(i) Here’s a fun one: the Boltzmann Brain thought experiment named after Ludwig Boltzmann, the 19th century physicist who first proposed it.

Given the projected lifespan of the entropic universe (plus any and all manifestations of a multiverse) the likelihood that that your brain, in its precise atomic state at the moment you are reading this page, has materialized out of sheer randomness in the middle of a cosmic gas cloud, may be greater than the likelihood that it is the product of a causal set of steps including your life experience, human evolution, the making of this planet, the birth of the sun, etc. IF this is the case, then at this exact moment your brain has winked into existence only to presumably die a moment later, absent life support in the near-vacuum of space. Sound absurd? Of course it does.

It’s an interesting manifestation of what I’ve seen termed Last Thursdayism. The idea being that we have no way of knowing whether what we understand as our past experiences are (a) genuine, (b) the product of random physical fluctuations or (c) the programming of a nefarious demon.

The thing is, I used to be that guy who would proclaim the inevitability of walking through a wall if you had an eternity to attempt it, to wait for the perfect, serendipitous atomic alignment. I’d imagine all of the possible permutations from the faint and unnoticeable to the disastrous (being stuck in the wall). I’d like to think I take a more pragmatic approach now to the question of what is “possible”. If the number of years it would take for something to eventually happen has 1,000 zeros, then it’s safe to say that that something doesn’t actually exist in any real sense. Right? This particular example is also rooted in an erroneous line of thought which imagines the reality of particles in the quantum realm can be extrapolated to the macro reality that we experience.

I remember an instructor of a mineralogy class telling us that systems, which at small scales are chaotic and random, will paradoxically look uniform at large scales. Like the quantum spookiness, the disorder will cancel out at sufficient volume, producing something isotropic from our vantage.

An example is silicon dioxide, commonly encountered as the mineral quartz, an oxide made up of one atom of silicon and two atoms of oxygen. These are by far the two most abundant elements in the Earth’s crust. This molecule forms a tetrahedral structure (SiO₄) which can exist in crystalline, amorphous or fine-grained (cryptocrystalline or microcrystalline) forms. The most common example is glass, itself, which owes its appearance to a lack of large-scale structural organization.

Flint and chert are brittle rocks with fine-grained, cryptocrystalline molecular structure based on the SiO₄ tetrahedron. They have long been utilized in the manufacture of stone tools due to their conchoidal fracture, that is, fracture that does not occur along cleavage planes, allowing for sharp edges and greater control over the shape of the final product. The distinct fracture creates rippling shock waves, visible in the material, useful for distinguishing between naturally broken rocks and cultural artifacts.

Flint is also associated with fire-making, though it’s not actually the flint that is important. Rather, flint is a very hard rock, allowing it to be used to scrape off small pieces of iron from a steel knife or other iron implement. It is the exposed, high-surface-area iron flakes which have the ability to spontaneously ignite.

(ii) Right around the time you learn that atoms are very small, you also learn that atoms are mostly empty space and that the mass of an electron is 1/1837 the mass of a proton. I was misled for a long time by that final point into believing that electrons were in some sense smaller than protons or the nucleus itself. Ask anyone to draw an atom and you will undoubtedly see a big circle in the middle surrounded by smaller dots on the periphery. This conception of subatomic size leads directly to errant characterizations of the atom as a miniature solar system with electron planets orbiting the nuclear sun: “if positive and negative charges attract, why don’t the electrons crash into the nucleus!?”

But what does “size” actually mean at subatomic scales. I won’t pretend here to understand the subtleties of quantum mathematics, but suffice it to say, that very, very small particles have the peculiar property of also behaving like waves, thus limiting the utility of intuitions that derive extreme differences in volume from extreme differences in mass. As far as these concepts do apply, it makes more sense to think of the massive nucleus as very small and the less massive electron as large given their area of effect.

On a related note, a few years ago a conversation with a relative (something about cosmology) sparked a tangent about the importance of orders of magnitude when making comparisons related to size. For my part, I was enlightened on this logic by a comment on r/askscience (which you should be regularly visiting if you are not already).

When someone asks: are we (humans) closer to the size of an atom or closer the size of the galaxy, what does that imply? For an easier comparison, consider the more intuitive case: is a cat closer to the size of an atom or the size of a tree?

Clearly, a cat is closer in size to a tree than an atom. However, if you were to measure each in absolute terms, say in meters, you would actually find that a cat is “closer” in size to the atom. The confusion results from what is implied in the “closer,” that is, an understanding of orders of magnitude. The atom is many times smaller than the cat or the tree regardless of the absolute, cardinal value of the unit of measurement applied to each.

To the original question, the galaxy is approximately 100 light years across which converts to a diameter of approximately 9×10¹⁷ meters across. At a scalar comparison, it is clear that we are closer in size to an atom than our galaxy. The galaxy is quite large.

(iii) Cicadas are large insects known for their distinct, shrill call.

Some cicadas spend the majority of their lifespan underground feeding from tree roots, only to emerge as mature, breeding adults every 13 or 17 years. I remember reading about this phenomenon in one of Dawkins’ books, maybe The Blind Watchmaker, in which I recall him arguing the evolutionary advantage of this peculiar life cycle.

[That same book also introduced me to this, which is another mind-blower.]

The logic is as follows: in a world of competitor and predator species with varying multi-year life cycles, there is an advantage to periodicity based on a prime number due to that fact that there will be less chance of overlap in any given year. Of course, this is not the only way to go about being a cicada, as annual versions are common, but as always, there are trade-offs in any evolutionary development.

(iv) Bouvet Island. Love this one. Top-shelf mystery. And this is a brilliant write-up.

I just want to reemphasize the ridiculous isolation of the tiny island and the improbability of things randomly arriving there.

By my own measurements.

To Antarctica: 1,800 km

To Africa: 2,500 km

To South America: 4,200 km

I made a circle around Bouvet Island that touches the coasts of the surrounding continents:

Ocean circle circumference = 19,000 km; radius = 3,024 km; area = 28,728,533 sq. km

Island circle circumference = 35 km; radius = 6 km; area = 113 sq. km

10 million vs. 100; or 5 orders of magnitude greater; or a 1 in 100,00 chance of randomly selecting land instead of ocean (ignoring some of the pesky islands near the continents). Coincidentally, this is also the size of the nucleus of an atom relative to the size of the entire atom! It all ties together!

(v) This one has guitars: