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Uncertainty, Procrastination and Artificial Intelligence

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at Queens’ College SCR Talk on Mar 1, 2021 [reveal]
Neil D. Lawrence, Computer Lab, University of Cambridge

Abstract

In this talk I will introduce the importance of uncertainty in decision making and describe how it provides a mathematical justification for procrastination through the game of Kappenball.

Laplace’s Demon

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Figure:

Philosophical Essay on Probabilities Laplace (1814) pg 3

\[ \text{data} + \text{model} \stackrel{\text{compute}}{\rightarrow} \text{prediction}\]

If we do discover a theory of everything … it would be the ultimate triumph of human reason-for then we would truly know the mind of God

Stephen Hawking in A Brief History of Time 1988

Emergent Behaviour

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Life Rules

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loneliness

Figure: ‘Death’ through loneliness in Conway’s game of life. If a cell is surrounded by less than three cells, it ‘dies’ through loneliness.

overcrowding

Figure: ‘Death’ through overpopulation in Conway’s game of life. If a cell is surrounded by more than three cells, it ‘dies’ through loneliness.

birth

Figure: Birth in Conway’s life. Any position surounded by precisely three live cells will give birth to a new cell at the next turn.

Conway’s game of life has three simple rules.

  • Survival Every cell surrounded by two or three other cells survives for the next turn.
  • Death Each cell surrounded by four or more cells dies from overpopulation. Likewise, every cell next to one or no cells at all dies from isolation.
  • Birth Each square adjacent to exactly three cells gives birth to a new cell.

Loafers and Gliders

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Glider (1969)

Figure: Left A Glider pattern discovered 1969 by Richard K. Guy. Right. John Horton Conway, creator of Life (1937-2020).

Loafer (2013)

Figure: Left A Loafer pattern discovered by Josh Ball in 2013. Right. John Horton Conway, creator of Life (1937-2020).

Laplace’s Gremlin

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Figure: To Laplace, determinism is a strawman. Ignorance of mechanism and data leads to uncertainty which should be dealt with through probability.

Philosophical Essay on Probabilities Laplace (1814) pg 5

Figure: Gremlins are seen as the cause of a number of challenges in this World War II poster.

Boulton and Watt’s Lap Engine

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Lap Engine (1788)
total energy
=
available energy
+
temperature
\(\times\)
entropy

Figure: James Watt’s Lap Engine which incorporates many of his innovations to the steam engine, making it more efficient.

Theory of Ignorance

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Figure: Bertrand Russell (1872-1970), Albert Einstein (1879-1955), Norbert Wiener, (1894-1964)

Figure: Brownian motion of a large particle in a group of smaller particles. The movement is known as a Wiener process after Norbert Wiener.

James Clerk Maxwell
Ludwig Boltzmann
Josiah Willard Gibbs

Figure: James Clerk Maxwell (1831-1879), Ludwig Boltzmann (1844-1906) Josiah Willard Gibbs (1839-1903)

Entropy Billiards

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Entropy:

Figure: Bernoulli’s simple kinetic models of gases assume that the molecules of air operate like billiard balls.

Maxwell’s Demon

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Figure: Maxwell’s demon opens and closes a door which allows fast particles to pass from left to right and slow particles to pass from right to left. This makes the left hand side colder than the right.

Entropy:

Figure: Maxwell’s Demon. The demon decides balls are either cold (blue) or hot (red) according to their velocity. Balls are allowed to pass the green membrane from right to left only if they are cold, and from left to right, only if they are hot.

Procrastination

Score: Energy:

Figure: Kappen Ball

Information and Embodiment

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Claude Shannon

Figure: Claude Shannon (1916-2001)

bits/min billions 2,000
billion
calculations/s
~100 a billion
embodiment 20 minutes 5 billion years

Figure: Embodiment factors are the ratio between our ability to compute and our ability to communicate. Relative to the machine we are also locked in. In the table we represent embodiment as the length of time it would take to communicate one second’s worth of computation. For computers it is a matter of minutes, but for a human, it is a matter of thousands of millions of years.

Bandwidth Constrained Conversations

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Figure: Conversation relies on internal models of other individuals.

Figure: Misunderstanding of context and who we are talking to leads to arguments.

Embodiment factors imply that, in our communication between humans, what is not said is, perhaps, more important than what is said. To communicate with each other we need to have a model of who each of us are.

To aid this, in society, we are required to perform roles. Whether as a parent, a teacher, an employee or a boss. Each of these roles requires that we conform to certain standards of behaviour to facilitate communication between ourselves.

Control of self is vitally important to these communications.

The high availability of data available to humans undermines human-to-human communication channels by providing new routes to undermining our control of self.

The consequences between this mismatch of power and delivery are to be seen all around us. Because, just as driving an F1 car with bicycle wheels would be a fine art, so is the process of communication between humans.

If I have a thought and I wish to communicate it, I first of all need to have a model of what you think. I should think before I speak. When I speak, you may react. You have a model of who I am and what I was trying to say, and why I chose to say what I said. Now we begin this dance, where we are each trying to better understand each other and what we are saying. When it works, it is beautiful, but when misdeployed, just like a badly driven F1 car, there is a horrible crash, an argument.

Stories, between humans.

I have a great dislike for Russell; I cannot explain it completely, but I feel a detestation for the man. As far as any sympathy with me, or with anyone else, I believe, he is an iceberg. His mind impresses one as a keen, cold, narrow logical machine, that cuts the universe into neat little packets, that measure, as it were, just three inches each way. His type of mathematical analysis he applies as a sort of Procrustean bed to the facts, and those that contain more than his system provides for, he lops short, and those that contain less, he draws out.

Norbert Wiener in a letter to his family, 1913

Heider and Simmel (1944)

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Figure: Fritz Heider and Marianne Simmel’s video of shapes from Heider and Simmel (1944).

Fritz Heider and Marianne Simmel’s experiments with animated shapes from 1944 (Heider and Simmel, 1944). Our interpretation of these objects as showing motives and even emotion is a combination of our desire for narrative, a need for understanding of each other, and our ability to empathise. At one level, these are crudely drawn objects, but in another key way, the animator has communicated a story through simple facets such as their relative motions, their sizes and their actions. We apply our psychological representations to these faceless shapes in an effort to interpret their actions.

See also a recent review paper on Human Cooperation by Henrich and Muthukrishna (2021).

Computer Conversations

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Figure: Conversation relies on internal models of other individuals.

Figure: Misunderstanding of context and who we are talking to leads to arguments.

Similarly, we find it difficult to comprehend how computers are making decisions. Because they do so with more data than we can possibly imagine.

In many respects, this is not a problem, it’s a good thing. Computers and us are good at different things. But when we interact with a computer, when it acts in a different way to us, we need to remember why.

Just as the first step to getting along with other humans is understanding other humans, so it needs to be with getting along with our computers.

Embodiment factors explain why, at the same time, computers are so impressive in simulating our weather, but so poor at predicting our moods. Our complexity is greater than that of our weather, and each of us is tuned to read and respond to one another.

Their intelligence is different. It is based on very large quantities of data that we cannot absorb. Our computers don’t have a complex internal model of who we are. They don’t understand the human condition. They are not tuned to respond to us as we are to each other.

Embodiment factors encapsulate a profound thing about the nature of humans. Our locked in intelligence means that we are striving to communicate, so we put a lot of thought into what we’re communicating with. And if we’re communicating with something complex, we naturally anthropomorphize them.

We give our dogs, our cats and our cars human motivations. We do the same with our computers. We anthropomorphize them. We assume that they have the same objectives as us and the same constraints. They don’t.

This means, that when we worry about artificial intelligence, we worry about the wrong things. We fear computers that behave like more powerful versions of ourselves that will struggle to outcompete us.

In reality, the challenge is that our computers cannot be human enough. They cannot understand us with the depth we understand one another. They drop below our cognitive radar and operate outside our mental models.

The real danger is that computers don’t anthropomorphize. They’ll make decisions in isolation from us without our supervision, because they can’t communicate truly and deeply with us.

Figure: Humans and computers interacting should be a major focus of our research and engineering efforts.

Figure: Humans use culture, facts and ‘artefacts’ to communicate.

Richard Feynmann on Doubt

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One thing is I can live with is doubt, and uncertainty and not knowing. I think it’s much more interesting to live with not knowing than to have an answer that might be wrong.

Richard P. Feynmann in the The Pleasure of Finding Things Out 1981.

Thanks!

For more information on these subjects and more you might want to check the following resources.

References

Heider, F., Simmel, M., 1944. An experimental study of apparent behavior. The American Journal of Psychology 57, 243–259.
Henrich, J., Muthukrishna, M., 2021. The origins and psychology of human cooperation. Annual Review of Psychology 72, 207–240. https://doi.org/10.1146/annurev-psych-081920-042106
Laplace, P.S., 1814. Essai philosophique sur les probabilités, 2nd ed. Courcier, Paris.