system
Given the following post, respond as if you're commenting on Reddit:
human
As long as you also scaled all building materials proportionally, would it be possible to simply scale up a structure to a massive size while maintaining structural integrity?

I always wonder why things are the size that they are, or if it would be possible for giant humans to exist. That's a complicated topic, so to simplify lets talk about buildings.

Very simply: could you rebuild the empire state building, for example, to 200X as long as you used metal support beams that were 200x larger? Intuitively it would seem like it wouldnt work, but I'm not even sure why I would think that.

It seems like the atomic forces that keep things solid and from bending have limits, and that these limits would reach a breaking point at a certain scale.

Thanks in advance!
gpt
Even if you scale all dimensions proportionally, not all properties of the building or object would scale the same way.

Consider a standard block-shaped building of size X * Y * Z. If you scale everything up by a factor of 2, you get a building of 2X * 2Y * 2Z. The volume of the building (and by extension its mass) has gone up by a factor of 2 * 2 * 2 = 8, while the surface area of the ground floor has gone up by a factor of 2 * 2 = 4.

The same will be true for all the support beams and other structural components: surface areas go up by a factor of 4, while volumes and masses go up by a factor of 8.

This means that pressure, which is defined as force divided by surface area, goes up by a factor of 2 in many areas. So despite all 3 dimensions being scaled up proportionally, pressure on supporting structures will increase since the mass has increased more than the surface areas and cross sections.

A similar argument can be made for why an ant scaled up in all dimensions by a factor 100 would instantly have its legs collapse, while it's perfectly fine at its regular size.