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Michael's avatar

Not sure why a physicalist would be repulsed by the conscious board game. It seems like an easier pill to swallow than saying a room or China itself could be conscious

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Michael A Alexander's avatar

The Boltzmann brain concept seems flawed to me. The frequency at which random bits come together to form any complex object in a particular region in space is directly related to the density D of the bits in that region (more bits means more chances of collision in that volume). The volumetric rate of coming together of N bits to form a complex object like a Boltzman brain is then proportional to D^N. The density is proportional to the total matter in the universe M divided by the volume of the universe V. The volumetric rate then becomes

rate/vol = K' * M^N / V^N where K' is the constant of proportionality

The total rate over a universe of size V is the above expression multiplied by V or

total rate [K' * M^N] / V^(N-1) = K * V^(1-N) where K = K'*M^N

Let v be the expansion rate (distance v per time) of the universe from the big bang at t = 0, then the volume of the universe at time t would be V = 4/3 PI * (vt)^3

Putting this into the expression for total rate yields

total rate = K * [(4/3 PI v^3]^(1-N)] * t^(3 -3N)

The quantity in brackets is constant for a given value of complexity (N). This is multiplied by another constant K to give the new constant G for a given complexity N and the total rate becomes

total rate = G * t^(3-3N)

As time t rises the frequency of collisions falls, which make sense as the bits become ever further apart and less likely to ever meet.

But as time goes on we have more time for such collisions to happen. To get an idea of how many collisions can happen we multiply the rate by time to get the total expected number EN or

EN = G * t^(4 - 3N)

For N = 2 we have EN = G * t^-2.

As t goes to infinity, the expected number goes to 0 as the square of time. For N larger than 2 the number falls to zero more rapidly. For N in the quadrillions as expected for atoms forming into a brain, the number falls to zero almost instantly. Only in the very early existence of the universe could any brains form after which, given the very high temperatures present then they would fly apart and cease to exist. Therefore the number of Boltzman brains in the universe would be vanishingly close to zero.

Hence it is extremely unlikely we are Boltzman brains.

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