Human Thoughts and Memory Are Gigantically Connective, But Brains Have Only Low Connectivity

The human mind and human memory are gigantically connective. A person's thoughts can quickly dart around between vastly different areas of human knowledge. For example, suppose you ask me, "How could modern technology have made a difference if the ancient Romans had possessed it?" Darting around instantly between many different pieces of knowledge in my memory, I might very quickly give an answer like this:

"It's easy to think of many different ways modern technology could have made a difference around the time of Julius Caesar and Octavian. Julius Caesar might have avoided his assassination, maybe by wearing a Kevlar vest and Kevlar collar, or maybe by installing metal detectors at the Senate building. Mark Antony might have won the battle of Actium, by having jet fighters bomb the ships of Octavian into pieces. The Romans might have used tanks and bombers to wipe out the barbarian hordes, preventing the fall of Rome from ever happening. And with smartphones and TV helping everyone to instantly communicate, there would been none of the 'too big an empire' problem that plagued the Romans. The Roman empire might have spread across half of Eurasia."

Or, to give another example, when asking myself, "Name some famous Johns," I quickly wrote down the following, extracting things from a variety of historical eras, and from both fact and fiction:

"Well there's Prince John and Little John in the Robin Hood story. And there's John the author of one of the gospels. Then there's John Updike, an American writer. And there's the famous assassin John Wilkes Booth. Then there's Pope John Paul II. And there's John Lennon.  And Johnny Walker and Johnny Carson. Then there's US presidents John Adams and John Quincy Adams. Then there's John Brown who raided Harper's Ferry. And don't forget the scientist John Dalton."

It seems that the human mind and human memory are gigantically connective. But does the human brain have any degree of connectivity that can explain the almost perfect connectivity of the human mind and human memory? A person might claim that the brain has perfect connectivity, on the grounds that it is possible to trace a path between any two regions of the brain. But it would be hasty to draw a conclusion about brain connectivity from so simple a fact. Analyzing how connective the brain is turns out to be a much more complicated task. 

Neurons in the brain can be analyzed as nodes in a network. With any network there are ways of quantifying how connective the network is. Some important questions may be asked to judge the connectivity of a network:

(1) What is the ratio between the total number of nodes in the network and the total number of connections between nodes in the network?

(2) What percentage of the total nodes in the network is the average node in the network directly connected to?

(3) What is the average time needed to communicate between two random nodes of the network?

(4) How reliably does a signal travel between two nodes in the network?

Let me give some very simple examples of answering some of these questions. Let's consider the very simple network shown below:

Here is a partial analysis of this network's connectivity:

Number of nodes: 7.

Number of connections: 12.

Average number of connections per node: 3.28.

What fraction of the total nodes in the network is the average node in the network directly connected to? 3.28 divided by 7, or .468

A network with  higher connectivity is shown below:

Here is a partial analysis of this network's connectivity:

Number of nodes: 7.

Number of connections: 17.

Average number of connections per node: 4.57.

What fraction of the total nodes in the network is the average node in the network directly connected to? 4.57 divided by 7, or .65, which is roughly two-thirds.

It is the last question that gives us the "bottom line" on how much connectivity the network has. The first network has a "bottom line" connectivity of only .468, but the second network has a substantially higher "bottom line" connectivity of .65.  A network with perfect connectivity would have a "bottom line" connectivity of 1.0. 

Now, having got a bit "warmed up" in analyzing the connectivity of networks, let us consider the question: just how connective is the human brain? We can use the same format as above.

Number of nodes: about 100 billion (which is the number of neurons in the human brain).

Number of connections: about 100 trillion (which is the number of synapses in the human brain, each neuron having an average of about 1000 synapses).

Average number of connections per node: about 1000. Although it is sometimes claimed there are thousands of synapses per neuron, the 2021 study here (Table 1) finds fewer than 100 connections per neuron in primates, finding 25 excitatory synapses per neuron in primates and 44 inhibitory synapses per neuron in primates.

What percentage of the total nodes in the network is the average node in the network directly connected to? 1000 divided by 100 billion, or 0.00000001.

We are left with a shockingly low "bottom line" number on the connectivity of the human brain. The human brain would seem to have a connectivity very, very many times lower than the two networks depicted above. The "bottom line" connectivity of the brain is a number only about 1 in 100 million. 

Here are some interesting findings from the neuroscience literature. The source here says, "Electrophysiological studies detect connections only in approximately 10% of pairs of neurons." This would seem to mean that when scientists check whether two neurons right next to each other are connected, they find that in only about 1 case in 10 are such neurons connected. Referring to a type of brain structure in which neurons are rather densely packed (pyramidal cells), the paper states, "Virtually all electrophysiological studies in vitro find connection probabilities of order 0.1–0.2 for pairs of nearby pyramidal cells."

Using older and different estimates about the number of brain cells and the number of connections (synapses) between brain cells, a scientific paper ("Is the brain really a small-world network?") states the following:

"On average, the density of human brain connectivity at the cellular level is very sparse. The average number of synapses of neurons (~104) (Braitenberg and Schüz 1998) divided by the number of neural elements (~1010) (Herculano-Houzel 2012) results in a very low average probability of any two neurons in the brain making contact (10−6), implying a highly dispersed network." 

The paragraph above is telling us that if you were to pick two random neurons in the brain, there would be only about 1 chance in a million that they are directly connected. It seems that the connectivity of neurons in the brain is very low, way too low to explain the almost perfect connectivity of ideas, thoughts and memories in the human mind. 

There are two other crucial factors we should consider when considering the connectivity of the brain:

(1) How fast do signals travel between neurons?

(2) How reliably does a signal travel when it passes between two neurons?

Considering the first of these questions, the widely quoted figure of about 100 meters per second for brain signals is very misleading. That is the fastest that a signal can travel in any part of the brain, when signals pass through myelinated axons. But most axons in the cortex are not myelinated, and most of the tissue in the brain consists of relatively slow dendrites. According to neuroscientist Nikolaos C Aggelopoulos, there is an estimate of 0.5 meters per second for the speed of nerve transmission across dendrites (see here for a similar estimate). That is a speed 200 times slower than the nerve transmission speed commonly quoted for myelinated axons. Then there is the enormous slowing factor caused by the need for brain signals to cross across synapses, serious "speed bumps" that should slow down brain signals very much. 

There is a scientific term used for the delay caused when a nerve signal travels across a synapse. The delay is called the synaptic delay. According to this 1965 scientific paper, most synaptic delays are about .5 milliseconds, but there are also quite a few as long as 2 to 4 milliseconds. A more recent (and probably more reliable) estimate was made in a 2000 paper studying the prefrontal monkey cortex. That paper says, "the synaptic delay, estimated from the y-axis intercepts of the linear regressions, was 2.29" milliseconds. It is very important to realize that this synaptic delay is not the total delay caused by a nerve signal as it passes across different synapses. The synaptic delay is the delay caused each and every time that the nerve signal passes across a synapse. 

Such a delay may not seem like too much of a speed bump. But consider just how many such "synaptic delays" would have to occur for, say, a brain signal to travel from one region of the brain to another. It has been estimated that the brain contains 100 trillion synapses (a neuron may have thousands of them).  So it would seem that for a neural signal to travel from one part of the brain to another part of the brain that is a distance away only 5% or 10% of the length of the brain, that such a signal would have to endure many thousands of such "synaptic delays" requiring a total of quite a few seconds of time. 

There is no reason to think that the average speed of signals in the brain should be much faster than the speed at which electrical signals travel around the brain during seizures. The paper here lists a speed of only about 1 millimeter per second for seizures in the human brain, saying, "Seizures propagate slowly to connected areas with speeds on the order of 1 mm/s."  There is no reason to think that some hypothetical brain signals involved in thinking would occur much faster than seizures. 

How reliably does a signal travel when it passes between two neurons? It has been repeatedly stated in neuroscience literature that brain signals travel across chemical synapses with a reliability of only .5 or smaller, and almost all synapses in the brain are chemical synapses.  In an interview, an expert on neuron noise states the following:

"There is, for example, unreliable synaptic transmission. This is something that an engineer would not normally build into a system. When one neuron is active, and a signal runs down the axon, that signal is not guaranteed to actually reach the next neuron. It makes it across the synapse with a probability like one half, or even less. This introduces a lot of noise into the system."

 A scientific paper tells us the same thing. It states, "Several recent studies have documented the unreliability of central nervous system synapses: typically, a postsynaptic response is produced less than half of the time when a presynaptic nerve impulse arrives at a synapse." Another scientific paper says, "In the cortex, individual synapses seem to be extremely unreliable: the probability of transmitter release in response to a single action potential can be as low as 0.1 or lower."

A 2020 paper states this:

"Neurons communicate primarily through chemical synapses, and that communication is critical for proper brain function. However, chemical synaptic transmission appears unreliable: for most synapses, when an action potential arrives at an axon terminal, about half the time, no neurotransmitter is released and so no communication happens... Furthermore, when neurotransmitter is released at an individual synaptic release site, the size of the local postsynaptic membrane conductance change is also variable. Given the importance of synapses, the energetic cost of generating action potentials, and the evolutionary timescales over which the brain has been optimized, the high level of synaptic noise seems surprising."

Such a result (a very serious brain physical shortfall) is surprising only to those who believe that your brain stores your memories and that your brain makes your mind.  Those who disbelieve such a thing may expect exactly such shortfalls to be repeatedly found. 

To summarize, there are three gigantic reasons why a human brain cannot be regarded as any kind of high-connectivity network:

(1) The "bottom line" connectivity of the brain (as defined above) is very low, with the average neuron being directly connected to fewer than 1 in a million of the brain's neurons, and as few as 1 in 100 million of the brain's neurons. 

(2) You cannot assume that this shortfall is fixed by signals traveling reliably between many neurons (such as from Neuron 1 to Neuron 2 to Neuron 3 to Neuron 4 to Neuron 5 to Neuron 6), because the reliability of signal transmission across synapses is so low that the signal would very probably be lost when even trying to pass across only four different neurons.

(3) Very serious slowing factors such as the low transmission speed of dendrites and synaptic delays should worsen brain connectivity even further. 

Your mind and memory are almost perfectly connective. But your brain has poor physical connectivity. Such a discrepancy is one of very many reasons for thinking that your brain cannot be the source of your mind. 

Postscript: The 2022 paper "What Kind of Network Is the Brain?" by John D. Mollon  and others gives us some facts that cast doubt on claims that the brain is a very highly connected network. We read this:

"Excluding callosal neurons, efferent neurons, and all non-pyramidal cells, they estimate that the total number of neurons making ipsilateral connections within one hemisphere is 6 × 10⁹. However, they estimate that there are only ~10⁸ axons in all the major long-range tracts combined. Thus, of all the cells that make cortico-cortical connections, most are local in their projections, and only ~2% have access to the long-range tracts within one hemisphere (and the proportion having access to any individual tract is likely to be still smaller) [46]. The proportion of non-efferent cells contributing axons to the corpus callosum is similarly ~2%.

The estimates obtained by Schüz and Braitenberg were based on classical histology, but they draw confirmation from a recent analysis of diffusion MRI (dMRI) data. Rosen and Halgren [48] analyzed tractography data for 1065 individuals in the Human Connectome Project. They calibrated their dMRI measure by reference to the known density of axons in the corpus callosum and the cross-sectional area of the corpus callosum of each individual (obtained by structural MRI). They then used this conversion factor to estimate the number of axons in the long-distance fasciculi. For each of the 360 'parcels' [49] of cortex, they calculated the number of fibers connecting to every other parcel. Long-range connections (callosal plus intra-hemispheric) were sparse, about 3.7% in total – a value close to Schüz and Braitenberg's estimate of 4%. The limited capacity of the long-distance tracts is difficult to reconcile with models that suppose the brain is a meta-net [9] or with accounts of memory in which cell assemblies depend on many long-range excitatory connections. [50]"