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Symmetry
provides a Turing-type test
for 3D vision
Zygmunt Pizlo
Psychology, Purdue
Will robots be smarter than we are?
• Soon?
• Ever?
Can robots even hope to be smarter
than we are?
• If we want to answer this question, we must first
find a way to determine whether robots actually
have minds, and if they do, what’s in them?
• Note that a robot CANNOT produce what looks like
smart behaviors if it has no mind.
– Having mind means, at the very least, that one keeps and
uses a representation (a model) of the external
environment and events.
– There isn’t time to explain this now, so just take my word
for it.
Can robots have a mind and be intelligent?
• This is one of the oldest questions in Artificial
Intelligence. It started with Alan Turing:
– (see the recent movie “The imitation game”)
• Turing (1950) proposed a simple test to determine
whether computers can think, and show signs of
having intelligence:
– do this by simply “talking” with a person or a computer
via email and see whether you can tell the difference
between talking with the person and with the machine.
How good is Turing’s test?
• Searle (1980), a Philosopher of Mind, criticized
Turing’s test in his “Chinese room” argument in which:
– having a set of rules that allow one to produce responses in
Chinese to questions in Chinese, in itself, does not imply
understanding what is being said.
– there is also no reason to believe, or to claim, that a Googletype translator understands what is being said.
• Searle went even further when he said that computers
and robots will never be intelligent, as we humans are,
because contemporary computers are made of
transistors (physical), not neurons (biological) stuff.
• I will return to Searle’s claim that there can be no
intelligence in a robot made from physical stuff
after examining Searle’s observation that it is
impossible to be sure of what is actually in
someone’s mind simply by observing his behavior.
– Take four examples.
Color perception
We can verify experimentally whether an observer (human or
robot) can tell different colors apart. So, we can know that
both observers have different “percepts” when presented with
red and green, but we will probably never know what either
observer actually sees when she/it looks at red or green.
Detecting a Lie
• When I tell you which of two works of art I like more, you
cannot easily, if at all, determine whether I am telling the truth.
Weissman
Gradus
Observing Thinking During Problem
Solving
• A student is presented with a difficult problem,
say, construct a triangle given its perimeter, the
angle at one vertex and the length of the
altitude drawn from this vertex.
– This student does nothing for quite a while. Was
she thinking about this problem or about the failing
grade she is surely going to earn?
• Note that neither “Deep Blue” nor “Watson”,
two recent successes of AI, can even begin
trying to solve this problem.
Now, let’s consider an example where
it is not only possible, but actually easy
to uncover the state of somebody’s
mind.
Any observer looking at an animal, like this cat, says
that he sees a symmetrical animal.
We know that he perceives symmetry because we can
demonstrate experimentally that he can tell when two
halves of an object are the same or different. So, we
can know that symmetry is in his mind when he looks
at a symmetrical object.
Symmetry connects physical,
biological and mental events
• The cat is actually symmetrical, so symmetry exists
both in the biological world (the animal’s body) and
in the mental world (the observer’s percept).
• If we want to extend this argument to robots, which
are made of physical stuff, we must show that
symmetry exists in the physical world, as well:
– Remember Searle’s argument that robots will never be
like us because their CPU (the robot’s brain) is made of
transistors, not neurons, like our brain.
Symmetry does exist in the physical world.
• Atoms and compounds are symmetrical:
– Take carbon, C, the basis of organic chemistry,
Astronomy
• Stars and planets are symmetrical, too.
Crystals are characterized by their
symmetries
Snowflakes have multiple symmetries –
they are ice crystals
Forces – Earth’s gravity is symmetrical
Electric fields are symmetrical
Plants are
symmetrical,
too.
Thepotter_2006
And so are
animals
Butterfly Hunter
Actually, almost all
animals are
symmetrical.
I only know of one
that is not, the
fiddler crab.
Your brain is symmetrical – you have
two similar hemispheres
Your DNA is symmetrical, too.
Symmetry is ubiquitous.
We find it everywhere we look!
For the record:
• the concept of symmetry is much more general
than I illustrated up to now, but
• what I showed you should be sufficient to
support the rest of my story.
Symmetry provides building blocks:
• for physical, biological and mental phenomena.
• So, symmetry does not belong exclusively to any of
these worlds.
• Symmetry can be considered the “neutral stuff”, in
the terminology used by Baruch Spinoza, Gustav
Theodor Fechner, William James, and Bertrand
Russell.
• Whether we observe physical, biological or mental
(cognitive) symmetry simply depends on the
observational tools we choose to use:
– Perceiving a cat, vs. describing its body, vs. describing
the carbon compounds in the individual cells.
Sadly, Searle ignored the concept of
symmetry entirely
• and so did everyone else in the fields called
Philosophy of Mind, Artificial Intelligence, as well as
in popular science.
• Transistors are very different physically than neurons,
but symmetry resides in both.
• Furthermore, symmetry makes it possible to compare
a computer’s CPU and a human’s mind in a
meaningful way.
• In fact, symmetry is the essential feature of both. All
of the remaining features are probably unimportant or
superficial, at best.
But there is even more…
• I will now take two important additional steps
in making my comparison of physical stuff
(robots) and human beings.
Physics is based on 3 Fundamental
Principles.
• Symmetry – just discussed.
• A Least-action Principle.
• Conservation Laws.
• All three can, and should, be applied to the
analysis of cognitive phenomena because this
gives us a more complete understanding of
what we mean by intelligence.
Examples of Conservation Laws in
Physics
• Conservation of:
– Energy
– Momentum
– Angular momentum
–…
– There are many conservations in physics.
– I will illustrate only two.
Conservation of momentum
• https://www.youtube.com/watch?v=4IYDb6K5UF8
• Collision is a transformation.
– Things are different after and before the transformation:
– Speeds change and directions of motion change, too.
• But some things (here momentum) are “conserved”.
Conservation of angular momentum
• Pirouette
• A pirouette is a transformation.
– Things change during the pirouette
– Angular velocity
– Distances of the body parts from the axis of rotation
• But angular momentum is conserved.
Can we talk about conservations in 3D
vision?
3D percept from a single 2D image
The world is 3D, the retinal image is 2D, and the
percept is 3D. The 3D shapes of objects are conserved.
3D vision as a conservation
• An observer looks at a 3D object:
– There is a transformation of the physical object into the
object’s representation in the observer’s mind.
• First, the 3D shape is transformed into 2D retinal
image by the rules of optics.
• Second, the observer’s visual system infers the 3D
shape from the 2D retinal image.
– The observer knows that’s there…
• If the perceived (inferred) 3D shape is identical to
the geometrical shape of an object, then we can talk
about conservation of shape.
What is the nature of this inference?
• Can a robot infer something?
• If it can, is this inference human-like?
We need the third Fundamental Principle
of Physics, the least action principle to
answer this question:
• In perception and cognition, it is called the
simplicity principle.
• In Philosophy of Science, it is called Occam’s
razor, and
• In Information Theory it is called a Minimum
Description Length principle.
Ames's chair
• Demo: http://shapebook.psych.purdue.edu/1.3/
• The 3D geometrical configuration we call a
chair is the simplest interpretation (here by
simplest we mean symmetrical).
• It turns out that this simplicity principle leads
to veridical percepts, which are conservations.
Shape veridicality
• Veridicality means that we see things the way they
are “out there.”
• Demos: http://shapebook.psych.purdue.edu/1.2/
• You see these shapes veridically and so does our
robot.
• In both cases, shape veridicality is produced by the
least action principle, called simplicity.
The Simplicity principle works the
same way in all other aspects of 3D
vision, including the perception of 3D
scenes.
The simplicity principle in 3D vision is
completely analogous to the least action
principle in Physics
• Two examples:
– Optics.
– Electricity
Fermat’s Principle
• Light “chooses” a trajectory that minimizes time of
travel.
Kirchhoff's Laws for circuits
• Current divides itself in such a way so that the total
amount of heat generated in resistors is minimal.
The least action principle is the link
• between symmetries in nature and conservations.
• It turns out that every conservation in Physics is a
consequence of applying the least action principle to
the symmetry of a natural phenomenon (Nöther’s,
1918, theorem).
• Examples:
• Time symmetry – conservation of energy.
• Space symmetry – conservation of momentum.
3D vision in a nutshell
• A simplicity (least action) principle is applied to the
image of…
• symmetrical objects, resulting in…
• veridical 3D vision (the conservation of 3D shape)
• Recall the 3 fundamental principles of Physics:
– A least-action principle is applied to…
– the symmetry of a phenomenon, resulting in
– a conservation law.
Can this approach be extended beyond 3D
vision?
• Almost certainly.
– Language, problem solving, data mining…
• There is always enough structure and regularity in
these cognitive functions to allow symmetries
(invariances) to be defined.
• Once symmetries exist, the next challenge is to
define a simplicity principle to allow something
meaningful to be inferred.
• This will lead to conservations that provide the
key to understanding how the mind is related to
the outside world and to other minds.
Summary
• Nöther (1918) showed that without a least-action
principle there would be no conservations in
Physics.
• Wigner (1960), a Nobel prize winner in Physics,
pointed out that without symmetries there would be
no Laws of Nature.
• I am suggesting that without all of these three
principles, namely, symmetry, least action and
conservations, there would be no human mind as
we know it, and no intelligence.
– We wouldn't be able to understand the environment and
each other.
What does this mean for the intelligence of robots?
• If a robot does not use these 3 principles, it cannot
be smart.
• If the robot uses these principles, we will understand
the robot’s mind.
• Our natural sciences do not offer any magical 4th
principle that would allow a robot to be smarter than
we are.
– So, a “singularity”, defined as super-intelligent robots,
that is, robots too smart for us to comprehend them, is
not likely to happen.
– If it does happen, it is not likely to be an elaboration of
currently existing AI systems.
Conclusion
• The important issue is not whether superintelligent robots are possible, that is, the issue
addressed in this lecture series.
• The really important issue is that the 3
fundamental principles now used to establish the
merit of the hard sciences, namely, symmetry,
least-action and conservations, provide a
formalism that can be used both to explain the
human mind and to develop an artificial mind as
good, or perhaps even better than ours.