Leonardo Da Vinci, in his Treatise on Painting (Trattato della Pittura), advises painters to pay particular attention to the motions of the mind, moti mentali. “The movement which is depicted must be appropriate to the mental state of the figure,” he advises; otherwise the figure will be considered twice dead: “dead because it is a depiction, and dead yet again in not exhibiting motion either of the mind or of the body.” Francesco Melzi, student and friend to Da Vinci, compiled the Treatise posthumously from fragmented notes left to him. The vivid portrayal of emotions in the paintings from Leonardo’s school shows that his students learned to read the moti mentali of their subjects in exquisite detail.

Associating an emotional expression of the face with a “motion of the mind” was an astonishing insight by Da Vinci and a surprisingly modern metaphor. Today we correlate specific patterns of electrochemical dynamics (i.e. “motions”) of the central nervous system, with emotional feelings. Consciousness, the substrate for any emotional feeling, is itself a “motion of the mind,” an ephemeral state characterized by certain dynamical patterns of electrical activity. Even if all the neurons, their constituent parts and neuronal circuitry remained structurally the same, a change in the dynamics can mean the difference between consciousness and unconsciousness.

But what kind of motion is it? What are the patterns of electrical activity that correspond to our subjective state of being conscious, and why? Can they be measured and quantified? This is not only a theoretical or philosophical question but also one that is of vital interest to the anesthesiologist trying to regulate the level of consciousness during surgery, or for the neurologist trying to differentiate between different states of consciousness following brain trauma.

Recently, Casali et al have presented a quantitative metric. It provides, according to the authors, a numerical measure of consciousness, separating vegetative states from minimally conscious states. The study provides hints of being able to identify the enigmatic locked-in state, in which the subject is conscious but is unable to communicate with the external world due to motor deficits. What is most interesting is the claim that the measures provide scientific insight into consciousness, by providing an objective measure.

Their metric, like other existing clinical measures of consciousness, is based on Electroencephalography (EEG), where voltages recorded from electrodes placed on the scalp provide a coarse picture of neural activity in the brain. EEG can be used to measure either ongoing brain activity, or that evoked by an external stimulus. In Casali’s case, the activity in question is evoked directly in the brain using a transient magnetic field (Transcranial Magnetic Stimulation). This involves applying a transient magnetic field, which generates an electric field in a particular region of the brain due to Faraday’s law, a bit like attaching a battery to the neural circuitry. This causes currents to flow in the brain, not just in the stimulated region, but in other regions connected to it as well. The spatial and temporal patterns of these currents in the brain are then inferred from the EEG measurements and quantified to produce the metric.

The novelty in the study lies in the method used to quantify the spatiotemporal distribution of current, which is also the basis of the theoretical claims. The idea is that when the brain is unconscious, the evoked activity is either localized (the authors call this “lack of integration”), or widespread and uniform, as might be expected during slow wave sleep or epileptic seizures (“lack of differentiation”). The conscious state on the other hand is supposed to correspond to a distributed, but non-uniform spatiotemporal pattern of current sources. The authors apply a standard data compression scheme (the Lempel-Ziv algorithm, which is used for example in the GIF image format) to distinguish between the two scenarios. The degree of compressibility of the current distribution as inferred from EEG is the consciousness metric they propose.

The scientists report that their measure performs impressively in distinguishing states of consciousness within subjects, as well as across subjects in different clinically identified consciousness stages. These promising results will no doubt attract further study. However, the claim that the measure is theoretically grounded in a conceptual understanding of consciousness deserves a closer look. It is tempting to think that a concretely grounded clinical study of consciousness naturally advances our scientific understanding of the phenomenon, but is this necessarily the case?

It is common in medicine to see engineering-style associative measurements, measurements which aid pragmatic actions but do not originate from a fundamental understanding. Physicians in antiquity were able to diagnose diabetes mellitus (etymologically “sweet urine”, a reference to this original diagnostic method), without any particular insights into the underlying pathology. Clinical utility is not automatically a guarantee of scientific understanding.

There is reason to be cautious even in clinical terms. Some previous attempts to numerically quantify consciousness have proven problematic, a serious matter since awareness during surgery could lead to real suffering. An anesthesiologist cautions in a commentary not to “trust the BIS or any other monitor over common sense and experience.” A human expert still remains the ultimate arbiter of the state of consciousness of another human. This is unlikely to change soon.

There are both practical and conceptual hurdles to developing a “consciousness metric.” In practical terms, we have very little access to the details of the neuronal dynamics in the human brain. DARPA, not shy of ambitious technical challenges, has limited itself to 200 electrodes in a recent call for proposals to directly record from and stimulate the human brain for deep brain stimulation therapy. That is about one billionth of the estimated number of neurons in the brain. The EEG provides a very low capacity, indirect measurement channel into the brain. If we can’t measure the dynamics of the brain neurons in any detail, this could limit any attempt to quantify consciousness.

However, it is theoretically possible that even a limited measurement channel could carry the necessary information. We are looking for a categorical judgment between conscious and unconscious states, a single bit of information that can be solicited from a conscious and communicative subject in an eye-blink or a nod of the head. The conceptual hurdle is the more significant one. The defining characteristic of the conscious state is that of subjective, first person awareness, which fundamentally militates against objective measurements by an independent observer, who can have no access to the primary phenomena except through the subjective report of the conscious individual. It may be possible (and useful) to obtain better and better correlative measurements of this subjective report; but do the measurements themselves shed any light into the phenomenon of consciousness?

To clarify the underlying issues, consider a Turing-like test for consciousness metrics. If a measure of consciousness is to have scientific status, it should not ascribe a high degree of consciousness to a passive, inanimate system at thermodynamic equilibrium. Otherwise we are left with some kind of pan-psychic notion of consciousness. Nevertheless, a simple thought experiment shows that it would be easy to construct such a system for the metric under discussion.

The measure in question relies on the spatiotemporal patterns of currents invoked by a transient magnetic field. However, Maxwell’s equations dictate that a transient magnetic field will generate a pattern of currents in any chunk of matter – matching up some distribution of those evoked currents is simply a matter of the material properties. Consider for example a network of resistor, capacitors and inductors with circuit time-constants tuned to be in the hundred-millisecond range (to match EEG timescales). A radio antenna could be used to detect the changing magnetic field and absorb its energy. It should not be difficult to produce a circuit arrangement that produces a transient, spatiotemporally non-uniform current distribution that is adequately incompressible, and therefore fools the device into producing a high consciousness score.

One could also ask if the metric helps us answer a basic evolutionary question: can it differentiate organisms into “conscious” and “non-conscious” categories? While most neuroscientists would not hesitate to ascribe consciousness to vertebrate animals or to invertebrates with complex brains (think Octopus or Honeybee), they would hesitate when it comes to the invertebrates with simpler nervous systems (Are Jellyfish conscious? How about the Sponges?) Since the methodology under discussion has been prepared with humans in mind, and ultimately depends on correlating with subjective reporting, it is difficult to see how it could be extended across the phylogenetic tree in a way that would help resolve these basic science questions about consciousness.

Where to look for measures of consciousness that advance our scientific understanding? Most neuroscientists would agree that consciousness is associated specifically with animal nervous systems (not trees or rocks). Rather than look generically for abstract mathematical descriptions of consciousness, we may need to specifically study the detailed architecture of brain systems involved in arousal, attention, and so on. Complex animal nervous systems have presumably evolved consciousness because it has some important utility. If the architecture of brain systems involved in arousal shows convergent evolution between invertebrates and vertebrates, this could give us important scientific insights into consciousness as a biological phenomenon. Better neurobiological insights into consciousness could in turn generate advances in clinical measures.

We have come a long way since Da Vinci, but human observers, in the form of teams of expert physicians, remain essential to judging the subtleties of the “motions of the mind” that we call consciousness. No matter how sophisticated our tools, consciousness is still a core mystery with ample scope for conceptual breakthroughs and creative thinking.

Are you a scientist who specializes in neuroscience, cognitive science, or psychology? And have you read a recent peer-reviewed paper that you would like to write about? Please send suggestions to Mind Matters editor Gareth Cook, a Pulitzer prize-winning journalist and regular contributor to NewYorker.com. Gareth is also the series editor of Best American Infographics, and can be reached at garethideas AT gmail.com or Twitter @garethideas.