Genady

So, you can "measure the increase in volume from inside the volume."

But the ruler is not a wavelength of a travelling photon. The ruler is defined locally. For example, like this: (Metre - Wikipedia) Such rulers do not expand. PS. I've picked that half a line because I saw it a pivot for the rest. It is relevant.

IOW, define metric. Exactly.

The ruler does not expand. The expansion is present on the distances of hundreds Mpc's. Expansion of space is a feature of homogenous isotropic space. But the physical space is not homogenous and isotropic. It has local areas of various densities of energy and momentum. They are sources of gravity, and they cause the spacetime to curve this way and that way, to shrink and to expand here and there with various rates. Only when all these local effects are averaged on the distances of hundreds Mpc's, the net effect of them becomes a uniform expansion of space.

And now?

You can say whatever you want about your pictures. But it is not how GR works. In GR, distances are determined via metric. Take two events in Minkowski spacetime, for example, events A and B: Which one is closer to 0?

Globally, regionally, locally ... Mentally, culturally, behaviorally ... Thank you for playing. As I don't intend to discuss this topic any deeper, I rather excuse myself.

I am not sure about it either, unless 'fewer humans' is 0. It changes all the time, IMO.

I don't see how it follows. (We are causing mass extinctions ⇒ we are too many)

If the axes in the images above (see https://www.scienceforums.net/topic/131720-cosmological-redshift-and-metric-expansion/?do=findComment&comment=1248849) were labeled with metric units, e.g., 1 km, 2 km, etc., then they could represent a metric. In that case, it would be immediately obvious that they are just two different pictures of the same thing, i.e., a 2 km by 2 km area. But without units, they can mean anything, for example degrees of latitude and longitude. In this case, they show two shapes, both taking up 2 degrees of latitude and 2 degrees of longitude. Which is larger? This is impossible to tell as it depends where on Earth are they. Moreover, if they are on different planets, it also depends on the planets' radii.

I too value other species and hate to see that. But it does not answer the question.

Can you clarify your statements with an example? If you don't mind, please describe the Pythagoras theorem in your terminology.

Is the Earth overpopulated?

It also would have to be all the bacteria and archaea which live within the larger organisms, and which are necessary for these organisms' functioning.

You are right, 'null' is not strictly applicable here. I use it here rather in the sense of 'default setting.' (Re: )

You might be just an atheist in disguise, like the ones described here (from the same wiki article): 😄

Wanted to add a couple of examples to my previous comment and to demonstrate why this ^^^ is incorrect. One example is metric that measures number of colored pixels. In this metric, the second shape is larger than the first. Another metric is square of difference between the pixels in vertical and in horizontal directions. In this metric, the first shape is larger than the second.

I think it is rather a different aspect of the question. Agnosticism is about knowledge. Atheism is about attitude.

Yes, but as a matter of curiosity, here are three different atheisms, from Atheism - Wikipedia: There are more nuances described in the article. You seem to refer to the "narrow atheism". I'd call myself tentatively, a rational atheist or simply, a non-believer.

Maybe I am wrong, but agnosticism sounds to me like a model with two or several alternative hypotheses, while I prefer a model with one null hypothesis and one or more alternative hypotheses. This is why I'd like to have a different label.

Or to change them, right?

Then we are back to my previous question: assuming that atheism is a belief that no deities exist, what is the correct label for taking not existence of deities as a null hypothesis rather than a belief?

This truth is so simple that it is trivial and irrelevant. We don't know if neutrinos have mass. We don't know if there ever was life on Mars. Etc. End of story?

I disagree that every null hypothesis is a belief. I think it is a wordplay.

Yes, I do. So, the rest of the conclusions are wrong. Coordinates don't say anything about the length, area, and volume. Coordinates are arbitrary. Expansion of space is a solution of the field equation in these conditions.