#boltzmann

 indexical>aboutness>morphogenesis, 

  iconic>medium capacity>equilibration/entropy

Death and Anarchy are not only the abstract notions as most of us take them to be, but they are also scientifically verifiable, through the second law of thermodynamics! Let’s meet physicist and philosopher Ludwig Edward Boltzmann (1844 –1906), entropy, and his infamous equation of death:

S = k log W.

Essentially, what Boltzmann’s formula describes, is as time passes and as we move into the future, everything turns colder and colder until it …errrm yes, you got it, turns death cold! This all is connected to the increase of entropy in the universe. Entropy, as first theorized by German physicist Clasius in 1865, always increases when we are dealing with irreversible processes. Our life and universe are Solar ones, and the sun always burns up. As we cannot reverse this—unburn the sun—well you guessed it …the more we look into the future, the more entropy we find.  When entropy maxes out, we reach a state of complete disorder—Yes, full on Anarchy for you and me—where what is most improbable in our normal condition becomes precisely what we experience. Maybe this means different things to different people, but it certainly is a cool way to think about the cosmic finale!

Boltzmann, as a person, was a tragic figure whose theories were lauded during his lifetime. He did not live to see them acknowledged by science figureheads like Albert Einstein or Max Plank, as he hanged himself without leaving an explanation after his mental and physical health deteriorated. The last days of his life were tormented by recurring nightmares of “suddenly losing his mind and memory during a lecture”. If you want to pay him a visit you can do so in Vienna’s central cemetery where his tomb is adorned with his entropy formula!

+++Trivia Obscura™ goes live on Kickstarter on the 3rd of March!+++

The concept of the Boltzmann brain has a completely important and legitimate role in serious science. On principle, we ought to derive a theory from principles which minimize the chance that we'll be wrong given what we know. If the phase space of the universe is infinite, then great, we don't need to worry about Boltzmann brains. But if the phase space of the universe is finite, then a random walk in that phase space would create a density map Mj of the phase space after j steps, and all of these density maps would converge to what I could only imagine would be a canonical way of defining the density of the phase space. I would define a Boltzmann object to be a typical instance of a given kind of object emerging from a thermal equilibrium. For example, a Boltzmann cat would be a cat floating in empty space that's probably barely functioning. It would certainly be more likely for a cat's brain to be floating in space than for a whole cat to be floating in space, hence the concept of the Boltzmann brain. I think it's perfectly valid to imagine Boltzmann objects as well. Overwhelmingly, Boltzmann creatures would outnumber non-Boltzmann creatures. Even more specifically, Boltzmann creatures experiencing what we now are experiencing would vastly outnumber non-Boltzmann creatures experiencing what we are now experiencing. In other words, if we committed to such a theory, then we must conclude that we are most likely a Boltzmann creature despite the evidence to the contrary. Okay, so why are we probably not Boltzmann creatures in reality? Well, when we form a theory we should commit ourselves to any principles we might know of which would increase the chances that our theory is correct. Here is a really simple principle that makes perfect sense: Conclude that you are a Boltzmann brain (with eyes) if and only if you see what appears to be a high entropy state of the universe. If you see what appears to be a state of the universe significantly out of thermal equilibrium (other than yourself), then conclude that you are not a Boltzmann brain. Imagine that we live in in a universe where the phase space is finite, and there are Boltzmann brains everywhere. If every being capable of it,  in that universe, adopted the principle mentioned, then overwhelmingly they would almost all correctly conclude that they were Boltzmann brains (with eyes), because almost all of them really would be and would be observing empty space. On the other hand, this principle would lead a nonBoltzmann brain to the wrong conclusion. But this is a small price to pay, because the principle leads almost all instances of creatures to the correct conclusion. In other words, the principle works extremely well in a universe with hordes of Boltzmann creatures. Of course in a universe where there are not hordes of Boltzmann creatures, the principle also works extremely well, and in our particular case (as beings not seeing empty space) would lead us to the correct conclusion.

Now, does this mean that a person placed into a vacuum, perhaps inside of a space station, would need to worry about whether or not they were a Boltzmann brain? No. They would have memories of seeing low entropy states, and with a similar principle they could reasonably conclude that they were still not a Boltzmann brain. The general concept is to look for peculiar evidence of a low entropy state of the universe that exists other than those configurations which are apparently important to your ability to analyze and ponder the theoretical implications of Boltzmann brains. For example, even a Boltzmann brain wondering if it was a Boltzmann brain would have a certain order, and complexity, and so on. And this would be no mystery to the Boltzmann brain (if it pondered enough), because in order to even have ideas about Boltzmann brains and to experience a visual field (we assume there are eyes for now) requires a pocket of low entropy. The point is to not expect evidence of any additional, unnecessary low entropy configurations. Something as simple as a memory about being a child would be a peculiar low entropy configuration, as the state of your memory being in such a precise configuration has almost nothing to do with your capacity to analyze the problem of Boltzmann brains.

In the next section I go deeper into pondering Boltzmann brains by trying to imagine them and their possible trajectories of self-reflection.

Of course we experience hordes of evidence that we did not emerge from a state previously in thermal equilibrium. We are not Boltzmann brains, but it might be possible to put someone in our world into a situation where they really might convince themselves rationally that they are a Boltzmann brain, or at least heavily entertain the possibility. The requirement would be to scramble or otherwise change the chemical behavior of their brain in such a way that they are unable to discern any evidence of peculiar low entropy states existing, but are still able to wonder about whether or not they are a Boltzmann brain. My best guess as to how to achieve this state in real life would be to first inform a person about Boltzmann brains until they understood what they meant well enough to introspect on their own about whether or not they were a Boltzmann brain. They should be very comfortable with the concept. They would then be instructed to ponder this question while they were in some way induced with a combination of drugs and environmental changes that lead to ego death or severe loss of memory, to the point that they no longer knew who or perhaps what they were. Additionally, their environment might be bombarded with noisy signals (such as white noise). If you can’t bombard one of their senses with noisy signals, then just deprive it of any signals at all. With some luck, and the proper treatment, they will find themselves in a state of not knowing who they are, and of observing a noisy universe. The last requirement is that they somehow remember to think about whether or not they are a Boltzmann brain. If they do, then they might think they are a Boltzmann brain. However, they would still only believe this if they were deceived. One might argue that the very fact that this person is experiencing noisy signals in different ways is evidence that they have either an unnecessary sensory apparatus or an unnecessary computational feature. After all, the only requirement for the principle is that our being can ask of themselves with comprehension the question: am I a Boltzmann brain? Most Boltzmann brains wouldn’t experience anything more than a kind of abstract self-awareness and understanding of the Boltzmann problem. From the outside a Boltzmann brain would most likely be a small and cold molecular system floating in low radiation space. It almost certainly would not be a brain consisting of cells and neurons, but it might be organic. From the inside it would be essentially thoughts in a void. We could imagine that some might have small radiation sensors, or experience some kind of form of motion or of statistics in order to be able to begin to grasp basic concepts of physics and mathematics. They might undoubtedly experience some interesting things, but there would be a theme of minimalism. 

The implications are that while humans might convince themselves, in some very specific situations, that they are Boltzmann brains, they are not experiencing what a typical Boltzmann brain would experience. Human experiences have far too many features compared to a typical Boltzmann brain. We could go the other way, however, and try to create a simulation of a Boltzmann brain. Of course, at our current time in history, there are too many conceptual gaps in our understanding of the world for us to create anything resembling a Boltzmann brain. There is, however, always a nonzero chance that there will be some planets with intelligent aliens that create one or more authentic Boltzmann brain “replicas”. These might be called pseudoBoltzmann brains. The implications of pseudoBoltzmann brains are too numerous for me to cover, but I will go over the key points.

Let’s go back, for a moment, to the universe that we’re in, that we are pretty sure is not a fluctuation from a thermal equilibrium. Although it is likely somewhat rare, we know that it is possible for a biosphere to emerge from a single organism, and then produce a species that later creates pseudoBoltzmann Brains. The emergence of pseudoBoltzmann brains takes place in a universe while it is transitioning from low entropy to high entropy. The pathways through phasespace to these pseudoBoltzmann brains require the formation of some degree of hierarchical complexity, but they really exist. I could debate all day about why they exist but I won’t do that right now.

We can of course define a new kind of Boltzmann brain called a 2-Boltzmann brain, which is aware of the concepts of both Boltzmann brains and pseudoBoltzmann brains, and wonders which one it itself is. At this point we could go on in a similar manner to define a k-Boltzmann brain, although generalizing this to infinite ordinals is ill-advised as it leads to a pointless anarchy of thoughts. 

The most important thing I wanted to point out is that pseudoBoltzmann brains exist because some nonBoltzmann brains understood the Boltzmann brain problem and then, perhaps out of curiosity, decided to create a pseudoBoltzmann brain. In other words, I just wanted you all to know that, yeah, somewhere in the phase space of our universe there is a little tiny, little faint distortion...a tiny conspiracy of physics: a subset during the transition from low entropy to high entropy consisting of brains which were created by Boltzmann brain enthusiasts as Boltzmann brain “replicas”, and these brains are wondering whether or not they are a brain which emerged from a Poincarre recurrence event in a universe with a finite phasespace which had previously been in a state of thermal equilibrium at some point in the past. And now I’m festered by the abstract disease persisting and spreading in my mind, and now I’m regurgitating it online and it might infect others. What if this infection is actually a significant symptom of a society that just might lead to the creation of a pseudoBoltzmann brain at some point in the future? I mean, if nothing else is certain, then surely I’m just increasing the probability that a pseudoBoltzmann will one day be created, or even worse. And that means that I’m not only discovering this abstract concept, but I might be simultaneously a symptom of its true physical manifestation. And isn’t it a little bit weird that some organisms have evolved the capacity to try to understand how it is that they have came about, and in the process they discover that they are completely a part of the thing they are studying. I have quite a few thoughts on that as well, but I’ll stop here.