Hilbert's paradox of the Grand Hotel

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Hilbert's Hotel

Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely often. The idea was introduced by David Hilbert in a 1924 lecture "Über das Unendliche", reprinted in (Hilbert 2013, p.730), and was popularized through George Gamow's 1947 book One Two Three... Infinity.

The paradox

Consider a hypothetical hotel with a countably infinite number of rooms, all of which are occupied. One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms, where the pigeonhole principle would apply.

Finitely many new guests

Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on, moving every guest from their current room n to room n+1. After this, room 1 is empty and the new guest can be moved into that room. By repeating this procedure, it is possible to make room for any finite number of new guests. In general, assume that k guests seek a room. We can apply the same procedure and move every guest from room n to room n + k. In a similar manner, if k guests wished to leave the hotel, every guest moves from room n to room n − k.

Infinitely many new guests

It is also possible to accommodate a countably infinite number of new guests: just move the person occupying room 1 to room 2, the guest occupying room 2 to room 4, and, in general, the guest occupying room n to room 2n (2 times n), and all the odd-numbered rooms (which are countably infinite) will be free for the new guests.

Infinitely many coaches with infinitely many guests each

Further information: Pairing function

It is possible to accommodate countably infinitely many coachloads of countably infinite passengers each, by several different methods. Most methods depend on the seats in the coaches being already numbered (or use the axiom of countable choice). In general any pairing function can be used to solve this problem. For each of these methods, consider a passenger's seat number on a coach to be ${\displaystyle n}$, and their coach number to be ${\displaystyle c}$, and the numbers ${\displaystyle n}$ and ${\displaystyle c}$ are then fed into the two arguments of the pairing function.

Prime powers method

Empty the odd numbered rooms by sending the guest in room ${\displaystyle i}$ to room ${\displaystyle 2^{i}}$, then put the first coach's load in rooms ${\displaystyle 3^{n}}$, the second coach's load in rooms ${\displaystyle 5^{n}}$; for coach number ${\displaystyle c}$ we use the rooms ${\displaystyle p^{n}}$ where ${\displaystyle p}$ is the ${\displaystyle c}$th odd prime number. This solution leaves certain rooms empty (which may or may not be useful to the hotel); specifically, all odd numbers that are not prime powers, such as 15 or 847, will no longer be occupied. (So, strictly speaking, this shows that the number of arrivals is less than or equal to the number of vacancies created. It is easier to show, by an independent means, that the number of arrivals is also greater than or equal to the number of vacancies, and thus that they are equal, than to modify the algorithm to an exact fit.) (The algorithm works equally well if one interchanges ${\displaystyle n}$ and ${\displaystyle c}$, but whichever choice is made, it must be applied uniformly throughout.)

Prime factorization method

You can put each person of a certain seat ${\displaystyle s}$ and coach ${\displaystyle c}$ into room ${\displaystyle 2^{s}3^{c}}$ (presuming c=0 for the people already in the hotel, 1 for the first coach, etc. ...). Because every number has a unique prime factorization, it's easy to see all people will have a room, while no two people will end up in the same room. For example, the person in room 2592 (${\displaystyle 2^{5}3^{4}}$) was sitting in on the 4th coach, on the 5th seat. Like the prime powers method, this solution leaves certain rooms empty.

This method can also easily be expanded for infinite nights, infinite entrances, etc. ... ( ${\displaystyle 2^{s}3^{c}5^{n}7^{e}}$ )

Interleaving method

For each passenger, compare the lengths of ${\displaystyle n}$ and ${\displaystyle c}$ as written in any positional numeral system, such as decimal. (Treat each hotel resident as being in coach #0.) If either number is shorter, add leading zeroes to it until both values have the same number of digits. Interleave the digits to produce a room number: its digits will be [first digit of coach number]-[first digit of seat number]-[second digit of coach number]-[second digit of seat number]-etc. The hotel (coach #0) guest in room number 1729 moves to room 01070209 (i.e., room 1,070,209). The passenger on seat 1234 of coach 789 goes to room 01728394 (i.e., room 1,728,394).

Unlike the prime powers solution, this one fills the hotel completely, and we can reconstruct a guest's original coach and seat by reversing the interleaving process. First add a leading zero if the room has an odd number of digits. Then de-interleave the number into two numbers: the coach number consists of the odd-numbered digits and the seat number is the even-numbered ones. Of course, the original encoding is arbitrary, and the roles of the two numbers can be reversed (seat-odd and coach-even), so long as it is applied consistently.

Triangular number method

Those already in the hotel will be moved to room ${\displaystyle (n^{2}+n)/2}$, or the ${\displaystyle n}$th triangular number. Those in a coach will be in room ${\displaystyle ((c+n-1)^{2}+c+n-1)/2+n}$, or the ${\displaystyle (c+n-1)}$ triangular number plus ${\displaystyle n}$. In this way all the rooms will be filled by one, and only one, guest.

This pairing function can be demonstrated visually by structuring the hotel as a one-room-deep, infinitely tall pyramid. The pyramid's topmost row is a single room: room 1; its second row is rooms 2 and 3; and so on. The column formed by the set of rightmost rooms will correspond to the triangular numbers. Once they are filled (by the hotel's redistributed occupants), the remaining empty rooms form the shape of a pyramid exactly identical to the original shape. Thus, the process can be repeated for each infinite set. Doing this one at a time for each coach would require an infinite number of steps, but by using the prior formulas, a guest can determine what his room "will be" once his coach has been reached in the process, and can simply go there immediately.

Arbitrary enumeration method

Let ${\displaystyle S:=\{(a,b)\mid a,b\in \mathbb {N} \}}$. ${\displaystyle S}$ is countable since ${\displaystyle \mathbb {N} }$ is countable, hence we may enumerate its elements ${\displaystyle s_{1},s_{2},\dots }$. Now if ${\displaystyle s_{n}=(a,b)}$, assign the ${\displaystyle b}$th guest of the ${\displaystyle a}$th coach to the ${\displaystyle n}$th room (consider the guests already in the hotel as guests of the ${\displaystyle 0}$th coach). Thus we have a function assigning each person to a room; furthermore, this assignment does not skip over any rooms.

Further layers of infinity

Suppose the hotel is next to an ocean, and an infinite number of car ferries arrive, each bearing an infinite number of coaches, each with an infinite number of passengers. This is a situation involving three "levels" of infinity, and it can be solved by extensions of any of the previous solutions.

The prime factorization method can be applied by adding a new prime number for every additional layer of infinity ( ${\displaystyle 2^{s}3^{c}5^{f}}$, with ${\displaystyle f}$ the ferry).

The prime power solution can be applied with further exponentiation of prime numbers, resulting in very large room numbers even given small inputs. For example, the passenger in the second seat of the third bus on the second ferry (address 2-3-2) would raise the 2nd odd prime (5) to 49, which is the result of the 3rd odd prime (7) being raised to the power of his seat number (2). This room number would have over thirty decimal digits.

The interleaving method can be used with three interleaved "strands" instead of two. The passenger with the address 2-3-2 would go to room 232, while the one with the address 4935-198-82217 would go to room #008,402,912,391,587 (the leading zeroes can be removed).

Anticipating the possibility of any number of layers of infinite guests, the hotel may wish to assign rooms such that no guest will need to move, no matter how many guests arrive afterward. One solution is to convert each arrival's address into a binary number in which ones are used as separators at the start of each layer, while a number within a given layer (such as a guest's coach number) is represented with that many zeroes. Thus, a guest with the prior address 2-5-1-3-1 (five infinite layers) would go to room 10010000010100010 (decimal 295458).

As an added step in this process, one zero can be removed from each section of the number; in this example, the guest's new room is 101000011001 (decimal 2585). This ensures that every room could be filled by a hypothetical guest. If no infinite sets of guests arrive, then only rooms that are a power of two will be occupied.

Infinite layers of nesting

Although a room can be found for any finite number of nested infinities of people, the same is not always true for an infinite number of layers, even if a finite number of elements exists at each layer.

Analysis

Hilbert's paradox is a veridical paradox: it leads to a counter-intuitive result that is provably true. The statements "there is a guest to every room" and "no more guests can be accommodated" are not equivalent when there are infinitely many rooms.

Initially, this state of affairs might seem to be counter-intuitive. The properties of "infinite collections of things" are quite different from those of "finite collections of things". The paradox of Hilbert's Grand Hotel can be understood by using Cantor's theory of transfinite numbers. Thus, in an ordinary (finite) hotel with more than one room, the number of odd-numbered rooms is obviously smaller than the total number of rooms. However, in Hilbert's aptly named Grand Hotel, the quantity of odd-numbered rooms is not smaller than the total "number" of rooms. In mathematical terms, the cardinality of the subset containing the odd-numbered rooms is the same as the cardinality of the set of all rooms. Indeed, infinite sets are characterized as sets that have proper subsets of the same cardinality. For countable sets (sets with the same cardinality as the natural numbers) this cardinality is ${\displaystyle \aleph _{0}}$.

Rephrased, for any countably infinite set, there exists a bijective function which maps the countably infinite set to the set of natural numbers, even if the countably infinite set contains the natural numbers. For example, the set of rational numbers—those numbers which can be written as a quotient of integers—contains the natural numbers as a subset, but is no bigger than the set of natural numbers since the rationals are countable: there is a bijection from the naturals to the rationals.

References in fiction

• BBC Learning Zone repeatedly screened a 1996 one-off educational docudrama Hotel Hilbert set in the hotel as seen through the eyes of a young female guest Fiona Knight, her name a pun on finite. The programme was designed to educate viewers about the concept of infinity.
• The novel White Light by mathematician/science fiction writer Rudy Rucker includes a hotel based on Hilbert's paradox, and where the protagonist of the story meets Georg Cantor.
• Stephen Baxter's science fiction novel Transcendent has a brief discussion on the nature of infinity, with an explanation based on the paradox, modified to use soldiers rather than hotels.
• Geoffrey A. Landis' Nebula Award-winning short story "Ripples in the Dirac Sea" uses the Hilbert hotel as an explanation of why an infinitely-full Dirac sea can nevertheless still accept particles.
• In Peter Høeg's novel Miss Smilla's Feeling for Snow, the titular heroine reflects that it is admirable for the hotel's manager and guests to go to all that trouble so that the latecomer can have his own room and some privacy.
• In Ivar Ekeland's novel for children, The Cat in Numberland, a "Mr. Hilbert" and his wife run an infinite hotel for all the integers. The story progresses through the triangular method for the rationals.
• In Will Wiles's novel The Way Inn, about an infinitely large motel, the villain's name is Hilbert.
• In Reginald Hill's novel "The Stranger House" the character Sam refers to the Hilbert Hotel paradox.
• The short story by Naum Ya. Vilenkin The Extraordinary Hotel (often erroneously attributed to Stanislaw Lem) shows the way in which Hilbert's Grand Hotel may be reshuffled when infinite new hosts arrive.
• The comic book saga The Tempest from the League of Extraordinary Gentlemen series by Alan Moore and Kevin O'Neill shows a villain called Infinity. In the story it is suggested that the villain goes to the hotel based on Hilbert's paradox. Georg Cantor is mentioned as well.

Kalam cosmological argument

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

The Kalam cosmological argument is a modern formulation of the cosmological argument for the existence of God. It is named after the kalam (medieval Islamic scholasticism) from which its key ideas originated. William Lane Craig was principally responsible for giving new life to the argument, due to his The Kalām Cosmological Argument (1979), among other writings. The kalam cosmological argument's premises surrounding causation and the beginning of the universe were discussed by various philosophers, the philosophical view of causation being a subject of David Hume's An Enquiry Concerning Human Understanding and the metaphysical arguments for a beginning of the universe being the subject of Kant's first antinomy.

The argument's key underpinning idea is the metaphysical impossibility of actual infinities and of a temporally past-infinite universe, traced by Craig to 11th-century Persian Muslim scholastic philosopher Al-Ghazali. This feature distinguishes it from other cosmological arguments, such as that of Thomas Aquinas, which rests on the impossibility of a causally ordered infinite regress, and those of Leibniz and Samuel Clarke, which refer to the Principle of Sufficient Reason.

Since Craig's original publication, the Kalam cosmological argument has elicited public debate between Craig and Graham Oppy, Adolf Grünbaum, J. L. Mackie and Quentin Smith, and has been used in Christian apologetics. According to Michael Martin, the cosmological arguments presented by Craig, Bruce Reichenbach, and Richard Swinburne are "among the most sophisticated and well argued in contemporary theological philosophy".

Form of the argument

The most prominent form of the argument, as defended by William Lane Craig, states the Kalam cosmological argument as the following syllogism:

1. Everything that begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.

Given the conclusion, Craig appends a further premise and conclusion based upon a philosophical analysis of the properties of the cause of the universe:

4. The universe has a cause.
5. If the universe has a cause, then an uncaused, personal Creator of the universe exists who sans (without) the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful.
6. Therefore, an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful.

Referring to the implications of Classical Theism that follow from this argument, Craig writes:

"... transcending the entire universe there exists a cause which brought the universe into being ex nihilo ... our whole universe was caused to exist by something beyond it and greater than it. For it is no secret that one of the most important conceptions of what theists mean by 'God' is Creator of heaven and earth."

Historical background

The kalam cosmological argument is based on the concept of the prime-mover, introduced by Aristotle, and entered early Christian or Neoplatonist philosophy in Late Antiquity, being developed by John Philoponus. Along with much of classical Greek philosophy, the concept was adopted into medieval Islamic tradition during the Islamic Golden Age, where it received its fullest articulation at the hands of Muslim scholars, most directly by Islamic theologians of the Sunni tradition.

Its historic proponents include Al-Kindi, Al-Ghazali, and St. Bonaventure.

One of the earliest formulations of the kalam cosmological argument in the Islamic philosophical tradition comes from Al-Ghazali, who writes:

"Every being which begins has a cause for its beginning; now the world is a being which begins; therefore, it possesses a cause for its beginning."

Between the 9th to 12th centuries, the cosmological argument developed as a concept within Islamic theology. It was refined in the 11th century by Al-Ghazali (The Incoherence of the Philosophers), and in the 12th by Ibn Rushd (Averroes). It reached medieval Christian philosophy in the 13th century and was discussed by Bonaventure, as well as Thomas Aquinas in his Summa Theologica (I, q.2, a.3) and Summa Contra Gentiles (I, 13).

Islamic perspectives may be divided into positive Aristotelian responses strongly supporting the argument, such as those by Al-Kindi, and Averroes, and negative responses critical of it, including those by Al-Ghazali and Muhammad Iqbal. Al-Ghazali was unconvinced by the first-cause arguments of Al-Kindi, arguing that only the infinite per se (that is an essentially ordered infinite series) is impossible, arguing for the possibility of the infinite per accidens (that is an accidentally ordered infinite series). He writes:

"According to the hypothesis under consideration, it has been established that all the beings in the world have a cause. Now, let the cause itself have a cause, and the cause of the cause have yet another cause, and so on ad infinitum. It does not behove you to say that an infinite regress of causes is impossible."

Muhammad Iqbal also stated:

"To finish the series at a certain point, and to elevate one member of the series to the dignity of an uncaused first cause, is to set at naught the very law of causation on which the whole argument proceeds."

Contemporary discourse

According to the atheist philosopher Quentin Smith, "a count of the articles in the philosophy journals shows that more articles have been published about Craig’s defense of the Kalam argument than have been published about any other philosopher’s contemporary formulation of an argument for God’s existence."

The Kalam cosmological argument has received criticism from philosophers such as J. L. Mackie, Graham Oppy, Michael Martin, Quentin Smith, physicists Paul Davies, Lawrence Krauss and Victor Stenger, and authors such as Dan Barker.

Modern discourse encompasses the fields of both philosophy and science (e.g. the fields of quantum physics and cosmology), which Bruce Reichenbach summarises as:

"... whether there needs to be a cause of the first natural existent, whether something like the universe can be finite and yet not have a beginning, and the nature of infinities and their connection with reality".

Since the temporal ordering of events is central, the kalam argument also brings issues of the nature of time into the discussion.

Premise one: "Whatever begins to exist has a cause."

Craig and Sinclair have stated that the first premise is obviously true, at least more plausibly true than its negation. Craig offers three reasons why the first premise is true:

1. Rational intuition: Craig states that the first premise is self-evidently true, being based upon the metaphysical intuition that "something cannot come into being from nothing", or "Ex nihilo nihil fit", originating from Parmenidean philosophy. He states that for something to come into being without any cause is to come into being from nothing, which he says is "surely absurd."
2. Reductio ad absurdum: if false, it would be inexplicable why just anything and everything does not randomly come into existence without a cause.
3. Inductive reasoning from both common experience and scientific evidence, which constantly verifies and never falsifies the truth of the first premise.

According to Reichenbach, "the Causal Principle has been the subject of extended criticism", which can be divided into philosophical and scientific criticisms.

Philosophical objections

Graham Oppy, J. L. Mackie and Wes Morriston have objected to the intuitiveness of the first premise. Oppy states:

"Mackie, [Adolf] Grunbaum, [Quentin] Smith and I—among many others—have taken issue with the first premise: why should it be supposed that absolutely everything which begins to exist has a cause for its beginning to exist?"

Mackie affirms that there is no good reason to assume a priori that an uncaused beginning of all things is impossible. Moreover, that the Causal Principle cannot be extrapolated to the universe from inductive experience. He appeals to David Hume's thesis (An Enquiry Concerning Human Understanding) that effects without causes can be conceived in the mind, and that what is conceivable in the mind is possible in the real world. This argument has been criticised by Bruce Reichenbach and G.E.M. Anscombe, who point out the phenomenological and logical problems in inferring factual possibility from conceivability. Craig notes:

"Hume himself clearly believed in the causal principle. He presupposes throughout the Enquiry that events have causes, and in 1754 he wrote to John Stewart, 'But allow me to tell you that I never asserted so absurd a Proposition as that anything might arise without a cause'".

Morriston asserts that causal laws are physical processes for which we have intuitive knowledge in the context of events within time and space, but that such intuitions do not hold true for the beginning of time itself. He states:

"We have no experience of the origin of worlds to tell us that worlds don't come into existence like that. We don't even have experience of the coming into being of anything remotely analogous to the “initial singularity” that figures in the Big Bang theory of the origin of the universe."

In reply, Craig has maintained that causal laws are unrestricted metaphysical truths that are "not contingent upon the properties, causal powers, and dispositions of the natural kinds of substances which happen to exist", remarking:

"The history of twentieth century astrophysical cosmology belies Morriston's claim that people have no strong intuitions about the need of a causal explanation of the origin of time and the universe."

Quantum physics

A common objection to premise one appeals to the phenomenon of quantum indeterminacy, where, at the subatomic level, the causal principle; "everything that begins to exist has a cause" appears to break down. Craig replies that the phenomenon of indeterminism is specific to the Copenhagen Interpretation of Quantum Mechanics, pointing out that this is only one of a number of different interpretations, some of which he states are fully deterministic (mentioning David Bohm) and none of which are as yet known to be true. He concludes that subatomic physics is not a proven exception to the first premise.

The philosopher Quentin Smith has cited the example of virtual particles, which appear and disappear from observation, apparently at random, to assert the tenability of uncaused natural phenomena. In his book A Universe from Nothing: Why There is Something Rather Than Nothing, cosmologist Lawrence Krauss has proposed how quantum mechanics can explain how space-time and matter can emerge from 'nothing' (referring to the quantum vacuum). Philosopher Michael Martin has also referred to quantum vacuum fluctuation models to support the idea of a universe with uncaused beginnings. He writes:

"Even if the universe has a beginning in time, in the light of recently proposed cosmological theories this beginning may be uncaused. Despite Craig's claim that theories postulating that the universe 'could pop into existence uncaused' are incapable of 'sincere affirmation,' such similar theories are in fact being taken seriously by scientists."

Philosopher of science David Albert has criticised the use of the term 'nothing' in describing the quantum vacuum. In a review of Krauss's book, he states:

"Relativistic-quantum-field-theoretical vacuum states—no less than giraffes or refrigerators or solar systems—are particular arrangements of elementary physical stuff. The true relativistic-quantum-field-theoretical equivalent to there not being any physical stuff at all isn’t this or that particular arrangement of the fields—what it is (obviously, and ineluctably, and on the contrary) is the simple absence of the fields."

Likewise, Craig has argued that the quantum vacuum, in containing quantifiable, measurable energy, cannot be described as 'nothing', therefore, that phenomena originating from the quantum vacuum cannot be described as 'uncaused'. On the topic of virtual particles, he writes:

"For virtual particles do not literally come into existence spontaneously out of nothing. Rather the energy locked up in a vacuum fluctuates spontaneously in such a way as to convert into evanescent particles that return almost immediately to the vacuum."

Cosmologist Alexander Vilenkin has stated that even "the absence of space, time and matter" cannot truly be defined as 'nothing' given that the laws of physics are still present, though it would be "as close to nothing as you can get".

Premise two: "The universe began to exist."

Craig defends premise two using both physical arguments with evidence from cosmology and physics, and metaphysical arguments for the impossibility of actual infinities in reality.

Cosmology and physics

For physical evidence, Craig appeals to:

1. Scientific confirmation against a past-infinite universe in the form of the Second Law of Thermodynamics.
2. Scientific evidence that the universe began to exist a finite time ago at the Big Bang.
3. The Borde–Guth–Vilenkin theorem, a cosmological theorem which deduces that any universe that has, on average, been expanding throughout its history cannot be infinite in the past but must have a past space-time boundary.

Professor Alexander Vilenkin, one of the three authors of the Borde-Guth-Vilenkin theorem, writes:

"A remarkable thing about this theorem is its sweeping generality. We made no assumptions about the material content of the universe. We did not even assume that gravity is described by Einstein’s equations. So, if Einstein’s gravity requires some modification, our conclusion will still hold. The only assumption that we made was that the expansion rate of the universe never gets below some nonzero value, no matter how small."

Victor J. Stenger has referred to the Aguirre-Gratton model for eternal inflation as an exemplar by which others disagree with the Borde-Guth-Vilenkin theorem. In private correspondence with Stenger, Vilenkin remarked how the Aguirre-Gratton model attempts to evade a beginning by reversing the "arrow of time" at t = 0, but that: "This makes the moment t = 0 rather special. I would say no less special than a true beginning of the universe."

At the "State of the Universe" conference at Cambridge University in January 2012, Vilenkin discussed problems with various theories that would claim to avoid the need for a cosmological beginning, alleging the untenability of eternal inflation, cyclic and cosmic egg models, eventually concluding: "All the evidence we have says that the universe had a beginning."

Actual infinities

On the metaphysical impossibility of actual infinities, Craig asserts:

1. The metaphysical impossibility of an actually infinite series of past events by citing David Hilbert's famous Hilbert's Hotel thought experiment.
2. The impossibility of forming an actual infinite by successive addition, referencing Bertrand Russell's example of Tristram Shandy.

Michael Martin disagrees with these assertions by Craig, saying:

"Craig's a priori arguments are unsound or show at most that actual infinities have odd properties. This latter fact is well known, however, and shows nothing about whether it is logically impossible to have actual infinities in the real world."

Andrew Loke has argued against the metaphysical possibility of a beginningless universe as well as that of an actual infinite existing in the real world.

Another criticism comes from Thomist philosopher Dr. Edward Feser who claims that past and future events are potential rather than actual, meaning that an infinite past could exist in a similar way to how an infinite number of potential halfway points exist between any two given points.

Conclusion: "The universe has a cause."

Given that the Kalam cosmological argument is a deductive argument, if both premises are true, the truth of the conclusion follows necessarily.

In a critique of Craig's book The Kalam Cosmological Argument, published in 1979, Michael Martin states:

"It should be obvious that Craig's conclusion that a single personal agent created the universe is a non sequitur. At most, this Kalam argument shows that some personal agent or agents created the universe. Craig cannot validly conclude that a single agent is the creator. On the contrary, for all he shows, there may have been trillions of personal agents involved in the creation."

Martin also claims that Craig has not justified his claim of creation "ex nihilo", pointing out that the universe may have been created from pre-existing material in a timeless or eternal state. Moreover, that Craig takes his argument too far beyond what his premises allow in deducing that the creating agent is greater than the universe. For this, he cites the example of a parent "creating" a child who eventually becomes greater than he or she.

In the subsequent Blackwell Companion to Natural Theology, published in 2009, Craig discusses the properties of the cause of the universe, arguing that they follow as consequences of a conceptual analysis and of the cause of the universe and by entailment from the initial syllogism of the argument:

1. A first state of the material world cannot have a material explanation and must originate ex nihilo in being without material cause, because no natural explanation can be causally prior to the very existence of the natural world (space-time and its contents). It follows necessarily that the cause is outside of space and time (timeless, spaceless), immaterial, and enormously powerful, in bringing the entirety of material reality into existence.
2. Even if positing a plurality of causes prior to the origin of the universe, the causal chain must terminate in a cause which is absolutely first and uncaused, otherwise an infinite regress of causes would arise, which Craig and Sinclair argue is impossible.
3. Occam's Razor maintains that the unicity of the First Cause should be assumed unless there are specific reasons to believe that there is more than one causeless cause.
4. Agent causation, volitional action, is the only ontological condition in which an effect can arise in the absence of prior determining conditions. Therefore, only personal, free agency can account for the origin of a first temporal effect from a changeless cause.
5. Abstract objects, the only other ontological category known to have the properties of being uncaused, spaceless, timeless and immaterial, do not sit in volitional causal relationships.

Craig concludes that the cause of the existence of the universe is an "uncaused, personal Creator ... who sans the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful"; remarking upon the theological implications of this union of properties.

Theories of time

Craig holds to the A-theory of time, also known as the "tensed theory of time" or presentism, as opposed to its alternative, the B-theory of time, also known as the "tenseless theory of time" or eternalism. The latter would allow the universe to exist tenselessly as a four-dimensional space-time block, under which circumstances the universe would not "begin to exist": The form of the kalam he presents in his earlier work rests on this theory:

"From start to finish, the kalam cosmological argument is predicated upon the A-Theory of time. On a B-Theory of time, the universe does not in fact come into being or become actual at the Big Bang; it just exists tenselessly as a four-dimensional space-time block that is finitely extended in the earlier than direction. If time is tenseless, then the universe never really comes into being, and, therefore, the quest for a cause of its coming into being is misconceived."

Craig has defended the A-theory against objections from J. M. E. McTaggart and hybrid A–B theorists. Philosopher Yuri Balashov has criticised Craig's attempt to reconcile the A-theory with special relativity by relying on a ‘neo‐Lorentzian interpretation’ of Special Relativity. Balashov claims:

"Despite the fact that presentism has the firm backing of common sense and eternalism revolts against it, eternalism is widely regarded as almost the default view in contemporary debates, and presentism as a highly problematic view."

Craig has criticised Balashov for adopting a verificationist methodology that fails to address the metaphysical and theological foundations of the A-theory.

It has recently been argued that a defense of the Kalam cosmological argument does not have to involve such a commitment to the A-theory. Craig has since modified his view of the A-theory being necessary for the Kalam, stating that while the Kalam would need to be reformulated, "it wouldn't be fatal" on a B-theory.

Fred Hoyle

From Wikipedia, the free encyclopedia

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

Sir Fred Hoyle FRS
Born	24 June 1915 Gilstead, Bingley, West Riding of Yorkshire, England
Died	20 August 2001 (aged 86) Bournemouth, England
Nationality	British
Citizenship	United Kingdom
Alma mater	Emmanuel College, Cambridge
Known for	Coining the phrase 'Big Bang' Stellar nucleosynthesis theory Hoyle's fallacy B2FH paper Hoyle-Narlikar theory Steady state theory Triple-alpha process Panspermia
Spouse(s)	Barbara Clark ​ (m. 1939)​
Children	Geoffrey Hoyle Elizabeth Butler
Awards	Mayhew Prize (1936) Smith's Prize (1938) FRS (1957)[2] Kalinga Prize (1967) RAS Gold Medal (1968) Bruce Medal (1970) Royal Medal (1974) Klumpke-Roberts Award (1977) Crafoord Prize (1997)
Scientific career
Fields	Astronomy
Institutions	Institute of Astronomy, Cambridge
Academic advisors	Rudolf Peierls Maurice Pryce Philip Worsley Wood
Doctoral students	John Moffat Chandra Wickramasinghe Cyril Domb Jayant Narlikar Leon Mestel Peter Alan Sweet Sverre Aarseth
Other notable students	Paul C. W. Davies Douglas Gough
Influenced	Jocelyn Bell Burnell Jayant Narlikar Donald D. Clayton

Sir Fred Hoyle FRS (24 June 1915 – 20 August 2001) was an English astronomer who formulated the theory of stellar nucleosynthesis. He also held controversial stances on other scientific matters—in particular his rejection of the "Big Bang" theory, a term coined by him on BBC radio, and his promotion of panspermia as the origin of life on Earth. He also wrote science fiction novels, short stories and radio plays, and co-authored twelve books with his son, Geoffrey Hoyle. He spent most of his working life at the Institute of Astronomy at Cambridge and served as its director for six years. He was one of the authors of the influential B²FH paper.

Biography

Early life and career

Hoyle was born near Bingley in Gilstead, West Riding of Yorkshire, England. His father, Ben Hoyle, who was a violinist and worked in the wool trade in Bradford, served as a machine gunner in the First World War. His mother, Mabel Pickard, had studied music at the Royal College of Music in London and later worked as a cinema pianist. Hoyle was educated at Bingley Grammar School and read mathematics at Emmanuel College, Cambridge.

In 1936, he won the Mayhew Prize (jointly with George Stanley Rushbrooke).

In late 1940, Hoyle left Cambridge to go to Portsmouth to work for the Admiralty on radar research, for example devising a method to get the altitude of the incoming aeroplanes. He was also put in charge of countermeasures against the radar guided guns found on the Graf Spee. Britain's radar project employed more personnel than the Manhattan project, and was probably the inspiration for the large British project in The Black Cloud. Two colleagues in this war work were Hermann Bondi and Thomas Gold, and the three had many and deep discussions on cosmology. The radar work paid for a couple of trips to North America, where he took the opportunity to visit astronomers. On one trip to the US, he learned about supernovae at Caltech and Mount Palomar and, in Canada, the nuclear physics of plutonium implosion and explosion, noticed some similarity between the two and started thinking about supernova nucleosynthesis. He had an intuition at the time "I will make a name for myself if this works out." Eventually (1954) his prescient and ground breaking paper came out. He also formed a group at Cambridge exploring stellar nucleosynthesis in ordinary stars and was bothered by the paucity of stellar carbon production in existing models. He noticed that one of the existing processes would be made a billion times more productive if the carbon-12 nucleus had a resonance at 7.7 MeV, but the nuclear physicists did not list such a one. On another trip, he visited the nuclear physics group at Caltech, spending a few months of sabbatical there and persuaded them against their considerable scepticism to look for and find the Hoyle state in carbon-12, from which developed a full theory of stellar nucleosynthesis, co-authored by Hoyle with some members of the Caltech group.

A blue plaque at Bingley Grammar School commemorating him

After the war, in 1945, Hoyle returned to Cambridge University, as a lecturer at St John's College, Cambridge. Hoyle's Cambridge years, 1945–1973, saw him rise to the top of world astrophysics theory, on the basis of a startling originality of ideas covering a very wide range of topics. In 1958, Hoyle was appointed Plumian Professor of Astronomy and Experimental Philosophy in Cambridge University. In 1967, he became the founding director of the Institute of Theoretical Astronomy (subsequently renamed the Institute of Astronomy, Cambridge), where his innovative leadership quickly led to this institution becoming one of the premier groups in the world for theoretical astrophysics. In 1971, he was invited to deliver the MacMillan Memorial Lecture to the Institution of Engineers and Shipbuilders in Scotland. He chose the subject "Astronomical Instruments and their Construction". Hoyle was knighted in 1972. Hoyle resigned his Plumian professor position in 1972 and his directorship of the institute in 1973, with this move effectively cutting him off from most of his establishment power-base, connections and steady salary.

After leaving Cambridge, Hoyle wrote many popular science and science fiction books, as well as presenting lectures around the world. Part of the motivation for this was simply to provide a means of support. Hoyle was still a member of the joint policy committee (since 1967), during the planning stage for the 150-inch Anglo-Australian Telescope at Siding Spring Observatory in New South Wales. He became chairman of the Anglo-Australian Telescope board in 1973, and presided at its inauguration in 1974 by Charles, Prince of Wales.

Decline and death

After his resignation from Cambridge, Hoyle moved to the Lake District and occupied his time with a mix of treks across the moors, writing books, visiting research centres around the world, and working on science ideas that have been nearly universally rejected. On 24 November 1997, while hiking across moorlands in west Yorkshire, near his childhood home in Gilstead, Hoyle fell into a steep ravine called Shipley Glen. Roughly twelve hours later, Hoyle was found by a search dog. He was hospitalised for two months with pneumonia and kidney problems (both resulting from hypothermia), as well as a broken shoulder from the fall. Thereafter he entered a marked decline, suffering from memory and mental agility problems. In 2001, he suffered a series of strokes and died in Bournemouth on 20 August of that year.

Views and contributions

Origin of nucleosynthesis

Hoyle authored the first two research papers ever published on the synthesis of the chemical elements heavier than helium by nuclear reactions in stars. The first of these in 1946 showed that the cores of stars will evolve to temperatures of billions of degrees, much hotter than temperatures considered for thermonuclear origin of stellar power in main-sequence stars. Hoyle showed that at such high temperatures the element iron can become much more abundant than other heavy elements owing to thermal equilibrium among nuclear particles, explaining the high natural abundance of iron. This idea would later be called the e Process. Hoyle's second foundational nucleosynthesis publication, published in 1954, showed that the elements between carbon and iron cannot be synthesized by such equilibrium processes. He attributed those elements to specific nuclear fusion reactions between abundant constituents in concentric shells of evolved massive, pre-supernova stars. This startlingly modern picture is the accepted paradigm today for the supernova nucleosynthesis of these primary elements. In the mid-1950s, Hoyle became the leader of a group of very talented experimental and theoretical physicists who met in Cambridge: William Alfred Fowler, Margaret Burbidge, and Geoffrey Burbidge. This group systematized basic ideas of how all the chemical elements in our universe were created, with this now being a field called nucleosynthesis. Famously, in 1957, this group produced the B²FH paper (known for the initials of the four authors) in which the field of nucleosynthesis was organized into complementary nuclear processes. They also added much new material on the synthesis of heavy elements by neutron-capture reactions, the so-called s process and the r process. So influential did the B²FH paper become that for the remainder of the twentieth century it became the default citation of almost all researchers wishing to cite an accepted origin for nucleosynthesis theory, and as a result, the path-breaking Hoyle 1954 paper fell into obscurity. Historical research in the 21st century has brought Hoyle's 1954 paper back to scientific prominence. Those historical arguments were first presented to a gathering of nucleosynthesis experts attending a 2007 conference at Caltech organized after the deaths of both Fowler and Hoyle to celebrate the 50th anniversary of the publication of B²FH. Ironically the B²FH paper did not review Hoyle's 1954 supernova-shells attribution of the origin of elements between silicon and iron despite Hoyle's co-authorship of B²FH. Based on his many personal discussions with Hoyle.  Donald D. Clayton has attributed this seemingly inexplicable oversight in B²FH to the lack of proofreading by Hoyle of the draft composed at Caltech in 1956 by G.R. Burbidge and E.M. Burbidge.

The second of Hoyle's nucleosynthesis papers also introduced an interesting use of the anthropic principle, which was not then known by that name. In trying to work out the routes of stellar nucleosynthesis, Hoyle calculated that one particular nuclear reaction, the triple-alpha process, which generates carbon from helium, would require the carbon nucleus to have a very specific resonance energy and spin for it to work. The large amount of carbon in the universe, which makes it possible for carbon-based life-forms of any kind to exist, demonstrated to Hoyle that this nuclear reaction must work. Based on this notion, Hoyle therefore predicted the values of the energy, the nuclear spin and the parity of the compound state in the carbon nucleus formed by three alpha particles (helium nuclei), which was later borne out by experiment.

This energy level, while needed to produce carbon in large quantities, was statistically very unlikely to fall where it does in the scheme of carbon energy levels. Hoyle later wrote:

Would you not say to yourself, "Some super-calculating intellect must have designed the properties of the carbon atom, otherwise the chance of my finding such an atom through the blind forces of nature would be utterly minuscule. A common sense interpretation of the facts suggests that a superintellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question."

— Fred Hoyle

His co-worker William Alfred Fowler eventually won the Nobel Prize for Physics in 1983 (with Subrahmanyan Chandrasekhar), but for some reason Hoyle's original contribution was overlooked by the electors, and many were surprised that such a notable astronomer missed out. Fowler himself in an autobiographical sketch affirmed Hoyle's pioneering efforts:

The concept of nucleosynthesis in stars was first established by Hoyle in 1946. This provided a way to explain the existence of elements heavier than helium in the universe, basically by showing that critical elements such as carbon could be generated in stars and then incorporated in other stars and planets when that star "dies". The new stars formed now start off with these heavier elements and even heavier elements are formed from them. Hoyle theorized that other rarer elements could be explained by supernovas, the giant explosions which occasionally occur throughout the universe, whose temperatures and pressures would be required to create such elements.

— William Fowler

Rejection of the Big Bang

While having no argument with the Lemaître theory (later confirmed by Edwin Hubble's observations) that the universe was expanding, Hoyle disagreed on its interpretation. He found the idea that the universe had a beginning to be pseudoscience, resembling arguments for a creator, "for it's an irrational process, and can't be described in scientific terms" (see Kalam cosmological argument). Instead, Hoyle, along with Thomas Gold and Hermann Bondi (with whom he had worked on radar in the Second World War), in 1948 began to argue for the universe as being in a "steady state" and formulated their Steady State theory. The theory tried to explain how the universe could be eternal and essentially unchanging while still having the galaxies we observe moving away from each other. The theory hinged on the creation of matter between galaxies over time, so that even though galaxies get further apart, new ones that develop between them fill the space they leave. The resulting universe is in a "steady state" in the same manner that a flowing river is—the individual water molecules are moving away but the overall river remains the same.

The theory was one alternative to the Big Bang which, like the Big Bang, agreed with key observations of the day, namely Hubble's red shift observations, and Hoyle was a strong critic of the Big Bang. He coined the term "Big Bang" on BBC radio's Third Programme broadcast on 28 March 1949. It was said by George Gamow and his opponents that Hoyle intended to be pejorative, and the script from which he read aloud was interpreted by his opponents to be "vain, one-sided, insulting, not worthy of the BBC". Hoyle explicitly denied that he was being insulting and said it was just a striking image meant to emphasize the difference between the two theories for the radio audience. In another BBC interview, he said, "The reason why scientists like the "big bang" is because they are overshadowed by the Book of Genesis. It is deep within the psyche of most scientists to believe in the first page of Genesis".

Hoyle had a famously heated argument with Martin Ryle of the Cavendish Radio Astronomy Group about Hoyle's steady state theory, which somewhat restricted collaboration between the Cavendish group and the Cambridge Institute of Astronomy during the 1960s.

Hoyle, unlike Gold and Bondi, offered an explanation for the appearance of new matter by postulating the existence of what he dubbed the "creation field", or just the "C-field", which had negative pressure in order to be consistent with the conservation of energy and drive the expansion of the universe. This C-field is the same as the later "de Sitter solution" for cosmic inflation, but the C-field model acts much slower than the de Sitter inflation model. They jointly argued that continuous creation was no more inexplicable than the appearance of the entire universe from nothing, although it had to be done on a regular basis. In the end, mounting observational evidence convinced most cosmologists that the steady state model was incorrect and that the Big Bang was the theory that agreed better with observations, although Hoyle continued to support and develop his theory. In 1993, in an attempt to explain some of the evidence against the steady state theory, he presented a modified version called "quasi-steady state cosmology" (QSS), but the theory is not widely accepted.

The evidence that resulted in the Big Bang's victory over the steady state model included the discovery of the cosmic microwave background radiation in the 1960s, and the distribution of "young galaxies" and quasars throughout the Universe in the 1980s indicate a more consistent age estimate of the universe. Hoyle died in 2001 having never accepted the validity of the Big Bang theory.

"How, in the big-bang cosmology, is the microwave background explained? Despite what supporters of big-bang cosmology claim, it is not explained. The supposed explanation is nothing but an entry in the gardener's catalogue of hypothesis that constitutes the theory. Had observation given 27 Kelvins instead of 2.7 Kelvins for the temperature, then 27 kelvins would have been entered in the catalogue. Or 0.27 Kelvins. Or anything at all."

— Hoyle, 1994

Theory of gravity

Together with Narlikar, Hoyle developed a particle theory in the 1960s, the Hoyle–Narlikar theory of gravity. It made predictions that were roughly the same as Einstein's general relativity, but it incorporated Mach's Principle, which Einstein had tried but failed to incorporate in his theory. The Hoyle-Narlikar theory fails several tests, including consistency with the microwave background. It was motivated by their belief in the steady state model of the universe.

Rejection of Earth-based abiogenesis

In his later years, Hoyle became a staunch critic of theories of abiogenesis to explain the origin of life on Earth. With Chandra Wickramasinghe, Hoyle promoted the hypothesis that the first life on Earth began in space, spreading through the universe via panspermia, and that evolution on Earth is influenced by a steady influx of viruses arriving via comets. His belief that comets had a significant percentage of organic compounds was well ahead of his time, as the dominant views in the 1970s and 1980s were that comets largely consisted of water-ice, and the presence of organic compounds was then highly controversial. Wickramasinghe wrote in 2003: "In the highly polarized polemic between Darwinism and creationism, our position is unique. Although we do not align ourselves with either side, both sides treat us as opponents. Thus we are outsiders with an unusual perspective—and our suggestion for a way out of the crisis has not yet been considered."

Hoyle and Wickramasinghe advanced several instances where they say outbreaks of illnesses on Earth are of extraterrestrial origins, including the 1918 flu pandemic, and certain outbreaks of polio and mad cow disease. For the 1918 flu pandemic, they hypothesized that cometary dust brought the virus to Earth simultaneously at multiple locations—a view almost universally dismissed by experts on this pandemic. In 1982, Hoyle presented Evolution from Space for the Royal Institution's Omni Lecture. After considering what he thought of as a very remote possibility of Earth-based abiogenesis he concluded:

If one proceeds directly and straightforwardly in this matter, without being deflected by a fear of incurring the wrath of scientific opinion, one arrives at the conclusion that biomaterials with their amazing measure of order must be the outcome of intelligent design. No other possibility I have been able to think of...

— Fred Hoyle

Published in his 1982/1984 books Evolution from Space (co-authored with Chandra Wickramasinghe), Hoyle calculated that the chance of obtaining the required set of enzymes for even the simplest living cell without panspermia was one in 10^40,000. Since the number of atoms in the known universe is infinitesimally tiny by comparison (10⁸⁰), he argued that Earth as life's place of origin could be ruled out. He claimed:

The notion that not only the biopolymer but the operating program of a living cell could be arrived at by chance in a primordial organic soup here on the Earth is evidently nonsense of a high order.

However, his calculations are not compatible with modern molecular evolution, including research on the RNA world and the evolution of proteins from simple peptides.

Though Hoyle declared himself an atheist, this apparent suggestion of a guiding hand led him to the conclusion that "a superintellect has monkeyed with physics, as well as with chemistry and biology, and ... there are no blind forces worth speaking about in nature." He would go on to compare the random emergence of even the simplest cell without panspermia to the likelihood that "a tornado sweeping through a junk-yard might assemble a Boeing 747 from the materials therein" and to compare the chance of obtaining even a single functioning protein by chance combination of amino acids to a solar system full of blind men solving Rubik's Cubes simultaneously. This is known as "the junkyard tornado", or "Hoyle’s Fallacy". Those who advocate the intelligent design (ID) belief sometimes cite Hoyle's work in this area to support the claim that the universe was fine tuned in order to allow intelligent life to be possible.

Other controversies

While Hoyle was well-regarded for his works on nucleosynthesis and science popularization, he held controversial positions on a wide range of scientific issues, often in direct opposition to the prevailing theories of the scientific community. Paul Davies describes how he "loved his maverick personality and contempt for orthodoxy", quoting Hoyle as saying "I don't care what they think" about his theories on discrepant redshift, and "it is better to be interesting and wrong than boring and right".

Hoyle often expressed anger against the labyrinthine and petty politics at Cambridge and frequently feuded with members and institutions of all levels of the British astronomy community, leading to his resignation from Cambridge in September 1971 over the way he thought Donald Lynden-Bell was chosen to replace retiring professor Roderick Oliver Redman behind his back. According to biographer Simon Mitton, Hoyle was crestfallen because he felt that his colleagues at Cambridge were unsupportive.

In addition to his views on steady state theory and panspermia, Hoyle also supported the following controversial hypotheses and speculations:

• The correlation of flu epidemics with the sunspot cycle, with epidemics occurring at the minimum of the cycle. The idea was that flu contagion was scattered in the interstellar medium and reached Earth only when the solar wind had minimum power.
• Two fossil Archaeopteryx were man-made fakes. This assertion was definitively refuted by, among other strong indications, the presence of microcracks extending through the fossils into the surrounding rock.
• The theory of abiogenic petroleum, held by Hoyle and by Thomas Gold, where natural hydrocarbons (oil and natural gas) are explained as the result of deep carbon deposits, instead of fossilized organic material. This theory is dismissed by the mainstream petroleum geochemistry community.
• In his 1977 book On Stonehenge, Hoyle supported Gerald Hawkins's proposal that the fifty-six Aubrey holes at Stonehenge were used as a system for neolithic Britons to predict eclipses, using them in the daily positioning of marker stones. The use of the Aubrey holes for predicting lunar eclipses was originally proposed by Gerald Hawkins in his book of the subject Stonehenge Decoded (1965).

Nobel Physics Prizes

Hoyle was also at the centre of two unrelated controversies involving the politics for selecting the winner of the Nobel Prize for Physics. The first came when the 1974 prize went, in part, to Antony Hewish for his leading role in the discovery of pulsars. Promptly Hoyle made an off-the-cuff remark to a reporter in Montreal that "Yes, Jocelyn Bell was the actual discoverer, not Hewish, who was her supervisor, so she should have been included." This remark received widespread international coverage. Worried about being misunderstood and by British libel laws, Hoyle carefully composed a letter of explanation to The Times.

The second controversy came when the 1983 prize went in part to William Alfred Fowler "for his theoretical and experimental studies of the nuclear reactions of importance in the formation of the chemical elements in the universe." The controversy arose because Hoyle had been the inventor of the theory of nucleosynthesis in the stars with two research papers published shortly after WWII. So some suspicion arose that Hoyle was denied the third share of this prize because of his earlier public disagreement with the 1974 award. British scientist Harry Kroto later said that the Nobel Prize is not just an award for a piece of work, but a recognition of a scientist's overall reputation and Hoyle's championing many disreputable and disproven ideas may have invalidated him. In Nature, editor John Maddox called it "shameful" that Fowler had been rewarded with a Nobel prize and Hoyle had not.

Media appearances

Hoyle appeared in a series of radio talks on astronomy for the BBC in the 1950s; these were collected in the book The Nature of the Universe, and he went on to write a number of other popular science books.

In the play Sur la route de Montalcino, the character of Fred Hoyle confronts Georges Lemaître on a fictional journey to the Vatican in 1957.

Hoyle also appeared in the 1973 short film Take the World From Another Point of View.

In the 2004 television movie Hawking, Fred Hoyle is played by Peter Firth. In the movie, Stephen Hawking (played by Benedict Cumberbatch) publicly confronts Hoyle at a Royal Society lecture in summer 1964, about a mistake he found in his latest publication.

Honours

A statue of Fred Hoyle at the Institute of Astronomy, Cambridge

Awards

• Elected a Fellow of the Royal Society (FRS) in 1957
• Gold Medal of the Royal Astronomical Society (1968)
• Bakerian Lecture (1968)
• Bruce Medal (1970)
• Henry Norris Russell Lectureship (1971)
• Jansky Lectureship before the National Radio Astronomy Observatory
• Knighthood (1972)
• President of the Royal Astronomical Society (1971–1973)
• Royal Medal (1974)
• Klumpke-Roberts Award of the Astronomical Society of the Pacific (1977)
• Balzan Prize for Astrophysics: evolution of stars (1994, with Martin Schwarzschild)
• Crafoord Prize from the Royal Swedish Academy of Sciences, with Edwin Salpeter (1997)

Named after him

• Hoyle Building, Institute of Astronomy, Cambridge
• Asteroid 8077 Hoyle
• Janibacter hoylei, species of bacteria discovered by ISRO scientists
• Sir Fred Hoyle Way, a stretch of the A650 dual carriageway in Bingley.
• Institute of Physics Fred Hoyle Medal and Prize

Memorabilia

The Fred Hoyle Collection at St John's College Library contains "a pair of walking boots, five boxes of photographs, two ice axes, some dental X-rays, a telescope, ten large film reels and an unpublished opera" in addition to 150 document boxes of papers.

Bibliography

Non-fiction

• The Nature of the Universe – a series of broadcast lectures, Basil Blackwell, Oxford 1950 (early use of the big bang phrase)
• Frontiers of Astronomy, Heinemann Education Books Limited, London, 1955. The Internet Archive. HarperCollins, ISBN 978-0060027605
• Burbidge, E.M., Burbidge, G.R., Fowler, W.A. and Hoyle, F., "Synthesis of the Elements in Stars" Archived 24 June 2016 at the Wayback Machine, Revs. Mod. Physics 29:547–650, 1957, the famous B²FH paper after their initials, for which Hoyle is most famous among professional cosmologists.
• Astronomy, A history of man's investigation of the universe, Crescent Books, Inc., London 1962, LCCN 62-14108
• Of men and galaxies, Seattle University of Washington, 1964, ASIN B0087VKR70
• Galaxies, Nuclei, and Quasars, Harper & Row, Publishers, New York, 1965, LCCN 65-20996
• Nicolaus Copernicus, Heinemann Educational Books Ltd., London, p. 78, 1973
• Astronomy and Cosmology: A Modern Course, 1975, ISBN 0-7167-0351-3
• Energy or Extinction? The case for nuclear energy, 1977, Heinemann Educational Books Limited, ISBN 0-435-54430-6. In this provocative book Hoyle establishes the dependence of Western civilization on energy consumption and predicts that nuclear fission as a source of energy is essential for its survival.
• Ten Faces of the Universe, 1977, W.H. Freeman and Company (San Francisco), ISBN 0-7167-0384-X, ISBN 0-7167-0383-1
• On Stonehenge, 1977, London : Heinemann Educational, ISBN 978-0-435-32958-7; San Francisco: W.H. Freeman and Company, ISBN 0-7167-0364-5, 0-7167-0363-7 pbk.
• Lifecloud – The Origin of Life in the Universe, Hoyle, F. and Wickramasinghe C., J.M. Dent and Sons, 1978. ISBN 0-460-04335-8
• Diseases from Space (with Chandra Wickramasinghe) (J.M. Dent, London, 1979)
• Commonsense in Nuclear Energy, Fred Hoyle and Geoffrey Hoyle, 1980, Heinemann Educational Books Ltd., ISBN 0-435-54432-2
• The big bang in astronomy, New Scientist 92(1280):527, 19 November 1981.
• Ice, the Ultimate Human Catastrophe,1981, ISBN 0-8264-0064-7 Snippet view from Google Books
• The Intelligent Universe, 1983
• From Grains to Bacteria, Hoyle, F. and Wickramasinghe N.C., University College Cardiff Press, ISBN 0-906449-64-2, 1984
• Evolution from space (the Omni lecture) and other papers on the origin of life 1982, ISBN 0-89490-083-8
• Evolution from Space: A Theory of Cosmic Creationism, 1984, ISBN 0-671-49263-2
• Viruses from Space, 1986, ISBN 0906449936
• With Jayant Narlikar and Chandra Wickramasinghe, The extragalactic universe: an alternative view, Nature 346:807–812, 30 August 1990.
• The Origin of the Universe and the Origin of Religion,1993, ISBN 1-55921-083-4 
• Home Is Where the Wind Blows: Chapters from a Cosmologist's Life (autobiography) Oxford University Press 1994, ISBN 0-19-850060-2
• Mathematics of Evolution, (1987) University College Cardiff Press, (1999) Acorn Enterprises LLC., ISBN 0-9669934-0-3
• With G. Burbridge and Narlikar J.V. A Different Approach to Cosmology, Cambridge University Press 2000, ISBN 0-521-66223-0

Science fiction

A mosaic by Boris Anrep depicting Fred Hoyle as a steeplejack climbing to the stars, with a book under his arm, in the National Gallery, London.

Hoyle also wrote science fiction. In his first novel, The Black Cloud, most intelligent life in the universe takes the form of interstellar gas clouds; they are surprised to learn that intelligent life can also form on planets. He wrote a television series, A for Andromeda, which was also published as a novel. His play Rockets in Ursa Major had a professional production at the Mermaid Theatre in 1962.

• The Black Cloud, 1957
• Ossian's Ride, 1959
• A for Andromeda, 1962 (co-authored with John Elliot)
• Fifth Planet, 1963 (co-authored with Geoffrey Hoyle)
• Andromeda Breakthrough, 1965 (co-authored with John Elliot)
• October the First Is Too Late, 1966
• Element 79, 1967
• Rockets in Ursa Major, 1969 (co-authored with Geoffrey Hoyle)
• Seven Steps to the Sun, 1970 (co-authored with Geoffrey Hoyle)
• The Inferno, 10/1973 (co-authored with Geoffrey Hoyle)
• The Molecule Men and the Monster of Loch Ness, 1973 (co-authored with Geoffrey Hoyle)
• Into Deepest Space, 1974 (co-authored with Geoffrey Hoyle)
• The Incandescent Ones, 1977 (co-authored with Geoffrey Hoyle)
• The Westminster Disaster, 1978 (co-authored with Geoffrey Hoyle and Edited by Barbara Hoyle)
• Comet Halley, 11/1985
• The Frozen Planet of Azuron, 1982 (co-authored with Geoffrey Hoyle)
• The Energy Pirate, 1982 (Ladybird Books, co-authored with Geoffrey Hoyle)
• The Planet of Death, 1982 (Ladybird Books, co-authored with Geoffrey Hoyle)
• The Giants of Universal Park, 1982 (co-authored with Geoffrey Hoyle)

Most of these are independent of each other. Andromeda Breakthrough is a sequel to A for Andromeda and Into Deepest Space is a sequel to Rockets in Ursa Major. The four Ladybird Books are intended for children.

Some stories of the anthology Element 79 are fantasy, in particular "Welcome to Slippage City" and "The Judgement of Aphrodite". Both introduce mythological characters.

The Telegraph (UK) called him a "masterful" science fiction writer.