"In another moment Alice was through the glass, and had jumped lightly down into the Looking-glass room." (1)
Most of us, as children, have pressed a hand against a mirror and met another hand pressing back, one that is ours but not quite ours, with its left on our right.
Consider how you know your own face. You have never seen it directly. You know it from mirrors, which reverse it, and from photographs, which flatten it. Remove the glass and you do not see yourself more truly. You do not see yourself at all.
The world is no different. It reaches us through eyes, nerves, and a mind that shapes it before we see it. If we strip the shaping away, we would not see the world more clearly. Rather - we would not see at all.
Alice’s experience in the Looking-Glass world, with its inverted reality and reversed logic, show that there exists a reality outside our perceived reflection. So the question we must ask is how much of what we see belongs to the world, and how much belongs to the glass. Philosophers have argued over it for millenia, and in the last hundred years physics has opened up this question once again.
A Brewtiful Form
David Brewster, a Scottish physicist working just after the turn of the 19th century, was investigating how light waves could be restricted to one plane (polarisation) by reflecting light back and forth between inclined reflective plates. In this process, while observing a candle, he noted down the “multiplication of the sectors formed by the extremities of the plates of glass” (2).
Impressed by the beauty from the symmetry of the image – presumably a distraction from dark and miserable 19th century Scotland – he had a candle moment and his eyes lit up with pound sterling signs. Brewster saw the commercial side quickly. Seeing its potential in "all the ornamental arts" for its capacity to produce "an infinite variety of beautiful figures and patterns" (2), he took the setup, fixed it in a tube with pieces of coloured glass at the end and proudly displayed it at the Royal Society of Edinburgh.
He built the name from three Greek words: καλός kalos (beautiful), εἶδος eidos (form) and σκοπέω skopeō (to look at) (2). A kaleidoscope was thus designed to be an instrument for looking at beautiful forms.
Unfortunately, the patent did him little good. Before the licensed maker had stock ready, one of the instruments was shown to London opticians to take orders, and the opticians copied it. An estimated two hundred thousand kaleidoscopes sold in London and Paris in three months, and Brewster reckoned that at most a thousand of them had made them with his patent specification (2). Alas, he should’ve consulted an intellectual property lawyer.
Its design is simple. At the far end of the tube sits the object cell, where loose fragments of coloured glass are held between a clear pane and a translucent one that diffuses the incoming light. Mirrors run the length of the tube, meeting along one edge. At the near end is the aperture. For the reflected copies of the cell to close up without a seam, the mirrors must meet at 180°/n for some whole number n. At 45°, the eye sees eight sectors, and at 30°, it sees twelve (2). Brewster tried (and wrote about!) many possible configurations of his product. His patent favoured angles of 18°, 20° and 22½° (3), while later treatises specified 45°, 36° and 30° (2).
Consider what the viewer does and does not see. While using the device, the glass fragments are never seen in the location where they actually lie; rather only their multiplied reflections reach the eye. The mirrors are never seen at all. They appear nowhere in the image, yet they fix the perceived shape and pattern.
An argument I propose is that human perception operates like Brewster’s kaleidoscope: what we observe is not a raw, unmediated external world, but a structured projection produced by the interaction between external content (the inflow of ambient light) and internal architecture (glass beads and mirrors). Extending this analogy, the loose, coloured fragments of glass at the far end of the cylinder represent mind-independent matter. We never observe their unreflected physical form directly; however we observe their effects. The mirrors and lenses that produce the symmetrical patterns can be thought of as the inner workings of our neurology that permit us to process and perceive external stimuli.
While Brewster's kaleidoscope postdates both Locke and Kant, I believe my proposed framework fits their theories of human perception well. Locke is concerned with the fragments: which qualities belong to objects themselves, and which exist only in the perceiver. Kant is concerned with the mirrors: what the mind contributes to every experience before any object appears in it.
Neither theory was built solely from deductive philosophy alone, as each was modelled on the physics of its time. Locke's primary qualities (extension, shape, motion, number) are variables of a mechanics problem, drawn from the corpuscular philosophy of Boyle and Newton. Kant's forms of intuition are Newton's space and time, Euclidean, absolute and independent of each other, except drawn from the world into the mind.
Finally, the relationship between physics and philosophy becomes strained when one of them is proven incorrect. We learnt that physical space could be curved, space and time merged into one, and particles no longer had a definite position and momentum at once. If Locke and Kant built on classical physics, to what extent can the framework of Brewster’s kaleidoscope persist today?
Separating the chaff from the grain
Locke's Essay Concerning Human Understanding (1690) contains one of philosophy's more pragmatic thought experiments:
Take a grain of wheat, divide it into two parts; each part has still solidity, extension, figure, and mobility: divide it again, and it retains still the same qualities; and so divide it on, till the parts become insensible; they must retain still each of them all those qualities (4, emphasis added).
Locke’s mill is an instrument of division. Grinding changes a grain's size and shape, but the main point is that the mill cannot take away the fact that every piece has some size and some shape. Properties that survive every division must belong to matter itself. Locke's list of descriptors of this nature is “solidity, extension, figure, motion and number”. He calls them primary qualities, that are "utterly inseparable from the body, in what state soever it be" (4, emphasis added). Colour, taste, smell, warmth, and sound are not of the same vein. Locke uses the example of granite. If you turn off the light, its natural reddish-brown colour can’t be examined, and hence does not exist (4)! For these descriptors, he labels them as secondary qualities.
Locke did not arrive at his list by introspection, rather deriving his theory of knowledge from the physics of the day. In the preface to his Essay he describes natural philosophers (a term that we would now call a physicist) as "master-builders," where he name-drops Robert Boyle and "the incomparable Mr. Newton," thus concluding that it is "ambition enough to be employed as an under-labourer in clearing the ground a little, and removing some of the rubbish that lies in the way to knowledge" (4). On this account, one can see that it is the philosopher's job to provide credence to the physicists’ theories.
The physics that Locke was “clearing the ground” for was Boyle's. Boyle's Origin of Forms and Qualities (1666) set out the corpuscular philosophy, that all matter consists of tiny solid bodies, each with a size, a shape, and a state of motion, whereby every other property of an object comes from how its corpuscles are arranged within the body (5). This was not a new philosophy, but rather the rehashing of a truly ancient belief. In a rather terse remark that perhaps could have found its way into The Flintstones, Democritus put it more bluntly in the fifth century BC; "By convention sweet, by convention bitter, by convention hot, by convention cold, by convention colour; but in reality atoms and void" (6).
However, what the seventeenth century added was the formalisation of mathematics. Galileo wrote that the book of nature "is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures" (7). Descartes gave geometry an algebraic form, and Newton's Principia (1687) could predict where a body would be on the Day of Judgement from its mass, position and velocity (8). F = ma does not predict a body's smell. This is why Locke's list of primary qualities looks the way that it does. Size, shape, number and motion are the quantities that can be written into equations. Primary qualities are the variables of seventeenth-century mechanics.
Galileo drew a hard conclusion about Locke’s secondary qualities. Tastes, odours and colours, he wrote, "reside only in the consciousness", so that "if the living creature were removed, all these qualities would be wiped away and annihilated" (7). Locke’s argument, however, was a little more nuanced. Rather than being a wishy-washy subjective experience unique to the observer, Locke writes that secondary qualities are "powers to produce various sensations in us by their primary qualities" (4, emphasis added). The redness of a rose is a real feature of itself; an arrangement of its particles that, given light and a human eye, produces the sensation of red. The sensation needs an observer. Its power does not.
A power of this kind is a relation. It is defined not by what the rose is on its own, but by what it does to light and to eyes. Locke ranked such relational properties second, below the intrinsic properties a body has in isolation.
Returning back to the kaleidoscope, the fragments at the end of the tube have a definite number and definite edges whether anyone is at the aperture. Those are its primary qualities. The colours that wash across our view are secondary; what the fragments' structure does to the light passing through them, and the effect that it has on the eye at the other end.
The mirrors of the mind
Kant thought Locke had stopped halfway. If colour belongs to how a thing appears rather than to the thing itself, why should shape and size be any different? In the Prolegomena (1783) he describes his completion of Locke’s theory:
If I go farther, and for weighty reasons rank as mere appearances the remaining qualities of bodies also, which are called primary, such as extension, place, and in general space … no one in the least can adduce the reason of its being inadmissible (9).
Kant’s main thesis is rather straightforward – everything we know about the fragments reaches us through the mirrors. We have never seen a fragment without them, so we have no way to verify which features belong to the fragment and which the reflection put there. Kant calls the thing as it is in itself (ding an sich), beyond any possible human experience as noumenon, and the thing as it appears to us as phenomenon. Locke's primary and secondary qualities are both forms of phenomena.
Since the fragments in themselves cannot be known, Kant went to the piece of the toy that we may study from the inside: the mirrors. Kant claims that space and time are not features of the world we observe. Rather they exist as forms of our inherent intuition, the fixed structure through which anything must pass in order to be experienced at all. The existence and immutability of space and time are a priori; not learned from empirical evidence, but rather an inherent logical deduction given to us at birth. We never perceive space itself, just as the viewer never sees the mirrors. Yet every experience we have is due to space. This is true for time.
Kant’s illustrious success as a philosopher often overshadows his independent research in theoretical physics. His Universal Natural History (1755) used Newton's gravitation to explain how solar systems form (11). Similarly, we see Kant’s “plagiarism” of Newton’s theory of space and time, albeit placing his theory in a newfound context. In Newton’s Principia, "absolute space, in its own nature, without relation to anything external, remains always similar and immovable", and "absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external" (8). To the human mind, space and time are uniform and universal, and are able to be intuited from our human instinct.
Consequently, space must be Euclidean, as our spatial intuition dictates "that the straight line between two points is the shortest" (10). Similarly, there must be a single time shared by every observer: "different times are only parts of one and the same time" (10). The question one must ask is: is our intuition true?
Melted glass, bent mirrors
Locke stopped the mill when the grain became “insensible,” and deduced the primary qualities from there. However, physics kept on grinding.
Consider the following listed primary qualities:
Bulk: Newton defined mass as a quantity of matter, something each corpuscle carries as its own. Upon grinding the wheat to its amylose and amylopectin starch chains, the molecules to atoms, the atoms to nuclei, and the nuclei to its protons and neutrons, we see that proton contains three quarks, but the quarks' own masses account for about one per cent of the proton's mass (12). The mass deficit is the energy of the strong nuclear force that binds the protons and neutrons together (13). Most of a proton's bulk belongs to none of its parts, rather the mass stems from relational energy from particles being in close proximity.
Extension and figure: The electron has no measured size or shape. Experiments have proved an upper bound of 10-18 metres, and the Standard Model treats it as a point particle (14). The "shape" of an atom is a variable probability distribution, with no fixed boundary that divides inside and outside.
Motion: In quantum mechanics, a particle cannot have an exact position and an exact momentum at the same time, and consequently motion cannot be found out without losing where it is or where it is going (15). Some quantum interpretations, such as Bohm's pilot wave theory, have tried to restore definite positions by having a guiding wave “push” the actual configuration of particles, however this causes each particle's motion to depend on the positions of all the others (16). Locke's self-contained corpuscle does not agree with this.
Solidity: Particles may experience quantum tunnelling effects, as the wave function representation of its position may result in a probability of finding the particle in a classically forbidden region. In practice, this is impossible due to the exponentially decaying probability of events happening for one, albeit an Avogadro’s number of particles. However, this still disproves Locke’s theory on the solidity of corpuscles.
Number: Surprisingly, not even the comfort of invariant counting is spared. In quantum field theory, particles are excitations of underlying fields, and how many excitations are present can depend on the reference frame of the observer. An observer accelerating through what an inertial observer calls empty space may detect many particles (17).
Every primary quality on Locke's list, probed to a microscopic scale, stops being an intrinsic property of a self-contained body and becomes a fact about relations; between quarks, between electrons, between a system and its measurement device. The fragments at the end of the tube, therefore, do not have a definite number or a fixed shape whether anyone is at the aperture.
The mirrors are not spared from the physics revolution. In 1905, Einstein showed simultaneity is not universal; two observers in relative motion can disagree about whether two distant events happened at the same time, and neither is incorrect (18). In 1915, his general theory went further. The geometry of space and time is not fixed in advance but shaped by the matter and energy within it, and near mass geometry is no longer Euclidean (19).
In Kant's kaleidoscope, the mirrors were fixed at one angle in every tube. Relativity dictates that the angle depends on how fast the tube is moving and the direction it is held. To make matters worse, the angle is not set by the viewer at all. The presence of external mass and energy determine the geometry, so the contents of the universe distort and bend the mirrors depending on where it is used.
A Kantian can reply that ordinary experience still looks Euclidean, which indeed is true; as deviations locally are far too small to see. However, recall that Kant did not claim that space looks Euclidean. He claimed we know, a priori, and therefore with certainty, that if our intuition dictates it to be so, it is so. Mathematicians (Lorentz, Poincaré and the like) had already shown in the nineteenth century that non-Euclidean geometries are perfectly consistent and functional (20). Einstein showed that solutions to his field equations demonstrate that the space we occupy is non-Euclidean (19).
Clearly, there is absolutely no hope for our kaleidoscope. Its fragments have melted and its mirrors have been bent, so our framework is futile, an antique relic that should best be left in the past?
Rebuilding the kaleidoscope
Let us first consider the glass fragments first. The history of physics is a graveyard of discarded things: caloric, phlogiston, the luminiferous aether. If our best theories have repeatedly been wrong about what exists, then who in their right mind would trust our newfangled current ones? Worrall answers that despite the incorrect precise detail of scientific theory, we still have the same mathematical structure persisting across time (21). He uses the example of light, where in 1820s Fresnel described light as a vibration in an elastic aether and derived equations for how much light a glass surface reflects and transmits for each polarisation. Maxwell's theory later replaced the aether with electric and magnetic fields. Whilst Fresnel was incorrect about what medium light vibrated in, his equations carried over unchanged.
Now looking back at Locke's qualities, we see that he ranked intrinsic properties of corpuscles over relational powers. Modern physics found that at its core, particles do not possess intrinsic bulk and figure, but relations; group symmetries, conservation laws, the ways systems act on one another. Since Eugene Wigner's work in 1939, physicists have classified elementary particles not by size or shape but rather how they behave under the symmetries of spacetime, which is what fixes their mass and spin (23). Others argue that fundamental properties are powers in Locke's sense: that there is nothing more inherent to an electron's charge than rather what its charge allows it to do (24). So, a neo-Lockean keeps his method, but rather inverts Locke’s original order. Secondary, then primary.
Now for the mirrors. Hans Reichenbach, writing in 1920 when general relativity was merely five years old, argued that Kant had combined two meanings of a priori (25). Its first meaning is that an a priori deduction is "necessarily true" or "true for all times." Evidently, an a priori belief that space is Euclidean has been proven necessarily false by Einstein’s relativity. However, its secondary meaning, and the one that Reichenbach claims can save Kant’s theory is "constituting the concept of object" (25). An a priori deduction must come after a framework before any test of its validity can mean anything. Michael Friedman develops this into what he calls the relativised a priori (26). Newton's mechanics presupposed Euclidean geometry and his calculus; Einstein's presupposed Riemannian geometry and the equivalence principle (gravitational mass equals inertial mass). Neither framework was learned from the experiments it made possible, since without it those experiments would have meant nothing. Yet each could be replaced when a scientific revolution replaced the whole system.
Inside the tube
So how much of what we see belongs to the world, and how much to the glass? There is no fixed share, because there is no barrier between them. Every observation is a physical interaction. Demanding to know what reality looks like without an observer is a logical fallacy; if you see a kaleidoscope from the outside without peering in, you wouldn’t know the pattern that emerges.
What we can and should trust is invariance, the structural patterns that never change, no matter which angle you look from. Physics looks past the shifting reference frames of observers to find the conservation laws, mathematical symmetries, and field equations that hold firm across all of them. Yet we only uncover these invariants because we can each observe reality from our own kaleidoscope, sharing, testing, and validating what we see to map the relationships across the observable universe, both within and without. Nagel called the old ideal of objectivity "the view from nowhere" (27). Physics has swapped it for something attainable: the view that holds from everywhere.
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