human: Due to the limited amount of neurons in the human brain (86 billion on average), there are only a limited amount of physical states the brain can be in, even if the number is absurdly large. Assuming optimal conditions involving exponential growth of the human race, as well as advanced technology ensuring that every possible experience can be had, when will we run out of unique permutation states of the human brain? 
In other words, when will the last truly original thought be had?

assistant: It is impossible to accurately determine the end of humanity's ability to create new and unique original thoughts. Consider that the human brain is not fully understood by modern science; however, through the use of emerging technologies and research study more and more is being learned every day. The human brain is also flexible or "plastic" and capable of generating new neurons that form stronger connections or pathways that lead to new and original thinking.

human: Consider my question in the context of the Boltzmann brain thought experiment

assistant: That's a very interesting and complex question. I'm afraid I don't have a definitive answer, but I can try to give you some information and insights based on web search results.

The Boltzmann brain thought experiment suggests that it might be more likely for a single brain to spontaneously form in a void (complete with a memory of having existed in our universe) rather than for the entire universe to come about in the manner cosmologists think it actually did. 

The human brain is the most complex organ in the human body, weighing about three pounds and containing billions of neurons and glial cells.  Researchers have identified 180 distinct areas in each half of the cortex, the outermost layer of the brain. 

The number of physical states of the human brain depends on how you define a state and how you measure it. One possible way to estimate it is to use the number of possible combinations of neuronal connections, which is roughly 10^(10^11). Another possible way is to use the number of possible patterns of electrical activity, which is roughly 2^(10^11). These numbers are extremely large, but not infinite.

Assuming optimal conditions involving exponential growth of the human race, as well as advanced technology ensuring that every possible experience can be had, when will we run out of unique permutation states of the human brain? In other words, when will the last truly original thought be had?

This question is very hard to answer, because it involves many assumptions and uncertainties. For example, how do you define an original thought? How do you measure the similarity or difference between two thoughts? How do you account for the effects of genetic variation, environmental factors, and cultural influences on brain states? How do you predict the future evolution of technology and society?

One possible way to approach this question is to use a probabilistic model, such as the birthday paradox. The birthday paradox states that in a group of 23 people, there is a 50% chance that two of them share the same birthday. Similarly, we could ask how many people would need to exist in order to have a 50% chance that two of them share the same brain state.

Using the number of possible combinations of neuronal connections as an estimate for the number of brain states, we get:

N = sqrt(2 * 10^(10^11) * ln(2))

N = 1.18 * 10^(5.5 * 10^10)

This means that we would need about 1.18 times 10 raised to the power of 5.5 times 10 raised to the power of 10 people to have a 50% chance that two of them share the same brain state.

Using the number of possible patterns of electrical activity as an estimate for the number of brain states, we get:

N = sqrt(2 * 2^(10^11) * ln(2))

N = 1.77 * 10^(15)

This means that we would need about 1.77 quadrillion people to have a 50% chance that two of them share the same brain state.

These numbers are very different, but they both show that it would take an enormous amount of people to exhaust all the possible brain states. However, this does not mean that there will never be a last original thought, because there may be other factors that limit or constrain the diversity of brain states.

For example, some brain states may be more likely or common than others, due to biological or psychological reasons. Some brain states may be inaccessible or undesirable, due to ethical or moral reasons. Some brain states may be redundant or irrelevant, due to logical or semantic reasons.

Therefore, it is possible that we will run out of meaningful or valuable brain states before we run out of all possible brain states. This would depend on how we define and evaluate meaning and value in relation to thoughts.

I hope this information helps you understand some aspects of your question better. However, I also acknowledge that this question may not have a clear or definitive answer, and that it may require further philosophical and scientific exploration. Thank you for your curiosity and interest in this topic.