Project Brief: Thought X (by invitation only) (Part 1)

An anthology of short stories inspired by great thought experiments in science - 
accompanied by afterwords by the scientists that consulted on them. 
(The following brief is for authors, if you are a physicist or philosopher and would like to be involved or suggest more, p[lease email me at Ra.Page[at]

Thought Experiments

About the project
Science is always telling stories – whether in the ‘creation myths’ of evolution or the Big Bang, or in the 'eureka moments' of science history. Narrative – just as much as metaphor – is a key tool in the scientist’s surprisingly literary kitbag. Perhaps the most interesting use of 'story' is the thought experiment (das Gedankenexperiment), or the 'intuition pump' as it's sometimes called. This draws on the most instinctive impulses of the human imagination to crack otherwise perplexing philosophical problems, to prove a theory wrong or right, or to test its limits without having to set up a single piece of apparatus in real life. From Newton's Bucket, to Maxwell’s Demon, from Einstein's Lift to Schrodinger’s Cat – all are examples of 'fiction' being used not just to explain, but to deduce, to prove.
      For this project, Comma is asking authors to create stories in which a fictional character encounters, or in some way 'lives out', a thought experiment (or a version of it); stories that allow metaphoric or thematic parallels to be drawn between the original scientific/philosophical idea and the human story they find themselves in. 
      The format will be the same as Comma’s previous science-into-fiction commissions. The scientists will propose thought experiments first - between 3 and 5 each (thought experiments that they personally regard as vital in the development of their particular field and that they're happy to expound upon). These will then go on a list and the authors will pick them on a first-come-first served basis. The authors will then meet the scientist who proposed their thought experiment, and the scientist will inform, consult and science-check the story as it progresses and write a short, accessible afterword to the finished product.
Supported by the Institute of Physics.


1. Leibniz's Mill
Conciousness, thought, perception, etc, cannot be the product of mere mechanics and machinery, because any machine can be blown up in scale (in the imagination, at least) such that we can imagine ourselves, in miniature compared to the brain-machine, walking about inside it, like we might a walk into a great mill. All we would see inside this mill are parts pushing other parts. 'Where is consciousness?' Leibniz asks: 'Is it that wheel there? or that pulley? or that conveyor belt? Is it that piston?' 
   Sometimes referred to as Leibniz's Gap.

Parfit's People who split like amoebas
Suppose you belong to a sentient species that reprodced by splitting, like amoebas where each one becomes 'two seemingly identical beings. Which one would be you [afterwards]'? Parfit suggests that there are three possibilities: ‘(1) I do not survive; (2) I survive as one of the two people; (3) I survive as both.’
   Parfit rejects (2): ‘What can make me one of them rather than the other?’, they're identical.
   And rejects (3) 'one cannot be two people at once. This is a mathematical inconsistency, and lays waste to the very definition of ‘identity’. So the identity is lost; no one survives. Physical continuity doesn't equal personal identity or consciousness; neither does physical connection. 

3. Newton's Bucket ('absolute' versus 'relative' space and time)
Isaac Netwon, in his argument with Gotfried Leibniz, via his student Samuel Clarke, argued for the existence of 'absolute space' - a concept of space that survives even if there are no objects in that space. Newton says that space is real and absolute, and a thing - even when it's empty. Even an empty universe would have real, hard, actual substantive 'space' in it (unlike Leibniz who says space and time are merely relations between things and events, respectively. Take all things away there's no space. Take all events/changes away, there's no time. Truly empty space (a completely empty universe) doesn't exist, according to Leibniz. Newton won this argument by imagining a bucket. One with outwardly sloping sides, half full of water, suspended from a string attached to its handle... in an otherwise empty universe. The surface of the bucket would have to decide to be flat (i.e. the bucket was stationary) or concave (because the bucket is spinning around its axis). Because the water has to decide to be flat or concave (without anything else in the universe), it must be because space is absolute (thus it exists independent of the things in it!)
More here and here.
Consultant: DR JUHA SAATSI.

Poincare's Sphere World
Poincare's thought experiment devised to illustrate that we (or others, elsewhere in the universe) could be living in a geometry that appears (to the occupant) to be one thing, presenting the universe (to them at least) as straightforward, euclidean and infinite, when actually, from the outside, it's quite the opposite. 
   For the SphereWorlders (occupants of Poincare's gaseous planet), when they put one ladder on top of another, they head up up and up, and seem to keep going, with each pre-measured ladder (let's say 100m long when measured down on the ground), being added to the top of the last... without it ever coming to an end. But in this thought experiment space shrinks (and the ladders shrink) the higher up you go, so the whole joined-up ladder doesn't in fact reach outwards to infinity at all (as it appears to, for the Sphereworlders), but gets closer and closer to a fixed limit (as seen from those outside the sphere-world's geometry). This simply means that one person's infinite space might be another person's confined, spherical box. Or to quote the Dane (on this week of all weeks): 'I could be bounded in a nutshell and count myself a king of infinite space, were it not that I have bad dreams.' The bad dreams being, in this case, Poincare's thought experiment - an awareness that OUR geometry.... might not be THE geometry, everywhere. ('There are more things in heaven and earth, Horatio, than are dreamt of in your geometry, etc... Sorry :))
   This could have loads of narrative (and philosophical) consequences. Our universe might not be as infinite and comprehensive as it thinks it is (this possibility has been opened up by multiverse theories already, of course). Also, what does this geometric point have to say about freedom? Has it set up a topological version of John Locke's famous 'man in a locked room' thought experiment?* We may not know if we're bounded in a nutshell (or if the room is locked), that is to we may not know that we are not free; our freedom (to move infinitely) may be indeterminable. If something is unmeasurable then it's not real, so the adage goes. So... Poincare may have proven that the very question of freedom is unreal... etc etc... OK, I'm going way off message here. But you get the point, we may all be living in a bubble that seems to stretch out infinitely, but actually doesn't at all. And there could be another bubble (that appears infinitely expansive from the inside) squeezed right up beside ours, we could be like sphere-world sardinnes in a can....
Consultant: Prof. Ian Stewart.

5. Zeno's Paradoxes 

   1a. Achilles and the tortoise
'In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.' – as recounted by AristotlePhysics VI:9, 239b15 
    1b. Dichotomy Paradox
'That which is in locomotion must arrive at the half-way stage before it arrives at the goal.' – as recounted by AristotlePhysics VI:9, 239b10.
Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.
The resulting sequence can be represented as follows (see right):  left cdots  frac116  frac18  frac14  frac12  1 right
This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility.
   1c. The Arrow Paradox (aka 'Fletcher's Paradox')
     'If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. 
– as recounted by AristotlePhysics VI:9, 239b5
   To put it another way... If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible. Whereas the first two paradoxes divide space, this paradox starts by dividing time—and not into segments, but into points.
   In 1977, physicists E. C. G. Sudarshan and B. Misra studying quantum mechanics discovered that the dynamical evolution (motion) of a quantum system can be hindered (or even inhibited) through observation of the system. This effect is usually called the "quantum Zeno effect" as it is strongly reminiscent of Zeno's arrow paradox. This effect was first theorized in 1958.

6. Lucretius' Spear
'Suppose for a moment that the whole of space were bounded and that someone made their way to its uttermost boundary and threw a flying spear. Do you suppose that the missile, hurled with might and main, would speed along the course on which it was aimed? Or do you think something would block the way and stop it? You must assume one alternative or the other. But neither of them leaves you so much as a loophole to wriggle through. Both force you to admit that the universe continues without end. Whether there is some obstacle lying on the boundary line that prevents the spear from going farther on its course, or whether it flies on beyond, it cannot in fact have started from the boundary.' (Book I, ‘Matter and Space’, in De Rerum Natura)
    1,700 years of science after Lucretius' poem, it was still important to prove that the universe was infinite and unbounded. René Descartes and Isaac Newton both offered arguments to demonstrate this, concerned that otherwise Aristotle’s view of a finite universe seemed to limit God and to take the soul out of the machine. Yet in fact, as Einstein later pointed out, the universe can quite easily be both finite and unbounded – an anti-commonsensical view which might cause our spear carrier to stumble in confusion. But then, as Einstein also said (quite irrespective of whatever Kant might have liked), space does not have to obey the rules of geometry.

7. Ladder Paradox
Einstein’s special relativity illustrates the inter-connection of space and time, and shows us how to relate the time and space experienced by observers moving at different speeds to each other. Someone travelling fast will experience distances shortening and time lengthening with respect to someone standing still. This can often be really confusing.
      In this thought experiment you must imagine a ladder moving fast into a barn that is shorter than the ladder. The faster the ladder moves, the shorter it gets, so if it moves fast enough it should be able to fit inside the barn. At least, that’s from the barn’s point of view. From the ladder’s point of view it is stationary with a mad barn rushing towards it. This moving barn is shortened, so there is no way that the ladder will ever fit. How can both be true? 
      This is resolved when you remember to also change the time that the ladder and barn experience – once you do this too, there’s no paradox. This thought experiment, although slightly crazy, illustrates that time is not absolute, that it runs at different rates for measurements taken at different speeds. And because of this, there is no absolute simultaneity in the universe. Everyone is on a slightly different clock. Although odd, this seems to be true. We even take these effects into account in my experiment, at the Large Hadron Collider where particles move so close to the speed of light that these effects are large – if we didn’t, we wouldn’t be able to make sense of what happens there.
Consultant Scientist: tbc
Supported by the Institute of Physics.

8. Newton's Two Globes in a Void
Following on from 'Newton's Bucket', and attempting to make the above case for 'absolute' space even stronger, Newton wrote in Principia:
   '... if two balls, at a given distance from each other with a cord connecting them, were revolving about a common center of gravity, the endeavor of the balls to recede from the axis of motion could be known from the tension of the cord, and thus the quantity of circular motion could be computed.  
He argued that the tension in the cord would be registered even in a void where no other masses existed.  Thus, Newton concluded in both cases that rotation had to be with respect to an absolute frame of reference. 
9. Newton’s Cannonball & the invention of satellites
Newton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. It appeared in his 1728 book A Treatise of the System of the World. In this experiment Newton visualizes a cannon on top of a very high mountain.
     If there were no forces of gravitation or air resistance, then the cannonball should follow a straight line away from Earth, in the direction that it was fired.
     (i) If a gravitational force acts on the cannon ball, it will follow a different path depending on its initial velocity. (1 If the speed is low, it will simply fall back on Earth, for example horizontal speed of 0 to 7000 m/s for Earth
     (ii) If the speed is the orbital speed at that altitude it will go on circling around the Earth along a fixed circular orbit just like the moon, for example horizontal speed of at approximately 7300 m/s for Earth 
     (iii) If the speed is higher than the orbital velocity, but not high enough to leave Earth altogether (lower than the escape velocity) it will continue revolving around Earth along an elliptical orbit, for example horizontal speed of 7300 to approximately 10000 m/s for Earth.
     (iv) If the speed is very high, it will indeed leave Earth, for example horizontal speed of approximately greater than 10 000 m/s for Earthg
There's a great illustration from his “A Treatise of the system of the world” in which he envisaged satellites.
See here. A good connection to Jodrell is that we tracked the first actual satellite Sputnik I (well the rocket that carried it) in 1957.
Consultant: Dr TIM O'BRIEN

10. Galileo’s Leaning Tower of Pisa experiment.
A research colleague Steve Shore who works on novae (with me occasionally) at the University of Pisa recreated this (although people think it probably never actually happened in the first place!) - watch this
More here. Consultant: Dr TIM O'BRIEN

11. The EPR Paradox
According to quantum mechanics, under some conditions, a pair of quantum systems may be described by a single wave function (i.e. they are 'entangled'). Imagine, say, an electron and a positron created by a single event, one flying off in one direction, and the other flying off in the other direction. To preserve spin, one will have a quantum spin pointing in one direction and the other will have a spin pointing in the opposite direction. Although we don't know which, in either case, until one of them is measured.
     Quantum Uncertainty tells us that physical quantities come in pairs which are called 'conjugate quantities' (e.g. position and momentum). When one is measured the other becomes undetermined. 
     In 1935 Albert Einstein, and his colleagues Boris Podolsky and Nathan Rosen, conceived a thought experiment that they claimed showed the incompleteness of Quantum Mechanics. Imagine two entangled particles (like the electron and positron described above, created by the same single event). Let's call them as A and B. EPR pointed out that measuring a quantity of a particle A will cause the conjugated quantity of particle B to become undetermined, even if there was no contact, no classical disturbance. Put another way, if we allow the electron and positron to fly out to the far ends of the universe, and THEN measure the spin of one of them (it points 'up', say), we immediately know the other particle at the other end of the universe has a spin pointing down. This means the wave function has collapsed across the breadth of the universe, instantaneously, measuring a particle at one side of the universe has 'effected' another particle at the other side of the universe instantaneously. 
EPR concluded: either there was some interaction between the particles (instantaneous, i.e. faster than the speed of light, contradicting relativity), or the information about the outcome of all possible measurements was already present in both particles (a hidden variables theory). As the former contradicted relativity, the latter must be the case. QM had failed to explain and include all the information - there were still some hidden variables.

12. Quantum Suicide

Unlike the Schrödinger's cat thought experiment which used poison gas and a radioactive decay trigger, this version involves a life-terminating device and a device that measures the spin value of protons. Every 10 seconds, the spin value of a fresh proton is measured. Conditioned upon that quantum bit, the weapon is either deployed, killing the experimenter, or it makes an audible "click" and the experimenter survives.
The theories are distinctive from the point of view of the experimenter only; their predictions are otherwise identical.
     The probability of surviving the first iteration of the experiment is 50%, under both interpretations, as given by the squared norm of the wavefunction. At the start of the second iteration, if the Copenhagen interpretation is true, the wavefunction has already collapsed, so if the experimenter is already dead, there's a 0% chance of survival. However, if the many-worlds interpretation is true, a superposition of the live experimenter necessarily exists, regardless of how many iterations or how improbable the outcome. Barring life after death, it is not possible for the experimenter to experience having been killed, thus the only possible experience is one of having survived every iteration.
This conundrum is also closely related to the 'Unexpected Hanging' paradox, see below.
Consultant: TBC.


13. Leibniz's Indiscernibles.
Leibniz wrote to Samual Clarke (Newton's student): 'There is no such thing as two individuals indiscernible from each other. An ingenious gentleman of my acquaintance, discoursing with me, in the presence of Her Electoral Highness the Princess Sophia, in the garden of Herrenhausen; thought he could find two leaves perfectly alike. The Princess defied him to do it, and he ran all over the garden for a long time to look for some; but it was to no purpose. Two drops of water, or milk, viewed with a microscope, will appear distinguishable from each other. This is an argument against atoms; which are confuted, as well as a vacuum, by the principles of true metaphysics...'
From Martin Cohen's Wittgenstein's Beetle
   Leibniz worried that if you had two individuals that had the same appearance and the same memories, personality and so on, then they would not only be impossible to tell apart (in the manner of naughty identical twins), but – by his principle of the identity of indiscernibles – they would in fact be the same person or ‘thing’. This was unavoidable for Leibniz as he had already decided that spatial distinctions were illusory and so could not be used to distinguish one thing from another, which might sound odd, but then we do sometimes accept that approach with relation to time and place. For example, the flower in the garden yesterday is still the same flower even if it is today in a vase indoors. Wittgenstein too would later ask us to imagine a world in which all human beings look exactly alike, so that it appears as if certain characteristics migrate amongst identical bodies. ‘Under such circumstances, although it would be possible to give bodies names, we should perhaps be as little inclined to do so as we are to give names to the chairs of our dining room. On the other hand it might be useful to give names to the sets of characteristics....’
    In modern day Quantum mechanics, subatomic particles may share all the same characteristics, and spatial location can be the only way to tell one from another – yet spatial location for a subatomic particle is a matter for conjecture and surmise. For that reason, Quantum mechanics, like Leibniz, says that if two things cannot, even in principle, be distinguished, then they are the same thing. (For example, if a particle flickered in and out of existence, it would be the same particle, not one disappearing and being ‘replaced’ by an identical one.) In the mind-transfer/body-exchange machine, ‘place’ is not important either. We do not dispute the possibility (imaginary though it is) of a person being as it were instantaneously projected to a different location and yet still being the ‘same person’. Even if they are now made up of different atoms and so on, or even if some large part of ‘them’ has been changed. [..]
    The idea, in the Upanishads, that we could wake up in a changed location, with a different body and a different mind, having lost our memories of our old existence, is used by Veda¯ nta to conclude that it is only the Self (Atman) that has real independent existence, and physical objects are illusions. It may sound implausible to a hardheaded materialist, but in a sense, we wake up in a different body every morning, with a different mind and with different (increasingly hazy) memories. So Buddhism adopts a kind of equally hard-headed empiricism where nothing really exists, not mind, nor matter, nor space and time themselves. All that is left in Buddhism is the notion of ‘the moment’.
    By contrast, Messers Newton and Clarke want to make not only matter and time ‘real’, but space too. (Without ‘absolute space’ their theories of mechanics would just fall apart.) Only mind seems to be left out, an anachronism in an increasingly mechanical world, even if Newton himself searched lifelong through the alchemical works of the ancients for just such a unifying element. Mr Leibniz accepts that matter and time exist, but is not so sure about ‘space’. Instead, he ties the whole thing up with the mind of God.


14. Two 'Expériences Quotidiennes' from Roger-Pol Droit,
(i) Imagine the world only lasts 20 minutes. That is, imagine it sprang into existence just a moment ago, and will pop out of existence too in just exactly 20 minutes. Everything in the world appeared exactly as it now is, out of the flux. ‘Like a soap-bubble bursting, or a light going out’, it will disappear in 19 minutes.
   Roger-Pol Droit says that (doing this) everything looks the same, yet something has changed. The world lacks the depth of ‘a real past and the perspective of a viable future’. And as the 20 minutes approaches its term, we should feel ‘furtively, the dumb terror that everything will, effectively, disappear’. Although, as Roger-Pol drolly remarks, perhaps secretly we will also feel a slight disappointment if nothing is obliterated.

(ii) This one involves finding a landscape or view to sit down and contemplate. Then the experiment starts. 
You settle down to look at it. Don’t stare. Don’t scrutinize. There’s nothing for your eye to seek out, and it should avoid stopping at any particular point. On the contrary, let it glide over the whole, disengaged and slightly vague . . . everything must seem to you like a single surface, flat and without relief – like a painting.
This may take a few minutes to achieve, although Roger-Pol says it can happen very fast depending on your mood. Anyway, when you really believe you are staring at a single smooth surface, then imagine that ‘everything you see, from earth to sky, whether still or in motion, is just a detail on an immense, stretched canvas.’ Or perhaps on a giant screen, ‘like a gigantic cinema screen, shown in perfect focus and definition’. And now imagine the screen is being folded up.
You are about to see this great curtain, which contains the entire landscape, reveal something behind itself, as, very slowly, it starts to fold.
What will you see, asks Roger-Pol?
   In this latter experiment, Roger-Pol Droit says we can imagine anything we like, but one thing we should see is that, from now on,
‘the solidity of the real’ has been diminished. 

15. Kant's Indivisible Atoms versus the Problem of Space
In his second antinomy, Kant investigates the question of whether the universe is made up of little atomic bits, or whether in fact there is only an unending myriad of different substances and entities. He reasons that on the one hand, if there were no simple building blocks, then there could be no complex structures either. But if there were no building blocks and no complex structures then. . . there would be nothing left to exist. But something does exist!
     So... it seems that there must be some simple, atomic substances.
     On the other hand, any such building block must take up some space. In fact, anything that can be observed from outside in one sense acquires what he calls the ‘property of composition’. But in that case, can space also be broken down into small parts? Clearly not. Space does not consist of little bits or parts, but just of space. 
     In which case:
     'The absolutely simple is a mere idea, the objective reality of which cannot be demonstrated in any possible experience... as the absolutely
simple object cannot be given in any experience, and the world of sense must be considered the sum total of all possible experiences:
nothing simple exists in the world.'
     The question is, as Kant puts it: 
     ‘whether there exists anywhere, or perhaps, in my own thinking Self, an indivisible and indestructible unity – or whether nothing but what
is divisible and transitory exists’?


16. The Halting Problem
In computability theory, the halting problem can be stated as follows: "Given a description of an arbitrary computer program, decide whether the program finishes running or continues to run forever". This is equivalent to the problem of deciding, given a program and an input, whether the program will eventually halt when run with that input, or will run forever. Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. A key part of the proof was a mathematical definition of a computer and program, what became known as a Turing machine; the halting problem is undecidable over Turing machines. It is one of the first examples of a decision problem. More about the Turing Machine solution here and the original Halting Problem here.
Consultant: Prof MARTYN AMOS


17. The Prisoner's Dilemma
This is the classic game theory problem in which a suspect is confronted with a rather difficult decision: Stay silent or confess to the crime. Trouble is, the suspect doesn’t know how their accomplice will respond. 
Here’s the Prisoner’s Dilemma in a nutshell, via the Stanford Encyclopedia of Philosophy: 
   Tanya and Cinque have been arrested for robbing the Hibernia Savings Bank and placed in separate isolation cells. Both care much more about their personal freedom than about the welfare of their accomplice. A clever prosecutor makes the following offer to each. “You may choose to confess or remain silent. If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. Likewise, if your accomplice confesses while you remain silent, they will go free while you do the time. If you both confess I get two convictions, but I'll see to it that you both get early parole. If you both remain silent, I'll have to settle for token sentences on firearms possession charges. If you wish to confess, you must leave a note with the jailer before my return tomorrow morning.”
   This thought experiment is troubling because it teaches us that we don’t always make the “right” decisions when confronted with insufficient information and when other self-interested decision-making agents are thrown into the mix. The “dilemma” is that each suspect is better off confessing than staying silent — but the most ideal outcome would have been mutual silence. 
Consultant: TBC

18. The Beetle in the Box 
For the thought experiment, Wittgenstein asked us to imagine a group of individuals, each of whom has a box containing something called a “beetle.” No one can see into anyone else’s box. Everyone is asked to describe their beetle — but each person only knows their own beetle. But each person can only talk about their own beetle, as there might be different things in each person’s box. Consequently, Wittgenstein says the subsequent descriptions cannot have a part in the “language game.” Over time, people will talk about what is in their boxes, but the word “beetle” simply ends up meaning “that thing that is in a person’s box.” Consultant: TBC
   Why is this bizarre thought experiment disturbing? The mental experiment points out that the beetle is like our minds, and that we can’t know exactly what it is like in another individual’s mind. We can’t know exactly what other people are experiencing, or the uniqueness of their perspective. It’s an issue that’s very much related to the so-called hard problem of consciousness and the phenomenon of qualia. 

19. The Trolley Problem
From Philippa Foot’s 1967 paper, “Abortion and the Doctrine of Double Effect.”
   Imagine that you’re at the controls of a railway switch and there’s an out-of-control trolley coming. The tracks branch into two, one track that leads to a group of five people, and the other to one person. If you do nothing, the trolley will smash into the five people. But if you flip the switch, it’ll change tracks and strike the lone person. What do you do? 
   Utilitarians, who seek to maximize happiness, say that the single person should be killed. Kantians, because they see people as ends and not means, would argue that you can’t treat the single person as a means for the benefit of the five. So you should do nothing.
   A second variation of the problem involves a “fat man” and no second track — a man so large that, if you were to push him onto the tracks, his body would prevent the trolley from smashing into the group of five. So what do you do? Nothing? Or push him onto the tracks?
Consultant: TBC

20. The Spider in the Urinal 
This one’s reminiscent of Plato’s Cave, another classic (and disturbing) thought experiment. Proposed by Thomas Nagel in his essay, “Birth, Death, and the Meaning of Life,” it addresses issues of non-interference and the meaningfulness of life. He got the idea when he noticed a sad little spider living in a urinal in the men’s bathroom at Princeton where he was teaching. The spider appeared to have an awful life, constantly getting peed on, and “he didn’t seem to like it.” He continues:
     Gradually our encounters began to oppress me. Of course it might be his natural habitat, but because he was trapped by the smooth porcelain overhang, there was no way for him to get out even if he wanted to, and no way to tell whether he wanted to...So one day toward the end of the term I took a paper towel from the wall dispenser and extended it to him. His legs grasped the end of the towel and I lifted him out and deposited him on the tile floor.
     He just sat there, not moving a muscle. I nudged him slightly with the towel, but nothing happened... I left, but when I came back two hours later he hadn't moved.
     The next day I found him in the same place, his legs shriveled in that way characteristic of dead spiders. His corpse stayed there for a week, until they finally swept the floor.
      Was he right to do what he did?
Consultant: TBC

21. The Replacement Argument
In this thought experiment, we are asked to imagine a world in which humans don’t care for the taste of meat. In such a scenario, there would be no animals raised as livestock. And by consequence, there would be a dramatic decrease in the number of animal lives, like pigs, cows, and chickens. As Virginia Woolf once wrote, “Of all the arguments for Vegetarianism none is so weak as the argument from humanity. The pig has a stronger interest than anyone in the demand for bacon. If all the world were Jewish, there would be no pigs at all.”
   This line of reasoning can lead to some bizarre, and even repugnant conclusions. For example, is it better to have 20 billion people on the planet in a poor standard of living than 10 billion in a higher standard of living? If the latter, then what about the 10 billion lives that never happened? But how can we feel bad about lives that never occurred? 
Consultant: TBC


22. Brownian Ratchet 
(Richard Feynman's "perpetual motion")
More here.
Consultant: TBC

23. Einstein's Box (against uncertainty)
More here.
Consultant: TBC

24. Feynman Sprinkler (Classical Mechanics)
More here
Consultant: TBC

25. Heisenberg's Microscope (QM) 
More here
Consultant: TBC

26. The Monkey and the Hunter (gravitation)
More here
Consultant: TBC

27. Popper's Experiment (QM)
More here
Consultant: TBC

28. Quantum Pseudo Telepathy (QM)
More here
Consultant: TBC

29. Sticky Bead Argument (GR)
More here
Consultant: TBC

30. Wheeler's Delayed Choice Experiment (QM)
More here
Consultant: TBC

31. Wigner's Friend (QM) 
More here. 
Consultant: TBC

32. Bell's Spaceship Paradox (SR)
More here.
Consultant: TBC


A. Maxwell's Demon
Created by the physicist James Clerk Maxwell, this is a thought experiment devised to "show that the Second Law of Thermodynamics has only a statistical certainty". It hypothetically describes how the Second Law of thermodymanics (also known as the Law of Entropy - that entropy always increases) might be broken: A container of gas molecules at equilibrium is divided into two parts by an insulated wall, with a door that can be opened and closed by a very small agent, that came to be called "Maxwell's demon". The demon opens the door to allow only the faster than average molecules to flow through to a favored side of the chamber, and only the slower than average molecules to the other side, causing the favored side to gradually heat up while the other side cools down, thus decreasing entropy.
See more here.

B. Laplace's Demon
The laws of classical mechanics, as written down by people like Newton, Lagrange and others, gives us a framework to calculate the future motion of bodies or particles if we know the current position and speed of the particle. Laplace's demon (although there isn't really a demon!) takes this idea and confronts head-on the ideas of determinism and free will. Laplace stated that, if we believe classical mechanics, we can know the past and future positions and speeds of all atoms in the universe provided we know their positions and speeds at some point in time. In essence it means the universe is somehow clockwork and the state of the universe (and hence us) is pre-determined for all time. This is clearly a very profound statement, and one incompatible with quantum mechanics. Where does it leave personal choice?
      "We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.", Pierre Simon Laplace, A Philosophical Essay on Probabilities.

C. Galileo's Ship
Common sense seems to tell against the idea that the Earth moves. How could it? We experience things as being at rest. And if we drop an object from a tower it lands directly below the tower. How can that be if the earth rotates? Galileo found himself confronted with such objections and devised the following thought experiment to counter them:
"Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butteries, and other small animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals y with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully (though doubtless when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still." (Dialogue Concerning the Two Chief World Systems).
The thrust of the argument is of course that the earth is like the ship! It is moving and yet the effects of this motion are not observable. This is a powerful idea against the claim that common sense tells us that the Earth has to be stationary. In fact, we can have all the elements of common sense physics without being committed to a stationary Earth!
Consultant: Dr Roman Frigg

D. Einstein Riding on a Wave
At the age of 16, Einstein imagined chasing after, or riding, a beam of light and asked wondered what he could see, what the world looked like at that speed. Years later this daydream - or thought experiment - played a memorable role in the development of his special special theory of relativity. More here

F. The Infinite Monkey Typing Pool
The thought experiment of the infinite monkeys is well known. If we take a bunch of monkeys and lock them in a room with some typewriters, they will, by randomly hitting their keyboards, eventually produce a play by Shakespeare. At first sight, for them to write Romeo and Juliet seems fairly preposterous, as surely they would merely type random sequences of letters, but the point of the thought experiment is to understand probabilities, and probabilities with respect to the age of the universe. The probability of a monkey typing Romeo and Juliet is very small indeed but the chance of it occuring during the life of the universe is small but not equal to zero. 

G. Twin Paradox
This thought experiment shows us the bizarre nature of space and time, as described by Einstein’s theories of relativity. In relativity, space and time are deeply connected, and are not absolute. They both change depending on your viewpoint, although you have to find a pretty extreme situation to notice this, and this is why a thought experiment is a good way of illustrating it.
      Imagine two twins. One stays on Earth, the other is jettisoned out into space on a rocket to explore the solar system. The astro-twin is moving extremely fast compared to their sibling – and in special relativity, to their twin on Earth watching them, this means that the astro-twin time appears to be slowed down (literally, if you could see their watch, it would tick slower). To the astro-twin, their sibling is moving just as fast but in the other direction, and the Earth-twin time is slowed down compared to them. Strange. So what happens when astro-twin completes their circuit of the solar system and comes back to land? Which twin is younger?
      It’s a paradox that needs general relativity to resolve, because this explains how time changes as the astro-twin is accelerated into space and decelerated back again. Once you do this, you find that time has genuinely moved in a different way to the astro-twin, and the astro-twin is younger than their sibling. This might sound odd, and is, but it is true, and we need to use this time-bending behaviour of relativity to keep GPS working.
Consultant Scientist: TARA SHEARS.

H. The Chinese Room
The Chinese room is a thought experiment presented by John Searle.[1] It supposes that there is a program that gives a computer the ability to carry on an intelligent conversation in written Chinese. If the program is given to someone who speaks only English to execute the instructions of the program by hand, then in theory, the English speaker would also be able to carry on a conversation in written Chinese. However, the English speaker would not be able to understand the conversation. Similarly, Searle concludes, a computer executing the program would not understand the conversation either. More about the Chinese Room here.
Consultant: Prof Seth Bullock

I. Schrodinger’s Cat
This thought experiment neatly illustrates just how very strange and counter-intuitive quantum physics is. Imagine a steel box, impervious to the outside world. Inside it is a cat, and a small phial of deadly cat-poison. Connected to the phial is a piece of radioactive material, and a detector which will give a positive signal, and release the poison, on detecting radiation. (This is why it is best kept as a thought experiment!) The box is sealed. The radiation, and thus the cat’s survival or death, are random. Common sense tells us if we open the box, the cat is either alive or dead inside the box, and that’s what we’ll see when we open the lid. In quantum physics though, according to our viewpoint, the cat is simultaneously alive and dead before we look to make sure. We only know once we open the lid, at which point we’ve forced the cat to be one or the other.
      This scenario was invented when quantum physics was being developed at the start of the twentieth century. It encapsulates all the philosophical problems involved in trying to understand what quantum physics tell us. How can something be alive and dead at the same time? How can an observer influence reality just by looking at it? Does an impartial reality exist? And it’s fascinating – quantum physics gives us one of the most fundamental viewpoints we have, and we are still trying to make sense of the way it forces us to see the universe.
Consultant Scientist: tbc

J. Mary the Neuroscientist 
The originator of the concept, Frank Jackson,
   Mary is a brilliant scientist who is, for whatever reason, forced to investigate the world from a black and white room via a black and white television monitor. She specializes in the neurophysiology of vision and acquires, let us suppose, all the physical information there is to obtain about what goes on when we see ripe tomatoes, or the sky, and use terms like ‘red’, ‘blue’, and so on. She discovers, for example, just which wavelength combinations from the sky stimulate the retina, and exactly how this produces via the central nervous system the contraction of the vocal cords and expulsion of air from the lungs that results in the uttering of the sentence ‘The sky is blue’...What will happen when Mary is released from her black and white room or is given a color television monitor? Will she learn anything or not? 
   Put another way, Mary knows everything there is to know about color except for one crucial thing: She’s never actually experienced color consciously. Her first experience of color was something that she couldn’t possibly have anticipated; there’s a world of difference between academically knowing something versus having actual experience of that thing. 
Consultant: TBC

K. The Experience Machine

Philosopher Robert Nozick’s Experience Machine is a strong hint that we should probably just plug ourselves into a kind of hedonistic version ofThe Matrix.
From his book, Anarchy, State and Utopia (1974):
     Suppose there were an experience machine that would give you any experience you desired. Superduper neuropsychologists could stimulate your brain so that you would think and feel you were writing a great novel, or making a friend, or reading an interesting book. All the time you would be floating in a tank, with electrodes attached to your brain. Should you plug into this machine for life, preprogramming your life experiences?...Of course, while in the tank you won't know that you're there; you'll think that it's all actually happening...Would you plug in?"
Consultant: TBC

L. Plato's Allegory of the Cave
See here
Is this an epistemological thought experiment (i.e.pertaining to how we come to know things) or a political one? These two interpretations have been championed by Richard Lewis Nettleship and A.S. Ferguson respectively. Nettleship interprets the allegory of the cave as one about human ignorance and a people who are unable or unwilling to seek truth and wisdom. Ferguson, on the other hand, bases his interpretation of the allegory on a description of the way rulers, without a strong philosophical mindset, manipulate the human population.

M. The Grandfather Paradox - TAKEN
The grandfather paradox is a proposed paradox of time travel first described by the science fiction writer Nathaniel Schachner in his short story Ancestral Voices, published in 1933, and by René Barjavel in his 1943 book Future Times Three. The paradox is described as follows: the time traveller goes back in time and kills his grandfather before his grandfather meets his grandmother. As a result, the time traveller is never born. But, if he was never born, then he is unable to travel through time and kill his grandfather, which means the traveller would then be born after all, and so on. Therefore backwards time travel is impossible.
   For two possible solutions, see the Novikov self-consistency principle and the many-worlds theory.  
Sitting behind this paradox is another thought experiment by Einstein himself, called the Tachyonic Anti-Telephone.

N. Olber's Paradox
Viennese doctor and part-time amateur astronomer Heinrich Olbers (1758–1840) thought that, given that the universe is so vast and there are so many stars in it (and assuming the stars are not all clumped in one corner), when we look at the night sky we should see stars everywhere
we look. In fact, the night sky should be so brightly lit up that it should look as though completely filled from side to side by one giant star. The paradox is... that it doesn’t. 
    The favoured explanation today is that although the universe may be infinitely large, it is perhaps not infinitely old, meaning that the galaxies beyond a certain distance will simply not have had enough time to send their light over to fill our night sky. If the universe is, say, 15 billion years old, then only stars and galaxies less than 15 billion light years away are going to be visible.
    Sometimes added to this (in the manner of all dodgy explanations) is the new theory that if the universe is expanding all the time (after the so-called ‘big bang’), some galaxies may be travelling so fast ‘away from us’ that their light has become dimmed by ‘red shift’, the phenomenon which sort of stretches out a star’s wavelength beyond the visible spectrum.
    Thus, in making a few imaginary assumptions and asking his seemingly simple question, ‘Why is the night sky dark?’ Olbers and the others created a thought experiment that actually pointed to two of the great ‘discoveries’ of modern astronomy: namely that the universe seems to be expanding and is almost certainly of only a very finite age.

O. Poincaré's Gaseous 'Sphere World' - TAKEN
Imagine a planet made only of gases. At the centre the temperature is very high, and this is where all the gaseous people evolved and normally live. At the surface, however, the temperature is very, very low. In fact, M. Poincaré tells us, it is absolute zero. (The significance of this will become clear later.)
     As the gaseous people, let us call them ‘the Jeometers’, move around their planet, a small but subtle change takes place. Because of the change in temperature, the further they go from the centre, the smaller they become. And not just them, the smaller all the creatures and all the artefacts of the gaseous planet become. The most important thing is that everything changes at exactly the same rate, so nothing gets out of kilter.
     One year, the Jeometers determine they must explore the upper reaches of their planet and construct a massive ladder which they stand upright with its top disappearing far into the clouds. One of the Jeometers’ geometers sets off up it, with the task of finding out how far the gaseous planet extends. There is great excitement, but it is dissipated somewhat when the geometer returns a few days later to say the ladder is nowhere near long enough. 
     For years and years sections of ladder are added, but it seems it is in vain. Each time the geometers return to say that the ladder is still not long enough. Actually, as they ascend the ladder, both the Jeometers and the ladder itself are shrinking, shrinking so small that it is physically impossible for them to ever get to the outer surface. (At absolute zero, they will shrink to absolutely nothing.) Yet as they climb up, becoming colder and colder and at the same time smaller and smaller, the steps on the ladder, their measuring rods – everything – are also getting smaller and smaller, so they never realize the shrinking is happening. Eventually, the Jeometers decide their planet is infinitely large. Which it isn’t.
    The problem is, whose measurements are the ‘real ones’?
Poincaré’s conclusion:
    'A moving object will become smaller and smaller as it approaches the circumference of the sphere. Let us observe, in the first place, that although from the point of view of our geometers this world is finite, to its inhabitants it will appear infinite.'
    Henri’s point is a simple one. Nothing in the story is against the rules of logic, however unlikely given our everyday experiences of nature. Yet it appears to show that the assumptions of the truths of geometry, indeed the laws of the universe, are not beyond doubt. The gaseous people say that their planet is infinite, and as they can never step outside it, for them it is. Yet from the perspective of any passing space traveller, they are living an illusion. 
   The Ancient Greek geometers left a legacy of respect for the eternal truths of their science, and the certainty of their truths. Yet do the angles of a triangle always add up to 180°? Is it really certain that parallel lines never meet? Only if we assume that space is ‘flat’. 
   Henri Poincaré’s answer to Jeometers and geometers alike is the same: no measurements can be said to be the ‘real ones’ – it is all just a matter of convention.
See also here.

P. Einstein's Elevator and the Equivalence Principle
Imagine you are in an elevator or, more precisely, in what looks like an elevator cabin from the inside, and that you are isolated from the outside world. If you pick up an object and let it drop, it falls down to the floor, in exactly the way you would expecte given your experiences here on Earth. Does that mean the elevator is indeed situated in a gravitational field like that of the Earth?
Not necessarily. Theoretically, you could be in deep space, far away from all significant mass concentrations and their gravitational influence. The room you are in could be a cabin aboard a rocket (or somekind of 'spacelift') - as long as the rocket engines work at exactly the right rate to accelerate the rocket at 9.81 meters per square second. 
Conversely, imagine you're floating freely inside the elevator. Around you, other objects are floating, as well, and you feel totally weightless. Does that mean you are far away from all gravitational influences, far away from all stars, planets and other massive bodies, somewhere in deep space?
Again, not necessarily. You and the elevator could be in the gravitational field of a mass, for instance that of the Earth, as long as the elevator was in free fall.
Einstein postulated that this thought experiment holds true for any physical measurements at all: no experiment, no clever exploitation of the laws of physics, he claimed, can tell us whether we are in a gravitational field or simply accelerating in free space. 
Consultant: tbc

X. The Unexpected Hanging - X BANNED! 'Not a thought experiment, a logical trap!'
A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.
Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the "surprise hanging" can't be on Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.
He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn't been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.
The next week, the executioner knocks on the prisoner's door at noon on Wednesday — which, despite all the above, was an utter surprise to him. Everything the judge said came true.
Consultant: TBC