There is no firm line at which a piano bench becomes a table. It’s contextual, it’s idiosyncratic. No firm line for when red becomes yellow, no firm line for when stacked grains of sand become a heap, for when a jog becomes a run. At the demand of convenience, we think of a table, or a heap, or a jog as a discrete and coherent thing, but it’s… not. At all times there are molecules attaching to and detaching from any table you meet, at all times there are edge cases you would consider a table that someone else would not, and neither of you can be reasonably said to be privileged with some secret table knowledge. Table-ness is a continuum. A spectrum. The overwhelming majority of concepts you encounter in your daily life are like this. They’re associative; the lines between related concepts are blurry and cannot be reliably separated, because the concepts themselves are stored in a fundamentally blurry information system.

But there are places where they can be separated perfectly.

The first is in logic. P = P, P ≠ –P. Modus ponens. But logic is… circular. It operates like this because we demand it to.

The second and most obvious is in numbers, in math. Quantity has joints, in a way that tables and apples do not. There is or is not three of something. One plus x is or is not five. We can even use numbers to describe a number of tables, as long as we limit ‘table’ to just mean only the part of the universe within a circle we’ve drawn, recognizing (or not) that the circles aren’t real—you can take a rainbow and circle six colors and it is true that there are six circles, even if it’s not true that the circles have cut reality at the joints. But those circles have the same… well, the same circularity as with logic. You’re not cutting reality, you’re just cutting at the joints of this thing you invented which you gave joints for you to cut.

For both logic and quantity, if there were nothing in reality that truly acted like this—if everything were infinitely granular spectra and idiosyncratic object-name-bounds, the applicability to practical understanding would be irrelevant. The existence of all-or-nothings would be purely thought experiments.

But there is a part of reality that does have joints.

Electrons are a probability waveform, and are simultaneously particles, that can/do/don’t exist in any given space in a technically pan-universal possibility-cloud. There is at any given moment an exceedingly small (probably has never and will never happen for the entire length of the universe, but it could) possibility that some electron in the blurry-edged thing you call your body has found itself miles away, for some infinitesimal moment. Some traits of electrons are quite blurry. But when an electron moves to a lower energy state, there is no in-between, no gradient. It is at one state, and then it is at another, releasing a packet of energy equal to the energy loss—a photon. And electrons, to the best of human knowledge, are not composed of anything; they cannot be divided. They are fundamental particles. Quantum physics are called as such because they have found the universe, at a sufficiently small scale, to operate in quantities. Countable numbers. Things—electrons, photons, quarks, quantities of energy—that cannot be divided, things that are not further composed of other things, that do not exist on gradients.

Whether something is seen as a table is dependent just as much on objective facts of its existence as it is on subjective assessment by its observer. The energy state of an electron is not—identical observers capturing observations at identical points of an energy transition see a random result of either the first or second state. There is no subjectivity, no gradient of existence for electrons. There is 0, or there is 1. Do not pass 0.5, do not collect a half-charge. Their joints are real.

And we know that literally everything, everywhere is built out of these quantum mechanisms. Which tells us two things: reason can cut our universe at the joints, but those cuts only ever separate the most basic, indivisible building blocks of reality.

Everything else is emergent spectra.