scale factor

[michel123456]

I couldn't find the exact place to put this topic. It's about geometry, but also about the way we observe objects, and space more generally.

In another thread, I made a comparison between a flat 2d diagram representing the expansion of the universe, and a perspective drawing. Of course, the answer was "it is not a perspective drawing". Which is undoubtedly a correct answer.

But there is a common point, which is the scale factor.

 

Explaining.

Lets take a simple square like the one here below:

1

 

Lets put a scale factor of 2, and approximatively double the size of the square, and lets represent both squares side to side so that we can compare:

2

 

We have the result of the operation "scale".

 

Now, let's join the corners of the 2 squares. Something like this:

3

 

Fig. 3 here above is a perspective drawing. when you extend the Grey lines, they join to the vanishing point.

4

 

The vanishing point can be anywhere you want, even inside the square, like in the following fig.

5

And of course, it is equally a representation of a scale factor.

Which means that in our everyday life, when we look around us, we see the living image of a kind of scale factor. The same counts for picture we get looking at the stars. Perspective always count, even without Earth's horizon.

My point is that what we understand as an image of 3d space can also be interpreted as the image of a scale factor. The geometric laws that apply for both are the same. Perspective is a geometric construction, scale factor is a mathematic one. The result is the same.

6

there are much better pictures on the web, but they are all copyrighted.

a link I liked:

Edited November 14, 2010 by michel123456

[John Cuthber]

"Lets put a scale factor of 2, and approximatively double the size of the square,"

Double the size in the sense of make it 4 times bigger.

[michel123456]

Yes.

When you double the size of each side, ou quadruple the surface.

[michel123456]

Upon the last picture, here is what is happening:

7

 

It is not speculation, it is really what we learn from physics.

So, a form of scale factor, which is observed by us through common perspective view, is also an indication of the flow of time. I say that without clearly understanding what it means, but that's the way things seem to go. If I made any mistake somewhere, please correct me.

 

Of course, one may say there is nothing weird happening, be cause what I call "past" is not "my" past (i.e. I was not in the past standing in the end of the corridor). It is simply an indication that the speed of light, which carry the image I get from reality, takes a certain amount of time to reach me. So, nothing is bizarre, everything is normal.

Edited November 15, 2010 by michel123456