The Shape Of Time

TheMadFool

A couple of months ago, maybe it was a year before now, can't remember, I came across an article that gives an account of Immanuel Kant's views on space and time. According to it, Kant thought of space as geometry and time as arithmetic and he did that perhaps in order to fit spacetime into a mathematical framework that was inclusive of two fundamental concepts in math viz. arithmetic (numbers) and geometry (shapes).

It's not that difficult to understand where Kant was coming from. There's a very basic link between space and geometry - space is filled with objects of all shapes and sizes. As for time, it's obvious that we use arithmetic (numbers) to make sense of its passing.

Now, it's clear that geometry can be/has been subjected to arithmetization - coordinate geometry, and we measure the dimensions of various geometric shapes with numbers. The converse must be true too as certain relationships between numbers can be geometrized e.g. there are such things as "triangular" numbers.

Space, being about shapes, its own and that of its contents, has also been arithmetitized (translated into numbers so to speak) and that's that.

What I want to discuss is the geometrization of time.

Can we construct figures/shapes using time?

For instance, we can construct a triangle in space with, say, lengths 3 cm, 4 cm, and 5 cm (this is right triangle if you'd like to know). Likewise, can we construct a time-triangle with lengths 3 minutes, 4 minutes, and 5 minutes? The same goes for other spatial geometric figures? Can we construct a time-circle with a radius of 2 hours and a circumference (2*pi*r) of 4pi hours?

It seems that we can. If I fix the speed of my pen at 1 cm/sec, and I draw a triangle with lengths 3 cm, 4 cm, and 5 cm, that would be a time-triangle of 3 seconds, 4 seconds, and 5 seconds. Now, if I double my speed, the space-triangle with lengths 3 cm, 4 cm, and 5 cm remains unchanged but my time triangle is scaled down by a factor of half. Likewise if I halve my speed, the space-triangle (3 cm, 4 cm, 5 cm) stays the same but my time triangle is scaled up by a factor of 2.

Lastly, just like our universe's space is thought to have a specific shape, does time have a shape of its own?

tim wood

It's a mistake in many cases to rely on articles to understand Kant's thinking. Far better to just read him himself. Challenging but not the ordeal that most non-readers seem to think it is. In any case I.cannot connect your comments on Kant's thinking to anything I'm acquainted with.

In any case, your interest appears to be something else.

What I want to discuss is the geometrization of time. Can we construct figures/shapes using time? — TheMadFool

I request you complete the following sentence:
For the purposes of my question, I am thinking that time is _________________________, and also that figures/shapes are ______________________.

I think if you think about these, that the more you think about them, the more you will recognize a need to establish some starting point - or range.

Who knows, you may attract one of TPF's more learneds to make a connection between your question and vectors and forces in physics, if possible - or not if impossible

TheMadFool

↪tim wood

:up: :ok:

Even if it Kant's position on the matter were misrepresented by me, it doesn't seem to invalidate the general idea that space is geometry and time is arithmetic.

Gregory

Kant said time can only be represented by a single line. He might be wrong. There are esoteric materials that apply sacred geometry to quantum mechanics. I don't know if it has any value, if it can be applied to time, or if it's implicit Platonism makes thinking about time easier. Just something that came to mind

Gregory

One last shot in the dark before I go to sleep: Bertrand Russell said "Weierstrass, by strictly banishing from mathematics the use of infinitesimals, has at last shown that we live in an unchanging world". So somehow by taking infinity away from space (although it seems to truly belong to it) Russell thought you get to some kind of eternalism. I want to research this more tomorrow (how can one do calculus without infinitesimals for example?). Be well everyone

Metaphysician Undercover

Kant said time can only be represented by a single line. He might be wrong. — Gregory

Not even a line can represent time. It's non-dimensional, simply order.

noname

As far as science is concerned, time is a dimension. It can only have two opposite directions.

jgill

Here's a shape of time:

Lorentz Factor

noname

It's like asking what the shape of a line is situated from East to West.

Changeling

↪TheMadFool

What is the time of shapes? Like when did specific shapes come into existence?

TheMadFool

↪The Opposite

↪Metaphysician Undercover

It appears that the widely held view is that time has no shape like space is thought to have (3D space can be spherical, maybe even a cube) or if one is forced to answer the question, time can be construed as a straight line but I'm not sure if straight lines are shapes per se. If straight lines are legit shapes then it's not too much of a stretch to imagine time being curved, coiled, loopy, and such.

Now that I think of it gravity is proven to affect space, classicaly depicted with massive objects producing dips and dimples in the fabric of space and it's also scientifically proven that mass can cause time dilation and it seems plausible that time dilations can be explicated as mass bending/curving time but that's only a hunch.

Metaphysician Undercover

Now that I think of it gravity is proven to affect space, classicaly depicted with massive objects producing dips and dimples in the fabric of space and it's also scientifically proven that mass can cause time dilation and it seems plausible that time dilations can be explicated as mass bending/curving time but that's only a hunch. — TheMadFool

Gravity affects spacetime not ""space". When you are talking about things like this within that conceptual framework, it is not appropriate to speak of space and time separately. That is because there is no real method to separate what time is doing, from what space is doing.

noname

↪TheMadFool

There are 4 dimensions with time being only one of them. You would need another temporal dimension for time to curve into.

Gregory

There are ways to correlate time experience between observers so there must be something overarching and connecting pieces of time. May this something is space, idn. Bertrand Russell thought modern mathematics indicated what came to be called B time. Einstein thought relativity indicated what came to be called B time. In B time the numeral for time is 0.

TheMadFool

Gravity affects spacetime not ""space". — Metaphysician Undercover

That's like saying economic policies affect the nation but not the people.

TheMadFool

There are 4 dimensions with time being only one of them. You would need another temporal dimension for time to curve into. — noname

Thought of that but I'm no mathematician.

Metaphysician Undercover

That's like saying economic policies affect the nation but not the people. — TheMadFool

Within that conceptual framework which produces these forms, "the dips and dimples" are in the fabric of spacetime, not space. Suppose we have two objects, and assume a straight line between them in a classical 3d representation. It's impossible to measure that distance all at the same time, because measuring takes a period of time. This amount of time is determined by the speed of light, the fastest known way of measuring. But the light, in travelling from the one object to the other will really take a non-straight path due to the influence of gravity. Since light is the fastest thing to travel from the one object to the other, the shortest path between the two, is represented as this non-straight path. That is called the curvature of spacetime.

There is a standard for creating this curvature in models, which is based in the presence of mass, and assumed gravitation. However, some activities will affect the applicability of the standard, so exceptions to the standard curvature must be allowed for. These are things like gravitational waves. What this implies is that light doesn't actually take the shortest route between two objects. We think that it does, because classical representations of 3d space will show light travelling in a straight line. And, since physicists know light as the fastest thing to travel that distance, they equate the 4d fastest route with the 3d shortest route, hence the 3d straight line is equivalent to the 4d curved line. However, since other things are known to alter the shape of this "fastest" route, so there are proven wrinkles in spacetime, we can conclude that it is not really the shortest route.

Gregory

From what I've gathered from videos in physics is there is massless mass and regular mass. Can the former be extended? Well light is so ye. It is wave-(massless particles). We see light as three dimensional yellow beams. The higgs boson with the higgs particle mediate between forms of massless mass to form regular mass, which has proper weight. Massless mass can put pressure on things, so a shadow on a wall in midday received less pressure than the sunlit sections. If you were a massless mass you wouldnt experience time (change) But gravity comes in and it becomes more confusing. How curvatory works with slowing light and the whole geodesic things i don't get

The Shape Of Time

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