey of five days across for an active walker”, indicating the kind of travel he has in mind.

The Greeks and especially the Romans with their road system brought longer lengths into common usage. There is the stadion or stadium, 600 Greek ft. or just under a furlong, and of course the Roman mile: Matthew 5:41; Luke 24:13; John 6:19; John 11:18; Revelation 14:20; Revelation 21:16.

Over the centuries space has supplanted time as the dominant way of viewing the universe. Since the discovery of artistic perspective and Newton’s notions of space and time as a container, the modern world has been oriented toward space. Even geometry changed from a realist view of the relation of objects to an anti-realist view of objects in an abstract space with Descartes’ analytic geometry.

That began to change with relativity and quantum mechanics, though the full implications are yet to be worked out, as Carlo Rovelli has noted (e.g., Are space, time, and all other physical quantities only relational? or his article in The Ontology of Spacetime). Scientifically, I think Poincaré’s point is correct: space and time are conventions, not arbitrary but convenient for understanding the universe (see his Science and Hypothesis).

For understanding the Bible and especially Genesis one should start with an ancient mindset that is realist and temporal. For example, when Genesis 1:3-5 says God created light and separated it into day and night, do not ask where the light was located because the separation concerns time, not space, and describes how the day was born.

Temporal and spatial references

I have written several times about differences between ancient and modern ways of thinking, for example, this post on Biblical geocentrism. Another way to look at this is whether time or space are primary. What does this mean?

We are most familiar with the primacy of space. Things exist within space as mere objects, and time is something added-on to take account of the motion of objects. But what if time came first? For example, what if a cycle of light and dark did not have any spatial reference? That sounds like Genesis 1:5, after God created light but no sun:

 5 God called the light Day, and the darkness He called Night. So the evening and the morning were the first day.

In that case, space would be added-on to time. One difference is that what is primary is three-dimensional, but what is secondary is only one-dimensional. That is the difference between measuring movement relative to space or time, or abstractly as derivatives relative to space or time.

The difference is whether zero represents rest (no movement) or instantaneous movement, and so which is the reference point for all movement. If instantaneous movement is the reference, then movement is understood as slowing down, and rest is associated with an extreme of either lethargy or peace. If rest is the reference, then movement is understood as speeding up, and instantaneous movement as an extreme of either frenzy or joy.

If time is primary, then what is local is more significant than what is global because a local frame of reference covers more time, is diachronic over a long span of time. If space is primary, then what is global is more significant than what is local because a global frame of reference covers more space, is synchronic over a wider region of space.

As we move toward a balance of space and time, we will find both of these perspectives limited but with some utility. It is best to consider movement as a ratio rather than a division so that space and time are on equal terms.