Friday, August 27, 2010

Thinking a Million Miles an Hour

The other day, someone said that they were thinking a million miles an hour. Naturally, this got me thinking about how fast they were really thinking, given all the various pulses traveling between all the various neurons. First, Google tells us that a million miles per hour is 670.616629 times slower than the speed of light. That's still pretty speedy. It's fast enough to take you around the world in 89.6447392 seconds, or get you to the sun in 3.87316198 days.

That's all well and good, but I really wanted to know: How fast do we think?

Unfortunately, I couldn't find the answer, or even enough solid information to compute an answer I was truly satisfied with. I will provide you with the best answer I can come up with, though. First, the relevant facts!

  1. Average number of neurons in the brain = 100 billion[1]
  2. Length of myelinated nerve fibers in brain = 150,000-180,000 km (Pakkenberg et al., 1997; 2003)[1,2]
  3. At the age of 20, the total length of myelinated fibers in males is 176,000 km while that of a female is 149,000 km[5]
  4. Number of synapses in cortex = 0.15 quadrillion (Pakkenberg et al., 1997; 2003)[1,2]
  5. The length of a single dendrite is usually several hundred micrometers. Due to branching, the total dendritic length of a pyramidal cell may reach several centimeters. The pyramidal cell’s axon is often even longer and extensively branched, reaching many centimeters in total length.[4]
  6. The number of dendrites varied between 4 and 13 (mean 9.1; ± 4.0) and the total dendritic length of adult cat VB neurons varied between 9,421 and 19,646 µm mean 13,120 µm; ± 2,605.[6]
  7. Dendritic length (µm) 1639 ± 341a 2140 ± 561 3397 ± 524[7]
  8. Apical dendrites possess a larger average total dendritic length (6332 vs 5062 micrometres) and surface area (12629 vs 9404 square micrometres) [this does not include spines].[11]
  9. Speed of impulses: 100 m/s (passive) ---- 20–30 m/s (thinking)8
  10. while nerve impulses in unmyelinated neurones have a maximum speed of around 1 m/s, in myelinated neurones they travel at 100 m/s.[12]
  11. The speed of propagation for mammalian motor neurons is 10 - 120 m / s, while for nonmyelinated sensory neurons it's about 5 - 25 m/s.[13]
  12. Human neurons fire approximately 200 times per second, using signals that travel at a maximum of 100 meters per second.[9]
  13. Frequency of impulses: Thus, a maximum of 1,000 nerve impulses per second is possible. However, firing rates of 1 per second to 300-400 per second are more typical.[9]
  14. Resting firing rates are generally a few times per second; a stimulated neuron might fire 20 or 30 times a second.[9]
  15. Simple spikes occur at rates of 17 – 150 Hz (Raman and Bean, 1999) either spontaneously, or when Purkinje cells are activated synaptically by the parallel fibers, the axons of the granule cells. Complex spikes are rapid (>300 Hz) bursts of spikes caused by climbing fiber activation, and can involve the generation of calcium-mediated action potentials in the dendrites. Following complex spike activity simple spikes can be suppressed by the powerful complex spike input.[10]
  16. Average = about 100 action potentials per second.[12]
  17. Number of neocortical neurons (females) = 19.3 billion. ---- Number of neocortical neurons (males) = 22.8 billion[1]

(Actually, facts [9] through [11] aren't particularly relevant, but I spent a lot of time reading about them so I forced you to spend a tiny bit of time reading about them, too. The speed of the pulses doesn't matter for our calculations - it's more than fast enough to cover the length between any two neurons in much less than a second.)

One problem with brain studies is that they tend to focus on specific parts of the brain. This makes it rather difficult to piece together whole-brain statistics. For example, [1] refers to the number of neurons in the entire brain, while [2] and [3] are talking about the length of axons in just the white matter - I think. [4] is at minimum related to the surrounding gray matter, but it's unclear if it includes any of the inner gray matter structures. Perhaps more importantly, the numbers vary considerably and are ambiguous as to exactly what they are measuring! [2] and [3] mention myelinated nerve fibers, which tends to be synonymous with axons, but the axon terminals aren't myelinated, so it's not 100% clear that they aren't included in this length measurement, or how long they would be otherwise. [5], [6], and [7] put the total length of dendrites per neuron at several centimeters, 0.9-1.9 cm, and 1.5-3.5 mm, respectively. Fact [8] gives an indication of where this difference comes from. Presumably, the length isn't tallied past a certain branching level, or below a minimum branch size, or something similar. [4] and [8] also indicate that the total length of all dendrites for a pyramidal neuron would be the sum of the two averages mentioned in [8], or ~11000 micrometers - again, not including the spines. In fact, the wording of [8] makes it unclear if that's total dendritic length for the cell, or for the single dendrite counting all its branches (up to a point). This uncertainty is frustrating, to say the least.

Neuron speeds vary, too, depending on the source. [9], [10], [11], and [12] give values between 10 and 120 m/s for myelinated axons, and between <1 and 30 m/s for unmyelinated fibers - dendrites and axon terminals? That's quite a range, but it isn't the only speed that varies. The frequency of the action potentials is reported as anywhere from 1Hz to 400Hz in [12] through [16], with a theoretical maximum of 1000Hz. So, what can we come up with using these ranges of numbers?

It turns out that we can be fairly pessimistic in our assumptions and still arrive at some staggering results. Let's take 150,000km of myelinated nerve fibers - the axons - and assume 10 impulses per second. 10 pulses seems to be a good compromise, given that we are thinking at a million miles an hour, not resting at a million miles an hour, but not all thinking would necessarily involve all portions of our brain. (That is not to say the myth about using only 3-10% of our brain is anything but a myth!) This alone gives us 150,000km * 10/s = 1,500,000,000 m/s5 times the speed of lightjust shy of a million miles a second! And we've only included one half of the synapse structure!

Let's be fairly conservative about the total length of the dendrites and axon terminals and any other unaccounted for lengths, and use 19.3 billion as the number of cells with dendrites, discounting everything but the neocortex (fact [17]). We'll go with 7.75 mm of dendrites per cell, since I really don't know what the source behind fact [7] was talking about, and source [14], which didn't have a fact to quote because the length had to be calculated out of other data, indicates total dendrite length of around 1.1 cm, so we're nearing a consensus of 1 cm or more. Anyway, I chose 7.75mm because 7.75 mm * 19.3 billion = 149,575 km, which means we can just double our previous results! Over 10 times the speed of light! 1,864,113 miles per second! And these are conservative estimates (I hope)!

Just for fun, let's see how fast I think. My neurons easily fire 100 times per second. I thought really hard about it, and sure enough all 100 billion neurons in my brain often fire at that rate. It turns out that my brain isn't very conservative when it measures itself, which makes my total dendritic length per neuron around the proposed average of 1.1 cm instead of 0.775 cm. So, when I'm thinking really hard, my mind is racing at (150,000 km + 100 billion * 1.1 cm) * 100/s = 125,000,000,000 m/s417 times the speed of light77,671,399 miles per second. I actually wouldn't be terribly surprised if this is closer to the true average speed of thinking really hard. (Are there any neuroscience folks out there that want to provide some different numbers?)

It's not a relevant fact, but it's pretty awesome: "% brain utilization of total resting oxygen = 20%[1]." I've always said that I remain thin because I think so much. Now I have evidence! Apparently, your brain running a million miles an hour is a pretty good workout. So, grab a puzzle book and lose some weight!

OK, so maybe this is the teensiest bit nerdy. And maybe it didn't warrant spending a total of about 72 hours of research spread out over three weeks.... But I lost 4 pounds!

  2. Awesomely, the most relevant paper cited in the first link is available in full:!
  7. which is part of


lauren said...

Darn. 9 -11 were some of my favorites! Also 15. I'm still reading the rest. :)

lauren said...

"It turns out that my brain isn't very conservative when it measures itself" -- :)