by Brian Tomasik
First written: 21 Jul. 2016; last update: 21 Mar. 2017


Smaller animals, in general, have greater temporal resolution of vision in the sense that they can tell that a light source is flickering up to a higher frequency than bigger animals can. This suggests the possibility that smaller animals might, in general, have higher rates of "subjective experience", loosely defined. However, the moral weight of an animal doesn't just depend on how quickly its retina or visual system sends along information but also on how much total processing its brain does. So a better proxy for the moral weight of a mind might be (some function of) brain metabolic rate, which should capture frequency of neuronal firing as one component. Insofar as smaller animals may have higher brain metabolic rates per unit of body mass, they probably do matter more than a simple weighting based on body size would suggest.

Note: I'm not an expert on the topics discussed here. Corrections are welcome.

Clock speed

In computers, "clock speed" is

the speed at which a microprocessor executes instructions. Every computer contains an internal clock that regulates the rate at which instructions are executed and synchronizes all the various computer components. The CPU requires a fixed number of clock ticks (or clock cycles) to execute each instruction. The faster the clock, the more instructions the CPU can execute per second.

In this piece, I'll use "clock speed" in a more general sense to refer to the rate at which a computer (digital or biological) processes information.

Insofar as we consider subjective experience to consist in operations running in a brain, rather than static features of a brain over physical time, then the pace of subjective experience is determined by how fast those operations run, without reference to the pace of physical time. If you're a brain running twice as fast, then your experience of a toothache over the course of one physical minute is indistinguishable from the experience of that toothache by the slower version over two physical minutes (ignoring the fact that the external world runs slower for the faster mind).

From "The Ethics of Artificial Intelligence":

Suppose that an upload [of a human brain] could be sentient. If we run the upload program on a faster computer, this will cause the upload, if it is connected to an input device such as a video camera, to perceive the external world as if it had been slowed down. For example, if the upload is running a thousand times faster than the original brain, then the external world will appear to the upload as if it were slowed down by a factor of thousand. Somebody drops a physical coffee mug: The upload observes the mug slowly falling to the ground while the upload finishes reading the morning newspaper and sends off a few emails. [...]

The variability of the subjective rate of time is an exotic property of artificial minds that raises novel ethical issues. For example, in cases where the duration of an experience is ethically relevant, should duration be measured in objective or subjective time? If an upload has committed a crime and is sentenced to four years in prison, should this be four objective years -- which might correspond to many millennia of subjective time -- or should it be four subjective years, which might be over in a couple of days of objective time? If a fast AI and a human are in pain, is it more urgent to alleviate the AI's pain, on grounds that it experiences a greater subjective duration of pain for each sidereal second that palliation is delayed?

The article "How fast is the brain?" (link broken) had a very rough estimation of clock speed in humans.

In theory one could care about objective, physical time in addition to subjective, mental time. Insofar as we can care about any features of a mind we like, we could place some value on the physical time independent of mental time. For instance, we might feel that a mind running 10 times as fast is only 8 times as important, not 10 times. One motivation for caring about objective time is that the fundamental physical operations (e.g., electron movements) that make up a computer or brain run at the same speed (assuming the same temperature and other conditions) whether the clock speed is fast or slow. Fundamental physical processes can be seen as "low-level subroutines" of the higher-level computation.

Finally, I should clarify that by "clock speed", I don't mean an individual's time perception, which is a matter of estimating the passage of time and can be distorted in various ways. Clock speed, as I use the term, is a more fundamental measure of the objective speed of brain processing as a whole, not the brain's subjective, fallible, and imprecise high-level evaluation and memory of the speed of its experiences. My moral intuitions suggest that objective clock speed matters more than perceived time when determining the moral importance of brain processing, though certainly one could care about both to some degree. We could imagine programming an agent who believes that it has subjectively perceived the passage of trillions of years of time, but I don't think this fake time perception would imply that we should treat this mind as having the same moral weight as someone who actually lives through trillions of years.

Do animal brains have clock signals?

Animal brains have many differences from computers, so it's clear that brains don't contain literal clock signals in the same sense that computers do. But it's interesting to explore whether there are analogies.

In the LIDA model of consciousness, it's hypothesized that human brains have cognitive cycles on the order of 10 Hz:

The LIDA Model hypothesizes that all human cognitive processing is via a continuing iteration of such cognitive cycles. These cycles emerge as an interleaved sequence, with each cognitive cycle taking roughly 300-600 milliseconds (Koivisto & Revonsuo, 2010; Madl, Baars, & Franklin, 2011). The cycles cascade; that is, overlapping cycles have processes that run in parallel. This cascading must, however, respect the way consciousness processes information serially in order to maintain the stable, coherent image of the world with which consciousness endows us (Franklin, 2005b; Merker, 2005). It must also respect the seriality of action selection. This cascading allows a rate of cycling in humans of five to ten cycles per second. A cognitive “moment” is thus quite short! For instance, for cascading cycles of 300 milliseconds each offset by 100ms, cycles would occur at ~10 Hz. There is considerable empirical evidence from neuroscience suggestive of and consistent with such cognitive cycling in humans (Doesburg, Green, McDonald, & Ward, 2009b; Massimini et al., 2005; Sigman & Dehaene, 2006; Uchida, Kepecs, & Mainen, 2006; Willis & Todorov, 2006).

A hypothesis that "cerebellar coordination of movement is timed by the oscillation of populations of inferior olivary cells" is disputed.

Critical flicker fusion frequency

Healy et al. (2013) showed that, in general, animals with faster metabolisms and smaller bodies sizes have higher critical flicker fusion frequencies (CFFs).

This study was widely popularized in a number of articles like "Slow-motion world for small animals" and "Small Animals See The World In Slow Motion". The latter article says:

Ever wonder how a fly or a chipmunk can evade your clumsy human grasp so easily? A new study published in Animal Behavior finds that, generally, the smaller the animal, the more information it can see in a small amount of time.

I've noticed this point myself when I

  • see chipmunks scurry up, down, and around tree branches extremely quickly
  • watch birds fly from branch to branch in an eyeblink, or
  • observe insects buzz back and forth, dodging around obstacles as fast as my eyes can follow.

Of course, gymnasts can be really fast too, but I think these animals maneuver faster, and in any case, the animals' environments are less uniform than that of a gymnast who can practice the same sequence of moves on the same kind of parallel bars for years on end.

Temporal integration

Healy et al. (2013) explain: "biological visual systems must discretize the continuous-time and continuous-space information reaching the retina and then integrate this information over some time period." In other words, visual signals are based on the time integral of brightness over some interval, and animals with higher CFFs have shorter time intervals before the next signal transmission.

This page reports: "As long as the modulation frequency is kept above the fusion threshold, the perceived intensity can be changed by changing the relative periods of light and darkness. One can prolong the dark periods and thus darken the image". I assume this is because if the frequency is above the CFF, the retina's time integral always includes both some bright and some dark parts, so the integral of brightness over time comes out as a weighted average of the two.

Speed of retinal/visual processing

I think differences in CFFs may be due to differences in retinal and visual processing speeds. Healy et al. (2013) mention that "In ERG studies, a direct measurement of the electrical response of the retina in reaction to a flashing light source is used as a measure of CFF (D'Eath, 1998 and Schwartz, 2009)." However, "there may be further processing of temporal information after it reaches the retina that may cause behavioural studies to measure lower CFF values (D'Eath 1998)".

This source says that temporal integration may take place at a higher level than the retina: "Physiological evidence in humans and monkeys shows that flicker rates above the perceptual critical flicker frequency threshold can nevertheless generate cortical and subcortical visual responses (Martinez-Conde et al., 2002). Thus the temporal integration underlying flicker fusion does not occur at the level of the retina, but must take place later in the visual hierarchy."

I think CFF can be changed by modifying properties of the retina or visual system without needing to change the animal's whole brain. According to Healy et al. (2013):

given the strong effect of metabolic rate on CFF, one obvious adaptation is to alter the physiology and metabolism associated with the visual processing systems as seen in the localized heating of tissues in the heads of blowflies (Tatler et al. 2000) and the eyes of predatory swordfish (Fritsches et al. 2005). These tissues increase the temperature around the sensory tissues associated with the blowfly's or swordfish's visual system, which allows for an upregulation of CFF. Similar adaptations are also seen across species of large, fast-swimming predatory billfish (Carey 1982) and Lamnidae sharks (Block & Carey 1985). Physiological adaptations for high-resolution motion detection are also found within specific areas of the retina in some flies, commonly referred to as the ‘love spot’, which allow them to identify female flight patterns accurately and thus detect mates (Land & Collett 1974).

So it looks like a 2X faster CFF doesn't necessarily imply that the entire brain is operating is operating 2X faster, although we might expect a priori that the rest of the brain would have to operate somewhat faster in order to keep up with the faster pace of visual stimuli?

Complexity of processing?

One explanation that Healy et al. (2013) propose for why bigger animals have smaller CFFs is that "larger body sizes decrease manoeuvrability", so it's less important for these animals to have a high degree of temporal resolution to their sensations.a Another speculative possibility, which I'm just making up, is that larger animals generally do more complex cognitive processing on any given batch of visual input, and this processing takes longer.b

Imagine running a single-threaded web server that performs only a simple task when it gets an HTTP request. You could hit this server many times per second. In contrast, if the server needs to do a more complex computation, you can't hit it as many times per second. Of course, in this analogy, one could continue hitting the slower server at the same rate as the faster one (it's just that more of those connection attempts would fail), which would be like the retina transmitting information just as fast in big-brained as little-brained individuals. But if the server is consistently slower, the program making HTTP requests may as well slow down its rate of hitting the server, which is similar to big-brained animals with more complex visual processing evolving to have slower retinal signaling?

Even a multi-threaded server can get overloaded. For example, a CloudFlare 524 error page "is commonly caused by a long-running process on the origin server, such as a PHP application or a database query which the web server must wait on before responding to a request."

Several theories to explain the attentional blink postulate the same basic idea as my server analogy: When the brain is busy doing complex visual processing on one image, another image that appears right afterward won't get processed because the "server" is still busy on the first image.c

If it's true that bigger-brained animals tend to do more complex processing on visual images, then this would somewhat counteract the idea that smaller animals matter more than we thought because of faster clock speeds. The total moral importance per second of visual processing would be (number of visual images processed per second) * (complexity of processing per image). Maybe the first factor is bigger for small animals but the second factor is bigger for big animals.

Brain metabolism as a key metric?

A computer's processing speed isn't just determined by clock speed but also by how much computation gets done per clock cycle:

It’s important to look not just at clock cycles but at the amount of work a CPU can do per clock cycle. [...]

[...] modern processors also have other improvements that allow them to perform faster. This includes additional CPU cores and larger amounts of CPU cache memory that the CPU can work with.

Similarly, a more complex brain might do more processing every time the retina is activated, and it might have more "cores" (parallel networks) on which to do that computing.d

If the moral importance of a brain's visual system is a function of (number of visual images processed per second) * (complexity of processing per image), then maybe rather than looking just at clock speed, we should look at brain metabolism, since faster processing and more complex processing both use more energy.

Brain metabolism is sort of like gross domestic product (GDP) in that it crudely approximates how much total information processing is occurring in a brain and doesn't rely on assumptions about how well a specific measure like CFF tracks a brain's processing speed.

GDP is the total value of goods and services produced in an economy per unit time, as measured in the currency with which people buy things. Similarly, we can think of brain components "buying" computational processing using energy stored in ATP, the so-called "'molecular unit of currency' of intracellular energy transfer". Brain metabolism is the total "value" of computational services produced per unit time in a brain, measured in the brain's unit of currency. See also "Metabolic Currency".

Also like GDP, brain metabolism is only a crude metric and doesn't capture the nuances of what portions of brain processing we care about more than others. For example, presumably brain processing related to hedonic experience matters more than cerebellar control of movements, but both of those probably use comparable amounts of energy per neuronal action potential.

If bigger animals have less energy-efficient neurons or computational processes (similar to inflation, where one dollar of nominal GDP buys less real value), then we might care about them less than their brain metabolisms alone would suggest.

What neuronal processes does brain metabolism power?

This study says "the total glucose use by neurons and astrocytes together is coupled directly to glutamate-mediated synaptic transmission [32], [34], [36], which accounts for 80–90% of total glucose use in the cerebral cortex [32]."

According to this page: "it is likely that most of the energy consumption of the brain is used for active transport of ions to sustain and restore the membrane potentials discharged during the processes of excitation and conduction".

This study estimates energy expenditure on different parts of gray-matter processing and finds that action potentials use the most energy: "Action potentials and postsynaptic effects of glutamate are predicted to consume much of the energy (47% and 34%, respectively), with the resting potential consuming a smaller amount (13%), and glutamate recycling using only 3%."

This study says:

Maintenance and restoration of ion gradients dissipated by signaling processes such as postsynaptic and action potentials, as well as uptake and recycling of neurotransmitters, are the main processes contributing to the high brain energy needs (Attwell and Laughlin, 2001, Alle et al., 2009). Among them, synaptic potentials, rather than action potentials, appear to represent by far the main energetic cost related to maintenance of excitability (Alle et al., 2009).

The cited Alle et al. (2009) paper elaborates:

From these data, we calculated that the cost ratio of the mossy fiber [action potential] AP itself to the downstream events [...] has an upper limit of about 0.15 [...], shifting the emphasis of activity-dependent energy demand to downstream processes elicited by transmitter release, as suggested by in vivo work [...].

So if one only considered action potentials (neurons firing) to be morally relevant, then much of the brain's metabolism (spent on synaptic potentials) wouldn't count. But I don't see why one would only focus on action potentials, given that synaptic potentials also represent important computational processes (summing excitatory and inhibitory inputs). This page explains: "Like thousands of voters, the synapses signal their aye or nay votes, and the neuron counts them all. [...] This neuronal activity is very similar to the fundamental activity of the whole nervous system. The integrative activity of the nervous system selects one output from all the competing alternatives." That is, in a similar way as high-level conscious attention is devoted to the dominant neuronal coalition in the brain, whether a neuron fires or not is determined by the dominant coalition among the excitatory vs. inhibitory postsynaptic potentials (plus the threshold for firing).

Brain metabolism tracks spiking frequency

This study mentions that the metabolic rate of a brain region somewhat tracks the activity of that region:

A striking feature of brain energy metabolism is the tight coupling that exists between energy demand and supply (reflected by glucose and oxygen delivery from the vasculature). Indeed, task-dependent increases in cerebral activity are invariably accompanied by changes in local blood flow and glucose utilization—these processes being referred to as neurovascular and neurometabolic coupling, respectively [...]. These close relationships constitute the basis for functional brain imaging techniques which have enabled “functional mapping” studies in the brain.

This page adds:

Neurons do not have internal reserves of energy in the form of sugar and oxygen, so their firing causes a need for more energy to be brought in quickly. Through a process called the hemodynamic response, blood releases oxygen to them at a greater rate than to inactive neurons.

This study found that percent changes in brain metabolism as measured by fMRI were approximately equal to percent changes in cerebral spiking frequency as measured by extracellular recordings. Why would this be the case given that lots of different processes in brains use energy, not just action potentials? The authors explain:

The apparent paradox of a range of energy-consuming processes being proportional to a single electrical activity may be resolved if these processes are all coupled to the averaged rate of the electrical activity (30), which in this case is the firing of an ensemble of pyramidal neurons. This coupling has been proposed by Attwell and Laughlin (31), who calculated the distribution of energy amongst these different processes. Their results suggested that almost all of the energy associated with cortical signaling is coupled to the ensemble firing frequency of pyramidal cells. Furthermore, they calculated that at a resting spiking frequency of 4 Hz per neuron, more than 80% of the total ATP is used for functional processes coupled to glutamate release.

Brain metabolism vs. animal size

As we might expect, smaller brains not only have faster CFFs but also higher metabolic rates (per unit of mass). Kleiber's law postulates that an animal's body metabolic rate is proportional to its mass raised to the 3/4. This doesn't speak to brain metabolism specifically, but assuming that brain metabolism is a fairly constant fraction of total body metabolism, Kleiber's law should also roughly apply to brain metabolism. However, this study argues for "the possibility that brain metabolism is not necessarily related to whole body metabolism in any determining way; any apparent relationship might be coincidental, and dependent on the rate with which brain size scales as a function of its number of neurons, which we have shown to vary across mammalian orders [24], [25], [41]."

This study finds that bigger brains have lower per-gram metabolic rates: "The scaling exponents for the total oxygen and glucose consumptions in the brain in relation to its volume are identical, at 0.86 ± 0.03, which is significantly larger than the exponents 3/4 and 2/3 that have been suggested for whole body basal metabolism on body mass." That is, if I understand correctly, brain metabolism is proportional to (brain volume)0.86. Combined with the fact that smaller animals generally have bigger brain-to-body-mass ratios, this suggests that smaller animals probably have more brain metabolism per kg of body mass.

The same study also mentions that bigger brains have lower average firing rates (i.e., lower "clock speeds"?): "the product of the firing rate and release probability should decrease as brains increase in size, with a power of about -0.15, which is in accord with the low firing rates in humans estimated from their basal cerebral metabolic rate [21, 42]. [...] That firing rate should decrease with brain (body) size is also consistent with allometric data on the firing rates of avian sensory neurons [43]."

Interestingly, this study found that "the total metabolic cost of a brain seems to be a simple, direct function of its number of neurons, each of them constrained to a fixed energy budget per neuron, regardless of brain size." This finding may support using number of neurons as a proxy for morally relevant brain computation.

It's worth remembering that some of the above statements are only true within a specific taxonomic set of animals. I would guess that, e.g., ecotherms have lower brain metabolic requirements than endotherms? If so, perhaps ectotherms matter less per second than endotherms of the same size.

Original post

The current essay began as this thread on Felicifia in 2011.


  1. Possibly related: Bigger animals have slower stride frequencies.  (back)
  2. In particular, my hypothesis is that the more complex processing in bigger brains takes longer in a way that involves back-and-forth communication among many components. If bigger brains only took longer to process images because those images were being sent in one direction down a longer feedforward processing pipeline, then this wouldn't affect the rate at which images could be processed. That situation would be like cars driving on a longer highway vs. a shorter one: An individual car can go the same speed in either case. But in the scenario where complex processing requires back-and-forth signaling and waiting on requests to other brain regions, more complex processing slows things down because later signals have to wait for the first batch of processing to finish. This is like how traffic moves slower on a busy street that has a traffic light at an intersection (i.e., more complex, interactive events between cars) rather than on a street that just goes unencumbered in one direction.  (back)
  3. For example, this study proposes a two-stage model of visual detection, where stage 2 is the more complex and thus slower:

    In accord with Duncan (1980), we assume that the representations resulting from early levels of processing (first stage) cannot serve as the basis for subsequent report or response but require additional processing. A representation of a candidate target stimulus that is momentarily active must be transferred into a more durable representation (such as verbal short-term memory) to be available for subsequent report or, as Duncan suggests, even to serve as a basis for a manual response. This transfer requires second-stage processing which results in full identification and consolidation of the target for subsequent report. We consider this stage to be capacity-limited and to exceed the item's stimulus duration at the high presentation rates used in [rapid serial visual presentation] RSVP tasks. This stage of processing does not commence with the onset of a stimulus, but only after first-stage target detection. We hypothesize that the second stage is initiated by a transient attentional response that occurs on first-stage detection of a (probable) target. This attentional response actively selects and enhances processing of the target (Nakayama & Mackeben, 1989; Weichselgartner & Sperling, 1987). [...] When [the second target] T2 appears before the second stage is free, it will be detected by Stage 1 processing, but Stage 2 processing will be delayed. The longer the delay, the greater the probability that T2 will have been lost, according to our previous assumption that Stage 1 representations are short-lived.

    Note: I haven't yet read the whole study quoted here.  (back)

  4. This is a loose analogy. A computer doesn't send off computations to different cores every clock cycle the way a brain does.  (back)