I didn’t know about logarithmic perception, that’s interesting! I bet you’re right about 7x being chosen due to the significance of the number seven in the Bible.

I was curious about this too. From random web searching (Syfy.com), the sun is 200,000 times brighter than the moon in the visible light region of the electromagnetic spectrum.

I think what you said is true but that also ketchup as a material is shear thinning—meaning as you shake or tap the bottle, this creates stress or “shear” on the liquid which causes the viscosity to decrease. It also takes a little bit of time for the liquid to re-thicken, so it will actually pour pretty well a few seconds after shaking it.

https://www.scientificamerican.com/article/ketchup-is-not-just-a-condiment-it-is-also-a-non-newtonian-fluid/

I had to check the math and I was surprised that 2^42 is “only” 4.4 trillion. Thought it would be a lot greater like there are less atoms in the universe similar to the uniqueness of a shuffled deck of cards.