In philosophy, the brain in a vat (BIV) is a scenario used in a variety of thought experiments intended to draw out certain features of human conceptions of knowledge, reality, truth, mind, consciousness, and meaning. It is a modern incarnation of René Descartes's evil demon thought experiment originated by Gilbert Harman. Common to many science fiction stories, it outlines a scenario in which a mad scientist, machine, or other entity might remove a person's brain from the body, suspend it in a vat of life-sustaining liquid, and connect its neurons by wires to a supercomputer which would provide it with electrical impulses identical to those the brain normally receives. According to such stories, the computer would then be simulating reality
(including appropriate responses to the brain's own output) and the
"disembodied" brain would continue to have perfectly normal conscious
experiences, such as those of a person with an embodied brain, without
these being related to objects or events in the real world.
Uses
The simplest use of brain-in-a-vat scenarios is as an argument for philosophical skepticism and solipsism.
A simple version of this runs as follows: Since the brain in a vat
gives and receives exactly the same impulses as it would if it were in a
skull, and since these are its only way of interacting with its
environment, then it is not possible to tell, from the perspective of that brain,
whether it is in a skull or a vat. Yet in the first case, most of the
person's beliefs may be true (if they believe, say, that they are
walking down the street, or eating ice-cream); in the latter case, their
beliefs are false. Since the argument says one cannot know whether one
is a brain in a vat, then one cannot know whether most of one's beliefs
might be completely false. Since, in principle, it is impossible to rule
out oneself being a brain in a vat, there cannot be good grounds for
believing any of the things one believes; a skeptical argument would
contend that one certainly cannot know them, raising issues with the definition of knowledge.
Other philosophers have drawn upon sensation and its relationship to
meaning in order to question whether brains in vats are really deceived
at all, thus raising wider questions concerning perception, metaphysics, and the philosophy of language.
Recently, many contemporary philosophers believe that virtual
reality will seriously affect human autonomy as a form of brain in a
vat. But another view is that VR will not destroy our cognitive
structure or take away our connection with reality. On the contrary, VR
will allow us to have more new propositions, new insights and new
perspectives to see the world.
Philosophical debates
While
the disembodied brain (the brain in a vat) can be seen as a helpful
thought experiment, there are several philosophical debates surrounding
the plausibility of the thought experiment. If these debates conclude
that the thought experiment is implausible, a possible consequence would
be that we are no closer to knowledge, truth, consciousness,
representation, etc. than we were prior to the experiment.
Argument from biology
One
argument against the BIV thought experiment derives from the idea that
the BIV is not – and cannot be – biologically similar to that of an
embodied brain (that is, a brain found in a person). Since the BIV is dis embodied, it follows that it does not have similar biology to that of an embodied brain. That is, the BIV lacks the connections from the body to the brain, which renders the BIV neither neuroanatomically nor neurophysiologically similar to that of an embodied brain.
If this is the case, we cannot say that it is even possible for the BIV
to have similar experiences to the embodied brain, since the brains are
not equal. However, it could be counter-argued that the hypothetical
machine could be made to also replicate those types of inputs.
Argument from externalism
A second argument deals directly with the stimuli coming into the brain. This is often referred to as the account from externalism or ultra-externalism.
In the BIV, the brain receives stimuli from a machine. In an embodied
brain, however, the brain receives the stimuli from the sensors found in
the body (via touching, tasting, smelling, etc.) which receive their
input from the external environment. This argument oftentimes leads to
the conclusion that there is a difference between what the BIV is
representing and what the embodied brain is representing. This debate
has been hashed out, but remains unresolved, by several philosophers
including Uriah Kriegel, Colin McGinn, and Robert D. Rupert, and has ramifications for philosophy of mind discussions on (but not limited to) representation, consciousness, content, cognition, and embodied cognition.
Argument from incoherence
A third argument from the philosopher Hilary Putnam
attempts to demonstrate the thought experiment's incoherence on the
basis that it is self-refuting. To do this, Putnam first argued in favor
of a theory of reference that would later become known as semantic externalism. He offers the "Twin Earth"
example to demonstrate that two identical individuals, one on our earth
and another on a "twin earth", may possess the exact same mental state
and thoughts, yet refer to two different things.
For instance, when we think of cats, the referent of our thoughts would
be the cats that we find here on earth. However, our twins on twin
earth, though possessing the same thoughts, would instead be referring
not to our cats, but to twin earth's cats. Bearing this in mind, he
writes that a "pure" brain in a vat, i.e., one that has never existed
outside of the simulation, could not even truthfully say that it was a
brain in a vat. This is because the BIV, when it says "brain" and "vat",
can only refer to objects within the simulation, not to things outside
the simulation it does not have a relationship with. Therefore, what it
says is demonstrably false. Alternatively, if the speaker is not
actually a BIV, then the statement is also false. He concludes, then,
that the statement "I'm a BIV" is necessarily false and self-refuting.
This argument has been explored at length in philosophical literature
since its publication. One counter-argument says that, even assuming
Putnam's reference theory, a brain on our earth that is "kidnapped",
placed into a vat, and subjected to a simulation could still refer to
"real" brains and vats, and thus correctly say it is a brain in a vat. However, the notion that the "pure" BIV is incorrect and the reference theory underpinning it remains influential in the philosophy of mind, language and metaphysics.
Ludwig Boltzmann, after whom Boltzmann brains are named
The Boltzmann brain argument suggests that it is more likely
for a single brain to spontaneously and briefly form in a void (complete
with a false memory of having existed in our universe) than it is for
the universe to have come about in the way modern science thinks it
actually did. It was first proposed as a reductio ad absurdum response to Ludwig Boltzmann's early explanation for the low-entropy state of our universe.
In this physicsthought experiment,
a Boltzmann brain is a fully formed brain, complete with memories of a
full human life in our universe, that arises due to extremely rare
random fluctuations out of a state of thermodynamic equilibrium.
Theoretically, over an extremely large but not infinite amount of time,
by sheer chance atoms in a void could spontaneously come together in
such a way as to assemble a functioning human brain. Like any brain in
such circumstances, it would almost immediately stop functioning and
begin to deteriorate.
The idea is named after the Austrian physicist
Ludwig Boltzmann (1844–1906), who in 1896 published a theory that tried
to account for the fact that humans find themselves in a universe that
is not as chaotic as the budding field of thermodynamics seemed to predict. He offered several explanations, one of them being that the universe, even one that is fully random (or at thermal equilibrium), would spontaneously fluctuate to a more ordered (or low-entropy) state.
Boltzmann brains gained new relevance around 2002, when some
cosmologists started to become concerned that, in many theories about
the Universe, human brains in the current universe appear to be vastly
less likely than Boltzmann brains will be in the future; this leads to
the conclusion that, statistically, humans are likely to be Boltzmann
brains. Such a reductio ad absurdum argument is sometimes used to argue against certain theories of the Universe. When applied to more recent theories about the multiverse, Boltzmann brain arguments are part of the unsolved measure problem of cosmology. Physics, being an experimental science, uses the Boltzmann brain thought experiment as a tool for evaluating competing scientific theories.
Boltzmann universe
In 1896, the mathematician Ernst Zermelo advanced a theory that the second law of thermodynamics was absolute rather than statistical. Zermelo bolstered his theory by pointing out that the Poincaré recurrence theorem
shows statistical entropy in a closed system must eventually be a
periodic function; therefore, the Second Law, which is always observed
to increase entropy, is unlikely to be statistical. To counter Zermelo's
argument, the Austrian physicist Ludwig Boltzmann
advanced two theories. The first theory, now believed to be the correct
one, is that the Universe started for some unknown reason in a
low-entropy state. The second and alternative theory, published in 1896
but attributed in 1895 to Boltzmann's assistant Ignaz Schütz,
is the "Boltzmann universe" scenario. In this scenario, the Universe
spends the vast majority of eternity in a featureless state of heat death;
however, over enough eons, eventually a very rare thermal fluctuation
will occur where atoms bounce off each other in exactly such a way as to
form a substructure equivalent to our entire observable universe.
Boltzmann argues that, while most of the universe is featureless, humans
do not see those regions because they are devoid of intelligent life;
to Boltzmann, it is unremarkable that humanity views solely the interior
of its Boltzmann universe, as that is the only place where intelligent
life lives. (This may be the first use in modern science of the anthropic principle).
In 1931, astronomer Arthur Eddington
pointed out that, because a large fluctuation is exponentially less
probable than a small fluctuation, observers in Boltzmann universes will
be vastly outnumbered by observers in smaller fluctuations. Physicist Richard Feynman published a similar counterargument within his widely-read 1964 Feynman Lectures on Physics.
By 2004, physicists had pushed Eddington's observation to its logical
conclusion: the most numerous observers in an eternity of thermal
fluctuations would be minimal "Boltzmann brains" popping up in an
otherwise featureless universe.
Spontaneous formation
In the universe's eventual state of ergodic
"heat death", given enough time, every possible structure (including
every possible brain) gets formed via random fluctuation. The timescale
for this is related to the Poincaré recurrence time.
Boltzmann-style thought experiments focus on structures like human
brains that are presumably self-aware observers. Given any arbitrary
criteria for what constitutes a Boltzmann brain (or planet, or
universe), smaller structures that minimally and barely meet the
criteria are vastly and exponentially more common than larger
structures; a rough analogy is how the odds of a real English word
showing up when one shakes a box of Scrabble letters are greater than the odds that a whole English sentence or paragraph will form.
The average timescale required for the formation of a Boltzmann brain
is vastly greater than the current age of the Universe. In modern
physics, Boltzmann brains can be formed either by quantum fluctuation, or by a thermal fluctuation generally involving nucleation.
Via quantum fluctuation
By one calculation, a Boltzmann brain would appear as a quantum fluctuation in the vacuum after a time interval of years. This fluctuation can occur even in a true Minkowski vacuum (a flat spacetime vacuum lacking vacuum energy).
Quantum mechanics heavily favors smaller fluctuations that "borrow" the
least amount of energy from the vacuum. Typically, a quantum Boltzmann
brain would suddenly appear from the vacuum (alongside an equivalent
amount of virtual antimatter), remain only long enough to have a single
coherent thought or observation, and then disappear into the vacuum as
suddenly as it appeared. Such a brain is completely self-contained, and
can never radiate energy out to infinity.
Via nucleation
Current evidence suggests that the vacuum permeating the observable Universe is not a Minkowski space, but rather a de Sitter space with a positive cosmological constant.
In a de Sitter vacuum (but not in a Minkowski vacuum), a Boltzmann
brain can form via nucleation of non-virtual particles gradually
assembled by chance from the Hawking radiation emitted from the de Sitter space's bounded cosmological horizon. One estimate for the average time required until nucleation is around years.
A typical nucleated Boltzmann brain will, after it finishes its
activity, cool off to absolute zero and eventually completely decay, as
any isolated object would in the vacuum of space. Unlike the quantum
fluctuation case, the Boltzmann brain will radiate energy out to
infinity. In nucleation, the most common fluctuations are as close to
thermal equilibrium overall as possible given whatever arbitrary
criteria are provided for labeling a fluctuation a "Boltzmann brain".
Theoretically a Boltzmann brain can also form, albeit again with a
tiny probability, at any time during the matter-dominated early
universe.
Modern reactions to the Boltzmann brain problem
The
consensus amongst cosmologists is that some yet to be revealed error is
hinted at by the surprising calculation that Boltzmann brains should
vastly outnumber normal human brains. Sean Carroll states "We're not arguing that Boltzmann Brains exist—we're trying to avoid them."
Carroll has stated that the hypothesis of being a Boltzmann brain
results in "cognitive instability". Because, he argues, it would take
longer than the current age of the universe for a brain to form, and yet
it thinks that it observes that it exists in a younger universe, this
shows that memories and reasoning processes would be untrustworthy if it
were indeed a Boltzmann brain. Seth Lloyd has stated "they fail the Monty Python test: Stop that! That's too silly!" A New Scientist
journalist summarizes that "the starting point for our understanding of
the universe and its behavior is that humans, not disembodied brains,
are typical observers."
Some argue that brains produced via quantum fluctuation, and maybe even brains produced via nucleation in the de Sitter vacuum,
do not count as observers. Quantum fluctuations are easier to exclude
than nucleated brains, as quantum fluctuations can more easily be
targeted by straightforward criteria (such as their lack of interaction
with the environment at infinity).
Some cosmologists believe that a better understanding of the degrees of freedom in the quantum vacuum of holographic string theory can solve the Boltzmann brain problem.
Brian Greene
states: "I am confident that I am not a Boltzmann brain. However, we
want our theories to similarly concur that we are not Boltzmann brains,
but so far it has proved surprisingly difficult for them to do so."
In single-Universe scenarios
In
a single de Sitter Universe with a cosmological constant, and starting
from any finite spatial slice, the number of "normal" observers is
finite and bounded by the heat death of the Universe. If the Universe
lasts forever, the number of nucleated Boltzmann brains is, in most
models, infinite; cosmologists such as Alan Guth worry that this would make it seem "infinitely unlikely for us to be normal brains". One caveat is that if the Universe is a false vacuum that locally decays into a Minkowski or a Big Crunch-bound anti-de Sitter space
in less than 20 billion years, then infinite Boltzmann nucleation is
avoided. (If the average local false vacuum decay rate is over 20
billion years, Boltzmann brain nucleation is still infinite, as the
Universe increases in size faster than local vacuum collapses destroy
the portions of the Universe within the collapses' future light cones). Proposed hypothetical mechanisms to destroy the universe within that timeframe range from superheavy gravitinos to a heavier-than-observed top quark triggering "death by Higgs".
If no cosmological constant exists, and if the presently observed vacuum energy is from quintessence that will eventually completely dissipate, then infinite Boltzmann nucleation is also avoided.
In eternal inflation
One class of solutions to the Boltzmann brain problem makes use of differing approaches to the measure problem in cosmology: in infinitemultiverse
theories, the ratio of normal observers to Boltzmann brains depends on
how infinite limits are taken. Measures might be chosen to avoid
appreciable fractions of Boltzmann brains.
Unlike the single-universe case, one challenge in finding a global
solution in eternal inflation is that all possible string landscapes
must be summed over; in some measures, having even a small fraction of
universes infested with Boltzmann brains causes the measure of the
multiverse as a whole to be dominated by Boltzmann brains.
The measurement problem in cosmology also grapples with the ratio
of normal observers to abnormally early observers. In measures such as
the proper time
measure that suffer from an extreme "youngness" problem, the typical
observer is a "Boltzmann baby" formed by rare fluctuation in an
extremely hot, early universe.
Identifying whether oneself is a Boltzmann observer
In
Boltzmann brain scenarios, the ratio of Boltzmann brains to "normal
observers" is astronomically large. Almost any relevant subset of
Boltzmann brains, such as "brains embedded within functioning bodies",
"observers who believe they are perceiving 3 K microwave background
radiation through telescopes", "observers who have a memory of coherent
experiences", or "observers who have the same series of experiences as
me", also vastly outnumber "normal observers". Therefore, under most
models of consciousness, it is unclear that one can reliably conclude
that oneself is not such a "Boltzmann observer", in a case where
Boltzmann brains dominate the Universe. Even under "content externalism"
models of consciousness, Boltzmann observers living in a consistent
Earth-sized fluctuation over the course of the past several years
outnumber the "normal observers" spawned before a Universe's "heat
death".
As stated earlier, most Boltzmann brains have "abnormal"
experiences; Feynman has pointed out that, if one knows oneself to be a
typical Boltzmann brain, one does not expect "normal" observations to
continue in the future.
In other words, in a Boltzmann-dominated Universe, most Boltzmann
brains have "abnormal" experiences, but most observers with only
"normal" experiences are Boltzmann brains, due to the overwhelming
vastness of the population of Boltzmann brains in such a Universe.
The law of truly large numbers (a statisticaladage), attributed to Persi Diaconis and Frederick Mosteller,
states that with a large enough number of samples, any outrageous (i.e.
unlikely in any single sample) thing is likely to be observed.
Because we never find it notable when likely events occur, we highlight
unlikely events and notice them more. The law is often used to falsify
different pseudo-scientific claims, as such it and its use are sometimes criticized by fringe scientists.
The law is meant to make a statement about probabilities
and statistical significance: in large enough masses of statistical
data, even minuscule fluctuations attain statistical significance. Thus
in truly large numbers of observations, it is paradoxically easy to find
significant correlations, in large numbers, which still do not lead to
causal theories (see: spurious correlation), and which by their collective number, might lead to obfuscation as well.
The law can be rephrased as "large numbers also deceive", something which is counter-intuitive to a descriptive statistician. More concretely, skeptic Penn Jillette has said, "Million-to-one odds happen eight times a day in New York" (population about 8,000,000).
Example
For
a simplified example of the law, assume that a given event happens with
a probability for its occurrence of 0.1%, within a single trial. Then,
the probability that this so-called unlikely event does not happen (improbability) in a single trial is 99.9% (0.999).
Already for a sample of 1000 independent trials, however, the probability that the event does not happen in any of them, even once (improbability), is only 0.9991000 ≈ 0.3677 = 36.77%. Then, the probability that the event does happen, at least once, in 1000 trials is 1 − 0.9991000 ≈ 0.6323
or 63.23%. This means that this "unlikely event" has a probability of
63.23% of happening if 1000 independent trials are conducted, or over
99.9% for 10,000 trials.
The probability that it happens at least once in 10,000 trials is 1 − 0.99910000 ≈ 0.99995 = 99.995%.
In other words, a highly unlikely event, given enough trials with some
fixed number of draws per trial, is even more likely to occur.
This calculation can be generalized, formalized to use in mathematical proof that: "the
probability c for the less likely event X to happen in N independent
trials can become arbitrarily near to 1, no matter how small the
probability a of the event X in one single trial is, provided that N is
truly large."
In criticism of pseudoscience
The law comes up in criticism of pseudoscience and is sometimes called the Jeane Dixon effect (see also Postdiction).
It holds that the more predictions a psychic makes, the better the odds
that one of them will "hit". Thus, if one comes true, the psychic
expects us to forget the vast majority that did not happen (confirmation bias). Humans can be susceptible to this fallacy.
Another similar (to some degree) manifestation of the law can be found in gambling, where gamblers tend to remember their wins and forget their losses,
even if the latter far outnumbers the former (though depending on a
particular person, the opposite may also be truth when they think they
need more analysis of their losses to achieve fine tuning of their
playing system).
Mikal Aasved links it with "selective memory bias", allowing gamblers
to mentally distance themselves from the consequences of their gambling
by holding an inflated view of their real winnings (or losses in the
opposite case - "selective memory bias in either direction").
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare. In fact, the monkey would almost surely type every possible finite text an infinite number of times. However, the probability that monkeys filling the entire observable universe would type a single complete work, such as Shakespeare's Hamlet, is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely
low (but technically not zero). The theorem can be generalized to state
that any sequence of events which has a non-zero probability of
happening, at least as long as it hasn't occurred, will almost certainly
eventually occur.
In this context, "almost surely" is a mathematical term with a precise meaning, and the "monkey" is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. One of the earliest instances of the use of the "monkey metaphor" is that of French mathematician Émile Borel in 1913, but the first instance may have been even earlier.
Variants of the theorem include multiple and even infinitely many
typists, and the target text varies between an entire library and a
single sentence. Jorge Luis Borges traced the history of this idea from Aristotle's On Generation and Corruption and Cicero's De Natura Deorum (On the Nature of the Gods), through Blaise Pascal and Jonathan Swift, up to modern statements with their iconic simians and typewriters. In the early 20th century, Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics.
Solution
Direct proof
There is a straightforward proof of this theorem. As an introduction, recall that if two events are statistically independent,
then the probability of both happening equals the product of the
probabilities of each one happening independently. For example, if the
chance of rain in Moscow on a particular day in the future is 0.4 and the chance of an earthquake in San Francisco on any particular day is 0.00003, then the chance of both happening on the same day is 0.4 × 0.00003 = 0.000012, assuming that they are indeed independent.
Suppose the typewriter has 50 keys, and the word to be typed is banana.
If the keys are pressed randomly and independently, it means that each
key has an equal chance of being pressed. Then, the chance that the
first letter typed is 'b' is 1/50, and the chance that the second letter
typed is 'a' is also 1/50, and so on. Therefore, the chance of the
first six letters spelling banana is
From the above, the chance of not typing banana in a given block of 6 letters is 1 − (1/50)6. Because each block is typed independently, the chance Xn of not typing banana in any of the first n blocks of 6 letters is
As n grows, Xn gets smaller. For n = 1 million, Xn is roughly 0.9999, but for n = 10 billion Xn is roughly 0.53 and for n = 100 billion it is roughly 0.0017. As n approaches infinity, the probability Xnapproaches zero; that is, by making n large enough, Xn can be made as small as is desired, and the chance of typing banana approaches 100%.
The same argument shows why at least one of infinitely many
monkeys will produce a text as quickly as it would be produced by a
perfectly accurate human typist copying it from the original. In this
case Xn = (1 − (1/50)6)n where Xn represents the probability that none of the first n monkeys types banana
correctly on their first try. When we consider 100 billion monkeys, the
probability falls to 0.17%, and as the number of monkeys n increases, the value of Xn – the probability of the monkeys failing to reproduce the given text – approaches zero arbitrarily closely. The limit, for n going to infinity, is zero. So the probability of the word banana appearing at some point in an infinite sequence of keystrokes is equal to one.
Infinite strings
This can be stated more generally and compactly in terms of strings, which are sequences of characters chosen from some finite alphabet:
Given an infinite string where each character is chosen uniformly at random, any given finite string almost surely occurs as a substring at some position.
Given an infinite sequence of infinite strings, where each character
of each string is chosen uniformly at random, any given finite string
almost surely occurs as a prefix of one of these strings.
Both follow easily from the second Borel–Cantelli lemma. For the second theorem, let Ek be the event that the kth string begins with the given text. Because this has some fixed nonzero probability p of occurring, the Ek are independent, and the below sum diverges,
the probability that infinitely many of the Ek
occur is 1. The first theorem is shown similarly; one can divide the
random string into nonoverlapping blocks matching the size of the
desired text, and make Ek the event where the kth block equals the desired string.
Probabilities
However, for physically meaningful numbers of monkeys typing for
physically meaningful lengths of time the results are reversed. If there
were as many monkeys as there are atoms in the observable universe
typing extremely fast for trillions of times the life of the universe,
the probability of the monkeys replicating even a single page of Shakespeare is unfathomably small.
Ignoring punctuation, spacing, and capitalization, a monkey
typing letters uniformly at random has a chance of one in 26 of
correctly typing the first letter of Hamlet. It has a chance of one in 676 (26 × 26) of typing the first two letters. Because the probability shrinks exponentially, at 20 letters it already has only a chance of one in 2620 = 19,928,148,895,209,409,152,340,197,376 (almost 2 × 1028). In the case of the entire text of Hamlet, the probabilities are so vanishingly small as to be inconceivable. The text of Hamlet contains approximately 130,000 letters. Thus there is a probability of one in 3.4 × 10183,946
to get the text right at the first trial. The average number of letters
that needs to be typed until the text appears is also 3.4 × 10183,946, or including punctuation, 4.4 × 10360,783.
Even if every proton in the observable universe were a monkey with a typewriter, typing from the Big Bang until the end of the universe (when protons might no longer exist), they would still need a far greater amount of time – more than three hundred and sixty thousand orders of magnitude longer – to have even a 1 in 10500 chance of success. To put it another way, for a one in a trillion chance of success, there would need to be 10360,641 observable universes made of protonic monkeys. As Kittel and Kroemer put it in their textbook on thermodynamics, the field whose statistical foundations motivated the first known expositions of typing monkeys, "The probability of Hamlet
is therefore zero in any operational sense of an event ...", and the
statement that the monkeys must eventually succeed "gives a misleading
conclusion about very, very large numbers."
In fact there is less than a one in a trillion chance of success
that such a universe made of monkeys could type any particular document a
mere 79 characters long.
Almost surely
The probability that an infinite randomly generated string of text
will contain a particular finite substring is 1. However, this does not
mean the substring's absence is "impossible", despite the absence having
a prior probability of 0. For example, the immortal monkey could
randomly type G as its first letter, G as its second, and G as every
single letter thereafter, producing an infinite string of Gs; at no
point must the monkey be "compelled" to type anything else. (To assume
otherwise implies the gambler's fallacy.)
However long a randomly generated finite string is, there is a small
but nonzero chance that it will turn out to consist of the same
character repeated throughout; this chance approaches zero as the
string's length approaches infinity. There is nothing special about such
a monotonous sequence except that it is easy to describe; the same fact
applies to any nameable specific sequence, such as "RGRGRG" repeated
forever, or "a-b-aa-bb-aaa-bbb-...", or "Three, Six, Nine, Twelve…".
If the hypothetical monkey has a typewriter with 90 equally
likely keys that include numerals and punctuation, then the first typed
keys might be "3.14" (the first three digits of pi) with a probability of (1/90)4,
which is 1/65,610,000. Equally probable is any other string of four
characters allowed by the typewriter, such as "GGGG", "mATh", or "q%8e".
The probability that 100 randomly typed keys will consist of the first
99 digits of pi (including the separator key), or any other particular sequence of that length, is much lower: (1/90)100. If the monkey's allotted length of text is infinite, the chance of typing only the digits of pi is 0, which is just as possible (mathematically probable) as typing nothing but Gs (also probability 0).
The same applies to the event of typing a particular version of Hamlet followed by endless copies of itself; or Hamlet immediately followed by all the digits of pi; these specific strings are equally infinite in length, they are not prohibited by the terms of the thought problem, and they each have a prior probability of 0. In fact, any particular infinite sequence the immortal monkey types will have had a prior probability of 0, even though the monkey must type something.
This is an extension of the principle that a finite string of random text has a lower and lower probability of being
a particular string the longer it is (though all specific strings are
equally unlikely). This probability approaches 0 as the string
approaches infinity. Thus, the probability of the monkey typing an
endlessly long string, such as all of the digits of pi in order, on a
90-key keyboard is (1/90)∞ which equals (1/∞) which is essentially 0. At the same time, the probability that the sequence contains
a particular subsequence (such as the word MONKEY, or the 12th through
999th digits of pi, or a version of the King James Bible) increases as
the total string increases. This probability approaches 1 as the total
string approaches infinity, and thus the original theorem is correct.
Correspondence between strings and numbers
In a simplification of the thought experiment, the monkey could have a
typewriter with just two keys: 1 and 0. The infinitely long string
thusly produced would correspond to the binary digits of a particular real number
between 0 and 1. A countably infinite set of possible strings end in
infinite repetitions, which means the corresponding real number is rational.
Examples include the strings corresponding to one-third (010101...),
five-sixths (11010101...) and five-eighths (1010000...). Only a subset
of such real number strings (albeit a countably infinite subset)
contains the entirety of Hamlet (assuming that the text is subjected to a numerical encoding, such as ASCII).
Meanwhile, there is an uncountably infinite set of strings which do not end in such repetition; these correspond to the irrational numbers. These can be sorted into two uncountably infinite subsets: those which contain Hamlet and those which do not. However, the "largest" subset of all the real numbers are those which not only contain Hamlet,
but which contain every other possible string of any length, and with
equal distribution of such strings. These irrational numbers are called normal.
Because almost all numbers are normal, almost all possible strings
contain all possible finite substrings. Hence, the probability of the
monkey typing a normal number is 1. The same principles apply regardless
of the number of keys from which the monkey can choose; a 90-key
keyboard can be seen as a generator of numbers written in base 90.
History
Statistical mechanics
In one of the forms in which probabilists now know this theorem, with its "dactylographic" [i.e., typewriting] monkeys (French: singes dactylographes; the French word singe covers both the monkeys and the apes), appeared in Émile Borel's 1913 article "Mécanique Statistique et Irréversibilité" (Statistical mechanics and irreversibility), and in his book "Le Hasard" in 1914.
His "monkeys" are not actual monkeys; rather, they are a metaphor for
an imaginary way to produce a large, random sequence of letters. Borel
said that if a million monkeys typed ten hours a day, it was extremely
unlikely that their output would exactly equal all the books of the
richest libraries of the world; and yet, in comparison, it was even more
unlikely that the laws of statistical mechanics would ever be violated,
even briefly.
The physicist Arthur Eddington drew on Borel's image further in The Nature of the Physical World (1928), writing:
If I let my fingers wander idly
over the keys of a typewriter it might happen that my screed made an
intelligible sentence. If an army of monkeys were strumming on
typewriters they might write all the books in the British Museum. The
chance of their doing so is decidedly more favourable than the chance of
the molecules returning to one half of the vessel.
These images invite the reader to consider the incredible
improbability of a large but finite number of monkeys working for a
large but finite amount of time producing a significant work, and
compare this with the even greater improbability of certain physical
events. Any physical process that is even less likely than such monkeys'
success is effectively impossible, and it may safely be said that such a
process will never happen.
It is clear from the context that Eddington is not suggesting that the
probability of this happening is worthy of serious consideration. On
the contrary, it was a rhetorical illustration of the fact that below
certain levels of probability, the term improbable is functionally equivalent to impossible.
Origins and "The Total Library"
In a 1939 essay entitled "The Total Library", Argentine writer Jorge Luis Borges traced the infinite-monkey concept back to Aristotle's Metaphysics. Explaining the views of Leucippus,
who held that the world arose through the random combination of atoms,
Aristotle notes that the atoms themselves are homogeneous and their
possible arrangements only differ in shape, position and ordering. In On Generation and Corruption, the Greek philosopher compares this to the way that a tragedy and a comedy consist of the same "atoms", i.e., alphabetic characters. Three centuries later, Cicero's De natura deorum (On the Nature of the Gods) argued against the atomist worldview:
He who believes this may as well
believe that if a great quantity of the one-and-twenty letters, composed
either of gold or any other matter, were thrown upon the ground, they
would fall into such order as legibly to form the Annals of Ennius. I doubt whether fortune could make a single verse of them.
Borges follows the history of this argument through Blaise Pascal and Jonathan Swift,
then observes that in his own time, the vocabulary had changed. By
1939, the idiom was "that a half-dozen monkeys provided with typewriters
would, in a few eternities, produce all the books in the British
Museum." (To which Borges adds, "Strictly speaking, one immortal monkey
would suffice.") Borges then imagines the contents of the Total Library
which this enterprise would produce if carried to its fullest extreme:
Everything would be in its blind volumes. Everything: the detailed history of the future, Aeschylus' The Egyptians,
the exact number of times that the waters of the Ganges have reflected
the flight of a falcon, the secret and true nature of Rome, the
encyclopedia Novalis would have constructed, my dreams and half-dreams
at dawn on August 14, 1934, the proof of Pierre Fermat's theorem, the unwritten chapters of Edwin Drood, those same chapters translated into the language spoken by the Garamantes, the paradoxes Berkeley invented concerning Time but didn't publish, Urizen's books of iron, the premature epiphanies of Stephen Dedalus, which would be meaningless before a cycle of a thousand years, the Gnostic Gospel of Basilides,
the song the sirens sang, the complete catalog of the Library, the
proof of the inaccuracy of that catalog. Everything: but for every
sensible line or accurate fact there would be millions of meaningless
cacophonies, verbal farragoes, and babblings. Everything: but all the
generations of mankind could pass before the dizzying shelves – shelves
that obliterate the day and on which chaos lies – ever reward them with a
tolerable page.
Borges' total library concept was the main theme of his widely read 1941 short story "The Library of Babel",
which describes an unimaginably vast library consisting of interlocking
hexagonal chambers, together containing every possible volume that
could be composed from the letters of the alphabet and some punctuation
characters.
Actual monkeys
In 2002, lecturers and students from the University of Plymouth MediaLab Arts course used a £2,000 grant from the Arts Council to study the literary output of real monkeys. They left a computer keyboard in the enclosure of six Celebes crested macaques in Paignton Zoo in Devon, England for a month, with a radio link to broadcast the results on a website.
Not only did the monkeys produce nothing but five total pages largely consisting of the letter 'S',
the lead male began striking the keyboard with a stone, and other
monkeys followed by soiling it. Mike Phillips, director of the
university's Institute of Digital Arts and Technology (i-DAT), said that
the artist-funded project was primarily performance art, and they had
learned "an awful lot" from it. He concluded that monkeys "are not
random generators. They're more complex than that. ... They were quite
interested in the screen, and they saw that when they typed a letter,
something happened. There was a level of intention there."
The full text created by the monkeys is available to read "here"(PDF). Archived from the original(PDF) on 2009-03-18.
In his 1931 book The Mysterious Universe, Eddington's rival James Jeans attributed the monkey parable to a "Huxley", presumably meaning Thomas Henry Huxley. This attribution is incorrect. Today, it is sometimes further reported that Huxley applied the example in a now-legendary debate over Charles Darwin's On the Origin of Species with the Anglican Bishop of Oxford, Samuel Wilberforce, held at a meeting of the British Association for the Advancement of Science
at Oxford on 30 June 1860. This story suffers not only from a lack of
evidence, but the fact that in 1860 the typewriter itself had yet to
emerge.
Despite the original mix-up, monkey-and-typewriter arguments are now common in arguments over evolution. As an example of Christian apologetics Doug Powell argued that even if a monkey accidentally types the letters of Hamlet, it has failed to produce Hamlet
because it lacked the intention to communicate. His parallel
implication is that natural laws could not produce the information
content in DNA. A more common argument is represented by Reverend John F. MacArthur,
who claimed that the genetic mutations necessary to produce a tapeworm
from an amoeba are as unlikely as a monkey typing Hamlet's soliloquy,
and hence the odds against the evolution of all life are impossible to
overcome.
Evolutionary biologistRichard Dawkins employs the typing monkey concept in his book The Blind Watchmaker to demonstrate the ability of natural selection to produce biological complexity out of random mutations. In a simulation experiment Dawkins has his weasel program produce the Hamlet phrase METHINKS IT IS LIKE A WEASEL,
starting from a randomly typed parent, by "breeding" subsequent
generations and always choosing the closest match from progeny that are
copies of the parent, with random mutations. The chance of the target
phrase appearing in a single step is extremely small, yet Dawkins showed
that it could be produced rapidly (in about 40 generations) using
cumulative selection of phrases. The random choices furnish raw
material, while cumulative selection imparts information. As Dawkins
acknowledges, however, the weasel program is an imperfect analogy for
evolution, as "offspring" phrases were selected "according to the
criterion of resemblance to a distant ideal target." In
contrast, Dawkins affirms, evolution has no long-term plans and does not
progress toward some distant goal (such as humans). The weasel program
is instead meant to illustrate the difference between non-random cumulative selection, and random single-step selection. In terms of the typing monkey analogy, this means that Romeo and Juliet could be produced relatively quickly if placed under the constraints of a nonrandom, Darwinian-type selection because the fitness function
will tend to preserve in place any letters that happen to match the
target text, improving each successive generation of typing monkeys.
A different avenue for exploring the analogy between evolution
and an unconstrained monkey lies in the problem that the monkey types
only one letter at a time, independently of the other letters. Hugh
Petrie argues that a more sophisticated setup is required, in his case
not for biological evolution but the evolution of ideas:
In order to get the proper analogy,
we would have to equip the monkey with a more complex typewriter. It
would have to include whole Elizabethan sentences and thoughts. It would
have to include Elizabethan beliefs about human action patterns and the
causes, Elizabethan morality and science, and linguistic patterns for
expressing these. It would probably even have to include an account of
the sorts of experiences which shaped Shakespeare's belief structure as a
particular example of an Elizabethan. Then, perhaps, we might allow the
monkey to play with such a typewriter and produce variants, but the
impossibility of obtaining a Shakespearean play is no longer obvious.
What is varied really does encapsulate a great deal of already-achieved
knowledge.
James W. Valentine,
while admitting that the classic monkey's task is impossible, finds
that there is a worthwhile analogy between written English and the metazoan
genome in this other sense: both have "combinatorial, hierarchical
structures" that greatly constrain the immense number of combinations at
the alphabet level.
Literary theory
R. G. Collingwood argued in 1938 that art cannot be produced by accident, and wrote as a sarcastic aside to his critics,
... some ... have denied this
proposition, pointing out that if a monkey played with a typewriter ...
he would produce ... the complete text of Shakespeare. Any reader who
has nothing to do can amuse himself by calculating how long it would
take for the probability to be worth betting on. But the interest of the
suggestion lies in the revelation of the mental state of a person who
can identify the 'works' of Shakespeare with the series of letters
printed on the pages of a book ...
What Menard wrote is simply another
inscription of the text. Any of us can do the same, as can printing
presses and photocopiers. Indeed, we are told, if infinitely many
monkeys ... one would eventually produce a replica of the text. That
replica, we maintain, would be as much an instance of the work, Don Quixote, as Cervantes' manuscript, Menard's manuscript, and each copy of the book that ever has been or will be printed.
In another writing, Goodman elaborates, "That the monkey may be
supposed to have produced his copy randomly makes no difference. It is
the same text, and it is open to all the same interpretations. ..." Gérard Genette dismisses Goodman's argument as begging the question.
For Jorge J. E. Gracia, the question of the identity of texts leads to a different question, that of author. If a monkey is capable of typing Hamlet,
despite having no intention of meaning and therefore disqualifying
itself as an author, then it appears that texts do not require authors.
Possible solutions include saying that whoever finds the text and
identifies it as Hamlet is the author; or that Shakespeare is the
author, the monkey his agent, and the finder merely a user of the text.
These solutions have their own difficulties, in that the text appears
to have a meaning separate from the other agents: What if the monkey
operates before Shakespeare is born, or if Shakespeare is never born, or
if no one ever finds the monkey's typescript?
Random document generation
The theorem concerns a thought experiment
which cannot be fully carried out in practice, since it is predicted to
require prohibitive amounts of time and resources. Nonetheless, it has
inspired efforts in finite random text generation.
One computer program run by Dan Oliver of Scottsdale, Arizona, according to an article in The New Yorker,
came up with a result on 4 August 2004: After the group had worked for
42,162,500,000 billion billion monkey-years, one of the "monkeys" typed,
"VALENTINE. Cease toIdor:eFLP0FRjWK78aXzVOwm)-‘;8.t" The
first 19 letters of this sequence can be found in "The Two Gentlemen of
Verona". Other teams have reproduced 18 characters from "Timon of
Athens", 17 from "Troilus and Cressida", and 16 from "Richard II".
A website entitled The Monkey Shakespeare Simulator, launched on 1 July 2003, contained a Java applet
that simulated a large population of monkeys typing randomly, with the
stated intention of seeing how long it takes the virtual monkeys to
produce a complete Shakespearean play from beginning to end. For
example, it produced this partial line from Henry IV, Part 2, reporting that it took "2,737,850 million billion billion billion monkey-years" to reach 24 matching characters:
RUMOUR. Open your ears; 9r"5j5&?OWTY Z0d
Due to processing power limitations, the program used a probabilistic model (by using a random number generator
or RNG) instead of actually generating random text and comparing it to
Shakespeare. When the simulator "detected a match" (that is, the RNG
generated a certain value or a value within a certain range), the
simulator simulated the match by generating matched text.
More sophisticated methods are used in practice for natural language generation.
If instead of simply generating random characters one restricts the
generator to a meaningful vocabulary and conservatively following
grammar rules, like using a context-free grammar,
then a random document generated this way can even fool some humans (at
least on a cursory reading) as shown in the experiments with SCIgen, snarXiv, and the Postmodernism Generator.
In February 2019, the OpenAI group published the Generative Pre-trained Transformer 2 (GPT-2) artificial intelligence to GitHub,
which is able to produce a fully plausible news article given a two
sentence input from a human hand. The AI was so effective that instead
of publishing the full code, the group chose to publish a scaled-back
version and released a statement regarding "concerns about large language models being used to generate deceptive, biased, or abusive language at scale."
Testing of random-number generators
Questions about the statistics describing how often an ideal monkey is expected to type certain strings translate into practical tests for random-number generators; these range from the simple to the "quite sophisticated". Computer-science professors George Marsaglia and Arif Zaman report that they used to call one such category of tests "overlapping m-tuple
tests" in lectures, since they concern overlapping m-tuples of
successive elements in a random sequence. But they found that calling
them "monkey tests" helped to motivate the idea with students. They
published a report on the class of tests and their results for various
RNGs in 1993.
In popular culture
The infinite monkey theorem and its associated imagery is considered a
popular and proverbial illustration of the mathematics of probability,
widely known to the general public because of its transmission through
popular culture rather than through formal education.
This is helped by the innate humor stemming from the image of literal
monkeys rattling away on a set of typewriters, and is a popular visual
gag.
A quotation attributed
to a 1996 speech by Robert Wilensky stated, "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."
The enduring, widespread popularity of the theorem was noted in
the introduction to a 2001 paper, "Monkeys, Typewriters and Networks:
The Internet in the Light of the Theory of Accidental Excellence". In 2002, an article in The Washington Post
said, "Plenty of people have had fun with the famous notion that an
infinite number of monkeys with an infinite number of typewriters and an
infinite amount of time could eventually write the works of
Shakespeare". In 2003, the previously mentioned Arts Council funded experiment involving real monkeys and a computer keyboard received widespread press coverage. In 2007, the theorem was listed by Wired magazine in a list of eight classic thought experiments.
Sir Isaac Newton, among other leaders in the scientific revolution, including René Descartes,
upheld "that the physical laws he had uncovered revealed the mechanical
perfection of the workings of the universe to be akin to a watch,
wherein the watchmaker is God."
The 1859 publication of Charles Darwin's theory of natural selection put forward an explanation for complexity and adaptation, which reflects scientific consensus on the origins of biological diversity. This provides a counter-argument to the watchmaker analogy: for example, the evolutionary biologistRichard Dawkins referred to the analogy in his 1986 book The Blind Watchmaker giving his explanation of evolution. Others, however, consider the watchmaker analogy to be compatible with evolutionary creation, opining that the two concepts are not mutually exclusive. In the 19th century, deists, who championed the watchmaker analogy, held that Darwin's theory fit with "the principle of uniformitarianism—the idea that all processes in the world occur now as they have in the past" and that deistic evolution "provided an explanatory framework for understanding species variation in a mechanical universe."
The scientific revolution
"nurtured a growing awareness" that "there were universal laws of
nature at work that ordered the movement of the world and its parts." Amos Yong
writes that in "astronomy, the Copernican revolution regarding the
heliocentrism of the solar system, Johannes Kepler's (1571–1630) three
laws of planetary motion, and Isaac Newton's (1642–1727) law of
universal gravitation—laws of gravitation and of motion, and notions of
absolute space and time—all combined to establish the regularities of
heavenly and earthly bodies".
Simultaneously, the development of machine technology and the emergence of the mechanical philosophy
encouraged mechanical imagery unlikely to have come to the fore in previous ages.
With such a backdrop, "deists suggested the watchmaker analogy: just as
watches are set in motion by watchmakers, after which they operate
according to their pre-established mechanisms, so also was the world
begun by the God as creator, after which it and all its parts have
operated according to their pre-established natural laws. With these
laws perfectly in place, events have unfolded according to the
prescribed plan." For Sir Isaac Newton, "the regular motion of the planets made it reasonable to believe in the continued existence of God".
Newton also upheld the idea that "like a watchmaker, God was forced to
intervene in the universe and tinker with the mechanism from time to
time to ensure that it continued operating in good working order".
Similar to Newton, René Descartes
(1596–1650) speculated on "the cosmos as a great time machine operating
according to fixed laws, a watch created and wound up by the great
watchmaker".
William Paley
Watches and timepieces have been used as examples of complicated technology in philosophical discussions. For example, Cicero, Voltaire and René Descartes all used timepieces in arguments regarding purpose. The watchmaker analogy, as described here, was used by Bernard le Bovier de Fontenelle in 1686, but was most famously formulated by Paley.
In crossing a heath, suppose I
pitched my foot against a stone, and were asked how the stone came to be
there; I might possibly answer, that, for anything I knew to the
contrary, it had lain there forever: nor would it perhaps be very easy
to show the absurdity of this answer. But suppose I had found a watch
upon the ground, and it should be inquired how the watch happened to be
in that place; I should hardly think of the answer I had before given,
that for anything I knew, the watch might have always been there. ...
There must have existed, at some time, and at some place or other, an
artificer or artificers, who formed [the watch] for the purpose which we
find it actually to answer; who comprehended its construction, and
designed its use. ... Every indication of contrivance, every
manifestation of design, which existed in the watch, exists in the works
of nature; with the difference, on the side of nature, of being greater
or more, and that in a degree which exceeds all computation.
— William Paley, Natural Theology (1802)
Paley went on to argue that the complex structures of living things
and the remarkable adaptations of plants and animals required an
intelligent designer. He believed the natural world was the creation of
God and showed the nature of the creator. According to Paley, God had
carefully designed "even the most humble and insignificant organisms"
and all of their minute features (such as the wings and antennae of earwigs). He believed, therefore, that God must care even more for humanity.
Paley recognised that there is great suffering in nature and
nature appears to be indifferent to pain. His way of reconciling that
with his belief in a benevolent God was to assume that life had more pleasure than pain.
As a side note, a charge of wholesale plagiarism from this book was brought against Paley in The Athenaeum
for 1848, but the famous illustration of the watch was not peculiar to
Nieuwentyt and had been used by many others before either Paley or
Nieuwentyt. But the charge of plagiarism was based on more similarities.
For example, Niewentyt wrote "in the middle of a Sandy down, or in a
desart {sic} and solitary Place, where few People are used to pass, any
one should find a Watch ..."
Joseph Butler
William Paley taught the works of Joseph Butler
and appears to have built on Butler's 1736 design arguments of
inferring a designer from evidence of design. Butler noted:
"As the manifold Appearances of Design and of final Causes, in the
Constitution of the World, prove it to be the Work of an intelligent
Mind ... The appearances of Design and of final Causes in the constitution of nature as really prove this acting agent to be an intelligent Designer... ten thousand Instances of Design, cannot but prove a Designer.".
Jean-Jacques Rousseau
Rousseau also mentioned the watchmaker theory. He wrote the following in his 1762 book, Emile:
I am like a man who sees the works of a watch for the first time; he is
never weary of admiring the mechanism, though he does not know the use
of the instrument and has never seen its face. I do not know what this
is for, says he, but I see that each part of it is fitted to the rest, I
admire the workman in the details of his work, and I am quite certain
that all these wheels only work together in this fashion for some common
end which I cannot perceive. Let us compare the special ends, the
means, the ordered relations of every kind, then let us listen to the
inner voice of feeling; what healthy mind can reject its evidence?
Unless the eyes are blinded by prejudices, can they fail to see that the
visible order of the universe proclaims a supreme intelligence? What
sophisms must be brought together before we fail to understand the
harmony of existence and the wonderful co-operation of every part for
the maintenance of the rest?
Criticism
David Hume
Before Paley published his book, David Hume
(1711–1776) had already put forward a number of philosophical
criticisms of the watch analogy, and to some extent anticipated the
concept of natural selection. His criticisms can be separated into three major distinctions:
His first objection is that we have no experience of
world-making. Hume highlighted the fact that everything we claim to know
the cause of, we have derived the inductions from previous experiences
of similar objects being created or seen the object itself being created
ourselves. For example, with a watch, we know it has to be created by a
watch-maker because we can observe it being made and compare it to the
making of other similar watches or objects to deduce they have alike
causes in their creation. However, he argues that we have no experience
of the universe's creation or any other universe's creations to compare
our own universe to and never will; therefore, it would be illogical to
infer that our universe has been created by an intelligent designer in
the same way that a watch has.
The second criticism that Hume offers is about the form of the
argument as an analogy in itself. An analogical argument claims that
because object X (a watch) is like object Y (the universe) in one
respect, both are therefore probably alike in another, hidden, respect
(their cause, having to be created by an intelligent designer). He
points out that for an argument from analogy to be successful, the two
things that are being compared have to have an adequate number of
similarities that are relevant to the respect that are analogised. For
example, a kitten and a lion may be very similar in many respects, but
just because a lion makes a "roar", it would not be correct to infer a
kitten also "roars": the similarities between the two objects being not
enough and the degree of relevance to what sound they make being not
relevant enough. Hume then argues that the universe and a watch also do
not have enough relevant or close similarities to infer that they were
both created the same way. For example, the universe is made of organic
natural material, but the watch is made of artificial mechanic
materials. He claims that in the same respect, the universe could be
argued to be more analogous to something more organic such as a
vegetable (which we can observe for ourselves does not need a 'designer'
or a 'watchmaker' to be created). Although he admits the analogy of a
universe to a vegetable to seem ridiculous, he says that it is just as
ridiculous to analogize the universe with a watch.
The third criticism that Hume offers is that even if the argument
did give evidence for a designer; it still gives no evidence for the
traditional 'omnipotent', 'benevolent' (all-powerful and all-loving) God
of traditional Christian theism. One of the main assumptions of Paley's
argument is that 'like effects have like causes'; or that machines
(like the watch) and the universe have similar features of design and so
both also have the same cause of their existence: they must both have
an intelligent designer. However, Hume points out that what Paley does
not comprehend is to what extent 'like causes' extend: how similar the
creation of a universe is to the creation of a watch. Instead, Paley
moves straight to the conclusion that this designer of the universe is
the 'God' he believes in of traditional Christianity. Hume, however
takes the idea of 'like causes' and points out some potential
absurdities in how far the 'likeness' of these causes could extend to if
the argument were taken further as to explain this. One example that he
uses is how a machine or a watch is usually designed by a whole team of
people rather than just one person. Surely, if we are analogizing the
two in this way, it would point to there being a group of gods who
created the universe, not just a single being. Another example he uses
is that complex machines are usually the result of many years of trial
and error with every new machine being an improved version of the last.
Also by analogy of the two, would that not hint that the universe could
also have been just one of many of God's 'trials' and that there are
much better universes out there? However, if that were taken to be true,
surely the 'creator' of it all would not be 'all loving' and 'all
powerful' if they had to carry out the process of 'trial and error' when
creating the universe?
Hume also points out there is still a possibility that the
universe could have been created by random chance but still show
evidence of design as the universe is eternal and would have an infinite
amount of time to be able to form a universe so complex and ordered as
our own. He called that the 'Epicurean hypothesis'. It argued that when
the universe was first created, the universe was random and chaotic, but
if the universe is eternal, over an unlimited period of time, natural
forces could have naturally 'evolved' by random particles coming
together over time into the incredibly ordered system we can observe
today without the need of an intelligent designer as an explanation.
The last objection that he makes draws on the widely discussed problem of evil.
He argues that all the daily unnecessary suffering that goes on
everywhere within the world is yet another factor that pulls away from
the idea that God is an 'omnipotent' 'benevolent' being.
When Darwin completed his studies of theology at Christ's College, Cambridge in 1831, he read Paley's Natural Theology and believed that the work gave rational proof of the existence of God. That was because living beings showed complexity and were exquisitely fitted to their places in a happy world.
Subsequently, on the voyage of the Beagle, Darwin found that nature was not so beneficent, and the distribution of species did not support ideas of divine creation. In 1838, shortly after his return, Darwin conceived his theory that natural selection,
rather than divine design, was the best explanation for gradual change
in populations over many generations. He published the theory in On the Origin of Species in 1859, and in later editions, he noted responses that he had received:
It can hardly be supposed that a
false theory would explain, in so satisfactory a manner as does the
theory of natural selection, the several large classes of facts above
specified. It has recently been objected that this is an unsafe method
of arguing; but it is a method used in judging of the common events of
life, and has often been used by the greatest natural philosophers ...
I see no good reason why the views given in this volume should shock the
religious feelings of any one. It is satisfactory, as showing how
transient such impressions are, to remember that the greatest discovery
ever made by man, namely, the law of the attraction of gravity, was also
attacked by Leibnitz, "as subversive of natural, and inferentially of
revealed, religion." A celebrated author and divine has written to me
that "he has gradually learnt to see that it is just as noble a
conception of the Deity to believe that He created a few original forms
capable of self-development into other and needful forms, as to believe
that He required a fresh act of creation to supply the voids caused by
the action of His laws."
— Charles Darwin, The Origin of Species (1859)
Darwin reviewed the implications of this finding in his autobiography:
Although I did not think much about
the existence of a personal God until a considerably later period of my
life, I will here give the vague conclusions to which I have been
driven. The old argument of design in nature, as given by Paley, which
formerly seemed to me so conclusive, fails, now that the law of natural
selection has been discovered. We can no longer argue that, for
instance, the beautiful hinge of a bivalve shell must have been made by
an intelligent being, like the hinge of a door by man. There seems to be
no more design in the variability of organic beings and in the action
of natural selection, than in the course which the wind blows.
Everything in nature is the result of fixed laws.
— Charles Darwin, The Autobiography of Charles Darwin 1809–1882. With the original omissions restored.
The idea that nature was governed by laws was already common, and in 1833, William Whewell as a proponent of the natural theology
that Paley had inspired had written that "with regard to the material
world, we can at least go so far as this—we can perceive that events are
brought about not by insulated interpositions of Divine power, exerted
in each particular case, but by the establishment of general laws." Darwin, who spoke of the "fixed laws" concurred with Whewell, writing in his second edition of On The Origin of Species:
There is grandeur in this view of
life, with its several powers, having been originally breathed by the
Creator into a few forms or into one; and that, whilst this planet has
gone cycling on according to the fixed law of gravity, from so simple a
beginning endless forms most beautiful and most wonderful have been, and
are being, evolved.
— Charles Darwin, The Origin of Species (1860)
By the time that Darwin published his theory, theologians of liberal Christianity
were already supporting such ideas, and by the late 19th century, their
modernist approach was predominant in theology. In science, evolution theory incorporating Darwin's natural selection became completely accepted.
Richard Dawkins
Richard Dawkins
In The Blind Watchmaker, Richard Dawkins
argues that the watch analogy conflates the complexity that arises from
living organisms that are able to reproduce themselves (and may become
more complex over time) with the complexity of inanimate objects, unable
to pass on any reproductive changes (such as the multitude of parts
manufactured in a watch). The comparison breaks down because of this
important distinction.
In a BBC Horizon episode, also entitled The Blind Watchmaker,
Dawkins described Paley's argument as being "as mistaken as it is
elegant". In both contexts, he saw Paley as having made an incorrect
proposal as to a certain problem's solution, but Dawkins did not
disrespect him. In his essay The Big Bang, Steven Pinker
discusses Dawkins's coverage of Paley's argument, adding: "Biologists
today do not disagree with Paley's laying out of the problem. They
disagree only with his solution."
In his book The God Delusion,
Dawkins argues that life was the result of complex biological
processes. He makes the argument that the comparison to the lucky
construction of a watch is fallacious because proponents of evolution do
not consider evolution "lucky". Rather than luck, the evolution of
human life is the result of billions of years of natural selection. He
concludes that evolution is a fair contestant to replace God in the role
of watchmaker.
In addition, he argues that the watchmaker's creation of the
watch implies that the watchmaker must be more complex than the watch.
Design is top-down, someone or something more complex designs something
less complex.
To follow the line upwards demands that the watch was designed by a
(necessarily more complex) watchmaker, the watchmaker must have been
created by a more complex being than himself. So the question becomes
who designed the designer?
Dawkins argues that (a) this line continues ad infinitum, and (b) it
does not explain anything.
Evolution, on the other hand, takes a bottom-up approach; it
explains how more complexity can arise gradually by building on or
combining lesser complexity.
In response to such claims, Nathan Schneider writes, "Paley died decades before The Origin of Species
was published, and ever since his views have been so repeatedly set in
opposition to Darwin's that Richard Dawkins titled one of his books on
evolution The Blind Watchmaker. A closer look at Paley's own
thinking reveals, however, a God who works through the laws of nature,
not beyond them like the modern ID theorists' designer. Paley had no
objection to species changing over time. It's only in today's highly
polarized culture-war climate that we don't bother to notice that one of
the forefathers of intelligent design theory might have been perfectly
comfortable with evolution."
Richerson and Boyd
Biologist Peter Richerson and anthropologist Robert Boyd
offer an oblique criticism by arguing that watches were not "hopeful
monsters created by single inventors," but were created by watchmakers
building up their skills in a cumulative fashion over time, each
contributing to a watch-making tradition from which any individual
watchmaker draws their designs.
Contemporary usage
In the early 20th century, the modernist theology of higher criticism was contested in the United States by Biblical literalists, who campaigned successfully against the teaching of evolution and began calling themselves creationists in the 1920s. When teaching of evolution was reintroduced into public schools in the 1960s, they adopted what they called creation science that had a central concept of design in similar terms to Paley's argument. That idea was then relabeled intelligent design,
which presents the same analogy as an argument against evolution by
natural selection without explicitly stating that the "intelligent
designer" was God. The argument from the complexity of biological
organisms was now presented as the irreducible complexity argument, the most notable proponent of which was Michael Behe, and, leveraging off the verbiage of information theory, the specified complexity argument, the most notable proponent of which was William Dembski.
The watchmaker analogy was referenced in the 2005 Kitzmiller v. Dover Area School District trial. Throughout the trial, Paley was mentioned several times. The defense's expert witness John Haught noted that both Intelligent Design and the watchmaker analogy are "reformulations" of the same theological argument.
On day 21 of the trial, Mr. Harvey walked Dr. Minnich through a
modernized version of Paley's argument, substituting a cell phone for
the watch.
In his ruling, the judge stated that the use of the argument from design
by intelligent design proponents "is merely a restatement of the
Reverend William Paley's argument applied at the cell level,"
adding "Minnich, Behe, and Paley reach the same conclusion, that
complex organisms must have been designed using the same reasoning,
except that Professors Behe and Minnich refuse to identify the designer,
whereas Paley inferred from the presence of design that it was God."
The judge ruled that such an inductive argument is not accepted as
science because it is unfalsifiable.
