Maybe it's time to retire the phrase "mind-independent reality"

On invariance and transformation

“Mind-independent reality” is a phrase one comes across from time to time in science and philosophy. It is a way of asserting that reality is not a matter of private whims: there are hard facts ‘out there’ that we cannot wish away. Moreover, these facts would persist even if no one were ‘out there’ at all.

This sort of assertion is uncontroversial among the majority of scientists and philosophers, who probably see it as a restatement of physicalism or a pledge of allegiance to scientific methods. But when we investigate what exactly a ‘fact’ is, the situation soon becomes murky.

A fact is something that is known to be true. If there are no knowers, how can anything be true or false?

The roots of this way of thinking can be traced back to the dawn of western philosophy. Since the era of Plato and Aristotle, if not earlier, it has been routine to separate knowledge into a study of what exists (“ontology”), and a study of how we know what exists (“epistemology”).

I have always found this division of labor unnatural and bizarre. We could pause here to speculate about why this state of affairs arose and why it persists to the present day¹. But my goal is to suggest that we now have a more integrated way of looking at knowledge: the invariance perspective.

Invariance means immunity to a possible change. It is also known as symmetry. The mathematicians’ framing might seem strange at first, but I think it helps us make explicit our unstated intuitions about symmetry. I sometimes think this framework is so convincing that it can displace earlier notions. So maybe you should write down what you think symmetry is, because you might not even remember your ‘pre-invariance’ perspective.

As is suggested by the name, invariance conveys some kind of resistance to variation. Mathematicians and physicists typically use the word ‘transformation’ for a process that causes a specific variation. Consider a square. It is a paragon of symmetry. But can we say something more specific?

A square is invariant with respect to several transformations. It looks the same if we rotate it by 90 degrees, 180 degrees, 270 degrees, or 360 degrees. We can also flip the square around the two perpendicular bisectors, or around the two diagonals passing through the center. These modifications to the square are all transformations, and they are the keys to the chamber of symmetry. The fewer transformations there are that render a shape the same as it was initially, the more asymmetrical it looks.

Here’s a little exercise: how would you describe the symmetries of a yin-yang diagram? What transformations leave it looking unchanged? Sometimes a combination of distinct transformations is required.

Any object or process that we can identify, however abstract, displays some degree of symmetry or invariance. Rigid objects retain their shape when we move them around. In fact we can use transformations to define rigidity. Rigidity means invariance with respect to forces — up to a certain magnitude. (Any real physical object will break, losing it’s rigidity, if you subject it to a large enough force.)

Analogies are a type of invariant. “Dog is to puppy as kitten is to cat.” Or “Sailor is to navy as soldier is to army”. These analogies are often written like this “A: B :: C : D” (“A is to B as C is to D”). We can say that the relationship, which isn’t explicitly named or described, is invariant to swapping out pairs (A,B) with (C,D). However complicated an analogy may be, you can boil it down to some relationship among concepts that is invariant with respect to replacing certain specific details. In a deck of cards, every card in each suit has a counterpart in each of the other 3 suits. So the concept of a flush is invariant with respect to the specific deck: in poker you can make a flush with spades, hearts, diamonds, or clubs.

Every scientific discipline involves the hunt for invariants: the stable patterns that show up, often fleetingly, against the incessant transformations of nature. My own field, computational neuroscience, might be described as a second-order quest for invariants: we seek not only invariants in neural and behavioral data, but also a mechanistic understanding of how organisms recognize and construct invariants in the first place.

Language and music reveal some very interesting invariants. For example, we can comprehend a sentence even when spoken by very different voices, or at very different speeds. And we can recognize the same tune played on different instruments, in different keys, and even with jazzy interpolations and syncopation. We still don’t have particularly good neuroscientific models of this kind of behavior².

One of my favorite human invariants involves how we implicitly represent shapes. You can trace out the shape of the letter ‘A’ with your elbow, or your foot, even if you have never done this before. This shows that your implicit motor representation of the letter ‘A’ is invariant to the effector, which is the specific body part or device you employ as the tip of your virtual pen. This example also reveals how important transformations are: when we do things that are outside our usual habits, we might uncover new aspects of our implicit representations.

The human ability to construct invariants is not perfect: if you speed up or slow down an utterance too much, it becomes incomprehensible. It is safe to assume that natural invariants have limits. An ideal sphere is invariant to rotations around its center, but a physical sphere will have tiny scratches and indentations, so a careful observer might be able to tell that it has been rotated.³

The lens of invariance and transformation can thus be used to magnify the gap between idealized theory and practical know-how. By keeping track of not just the invariants but the specific transformations that accompany them, we get a sense of where the bounds of our claims are. And by learning how to actually perform these transformations, we move from the armchair to the laboratory (or factory, or kitchen, or studio).

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So what does any of this have to do with “mind-independent reality”?

I think the word “independence”, unlike “invariance”, connotes disconnection or separability. When we pluck a fruit from a tree, it is independent of the tree: even if the tree were destroyed, the fruit would retain its identity. When a country declares independence from another, it is (in principle) breaking bonds of political and economic dependency, so that the former ruler’s existence ceases to affect it. When we say a machine has a certain number of independent moving parts, we mean that these parts can be detached from each other and examined individually.⁴

From this perspective, “mind-independence” is a meaningless concept: there is no way, even in principle, that we can slice off the mind from reality and examine the two separately. No one would be ‘there’ to verify our story! Mind-independent reality is often described as the “view from nowhere.” Perhaps it could also be called a “non-view from everywhere”?⁵

Without the concept of mind-independence, does scientific objectivity go out the window? Are we giving intellectual shelter to every flat-earther and conspiracy theorist?

Not really, because we have a concept that is far better than mind-independence: observer-invariance. Objective truths are invariant with respect to swapping out observers. The sun is not “real because it’s there even when no one is looking”, but rather it is “real because almost everyone can observe it and agree on at least some of its properties.” Instead of painting a picture of objectivity that demands the (impossible!) removal of minds from reality, invariance allows us to recognize that minds are the very foundation of objectivity.

I sometimes think that declarations of faith in “mind-independent reality” or “cold hard facts” are a way to avoid the hard work of understanding how the invariants of reality are discovered. It is convenient to imagine that facts are just floating out there independent of us — one can then savor the trappings of objectivity without any real awareness of the transformations that establish invariance.

Perhaps I am being hard on people who simply don’t have the time to get into the nitty-gritty of how we know, for instance, that masks help curtail the spread of COVID-19, or that global warming is real. But surely something about our public conversations needs to change if we are to improve trust in scientific institutions — and more fundamentally, (re)build an objective world in which we agree on basic facts. The alternative is a return to rigid social hierarchy, where truths are stipulated by our “betters”, and the rest of us accept them as baffling revelations.

No doubt, each person has a limited ability to understand how an invariant was discovered. But there has never been a better time for people to learn about the human transformations that engender objective knowledge: YouTube, for example, has excellent videos on scientific topics at various levels of detail and rigor⁶. Perhaps this is naive idealism, but I think that even a taste of ‘applied epistemology’ can make us simultaneously more humble about the limits of our individual know-how and more curious about how collective expertise is gradually constructed.

We live on the precipice of an epistemological apocalypse. Faced with crises that require coordinated global action, vast sections of humanity seek out excuses to do the opposite. They are succumbing to nihilistic skepticism, rejecting the painstaking work of experts in favor of self-serving nonsense. But we should refrain from simply dismissing such people as ‘stupid’. There are no simple explanations for how we got to this point, but one thing I’ve noticed is that imperiously distributing ‘facts’ from on high can rub people the wrong way. What we need is some degree of epistemological participation. We need people to see for themselves that their minds are not superfluous to objectivity, but central to it. This is precisely what “observer-invariance” can convey, and what “mind-independence” does not.

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Notes

1. On the origins of the ontology-epistemology split: It is tempting to attribute this way of thinking — abstracting truths from the paths by which we get there — to the fact that the ancient Greek philosophers lived in slave-owning societies. Many with the luxury to theorize about nature probably had little interest in (or even awareness of) how the sausage gets made. Any sort of sausage, including literal sausages.

I am of course oversimplifying wildly, but it remains the case 2500 years after the dawn of western philosophy that people who concoct overarching theories about reality tend to come from privileged backgrounds.

But there is surely more to it. Perhaps a global view requires throwing away details about how that view was constructed? When one is all set to lay out a grand narrative about the universe, someone piping up with “well how do we know that?” probably gets very annoying.

2. On invariance in neuroscience: I discuss the uses of invariance/symmetry in neuroscience in more detail in this video: Invariance and Information.

3. On the limits of invariance: Invariance can initially seem like another synonym for the concept of eternal unchanging truths. Across the world, many religions and philosophies have been founded on the idea that the underlying reality of the universe is some kind of unchanging essence. The invariance perspective precludes this possibility. As physicist Joe Rosen points out in his book Symmetry Rules: How Science and Nature Are Founded on Symmetry, every symmetry necessarily implies an underlying asymmetry. In order to tell that a square has successfully been rotated by 90 degrees, we need something that is not invariant with respect to this rotation. So in order to find an invariant, there must be some ‘raw material’ of variation, so we can tell that a transformation has actually taken place! Instead of a hidden unchanging foundation for reality, invariance seems to require that we posit change as the fundamental…. constant? This is akin to certain key ideas in Buddhism, including anatta. I muse further on this paradoxical situation at the end of this essay: Science: the Quest for Symmetry.

4. On separability: While writing this essay I began reading Introduction to Phenomenology by Robert Sokolowski. It turns out that phenomenologists have long been making the same point I make here about the difference between invariance and independence. They use the term “pieces” for parts that are separable, and “moments” for parts that are not separable. Here is Sokolowski:

“… people will often take the mind to be a self-enclosed sphere, that is, a piece that can be separated from the worldly context to which it naturally and essentially belongs. Then they will ask how the mind can ever get outside itself and find out what is going on in the world. But the mind cannot be separated out in this way; the mind is a moment to the world and the things in it; the mind is essentially correlated with its objects.” [Emphasis added.]

5. On the view from nowhere: The historian of science Lorraine Daston has done excellent work tracing the evolution of our conceptions of objectivity. I recommend her paper Objectivity and the Escape from Perspective. I shared some excerpts from the paper in this twitter thread.

6. On YouTube resources: There are several excellent YouTube channels devoted to ‘big picture science’, but they often tend to focus on what is known, rather than how we came to know it. Here are a few channels that do a good job of illustrating how theory and experiment are woven together:

Kathy Loves Physics & History - I really like her videos on the history of spectroscopy, which is the gateway to almost all modern physics.

Science Asylum - in-depth science videos, but still quite accessible.

ElectroBOOM - hands-on engineering experiments (also very funny!)

There are also lots of videos reconstructing technologies from humanity’s past. Here’s one on making bread from scratch — including making the requisite Bronze age tools!

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Images:

‘Study’ by Paul Avril

‘A tree of marvelous beauty’ by Virginia Frances Sterrett

Other images from Wikimedia.