To illustrate non-linear time, this graph shows the correspondence between ground observer time (horizontal axis) and proper time (vertical axis) for a spaceship going at v(t)=ct^(.1) over a time interval [0,1]. Although the clock on board ticks at a linear rate, to the ground observer a short interval in his time frame on the horizontal axis, going up to the red curve and over to the vertical axis shows a smaller interval of elapsed time on board the ship. The blue curve shows that, for a stationary spaceship, the elapsed times are the same, measured in linear form. (ignore gravity)

A group of writer is psychology and phenomenology have put for their their own notion of non clock-time which draws from dynamical systems theory. I wonder what connection this may have to your comment on non-linear time.

Shaun Gallagher(2011) elaborates:

“A number of theorists have proposed to capture the subpersonal processes that would instantiate this Husserlian model [of time] by using a dynamical systems approach (Thompson 2007; van Gelder 1996; Varela 1999). On this view, action and our consciousness of action arise through the concurrent participation of distributed regions of the brain and their sensorimotor embodiment (Varela et al. 2001).”

Thompson(2007) says:

“The present moment manifests as a zone or span of actuality, instead of as an instantaneous flash, thanks to the way our consciousness is structured. As we will see later, the present moment also manifests this way because of the nonlinear dynamics of brain activity. Weaving together these two types of analysis, the phenomenological and neuro biological, in order to bridge the gap between subjective experience and biology, defines the aim of neuro-phenomenology (Varela 1996), ` an offshoot of the enactive approach.”

Varela's attempt to ‘phenomenologize' empirical accounts of time consciousness involves rejecting time as a fixed linear sequence of nows (what Husserl calls clock time)

“In fact, we have inherited from classical physics a notion of time as an arrow of infinitesimal moments, which flows in a constant stream. It is based on sequences of finite or infinitesimal elements, which are even reversible for a large part of physics. This view of time is entirely homologous to that developed by the modern theory of computation. […] This strict adherence to a computational scheme will be, in fact, one of the research frameworks that needs to be abandoned as a result of the neuro-phenomenological examination proposed here”

“The traditional sequentialistic idea is anchored in a framework in which the computer metaphor is central, with its associated idea that information flows up-stream . Here, in contrast, I emphasize a strong dominance of dynamical network properties where sequentiality is replaced by reciprocal determination and relaxation time.” ( Varela 1997)

Varela(1997) offers a concept of duration that is independent of linear time:

“…time in experience is quite a different story from a clock in linear time. Thus, we have neuronal-level constitutive events that have a duration on the 1/10-scale, forming aggregates that manifest as incompressible but complete cognitive acts on the 1-scale . This completion time is dynamically dependent on a number of dispersed assemblies and not a fixed integration period, in other words it is the basis of the origin of duration without an external or internally ticking clock.”. “the fact that an assembly of coupled oscillators attains a transient synchrony and that it takes a certain time for doing so is the explicit correlate of the origin of nowness.”

Time and change have no special relation.

Change occurs from place to place as well as from time to time.

Francisco Varela's homepage: F. Varela's Homepage

A bit confusing for me. The math is pretty vague with the first appearance making no sense. A little later on his discussion of dynamical systems is a tad more palatable. Overall, what he writes (in great length) could be brilliant or a satire on science. I assume the former since Stanford is behind the publication.

Peter Lynds writings make more sense to me, although he is an amateur physicist. Initially, he agreed with Bergson that time had no "instants", but rather interludes, an approach to the nature of time that drew considerable criticisms from the physics community.

I think there are two kinds of times, mutually exclusive. — Raymond

Regarding the "mystery" of Time, here's a link to an article with a unique concept of "why time flies". Apparently Time is Relative, not just to Space, and personal experience, but to our empathic connection to other time voyagers. :smile:


Empathy Is a Clock That Ticks in the Consciousness of Another :
. . . Kierkegaard’s assertion that “the moment is not properly an atom of time but an atom of eternity.” Time is a social phenomenon. This property is not incidental to time; it is its essence.
https://www.themarginalian.org/2017/09/04/alan-burdick-why-time-flies-empathy/

So, the pre-inflationary Planck cell can be compared with Aristotle's objective unmoved mover and the perfect circular motion. Our friend was ahead of his "time"! — Raymond

Yes. As in so many other philosophical quandaries, Aristotle tried to dispel mysteries -- such as Plato's "Forms" -- with practical applications. For example, a designing engineer envisions the "structure" of a future building, not as concrete beams & columns, but as abstract relationships, represented by vectors (arrows & values)

By defining Time as our perception of the sequential structure of evolving reality (order),he focused on what we are measuring : non-spatial relationships that evolve in an orderly mathematical manner. Those relationships are what I call "Information", a mental geometry, by which we measure the differences (or ratios) between Instants or Instances in terms of Meaning or Value to Self. We perceive those non-spatial ratios by Reason (rational thinking). :nerd:

Aristotle claims that time is not a kind of change, but that it is something dependent on change. . . . this means that time is a kind of order (not, as is commonly supposed, that it is a kind of measure)
https://oxford.universitypressscholarship.com/view/10.1093/0199247900.001.0001/acprof-9780199247905
Note -- we don't perceive Change itself, but the difference between point A and point B in a sequence --- like frames in a movie.

Information :
Knowledge and the ability to know. Technically, it's the ratio of order to disorder, of positive to negative, of knowledge to ignorance. It's measured in degrees of uncertainty. Those ratios are also called "differences". So Gregory Bateson* defined Information as "the difference that makes a difference". The latter distinction refers to "value" or "meaning". Babbage called his prototype computer a "difference engine". Difference is the cause or agent of Change. In Physics it’s called "Thermodynamics" or "Energy". In Sociology it’s called "Conflict".
BothAnd Blog Glossary

MENTAL GEOMETRY OF ABSTRACT VECTORS

How does this relate to Kant’s model of time? — Joshs

I wasn't familiar with Kant's opinion of Time. But a quick Google indicates that his Critique of Pure Reason ("which is a combination of rationalism and empiricism") treats Time & Change, not as objectively Real, but as subjectively Ideal. We imagine time by Intuition or infer it by Reason, because we can't see it with our objective empirical senses. So, we impute Time to Reality. And that's essentially what I was saying. :smile:

Kant believes that time, for us, is intuitive
https://decodedpast.com/immanuel-kant-on-time-a-theory-from-the-heart/

Impute : to represent something as being done, caused, or possessed by someone; to attribute.

Time and change have no special relation.

Change occurs from place to place as well as from time to time. — Banno

Two places might be different at a point in time, but nothing changes at a point in time.

Time is required to get "from place to place" or to perceive (and compare) one place and then another.

Two places might be different at a point in time, but nothing changes at a point in time.

Time is required to get "from place to place" or to perceive (and compare) one place and then another. — Luke

Indeed that's a very important point. This also is very much the point Kant was making in the
Second Analogy of Experience (in the Critique of Pure Reason). Let me quote from this course handout.

"In the Second Analogy, Kant compares our perceptions of a concrete particular, a house, and an event, the floating of a ship down a river. In the former case, the order of the perceptions is not determined; in the latter case, the order is. In other words, in looking at a house, I can look at the chimney first, then the shingles, then the windows; or I can look at the windows first, then the chimney, etc. Nevertheless, I suppose that these perceptions refer to the same permanent object. When the boat is moving down the river, I must perceive a certain order."

Kant's Second Analogy is discussed quite enlighteningly in Sebastian Rödl's book Categories of the Temporal: An Inquiry into the Forms of the Finite Intellect.

Two places might be different at a point in time, but nothing changes at a point in time. — Luke

My floor changes from wood to bamboo, from one room to another, at the one time.

This very text you see before you, you can only see in virtue of the change from one colour to another across space - in most cases the text being dark, the background white.

I would say you just have different flooring in different rooms. How does it change?

The floor changes from wood to bamboo.

When?

Now.

:point:

is the :fire: in which we burn

One room has a wood floor; the other room has a bamboo floor. That changed just now?

My floor changes from wood to bamboo, from one room to another, at the one time. — Banno

They are two different floors, or two separate parts of one floor. So the analogy with temporal change only really holds if we assume something like a perdurantist conception of persistence and identity whereby things that appear to be changing in time don't really change at all but rather merely have dissimilar temporal parts. This meshes well with a block-universe view or time but that is also, just like perdurantism, debatable.

↪Banno One room has a wood floor; the other room has a bamboo floor. That changed just now? — Luke

The house has a floor that changes from room to room.

You seem to be just looking for a particular phrasing to save a broken theory.

You seem to be just looking for a particular phrasing to save a broken theory. — Banno

According to your own theory of change, would you say that natural numbers change from being even to being uneven, and back to being even again, alternatively, from one number to the next? What is it that is changing then? Or is it just pure change without any underlying substrate that persists (or endures) through change?

The house has a floor that changes from room to room. — Banno

How does the floor change? One room has a wood floor, the other room has a bamboo floor.

They are two different floors, or two separate parts of one floor. — Pierre-Normand

No, it's the same floor.

I've no idea what the remainder of your post says. Can you clarify?

I think folk are trying to defend a broken notion - that change can only occur over time. Observation shows this to be false. The replies here indicate the rather than adjust their thinking about change, they would rather redefine change as that which occurs over time...

Edit: By way of example...

How does the floor change? One room has a wood floor, the other room has a bamboo floor. — Luke

As if there were never one room with two types of floor. The carpet changes from thick pile to thin, from red to blue, from right to left. The wall changes from light green to duck-egg blue, with height, not with time.

This very text you see before you, you can only see in virtue of the change from one colour to another across space - in most cases the text being dark, the background white. — Banno

I put it to you that the following image changes from one colour to another, from left to right; and that this change does not occur over time.



I suggest that the notion that change only occurs over time is the result of considering selective, and too few, examples

And we conclude that time is not essential for change.

...from right to left. — Banno

The only change here is your implicit assumption of a change in perception as you look "from right to left", from room to room, or "from place to place". But as I said earlier, a change in perception requires time.

The only change here is your implicit assumption of a change in perception — Luke

It's not an assumption. It is there before you. Use your eyes. Rethink you account.

It is there before you. Use your eyes. — Banno

Of course it is, but a change in perception requires time. As I said.

According to your own theory of change, would you say that natural numbers change from being even to being uneven, and back to being even again, alternatively, from one number to the next? What is it that is changing then? — Pierre-Normand

:up:

No, it's the same floor.

I've no idea what the remainder of your post says. Can you clarify?

I think folk are trying to defend a broken notion - that change can only occur over time. Observation shows this to be false. The replies here indicate the rather than adjust their thinking about change, they would rather redefine change as that which occurs over time... — Banno

Even if it's the same floor, then it still has different parts. Would you say of a banana that it is a thing that changes from being thin to being thick and then ends up being thin again? In you floor example, you seem to be taking as the underlying substrate of the change the vantage point of a local observer who surveys it from a moving perspective. In that case, the change that is being referred to is being premised on a temporal change in the location or vantage point of the observer.

Here is another example. You want to skate on a lake and inquire if the ice is thick enough. Other skaters tell you that the ice becomes thinner towards the center of the lake. What this means is that the part of the frozen surface of the lake that is in the immediate vicinity of whoever is skating on it (and hence affords support to that person) is thinner when the skater is nearer to the center of the lake. It's not the thickness of the ice itself that changes but rather, the spatial movement of the skater brings about that, as they move towards the center of the lake, that thicker areas get replaced by (different) thinner areas. It is the tacit embedding in a determinate pragmatic context that give meaning to the phrase "the ice is becoming thinner..." since this context tells us in what order and for what purpose the different parts of the unchanging ice sheet are being surveyed.

I put it to you that the following image changes from one colour to another, from left to right; and that this change does not occur over time. — Banno

When you used the nominal phrase "the following image", did you mean to refer to a picture that is square shaped or you did you mean to refer to a thin vertical segment of the whole square area ? I ask because if you meant the former, then your statement is false. And if you meant the latter, then there are very many such images and none of them change at all.

What?

I referred to, and showed, the image at https://i.stack.imgur.com/5chm6.png