A Cubic Millimeter of Your Brain

Are there more connections in a cubic millimeter of your brain than there are stars in the Milky Way? We are going to answer that question in a moment, but first take a look at this image of hippocampal neurons in a mouse's brain. It is an actual color image from a transgenic mouse in which fluorescent protein variations are expressed quasi-randomly in different neurons. This kind of image is known as a brainbow and is aesthetically awesome further it may be one way to empirically examine a cubic millimeter of the brain (neuron tomography).

In reality mapping even an entire cubic millimeter of the brain is an extremely daunting task, but we can still answer my original question. First, I know that there are different kinds of neurons that vary in size and that some neurons can have a soma (the big part that has the nucleus from which the dendrites extend) spanning a millimeter in size. Thus if you picked a random cubic millimeter of brain you could run right into the heart of a neuron and you would find very few connections. Given this fact, we can very easily answer this question with a resounding no, however, this seems like an unsatisfactory trite approach. So I looked up some numbers on how many neurons are in the brain, how many connections are in the brain, and how many stars are in the Milky Way. Lets answer the question using the 'average' number of connections per cubic millimeter.

How many neurons and connections there are in the brain? This is kind of a tricky question and I am not a nuerobiologist so I have gone to several resources for the answer. Professor of Computational Neuroscience at MIT Sebastung Seung says in a TED talk

your brain contains 100 billion neurons and 10,000 times as many connections

Professor of Molecular Cellular Physiology at Stanford Stephen Smith says in a press release on brain imaging that

In a human, there are more than 125 trillion synapses just in the cerebral cortex alone

René Marois from the Center for Integrative and Cognitive Neurosciences at Vanderbilt Vision Research Center states in a recent paper ^[1]

The human brain is heralded for its staggering complexity and processing capacity: its hundred billion neurons and several hundred trillion synaptic connections can process and exchange prodigious amounts of information over a distributed neural network in the matter of milliseconds.

I have enough expert sources now to confidently say these experiments agree that the human brain has some 100 billion neurons (10¹¹). The number of connections seems less precise, but it is at least several 100 trillion connections (10¹⁴) as judged by Marios and Smith and as much as 10¹⁵ as judged by Seung.

The number of connections in the brain is tricky to define. We may define a synaptic connection as each place the neuron touches another neuron and a synapse is present. It doesn't seem to make sense to simply count incidental contact. Further, there is the question of whether we should count redundant contacts between neurons. We can obtain an upper bound on the number of connections in the brain by considering the case in which every neuron is connected to every other neuron. Coincidentally the operation of connecting every node in a network with every other node is a process I am familiar with from cross correlating radio signals. Anyways, the equation we are looking for is N(N-1)/2 where N is the number of nodes in the network. Thus, for our N=10¹¹ neurons the maximum number of non-redundant connections is about 10²². This maximum bound is huge! But how huge is it really? Hilariously, while searching for an answer to my original question I found a message board pondering the grand statement

There are more connections in the brain than atoms in the Universe.

A really clever person pointed out that

Theoretically, if we took all the atoms in the universe; wouldn't that include the atoms within the brain?

People have this feeling that the number of connections between items can be much larger than the number of actual items in the collection and while this intuition is true the idea that there are more connections in the brain than there are atoms in the universe is absurd. Lets put it in perspective that a few grams of any substance, like water, is measured units of moles. A mole is standard unit of measurement corresponding to the absolute 6.02 x 10²³. Thus even a drop of water contains more atoms than there are connections in the brain.

Now we need to know how many neurons and connections are in an average cubic millimeter of the brain. How big is the brain? John S. Allen of the Department of Neurology at University of Iowa stated in a recent paper that^[2]

The mean total brain volumes found here (1,273.6 cc for men, and 1,131.1 cc for women) are very comparable to the results from other high-resolution MRI-volumetric studies.

We can take the volume of the brain as 1000cc as a low estimate (which will only over estimate the density of connections).

The final thing we need to know to answer the question at hand is the number of stars in the Milky Way. Like every other number we have been working with it is rather uncertain. Even if we define a star as only those spheres of gas which are large enough to fuse hydrogen at some point in their lifetime we don't know the answer because we can't see the multitudes of dim stars. There are probably at least 500 billion star like objects in the Milky Way. Lets take 100 billion as the number to be conservative.

Finally, lets bring all the numbers together. One cubic millimeter is 1/1000 of a cubic centimeter and 1/1000000 (10^-6) of the entire volume of the brain. We can scale the total number of connections in the brain (using the high estimate of 10¹⁵ connections in the brain) then we find that there are 10⁹ connections in a cubic millimeter of the brain. The 10⁹ connections in a cubic millimeter of the brain is two orders of magnitude smaller than a low estimate of the number of stars in the Milky Way. No, on average there are not more connections in a cubic millimeter of your brain than there are stars in the Milky Way. 

My first response to this question was bullshit! This question (or rather statement) is made by David Eagleman here at a TEDx talk and here on the Colbert Report. Colbert also called out Eagleman when he dropped this factoid, but it didn't stop the interview. I have also contacted some actual neuroscientists to see what they thought of this statement and they agree with me that it is not true. Maybe there is special part of the brain particularly more dense in connections than the brain on average, but that would be misleading like saying the density of the Milky Way is that of water because, you know, certain parts of the Milky Way are water. The better statement would be to say that there are are more connections in the brain than there are stars in the Milky Way. As Colbert would say, I am putting you on notice Eagleman.

While we are on the subject I want to mention my favorite talk about the brain which mixes just the right amount of wonder and fact. It is the TED talk I mentioned earlier by Sebastian Seung on what he calls the connectome - the network of connections in your brain between neurons which physically dictates how you think. In the video he discusses another volume tomography technique in the brain using a cube of mouse brain tissue just 6 microns on a side. It is another great visualization for what is actually in a cubic millimeter of your brain.

References

[1] Marois, R., & Ivanoff, J. (2005). Capacity limits of information processing in the brain Trends in Cognitive Sciences, 9 (6), 296-305 DOI: 10.1016/j.tics.2005.04.010

[2] Allen, J., Damasio, H., & Grabowski, T. (2002). Normal neuroanatomical variation in the human brain: An MRI-volumetric study American Journal of Physical Anthropology, 118 (4), 341-358 DOI: 10.1002/ajpa.10092

On Replications

Repetition is ubiquitous and has many different meanings in education, art, literature, science, and life Ideas replicate and mutate; cultural memes spread through culture seamlessly. Manufactured goods are produced as nearly identical as possible. Deviations from the mold are discarded and parts are interchangeable. Digital data is almost limitlessly replicable. Any data or idea committed to the digital world is perfectly copied (sparing the occurrence of a flipped bit) until it is intentionally modified. This characteristic of digital ideas presents a unique challenge for creators of content, distributors, and bored people on the internet. And of course animals and plants on Earth have the ability to self replicate themselves with minor variations. What do we make of all of this?

I am keen on the intersection of art and science on this matter. I like making collages and have highlighted repeated images before with 35 images of space helmet reflections and 100 images of macchiatos. Through repetition and distortion images may be amplified or diminished. It depends on perspective. Generally in artistic endeavors, as in life, the slight variations of a repeated theme are aesthetically pleasing. On the other hand technical work such as engineering, data analysis, or manufacturing requires precise replication. I work in radio astronomy where each radio telescope in the array is nearly identical and the need for precision trumps all other considerations. I find that randomness is never particularly interesting, but neither is absolute order. Somewhere in between these extremes we have something really beautiful.

Looking back and looking forward

This photo was taken on the last US manned space flight in 1975 before the first shuttle launch in 1981. Portrayed is the historic handshake between Tom Stafford and Alexey Leonov through the open hatch between the American Apollo and Russian Soyuz ships. Today the Atlantis shuttle lifted off for the the last shuttle mission. It is the end of an era. Alas, all good things must end.

Mars Rover Curiosity

This animation depicts what will happen in August 2012 if all goes as planned for Curiosity, NASA's next Mars rover. This rover is much larger and and more competent than the previous rovers. It is about the size of a small car and has an entire suite of experiments on board. During entry it uses a series of thrusters to maneuver to the designated landing area. Once the ship has slowed down to Mach two (keep in mind that the atmospheric pressure on the surface of Mar's is of the order .05% that of Earth's) a parachute is deployed. As the vehicle slows the heat shield comes off and a radar detects how close the surface is approaching in order to slow for a smooth landing. The last daring step is a so called 'sky crane' which lowers the rover with a long cable from the rocket thrusted ship above. Eventually Curiosity will begin roving, but it won't be limited to roving only during the day by solar panels as the previous rovers were. The large tilted box on the back of the rover contains 4.8 kg of plutonium dioxide which emits heat serving as the power source of the rover. The power should keep flowing for much longer than the minimum specked science mission of two Earth years. The rover will seek out rough rocks such as ancient Martian riverbeds or canyons where evidence of early environments on Mars can be found. The ability to navigate to these areas is an important science requirement for the rover and is one of the reasons for the rover's large size and nuclear battery which should allow it to travel at least 20 kilometers during its lifetime. Geologists and astrobiologists also want to know if certain conditions such as those necessary for organic molecules are present. In the video a laser and a drill are shown performing experiments. The laser is ChemCam which will project onto hard to reach rocks and detect the reflected light in order to discern the chemical composition of rocks. The drill is about a centimeter in diameter and will extract the dust from the holes it creates to run experiments in mineralogy (the laser device inside the rover shown in the video) or detecting organic molecules. All of these experiments aim to answer the question, could Mars have had an environment capable of supporting life at one time?

If the sky crane works we may soon know the answer to this question. Curiosity has a launch window from November 25 to December 18, 2011 from Kennedy Space Center in Florida. And in other news NASA's James Webb Space Telescope is being threatened with the axe in budget bill in the U.S. House of Representatives today. NASA will never run out of adversaries pulling it down: Gravity and the budget.