Boltzmann Brains and Epistemology
Entropy
Entropy is one of the most interesting concepts in physics. It has sometimes been defined as the amount of disorder in a system or our lack of knowledge of the system. It is remarkable that entropy, a technical concept ubiquitous in physics equations, can be described in such non-scientific ways. Because of its high level of intuitive meaning, it has inspired quite a few flawed arguments. One notable argument is the theory of Boltzmann Brains, which claims that all our memories and experiences are false byproducts of random chance that will cease in an instant. While this argument is scientifically sound, it makes an epistemological error, meaning that it does not correctly understand how we know things. The refutation of this argument points to the significance of conscious experience and the importance and primacy of philosophy in understanding science.
Entropy can be calculated with a concept called multiplicity. The multiplicity is the number of indistinguishable possibilities that could cause the results we observe. For instance, consider a friend who tells you that she rolled two dice, a red one and a green one, and added the numbers together. If your friend tells you that she got a four, there are three possible ways in which this could happen: the red die has a three and the green has a one, the green die has a three and the red has a one, or both have twos. In this case, the multiplicity is 3. In contrast, if your friend tells you she got a two, there is only one possibility, namely both dice have a one. Thus, the multiplicity would be only 1.
From this concept, one can see why entropy is sometimes called our lack of information about a system. When the number given has low multiplicity, for instance the number 2, you know the exact value of each die. On the other hand, if there is high multiplicity, you know very little about each individual die. Entropy tells you how little information your friend’s number gives you about the value of the dice.
To see why entropy is called disorder, it helps to consider a toddler’s house with a fenced off corner for toys. When the house is orderly, all the toys are in the pen. If you know all the toys are in the pen, you have a good idea of where each one is. There are not many possibilities for the positions of the toys, thus the system is in a low-entropy state. On the other hand, if the toddler is allowed to run wild, picking up toys and randomly carrying them until he feels the urge to drop them, the toys will eventually become spread throughout the whole room. In that case, the system would be in a high entropy state. This is why entropy is associated with disorder.
One of the most fundamental results in all of physics is the second law of thermodynamics which says that the entropy of a closed system can either increase or stay the same but not decrease. This law arises from the fact that it is more probable to find a system in a state with high multiplicity. Given a large enough system, this probability becomes a near certainty. The toddler’s living room helps to visualize why the entropy can only increase; random processes can spread the toys across the room, but they cannot bring all the toys back into the corner of the room.
This law seems counterintuitive in light of the existence of life. Even the simplest organisms grow and become more ordered, decreasing their entropy. They even reproduce which seems to cause a large-scale decrease in entropy. However, the organisms are not a closed system. Each organism decreases its own entropy, but it considerably increases the entropy of its environment. Thus, any environment with life will experience an increase in entropy, in accord with the second law of thermodynamics.
The universe, treated as a whole, is a closed system and thus its entropy can only rise. This means that if the physical laws continue for an uncountably long period of time, the universe could end up in the state of maximum entropy. This outcome depends on the four-dimensional geometry of the universe. Trapped in our limited sphere, it is hard to determine the exact shape of the universe and different shapes could lead to different possible outcomes. Nevertheless, it is a real possibility that our geometry will reach its maximum entropy state and stay there.
In such a state, known as the heat death of the universe, all particles, and all quantities, would be maximally spread out, like the toys of the unrestrained toddler. In such a situation, not only life, but all signs of order would vanish. This fate is known as the heat death of the universe. If nothing interfered with the physical processes, the universe would spend an infinite amount of time in this lifeless tomb.
One should remember that the second law of thermodynamics arises from probability. The reason why it is called a law, rather than a tendency, is because in any substance, the number of particles is so great that any deviation from the average can only be seen at the microscopic level. In principle, however, there is a vanishingly tiny, but non-zero probability that the total entropy of the universe could decrease.
Boltzmann brains
This fact is used in the argument for Boltzmann Brains. In the heat death of the universe, in which all matter is spread out uniformly for time spans longer than we can comprehend, there is ample opportunity for low probability events to occur. If the human brain is nothing more than a collection of unthinking atoms, then, in the heat death of the universe, countless similar brains, called Boltzmann brains, would form. Because they were the result of random fluctuation, these brains would cease existence as quickly as they began. If memory was nothing more than software on the brain, each brain would come with its own set of memories that, for its instant of existence, would seem real. Even though it is infinitesimally improbable that such a collection of atoms would form a human brain, the unlimited number of opportunities would guarantee that it would happen repeatedly.
The assumption that minds can be explained through material processes leads to a paradox. There would be nearly infinitely many more Boltzmann Brains than there are brains that were created through a gradual process of evolution. If each of these collections of atoms was capable of internal experience, it would come with false memories that it honestly believed were records of its past. If Boltzmann brains will one day exist, how do we know that we are not Boltzmann brains, doomed to have an instant’s thought filtered through the lens of false memories before we pop out of existence? The argument goes that there would be a nearly infinite number of Boltzmann brains and a much smaller number of brains that arose during the early, low-entropy state of the universe. Thus, if we know that we are brains and have no other information that would prove anything else, we might assume we are Boltzmann brains because there are many more of them.
Are we Boltzmann brains?
What does this mean for us? Is it reasonable to conclude that we are nothing more than fluctuations who will vanish in the blink of an eye? Are all our experiences, thoughts, and loved ones really just arbitrary patterns from electrons stored in the memory of an ephemeral brain? Most physicists and philosophers would answer no. But the question we must ask is, why can we reject this argument?
One solution is that we just reject any physical theory that implies we are most likely Boltzmann brains. This approach is tempting because there are some potential universe geometries that don’t lead to Boltzmann brains. But this approach is flawed. If the universe is merely dominated by random unguided physical laws, there’s no reason why parameters would be adjusted to give us results we like.
To see the proper response, we must consider what happens when we do science. As a species capable of science, we first experience consciousness and memory. We use these faculties to observe the world around us. With these observations, we follow the scientific method to make powerful conclusions about the natural world. Scientific conclusions are the results of our consciousness and memory. Any scientific result that denies the existence of these faculties undercuts its own evidence. Thus, the argument behind Boltzmann brains does not need a scientific rebuttal. Either we should accept that minds are not merely made up of matter and therefore we know we’re not Boltzmann Brains or we can conclude that we might be Boltzmann Brains whose experiences cannot be trusted and, therefore, we have no reason to believe in scientific conclusions like Boltzmann Brains. Either way, the conclusion that our minds don’t exist is incorrect.
The benefit of refuting Boltzmann Brains extends beyond merely knowing that we have permanent existence. It demonstrates that certain philosophical conclusions should be given greater certainty than scientific ones. Very few people in mainstream society believe that they are merely Boltzmann Brains and even those who profess the belief do not live like it is true. Thus, there is little point in proving, for its own sake, that we have permanent existence. However, the argument demonstrates that the idea of a conscious mind should take epistemological primacy over our understanding of matter. Phrased a different way, the understanding that our nature is fundamentally human is less shakable and more certain than any scientific conclusion.
What is consciousness?
It is not surprising that problems arise from a model of reality where consciousness arises merely from mechanistic processes. Science unaided by philosophy cannot answer what David Benatar called The Hard Problem of Consciousness. He argues that, to explain consciousness, one must answer two questions. The first question is, why do conscious minds behave the way they do? The second question is, why do conscious minds experience what they do? The question of predicting why a brain operates in a certain way is different from the question of why it feels a certain way to think with your brain.
The first question is prohibitively difficult but is easier to answer using science than the second. Even though there is much work to be done on this subject, neuroscientists, psychologists, and biologists have all made some progress in answering the question. On the other hand, no scientist has made progress towards an understanding of what causes us to be able to experience things. Unlike a machine, which can be understood by looking at the operation of its parts, we cannot break a mind or an experience into parts. Thus, science is left without any knowledge of this harder question of consciousness.
The fact that we have no scientific explanation for our experiences gives further confirmation that the mind, not the subatomic particle, should be the starting point for our investigation of reality. The argument for Boltzmann Brains assumed that a mind can entirely be explained with chemistry, biology, and physics. But the only reason to make this assumption is the desire to extend the scientific method beyond its domain. We have good reasons to conclude that mankind is not merely a medley of molecules. Instead, we can use real minds to really know the world around us.
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Daniel Sadasivan on Daily Philosophy:
Cover image: Midjourney.
