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.

This article is talking about benzene, not benzine FYI.

The allowable limit in drinking water by the EPA is 5 ppb. Inhalation exposure limit by OSHA is 1 a 5 ppm per day (inhalation is not an apples to apples comparison to consumption though). I’m not a toxicologist so I don’t know what exposure amount is “safe”, but dosage does matter.

This article mentions benzene coming from the carbomer in these formulas. The benzene is a residual impurity in the carbomer making process, and there are carbomer on the marketplace that don’t use benzene in their manufacturing process, but they are more expensive. I’m not sure the source of carbomer for these products, but I’ve seen reported on carbomer I’ve looked at to have up to 1 ppm of benzene impurity. Products like this might use carbomer up to 0.5 to 1%. So you’d expect maximum levels of benzene to be in the product (at the aforementioned levels) to be 10 ppb. So possibly at double the amount allowable in drinking water by EPA. People drink a lot more water than cough syrup (I hope) so it might not be that concerning.

The article frustratingly does not give amounts of benzene found in these products so it could be sensationalist—I just don’t know. So is benzene bad—yes. Does the cough syrup have concerning levels of benzene? Maybe, but just saying benzene might be present isn’t enough information in my opinion.

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.