論文; papers

Conway’s Game of Life Concludes

Cu Packed Costs More than Na+/Ka+ Expanded in Cytoplasm

This was written for PSYCH-384; Sensation [and Perception] in response to a question as to why wires and axons are dissimilar. Minor edits have been made to cleanup a few issues.

Introduction

All these are fantastic questions, yet it seems in terms of weaknesses in knowledge and intuition-verbalization, it seems best to select the third question, however with a caveat stated. I was an electronics technician in the U.S. Army for a period, so for the purposes of this answer, I’m going to try to make it as simple as I can from a classical perspective, full knowing that electrons are quantifiable units that can be said to “jump”, and some electronics teachers use this concept to explain how current flows (i.e., hole current vs. electron current [Hanania, Stenhouse, & Donev, 2018]), and under the knowledge that in alternating current (a nearer, yet invalid analogy to ion/charge flow in axons), electrons flow through “wires” by skin-effect which complicates matters (Missouri S&T, n.d.). At first, very basic concepts of principal players in wires will be offered (without Ohm’s law, it’s a promise), then onto principal players in axons, followed by a comparison, and conclusion.

A Sea of Electrons

In an electronic “wire” such as copper with minor impurities of other elements for purposes to be omitted here (e.g., alloys, coatings, and oxidation of surfaces), elemental atoms such as copper share ionic bonds which allow electrons in valence shells to “flow” between each atom, where this “flow” is sensitive to both magnetic fields external, and to a “pool” of electrons (i.e., negative/positive side of a battery, or negative/positive side of a generator coil). Without going into too much detail, the electrons ebb and flow, but unlike common understanding, the electrons are quasi-individualistic. An electron has to have some place in a copper atom’s shell to move to, before it can move. This place is called a hole, and can flow like electrons, but in the opposite direction. Think of a line of people at a very busy grocery store; you can only move forward in the back of the line if the person in front of you can move forward, and so on. So, the only way to allow the back of the line to move is to move the person at checkout through, and the person behind them, and the person behind them, and so on. This will be important here in a moment when comparing electronic wires to axons. Now, remember, the whole reason the line moves at the checkout is because the person wants to leave, there is some motive that is driving the person to exit the line. Don’t forget this, because electrons too are motivated to a place with a whole lot of positive (hole) potential (aka: the positive side of a battery devoid of electrons [oh there’s so much to say here, but not in this context]).

Now unlike the grocery store, the wire’s atoms are significantly more than the checkouts in a grocery store (yeah copper atoms get all the checkouts as limited by ionic bonds). We’re talking a massive number of atoms here, hence the “throwing hands up” for the purpose of simplicity in electronics (remember, science is about predictability), and just coming up with some core concepts for the electrons as a whole: enter volts. Volts is just that measure of electron “pressure” between not so many electrons to many electrons. Ok, now that’s checked off right? Not so fast. So now there’s a general “sea” of electrons and it sloshes around depending on where the “volts” are positive and negative, and this sea meets resistance (yeah) in heat generating phenomena (oh no, here it comes, I though he said he promised): ohms. Really quick, the number of electrons passing any position per unit of time is, current. All that without mentioning the relationship between volts, ohms, and current (i.e., Ohm’s Law).

So basically, a simple wire, is carrying an insane number of atoms, and an even more insane number of electrons, which is simplified by general measures of the entirety of these numbers for the purposes of arriving at predictable results faster (i.e., volts, ohms/impedance, and current), which leads to a whole lot of misunderstanding when comparing wires with axons. That said, wires have the function of “carrying” charge to do work. If you could make a wire one copper atom in diameter, then you’d see the whole process much clearer, but this is rare, though one four atoms wide and one atom tall was created by a team of researchers at Perdue University (Weber et al., 2012). So, if there was a hypothetical probe at just one ionic bond, this probe could theoretically see single electrons flowing, but it wouldn’t be a flow, it’d be a bunch of “on” and “off” states (sound familiar?) as electrons and holes pass (sort of like watching one spot on a sliding tile puzzle). So, with wires, there’s a tremendous sea of electrons, and this is generally considered as a field. Regardless of whether a voltage potential is short and brief, or long, the electrons can move in this sea, on the “surfaces” of ionic bonds, but it’s a unique sea, because positive and negative potential both are in operation—electrons just don’t spill out of your outlet, nor spill out of the negative side of a battery.

Life’s Little Pumps, That Could

Now with axons, while there are atoms at play, the scale of the work is much bigger than individual atoms and electrons, and this is the reason for the difference in how the work is carried out. Somehow, biology formed these amazing structures of axons which are surrounded by a semi-permeable membrane, all of which is in cytoplasm containing a rich “soup” of molecules and elements useful for biology. In this case, the cytoplasm’s components useful for axons is Na+ and K+ ions, where the membrane of the axon has what’s called a Na+/K+ pump which “reads membrane voltage history to shape future membrane voltages” (Forrest, 2014, 1). Without going further into detail, the pump works to maintains Na+ external to the axon, and K+ internal, but considering the understanding that these Na+/K+ pumps not only maintain, but modulate, really makes this a whole lot more complex. Na+/K+ pumps are effectively performing their own neural modulation (i.e., computation), and here common scientific understanding as sampled by this very author in an accessible field of public opinion (i.e., anecdotal evidence) reveals a refrain that axons, dendrites (sans dendritic spines) are the end-all-be-all of neural “circuitry”.

At this point, I would declare the analogy between electronic wires and axons dead, but some still assert similarity due to lesser complex understanding, so that shall also be addressed. The way signals travel down an axon is by what’s generalized as an action potential, which specifically is the result of the aformentiond modulation in combination with the opening of sodium channels allowing K+ to exit the membrane to the cytoplasm, and Na+ to enter the membrane from the cytoplasm. The voltage difference at resting is -70 mV, whereas the opening of the sodium channels where K+ exits and Na+ enters peaks at about +40 mV, where the pumps close and return to -70 mV differences (ignoring discussion about refractory periods etc.). This activity happens in a sequence, as the signal traverses the length of the axon. Signals are being transmitted by altering topologies of chemicals by way of the amazing biological membranes as both natural and artificial selection has selected for, where the “axon” is essentially a portion of the topology as bounded by a membrane. Humanity, generally, in the common understanding places a border at the axon at the membrane, but in reality, the border is… sort of squishy isn’t it? And this suddenly starts feeling familiar again, sort of like electron fields, but not.

The Game of Life Concludes

Skipping to the end of the argument, for sake of simplicity, as this has now run into an entire treatise on beating the proverbial horse dead (I’ve had this conversation with numerous directors, executives, and soldiers, though without the additional modulating Na+/K+ pump knowledge), let’s simplify this, now that all the cards are on the table. Let’s push out what we don’t need, and keep what we do need (cough). Wires principally gain their utility on electron-hole flows between electron modulating phenomena like magnets, electrons, and protons altering the topology of electrical voltage across the wire in general with imprecise/de-localized control. Axons principally gain their utility on Na+/K+ exchange exterior and interior to the axon where Na+/K+ are literally pumped and channeled to alter a topology of electrical voltage in specificity with precise/localized control. Now, just as in statistics, we can find a clever way to make this analogy work by cherry-picking data, but when considering the aforementioned, these are clearly not similar categories of phenomena. Now one more swing to nail this dead, while axons get a lot of attention in biological explanations of neural behavior, dendritic spines get less attention, and that’s a whole different world of amazing “circuitry” that blows this whole analogy out of the water—the brain is not anything like an electronic circuit, but… as I said before, one can ultimately explain it as one, and there’s an airtight seal, but it’s a question of utility. What’s valuable? Is it valuable to find the equivalent explanation or the non-equivalent explanation? Because from where I sit in the cheap seats, isn’t it curious that electronics are manipulating voltage gradients (e.g., analog, digital on/off, superpositional qubits… etc. [base-n]) approaching more and more precise/localized control? Just look at a photograph of a central-processing-unit (CPU). All those wires are being used to “pull in” and “push out” to move meta-information “through”, which is what an axon is doing. And the final nail? All phenomena can be boiled down to John Conway’s Game of Life… but there’s a catch.

I propose that biological life is the limit to which digital life cannot reach and THIS is the reason axons cannot be like wires. While wires may be more efficient in carrying an electrical signal, its substrate is copper, and if I read my periodic table of elements correctly, a wire of Cu requires tremendously more resources than individual K+ and Na+ elements floating at greater distances in a fluid of lesser mass elements (all that fun stuff in and of cytoplasm) than Cu elements “pulled” together by Holocene inducing economistic human activity to wire (this pulling/pushing process is of high value in life eh?). Life is much more efficient; a simulation using elements of greater mass, if any, is a whole less so. Pretty funny that this all came from a question on the difference between a wire and an electron, isn’t it? Protect life, the economic games can wait—we’re not machines.

[Cu is an interchangeable indicator for Si, and wire is an interchangeable indicator for semi-conductors. This can be extended further.]

REFERENCES

Forrest, M. D., (2014). The sodium-potassium pump is an information processing element in brain computation. Frontiers in Physiology, 5, 1-2.   

Hanania, J., Stenhouse, K., Donev, J. (2018, June 4). Electron hole. Energy Education. https://energyeducation.ca/encyclopedia/Electron_hole. Accessed 19 January 2022.

Missouri S&T. (n.d.). Skin Effect. web.mst.edu. https://web.mst.edu/~kosbar/ee3430/ff/transmissionlines/LC_of_lines/resistance/skin.html. Accessed 19 January 2022.

Weber, B., Mahapatra, S., Simmons, M. Y., Ryu, H., Lee, S., Fuhrer, A., Reusch, T. C. G., Thompson, D. L., Lee, W. C. T., Klimeck, G., & Hollenberg, L. C. L. (2012). Ohm’s Law Survives to the Atomic Scale. Science, American Association for the Advancement of Science335(6064), 64–67. https://doi.org/10.1126/science.1214319