Indeterminism

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Indeterminism

Indeterminism is the idea that events (or certain events, or events of certain types) are not caused, or are not caused deterministically.

It is the opposite of determinism and related to chance. It is highly relevant to the philosophical problem of free will, particularly in the form of metaphysical libertarianism. In science, most specifically quantum theory in physics, indeterminism is the belief that no event is certain and the entire outcome of anything is probabilistic. Heisenberg's uncertainty principle and the "Born rule", proposed by Max Born, are often starting points in support of the indeterministic nature of the universe. Indeterminism is also asserted by Sir Arthur Eddington, and Murray Gell-Mann. Indeterminism has been promoted by the French biologist Jacques Monod's essay "Chance and Necessity". The physicist-chemist Ilya Prigogine argued for indeterminism in complex systems.

Necessary but insufficient causation

Further information: Necessary and sufficient conditions

Indeterminists do not have to deny that causes exist. Instead, they can maintain that the only causes that exist are of a type that do not constrain the future to a single course; for instance, they can maintain that only necessary and not sufficient causes exist. The necessary/sufficient distinction works as follows:

If x is a necessary cause of y; then the presence of y implies that x definitely preceded it. The presence of x, however, does not imply that y will occur.

If x is a sufficient cause of y, then the presence of y implies that x may have preceded it. (However, another cause z may alternatively cause y. Thus the presence of y does not imply the presence of x, or z, or any other suspect.)

It is possible for everything to have a necessary cause, even while indeterminism holds and the future is open, because a necessary condition does not lead to a single inevitable effect. Indeterministic (or probabilistic) causation is a proposed possibility, such that "everything has a cause" is not a clear statement of indeterminism.

Probabilistic causation

Main article: Probabilistic causation

Interpreting causation as a deterministic relation means that if A causes B, then A must always be followed by B. In this sense, however, war does not always cause deaths (see Cyberwarfare), nor does a singular moment of smoking always cause cancer. As a result, many turn to a notion of probabilistic causation. Informally, A probabilistically causes B if A's occurrence increases the probability of B. This is sometimes interpreted to reflect the imperfect knowledge of a deterministic system but other times interpreted to mean that the causal system under study has an inherently indeterministic nature. (Propensity probability is an analogous idea, according to which probabilities have an objective existence and are not just limitations in a subject's knowledge).

It can be proved that realizations of any probability distribution other than the uniform one are mathematically equal to applying a (deterministic) function (namely, an inverse distribution function) on a random variable following the latter (i.e. an "absolutely random" one); the probabilities are contained in the deterministic element. A simple form of demonstrating it would be shooting randomly within a square and then (deterministically) interpreting a relatively large subsquare as the more probable outcome.

Intrinsic indeterminism versus unpredictability

A distinction is generally made between indeterminism and the mere inability to measure the variables (limits of precision). This is especially the case for physical indeterminism (as proposed by various interpretations of quantum mechanics). Yet some philosophers have argued that indeterminism and unpredictability are synonymous.

Philosophy

Ancient Greek philosophy

Leucippus

The oldest mention of the concept of chance is by the earliest philosopher of atomism, Leucippus, who said:

"The cosmos, then, became like a spherical form in this way: the atoms being submitted to a casual and unpredictable movement, quickly and incessantly".

Aristotle

Main article: Four causes

Aristotle described four possible causes (material, efficient, formal, and final). Aristotle's word for these causes was αἰτίαι (aitiai, as in aetiology), which translates as causes in the sense of the multiple factors responsible for an event. Aristotle did not subscribe to the simplistic "every event has a (single) cause" idea that was to come later.

In his Physics and Metaphysics, Aristotle said there were accidents (συμβεβηκός, sumbebekos) caused by nothing but chance (τύχη, tukhe). He noted that he and the early physicists found no place for chance among their causes.

We have seen how far Aristotle distances himself from any view which makes chance a crucial factor in the general explanation of things. And he does so on conceptual grounds: chance events are, he thinks, by definition unusual and lacking certain explanatory features: as such they form the complement class to those things which can be given full natural explanations.

— R.J. Hankinson, "Causes" in Blackwell Companion to Aristotle

Aristotle opposed his accidental chance to necessity:

Nor is there any definite cause for an accident, but only chance (τυχόν), namely an indefinite (ἀόριστον) cause.

It is obvious that there are principles and causes which are generable and destructible apart from the actual processes of generation and destruction; for if this is not true, everything will be of necessity: that is, if there must necessarily be some cause, other than accidental, of that which is generated and destroyed. Will this be, or not? Yes, if this happens; otherwise not.

Pyrrhonism

The philosopher Sextus Empiricus described the Pyrrhonist position on causes as follows:

...we show the existence of causes are plausible, and if those, too, are plausible which prove that it is incorrect to assert the existence of a cause, and if there is no way to give preference to any of these over others – since we have no agreed-upon sign, criterion, or proof, as has been pointed out earlier – then, if we go by the statements of the Dogmatists, it is necessary to suspend judgment about the existence of causes, too, saying that they are no more existent than non-existent

Epicureanism

Epicurus argued that as atoms moved through the void, there were occasions when they would "swerve" (clinamen) from their otherwise determined paths, thus initiating new causal chains. Epicurus argued that these swerves would allow us to be more responsible for our actions, something impossible if every action was deterministically caused. For Epicureanism, the occasional interventions of arbitrary gods would be preferable to strict determinism.

Early modern philosophy

In 1729 theTestament of Jean Meslier states:

"The matter, by virtue of its own active force, moves and acts in blind manner".

Soon after Julien Offroy de la Mettrie in his L'Homme Machine. (1748, anon.) wrote:

"Perhaps, the cause of man's existence is just in existence itself? Perhaps he is by chance thrown in some point of this terrestrial surface without any how and why".

In his Anti-Sénèque [Traité de la vie heureuse, par Sénèque, avec un Discours du traducteur sur le même sujet, 1750] we read:

"Then, the chance has thrown us in life".

In the 19th century the French Philosopher Antoine-Augustin Cournot theorized chance in a new way, as series of not-linear causes. He wrote in Essai sur les fondements de nos connaissances (1851):

"It is not because of rarity that the chance is actual. On the contrary, it is because of chance they produce many possible others."

Modern philosophy

Charles Peirce

Tychism (Greek: τύχη "chance") is a thesis proposed by the American philosopher Charles Sanders Peirce in the 1890s. It holds that absolute chance, also called spontaneity, is a real factor operative in the universe. It may be considered both the direct opposite of Albert Einstein's oft quoted dictum that: "God does not play dice with the universe" and an early philosophical anticipation of Werner Heisenberg's uncertainty principle.

Peirce does not, of course, assert that there is no law in the universe. On the contrary, he maintains that an absolutely chance world would be a contradiction and thus impossible. Complete lack of order is itself a sort of order. The position he advocates is rather that there are in the universe both regularities and irregularities.

Karl Popper comments that Peirce's theory received little contemporary attention, and that other philosophers did not adopt indeterminism until the rise of quantum mechanics.

Arthur Holly Compton

In 1931, Arthur Holly Compton championed the idea of human freedom based on quantum indeterminacy and invented the notion of amplification of microscopic quantum events to bring chance into the macroscopic world. In his somewhat bizarre mechanism, he imagined sticks of dynamite attached to his amplifier, anticipating the Schrödinger's cat paradox.

Reacting to criticisms that his ideas made chance the direct cause of our actions, Compton clarified the two-stage nature of his idea in an Atlantic Monthly article in 1955. First there is a range of random possible events, then one adds a determining factor in the act of choice.

A set of known physical conditions is not adequate to specify precisely what a forthcoming event will be. These conditions, insofar as they can be known, define instead a range of possible events from among which some particular event will occur. When one exercises freedom, by his act of choice he is himself adding a factor not supplied by the physical conditions and is thus himself determining what will occur. That he does so is known only to the person himself. From the outside one can see in his act only the working of physical law. It is the inner knowledge that he is in fact doing what he intends to do that tells the actor himself that he is free.

Compton welcomed the rise of indeterminism in 20th century science, writing:

In my own thinking on this vital subject I am in a much more satisfied state of mind than I could have been at any earlier stage of science. If the statements of the laws of physics were assumed correct, one would have had to suppose (as did most philosophers) that the feeling of freedom is illusory, or if [free] choice were considered effective, that the laws of physics ... [were] unreliable. The dilemma has been an uncomfortable one.

Together with Arthur Eddington in Britain, Compton was one of those rare distinguished physicists in the English speaking world of the late 1920s and throughout the 1930s arguing for the “liberation of free will” with the help of Heisenberg’s indeterminacy principle, but their efforts had been met not only with physical and philosophical criticism but most primarily with fierce political and ideological campaigns.

Karl Popper

In his essay Of Clouds and Clocks, included in his book Objective Knowledge, Popper contrasted "clouds", his metaphor for indeterministic systems, with "clocks", meaning deterministic ones. He sided with indeterminism, writing

I believe Peirce was right in holding that all clocks are clouds to some considerable degree — even the most precise of clocks. This, I think, is the most important inversion of the mistaken determinist view that all clouds are clocks

Popper was also a promoter of propensity probability.

Robert Kane

Kane was one of the leading contemporary philosophers on free will. Advocating what is termed within philosophical circles "libertarian freedom", Kane argues that "(1) the existence of alternative possibilities (or the agent's power to do otherwise) is a necessary condition for acting freely, and (2) determinism is not compatible with alternative possibilities (it precludes the power to do otherwise)". The crux of Kane's position is grounded not in a defense of alternative possibilities (AP) but in the notion of what Kane refers to as ultimate responsibility (UR). Thus, AP is a necessary but insufficient criterion for free will. It is necessary that there be (metaphysically) real alternatives for our actions, but that is not enough; our actions could be random without being in our control. The control is found in "ultimate responsibility".

What allows for ultimate responsibility of creation in Kane's picture are what he refers to as "self-forming actions" or SFAs — those moments of indecision during which people experience conflicting wills. These SFAs are the undetermined, regress-stopping voluntary actions or refrainings in the life histories of agents that are required for UR. UR does not require that every act done of our own free will be undetermined and thus that, for every act or choice, we could have done otherwise; it requires only that certain of our choices and actions be undetermined (and thus that we could have done otherwise), namely SFAs. These form our character or nature; they inform our future choices, reasons and motivations in action. If a person has had the opportunity to make a character-forming decision (SFA), he is responsible for the actions that are a result of his character.

Mark Balaguer

Mark Balaguer, in his book Free Will as an Open Scientific Problem argues similarly to Kane. He believes that, conceptually, free will requires indeterminism, and the question of whether the brain behaves indeterministically is open to further empirical research. He has also written on this matter "A Scientifically Reputable Version of Indeterministic Libertarian Free Will".

Science

See also: Philosophy of physics and indeterminism

Mathematics

In probability theory, a stochastic process, or sometimes random process, is the counterpart to a deterministic process (or deterministic system). Instead of dealing with only one possible reality of how the process might evolve over time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths may be more probable and others less so.

Classical and relativistic physics

The idea that Newtonian physics proved causal determinism was highly influential in the early modern period. "Thus physical determinism [..] became the ruling faith among enlightened men; and everybody who did not embrace this new faith was held to be an obscurantist and a reactionary". However: "Newton himself may be counted among the few dissenters, for he regarded the solar system as imperfect, and consequently as likely to perish".

Classical chaos is not usually considered an example of indeterminism, as it can occur in deterministic systems such as the three-body problem.

John Earman has argued that most physical theories are indeterministic. For instance, Newtonian physics admits solutions where particles accelerate continuously, heading out towards infinity. By the time reversibility of the laws in question, particles could also head inwards, unprompted by any pre-existing state. He calls such hypothetical particles "space invaders".

John D. Norton has suggested another indeterministic scenario, known as Norton's Dome, where a particle is initially situated on the exact apex of a dome.

Branching space-time is a theory uniting indeterminism and the special theory of relativity. The idea was originated by Nuel Belnap. The equations of general relativity admit of both indeterministic and deterministic solutions.

Boltzmann

Ludwig Boltzmann was one of the founders of statistical mechanics and the modern atomic theory of matter. He is remembered for his discovery that the second law of thermodynamics is a statistical law stemming from disorder. He also speculated that the ordered universe is only a small bubble in a larger sea of chaos. The Boltzmann brain is a similar idea.

Evolution and biology

Darwinian evolution has an enhanced reliance on the chance element of random mutation compared to the earlier evolutionary theory of Herbert Spencer. However, the question of whether evolution requires genuine ontological indeterminism is open to debate

In the essay Chance and Necessity (1970) Jacques Monod rejected the role of final causation in biology, instead arguing that a mixture of efficient causation and "pure chance" lead to teleonomy, or merely apparent purposefulness.

The Japanese theoretical population geneticist Motoo Kimura emphasises the role of indeterminism in evolution. According to neutral theory of molecular evolution: "at the molecular level most evolutionary change is caused by random drift of gene mutants that are equivalent in the face of selection.

Prigogine

In his 1997 book, The End of Certainty, Prigogine contends that determinism is no longer a viable scientific belief. "The more we know about our universe, the more difficult it becomes to believe in determinism." This is a major departure from the approach of Newton, Einstein and Schrödinger, all of whom expressed their theories in terms of deterministic equations. According to Prigogine, determinism loses its explanatory power in the face of irreversibility and instability.

Prigogine traces the dispute over determinism back to Darwin, whose attempt to explain individual variability according to evolving populations inspired Ludwig Boltzmann to explain the behavior of gases in terms of populations of particles rather than individual particles. This led to the field of statistical mechanics and the realization that gases undergo irreversible processes. In deterministic physics, all processes are time-reversible, meaning that they can proceed backward as well as forward through time. As Prigogine explains, determinism is fundamentally a denial of the arrow of time. With no arrow of time, there is no longer a privileged moment known as the "present," which follows a determined "past" and precedes an undetermined "future." All of time is simply given, with the future as determined or undetermined as the past. With irreversibility, the arrow of time is reintroduced to physics. Prigogine notes numerous examples of irreversibility, including diffusion, radioactive decay, solar radiation, weather and the emergence and evolution of life. Like weather systems, organisms are unstable systems existing far from thermodynamic equilibrium. Instability resists standard deterministic explanation. Instead, due to sensitivity to initial conditions, unstable systems can only be explained statistically, that is, in terms of probability.

Prigogine asserts that Newtonian physics has now been "extended" three times, first with the use of the wave function in quantum mechanics, then with the introduction of spacetime in general relativity and finally with the recognition of indeterminism in the study of unstable systems.

Quantum mechanics

Main article: Quantum indeterminacy

At one time, it was assumed in the physical sciences that if the behavior observed in a system cannot be predicted, the problem is due to lack of fine-grained information, so that a sufficiently detailed investigation would eventually result in a deterministic theory ("If you knew exactly all the forces acting on the dice, you would be able to predict which number comes up").

However, the advent of quantum mechanics removed the underpinning from that approach, with the claim that (at least according to the Copenhagen interpretation) the most basic constituents of matter at times behave indeterministically. This comes from the collapse of the wave function, in which the state of a system upon measurement cannot in general be predicted. Quantum mechanics only predicts the probabilities of possible outcomes, which are given by the Born rule. Non-deterministic behavior in wave function collapse is not only a feature of the Copenhagen interpretation, with its observer-dependence, but also of objective collapse and other theories.

Opponents of quantum indeterminism suggested that determinism could be restored by formulating a new theory in which additional information, so-called hidden variables, would allow definite outcomes to be determined. For instance, in 1935, Einstein, Podolsky and Rosen wrote a paper titled "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" arguing that such a theory was in fact necessary to preserve the principle of locality. In 1964, John S. Bell was able to define a theoretical test for these local hidden variable theories, which was reformulated as a workable experimental test through the work of Clauser, Horne, Shimony and Holt. The negative result of the 1980s tests by Alain Aspect ruled such theories out, provided certain assumptions about the experiment hold. Thus any interpretation of quantum mechanics, including deterministic reformulations, must either reject locality or reject counterfactual definiteness altogether. David Bohm's theory is the main example of a non-local deterministic quantum theory.

The many-worlds interpretation is said to be deterministic, but experimental results still cannot be predicted: experimenters do not know which 'world' they will end up in. Technically, counterfactual definiteness is lacking.

A notable consequence of quantum indeterminism is the Heisenberg uncertainty principle, which prevents the simultaneous accurate measurement of all a particle's properties.

Cosmology

Primordial fluctuations are density variations in the early universe which are considered the seeds of all structure in the universe. Currently, the most widely accepted explanation for their origin is in the context of cosmic inflation. According to the inflationary paradigm, the exponential growth of the scale factor during inflation caused quantum fluctuations of the inflaton field to be stretched to macroscopic scales, and, upon leaving the horizon, to "freeze in". At the later stages of radiation- and matter-domination, these fluctuations re-entered the horizon, and thus set the initial conditions for structure formation.

Neuroscience

Neuroscientists such as Björn Brembs and Christof Koch believe thermodynamically stochastic processes in the brain are the basis of free will, and that even very simple organisms such as flies have a form of free will. Similar ideas are put forward by some philosophers such as Robert Kane.

Despite recognizing indeterminism to be a very low-level, necessary prerequisite, Björn Brembs says that it's not even close to being sufficient for addressing things like morality and responsibility.

Other views

Against Einstein and others who advocated determinism, indeterminism—as championed by the English astronomer Sir Arthur Eddington—says that a physical object has an ontologically undetermined component that is not due to the epistemological limitations of physicists' understanding. The uncertainty principle, then, would not necessarily be due to hidden variables but to an indeterminism in nature itself.

Determinism and indeterminism are examined in Causality and Chance in Modern Physics by David Bohm. He speculates that, since determinism can emerge from underlying indeterminism (via the law of large numbers), and that indeterminism can emerge from determinism (for instance, from classical chaos), the universe could be conceived of as having alternating layers of causality and chaos.

Incompatibilism

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Incompatibilism 

Classical incompatibilists hold that determinism leaves no room for free will.

Incompatibilism is the view that the thesis of determinism is logically incompatible with the classical thesis of free will. The term was coined in the 1960s, most likely by philosopher Keith Lehrer. The term compatibilism was coined (also by Lehrer) to name the view that the classical free will thesis is logically compatible with determinism, i.e. it is possible for an ordinary human to exercise free will (the freedom-relevant ability to do otherwise), even in a universe where determinism is true.

These terms were originally coined for use within a research paradigm that was dominant among academics during the so-called "classical period" from the 1960s to 1980s, or what has been called the "classical analytic paradigm". Within the classical analytic paradigm, the problem of free will and determinism was understood as a compatibility question: "Is it possible for an ordinary human to exercise free will (classically defined as an ability to do otherwise) when determinism is true?" Those working in the classical analytic paradigm who answered "no" were incompatibilists in the original, classical-analytic sense of the term, now commonly called classical incompatibilists; they proposed that determinism precludes free will because it precludes the ability to do otherwise. Those who answered "yes" were compatibilists in the original sense of the term, now commonly called classical compatibilists. Given that classical free will theorists (i.e. those working in the classical analytic paradigm) agreed that it is at least metaphysically possible for an ordinary human to exercise free will, all classical compatibilists accepted a compossibilist account of free will (i.e. a compossibilist interpretation of the ability to do otherwise) and all classical incompatibilists accepted a libertarian account of free will (i.e. a libertarian interpretation of the ability to do otherwise).

The classical analytic paradigm has fallen out of favor over the last few decades, largely because philosophers no longer agree that free will is equivalent to some kind of ability to do otherwise; many hold that it is, instead, a type of sourcehood that does not require an ability to do otherwise. The number of philosophers who reject the classical assumption of anthropocentric possibilism, i.e. the view that it is at least metaphysically possible for a human to exercise free will, has also risen in recent years. As philosophers adjusted Lehrer's original (classical) definitions of the terms incompatibilism and compatibilism to reflect their own perspectives on the location of the purported "fundamental divide" among free will theorists, the terms incompatibilism and compatibilism have been given a variety of new meanings. At present, then, there is no standard meaning of the term incompatibilism (or its complement compatibilism).

Definition

On one recent taxonomy, there are now at least three substantively different, non-classical uses of the term incompatibilism, namely: neo-classical incompatibilism, post-classical incompatibilism (a.k.a. incompossibilism), and anti-classical incompatibilism. Correspondingly, there are neo-classical, post-classical (compossibilist), and anti-classical versions of compatibilism as well. Neo-classical incompatibilism is a two-tenet view: incompossibilism is true (i.e. it is metaphysically impossible for an ordinary human to act freely when determinism is true), and determinism-related causal/nomological factors preclude free will (which explains why incompossibilism is true). Correspondingly, neo-classical compatibilism is the two-tenet view that: the negative, non-explanatory tenet of neo-classical incompatibilism is false (i.e. compossibilism is true), and that the positive, explanatory tenet of neo-classical incompatibilism is false. Anti-classical incompatibilism is the explanatory thesis of neo-classical incompatibilism; anti-classical incompatibilism is neutral on the truth-value of incompossibilism. Correspondingly, anti-classical compatibilism is the negation of neo-classical incompatibilism's positive tenet, i.e. anti-classical compatibilism is the contradictory of anti-classical incompatibilism. Post-classical incompatibilism is just the negative, non-explanatory thesis of neo-classical incompatibilism; this view is neutral on whether the positive, explanatory thesis of neo-classical incompatibilism is true. (Put another way, on the post-classical redefinition of incompatibilism, it is just an alternative name for incompossibilism, a view which is completely silent on whether determinism-related causal factors are relevant to free will or are a total "red herring" in discussions of free will.) Correspondingly, post-classical compatibilism is identical to compossibilism (i.e. on the post-classical redefinition of compatibilism, it denotes mere compossibilism).

The ambiguity of incompatibilism can be a source of confusion because arguments with very different (even inconsistent) conclusions are currently lumped together under the umbrella phrase "arguments for incompatibilism". For example, it is easy for the casual reader to overlook that some arguments for post-classical incompatibilism (a.k.a. incompossibilism) are not arguments for neo-classical incompatibilism on the grounds that the argument does not aim to support the latter's explanatory tenet (a.k.a. anti-classical incompatibilism). Other arguments support post-classical incompatibilism (a.k.a. incompossibilism) but conclude that neo-classical incompatibilism is false on the grounds that its explanatory tenet (a.k.a. anti-classical incompatibilism) is false. Arguments in the last category conclude that people lack free will when determinism is true but not at all because determinism is true (i.e. not at all because certain causal/nomological factors obtain); most propose that the real threat to free will is that people lack adequate control over their own constitutive properties, or what is often called their "constitutive luck" (as opposed to causal luck).

Libertarianism

Main article: Libertarianism (metaphysics)

Free-will libertarianism is the view that the free-will thesis (that we, ordinary humans, have free will) is true and that determinism is false; in first-order language, it is the view that we (ordinary humans) have free will and the world does not behave in the way described by determinism. Libertarianism is one of the popular solutions to the problem of free will, roughly the problem of settling the question of whether we have free will and the logically prior question of what free will amounts to. The main rivals to libertarianism are soft determinism and hard determinism.

Libertarian Robert Kane (editor of the Oxford Handbook of Free Will) is a leading incompatibilist philosopher in favour of free will. Kane seeks to hold persons morally responsible for decisions that involved indeterminism in their process. Critics maintain that Kane fails to overcome the greatest challenge to such an endeavor: "the argument from luck". Namely, if a critical moral choice is a matter of luck (indeterminate quantum fluctuations), then the question of holding a person responsible for their final action arises. Moreover, even if we imagine that a person can make an act of will ahead of time, to make the moral action more probable in the upcoming critical moment, this act of 'willing' was itself a matter of luck. Kane objects to the validity of the argument from luck because the latter misrepresents the chance as if it is external to the act of choosing. The free will theorem of John H. Conway and Simon B. Kochen further establishes that if we have free will, then quantum particles also possess free will. This means that starting from the assumption that humans have free will, it is possible to pinpoint the origin of their free will in the quantum particles that constitute their brain.

Such philosophical stance risks an infinite regress, however; if any such mind is real, an objection can be raised that free will would be impossible if the choosing is shaped merely by luck or chance.

Libertarianism in the philosophy of mind is unrelated to the like-named political philosophy. It suggests that we actually do have free will, that it is incompatible with determinism, and that therefore the future is not determined.

One famous proponent of this view was Lucretius, who asserted that the free will arises out of the random, chaotic movements of atoms, called "clinamen". One major objection to this view is that science has gradually shown that more and more of the physical world obeys completely deterministic laws, and seems to suggest that our minds are just as much part of the physical world as anything else. If these assumptions are correct, incompatibilist libertarianism can only be maintained as the claim that free will is a supernatural phenomenon, which does not obey the laws of nature (as, for instance, maintained by some religious traditions).

However, many libertarian view points now rely upon an indeterministic view of the physical universe, under the assumption that the idea of a deterministic, clockwork universe has become outdated since the advent of quantum mechanics. By assuming an indeterministic universe, libertarian philosophical constructs can be proposed under the assumption of physicalism.

There are libertarian view points based upon indeterminism and physicalism, which is closely related to naturalism. A major problem for naturalistic libertarianism is to explain how indeterminism can be compatible with rationality and with appropriate connections between an individual's beliefs, desires, general character and actions. A variety of naturalistic libertarianism is promoted by Robert Kane, who emphasizes that if our character is formed indeterministically (in "self-forming actions"), then our actions can still flow from our character, and yet still be incompatibilistically free.

Alternatively, libertarian view points based upon indeterminism have been proposed without the assumption of naturalism. At the time C. S. Lewis wrote Miracles, quantum mechanics (and physical indeterminism) was only in the initial stages of acceptance, but still Lewis stated the logical possibility that, if the physical world was proved to be indeterministic, this would provide an entry (interaction) point into the traditionally viewed closed system, where a scientifically described physically probable/improbable event could be philosophically described as an action of a non-physical entity on physical reality (noting that, under a physicalist point of view, the non-physical entity must be independent of the self-identity or mental processing of the sentient being). Lewis mentions this only in passing, making clear that his thesis does not depend on it in any way.

Others may use some form of Donald Davidson's anomalous monism to suggest that although the mind is in fact part of the physical world, it involves a different level of description of the same facts, so that although there are deterministic laws under the physical description, there are no such laws under the mental description, and thus our actions are free and not determined.

Consequence argument

Main article: Consequence argument

Peter van Inwagen proposed his consequence argument to argue that free will is not compatible with determinism. He assumes the truth of determinism to argue that a person could not have acted differently from how they actually did. from this, he rejects that determinism is true to preserve free will, but concludes that they are mutually exclusive. His argument is formally valid as follows:

(1) If determinism is true, then the conjunction of P0 and L entail P (2) It is not possible that J have raised his hands at T and P be true (3) If (2) is true, then if J could have raised his hand at T, J could have rendered P false (4) If J could have rendered P false, and if the conjunction of P0 and L entails P, then J could have rendered the conjunction of P0 and L false (5) If J could have rendered the conjunction of P0 and L false, then J could have rendered L false (6) J could not have rendered L false (7) If determinism is true, J could not have raised his hand at T

Where J is a judge who did not raise their hand at time T, P is the entire physical state of the world at T, P0 is the entire physical state of the world in the remote past, and L is the conjunction of all the laws of nature, which by definition cannot actually be rendered false.

Van Inwagen then presents a dilemma, we can either:

• Deny determinism and accept incompatibilism
• Accept that contradictions could be true in the actual world
• Accept that we can change the remote past
• Accept that we can render false the laws of nature
• Deny Free will and accept incompatibilism

The compatibilist is committed to rejecting the former and the latter, so they choose option 2, 3, or 4 to maintain their position. David Lewis objected by denying that laws of nature are never violated with counterpart theory, although counterpart theory is very controversial, and this leaves us with a significantly diluted version of free will.

Kadri Vihvelin rejected the argument by dismissing the conclusion, but refused to choose a premise to deny, arguing that the conclusion is false; therefore, one of the premises must be too. She later accepted Lewis's position, which is known as "local miracle compatibilism."

Semicompatibilism

Main article: Semicompatibilism

Semicompatibilism is unaffected by the consequent argument, as it is indifferent as to whether or not free will is compatible with determinism. It had previously been assumed that free will is required for moral responsibility, meaning that if determinism threatened free will, it would threaten moral responsibility as well. Semi-compatibilists deny this entailment, arguing that, regardless of free will's compatibility, moral responsibility is compatible with determinism. However, Van Inwagen's Direct Argument argues in a similar manner for the incompatibility of determinism with moral responsibility. A semicompatibilist would have to engage with this argument, although its validity is questioned over modal logic.

Hard determinism

Main article: Hard determinism

Schopenhauer said "Man is free to do what he wills, but he cannot will what he wills." The hard determinist says then, there is no "free will".

Those who reject free will and accept determinism are variously known as "hard determinists", hard incompatibilists, free will skeptics, free will illusionists, or impossibilists. They believe that there is no free will and that any sense of the contrary is an illusion. Hard determinists do not deny that one has desires, but say that these desires are causally determined by an unbroken chain of prior occurrences. According to this philosophy, no wholly random, spontaneous, mysterious, or miraculous events occur. Determinists sometimes assert that it is stubborn to resist scientifically motivated determinism on purely intuitive grounds about one's own sense of freedom. They reason that the history of the development of science suggests that determinism is the logical method in which reality works.

William James said that philosophers (and scientists) have an "antipathy to chance". Absolute chance, a possible implication of quantum mechanics and the indeterminacy principle, supports the existence of indefinite causal structures.

Moral implications

Since many believe that free will is necessary for moral responsibility, hard determinism may imply disastrous consequences for their theory of ethics, resulting in a domino theory of moral nonresponsibility.

As something of a solution to this predicament, one might embrace the so-called illusion of free will. This thesis argues in favor of maintaining the prevailing belief in free will for the sake of preserving moral responsibility and the concept of ethics. However, critics argue that this move renders morality merely another "illusion", or else that this move is simply hypocritical.

The determinist will add that, even if denying free will does mean morality is incoherent, such a result has no effect on the truth. However, hard determinists often have some sort of moral system that relies explicitly on determinism. A determinist's moral system simply bears in mind that every person's actions in a given situation are, in theory, predicted by the interplay of environment and upbringing.

Hard incompatibilism

Hard incompatibilism, like hard determinism, is a type of skepticism about free will. Hard incompatibilism is a term coined by Derk Pereboom to designate the view that both determinism and indeterminism are incompatible with having free will and moral responsibility. Like the hard determinist, the hard incompatibilist holds that if determinism were true, people would not have free will. But Pereboom argues in addition that if decisions were indeterministic events, free will would also be precluded. In his view, free will is the control in action required for the desert aspect of moral responsibility—for people to deserve to be blamed or punished for immoral actions, and to be praised or rewarded for morally exemplary actions. He contends that if people's decisions were indeterministic events, their occurrence would not be in the control of the agent in the way required for such attributions of desert. The possibility for free will that remains is libertarian agent causation, according to which agents as substances (thus not merely as having a role in events) can cause actions without being causally determined to do so. Pereboom argues that for empirical reasons it is unlikely that people are agent causes of this sort, and that as a result, it is likely that they lack free will.

Experimental research

In recent years researchers in the field of experimental philosophy have been working on determining whether ordinary people, who are not experts in this field, naturally have compatibilist or incompatibilist intuitions about determinism and moral responsibility. Some experimental work has even conducted cross-cultural studies. The debate about whether people naturally have compatibilist or incompatibilist intuitions has not come out overwhelmingly in favor of one view or the other. Still, there has been some evidence that people can naturally hold both views. For instance, when people are presented with abstract cases which ask if a person could be morally responsible for an immoral act when they could not have done otherwise, people tend to say no, or give incompatibilist answers, but when presented with a specific immoral act that a specific person committed, people tend to say that that person is morally responsible for their actions, even if they were determined (that is, people also give compatibilist answers).

Drake equation

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Drake_equation 

Frank Drake in c. 1960s

The Drake equation is a probabilistic argument used to estimate the number of active, communicative extraterrestrial civilizations in the Milky Way Galaxy.

The equation was formulated in 1961 by Frank Drake, not for purposes of quantifying the number of civilizations, but as a way to stimulate scientific dialogue at the first scientific meeting on the search for extraterrestrial intelligence (SETI). The equation summarizes the main concepts which scientists must contemplate when considering the question of other radio-communicative life. It is more properly thought of as an approximation than as a serious attempt to determine a precise number.

Criticism related to the Drake equation focuses not on the equation itself, but on the fact that the estimated values for several of its factors are highly conjectural, the combined multiplicative effect being that the uncertainty associated with any derived value is so large that the equation cannot be used to draw firm conclusions.

Equation

The Drake equation is:

$${\displaystyle N=R_{\ast }\cdot f_{\mathrm{p}}\cdot n_{\mathrm{e}}\cdot f_{\mathrm{l}}\cdot f_{\mathrm{i}}\cdot f_{\mathrm{c}}\cdot L}$$

where

• N = the number of civilizations in the Milky Way galaxy with which communication might be possible (i.e. which are on the current past light cone);

and

• R_∗ = the average rate of star formation in our galaxy.
• f_p = the fraction of those stars that have planets.
• n_e = the average number of planets that can potentially support life per star that has planets.
• f_l = the fraction of planets that could support life that actually develop life at some point.
• f_i = the fraction of planets with life that go on to develop intelligent life (civilizations).
• f_c = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space.
• L = the length of time for which such civilizations release detectable signals into space.

This form of the equation first appeared in Drake's 1965 paper.

History

Completed 300 Foot Telescope. Frank Drake is the second from left.

In September 1959, physicists Giuseppe Cocconi and Philip Morrison published an article in the journal Nature with the provocative title "Searching for Interstellar Communications". Cocconi and Morrison argued that radio telescopes had become sensitive enough to pick up transmissions that might be broadcast into space by civilizations orbiting other stars. Such messages, they suggested, might be transmitted at a wavelength of 21 cm (1,420.4 MHz). This is the wavelength of radio emission by neutral hydrogen, the most common element in the universe, and they reasoned that other intelligences might see this as a logical landmark in the radio spectrum.

Two months later, Harvard University astronomy professor Harlow Shapley speculated on the number of inhabited planets in the universe, saying "The universe has 10 million, million, million suns (10 followed by 18 zeros) similar to our own. One in a million has planets around it. Only one in a million million has the right combination of chemicals, temperature, water, days and nights to support planetary life as we know it. This calculation arrives at the estimated figure of 100 million worlds where life has been forged by evolution."

Seven months after Cocconi and Morrison published their article, Drake began searching for extraterrestrial intelligence in an experiment called Project Ozma. It was the first systematic search for signals from communicative extraterrestrial civilizations. Using the 85 ft (26 m) dish of the National Radio Astronomy Observatory, Green Bank in Green Bank, West Virginia, Drake monitored two nearby Sun-like stars: Epsilon Eridani and Tau Ceti, slowly scanning frequencies close to the 21 cm wavelength for six hours per day from April to July 1960. The project was well designed, inexpensive, and simple by today's standards. It detected no signals.

Soon thereafter, Drake hosted the first search for extraterrestrial intelligence conference on detecting their radio signals. The meeting was held at the Green Bank facility in 1961. The equation that bears Drake's name arose out of his preparations for the meeting.

As I planned the meeting, I realized a few day[s] ahead of time we needed an agenda. And so I wrote down all the things you needed to know to predict how hard it's going to be to detect extraterrestrial life. And looking at them it became pretty evident that if you multiplied all these together, you got a number, N, which is the number of detectable civilizations in our galaxy. This was aimed at the radio search, and not to search for primordial or primitive life forms.

— Frank Drake

The ten attendees were conference organizer J. Peter Pearman, Frank Drake, Philip Morrison, businessman and radio amateur Dana Atchley, chemist Melvin Calvin, astronomer Su-Shu Huang, neuroscientist John C. Lilly, inventor Barney Oliver, astronomer Carl Sagan, and radio-astronomer Otto Struve. These participants called themselves "The Order of the Dolphin" (because of Lilly's work on dolphin communication), and commemorated their first meeting with a plaque at the observatory hall.

Usefulness

The Allen Telescope Array for SETI

The Drake equation results in a summary of the factors affecting the likelihood that we might detect radio-communication from intelligent extraterrestrial life. The last three parameters, f_i, f_c, and L, are not known and are very difficult to estimate, with values ranging over many orders of magnitude (see § Criticism). Therefore, the usefulness of the Drake equation is not in the solving, but rather in the contemplation of all the various concepts which scientists must incorporate when considering the question of life elsewhere, and gives the question of life elsewhere a basis for scientific analysis. The equation has helped draw attention to some particular scientific problems related to life in the universe, for example abiogenesis, the development of multi-cellular life, and the development of intelligence itself.

Within the limits of existing human technology, any practical search for distant intelligent life must necessarily be a search for some manifestation of a distant technology. After about 50 years, the Drake equation is still of seminal importance because it is a 'road map' of what we need to learn in order to solve this fundamental existential question. It also formed the backbone of astrobiology as a science; although speculation is entertained to give context, astrobiology concerns itself primarily with hypotheses that fit firmly into existing scientific theories. Some 50 years of SETI have failed to find anything, even though radio telescopes, receiver techniques, and computational abilities have improved significantly since the early 1960s. SETI efforts since 1961 have conclusively ruled out widespread alien emissions near the 21 cm wavelength of the hydrogen frequency.

Estimates

Original estimates

There is considerable disagreement on the values of these parameters, but the 'educated guesses' used by Drake and his colleagues in 1961 were:

• R_∗ = 1 yr⁻¹ (1 star formed per year, on the average over the life of the galaxy; this was regarded as conservative)
• f_p = 0.2 to 0.5 (one fifth to one half of all stars formed will have planets)
• n_e = 1 to 5 (stars with planets will have between 1 and 5 planets capable of developing life)
• f_l = 1 (100% of these planets will develop life)
• f_i = 1 (100% of which will develop intelligent life)
• f_c = 0.1 to 0.2 (10–20% of which will be able to communicate)
• L = somewhere between 1000 and 100,000,000 years

Inserting the above minimum numbers into the equation gives a minimum N of 20 (see: Range of results). Inserting the maximum numbers gives a maximum of 50,000,000. Drake states that given the uncertainties, the original meeting concluded that N ≈ L, and there were probably between 1000 and 100,000,000 planets with civilizations in the Milky Way Galaxy.

Current estimates

This section discusses and attempts to list the best current estimates for the parameters of the Drake equation.

Rate of star creation in this Galaxy, R_∗

Calculations in 2010, from NASA and the European Space Agency indicate that the rate of star formation in this Galaxy is about 0.68–1.45 solar masses (M_☉; 1.35×10³⁰–2.88×10³⁰ kg) of material per year. To get the number of stars per year, we divide this by the initial mass function (IMF) for stars, where the average new star's mass is about 0.5 M_☉. This gives a star formation rate of about 1–3 stars per year.

Fraction of those stars that have planets, f_p

Analysis of microlensing surveys, in 2012, has found that f_p may approach 1—that is, stars are orbited by planets as a rule, rather than the exception; and that there are one or more bound planets per Milky Way star.

Average number of planets that might support life per star that has planets, n_e

In November 2013, astronomers reported, based on Kepler space telescope data, that there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of Sun-like stars and red dwarf stars within the Milky Way Galaxy. 11 billion of these estimated planets may be orbiting Sun-like stars. Since there are about 100 billion stars in the galaxy, this implies f_p · n_e is roughly 0.4. The nearest planet in the habitable zone is Proxima Centauri b, which is as close as about 4.2 light-years away.

The consensus at the Green Bank meeting was that n_e had a minimum value between 3 and 5. Dutch science journalist Govert Schilling has opined that this is optimistic. Even if planets are in the habitable zone, the number of planets with the right proportion of elements is difficult to estimate. Brad Gibson, Yeshe Fenner, and Charley Lineweaver determined that about 10% of star systems in the Milky Way Galaxy are hospitable to life, by having heavy elements, being far from supernovae and being stable for a sufficient time.

The discovery of numerous gas giants in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the formation of their stellar systems. So-called hot Jupiters may migrate from distant orbits to near orbits, in the process disrupting the orbits of habitable planets.

On the other hand, the variety of star systems that might have habitable zones is not just limited to solar-type stars and Earth-sized planets. It is now estimated that even star systems of tidally locked planets close to red dwarf stars might have habitable zones, although the flaring behavior of these stars might speak against this. The possibility of life on moons of gas giants (such as Jupiter's moon Europa, or Saturn's moons Titan and Enceladus) adds further uncertainty to this figure.

The authors of the rare Earth hypothesis propose a number of additional constraints on habitability for planets, including being in galactic zones with suitably low radiation, high star metallicity, and low enough density to avoid excessive asteroid bombardment. They also propose that it is necessary to have a planetary system with large gas giants which provide bombardment protection without a hot Jupiter; and a planet with plate tectonics, a large moon that creates tidal pools, and moderate axial tilt to generate seasonal variation.

Fraction of the above that actually go on to develop life, f_l

Geological evidence from the Earth suggests that f_l may be high; life on Earth appears to have begun around the same time as favorable conditions arose, suggesting that abiogenesis may be relatively common once conditions are right. However, this evidence only looks at the Earth (a single model planet), and contains anthropic bias, as the planet of study was not chosen randomly, but by the living organisms that already inhabit it (ourselves). From a classical hypothesis testing standpoint, without assuming that the underlying distribution of f_l is the same for all planets in the Milky Way, there are zero degrees of freedom, permitting no valid estimates to be made. If life (or evidence of past life) were to be found on Mars, Europa, Enceladus or Titan that developed independently from life on Earth it would imply a value for f_l close to 1. While this would raise the number of degrees of freedom from zero to one, there would remain a great deal of uncertainty on any estimate due to the small sample size, and the chance they are not really independent.

Countering this argument is that there is no evidence for abiogenesis occurring more than once on the Earth—that is, all terrestrial life stems from a common origin. If abiogenesis were more common it would be speculated to have occurred more than once on the Earth. Scientists have searched for this by looking for microbes that are unrelated to other life on Earth, constituting what would be called a shadow biosphere, but none have been found yet. It is also possible that life arose more than once, but that other branches were out-competed, or died in mass extinctions, or were lost in other ways. Biochemists Francis Crick and Leslie Orgel laid special emphasis on this uncertainty: "At the moment we have no means at all of knowing" whether we are "likely to be alone in the galaxy (Universe)" or whether "the galaxy may be pullulating with life of many different forms." As an alternative to abiogenesis on Earth, they proposed the hypothesis of directed panspermia, which states that Earth life began with "microorganisms sent here deliberately by a technological society on another planet, by means of a special long-range unmanned spaceship".

In 2020, a paper by scholars at the University of Nottingham proposed an "Astrobiological Copernican" principle, based on the Principle of Mediocrity, and speculated that "intelligent life would form on other [Earth-like] planets like it has on Earth, so within a few billion years life would automatically form as a natural part of evolution". In the authors' framework, f_l, f_i, and f_c are all set to a probability of 1 (certainty). Their resultant calculation concludes there are more than thirty current technological civilizations in the galaxy (disregarding error bars).

Fraction of the above that develops intelligent life, f_i

This value remains particularly controversial. Those who favor a low value, such as the biologist Ernst Mayr, point out that of the billions of species that have existed on Earth, only one has become intelligent and from this, infer a tiny value for f_i. Likewise, the Rare Earth hypothesis, notwithstanding their low value for n_e above, also think a low value for f_i dominates the analysis. Those who favor higher values note the generally increasing complexity of life over time, concluding that the appearance of intelligence is almost inevitable, implying an f_i approaching 1. Skeptics point out that the large spread of values in this factor and others make all estimates unreliable. (See Criticism).

In addition, while it appears that life developed soon after the formation of Earth, the transition from single-celled prokaryotes to eukaryotes, and the resulting increase in complexity, including a change in life's "operating system", required a considerable amount of time as the complexity of living organisms grew. Subsequently, the Cambrian explosion, in which a large variety of multicellular life forms came into being, occurred a considerable amount of time after this event, which suggests the possibility that special conditions for complex life were necessary. Some scenarios such as the snowball Earth or research into extinction events have raised the possibility that life on Earth is relatively fragile. Research on any past life on Mars is relevant since a discovery that life did form on Mars but ceased to exist might raise the estimate of f_l but would indicate that in half the known cases, intelligent life did not develop.

Estimates of f_i have been affected by discoveries that the Solar System's orbit is circular in the galaxy, at such a distance that it remains out of the spiral arms for tens of millions of years (evading radiation from novae). Also, Earth's large moon may aid the evolution of life by stabilizing the planet's axis of rotation.

There has been quantitative work to begin to define ${\displaystyle f_{\mathrm{l}}\cdot f_{\mathrm{i}}}$. One example is a Bayesian analysis published in 2020. In the conclusion, the author cautions that this study applies to Earth's conditions. In Bayesian terms, the study favors the formation of intelligence on a planet with identical conditions to Earth but does not do so with high confidence.

Planetary scientist Pascal Lee of the SETI Institute proposes that this fraction is very low (0.0002). He based this estimate on how long it took Earth to develop intelligent life (1 million years since Homo erectus evolved, compared to 4.6 billion years since Earth formed).

Fraction of the above revealing their existence via signal release into space, f_c

For deliberate communication, the one example we have (the Earth) does not do much explicit communication, though there are some efforts covering only a tiny fraction of the stars that might look for human presence. (See Arecibo message, for example). There is considerable speculation why an extraterrestrial civilization might exist but choose not to communicate. However, deliberate communication is not required, as other technosignatures may be detectable. Calculations indicate that current or near-future Earth-level technology might well be detectable to civilizations not too much more advanced than present day humans. By this standard, the Earth is a communicating civilization.

Another question is what percentage of civilizations in the galaxy are close enough for us to detect, assuming that they send out signals. For example, existing Earth radio telescopes could only detect Earth radio transmissions from roughly a light year away.

Lifetime of such a civilization wherein it communicates its signals into space, L

Michael Shermer estimated L as 420 years, based on the duration of sixty historical Earthly civilizations. Using 28 civilizations more recent than the Roman Empire, he calculates a figure of 304 years for "modern" civilizations. It could also be argued from Michael Shermer's results that the fall of most of these civilizations was followed by later civilizations that carried on the technologies, so it is doubtful that they are separate civilizations in the context of the Drake equation. In the expanded version, including reappearance number, this lack of specificity in defining single civilizations does not matter for the result, since such a civilization turnover could be described as an increase in the reappearance number rather than increase in L, stating that a civilization reappears in the form of the succeeding cultures. Furthermore, since none could communicate over interstellar space, the method of comparing with historical civilizations could be regarded as invalid.

David Grinspoon has argued that once a civilization has developed enough, it might overcome all threats to its survival. It will then last for an indefinite period of time, making the value for L potentially billions of years. If this is the case, then he proposes that the Milky Way Galaxy may have been steadily accumulating advanced civilizations since it formed. He proposes that the last factor L be replaced with f_IC · T, where f_IC is the fraction of communicating civilizations that become "immortal" (in the sense that they simply do not die out), and T representing the length of time during which this process has been going on. This has the advantage that T would be a relatively easy-to-discover number, as it would simply be some fraction of the age of the universe.

It has also been hypothesized that once a civilization has learned of a more advanced one, its longevity could increase because it can learn from the experiences of the other.

The astronomer Carl Sagan speculated that all of the terms, except for the lifetime of a civilization, are relatively high and the determining factor in whether there are large or small numbers of civilizations in the universe is the civilization lifetime, or in other words, the ability of technological civilizations to avoid self-destruction. In Sagan's case, the Drake equation was a strong motivating factor for his interest in environmental issues and his efforts to warn against the dangers of nuclear warfare. Paleobiologist Olev Vinn suggests that the lifetime of most technological civilizations is brief due to inherited behavior patterns present in all intelligent organisms. These behaviors, incompatible with civilized conditions, inevitably lead to self-destruction soon after the emergence of advanced technologies.

An intelligent civilization might not be organic, as some have suggested that artificial general intelligence may replace humanity.

Range of results

As many skeptics have pointed out, the Drake equation can give a very wide range of values, depending on the assumptions, as the values used in portions of the Drake equation are not well established. In particular, the result can be N ≪ 1, meaning we are likely alone in the galaxy, or N ≫ 1, implying there are many civilizations we might contact. One of the few points of wide agreement is that the presence of humanity demonstrates that the probability of intelligence arising is greater than zero.

As an example of a low estimate, combining NASA's star formation rates, the rare Earth hypothesis value of f_p · n_e · f_l = 10⁻⁵, Mayr's view on intelligence arising, Drake's view of communication, and Shermer's estimate of lifetime:

R_∗ = 1.5–3 yr⁻¹, f_p · n_e · f_l = 10⁻⁵, f_i = 10⁻⁹, f_c = 0.2^{[Drake, above]}, and L = 304 years

gives:

N = 1.5 × 10⁻⁵ × 10⁻⁹ × 0.2 × 304 = 9.1 × 10⁻¹³ (0.00000000000091 in non scientific notation)

i.e., suggesting that we are probably alone in this galaxy, and possibly in the observable universe.

On the other hand, with larger values for each of the parameters above, values of N can be derived that are greater than 1. The following higher values that have been proposed for each of the parameters:

R_∗ = 1.5–3 yr⁻¹, f_p = 1, n_e = 0.2, f_l = 0.13, f_i = 1, f_c = 0.2^{[Drake, above]}, and L = 10⁹ years

Use of these parameters gives:

N = 3 × 1 × 0.2 × 0.13 × 1 × 0.2 × 10⁹ = 15,600,000 civilizations in the Milky Way with which communication might be possible

Monte Carlo simulations of estimates of the Drake equation factors based on a stellar and planetary model of the Milky Way have resulted in the number of civilizations varying by a factor of 100.

Possible former technological civilizations

In 2016, Adam Frank and Woodruff Sullivan modified the Drake equation to determine just how unlikely the event of a technological species arising on a given habitable planet must be, to give the result that Earth hosts the only technological species that has ever arisen, for two cases: (a) this Galaxy, and (b) the universe as a whole. By asking this different question, one removes the lifetime and simultaneous communication uncertainties. Since the numbers of habitable planets per star can today be reasonably estimated, the only remaining unknown in the Drake equation is the probability that a habitable planet ever develops a technological species over its lifetime. For Earth to have the only technological species that has ever occurred in the universe, they calculate the probability of any given habitable planet ever developing a technological species must be less than 2.5×10⁻²⁴. Similarly, for Earth to have been the only case of hosting a technological species over the history of this Galaxy, the odds of a habitable zone planet ever hosting a technological species must be less than 1.7×10⁻¹¹ (about 1 in 60 billion). The figure for the universe implies that it is extremely unlikely that Earth hosts the only technological species that has ever occurred. On the other hand, for this Galaxy one must think that fewer than 1 in 60 billion habitable planets develop a technological species for there not to have been at least a second case of such a species over the past history of this Galaxy.

Modifications

As many observers have pointed out, the Drake equation is a very simple model that omits potentially relevant parameters, and many changes and modifications to the equation have been proposed. One line of modification, for example, attempts to account for the uncertainty inherent in many of the terms. Combining the estimates of the original six factors by major researchers via a Monte Carlo procedure leads to a best value for the non-longevity factors of 0.85 per year. This result differs insignificantly from the estimate of unity given both by Drake and the Cyclops report.

Others note that the Drake equation ignores many concepts that might be relevant to the odds of contacting other civilizations. For example, Glen David Brin states: "The Drake equation merely speaks of the number of sites at which ETIs spontaneously arise. The equation says nothing directly about the contact cross-section between an ETIS and contemporary human society". Because it is the contact cross-section that is of interest to the SETI community, many additional factors and modifications of the Drake equation have been proposed.

Colonization

Brin proposed to generalize the Drake equation to include additional effects of alien civilizations colonizing other star systems. Each original site expands with an expansion velocity v, and establishes additional sites that survive for a lifetime L. The result is a more complex set of 3 equations.

Reappearance factor

The Drake equation may furthermore be multiplied by how many times an intelligent civilization may occur on planets where it has happened once. Even if an intelligent civilization reaches the end of its lifetime, life may still prevail on the planet for billions of years, permitting the next civilization to evolve. Thus, several civilizations may come and go during the lifespan of one and the same planet. Thus, if n_r is the average number of times a new civilization reappears on the same planet where a previous civilization once has appeared and ended, then the total number of civilizations on such a planet would be 1 + n_r, which is the actual reappearance factor added to the equation.

METI factor

Alexander Zaitsev said that to be in a communicative phase and emit dedicated messages are not the same. For example, humans are in a communicative phase, but are not a communicative civilization; there are no purposeful and regular transmission of interstellar messages. For this reason, he suggested introducing the METI factor (messaging to extraterrestrial intelligence) to the classical Drake equation. He defined the factor as "f_m = The fraction of communicative civilizations with clear and non-paranoid planetary consciousness (that is, those which actually engage in deliberate interstellar transmission)".

Biogenic gases

Astronomer Sara Seager proposed a revised equation that focuses on the search for planets with biosignature gases. These gases are produced by living organisms that can accumulate in a planet atmosphere to levels that can be detected with remote space telescopes.

The Seager equation looks like:

$${\displaystyle N=N_{\ast }\cdot F_{\mathrm{Q}}\cdot F_{\mathrm{H}\mathrm{Z}}\cdot F_{\mathrm{O}}\cdot F_{\mathrm{L}}\cdot F_{\mathrm{S}}}$$

where:

N = the number of planets with detectable signs of life

N_∗ = the number of stars observed

F_Q = the fraction of stars that are quiet

F_HZ = the fraction of stars with rocky planets in the habitable zone

F_O = the fraction of those planets that can be observed

F_L = the fraction that have life

F_S = the fraction on which life produces a detectable signature gas

Carl Sagan's version of the Drake equation

American astronomer Carl Sagan made some modifications in the Drake equation and presented it in the 1980 program Cosmos: A Personal Voyage. The modified equation is:

$${\displaystyle N=N_{\ast }\cdot f_{\mathrm{p}}\cdot n_{\mathrm{e}}\cdot f_{\mathrm{l}}\cdot f_{\mathrm{i}}\cdot f_{\mathrm{c}}\cdot f_{\mathrm{L}}}$$

where:

N = the number of civilizations in the Milky Way galaxy with which communication might be possible (i.e. which are on the current past light cone);

N_∗ = Number of stars in the Milky Way Galaxy

f_p = the fraction of those stars that have planets.

n_e = the average number of planets that can potentially support life per star that has planets.

f_l = the fraction of planets that could support life that actually develop life at some point.

f_i = the fraction of planets with life that go on to develop intelligent life (civilizations).

f_c = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space.

f_L = fraction of a planetary lifetime graced by a technological civilization

Plate tectonics factor

Robert J. Stern and Taras V. Gerya proposed to add plate tectonics factors in the 2024 paper:

We resolve the Fermi Paradox (1) by adding two additional terms to the Drake Equation: f_oc (the fraction of habitable exoplanets with significant continents and oceans) and f_pt (the fraction of habitable exoplanets with significant continents and oceans that have had plate tectonics operating for at least 0.5 Ga); and (2) by demonstrating that the product of f_oc and f_pt is very small (< 0.00003–0.002). We propose that the lack of evidence for ACCs [active, communicative civilizations] reflects the scarcity of long-lived plate tectonics and/or continents and oceans on exoplanets with primitive life.

Criticism

Criticism of the Drake equation is varied. Firstly, many of the terms in the equation are largely or entirely based on conjecture. Star formation rates are well-known, and the incidence of planets has a sound theoretical and observational basis, but the other terms in the equation become very speculative. The uncertainties revolve around the present day understanding of the evolution of life, intelligence, and civilization, not physics. No statistical estimates are possible for some of the parameters, where only one example is known. The net result is that the equation cannot be used to draw firm conclusions of any kind, and the resulting margin of error is huge, far beyond what some consider acceptable or meaningful.

Others point out that the equation was formulated before our understanding of the universe had matured. Astrophysicist Ethan Siegel, said:

The Drake equation, when it was put forth, made an assumption about the Universe that we now know is untrue: It assumed that the Universe was eternal and static in time. As we learned only a few years after Frank Drake first proposed his equation, the Universe doesn’t exist in a steady state, where it’s unchanging in time, but rather has evolved from a hot, dense, energetic, and rapidly expanding state: a hot Big Bang that occurred over a finite duration in our cosmic past.

One reply to such criticisms is that even though the Drake equation currently involves speculation about unmeasured parameters, it was intended as a way to stimulate dialogue on these topics. Then the focus becomes how to proceed experimentally. Indeed, Drake originally formulated the equation merely as an agenda for discussion at the Green Bank conference.

Fermi paradox

Main article: Fermi paradox

A civilization lasting for tens of millions of years could be able to spread throughout the galaxy, even at the slow speeds foreseeable with present-day technology. However, no confirmed signs of civilizations or intelligent life elsewhere have been found, either in this Galaxy or in the observable universe of 2 trillion galaxies. According to this line of thinking, the tendency to fill (or at least explore) all available territory seems to be a universal trait of living things, so the Earth should have already been colonized, or at least visited, but no evidence of this exists. Hence Fermi's question "Where is everybody?".

A large number of explanations have been proposed to explain this lack of contact; a book published in 2015 elaborated on 75 different explanations. In terms of the Drake Equation, the explanations can be divided into three classes:

• Few intelligent civilizations ever arise. This is an argument that at least one of the first few terms, R_∗ · f_p · n_e · f_l · f_i, has a low value. The most common suspect is f_i, but explanations such as the rare Earth hypothesis argue that n_e is the small term.
• Intelligent civilizations exist, but we see no evidence, meaning f_c is small. Typical arguments include that civilizations are too far apart, it is too expensive to spread throughout the galaxy, civilizations broadcast signals for only a brief period of time, communication is dangerous, and many others.
• The lifetime of intelligent, communicative civilizations is short, meaning the value of L is small. Drake suggested that a large number of extraterrestrial civilizations would form, and he further speculated that the lack of evidence of such civilizations may be because technological civilizations tend to disappear rather quickly. Common explanations include the nature of intelligent life to destroy itself and/or others, and that intelligent life may be destroyed by natural events.

These lines of reasoning lead to the Great Filter hypothesis, which states that since there are no observed extraterrestrial civilizations despite the vast number of stars, at least one step in the process must be acting as a filter to reduce the final value. According to this view, either it is very difficult for intelligent life to arise, or the lifetime of technologically advanced civilizations, or the period of time they reveal their existence must be relatively short.

An analysis by Anders Sandberg, Eric Drexler and Toby Ord suggests "a substantial ex ante (predicted) probability of there being no other intelligent life in our observable universe".

In popular culture

Commemorative plate on Europa Clipper

The equation was cited by Gene Roddenberry as supporting the multiplicity of inhabited planets shown on Star Trek, the television series he created. However, Roddenberry did not have the equation with him, and he was forced to "invent" it for his original proposal. The fictitious equation that Roddenberry created is:

$${\displaystyle F{f}^2(MgE)-C^{1}R{i}^1\cdot M=L/So}$$

Regarding this fictional version of the equation, Drake himself commented that a number raised to the first power is just the number itself.

A commemorative plate on NASA's Europa Clipper mission, which launched October 14, 2024, features a poem by the U.S. Poet Laureate Ada Limón, waveforms of the word 'water' in 103 languages, a schematic of the water hole, the Drake equation, and a portrait of planetary scientist Ron Greeley on it.