Quantum mechanics is the most accurate physical theory we possess, but also the one we are least able to picture. Quantum physics is renowned for the quote by Feynman “I think I can safely say that nobody understands quantum mechanics.”, this is often misinterpreted and it is in actuality not that its mathematics is unclear but that its content resists Anschauung - the German term, central to both Kant and Husserl, for the intuitive, perceptual givenness of an object to a mind. We can calculate a wavefunction with total precision and still be unable to picture what it describes. This then begs the question: is this lack of intuition a fact about quantum mechanics, or a fact about us? Would a mind that evolved inside the quantum domain, rather than the classical one, understand it?

Four panels showing electrons building up an interference pattern one at a time, from a sparse scatter of dots to a full fringe pattern
Figure. Tonomura's single-electron double-slit results: 11, then 200, then 6,000, then 140,000 electrons, each one landing as a single dot, the fringe pattern only visible once enough of them accumulate. This is exactly the kind of result that resists Anschauung — every individual event is a point, and the wave behaviour only exists as a fact about the distribution.

Anschauung and the shape of possible experience

For Kant, Anschauung is the foundation of cognition as opposed to a feature or secondary implication thereof. Space and time, in the first Critique, are forms of pure intuition - they are a priori scaffolding through which anything can be given to us as an object at all. We do not infer that objects are spatially extended and temporally successive; extension and succession are the conditions under which we can have objects presented to us in the first place. Crucially, Kant took this scaffolding to be Euclidean and strictly successive: one thing after another, each occupying a definite place. Quantum mechanics does not respect either commitment. Superposition does not present a particle as being in one place with unknown properties; it presents instead as all possible states at the same time. Entanglement correlates outcomes without a property of one event locally causing the other. If Kant is right that our Anschauung is inherently classical, then quantum phenomena are unpicturable because picturing is the operation that presupposes the classical form we are asking these phenomena to violate.

An evolutionary gloss on the same problem

A Kantian would say our intuition is transcendentally structured; a Darwinian would say it is evolutionarily structured, but the upshot is similar. The perceptual and cognitive apparatus we have i.e. the machinery that turns retinal activation into a stable, three-dimensional, ordered scene was not evolutionarily selected for the pursuit of truth about the fundamental structure of matter. It was selected for tracking macroscopic regularities relevant to survival and reproduction on the scale of metres, seconds, and kilograms: where the predator is, whether the branch will bear weight, which fruit is ripe. At that scale, decoherence has already done its work long before any signal reaches a nervous system; every object we evolved to perceive is, for all practical purposes, always definite. Our concepts of object, trajectory, and cause are extremely well-adapted tools for a world that has already been rendered classical by the huge number of degrees of freedom involved. There has never been any selection pressure to represent superposition, because nothing at the scale our ancestors operated on ever stayed in one long enough to matter.

The thought experiment, and where it breaks

Imagine a species that evolved at the scale of nanometres and femtoseconds - small and fast enough that quantum effects are prevalent in everyday life. Would such a species have direct Anschauung of superposition, the way we have direct Anschauung of solidity and the mesoscopic realm?

Any organism, at any scale, needs some stable structure to serve as the substrate of a nervous system, a memory, a persisting self that can learn from one moment to the next. Stability of this kind is inherently broken by the principle of superposition. A system that remained in a rich superposition long enough to be perceived as such would, by that very fact, struggle to maintain the kind of robust, redundantly-recorded, environment-selected state that information theorists call an einselected pointer state - the kind of state that can be copied, stored, and acted on reliably enough to be useful to a living thing. In other words, the features that make an organism viable - a persisting body, a memory, a self that survives from one instant to the next - are the features that push its environment, including its own perceptual apparatus, toward classicality regardless of the length scale involved. A mind “native” to the quantum domain would still need to stabilise itself against the fluctuations that constitute that domain, and it is not obvious that a stabilised, persisting mind could take superposition as an object of direct intuition without thereby ceasing to be the kind of stable thing a mind has to be.

What Husserl adds: intuition is not fixed

Husserl denies the premise that intuition is a fixed biological or transcendental given, incapable of extension. His notion of categorial intuition holds that we can have genuine, originary intuitive grasp not only of sensuous particulars but of categorial structures such as states of affairs, relations, ideal objects - that are not themselves perceivable in the way a colour or a shape is perceivable, yet are still given “in person” to a suitably prepared consciousness. And in the Origin of Geometry, Husserl describes how a mathematical formalism, once instituted, becomes a kind of sedimented intuition: a symbolic structure that a trained practitioner can come to grasp with something like the immediacy of perception, even though it was built up historically through acts of idealisation from an originally sensuous life-world. An example is the trained physicists making use of the idealised Hilbert space in order to understand quantum mechanics.

Perhaps no organism, however small and fast, would have sensuous Anschauung of quantum superposition, for the structural reasons above. But a physicist who has spent a decade with the formalism, who can look at a wavefunction and see what it implies - that physicist may already possess something functionally close to a categorial intuition of the quantum domain: not a picture, but a founded, symbolically-mediated grasp that stands in for the sensuous Anschauung that domain will simply never offer any embodied mind, evolved or otherwise. If that is right, the conclusion is mathematics itself may be the only Anschauung the quantum domain will ever allow.