If my book The Genius of the Invisible God ever gets published, and if you ever acquire a copy, you’ll come across a section about what I call ‘cognitive effigies’, which amount to:
“A repertoire of mental activity we use to orient ourselves in a world too complex for simple apprehensions, but in which we can distil higher meaning and purpose than we can find in its material constituent parts.”
I go into detail in the book about how the physical world out there resembles a useful fiction, and note in this passage:
“Take any of the following ideas; volume, heat, texture, fast, slow, particle, wave and light – each of these is a mental simulation of something related to external nature, but equally, each is human-centred too, and remains only a partially accurate simulacrum of reality ‘out there’. This is the 'cognitive effigy'. This book may be the first time you’ve considered the idea of the brilliant illusion of the 'cognitive effigy', and it must in some way shock, because the thought that things like gravity and weight and mass and energy are simulacra based on a kind of anthropocentric fiction of ideas seems alien to many.”
Once we apprehend reality out there in more depth, we understand that science is also a kind of useful fiction too. The main difference between science and other useful fictions is that science has the most practical (and predictive) empirical utility, but ultimately it still only relates to one kind of relation to reality, namely an implicitly physical one.
Consider for example Newton's law of gravity and Einstein's equivalence of mass and energy – they are both observations in physics, whereby the latter superseded the former. But from this standpoint, we do not say that Einstein showed Newton to be false, rather that Einstein's selected system of geometry, Riemannian Geometry, describes the observed phenomenon better than the Euclidean system employed by Newton, but neither is considered singularly true and neither is anything like a full explanation either - they are only one prong on Hume's fork.
I think this taps into the idea of scientific disciplines as a kind of useful fiction, and how our minds relate to reality. Even though mathematics has an existence more primary than physics, the mathematical symbols we use for deciphering laws in physics are very much part of the language we create. But if we could get a proper sense of the true reality, we’d actually understand that it’s the physics we use as a map to decipher the landscape of mathematical reality. And that is a big part of why we have to embody these cognitive effigies – there is no proper sense of the world except by way of symbolising, analogising, metaphorising, allegorising and narrativising those discrete packages of information to create meaning and purpose from our physical map reading.
Consider the geometry allusion above, by way of illustration. Geometries change according to which map of physical reality we are using. Euclidean geometry maps the base of geometry (lines, flat space), whereas hyperbolic geometry and elliptic geometry go beyond the Euclidian base, into the realms of curved space, geodesics, differentiable manifolds, and what have you. Riemann's geometry moves us into the field of geodesics, differentiable manifolds and the generalised principle of dealing with higher dimensions (Einstein's General Relativity emerges from Riemannian geometry, for example).
If you consider any space of dimension N, you can select a curvature giving it a Euclidean, elliptic or hyperbolic nature - just upping the number of dimensions doesn't make any fundamental difference at all. But a Euclidian shape is still an ideal shape, which means it falls within the category of ideation (an idea). But Euclidian geometry and Riemannian geometry are not at odds, of course - just different lenses through which we map physical reality. Our future science will probably consist of maps that go beyond Euclidian and Riemannian geometry - it's just that we need further experience and discovery before we can say what lies ahead.
This taps into Kant's conditions for understanding things (such as an awareness of space and time - that he called "forms of intuition" in his Critique of Pure Reason) and how they are derived from the structure of the mind itself. In other words, they are phenomenal, and transcendentally ideal because they are presupposed by our experience as concepts of our mind (recall his distinction too in the same work between phenomena, the world as it appears to us, and noumena, the world as it is in itself).
Here's another example. When Maxwell proved that light consists of electromagnet waves, we might picture the analogous image of water waves or sound waves when trying to apprehend this. Well, bearing in mind that waves are really a physical metaphor expressed as an equation, something very interesting followed. Einstein analogised the situation with two models – one of ideal gas, and one of a black body. The former had bouncing molecules and the latter had bouncing light waves – and he returned the same equations for each, except for one difference. With the ideal gas, the exponent was the number of molecules, whereas with the black body was the total energy divided by n energy, where n is a fraction of the total. From these equations, Einstein forecasted that the energy of the molecules of light would be analogically linked to the number of gas molecules, and he turned out to be right, and it was from this that our concept of the photon (a quantum of light) emerged.
These are interesting examples of how humans, often without thinking of reality this way, extract from physical observations, and use symbolism and metaphor to describe reality in a way that draws a map-like representation of the territory of mathematics, and feeds into a narrative that enables us to link our segments together to make a giant, complex three dimensional story of physical reality – a story that only exists in that way because of the cognitive effigies we construct by virtue of being physical beings.
That is the ultimate useful fiction of science - our cognitive effigies provide utility because they enable us to tap into a system of pattern deciphering related to the physical world. And I think the only reason why anyone would confuse the map (physics) and the territory (mathematics) is because, being physical beings in a physical universe, we cannot easily escape the first person physical perspective and conceive of more primary realities beyond the physical – a bit like if the characters in Hamlet could come alive enough to realise they are confined to the acts and scenes on the pages, but also that their creator lives in Shakespeare-land, in a higher dimension of reality than the one in which their plots and dialogue exist.
