Can we measure consciousness? If not, how can we even begin to consider it from a scientific perspective? The main point of this essay is that an experimental approach to understanding consciousness will treat it as the product of an evolutionary process leading to a quantifiable threshold complexity of the nervous system. It follows that consciousness and intelligence are graded phenomena related to increments in complexity. This essay describes a quantitative approach to define the gradation and fulfill Lord Kelvin's challenge in the quotation above.

1. Evolution of Nervous Function

Much of what follows will seem obvious, yet it should be made explicit in order to provide a foundation for later discussion. I will argue that consciousness is best understood in terms of an evolutionary process that began when animal life developed the first differentiated cells, or neurons, associated with communication between different tissues. Fedonkin (2003) provided a detailed and critical review of precambrian animal fossils, and Peterson and Butterfield (2005) used genetic information to calculate that metazoans emerged between 826 and 634 million years ago, in accordance with the fossil record. The earliest animals probably resembled Placozoa, perhaps the simplest form of animal life today. The one known species, Trichoplax adhaerans, has only a few thousand cells of four cell types, and the smallest genome of any animal (Srivastava et al. 2008). There is no defined nervous system present, but one of the cell types is present as a syncytium that may help coordinate movement of the organism. .

During the Cambrian radiation between 580 and 500 million years ago, more complex animals appeared that are now called Bilateria (Shierwater et al. 2009). It is reasonable to assume that these organisms had nervous systems, but it is uncertain whether they represented the single origin of nervous function that later evolved into the nervous systems of today’s animals. No doubt it would have been a major selective advantage for the predators and prey of that era to be able to sense their environment and respond with appropriate behavior. The chief characteristic of this level of nervous function is that the response to variable sensory inputs would have been a reflexive sensory-motor response with minimal modulation. This basic function is preserved in higher organisms as well, for instance in the spinal reflex response to a painful stimulus.

The next step came with the ever increasing complexity of animal nervous systems as life evolved into larger aquatic organisms like fish over 500 million years ago, then into terrestrial animal life over four hundred million years ago. As we compare the behavior of fish, reptiles, birds and mammals, it is clear from observations that the vertebrate animals are aware of their environment. Instead of being entirely reflexive, their responses to sensory input can be modulated within certain limitations. Their modulated responses apparently reflect a short term memory measured in seconds, so that intelligent behavior is not possible. With rare exceptions, most birds and mammals are unable to match even the most minimal human intelligence in terms of problem-solving.

The behavior that characterizes self-awareness arose in the increasingly complex nervous systems of primates, and also in other large-brained animals such as elephants and dolphins (Plotnik et al. 2006; Reiss and Marino 2001). A self-aware organism recognizes itself in a mirror, and Homo neanderthalensis 400,000 years ago would likely have had no difficulty passing this test. Self-awareness evolved into modern consciousness 200,000 years ago with the appearance of Homo sapiens in Africa. If a child from that era could somehow be transported forward in time to today's world, it would presumably be indistinguishable from other children in its ability to develop language and adapt to contemporary culture.

The most striking property of a conscious human being is not just self-awareness, but to varying degrees human brains can indefinitely maintain an internal model of sensory input and manipulate the model in order to predict future outcomes. Short term memory is therefore not measured in seconds, but instead can be maintained throughout a problem-solving interval. The word intelligence defines a semi-quantitative measure of the ability of the conscious nervous system to perform such tasks.

2. Three Postulates

I will now present a set of postulates that can be used to clarify the discussion of human consciousness. The postulates, taken together, also suggest experimental and observational tests of hypotheses related to consciousness.

The first postulate is that consciousness will ultimately be understood in terms of ordinary chemical and physical laws. This postulate links consciousness directly to nervous processes in the brain. and arises from a consideration of the principle of parsimony (Occam's Razor). Quantum mechanical involvement, mind-brain duality, and supernatural concepts such as spirit and soul are excluded. The postulate is not simply parsimonious, but is supported by the fact that the conscious state is strongly affected by chemical and physical conditions imposed on the brain. For instance, consciousness is abolished simply by lowering the temperature of the brain by ten degrees, from 310 to 300 degrees Kelvin. When the brain is warmed, consciousness returns. A similar effect is produced by general anesthetics which diffuse from the lungs into the blood, then partition into cell membranes of the brain and interact with protein channels such as GABA and glutamate receptors (Olsen and Li, 2011). Excitability is inhibited, and consciousness disappears. Anesthetics are specific examples of a large number of chemicals that interact with receptors in the cell membranes of cerebral neurons and thereby produce effects ranging from the mild stimulation of nicotine and caffeine to deep anesthesia. If small amounts of such chemicals interacting with neurons can reversibly affect consciousness, it seems inescapable that the mechanisms underlying consciousness most likely involve biochemical and physical processes occurring at the level of cortical neurons and their interactions with one another.

The second postulate is that consciousness is related to the evolution of anatomical complexity in the nervous system. The reason consciousness seems so mysterious at present is that we have not advanced far enough in our knowledge of complex interactions within the brain's neurons. This is analogous to the evolution of computer engineering over the past 70 years. Imagine that somehow a functioning laptop computer could be transported back in time to Los Alamos in 1943, where some of the worlds most brilliant physicists had gathered in wartime to design and test the first nuclear weapon. They would have been astonished by the color screen, the fact that an entire movie could be stored, the WiFi capacity, the internet. No matter how brilliant, their collective genius would be baffled by this seeming miracle. I think that we are like those scientists when today we attempt to understand how the phenomenon of consciousness emerges from nervous function in the brain.

The second postulate suggests that consciousness can emerge only when a certain level of anatomical complexity has evolved in the brain that is directly related to the number of neurons, the number of synaptic connections between neurons, and the anatomical organization of the brain. Again by analogy to the evolution of computers, a certain number of components and interacting connections are required to perform increasingly complex tasks. Consider the evolution of the integrated circuit. The first IC was developed by Kirby and Noyce in the 1950s, and incorporated only a few semiconductor-based transistors. In the late 1960s the number of transistors in an IC had increased to 100s, then to thousands in the mid-1970s. The number increased again to the 100,000 range in the 1980s, to millions in 1990s, and most recently billions. Each of the advances represents a threshold relating the number of transistors to the complexity of computational function.

It is interesting to compare this history to the evolution of the nervous system. The earliest animals were well served by a nervous system having perhaps a few hundred neurons. The different cell types in C. elegans have been counted: there are precisely 302 neurons and a total of 7000 synaptic connections (White et al. 1986). In contrast, the human cerebral cortex is estimated to have 10 - 20 billion neurons and a total of ~10¹⁵ synapses (see Roth and Dicke, 2005). If in fact consciousness and intelligence are related to complexity of nervous systems, it should be possible to establish a quantitative measure of the complexity, then compare it with our observation of animal behavior.

This brings us to the third postulate, that consciousness, intelligence, self-awareness and awareness are graded, and have a threshold that is related to the complexity of nervous systems. I will now propose a quantitative formula that gives a rough estimate of the complexity of nervous systems. Only two variables are required: the number of units in a nervous system, and the number of connections (interactions) each unit has with other units in the system. The formula is simple: C (complexity) = log(N) * log(Z) where N is the number of units and Z is the average number of synaptic inputs to a single neuron. The idea that complexity arises from interconnecting systems is not a new concept. W. Grey Walter suggested much the same thing in his book The Living Brain published in 1953. A more detailed version of this relationship was previously used to calculate C for the nervous systems of animals ranging from nematodes through insects and frogs and then mammalian brains including humans (Deamer and Evans, 2006). Here I will restrict the list to a set of mammalian species for which I could find estimates of cortical cell number and synaptic junctions per cell. I will present a ranked list calculated from the complexity formula, and then normalize the results to take into account a third variable called encephalization quotient. I will then ask whether threshold levels of complexity can be discerned in the results, and how well they fit our expectations.

3. Measuring Cortical Complexity

The number of neurons (N) increases markedly within the nervous systems of animals ranging from nematodes to humans. The number of synapses per neuron (Z) also varies significantly. Z is difficult to estimate, but has been measured for cortical neurons in the human, rat and mouse brains (DeFilipe et al. 2002). The numbers vary by a factor of 2 within the six cell layers of the neocortex, and again by a factor of 2 when the human, rat and mouse brain are compared in terms of average number of synapses per neuron for all six layers. Each human cortical neuron has approximately 30,000 synapses per cell, each mouse neuron 20,000 synapses per cell and each rat neuron 17,000 synapses per cell. I will assume Z = 30,000 for the brains of primates, dolphin,s elephants and monkeys, and Z = 20,000 for the brains of all other animals in the list. For the order of magnitude calculations reported here, these rough estimates of Z are sufficient.

Table 1 shows the list of mammals ranked according to the number of cortical neurons and log (N). The last two columns show log(Z) and the value of C calculated as log(N)*log(Z). Brain weight is also given for comparison.

The next step is to incorporate the encephalization quotient (EQ) in the analysis. When the amount of brain tissue in a series of animals is plotted against body mass, from mice to elephants, there is a roughly linear relationship (Roth and Dicke, 2005). However, the value for some animals lies significantly above the line, while others are well below the line. A relatively large animal like an elephant needs a greater absolute number of neurons to serve the much larger number of cells in their bodies, but these neurons are not necessarily given over to consciousness or intelligent behavior. Humans, with the highest EQ (7.6) have developed larger brains in relation to body size because our evolutionary pathway happened to select for the nervous activity called intelligence, which presumably requires more brain tissue devoted to that function. Deaner et al. (2007) presented evidence that EQ alone is not the best indicator of intellectual capacity within primates, but that brain mass shows a better correlation. However, here I must use relative EQ to correct for the effect of a much larger range of body size (from mouse to elephant) by normalizing against human EQ. The complexity equation then becomes C = log(N*EQa/EQh)*log(Z), where EQa is the animal EQ and EQh is the human EQ, taken to be 7.6.

Table II shows the list of mammals according to EQ, and the values of C normalized with respect to complexity.

4. Discussion and Conclusions

If we asked a hundred thoughtful colleagues to rank this list of mammals according to their experience and observations, I predict that their lists, when averaged to reduce idiosyncratic choices, would closely reflect the calculated ranking. It is interesting that all six animals with normalized complexity values of 40 and above are self-aware according to the mirror test, the rhesus monkey is borderline at 36.5,while the animals with complexity values of 35 and below do not exhibit this behavior. This jump between C = 36.5 and 40 appears to reflect a threshold related to self-awareness.

Although mammals with normalized complexity values between 40 and 43.2 are self-aware and are perhaps conscious in a limited capacity, they do not exhibit what we recognize as human intelligence. It seems that a normalized complexity value of 45.5 is required for human consciousness and intelligence, that is, 10 - 20 billion neurons, each on average with 30,000 connections to other neurons, and an EQ of 7.6. Only the human brain has achieved this threshold.

If we take the claim of threshold complexities in nervous systems as a hypothesis, it will only be useful if there are testable predictions. One is that in diseases such as Alzheimer’s, the reduced intellectual capacity and lowered state of consciousness begin to occur when the number of active neurons or the number of synaptic connections is reduced below threshold values required for intelligent behavior. In fact, in patients with advanced Alzheimer’s disease the number of synapses per neuron was reduced by 25 – 35 percent (see Selkoe 2002 for review). Similarly, when general anesthesia produces an unconscious state, we will find that the threshold is again breached, not in terms of cell number but instead due to a reduced number of functioning synapses and associated membrane receptors caused by the action of the anesthetic compound.

Closely related to the argument presented here is the concept of the connectome, which consists of the white matter connections between different regions of the brain. A study of the human connectome is now underway in several laboratories (Sporns et al. 2005; Thompson and Swanson 2010). Chiang et al. (2009) reported correlations of connectome architecture with human intelligence. When the human connectome can be compared to the brains of other primates, it seems likely we will observe a threshold of anatomical complexity that is related to self-awareness, and a second threshold related to human consciousness.

A third prediction is that because of the limitations of computer electronics, it will be virtually impossible to construct a conscious computer in the foreseeable future. Even though the number of transistors (N) in a microprocessor chip now approaches the number of neurons in a mammalian brain, each chip has a Z of 2, that is, its input-output response is directly connected to just two other transistors. This is in contrast to a mammalian neuron, in which function is modulated by thousands of synaptic inputs and output relayed to hundreds of other neurons. According to the quantitative formula described above, the complexity of the human nervous system is log(N) * log (Z) = 45.5, while that of a microprocessor with 781 million transistors is 8.9 * .3 = 2.67, many orders of magnitude less. Of course, what the microprocessor lacks in connectivity can potentially be compensated in part by speed, which in the most powerful computers is measured in terraflops compared with the kilohertz activity of neurons. Interestingly, for the nematode the calculated complexity C = 3.2, assuming an average of 20 synapses per neuron, so the functioning nervous system of this simple organism could very well be computationally modeled.