Mint. He is said to have taken great pleasure in having forgers hanged
on Tower Hill. He claimed the invention of differential calculus despite it
being invented independently by Gottfried Leibniz. Newton managed to
have himself appointed to chair the committee reviewing Leibniz’s work
and determine who had come up with the idea first. Unsurprisingly, the
committee found for Newton!
We see Newton’s laws of reflection and transmission in all manner
of everyday products, for example, the antireflective coatings of camera
lenses or the screen of your smartphone. Manufacturers cover the glass
in these products with coatings just a few molecules thick. Interference
between the layers kills the reflections. On a very expensive lens several
different layers are used; some kill red light and others kill blue light.
Together they suppress most of the reflection. If it were not for these
coatings you would be unable to go to the park on a summer’s day and
read your iPad. We need to think about reflection and transmission to
demonstrate our role as observers.
A windowpane has two surfaces. Both surfaces reflect light, and if
you look closely you will see your face is really reflected twice. You might
think this is simply a double reflection but this is not so. Light behaves
like waves. As with water waves, they interfere with one another. If two
light waves are at the top of a crest as they meet, the result is a crest of
double height. If both are at the bottom, you have a double trough, and if
one is a crest and the other a trough you get nothing as they cancel each
other out. You can see this effect in waves on the surface of a pond.
When light strikes a window pane, the light has two chances to
reflect: one from the front surface and the second from the back surface.
These two reflections interfere with each other. And, again, when you
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Wave Interference
have interference you sometimes get constructive interference – the
double crest or trough – and sometimes destructive interference – the
crest and trough canceling each other.
The reason we don’t see this effect in every reflection is because of
imperfection. Windows are not perfectly flat and light is multicolored, so
the effect is hard to see. But it is definitely there, and if you look really hard
at a reflection in a window, you can sometimes see it at the boundary of
sharp objects. The effect is very clear in the next picture which has been
set up with two flat pieces of glass resting against each other. There is a
tiny air gap between them. It is also commonly seen on puddles in cities.
In this case the puddle usually has a slight film of oil on it. Unlike glass,
puddles are perfectly flat thanks to gravity, but the oil film is thick in the
center and thin at the edges. The light reflecting off a puddle will show a
rainbow of colors. This is because each color is giving us a pattern of light
and dark. If you look at the same puddle at night in a yellow streetlight,
you will just see a monochrome pattern of light and dark. Look at the
picture of waves on a pond.
The patterns of light and dark are usually explained by imagining
the photons interfere with each other. This explanation is insufficient.
Imagine for a moment you can see as well as a frog, and perceive one
photon at a time. One moonless night just one photon comes to the two
glass surfaces and reflects. What happens?
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Newton’s Rings
It turns out a single photon can interfere with itself! How can this
be? It must somehow split up and consider both the available paths
reflecting off the glass surfaces.
Now that we have these two concepts in our head, that a photon
sometimes reflects and sometimes does not, and a single photon must
consider both paths, we can ask: what tells the photon what to do?
There are only three possible answers: the light source that emitted
the photon, the pane of glass that reflected the photon or the observer
that saw the photon – me.
The first obvious place that might control the photon is the original
source of the photon; the light bulb. The photon might leave the bulb
already knowing what path to follow, whether it will be reflected and
whether that reflection will be affected by the gap between the two
surfaces in a positive or negative way. This is sometimes called a pilot
wave theory. The problem with this theory is I could insert a piece of
glass into the experiment after the photon has left the light source. This
will affect the photon but the light source could not have known my
intention in advance and told the photon what to do. Therefore, the path
of the photon is not pre-programmed by the light source.
Now our photon has left the bulb and is traveling toward the glass.
The glass has two surfaces. The photon reaches the first surface and has
to decide if it will reflect. But there is a problem. The second surface
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will have an effect on this decision – constructively or destructively. The
photon can’t make up its mind at the first surface. It has not yet seen the
second surface.
The photon travels on and reaches the second surface. It needs to
make a decision: Shall I reflect or not? It cannot decide that it should
have been reflected from the first surface because it is already at the
second surface; it’s too late.
The photon is stuck. It cannot make the decision at the first surface
because that is too early, nor at the second surface because that is too late.
The glass surfaces cannot be the source of the decision.
This leaves only one remaining option: I, the observer, tell the
photon what to do. The word ‘tell’ is probably a little strong. Sadly, I am
not that powerful. All I can do is tell the photon to make up its mind.
When the photon reaches my eye, it must decide what happened to it
along the journey, but this decision appears purely random and I have
no effect upon it. The best way physicists have found to describe what is
going on is to say particles, such as a photons, behave according to a wave
function. Particles oscillate between all the possible options available to
them and when we take a measurement this freezes the oscillations and
gives a single result.
Where exactly is the measurement made? At my eye when the
photon is refracted by the lens, when the photon enters the aqueous
humor, or perhaps as it interacts with the rods and cones in the retina.
Maybe we must wait until the detection of the photon is converted into
an electrical impulse in the optic nerve or even the point at which my
human consciousness perceives it.
This prompted the physicist John Bell to ask a slightly tonguein-cheek
question, “Was the world wave function waiting to jump for
thousands of millions of years until single-celled creatures appeared? Or,
did it have to wait a little longer for some more highly qualified measurer
– with a Ph.D.?” You see his point. Where is the bar set that defines a
measurement?
One of the most extreme answers to Bell’s question is the strong
anthropic principle. It argues humans – or at least sentient beings,
perhaps even cats – cause the Universe to exist. The Universe bubbles
along in a state of superposition with every possible event occurring and
bifurcating until an observer emerges in one of the branches and the
whole edifice collapses to that state. It is not clear if this produces many
concurrent universes or if the first universe with a sentient being wins!
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Solvay Conference
“There is no way to understand
the mechanism that turns the
water of the brain to the wine of
consciousness.”
Colin McGinn
“If you think this Universe is
bad, you should see some of the
others.”
Philip K. Dick
Schrödinger’s Cat
Measurement is a big puzzle. What causes the collapse of the
wave function so that the photon stops considering many
optional paths and makes a hard and fast decision. When light
passes through a series of glass surfaces, it is reflected or transmitted by
each. We can stack up as many pieces of glass as we want, but none of the
surfaces will cause a measurement – a collapse of the wave function. It is
not until the photon reaches a detector that a measurement is made and
all the potential reflections and transmissions that might have happened
‘collapse’ into the one choice that actually happened.
You might doubt this but there are ingenious experiments that can
be performed to prove it. One is quite simple to do and can be set up
on your kitchen table with a handheld laser and $100 worth of optical
components. You need three ordinary mirrors and a beam splitter. Beam
splitters are often made from half-silvered mirrors. They are similar to
your bedroom mirror except the silver coating is more thinly applied,
allowing only half the light to reflect while the rest passes straight
through. Arrange the mirrors and beam splitter on a table at the four
corners of an imaginary box, as in the diagram. If you point your laser at
the half-silvered mirror, half the light will go straight through and half
will be reflected upwards towards the first mirror. It is sent on around the
square until it meets the half-silvered mirror again, and the beams meet
up. You might expect that half the light reaches the detector but this is
not what happens. Depending on the way the mirrors are positioned,
either all the light reaches the detector, or none does. (The light does not
disappear it just gets sent back to the light source, energy is conserved.)
If you turn down the brightness of your laser, this does not change. Even
326 Are the Androids Dreaming Yet?
Interferometer
if only one photon is traveling at a time, still no light comes out in one
direction and all the photons come out the other. The wave functions
of each photon interfere with each other constructively or destructively.
The only conclusion available is the photon must be traveling along both
paths! They are said to be in ‘superposition’. If you introduce a measuring
device half way around the experiment, it will destroy the superposition
and the photons behave in the common sense way. Remove the measuring
device and, once again, the photons seem to take both paths. Richard
Feynman pointed out that you really have to imagine that the photons
take every possible path, not only the straight line paths. He received his
Nobel Prize for demonstrating how to add up these infinite paths to get
a finite answer with his ‘sum over histories method’. Superposition is a
strange idea when limited to the realm of small particles but what about
larger things? – cats for example.
Erwin Schrödinger’s unfortunate cat is trotted out to demonstrate
the paradox so often that Stephen Hawking is on record for wanting to
reach for a gun every time he hears mention of it.
The thought experiment works like this. A cat is put in a box with
a radioactive substance, a Geiger counter and a vial of poison. If the
counter detects a radioactive decay it breaks the bottle and the cat dies, if
no decay is detected the cat lives.
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Schrödinger’s Cat – both Alive and Dead
Since radioactive decay is a quantum event, we have to assume
it might or might not have happened right up until the point of
measurement. It is the same with any quantum event: photons reflecting
from a piece of glass, measuring the spin of an electron or measuring the
polarization of a photon. All these quantum effects exist in superposition
until measured. But in the real world, we don’t experience superposition.
If I miss the train, I miss it. I don’t partially catch it and partially miss
it, and I don’t experience any such quantum ambiguity. The only place
I ever see such effects is watching science fiction movies. In real life the
large scale world is certain. At what point does this quantum uncertainty
transition to our classical certainty? What is the state of the cat before I –
a sentient observer – open the box? Was the result of the decay measured
by the Geiger counter, the cat, or are we waiting for someone to open the
box and observe the result?
The Copenhagen interpretation of quantum mechanics – named
after the main center of early quantum theory at the Niels Bohr Institute
– says the cat is both alive and dead until I make a measurement. The cat
is said to be in superposition, meaning a live cat and a dead cat inhabit
the same volume of space-time ‘experiencing’ both alternatives and
waiting for my measurement. This seems nonsensical, but Copenhagen
quantum folk simply say, “That’s the way it is; the mathematics works, if
you don’t like it, tough. Nature does not have to explain herself.”
Einstein strongly disagreed with this position. He believed the
world is certain and laws must govern radioactive decay and, therefore,
the breaking of the vial and the life and death of the cat. There must be
some, as yet, undiscovered theory. He reasoned as follows: A particle
328 Are the Androids Dreaming Yet?
has position, velocity and spin. Why can it not have more hidden
information that tells it when to decay? Perhaps particles are composed
of sub-particles that cause the weird quantum effects we see.
We have discovered sub-particles – quarks and the like – but more
than a hundred years of experimentation have gradually ruled out any
form of theory explaining how these random events can be governed
by the properties of the particle. The collapse of the wave function just
seems to happen randomly.
There is one explanation for quantum mechanics that avoids
the measurement problem altogether but it is even stranger than the
Copenhagen interpretation: ‘the many worlds’ view’. The idea was first
put forward by Hugh Everett in 1957, and it claims measurements are
never made, there is never a collapse of the wave function, and every
wave continues to exist. We just can’t see them all. There is a version of
me that has seen a live cat and another in a parallel universe that saw a
dead one. The two versions of me are also in superposition, just like the
cat, so there are an infinity of parallel universes tracking every possible
option.
The only measurable consequence of this ‘many worlds’ idea is the
existence of enormously enjoyable science fiction plots and much poking
of fun between the many worlds camp, and the no-many-worlds camp.
The single-worlds proponents point out the whole idea is untestable and
just plain odd. For example, each choice we make, every reflection and
any quantum process generates a new branch in the Universe. This is a
vast amount of information to track and puts us back in a position where
moral choices have no consequence. Every decision I make spawns a
Universe where I made a different choice.
For a humorous take on this, you can visit a website and buy your
own Universe for $2.99. You pose a question based on the throw of a die,
let’s say, one to three I go to work today and, four to six, I take a sick day.
The website generates a quantum random number using an experimental
setup at a laboratory in California. You can make your choice based on
this quantum random number in the certain knowledge that another
Universe springs into existence where you made the alternate choice, so
somewhere you are not taking a sick day after all, and can be found hard
at work at your desk.
There is one more explanation for quantum measurement, proposed
by Roger Penrose. He proposes gravity comes to the rescue. Once enough
particles are involved in the superposition of states, the curvature in
space time becomes great enough to force a measurement event. In
his view, a measuring instrument is simply an amplifier which brings a
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quantum event to the point where gravity begins to matter. His solution
removes the requirement for many worlds and, indeed, our curious
position as the conscious beings that bring the world into existence. Of
course, Penrose does not stop there. He proposes the quantum gravity
interaction gives rise to conscious thought and this process is the root of
mathematical intuition.
The aim of our discussion is to show where determinism might break
down in the physical laws of the Universe. If our Universe is determined,
there will need to be a huge quantity of information stored somewhere
to tell it what to do at each step. Storing a script for the Universe is not
the conventional way people imagine determinism works. Rather they
explain the apparent complexity we see through the application of a
simple set of rules called ‘the laws of physics’. We imagine using these
laws to expand up a small set of starting conditions into the complexity
of the Universe we experience. This is similar to the way fractals produce
beautifully complex images from a tiny quantity of information. For
example, the Mandelbrot set is created from a single, simple mathematical
statement just twelve characters long, with one or two starting numbers.
If this is how our Universe works then our thoughts and actions are just
like the fronds of a fractal. It would mean the particles in the Universe
‘know’ what they will do next and carry enough information with them
to determine their next action. This is a testable hypothesis and the test
we have devised to measure this is the twin particle experiment.
Right and Left Socks
“Was the world wave-function
waiting to jump for thousands
of millions of years until singlecelled
creatures appeared? Or
did it have to wait a little longer
for some more highly qualified
measurer - with a Ph.D.?”
John Bell
Twins
There are several ways to make twin particles. The ‘easy’ way is with
a laser and a nonlinear crystal. A beam of ultraviolet photons
enters the crystal and about one in a billion times they interact
with quantum fluctuations in the crystal lattice to create two red photons.
This is known as ‘spontaneous down conversion’.
There are two types of down conversion. In a type I interaction the
twins have the same polarization, and in a type II they are at 90 degrees
to each other. You can set up the experiment with either type, but it
is important to remember which you used, or you will easily become
confused. When we talk about photon experiments, we are usually
referring to type I interactions because they are easier to understand.
Often the actual experiment uses oppositely polarized photons because
they are easier to generate.
Polarization is a wavelike property of photons. You can visualize
them wiggling up and down, side-to-side or something in between. We
use polarization to our advantage when we go on holiday to the beach;
light from the sun is randomly polarized, but when it glances off the ocean
it becomes predominantly horizontally polarized. If we wear vertically
polarized sunglasses the glare off the ocean is blocked and we can see the
ocean more clearly. The following two pictures show this effect.
The two photons we make with the crystal can be separated and
sent to different places. The record so far is two towns near Geneva, 50
kilometers apart. For this experiment scientists ‘borrowed’ the unused
fibers of Swisscom in the middle of the night – when phone traffic was
light. A detector was placed at the end of each fiber to measure the
particles.
332 Are the Androids Dreaming Yet?
Effect of Polaroid Lenses
When scientists examine the polarization of these photons, they
get random results. Sometimes the photon is oscillating side to side,
sometimes up and down and sometimes part way in between. This can
be determined simply by taking a lens out of a pair of Polaroid glasses,
holding it up at an angle and seeing if the photon can pass through.
Obviously laboratory grade Polaroid material is available, so scientists
don’t have to destroy an expensive pair of designer glasses, but the
principle is identical.
Very strange things happen when the measurements are made. The
polarizations appear to have no discernible pattern, but once one of the
photons has gone through a polarizer in the first town, its sister photon
will always be found to have the opposite polarization (or the same if it
was a type I)..
Einstein was uncomfortable with this for two reasons. The first related
to his famous statement, “God does not play dice with the Universe.”
He was deeply uncomfortable with the idea that the polarizations
were random. Even more troubling to him was the idea that the sister
photon somehow instantaneously had the opposite polarization. How
would it know? For the sister photon to immediately have the opposite
polarization, information would have to travel faster than the speed of
light from the first photon to tell its sister what to do. In 1935, Einstein
wrote a paper with Jacob Podolsky and Samuel Rosen describing this
‘EPR’ paradox. Since faster than light communication was impossible – it
breaks the law of special relativity – they concluded quantum mechanics
must be wrong, or at least incomplete. A deeper theory would be needed
to explain the particles’ behavior. One very simple explanation is by
analogy to socks! (Clothing analogies are one of the ways physicists try
to make quantum mechanics less intimidating.)
Consider sister photons as if they were right and left socks. If we
found a left sock on the bedroom floor, we would be unsurprised to find
the matching sock was a right one. There is no need for messages to flow
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between the socks faster than the speed of light to synchronize them,
they already know what they are! Einstein presumed sister photons
were like socks; they were emitted from the light source with their
polarizations already set, though you could not see this information until
you measured one of the photons. The information was dubbed ‘hidden’
and the theory is called hidden variable theory.
Einstein was to be proven wrong.
For many years after the EPR paper was published, physicists
split into factions: some thought the world random, some believed in
hidden variables, and others thought attempts to ‘understand’ quantum
mechanics were misguided. Why should physics make sense? The
equations work. Who cares why?
In 1964, John Bell, an Irish physicist working at the Conseil
Européen pour la Recherche Nucléaire (‘CERN’), devised a way to test
Einstein’s hidden variable theory. He pointed out that if photons possess
hidden variables and we randomly measure them with a detector set at
three angles, we would expect to see more than one-third of the photons
share the same result. But, in 1972, Freedman and Clauser performed
this experiment and showed the photons share the result only a little over
a quarter of the time. Since ‘a little over a quarter’ is less than ‘more than
a third’, Bell’s theory is false. Of course, Bell was entirely happy about
this, since he set the equation up to be disproven. His equation is called
an inequality because the equation contains a more than sign ‘>’ rather
than an equals ‘=’ sign, so people say that quantum mechanics violates
the Bell inequality. Because the inequality is violated, photons can have
no prior knowledge of their polarization.
Bell Test Experiment
334 Are the Androids Dreaming Yet?
This is quite a complex piece of mathematics so let me show you how
it works. Again, our thought experiment relies on an analogy involving
clothing – sorry.
In the Bell Test experiment three polarizers are set up at 0, ⅓ and ⅔
of the way around a circle, 120 degrees apart. For Einstein to be correct
photons must each carry at least three pieces of information:
If I meet the 0 degree polarizer do I go through or not?
If I meet the 120 degree polarizer do I go through or not?
If I meet the 240 degree polarizer do I go through or not?
If a photon had only one piece of information, say that it was
vertically polarized, it would not know what to do if it came across a
polarizer at 45 degrees. In that case the photon would sometimes go
through and sometimes not, with a fifty-fifty probability. But Einstein
did not want to countenance probability. “God does not play dice with
the Universe.” He required certainty. “I like to think the Moon is there
when I am not watching it.” The photons must know enough to handle,
with certainty, any eventuality they may come across. (We could set up
experiments with a more complex set of choices, dividing the photons
into quarters, fifths and so on, but thirds are simple numbers and we can
use the children’s clothing analogy to demonstrate the mathematics.)
Hats, Scarves, and Gloves
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We could liken photons knowing three pieces of information to
children in a playground choosing to wear either hats, scarfs or gloves in
some combination: hats for vertical, gloves for 120 degrees and scarfs for
240 degrees. There are eight choices for each child; nothing, hat, gloves,
scarf, hat and scarf, hat and gloves, scarf and gloves, or all three.
Bell asked how often we would see two measurements agree. Look
at the illustration and you can see when this happens. If a child was
wearing all the clothes then if you check any pair, say gloves and scarfs
you will always get a yes. If one of the children is wearing none of their
winter clothes, you will always get a no for any pair you check. In these
two cases, we are always sure to get agreement. For all the other cases,
only one in three of the tests will agree. So Bell said that any time you
have something with three hidden variables, there is at least a one in
three chance that the measurements you make will agree, since six of the
tests are one in three and the other two are certain.
Due to Heisenberg’s Uncertainty Principle we can only look at one
piece of clothing at a time. But, there is a trick. If there are identical twins
among the children – who always dress the same way in our analogy –
we can look at the gloves of one twin and the hat of another. Because they
are twins if the first twin is wearing a hat we know the second one is too,
without looking. We have a trick to measure two things at once.
When the test is done on twin photons only one in four, one
quarter, agree. So there is a problem with the children analogy. It turns
out photons don’t wear gloves, hats, and scarfs. There are no hidden
variables. A photon does not know what it will do before you measure it
and can only decide on the fly at the point of measurement.
This means quantum particles are not there when they are not being
observed. Observing them does appear to make them real. If the hidden
variables, the gloves, hats and scarfs were in set positions when we were
not observing them, the photon measurements would agree at least
one-third of the time, but they do not. When we measure them, the two
particles somehow communicate and agree to give a positive result only
one quarter of the time. Bizarre, but that’s just the way it is!
The Bell result is still somewhat controversial and has not been
proven to everyone’s satisfaction. Potential loopholes exist but are steadily
being eroded. An experiment by Nicolas Giseng of CERN using the fiber
optic network of Swiss Telecom to separate twin photons, shows the
coordination signals must travel at least 10,000 times the speed of light –
the limitation, and reason it is not infinitely fast, being the accuracy of his
clocks. Daniel Sego, Daniel Danziger and Michael Wise have performed
the Bell test experiment with an apparatus installed near Innsbruck
336 Are the Androids Dreaming Yet?
where the choice of detector orientation was made by a random number
generator after the photons had left the emitter. This shows the photons
really can’t know what they will do before they start their journey. Another
loophole is the loss of some photons. We don’t measure all the photons in
an optical experiment because some are absorbed by the apparatus. It has
been suggested all the ‘lost’ photons make up the error in the experiment.
This is not very likely, it’s akin to assuming all the voters who did not vote
in an election would have voted Democrat. To avoid this criticism, an
experiment has been performed with magnetized particles that don’t get
lost. The Bell result holds true.The loopholes are diminishing and it seems
likely Bell will win out in the end.
Although the coordination information appears instantaneous,
John Bell gave us an elegant explanation as to why this does not allow
us to use the effect to transfer information faster than the speed of light.
Imagine we are sitting at opposite ends of a room. We both toss coins and
each of us write down our results; heads, tails, heads, heads and so on.
I then acquire a magical power that causes your coin to make an extra
flip just before you catch it, so it always gives the opposite result to mine.
Although I am now controlling your coin, you cannot tell, as the result
looks as random as before. The difference is simply that at first the coin
orientation was random in its own right and then the opposite of my
random result. It is only when I walk over and compare our results we
can see they are matched in this strange way. There is no way to transmit
information using this effect. Only after the experiment is finished can
we exchange the necessary information to see the coordination that
existed, and that comparison required me to transfer information. The
fastest way to do that is at the speed of light.
Despite saying it is impossible, let us do a thought experiment and
try to transmit information using Morse code. I will set up a simple old
fashion telegraph machine. When I press the telegraph button at my end
this will cause a measurement and the photons at your end will be forced
to the opposite polarization. When I lift the key, your photons will revert
to being randomized. You can see this illustrated in the diagram. Although
I make your photon take up a polarization, analogous to making the coin
take an extra flip, you don’t have enough information to know this.
Now we are ready to use our quantum Morse machine to prove the
Universe must have free will, or at least a degree of non-determinism.
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Quantum Morse Machine
A Simple Free Will Theorem
In the quantum Morse machine, I do transmit information faster than the
speed of light. But the information I have transmitted is useless as it is, in
effect, encrypted using a one-time pad. The only person in possession of
a copy of this one-time pad is me: the sender.
Claude Shannon proved a one-time pad is unbreakable during the
Second World War. Yet the British succeeded in breaking it. How was
this possible?
The fatal weakness in the German one-time pads was the random
numbers used to code the messages were generated by a machine, and
were therefore not truly random. The numbers followed a sequence,
and it was possible for Allied code breakers to work out the sequence
and decode the messages. It follows that if we believe no message can
propagate faster than the speed of light, my sequence of numbers must
be non-computable. There must be no algorithm or computation that
could generate it. Otherwise it would be liable to the same sort of
decryption attack that the one-time pads suffered. If sequences of random
measurements taken in the universe are non-computable it follows the
Universe as a whole must be non-computable.
There are a few holes you could pick in this argument. Would it
be sufficient if it were impossible to decrypt the message in the age of
the Universe? What if there was an algorithm, but it was practically
unknowable? But, I am talking here of principle. In principle, the
Universe must be non-decryptable.
Richard Dawkins and the Atheist Tour Bus
“God exists, if only in the form
of a meme with high survival
value, or infective power, in the
environment provided by human
culture.”
Richard Dawkins
Does God have
Free Will?
ny discussion of free will is incomplete without some mention of
God. Scientists generally avoid the topic, but since we’re talking
about such a fundamental concept, we must consider whether
the Universe would be any different if it had a creator.
Recently there have been two widely publicized attacks on religious
belief from the scientific community: the head-on attack from Richard
Dawkins in The God Delusion or, the hard hitting sideswipe by Stephen
Hawking in The Universe in a Nutshell.
Hawking made the front pages in 2000 with the statement: “There
is then no need for a creator.” He was considering whether God needed
to ignite the Big Bang or if it occurred as a natural result of the laws of
physics. Hawking had run the mathematics and realized a god was not
needed to light the blue touch paper for the Big Bang - the laws of physics
spontaneously caused it. His argument does not actually preclude the
existence of a god, but it does move the point where we need a creator
one step further up the chain.
This is not a fundamental change to the progress of theological
argument over the last thousand years. Once we abandon our vision
of God as a master builder, literally breathing life into Adam while
putting the finishing touches to the Garden of Eden, we can move him
up the causal chain as far as we like, eventually reaching a point where
intervention is necessary to get things started. Hawking is only pointing
out an intervention is not needed at the point of the Big Bang. It still begs
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the question “Where did the laws of physics come from?” If you don’t
believe in a god then pushing a creator figure further and further up the
chain eventually makes him redundant. If you have faith, you can take
the position God is the creator of the fundamental rules.
Regardless of your personal position, I would like to make the
argument for free will independent of belief. We must resolve the ageold
paradox: How can God be all-knowing and all-powerful, and still
have free will?
This is a long-standing theological debate dating back to the 15 th
century. It splits theologians into two camps. The first maintains God has
both omniscience and omnipotence, and they are not inconsistent. This
is the compatibilism argument again. Despite the acknowledged paradox,
they argue that we should simply accept it and acknowledge that we are
unable to comprehend such things. I don’t like this argument because
it essentially denies reason. We are supposed to acknowledge that we
simply cannot understand the mind of God. I prefer the more modern
argument from the second camp that omnipotence trumps omniscience.
It preserves the view that man can reason about the Universe – “Man is
made in God’s image.”
This argument follows the logic: God must be able to choose not to
know what will happen in the future so that he can have free will.

Fork in the Road
“When making a decision of
minor importance, I have
always found it advantageous
to consider all the pros and cons.
In vital matters, however, such
as the choice of a mate or a
profession, the decision should
come from the unconscious,
from somewhere within
ourselves. In the important
decisions of personal life, we
should be governed, I think, by
the deep inner needs of our
nature.”
Alan Turing
The Free Will
Theorem
In 2006, John Conway and Simon Kochen published The Free Will
Theorem. The paper received huge press attention and has been widely
discussed in the scientific community. Their theorem states that;
provided experimenters are free to run their experiment as they choose,
the behavior of the particles they experiment upon is not determined in
advance. Particles have free will!
If we go back to the Bell Test experiment, this proved twin particles
do not carry around a parcel of information telling them what to do.
Perhaps they get their marching orders from some outside influence.
There are two possibilities. A particle is either told what to do by its
environment or it gets its information from some data source. Can we
use the laws of physics to test these possibilities? We don’t need to know
how the influence works, just that it might exist in principle.
Conway and Kochen prove there can be no external influence, and
when a particle reveals its spin, that spin was not known beforehand. It
is independent of any information in the history of the Universe up to
that point.
Conway and Kochen’s proof is elegant and involves some mental
gymnastics, but it is no harder than Archimedes’ proof of the infinity of
primes we looked at earlier. Let us start with our twin particles. We are
going to pick bosons, which have whole number spin. If you measure the
spin, you will always get a reading of -1, 0 or +1. ‘Spin’ is one of those
words physicists use to explain quantum things. It does not necessarily
denote rotation but, if your mental model is a spinning top, that’s not too
344 Are the Androids Dreaming Yet?
bad. If we measure something in the quantum world, it always yields a
classical result – in this case the magnitudes of spin are 1, 0 and 1. (Minus
one squared is one.)
We need to imagine measuring the spin of a particle along three
axes; x, y and z. Hold your hand up and make a shape that looks like
the one in the following picture. You might remember it from science
classes; it was used to help you understand Fleming’s left-hand rule. For
our purposes it does not matter which hand you use; it is just the shape
that matters. I am going to use my left hand for sentimental reasons.
Now, imagine the palm of your hand is the measuring apparatus:
your index finger the x axis, your middle finger, y and your thumb, z. At
any moment you can move your hand to point in any direction and take
a measurement. We will have to round up or down. Quantum mechanics
is named ‘quantum’ because all the readings must be whole numbers.
You will never see 10% spin in x, 90% in y and 85% in z; just ones, and
zeros. The measurements for a Boson will always be 1,0,1 in some order.
This is known as the ‘101’ rule.
Now, we ask the question: does a particle have a definite spin before
we take a measurement? The instinctive answer is yes, and this way of
viewing things is known as realism. It seems obvious that even if we did
not make a measurement, the particle would still have its spin; we just
wouldn’t know which type. Einstein explained realism by saying “I like
Kochen Specker
Free Will
345
to think the Moon is there when I am not looking at it.” But, how can we
test his statement? How can we know something is there without taking
a look? There is a way...
Let us suppose the particle had a definite spin before we measured
it. Perhaps its spin points at the top left hand corner of the room. Imagine
taking many measurements and seeing what happens. We can point our
hand in any direction: top of the room, bottom left corner, bottom right
corner and so on. Each time we point our hand in a direction we must
get 1, 0 and 1 in some combination (110, 011, 101). The particles are 101
particles and this is an absolute rule.
Let’s imagine doing the experiment. We fix the spin of a particle
and begin to take measurements, noting the answers as we go. If we get
a borderline condition we obey the 101 rule and give ourselves a 1, 0, 1
reading. As we move our hand to take measurements, a problem begins
to emerge. Every now and again we obtain a measurement that conflicts.
We chose a 1, 0, 1 when we were pointing our index finger towards the
floor, but if we point the finger toward the door, we need that original
middle number to have been a 1 for consistency. (The middle finger is
now pointing in the direction the index finger pointed to for the first
reading.) To fix the inconsistency we can change our original borderline
decision to a 1,1,0. All is well and we continue. But, as we get over 30
measurements, we can’t seem to find any way to make all the 1,0,1s fit
together. After scratching our
head for a while, we realize there
might be no solution. And indeed
there is not. This is the Kochen-
Specker Paradox. The odd shaped
cubes on the building in the
Escher print are an example of
one of these impossible figures.
An analogy to this problem
is trying to solve a broken
Rubik’s Cube. There is a really
mischievous trick you can play on
someone: reverse two colors on a
Rubik’s Cube. You can easily do
this by snapping one of the edge
blocks out, turning it around and
snapping it back in. When the
colors are already muddled up
1 0 1 puzzle piece
this is not obvious. Now give your

346 Are the Androids Dreaming Yet?
M. C. Escher’s Waterfall (Impossible Shapes)
friend the puzzle and they will spend hours trying to solve it! It can’t
be done because the puzzle is put together wrong. And in this matter
nature is also put together wrong! With as few as 33 measurements it is
impossible to construct a consistent three-dimensional shape that has
1s and 0s obeying the 101 rule in every place. The only way to complete
such a shape is with a measurement that is both simultaneously zero and
one: a paradox. We know what happens when we generate paradoxes. It
means one of the original assumptions is false and, in this instance, the
falsehood is that a particle has a definite spin before we measure it. It
Free Will
347
Kochen-Specker Cube
cannot. It must make up its mind on the fly. Einstein would be horrified.
Realism is violated by the quantum world: reality and measurement are
intertwined.
The Kochen-Specker paradox shows us that a particle only makes
its choice at the point of measurement. This does not prove it has free
will as it might still be told what to do by some external entity. It’s rather
like the famous game show, Who Wants to be a Millionaire? The particle
could answer the spin question in four possible ways. First, it could know
the answer, but we have just proven it does not. Second, it could phone a
friend obtaining the answer from some cosmic arbiter. Third, it could ask
the audience and take a vote from all the particles around it. Finally, it
could freely choose, without recourse to any of the other possible options
– in other words, it would guess!
348 Are the Androids Dreaming Yet?
A guess would mean particles have free will; no extraneous
influence or piece of information either on their person or from some
external source could have any effect. We are now going to prove the
particle does guess.
The Proof
Conway and Kochen construct their proof from a small set of axioms,
which form a rhyme. The axioms are; twin, fin and spin.
If two particles are separated by a distance (fin) and entangled
(twin), the spins of the particles (spin) cannot be determined by any
information in their history of the Universe up to that point. The proof
relies on a thought experiment.
Consider twin particles separated by a long distance. Physicists call
this ‘space like separation’. All this means is one particle is measured on, say,
Earth and the other on Mars, so relativity is significant in the experiment.
This may be impractical today but there is no reason the experiment
could not be done in principle. In the future, our children could set up
on the UN Moon base and fire one photon to a detector on Hubble II
and the other to the future Mars Orbital Station. Farfetched? If you had
told Einstein back in 1947 that in less than 70 years we would be able
to measure individual photons by sending them down spun glass fibers
to locations separated by 50 kilometers, involving a multidisciplinary
team composed of American, German, French and Russian scientists, all
working in harmony, he might have been equally incredulous.
As the proof introduces relativity we also need two imaginary
rocket ships. They must be traveling below the speed of light, so no Star
Trek Enterprise or Millennium Falcon. We will have to stick with an oldschool
spaceship, the Sulaco from Aliens should do the trick. They must
travel in opposite directions, passing our Moon Base just as the scientists
run the experiment.
Special Relativity shows our Universe has a strange property: there
is no such thing as a simultaneous event for two observers – at least if
they are separated by any distance. From the point of view of the first
spaceship, the measurement on Mars occurs first. But from the vantage
point of the second observer, the measurement on Hubble occurs first.
Now comes the proof by counter example. Let us suppose the
particles were influenced by an outside effect and had no free will.
Free Will
349
Let us say the Mars particle chooses its answer because of an
external influence. Its Hubble twin must choose the same answer. There
is no problem with this because the Hubble particle could have made its
decision before the Mars particle, so the decision was not predetermined.
But in another frame of reference the choice is made in the opposite
sequence. The Hubble particle chooses after the Mars particle. This is
predetermination and it breaks the Kochen-Specker theorem.
You can reverse the whole analysis and see the same problem from
the other point of view. There is a paradox here however you look at it.
The only solution to the paradox is that both particles make their
choice without any information from an outside source; particles have
free will. This means at least one new piece of information spontaneously
appears in the Universe – a ‘bit’ of free will, so to speak.
You might think there is a problem because the first particle affects
its twin, even if the second did not receive any outside influence. This
would result in the Kochen-Specker paradox reemerging. There is a
neat way out of this; time has no meaning for the particles. Or, I should
say, relative time has no meaning and, therefore, has no effect. There is
no concept of before or after between the particles. They live in a little
bubble of space-time where the order of events has no meaning. The
particles make their free choice together within this safe bubble, and the
paradox is avoided. When we come to measure them, we see they both
made a random decision together, but if we ask which made it first, the
question has no meaning. There is no clock valid for both particles, so
there is no possible answer to the question.
Conway and Kochen have proven sub-atomic particles have free will
– or at least entangled bosons do. At this point, their argument becomes
a philosophical one. They propose that these particles pass on this free
will to larger entities in the Universe and ultimately to us. Although
particles are small and insignificant, they are the fundamental building
blocks of nature, and the butterfly effect multiplies up tiny variations in
the microscopic world into the macroscopic events we see.
Although their theorem is very elegant, we still have to address the
question of whether the experimenter has the true freedom to run the
experiment in the first place: the determined determinist argument.
Russian Dolls
“Great fleas have little fleas upon
their backs to bite ‘em.
And little fleas have lesser fleas,
and so ad infinitum.
And the great fleas themselves, in
turn, have greater fleas to go on.
While these again have greater
still, and greater still, and so on.”
Augustus De Morgan
Free Will Universe
Ibelieve we live in a Universe where information comes into existence
through the creative endeavors of human beings. When Andrew
Wiles discovered his solution to Fermat’s Last Theorem, he did
something a computer cannot do and demonstrated non-computational
thought. But there is an alternative explanation put forward by the
determined determinists.
Daniel Dennett – the standard bearer for this camp – believes
everything in the Universe is entirely determined. He argues there is no
place in the laws of nature for free will to arise.
Both sides of the argument agree Turing prohibits a generalpurpose
machine from solving all mathematical problems, but that
seems to be the extent of agreement. The determinists solve the Wiles
Paradox by arguing he is a special purpose machine, perfectly able to
find answers to non-computable problems. The Turing prohibition only
applies to general purpose machines. Let us run a thought experiment
to see what sort of Universe we would live in if special purpose machines
were the answer to this puzzle.
If the Universe is determined, it can be modeled as a single algorithm.
If everything in the Universe evolves according to a set of rules, it will
run like a giant piece of clockwork or one large computer game. Each
solar system, planet, and individual mathematician would evolve along
preordained lines. Mathematicians would operate as software subroutine
and would rely on further subroutines to explain the beating of their
hearts and the way the molecules of their body interact.
If our Universe were organized in this way:
This Universe could not discover solutions to arbitrary problems.
352 Are the Androids Dreaming Yet?
This Universe could be preprogrammed with every theory we could
ever discover within it. (There would be no arbitrary problems.)
This argument neatly sidesteps Turing’s theorem by specifying
there is no such thing as an arbitrary problem – a random problem
picked from the infinite set of problems. At the same time, it sets certain
characteristics of such a Universe and I believe we can test these...
A computable Universe must already know the solution to every
problem it will encounter above the logic limit: It cannot discover
knowledge on the fly. For many problems, a small number of fundamental
rules can account for everything. Although our galaxy and the beautiful
nebulae we see through our telescopes look complex, they might be
the result of some such simple set of rules – just like a fractal. That’s
Stephen Wolfram’s solution to the mystery of our Universe. But some
problems are complex. The solution to Fermat’s Last Theorem is an 80
page document consisting of 5 million bits of information. All this must
be stored somewhere in the Universe. It might not be stored as a string
of bytes, it could be found in a set of equations governing the motion of
the atoms such that at some point – in 1995 to be exact – they all line
up in Andrew Wiles’ brain to direct his fingers to type out the proof. In
this case, the Universe has solved a mathematical puzzle because it was
specifically set up to do so from the time of the Big Bang, but this raises
three questions:
Where does the Universe store this enormous amount of
information?
How does The Universe hold the information reliably?
How did the pre-Universe solve the problem, so it might program
the Universe at the moment of the Big Bang?
The first question is probably answerable. The Universe is a big place
and could store sufficient information to solve the mysteries that puzzle
the inquisitive creatures that inhabit its planes. There are many practical
problems to consider, such as how to preserve the information through
all the strange evolutions of our Universe; inflation, star formation, and
so on. But it could be done.
The second question is insurmountable and presents the counter
argument to the determinists. Our Universe appears to be composed of
non-deterministic objects. Such objects exist in the mathematical world;
Kochen-Specker cubes, for example. Unfortunately for the determined
determinist, bosons behave according to the same principles. In case
you’re thinking thinking bosons are rare, light is formed of bosons. Our
Free Will
353
whole existence is surrounded by non-deterministic physics. Therefore,
your actions are not predetermined by anything in your local corner of
the Universe – the past light cone if you want to be strict about the physics.
The determined determinists are a determined bunch. Just because
the information that determines your actions cannot be encoded by the
particles you are made from, does not mean you are free. The information
could be stored in parts of the Universe we cannot see, or held outside
the Universe in some sort of cosmic hard drive. Every creative event in
the Universe would be specified in this store.
But this begs the third question: How was this store of information
generated in the first place? If a Universe contains creative things – as our
Universe does – there is no way to computably generate the necessary
determinist store of information. The Universe has free will because there
is no deterministic process that could generate it.
If our Universe were a Turing machine, everything within it
would be too. Think about the deterministic clockwork argument I
gave earlier. If you try to construct a better – say a more random –
machine inside a Turing machine, an observer could simply ignore the
better machine hidden within it, and watch the outer machine work.
The outer machine will predict the operation of the inner machine
perfectly, even if the inner machine is fiendishly complicated. We
have to consider the machine on which our human software runs. Our
bodies, our minds, all that we are, is software running on the Universe’s
hardware of quarks and photons. If the hardware is deterministic, then
so is our software. And if the hardware is deterministic, there can be no
creativity within the Universe.
So the free will camp has an argument easily as frustrating as the
one deployed by the determinists. Every time a determinist asks, “How
do you know you were not always going to do that?” the free will believer
can reply, “You asked me a question. If this dialogue is to have any
significance, then we must exist in a rational Universe and, therefore, the
laws of information give us creativity and free will. If you believe we are
fully determined, there is no point in my answering your question.”
I reason. Therefore, I have free will.
The Universe is not a machine.
354 Are the Androids Dreaming Yet?
Chapter 16
THE QUEST FOR
KNOWLEDGE
Darwin’s Beagle
“Sometimes I’ve believed as many
as six impossible things before
breakfast.”
Queen of Hearts in
Lewis Carroll’s Alice
“It is not the strongest of the
species that survives, nor the
most intelligent that survives.
It is the one that is the most
adaptable to change.”
Charles Darwin
We celebrate creativity with many competitions and prizes. I
have been a student of problem lists of over the years. Here
is my list of the problems remaining open in the modern
world. I’ve tied it in with other lists where relevant, and indicate what
you might win if you were to solve one. As I was writing this book, a few
of the questions were answered; the Higgs Boson was discovered and the
Poincaré Conjecture proven. I will keep the list up to date on the web site.
Fields Medal
1. Mathematics
1.1 The Birch and Swinnerton-Dyer Conjecture. C
1.2 Hodge Conjecture C
1.3 Navier-Stokes Equations C
1.4 A proof or disproof of P =NP C
1.5 The Poincaré Conjecture C – Solved
1.6 Riemann Hypothesis h8 C
1.7 Yang-Mills Theory C
1.8 Can we understand and solve all 23 Hilbert Problems h1-23
1.9 Goldbach Conjecture h8
1.10 Is mathematics fundamental to or simply a good model of
our Universe? H6
1.11 Is mathematics an emergent property in our Universe or
causal? Which is more fundamental?
1.12 Fermat’s own original proof of his theorem!
2. Physics
Nobel Prize for Physics
2.1 Are there many worlds or just one?
2.2 Does quantum collapse have meaning?
2.3 Will we find the Higgs-Boson? (Provisionally yes, 2012)
2.4 Do we need quantum gravity to explain human thought?
2.5 Will we observe gravitational waves, and what is the
current explanation for gravitational noise?
2.6 What causes the arrow of time and the asymmetry of
physical laws?
2.7 Do the constants of physics change over time?
2.8 Is quantum computation sufficient to simulate the universe,
or is the universe non-computational?
2.9 Can magnetic monopoles exist?
2.10 What is meant by quantum non-locality, a.k.a., spooky
action at a distance?
358 Are the Androids Dreaming Yet?
2.11 Is there a theory that would unite gravity with the other
three forces: a Theory of Everything?
2.12 Is Schrödinger’s cat alive or dead in the box?
2.13 Does ball lightning exist and can it be made in the
laboratory?
Nobel Prize for Physics
3. Cosmology
3.1 What is the nature of Dark Matter?
3.2 What is the nature of Dark Energy?
3.3 What is Dark Flow?
3.4 The slingshot anomaly.
3.5 Did inflation really happen?
3.6 Was there a singularity at the origin of our Universe, and
what happened before the first second? An eternity?
3.7 Can any information travel faster than the speed of light?
3.8 What is the cause of the Pioneer anomaly? (solved in 2011)
3.9 Are there aliens?
3.10 The Goldilocks question. Why are the cosmological
constants so finely tuned?
3.11 Do real numbers exist or is our Universe quantized?
3.12 Why is there little antimatter?
3.13 What are cosmic rays and where do they come from?
3.14 What was the WOW signal?
3.15 Does the fine structure constant vary over time?
3.16 If we live in an infinite Universe, why don’t we see more
strange things?
3.17 Why is the cosmic background radiation so smooth?
3.18 How can we explain the lack of total smoothness of the
cosmic background radiation!
3.19 Is there an explanation for any detail in the cosmic
background radiation map?
4. Engineering
Nobel Prize for Chemistry, Turing Award
4.1 Can we achieve economic nuclear fusion?
4.2 Will we realize cold fusion? (Partially demonstrated)
4.3 Can an amateur get to the moon?
4.4 Can an amateur collect a rock from the moon? X
4.5 Will we make an Artificial Intelligence?
4.6 Can we make a Tricorder? X
4.7 Can we power the world from renewable sources?
4.8 Will robots go to war in the future?
The Quest for Knowledge
359
4.9 Can we make a robot indistinguishable from a human and
cross the uncanny valley?
4.10 What is the tallest building we could build on planet Earth?
4.11 Will we routinely use flying cars by the end of this century?
4.12 Will we have a base on the Moon or Mars in this century?
Nobel Prize for Medicine
5. Biology
5.1 Why is the placebo effect so strong?
5.2 Can we cure the common cold?
5.3 Is there a generally effective treatment for cancer?
5.4 Can we find a vaccine against HIV?
5.5 Can we cure endemic diseases such as malaria, or is it an
arms race?
5.6 How plastic are our genes and is epigenetics a significant
factor?
5.7 Can we cure dementia? L
5.8 Can we make a desktop gene sequencer? X
5.9 Will we prove the Kurzweil Hypothesis that technology
will allow us to live forever?
5.10 How old will we live to with a reasonable quality of life?
5.11 Can genes jump between organisms? Even participating in
whole scale fusion?
5.12 Will we be able to grow organs?
5.13 Will we clone a human from an adult?
5.14 Can we clone a dinosaur?
6. The Mind
Nobel Prize for Medicine
6.1 Does the Flynn Effect mean we are really becoming more
intelligent?
6.2 What is the nature of consciousness?
6.3 Do we have free will?
6.4 Which is more important: Nature or Nurture?
6.5 What is humor for?
6.6 Do some people have photographic memory? (yes, recent)
6.7 What is the purpose of sleep and, in particular, dreams?
6.8 What is understanding?
6.9 Do we ever truly know something?
6.10 How does the brain think?
6.11 Is the brain a quantum device?
6.12 Why do we get stressed?
6.13 Why are some people more intelligent than others?
360 Are the Androids Dreaming Yet?
6.14 What limits our ability to concentrate and work hard
mentally?
Pulitzer prize for History
7. The Ancient World
7.1 What is the Linear-a script discovered in Crete?
7.2 Where are the ruins of the Light House at Alexandria and
indeed Alexandria itself?
7.3 What is the location of the Lost City of Atlantis if it is not a
myth?
7.4 Will we ever find King John’s Treasure?
7.5 What is the truth to the legend of El Dorado?
7.6 Why were the pyramids built?
7.7 What was the purpose of Stonehenge and who built it?
7.8 How many books and how much knowledge have we lost?
7.9 Did King Arthur and Camelot exist in any real way?
7.10 Why did the people of Easter Island build their statues?
7.11 Was there an ancient flood, suggested by the Bible and
other ancient texts?
7.12 Are the Seven Wonders of the Ancient World lost forever?
Nobel Peace Prize or Prize for Economics
8. The Modern World
8.1 Is there a best political organization for a country?
8.2 What is the best political balance of federation and
autonomy?
8.3 The Black Swan Effect: Why do improbable things happen?
8.4 Is there a right way to run the economies of the world?
8.5 When is it right to intervene in a conflict, and when is it
best to leave a country to its own devices?
8.6 What is the best way to choose a political representative?
8.7 Will we ever abolish war?
8.8 Why is the gap between rich and poor increasing in most
of the world today?
8.9 How powerful should states be compared with world
organizations?
8.10 Is there a right level of tax?
8.11 Are morals absolute or relative: euthanasia, abortion, gay
marriage, eating meat?
8.12 What will we do about our aging population?
Goldman Prize for the Environment
9. Planet Earth
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361
9.1 Is man-made global warming real, and if already proven
will we ever persuade the US government?
9.2 What caused the Tunguska Explosion?
9.3 What caused the extinction of the dinosaurs?
9.4 Can we predict earthquakes or eruptions?
9.5 What caused the reversing of the poles and when will the
next one occur?
9.6 What was the origin of life on Earth?
9.7 Will we be wiped out by an asteroid before we build a
suitable defense?
9.8 Can we grow enough food to feed the planet? L
9.9 Can we give clean water to everyone on the planet? L
9.10 Is increasing air travel compatible with survival of the
planet? L
Nobel Prize in Literature and others
10. Philosophy
10.1 Is there a God?
10.2 Where did we come from if we are not made by a god?
And if we were, then where did God come from?
10.3 Where do morals come from?
10.4 Is there a reality?
10.5 Is there life after death?
10.6 Do we have free will?
10.7 Is beauty in the eye of the beholder?
10.8 What is the meaning of life, the Universe and everything,
other than 42?
11. Conspiracy and Paranormal
11.1 Is there anything going on in the Bermuda Triangle?
11.2 Do aliens make crop circles? (disproven hoax)
11.3 Who was Jack the Ripper?
11.4 Can the mind bend spoons? (hoax, admitted)
11.5 Does the government suppress UFO existence?
11.6 Why was the Mary Celeste abandoned?
11.7 Is the Turin Shroud that of Christ?
11.8 Do the Abominable Snowman and Sasquatch exist?
11.9 Are there ghosts?
11.10 Is there a paranormal?
11.11 Do aliens live amongst us?
11.12 Was there a conspiracy in the shooting of JFK?
362 Are the Androids Dreaming Yet?
Cross reference to other lists
Hn: Hilbert’s Problem
C: Clay Mathematics Millennium Prizes
X: XPRIZE
L: Longitude Prize

Nobel Prize Medal
“If I could explain it to the
average person, I wouldn’t have
been worth the Nobel Prize.”
Richard P. Feynman
Awards
for Discovery
People like prizes. Competition drives humans forward in a way
we don’t properly understand. In film, we have the Academy
Awards, whilst on the web we have The Webbies. Some prizes,
such as the Nobel Prize, Fields Medal and Pulitzer Prizes, have a long
and distinguished history, while others such as the XPRIZE are more
recent creations. Some prizes, such as the Ig Nobel Prize and the Golden
Pineapples were mainly created for their humorous value. Prizes are
not a recent phenomenon. The Longitude Prize, originally won by
John Harrison, is being revived in Britain in 2014 to mark its 300 th
anniversary. The original prize, £10,000 in its day, was awarded by the
British government for making a device that allowed ships to determine
their East-West position (a sextant only gives north-south). The 2014
prize is £10m pounds and the topic will be chosen by public vote! Here is
a small history of some of the more famous prizes.
Nobel Prizes
Alfred Nobel spent his life developing weapons and explosives. His
laboratory was built in the middle of a lake with a bridge running to
it, so if he blew himself up doing an experiment, only he would die. He
managed to stabilize nitroglycerine by mixing it with saltpeter and created
366 Are the Androids Dreaming Yet?
Pulitzer Medal
dynamite. This was used in the mining industry but also extensively in
weaponry, so he came to be known as the Merchant of Death during his
lifetime.
To be known as the merchant of death would have a profound effect
on anyone. As Nobel pondered the balance of his life’s work he decided
to do something positive with the huge wealth he had accumulated. On
his death in 1896, he willed his entire fortune to create the awards we
now call Nobel Prizes.
There were five original prizes; physics, chemistry, peace, physiology
or medicine, and literature. A newer economic science prize is awarded
by the Royal Swedish Academy of Sciences.
You must be alive to receive a Nobel Prize; a few have been
awarded posthumously because the laureate died after the winner was
announced but before the award ceremony. The work must have been
proven experimentally, and although originally it was supposed to be for
discoveries in the previous year, nowadays a theory must have stood the
test of time. Consequently, winners tend to be quite old. The prize must be
for something with practical applicability – Einstein received his Nobel
Prize for the Photo Electric Effect, rather than his more famous Theory
of Relativity. The judges evidently thought particles more practical than
planets! The prize is usually awarded to a maximum of three people. This
has produced some controversial results but despite this the Nobel Prize
is the uncontested top prize in science.
The Quest for Knowledge
367
Pulitzer Prize
A Pulitzer Prizes is to the arts what a Nobel Prize is to science. Again
the Prize was the result of a bequest. They are awarded in the fields of
music, art and literature. Unlike Nobel Prizes, where there are no public
nominations and you might wait a lifetime for the phone call, you enter
your name for a Pulitzer Prize. Most people associate the term Pulitzer
Prize winner with journalism, but about 25 Pulitzers are awarded each
year. You must be a US citizen to enter.
Turing Award
Originally set up by the Association of Computer Machinery, this award
comes with prize money of $250,000, supported by Google and Intel,
and goes to a person who significantly advanced computer science or
artificial intelligence in the previous year. It is considered the Nobel Prize
for computing.
XPRIZE
XPRIZEs are awarded for technology and bear the democratic stamp
of the Internet age. Anyone can propose a challenge but they must also
provide the prize money! It’s big money. The Ansari XPRIZE for the first
XPRIZE First Award Ceremony
368 Are the Androids Dreaming Yet?
non-governmental organization to put a man in space was $10 million,
awarded in 2004. There are a growing number of XPRIZEs, including, at
the time of writing:
• Google Lunar XPRIZE, $30m to put a rover on the Moon.
• Qualcomm Tricorder XPRIZE, $10m to make your mobile
phone into a hand held medical health scanner, similar to the
Star Trek tricorder.
• Nokia Sensing CHALLENGE, $2.25m to build a hand-held
medical scanner.
• Wendy Schmidt Ocean Health XPRIZE, $2m to create a method
to measure the ocean’s pH.
Fields Medal
The equivalent of a Nobel Prize for mathematics is a Fields Medal.
Joseph Field provided the money and helped set up the prize. Today it
is administered as part of the International Mathematical Union. You
must be under 40 to receive the prize. Andrew Wiles was 45 when he
solved Fermat’s Last Theorem, so they created a special prize for him
called a Fields Fellowship. Until recently only men had received the
prize. However in 2014 Maryam Mirzakhani won the prize for her work
on the geometry of Riemann surfaces.
Fields Medal
The Quest for Knowledge
369
Riemann Surface

Chapter 17
THE FUTURE
Omar Khayyám
“Prediction is very hard,
especially about the future.”
Niels Bohr
“The Moving Finger writes: and,
having writ, Moves on: nor all
thy Piety nor Wit Shall lure it
back to cancel half a Line, Nor
all thy Tears wash out a Word of
it.”
Rubaiyat of Omar Khayyam,
Edward FitzGerald
مایخ رمع تایعابر
I
remember when I was eight years old, being asked to draw a vision
of the world in the year 2000. In my the home of the future, rather
than going to the shops to get milk, orange juice and cornflakes, they
would arrive by pipe. These days I know about microbiology and realize
this would have been highly impractical and perhaps rather dangerous.
I could claim some premonition of the Internet at this point; no selfrespecting
science book is complete without one of these!
Of course, the truth is I had no more idea of the way things would
turn out than anyone else. Now that I am a little older let’s see how much
trouble I can get into predicting the future.
I think we will build thinking machines – AIs – using our insights
into the operation of the brain. They will not be like the computers of
today but will still be physical devices. There is nothing overtly spiritual
in my conception of the way we operate, but I am arguing that the
human mechanism is more complex than a digital computer. Building
these machines will be hard, and they will not be ‘machines’ in the sense
I have used throughout this book. They will be minds.
When we build AIs that think and feel, will they acquire ‘human’
rights? Might one of my grandchildren fall in love with an AI, perhaps
even marry one? On the darker side, how will they view us: what place
would we have in their world once we had brought them into being?
However, I think this process of building an AI will be hard and in one
hundred years’ time we will still be struggling with the problem.
In this book, I have presented a way to understand the creative
process within our Universe. It relies on the existence of non-computable
processes in our brain and in the physical laws which govern them.
Currently, the laws contain a big hole. Although we can, perhaps, see
where freedom might come from – through randomness and nondeterminism
– we don’t understand where the will emanates to shape the
Universe. Over the next thirty years, I think we will begin to understand
this and see how creativity relates to the Universe we observe. I am not
suggesting any anthropic principle, or some grand interaction between
mankind and the Universe, just an important simple freedom: That we
humans are free to think and do as we please. When I choose to lift my
arm and raise a glass of wine with friends, this is my choice. I am the
cause. The effect is the displacement of my arm, causing photons and
gravitational waves to ripple out across the Universe, and in that sense I
freely affect my environment.
Da Vinci, Self Portrait
“A good painter is to paint two
main things, men and the
working of man’s mind.”
Leonardo da Vinci
Appendix 1
Acknowledgments
Front Matter
Cover
Spine Equations
Author Photograph
ACPMM, Wolfson College Cambridge
Mathematical Bridge, Cambridge
Introductory Image
Vladislav Ociacia
Illustration by Arabella Tagg
Arabella Tagg
James Tagg Personal Collection,
Course changed name to ACDMM in
1990.
Hipgnosis, www.shutterstock.com
Photograph by James Tagg
Chapter 1
Computer versus Human
Kasparov versus Deep Blue
The Music of Emily Howell
IBM’s Watson Plays Jeopardy
Watson Questions and Answers
Steve Wozniak
Turning Images to Music
Brain Image of Fish Hunting Prey
Babbage Difference Engine No. 2
Blutgruppe/Corbis
Louie Psihoyos/Corbis
Kind permission of David Cope and
Centaur Records. Emily Howell: From
Darkness, Light. Picture and Audio
Clip
Associated Press Carol Kaelson/
Jeopardy Productions, Inc.
Illustration by James Tagg
TIM CHONG/Reuters/Corbis
Credited to: Maxim Dupliy, Amir
Amedi and Shelly Levy-Tzedek
This work (or this video) was published
from Kawakami lab in National
Institute of Genetics , Japan (Muto,
A. et al. Current Biology 23, 307–311,
2013)”.
Photograph by James Tagg @ The
Computer History Museum
19 th Century Calculators Wikimedia, Ezrdr, CC3
Model of the Antikythera Mechanism Wikimedia, Geni, CC3
376 Are the Androids Dreaming Yet?
Moore’s Law
3D Chip
Richard Branson
ELIZA, DOCTOR
IQ Test
Metal Puzzle
Hole in the Wall Experiment
One Laptop per Child
Piano Practice
Dan McLaughlin
Astrological Clock, Hampton Court
Lava Lamp
Steve Jobs Collage
“Ascending and Descending”
Chapter 2
Afghanistan Stability/COIN Dynamics
McChrystal in Kabul
Gettysburg Address as PowerPoint
Space Shuttle Columbia Crew
Shuttle Tile
Shuttle Images
Searle’s Chinese Room
Black Box Diagrams
The Miracle Worker, Helen Keller
Human Person, or is it?
New Yorker Dog Internet Cartoon
Chapter 3
Body Language
Ronald Reagan and Mikael Gorbachev
Höfði House in Reykjavik
Fake or Real Smile
Yasser Arafat and Shimon Pérez
Learning Swedish, The Two Ronnies
Scripts of the World
Chinese Traditional and Simplified
Great Comedy Videos
Credited to Ray Kurzweil, CC1
Kind permission Intel Press
Department
kathclick, www.bigstock.com
Opensource project encapsulated into
widget by James Tagg
Illustrated by James Tagg based on a
Wechsler example question
www.shutterstock.com, fdpress
Courtesy Philippe Tarbouriech/Holein-the-Wall
Education Ltd.
One Laptop per Child project
Photograph by James Tagg
Kind permission of Dan McLaughlin,
www.thedanplan.com
Wazzaman, Wikimedia, CC3
Sean Gladwell, www.shutterstock.com
Kind permission: www.village9991.it
© 2014 The M.C. Escher Company-
The Netherlands. All rights reserved.
www.mcescher.com
US Government, Joint Chiefs of Staff,
PD
USA Navy Photo, PD
Kind permission of Peter Norvig
Credit NASA
US Government, PD
Credit NASA
Illustrated by James Tagg
Illustrated by James Tagg
Associated Press
Associated Press
New Yorker © Condé Nast Licensing
Kind permission of Conference on
Communication and Body Language.
US Government, PD
Wikimedia
Bigedhar, www.bigstock.com
UPI
Kind permission of BBC, hosted on
YouTube
Illustrated by James Tagg
Illustrated by James Tagg
Kind permission BBC hosted on
YouTube
Acknowledgements
377
Chapter 4
Child Having EEG
X-Ray of Rontgen’s Wife’s Hand
Lego Cubes Under Ultraviolet Light
Pit Viper
Einstein’s Brain
Thermal Image of a House
Flowers in Ultraviolet Light
Functional MRI, Response
Functional MRI: Working Memory
McGill Diffusion Tensor Image
Functional PET
Organization of Your Brain
Visual Processing System
Impressionist Painting, Monet Haystack
Frogs Eyes are Very Sensitive
Color is Not an Absolute Sense
McGurk Effect
Penrose Steps
Scintillating Blobs
Selective Attention video link
Tiger Woods Swing video
Neural Network
Synapse
Paramecium
Quantum Tubulin
Tubulin Molecule
Chapter 5
Chimpanzee and Typewriters
There are Holes in the Sky poem
Spike Milligan
Lewis Carroll’s Jabberwocky
Lewis Carroll’s Jabberwocky
Word’s Verdict on the Jabberwocky
dblight, www.iStockphoto.com
Wikimedia
www.public-domain-image.com
abcphotosystem, www.shutterstock.
com
Wikimedia
Fotoflash, www.bigstock.com
Bjørn Rørslett
National Institute of Mental Health,
Wikimedia, PD
Kind permission John Graner,
Neuroimaging Department, National
Intrepid Center of Excellence, Walter
Reed National Military Medical
Center, 8901 Wisconsin Avenue,
Bethesda, MD 20889, USA
Thomas Schultz, Wikimedia, CC3
Jens Maus, Wikimedia, PD
www.shutterstock.com and James
Tagg
Illustrated by James Tagg includes
www.shutterstock.com components.
Wikimedia, PD
Michiel de Wit, www.shutterstock.com
Illustrated by James Tagg
Kind permission of BBC, hosted on
YouTube
James Tagg, Sketchup Model
Illustrated by James Tagg
Kind permission to link provided by
Daniel Simons. DVDs can be purchased
from www.viscog.com
Kind permission of www.craighansongolf.com
Illustrated by James Tagg
Meletver, www.bigstock.com
micro_photo, istock
Kind permission Travis Craddock
Wikimedia
chippix, www.shutterstock.com
Spike Milligan Enterprises
TopFoto[]
Lewis Carroll, Out of Copyright
Lewis Carroll, Out of Copyright
Illustrated by James Tagg
378 Are the Androids Dreaming Yet?
Loch Ness Monster Picture
The Loch Ness Monster’s Song
Dyslexic Poem
Starry Night, van Gogh
Game of Battleship
Jesse our Creative Kitten
Chapter 6
Orangutan and Kitten
Twin Guards
Groucho Marx
Euclid’s Elements, Oxyrhynchus Papyrus
Chapter 7
Mandelbrot Set
Bubble Sort Ballet, video
Maze
Travelling Salesman Problem
Rubik’s Cube
Complexity Scale
Butterfly Beginnings of a Tornado?
Trajectories
Poincaré Portrait
Blue Marble, Weather Patterns
Lorenz Attractor
Nebula
Cellular Automaton
Conway’s ‘Life’
Chapter 8
Hilbert’s Hotel
Spears and Hunters
Unknown, Hoax
From Glasgow to Saturn (Carcanet,
1973) also published in Collected
Poems (Carcanet, 1990) Reprinted by
permission of Carcanet Press.
Kind permission of the copyright
holder: The Journal of Irreproducible
Results, the science humor magazine,
www.jir.com, 1994 and 2000, via the
author Jerrold H. Zar
Wikimedia, PD
www.shutterstock.com
James Tagg
Chris Butler, www.bigstock.com
Manamana, www.shutterstock.com
Library of Congress, PD
Wikimedia, PD
Steve Buckley, www.shutterstock.com
Created at Sapientia University, Tirgu
Mures (Marosvásárhely), Romania.
Directed by Kátai Zoltán and Tóth
László. In cooperation with “Maros
Művészegyüttes”, Tirgu Mures
(Marosvásárhely), Romania.
Vasilius, www.bigstock.com
Illustrated by James Tagg, map from
www.bigstock.com
Photograph by James Tagg
Illustrated by James Tagg
saichol chandee, www.shutterstock.
com
Kind permission Steinn Sigurðsson
(1991)
Eugène Pirou, Wikimedia, PD
Reto Stöckli, NASA Earth Observatory
zentilia, www.bigstock.com
Credit NASA
Weisstein, Eric W. “Cellular
Automaton.” From MathWorld--A
Wolfram Web Resource.
James Tagg screen capture of an MIT
opensource project
Karamysh www.bigstock.com
Munduruku, Wikimedia cc2.5
Acknowledgements
379
Traversing an Infinite plane with a Line
Spear and Hunter
Hilbert Hotel Video Link
Holding Infinity in Your Hand
Number Quiz 1
Number Quiz 2
Donate a Random Number
Which Number is Random
Smallpox Virus
Smallpox Child
Illustrated by James Tagg
Illustrated by James Tagg
Kind permission of BBC, hosted on
YouTube
Photograph by James Tagg
Illustrated by James Tagg
Illustrated by James Tagg
Illustrated by James Tagg
Illustrated by James Tagg
3d4Medical.com/Corbis
Associated Press, SANTOSH BASAK
Chapter 9
Donald Rumsfeld
US Army, Wikimedia, PD
Kurt Gödel, any Likeness is Accidental Unknown, Wikimedia, PD
IAF Rule 164
IAF rules excerpt
PM
Paul Hermans, Wikimedia, CC3
Amazon Listing for PM
Amazon excerpt (not in print version)
1+1 = 2, PM (1) PM excerpt
1+1 = 2, PM (2) PM excerpt
Konigsberg’s Bridges
Bogdan Giuşcă, Wikimedia, PD
Peano Portrait
Materialscientist, Wikimedia, PD
Beer Mug, Table and Chair
Photograph by James Tagg
Einstein and Gödel
Kind permission of the Archive of the
Institute of Advanced Study
Chapter 10
Alan Turing Portrait
Enigma Machine
Can you decode this?
Correct the code
Lego Turing Machine
Old Fashioned Relay Mechanism
3D Printing Machine
Block Print from ‘No Silver Bullet’
Chapter 11
Fred Brooks
Web Page (James Tagg’s Home Page)
Dilbert Software Specification
Long Multiplication
A Hypercube in Two Dimensions
Impossible Shapes, Devil’s Tuning Fork
Halting Program
Four Color Problem
Dalek Trouble
Augustus De Morgan Poem
National Portrait Gallery
Sperling, Wikimedia, PD
Illustrated by James Tagg
Illustrated by James Tagg
www.LegoTuringMachine.org
Wikimedia, Signalhead, CS3
360b / www.shutterstock.com
Wikimedia, PD
Copyright owned by SD&M,
Wikimedia CC3
Screen capture by James Tagg
DILBERT © 2006 Scott Adams.
Used By permission of UNIVERSAL
UCLICK. All rights reserved.
Illustrated by James Tagg
Mouagip, Wikimedia, CC3
Illustrated by James Tagg
Illustrated by James Tagg
chas zzz brown, Wikimedia, CC3
Birkett 1981, Permission Punch
Augustus De Morgan, (pd)
380 Are the Androids Dreaming Yet?
Word Puzzle
Creative Inoculation
Jackson Pollock
Jeopardy
Programming Cartoon
Specification Cartoon
Chapter 12
Two Digital Brains Communicating
Perpetual Motion from the 1600s
Black Hole Malament-Holgarth Space
Synapses and Tubulin
Chapter 13
World Communication
IMAX
Hologram
Gennadií Makanin Excerpt of paper
on Word Puzzles
Illustrated by James Tagg
Albright-Knox Art Gallery/CORBIS,
Pollock-Krasner Foundation / Artists
Rights Society (ARS), New York
Associated Press Carol Kaelson/
Jeopardy Productions Inc
Kind permission Geekherocomic
Credit Paragon Innovations
Photobank Gallery, www.shutterstock.
com
Robert Fludd’s 1618 “Water Screw”,
Wikimedia, PD
Crystal Graphics
Crystal Graphics
Antartis, www.bigstock.com
Louie Psihoyos/Corbis
videodoctor, www.shutterstock.com
Chapter 14
Invention of Light Bulb, Thomas Edison Corbis, Betmann
Steve Jobs Shows the iPhone
Corbis, Reuters
Stopwatch 60 seconds!
Studio 37, www.shutterstock.com
Paperclip Test
Illustrated by James Tagg
30 Things Test Illustrated by James Tagg
Paperclip Test2
Illustrated by James Tagg
Eureka
KoS, Wikimedia, PD
Circle with Dot, Problem
Illustrated by James Tagg
Thinking Outside the Box
Illustrated by James Tagg
John Cleese, Video Link
Picture from www.shutterstock, links
to World Innovation Forum, YouTube
talk in iBook version and on website.
Sketch Test
Illustrated by James Tagg
Hard Drives
www.shutterstock.com
Harold Cohen and AARON
James Tagg at the Computer Museum
Harold Cohen and AARON
James Tagg at the Computer Museum
Old Polo
Generic Polo Photo
New Polo
Fingerhut, www.shutterstock.com
Chapter 15
Dilbert on Free Will
Domino Toppling
DILBERT © 1993 Scott Adams.
Used By permission of UNIVERSAL
UCLICK. All rights reserved.
(c) www.austriandominoart.com
Acknowledgements
381
Newton’s Rings
Wave Interference
Solvay Conference
Interferometer
Schrödinger’s Cat
Polarized Glasses, Glare and No Glare
Bell Test
Left and Right Socks
Morse Signaling
Dawkins and Atheist Bus
Fork in the Road
Left Hand Rule
Orthogonal Sticks
M.C. Escher’s “Waterfall”
Kochen-Specker Cube
Russian Dolls
Chapter 16
The HMS Beagle
Nobel Prize Medal
Golden Hall, Sweden
Pulitzer Prize Medal
First XPRIZE Award Ceremony
Fields Medal
Chapter 17
Omar Khayyam
Appendices
Leonardo da Vinci, Self Portrait
British Library
Experiment, ATLAS, CERN
Panda
Conway and Kochen
Looney Tunes “That’s all Folks”
Wikimedia
Single image in Book. Slide show in
iBook, Various; Wikimedia www.
shutterstock.com, www.bigstock.com
Benjamin S. Couprie, Wikimedia, PD
Illustrated by James Tagg
Dhatfield, Wikimedia, CC3
HUB, Wikimedia, CC3
Illustrated by James Tagg
Hofmeester, Bigstock.com
Illustrated by James Tagg
Wikimedia, CC2
fivepointsix, www.bigstock.com
Photograph by James Tagg
Illustrated by James Tagg
© 2014 The M.C. Escher Company-
The Netherlands. All rights reserved.
www.mcescher.com
James Tagg modeled in Sketchup
Robyn Mackenzie, www.bigstock.com
Bettmann/Corbis
Wikimedia, PD
vichie81, www.shutterstock.com
Original Daniel Chester French, photo
upload Katpatuka, Wikimedia, PD
Kbh3rd, Wikimedia, CC3
Stefan Zachow, Wikimedia, PD
Wikimedia, PD
Wikimedia, PD
Diliff, Wikimedia, CC2.5
xdrew, www.shutterstock.com
leungchopan, www.shutterstock.com
Photograph courtesy of
Princeton University’s Office of
Communications; Denise Applewhite,
photographer
Wikimedia, PD
The Wikimedia Creative Commons Licenses 1, 2, 2.5 and 3 may be found at www.
wikimedia.com. PD indicates a public domain.
In the case of items marked ‘video’ clicking on the image in the iBook or eBook
will link to YouTube. The links are also available at www.jamestagg.com/videolinks
for book readers.
Reading Room at the British Museum
“From the moment I picked your
book up until I laid it down I
was convulsed with laughter.
Some day I intend reading it.”
Groucho Marx
Appendix 2
Bibliography
I
am not resident at an academic institution, nor do I work for a large
company with access to a broad range of journal subscriptions. I have
a degree in Physics and Computer Science, so I am no layman. The
modern web gives amateurs like me, easy access to enormous information
resources that would only have been available from the finest University
libraries even five years ago. Over time I have built up a personal library
of books in the field, many of them ex-library copies which, by their date
stamps, were never borrowed in their home universities!
I’m always skeptical of the enormous bibliographies found in the
back of science books and whether they are ever read. If you want a
pointer to the next books to read, here are some suggestions: A Brief
History of Time, The Man who Mistook his Wife for a Hat, The Emperor’s
New Mind, The Naked Jape, Gödel Escher Bach, Proust and the Squid,
Logic, A Five Day Course in Thinking, Your Brain on Music, The 4%
Universe, From Eternity to Here and Time.
384 Are the Androids Dreaming Yet?
Journal
Scientific American
Wikipedia
The Economist
Science: The American Institute
for the Advancement of Science.
Cost
Some free articles, Membership $150 p.a.
Free
Free to search but a subscription needed for
full articles, $200
Annual Subscription $151
Mind Annual Subscription, $200
Google Scholar
Free to search and often free to view, but
some articles require membership of underlying
services. From here you jump off into
an endless series of journals too numerous
to mention.
Google Books
Free, but you buy a lot of books!
Amazon
Some free material but again lot of book
buying
JStor
Variable, based on area of interest
Arxiv.org
All the pre- prints of forthcoming papers.
Invaluable. Free
SpringerLink
Article by article purchase, $35 each
Subscriptions and Sources
Chapter 1
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Dawkins, Richard. The Magic of Reality: How We Know What’s Really True. Bantam
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Ericsson, K. Anders. “Attaining Excellence through Deliberate Practice: Insights
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Ericsson, K. Anders, Ralf T. Krampe, and Clemens Tesch-Römer. “The Role of
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