At that point, I think pulling it out to an appendix is the right thing to do. Whenever I find a book with appendices, I do one of two things.

1. If an appendix looks like "prerequisite" material, I read it first.

2. If it looks like "further reading" or "deeper dive" material, I note where it's referenced in the main text and return to it later.

The main reason I prefer footnotes to end notes is the separation of concerns. When a book has end notes, they are usually mixed with citations. I don't mind managing 2 bookmarks or the eReader linking back and forth, but I really dislike following the reference to find that it just points at a whole other book.

Structurally, the most challenging book I've ever read was "The Message of THE QUR ĀN" by Muhammad Asad.

Start with the fact that the QUR ĀN itself is extremely non-linear. So much so that I think that this alone requires a great deal of study to address.

The text is 2 columns, the original Arabic adjacent to his English translation. There are copious and often long footnotes. The footnotes cross reference other footnotes, sometimes in chains. I read only the English.

I had to read it 4 times. Once just ignoring footnotes. Again, this time including just first-level footnotes. Again, following footnote chains back to their sources in the text. Finally, to reread just the text after pretending that I had everything figured out.

It took me a year to get through it to my satisfaction, although it was not the only reading, or even major project.

There is also the MRI intended to help kids understand what they will be going through.

It's always better to gain a full understanding of the system when trying to make important decisions.

The trolley has two sets of wheels, leading and trailing, both of which must remain on the same set of tracks.

The switch is designed to enable the trolley to change course, moving from one set of tracks to the other.

Throwing the switch after the leading set has passed, but before the trailing set has reached the switch points will cause the two sets to attempt travel on separate tracks. The trolley will derail, rapidly coming to a halt. If the trolley is moving slowly enough to permit this action, nobody dies.

Source: former brakeman (one of the people responsible for throwing switches), section hand (one of the people responsible for installing switches), and railroad welder (one of the people responsible for field repairs of switches).

I think for maximum uselessness, they should not be overlapping spheres, but deform at the interface, like soap bubbles or rubber balls. As long as the spheres are the same size and modelled with the same "surface tension" or "elasticity", the "intersection" of two sets would then be a circular interface with an area proportional to what would otherwise be an overlap (I think). If the spheres have different sizes or are modelled with different surface tension or elasticity, one would "intrude" into the other.

Multiple sets would have increasingly complex shapes that may or not also create volumes external to the deformed spheres but still surrounded by the various interfaces.

Time to break out the mathematics of bubbles and foam. This data ain't gonna obscure itself!

Might there actually be utility to something like this? Scrunch the spheres together but make invisible everything that is not an interface and label the faces accordingly. I suppose the same could be said of the shape described by overlapping. (Jesus, you'd think I was high or something. Just riffing.)

I read that as:

For decades, Nestle has been patenting milk proteins.

They've been doing it for a long time, not somehow getting extra-long patents.

Are you serious? They really have what amounts to an exoskeleton? Or maybe it's more accurate to call it a whole-body rib cage?

Just searched and found this fun article. Not really a skeleton but a collection of really stiff hairs or feathers (loosely: the genes are the same ones responsible for "other skin appendages" in vertebrates).

All great things start in a bar. Or coffee shop. Or in the shower. Or in a dream. But never in a meeting.

You've had a couple of pretty good responses. I would add that the very fact that you can ask that question demonstrates a failure of the education system and the fundamental problem of depending on business ideals to manage society.

In the first case, a proper education would have included, at all grade levels, examples and discussion of the various purely intellectual pursuits that ultimately proved critical to some technological advance that improved quality of life.

In the second case, the naive "businessification" of society means that any pursuit that doesn't make clear at the outset what practical (ie profitable) goal is being pursued is dismissed as folly unworthy of funding and support and education. (See my point above.)

What is this stop business? I have it on good authority that it's turtles all the way down.

As a non-geologist living next to Lake Diefenbaker (the reservoir formed by damming the South Saskatchewan River), I also like geological history.

I have a standard reply for when I'm asked why we chose to move to this "treeless wasteland". "I look out at the flat horizon and see how the glaciers planed the earth the way a woodworker flattens a board. I look around me at the river breaks and see how the meltwater from retreating glaciers carved the earth away into shapes that defy imagination." I don't know accurate any of that is, but it fits my mental model of what I was taught in high school.

(What we call the river breaks are twisted and braided networks of coulees, some with sides so steep as to require mountaineering equipment. Most still run with meltwater in the spring.)

Especially given that using π=3 is accurate enough for most daily use by ordinary people for ordinary things.