Information is physical, which means there is a limit to
the amount of information that can fit in a given volume. If you try to cram more information into that
volume, the physical mass of that information will literally collapse into a
black hole. That limit is called the Bekenstein bound and
is truly a massive limit. For instance,
the total informational bound that could be contained in a volume the size of
the human brain is around 10^42 bits, which means that the total number of
possible brain states is around 2^(10^42).
The total informational capacity of the entire visible universe is on
the order of 2^(10^120) states.
Why does this matter?
Physicalism (as contrasted with dualism) says that conscious states are
produced by physical states; if a first conscious state is distinct from a second
conscious state, then they must be produced by different physical states. All of my papers (and most or all of my blog
posts) so far have assumed physicalism is true, in part because anyone who
doubts physicalism is usually condescendingly dismissed, ignored, or scoffed at
by the scientific community, and in part because I don’t see why the Creator
of the already ridiculously complicated universe would have omitted a physical explanation/mechanism
for consciousness. In other words,
unless there is a reason to believe that consciousness does not entirely depend
on underlying physical state, I see no need, for now, to reject physicalism. Nevertheless, physicalism would be falsified if
one could show that the number of distinct conscious states exceeded the number
of physical states, because that would require that a single physical state
could produce more than one distinct conscious state.
One avenue for evaluating physicalism, then, is to literally
count distinct conscious states. For
example, if one could show that the total number of possible distinct conscious
states by a particular person exceeded 2^(10^42), then that would prove that
consciousness cannot depend (entirely) on the brain; if one could show that the
number of possible distinct conscious states exceeded 2^(10^120), then that
would literally falsify physicalism.
A few years ago, Doug Porpora wrote a fascinating paper that
attempted to prove that the total number of distinct conscious states is
actually infinite. One of his arguments,
for instance, is that if we assume that there are some natural numbers that we
cannot think about, then there must be a maximum number (call it Max) that we
can think about and a minimum number (call it Min) that we cannot think about. But if we can think about Max, certainly we
can think about Max+1 or Max^2, which means that Max is not the maximum number
we can think about and the original assumption (that there are some natural
numbers that we cannot think about) is false.
A related argument is that by identifying the minimum number that we
cannot think about (and even naming it Min), we are thinking about Min, which
means that Min is not in the set of numbers that we cannot think about! Again, the original assumption is false. There is more to the argument than this but it
gives you the general flavor of its proof-by-contradiction strategy. One commenter has attempted to refute Porpora’s
argument in this paper,
and Porpora may be working on a reply.
This got me thinking again about the importance of
counting distinct conscious states, which very few people seem to have attempted. Of course, if Porpora’s logical argument is
correct, then physicalism is false because even though 2^(10^120) is a ridiculously
and incomprehensively large number, it is still trumped by ∞. But we should also realize that both of the quantities
we are considering are extremes. Infinity
is extreme, of course, but so is the Bekenstein bound.
Let’s take a more realistic approach. There are something like 100 billion neurons
in the human brain. If each neuron acts
like a digital bit, then the total number of distinct brain states is 2^(100
billion). Neurons are actually complex
cells with very complicated connections to each other. I don’t think any neuroscientist seriously
regards neurons as acting in any way like digital bits. However, I do think it is interesting to ask
the question of whether or not the number of distinct conscious states exceeds
2^(100 billion). If there were a way to
answer that question – by somehow counting conscious states – then it would do a
couple things:
·
Assuming physicalism is true, discovering that
the number of distinct conscious states exceeds 2^(100 billion) would confirm that
the brain is not a digital computer with neurons acting as digital bits.
·
It would provide a methodology for counting
conscious states that may provide further insights about the physical nature of
consciousness.
On that note, let me suggest such a method. First, let me start with the notion of one stimulus
“frame,” which is the particular collection of physical stimuli that one might
detect through the five senses at any given moment. Let’s assume that there are N consciously
distinct (frames of) stimuli. What I
mean by that is that there are N different combinations of stimuli from the
person’s senses that the person would be able to distinguish. Consider these different sets of stimuli:
·
Watching a sunset while hearing crashing waves
while tasting white wine while smelling the salty ocean while feeling sand
under one’s feet;
·
Watching a sunset while hearing crashing waves
while tasting red wine while smelling the salty ocean while feeling sand under
one’s feet;
·
Watching a sunset while hearing seagulls while
tasting white wine while smelling the salty ocean while feeling sand under one’s
feet.
If we actually took the time to list them, we could
certainly produce a very, very long list of consciously distinct stimuli. Some of them might differ very subtly, such
as two stimuli that are identical except for the temperature of the sand differing
by one degree, or a slight difference in sound frequency distribution from the
seagulls, or a slight but perceptible difference in the cloud distribution
above the sunset.
What matters, in enumerating consciously distinct stimuli,
is whether a person could distinguish them, not whether he actually
does. If he could distinguish two stimuli,
either by consciously noticing the difference or simply having a (slightly)
different conscious experience based on the difference, then that difference
must be reflected in the underlying physical state.
So how many such distinct stimuli are there? Lots.
One could certainly distinguish millions of different visual stimuli, many
thousands of different sounds and tactile sensations, and at least hundreds of
different tastes and smells. This is a
ridiculously conservative claim, of course; there are professional chefs, for
example, who can probably differentiate millions of different tastes and
smells. On this very conservative basis,
there are probably far, far more than 10^18 (around 2^60) distinct stimuli for
any given person. If there were only
10^18 distinct conscious states or experiences, then in principle it would only
require about 60 bits to specify them.
However, history matters.
Conscious experience does not depend just on one’s stimuli in the
moment, but also on prior stimuli (as well as prior conscious experience). To specify a person’s conscious experience,
it is not enough to specify his current stimuli, as his experience will also
depend on past stimuli. For example,
imagine the different conscious experiences at time t1:
Case A – No significant change from t0 to t1:
t0: Watching a sunset while hearing crashing waves while
tasting red wine while smelling the salty ocean while feeling sand under one’s
feet.
t1: Watching a sunset while hearing crashing waves while
tasting red wine while smelling the salty ocean while feeling sand under one’s
feet.
Case B – Significant change from t0 to t1:
t0: Watching a sunset while hearing crashing waves while
tasting white wine while smelling the salty ocean while feeling sand
under one’s feet.
t1: Watching a sunset while hearing crashing waves while
tasting red wine while smelling the salty ocean while feeling sand under one’s
feet.
The stimulus at t1 is the same in both cases, but the conscious
experience would clearly be different. In
Case A, the person may simply be enjoying the surroundings, while in Case B, he
may be confused/surprised that his wine has suddenly changed flavor and color.
What that means is even if the information necessary to
specify the particular stimulus at time t1 is 60 bits, that information is not
sufficient to specify the person’s conscious experience at that time. In other words, history matters, and instead
of just counting the number of possible distinct stimuli, we need to consider
their order in time.
So, for N consciously distinct stimuli, let’s assume that
one’s conscious experience/state at a given time is sensitive to (i.e., depends
on) the time-ordering of M of these stimuli.
The total number of possible states, then, is just the permutation
N!/(N-M)!, but assuming that N>>M, this total number of states ≈ N^M.
So in the above example, the number of possible physical
states necessary to allow the person to consciously distinguish Case A from
Case B is not N, but N^2. If N requires,
say, 60 bits of information, then at least 120 bits are required to specify his
conscious state at time t1. But of
course the situation is far worse. We
can imagine a series of ten consecutive stimuli, ending at time t9, which the
person would consciously experience in a manner that depended on all ten
stimuli and their order. It makes no
difference whether the person actually remembers the particular stimuli or
their order of progression. As long as
he has a conscious experience at t9 that is in some (even miniscule) manner dependent
on the particular stimuli and their order, then that conscious state is one of
at least N^10 states, requiring at least 600 bits to specify.
Now note that his experience at t9 is a unique one of at
least N^10 states, just as his experience at later time t19 is a unique one of
at least N^10 states, and so forth until time t99. But if his conscious experience at time t99
is sensitive to the ordering of his conscious experiences at t9, t19, t29,
etc., then the conscious state at t99 is one of at least N^100 states,
requiring at least 6000 bits to specify.
Once again, this analysis has nothing to do with whether the person remembers
any specifics about his prior stimuli or experiences; all that matters is that
his conscious experience at t99 depends to some degree on the ordering of
experiences at t9, t19, etc., and that his experience at t9 depends to some degree
on the ordering of stimuli at t0, t1, etc.
It’s easy to show, then, that the total number of possible
conscious states is N^T, where T is the total number of individual “frames” of
stimulus that one experiences over his life.
How many is that? Well, 100 years
is about 3 billion seconds, and we certainly experience more than one “frame”
of stimulus per second. (Otherwise, TVs
would not need a refresh rate of around 30 frames/second.) So, for 10 frames/second, we might estimate
the total number of possible conscious states at about N^(30 billion). If N is 2^60, then the total number of
conscious states is 2^(1.8 trillion), requiring at least 1.8 trillion bits to
specify.
I find it fascinating how close this is to the number of
neurons (100 billion) in the human brain.
For extremely rough back-of-the-envelope calculations like this, an
order or two of magnitude is certainly “close.”
The storage capacity of the human brain has been estimated somewhere in
the tens to thousands of terabytes, and once again the above rough estimate is
within a couple of orders of magnitude of this amount.
What this tells me is that this method of counting distinct
conscious states is viable and potentially useful and valuable. By getting better estimates for the number of
stimuli that a person can distinguish, for example, we might find that the
rough estimate above (≈ trillion bits) is far too high or far too low, which
could then provide insights on our understanding of the brain as: a computer; a
digital computer; a digital computer with neurons acting as bits; and the independent
source of consciousness. Of course, such
an analysis will never get us anywhere near the Bekenstein bound or infinity,
as addressed by Porpora’s paper, but I still think we can learn interesting and
important things about the physical nature of consciousness by counting distinct
conscious states.
Finally, I think the above analysis hints at something fundamental:
that consciousness is history-dependent.
This is something I discuss at length in my paper on the Unique History
Theorem, but the above arguments suggest a similar conclusion by a very
different analysis. If one’s conscious
experience at time t99 depends to some degree on his experience at t98, which
in turn depends on his experience at t97, and so on back, then it may not be
possible to produce a person de novo in a particular conscious state C1
who has not already experienced the particular sequence of conscious states on
which state C1 depends.
In any event, I think it makes sense to seriously consider
and estimate the number of potentially distinct conscious states, taking into
account a human’s sensitivity to different stimuli and the extent to which
ordering of stimuli affect conscious states.
I think this approach could yield potentially fascinating knowledge and
implications about the brain and the physical nature of consciousness.