Hamlet, and an Infinite Number of Monkeys
Back in college, I once drove with two friends from Provo to Salt Lake CIty, and we spent the entire hour debating an abstract question. Assume an infinite number of monkeys sitting in front of keyboards, randomly pecking away. How long would it take until one of them typed To be, or not to be. That is the question? Our sophomoric ignorance did nothing to decrease the enthusiasm and decibel level of our conversation.
I recalled that experience last week while following J. Stapley’s post on Mind and Spirit. And then yesterday, when the link to an article about consciousness appeared on the left sidebar, I thought about it again. It really is an interesting question. Outside of a religious context, how do we explain consciousness?
It is said that C. S. Lewis once remarked, in conversation with a nonbeliever, “You can’t deduce Hamlet from the molecular structure of a mutton chop.” That statement works well as a rhetorical device, but I don’t know whether it is a good argument or not.  I really am interested in learning how a nonbeliever would respond. In a universe composed of matter and energy, where does self-awareness come from?
People: I hope we are all big enough to refrain from comparing blogging to an infinite number of monkeys with keyboards. In the first place, our numbers in the bloggernacle are quite finite. There is absolutely not connection at all. None.
Comment by Mark IV — January 30, 2007 @ 9:41 am
LOL. Thanks for my laugh of the day, Mark IV.
To blog, or not to blog? THAT is the question.
Comment by MikeInWeHo — January 30, 2007 @ 10:00 am
Let’s take the “to be” question and simplify it a little bit. Letters and spaces only, no caps. So there are 27 choices, and the probability of the correct choice at any given point is 1/27. We need to choose 39 letters correctly in a row, although we can disregard the first choice because the monkeys are allowed to type this phrase in the middle of nonsense, and the start point is arbitrary. So, given a start point, we need 38 subsequent choices to be correct and in the right order. The probability of that is (1/27)^38, which is about 4.0567 * 10^-55. Not very likely.
But that’s only one monkey, and one starting point. Suppose we have 10,000 monkeys, with one starting point each. How likely is it that at least one will write the phrase in question? The answer, not to put to fine a point on it, is still nearly zero — but now on the order of 10^-50. In fact, the limit of this probability as the number of monkeys approaches infinity is one. With only one starting point each. Essentially what this means is that, if there really is an infinite number of monkeys, it is essentially certain that the phrase in question will be written on the first try. In fact, it will be written on the first try by an infinite number of monkeys — although a much larger number of monkeys will not get it on the first try.
Comment by RoastedTomatoes — January 30, 2007 @ 10:11 am
If the number of monkeys with keyboards is really infinite, it will not take very long as there is a finite number of combinations of letters, spaces and grammatical characters in the space of the sought after phrase. That is, of course, assuming that the monkeys choose to type and not throw poop at each other.
Comment by john scherer — January 30, 2007 @ 10:15 am
DOH!
Simultaneous post. RT explains himself much better than I, though.
Comment by john scherer — January 30, 2007 @ 10:25 am
Monkey’s don’t engage in random typing:
http://www.cbsnews.com/stories/2003/05/12/national/main553500.shtml
Comment by anonymous chimp — January 30, 2007 @ 10:41 am
chimp, great news story — I enjoyed the link. So let’s take our hypothetical and call the central actors “monkeys,” i.e., random typing widgets. Although it seems in the experiment as if the monkeys were acquiring the taste for random typing as time went on? Perhaps all that’s required is an infinite amount of time for them to discover all the keys?
Comment by J. Nelson-Seawright — January 30, 2007 @ 10:46 am
“We’ve heard that a million monkeys at a million keyboards could produce the complete works of Shakespeare; now, thanks to the Internet, we know that is not true.”
- Robert Wilensky, speech at a 1996 conference
Comment by Ken — January 30, 2007 @ 11:09 am
The most accessible book I’ve run across that discusses the foundations of consciousness from a mechanical perspective is Antonio Damasio’s The Feeling of What Happens: Body and Emotion in the Making of Consciousness. It provides a pretty clear articulation of what is known about the neural structures upon which our consciousness depends, as well as a relatively clear articulation of the subjective elements that compose consciousness.
What Damasio does not do (and what you may be asking) is the “why” of consciousness, rather than the “what” or “how” of consciousness.
FWIW, I understand the why of consciousness in evolutionary terms, which gets at one sort of answer to “why,” but without the will-driven purpose element.
I recently posted elsewhere my take on why consciousness exists in the context of a discussion of animal rights and the nature of pain and suffering. I’ve taken the liberty of cutting and pasting, even while I acknowledge that this may be a longer response than you sought: long before consciousness evolved, organisms interacted with their environments through stimulus/response models of various levels of complexity, ranging from the operation of photosynthesis (stimulus: photon, response: Kreb cycle fabrication of glucose) to the more elaborate mechanisms needed to cause a self-mobile organism to move away from situations that caused damage to the organism’s cellular structure.
Even the latter stimulus (damage)/response (motion away from damaging situation) operation, consciousness isn’t a requirement. The mechanisms that run those operations are no more alive than a light switch is alive. The light turns on when the system receives the stimulus of the switch being flipped. So, too, biological damage-avoidance mechanisms can operate without anything more than mechanics. That makes, sense, since it’s evolutionarily a good idea to keep one’s cellular membranes intact, to say nothing of avoiding becoming a dinosaur’s meal.
Because damage-avoidance developed before consciousness did, responses that conscious beings make to painful stimuli are often identical to the responses that non-conscious beings make to organism-damaging stimuli, without ever perceiving anything like pain.
Once consciousness did develop, it created the ability to override the automatic responses triggered by stimuli. That had the potential to be very advantageous from an evolutionary perspective – it would allow an organism to keep fighting, even in situations in which it was being damaged. In a world where there is competition for limited resources, disabling the automatic “flee†mechanism was useful. Unfortunately, that same consciousness had the unfortunate effect of disconnecting organism-threatening stimuli from the automatic organism-protecting responses. In such an environment, it’s easy to see why the organism with emerging consciousness was benefited by developing a decidedly unpleasant signal to indicate damage to the organism – pain. Theoretically, there’s nothing necessary about damage to the organism being signaled by pain to consciousness. Instead, theoretically, damage could have been signaled by any other arbitrary perception – say a vision of a particular color or perception of a particular sound or smell. But pain – a signal that conscious beings innately dislike and want to avoid – was more adaptively advantageous. The organisms for whom the damage signal was a psychically neutral color, sound, or smell didn’t have a perception that would cause them to avoid the damaging stimulus. But pain turned out to be very useful, precisely because it was unpleasant to conscious beings. When that evolutionary change happened, it enabled the organisms to weigh in the balance the possibility of avoiding the pain against the possibility of advantages to be gained by suffering the pain. At that point – bingo – you have the LDS version of Eve: And Eve … heard all these things and was glad, saying: “Were it not for our transgression we never … should have known good and evil…â€
Comment by greenfrog — January 30, 2007 @ 11:46 am
Eep.
Comment by danithew — January 30, 2007 @ 11:56 am
I should also add that my take on the evolutionary genesis of consciousness is nothing more than that — my take. I’m not at all a scientist. Just an interested by-stander. Others with better backgrounds than mine (which is nearly everyone, except two of the chimps who were given detention for bad behavior) may have more developed ideas.
Comment by greenfrog — January 30, 2007 @ 11:58 am
greenfrog:
Can we get a link to the post to which you referred in #9? I’d be interested in reading that.
Comment by endlessnegotiation — January 30, 2007 @ 11:59 am
greenfrog, thanks, you answered my question as to how self-awareness might develop.
RT/JNS - simply awesome.
Comment by Mark IV — January 30, 2007 @ 12:03 pm
Neuroscientists still don’t “know,” so it’s important not to be dogmatic about–people proclaiming a given explanation as the final word are generally after fame, money, tenure, books (or are “true believers”). It remains their holy grail. Most of them I know so something about complexity theory, though I haven’t asked them recently.
I’ve wondered about the monkeys and hamlet, as what we’re actually after is not typing a phrase but a monkey who, when reading it, becomes suicidal over the pain Hamlet felt, identifying himself with Hamlet.
Comment by Sam MB — January 30, 2007 @ 12:03 pm
The humor scale, with #1 being funny and #3 being funniest:
1. Monkeys
2. Poop
3. Monkeys with poop
John Scherer wins this round.
Comment by Susan M — January 30, 2007 @ 12:13 pm
greenfrog: really interesting post. Thanks.
Comment by Christopher Smith — January 30, 2007 @ 12:19 pm
greenfrog. Interesting take on consciousness. I understand the evolutionary speculation about how consciuosness may have arisen (and I believe it is just speculation). It may even be just as you (and Damsio) say, but I don’t see any real evidence for any of these flights of fancy into explanation. Do you have any evidence that this is in fact how the evolutionary development occurred? (That’s a real question because I’m interested.
I’m still wondering how a population of firing neurons can produce consciousness at all. I mean — none of the neurons is conscious and if we reduce the causes to their parts we don’t explain consciousness. (That’s what Chalmers calls the hard problem). I think that all are agree that somehow something must arise from the function of the parts as a whole — but I’m convinced by Jagwoen Kim’s causal redundancy argument that non-reductive physicalism isn’t a live option and that functionalism is just paralyzed by the problem of multiple realizability.
Comment by Blake — January 30, 2007 @ 12:36 pm
endless negotiation,
The exchange was on a quasi-private board. I’ve promised others to assemble (for context) and post them on my (not-particularly-LDS) blog in the next week or two. I’ll do so and then post a link on this thread.
Comment by greenfrog — January 30, 2007 @ 12:37 pm
Darn. I thought this was going to be a post about Tom Stoppard. But to assauge my disappointment, let me offer the following anonymous gem:
“The Internet is proof that a million monkeys with a million typewriters can’t write Hamlet.”
Comment by herodotus — January 30, 2007 @ 12:42 pm
Blake wrote:
It is speculation, and it’s mine, though I probably got the idea from some other reading I have done and forgotten — I’m not claiming to be the first to have thought of those things. Also, I should be clear that Damasio doesn’t go down that road in the book I linked to — his book is entirely focused on the fundamental subjective aspects of consciousness and the neural structures that, when damaged, negate consciousness, and, when operative, seem to engender it.
No. That’s just a thought experiment of the sort that evolutionists perform when told things like “Yeah, but evolution couldn’t create an eye!” Damasio’s book makes the speculation a bit more plausible, as he identifies and differentiates core consciousness and extended consciousness. Those portions of his discussion seem to me easily comprehensible within an evolutionary model, but he isn’t investigating that particular question in his work.
I’m still wondering how a population of firing neurons can produce consciousness at all. I mean — none of the neurons is conscious and if we reduce the causes to their parts we don’t explain consciousness. (That’s what Chalmers calls the hard problem). I think that all are agree that somehow something must arise from the function of the parts as a whole — but I’m convinced by Jagwoen Kim’s causal redundancy argument that non-reductive physicalism isn’t a live option and that functionalism is just paralyzed by the problem of multiple realizability.
Comment by greenfrog — January 30, 2007 @ 12:48 pm
Rats, I hit the wrong button before finishing that post. Here’s the rest:
That is the question that Damasio addresses quite directly, though I’m not sure his response will satisfy you, as it won’t distinguish what organic neural structures do from what properly (and complexly) constructed machines could do.
I don’t know who Chalmers is, but I’ll google him later today. But you’ve got a pretty severe definitional assumption built into the first sentence. Damasio would agree with you, as he defines the term “conscious,” but to his way of thinking “conscious” is a word like “life.” At a particular level of de-construction, you don’t have it. At a particular level of construction, you do. As to life, maybe a mitochondrion inside a muscle cell in my arm is, itself, alive, but the surely the mitochondrial DNA inside it is not. As to consciousness, surely a neuron itself is not conscious, but when it’s assembled together with a few billion others, in particular configurations, the assemblage, is.
I’m afraid I’m not smart enough to know what that means.
Comment by greenfrog — January 30, 2007 @ 12:56 pm
#19, meet #8
Comment by greenfrog — January 30, 2007 @ 12:57 pm
Sorry greenfrog I made a bunch of bad assumptions. Kim’s argument is essentially that if I have a physical cause P that causes me to act, then any reference to consciousness or mental properties M to explain the act P end up being redundant and don’t provide anything to an explanation of our actions. In other words, if we assume a physical cause of consciousness in the brain (say by populations of neurons firing) then the mental or consciousness is eliminated and all explanation becomes physical or material.
Multiple realizability is the notion that there is not just one functional way things can work — there are multiple physical systems that can do the same thing so there is no uniuqe functional explanation. Thus, functionalism is difficult to support (that is, the view that the mind is just a function of neural patterns and so forth). In my mind, that means that physicalism (the view that attempts to explain consciousness by reference to physical properties such as the brain and neurons etc.) cannot explain consciousness.
Sorry about assuming too much.
Comment by Blake — January 30, 2007 @ 1:15 pm
“Ford — there’s an infinite number of monkeys outside who want to talk to us about this script for Hamlet they’ve worked out.” — Arthur Dent
Comment by Mike Parker — January 30, 2007 @ 1:44 pm
Of course no discussion of monkeys would be complete without a Simpsons quote;
Room in Mr. Burns house with a thousand monkeys on typewriters (hack-writer monkeys complete with cigarettes and coffee). Mr. Burns pulls a sheet out from typewriter and reads “‘It was the best of times, it was the blurst of times.’ You stupid monkey!”
It just goes to show that all a thousand monkeys will get you is erroneous Dickens.
Comment by Derek — January 30, 2007 @ 1:59 pm
Ah, thanks for filling in some of my blanks.
I’m not in a position to debate those assertions, but I do note that consciousness (subjectivity) is something that we can see and examine through pretty compelling circumstantial, if not actual direct, evidence.
One of the reasons I found Damasio’s book interesting was because of the detailed case studies he discusses where varying elements of consciousness were, quite specifically, not present, and how those elements correllated to various brain lesions or deficiencies that those patients also experienced.
So while there are apparently good arguments that physical substrates can’t create consciousness, there is pretty good evidence that messing with the physical substrate can certainly eliminate consciousness, even while life continues.
Despite my lack of training in this, I’m intrigued by your statement, “…that means physicalism (the view that attempts to explain consciousness by reference to physical properties such as the brain and neurons etc.) cannot explain consciousness.” That sounds more like a prediction than a fact — something like, “you’ll never turn that lead into gold.”
If that understanding of your point is right, I’m not sure I agree with it. There may be a point in the future where we reach a point beyond which we can’t go in discerning how consciousness is linked to physicality, but in the macro-sized world, isn’t consciousness obviously linked to physicality? Through physical action against a physical structure, we can terminate consciousness. Are you saying that we can never create consciousness by assembling physical elements? Isn’t that what fertilized eggs do? You probably mean something different than I understand from your point.
Comment by greenfrog — January 30, 2007 @ 2:01 pm
greenfrog: I’m an emergentist so I believe that the mind/consciousness arises from the physical activity of the brain/neural systems; but they don’t explain it. What arises from such activities is more than the sum of the parts. So what arises is a “person” or agent rather than a jumble of chaotic neural activity. So we now begin to explain activity as the activity of a whole on a new level rather than by analyzing it into it sub-partss. The agent is not a linear causal result of the input causes. Moreover, the agent as such has causal powers that the neurons alone don’t have — like making a choice or being conscious. The agent can exercise “downward causation” and we refer to mental properties like intentions, choices and purposes to explain an agent’s acts rather than to just the neural properties.
What that means is that the properties of mind are dependent on the underlying physical structures of the brain; however, the causal powers of the agent are not limited to the causal powers of the brain’s subparts. Let me give an example. A flame arises from burning a wick, oxygen and so forth. However, it sustains its own existence as such by maintaining a combustible temperature. The dance of the flame is impossible to predict because to sustain itself it must be in constant dynamic interaction with its environment. The flame has causal powers that its underlying consistuents alone don’t have, i.e., the power to sustain a flame and to draw in oxygen into the flame’s interactive system to keep it going. Further, because we must consider the environment in which the flame arises as essential to the flame’s definition, the flame’s relationships to what is outside of it is essential to what it is.
Human agents are like that. We are in dynamic interaction with our outside environment to be what and who we are. We cannot be defined simply by the matter that makes up our bodies because that matter is in constant flux and requires outside causes to sustain it — like food and oxygen. So there is no possibility of a linear explanation from physical states to a full explanation of an agent. There is more to an agent than merely brain matter — as is obvious from the fact that dead brains are different than living agents. It is the process of interaction that must be accounted for. So I suggest that in prinicple physicalism is inadequate. However, I agree with Damasio’s data that the agent depends on a functioning brain for the emergence of the agent from that process. So my view accounts for Damasio’s evidence without reducing to physicalism and it accounts for the evidence of human experience of consciousness and agency. I don’t believe that Damasio’s view accounts for consciousness (what you call subjectivity and we could call phenomenology) and agency (the fact that we make choice based on purposive behavior and we are moral agents). Anyway, that is what my thinking is right now.
Comment by Blake — January 30, 2007 @ 2:59 pm
Blake,
It is still not clear to me how you reconcile you emergentist view of consciousness with the Mormon view of spirits. Where does a spirit fit in with your view?
Comment by Geoff J — January 30, 2007 @ 4:12 pm
endlessnegotiation,
The larger discussion context you asked about can be found here:
http://inlimine.blogspot.com/
Comment by greenfrog — January 30, 2007 @ 4:43 pm
greenfrog: In my view there is an eternal field of force that has physical properties from which the properties of mind emerge — an intelligence. Further, these properties of mind are enhanced by taking on ourselves a body. There is a risk in bodily existence because we may take our bodily senses as the sole basis of detecting reality and forget the more fine and subtle forms of knowing available through the spirit. We require a brain for consciousness in this material sphere; but a brain made of bodies as we know them is not necessary for consciousness of other realms or spheres of existence. At least that is how I see it right now (and have for some time).
Comment by Blake — January 30, 2007 @ 6:01 pm
Blake,
I assume #30 is in response to my question in #28…
I don’t know what you mean by “an eternal field of force that has physical properties from which the properties of mind emerge”. Can you explain that a little better? Also, what is your take on the reportedly more refined matter that is spirit? If our mortal consciousness emerges from mortal brains do you think that implies our spirit consciousness arises from a spirit brain? I guess I am having trouble seeing how anything that is “me” could be eternal unless we have some kind of dualism in mortality.
Comment by Geoff J — January 30, 2007 @ 6:39 pm
See, this is what is so wonderful about this blogging venue. We get to have conversations like the one Geoff, Blake, and greenfrog are having, mixed in with insights from the Simpsons.
Comment by Mark IV — January 30, 2007 @ 6:43 pm
Goeff: You’re right. It wasn’t greenfrog. An eternal field of force is simply that: a field of force that has always existed. Such a field can exist based on whatever physical properties sustain fields (BTW the most basic forces of matter seems to be such fields). So yeah, there is something analogous to a spirit brain in the sense that it has the capacity to process information — not in the sense that it can interact with a neural system to move arms and legs. What is eternal is the characteristic ways information is processed (that is, your personality in its most basic form). There is an “I” that is self-aware because of feed-back loops in the data (that is what is required for self-consciousness). I don’t see why that couldn’t me a “me”.
Anyway, we know for example that a magnet can establish a field of force and that the field that emerges from the magnet may continue as such a field even after the underlying metal or matter that supports the field is taken away. such field can have a rather autonomous existence.
Comment by Blake — January 30, 2007 @ 6:55 pm
Blake: I don’t see why that couldn’t me a “meâ€.
Ok, I can buy that. My next question is how do you envision the pre-mortal “me” transferring into mortality and then out again while retaining the its “me-ness” (aka the same personal identity)? If the pre-mortal (and post-mortal) “me” emerged from a beginningless spirit-brain of sorts and the mortal “me” emerges from completely different hardware how is continuity of personal identity possible? In other words how does a personal identity endure hardware changes if we are entirely emergent? Again, I have trouble understanding how we could have ant continuity of personal identity could work in the absence of some kind of dualism.
Comment by Geoff J — January 30, 2007 @ 7:27 pm
Geoff: I believe that we maintain our characteristic ways of processing the information and assessing it from the premortal life to this life. That is our character comes through so that there an identity of: (a) the material substrate field; (b) the characteristic way information is processed; (c) our moral qualities are continued in this way of responding to the data. The character that we developed now faces new challenges in a context it has never encountered. That is an exciting adventure of creative advance into novelty to clone Whitehead’s description.
Further, the way the information is process is in part impacted by the body — but it is a matter of whether we will also allow our spirit or character from the pre-mortal life influence us. The field is already there — but it is also emergent with the new spirit-body unity we call a soul. So there is a kind of dualism — but it isn’t immaterial/material dualism. It is pre-mortal field and emergence/corporeal field emergence. Our spirits are “added upon” by the body, not obliterated. So the underlying spirit entity also contributes to the emergent consciousness unless we repress it and become natural men totally emerging solely from the mortal body. Even the person are depends on the way we choose to organize our data and emerge from the underlying manifold of these data both spirit/refined and crass matter. Amyway, that is how I see it right now.
Comment by Blake — January 30, 2007 @ 9:15 pm
Thanks Blake. That sounds like a pretty reasonable attempt at dealing with a difficult question. It seems to me that the most precarious part of your theory is the sort of dual/competing “brains” (spirit and mortal) from which our single consciousness emerges here mortality. I think it is safe to say that if the mortal brain gets damaged the “spirit brain” (for lack of a better term) won’t fill in for it. So I guess it is hard to see how in your theory the two “brains” interact with each other here in mortality and more specifically how the our spirit brain (or our personal identity that emerges from that hardware) would be changed by the mortal identity that emerges entirely (or almost entirely) from the mortal brain here on earth. Yet our ability to change the “me” that endures past the death of our mortal brain is a fundamental assumption we make about the plan of salvation.
I’ll have to let this subject marinate in my melon for a while. Despite my lingering questions about your theory I don’t have an alternative theory to offer. Maybe I’ll follow up on this subject later at the Thang.
Comment by Geoff J — January 30, 2007 @ 10:26 pm
An infinite number of monkey would be able to reproduce Hamlet. But they wouldn’t appreciate the significance or meaning of what had been written.
Comment by David Brosnahan — January 31, 2007 @ 1:01 am
The very notion of an infinite number of monkeys is impossible because monkeys begin to exist and thus there will always only be a finite number of monkeys. So the thought experiment is logically impossible and nothing at all follows from what is logically impossible.
Comment by Blake — January 31, 2007 @ 2:18 am
Blake,
From my understanding there are an infinite number of worlds. If monkeys exist on only a portion of those worlds, would not there be an infinite number of monkeys?
Re #15, Thanks Susan, I’ve always enjoyed a good monkey throwing poop joke myself.
Comment by john scherer — January 31, 2007 @ 7:34 am
John: What is the basis of the notion of an infinite # of worlds? However, even that doesn’t suggest there is an infinite number of monkeys unless there is an infinite number of those worlds that has monkeys!
Comment by Blake — January 31, 2007 @ 9:04 am
Geoff: If a functioning brain is necessary for the expression of the spirit-field in this order of existence, then the spirit-field cannot have any influence in the emergence of the person in the absence of a functioning brain. I agree that seems to be how it is. We don’t cease to be “us” when we die; we just cease to be able to express or act in this order of existence. When we die, only the spirit-field acts and thus nothing is expressed in this order of existence but there is no longer the necessity of the brain as a mediating means of experience so that it then experiences what a spirit-field alone can experience. It seems to me it more or less has to be that way given the notion of an eternal spirit.
Comment by Blake — January 31, 2007 @ 9:09 am
Blake, you’re confusing infinity with its asymptote. You can asymptotically approach inifinity from finitude–it’s a fairly common assumption in most statistical fields.
Comment by Sam MB — January 31, 2007 @ 9:38 am
for most intents and purposes 10^10 is getting pretty close to infinity, and for exceedingly rare events like we’re discussing just adding 3-4 orders of magnitude to whatever (im)probability you’re discussing is generally good enough to approximate infinity.
Comment by Sam MB — January 31, 2007 @ 9:40 am
“approach inifinity from finitude” — Let me be emphatic. Approaching infinity is still a finite order of number. We don’t go to infinite ordinals until we have an infinite order!
“for most intents and purposes 10^10 is getting pretty close to infinity” — no it isn’t. It is still a finite number and no matter how much you add to it in terms of integers you cannot reach an infinite order. Logically speaking, it is no closer to infinity than the number 1 — which is a very lonely number — and two can be as bad as 1, it’s the loneliest number since the number 1.
Comment by Blake — January 31, 2007 @ 9:50 am
Sam (#42) your confusing the result of a function with the input to the function. So yes, as you approach 0 the function 1/x approaches infinity. But the nature of infinity is quite different mathematically. Further there are many kinds of infinity. The set of real numbers, for instance, has a cardnality larger than the set of integers.
Comment by Clark — January 31, 2007 @ 12:36 pm