Abstract

What is artificial intelligence and what are the implications of advances in artificial intelligence for religion? How does artificial intelligences differ from natural intelligences. We consider these ideas from the perspective of information theory. In the context of these differences we then consider parallels between the perspectives on religion and AI both in today’s popular culture, but also with a more optimistic perspective looking forward.

Introduction

What is Machine Learning? [edit]

What is machine learning? At its most basic level machine learning is a combination of

$$\text{data} + \text{model} \xrightarrow{\text{compute}} \text{prediction}$$

where data is our observations. They can be actively or passively acquired (meta-data). The model contains our assumptions, based on previous experience. That experience can be other data, it can come from transfer learning, or it can merely be our beliefs about the regularities of the universe. In humans our models include our inductive biases. The prediction is an action to be taken or a categorization or a quality score. The reason that machine learning has become a mainstay of artificial intelligence is the importance of predictions in artificial intelligence. The data and the model are combined through computation.

In practice we normally perform machine learning using two functions. To combine data with a model we typically make use of:

a prediction function a function which is used to make the predictions. It includes our beliefs about the regularities of the universe, our assumptions about how the world works, e.g. smoothness, spatial similarities, temporal similarities.

an objective function a function which defines the cost of misprediction. Typically it includes knowledge about the world’s generating processes (probabilistic objectives) or the costs we pay for mispredictions (empiricial risk minimization).

The combination of data and model through the prediction function and the objectie function leads to a learning algorithm. The class of prediction functions and objective functions we can make use of is restricted by the algorithms they lead to. If the prediction function or the objective function are too complex, then it can be difficult to find an appropriate learning algorithm. Much of the acdemic field of machine learning is the quest for new learning algorithms that allow us to bring different types of models and data together.

A useful reference for state of the art in machine learning is the UK Royal Society Report, Machine Learning: Power and Promise of Computers that Learn by Example.

You can also check my post blog post on What is Machine Learning?..

Artificial Intelligence and Data Science [edit]

Machine learning technologies have been the driver of two related, but distinct disciplines. The first is data science. Data science is an emerging field that arises from the fact that we now collect so much data by happenstance, rather than by experimental design. Classical statistics is the science of drawing conclusions from data, and to do so statistical experiments are carefully designed. In the modern era we collect so much data that there’s a desire to draw inferences directly from the data.

As well as machine learning, the field of data science draws from statistics, cloud computing, data storage (e.g. streaming data), visualization and data mining.

In contrast, artificial intelligence technologies typically focus on emulating some form of human behaviour, such as understanding an image, or some speech, or translating text from one form to another. The recent advances in artifcial intelligence have come from machine learning providing the automation. But in contrast to data science, in artifcial intelligence the data is normally collected with the specific task in mind. In this sense it has strong relations to classical statistics.

Classically artificial intelligence worried more about logic and planning and focussed less on data driven decision making. Modern machine learning owes more to the field of Cybernetics (Wiener 1948) than artificial intelligence. Related fields include robotics, speech recognition, language understanding and computer vision.

There are strong overlaps between the fields, the wide availability of data by happenstance makes it easier to collect data for designing AI systems. These relations are coming through wide availability of sensing technologies that are interconnected by celluar networks, WiFi and the internet. This phenomenon is sometimes known as the Internet of Things, but this feels like a dangerous misnomer. We must never forget that we are interconnecting people, not things.

What does Machine Learning do? [edit]

Any process of automation allows us to scale what we do by codifying a process in some way that makes it efficient and repeatable. Machine learning automates by emulating human (or other actions) found in data. Machine learning codifies in the form of a mathematical function that is learnt by a computer. If we can create these mathematical functions in ways in which they can interconnect, then we can also build systems.

Machine learning works through codifing a prediction of interest into a mathematical function. For example, we can try and predict the probability that a customer wants to by a jersey given knowledge of their age, and the latitude where they live. The technique known as logistic regression estimates the odds that someone will by a jumper as a linear weighted sum of the features of interest.

$$ \text{odds} = \frac{p(\text{bought})}{p(\text{not bought})} $$

log odds = β₀ + β₁age + β₂latitude.
Here β₀, β₁ and β₂ are the parameters of the model. If β₁ and β₂ are both positive, then the log-odds that someone will buy a jumper increase with increasing latitude and age, so the further north you are and the older you are the more likely you are to buy a jumper. The parameter β₀ is an offset parameter, and gives the log-odds of buying a jumper at zero age and on the equator. It is likely to be negative¹ indicating that the purchase is odds-against. This is actually a classical statistical model, and models like logistic regression are widely used to estimate probabilities from ad-click prediction to risk of disease.

This is called a generalized linear model, we can also think of it as estimating the probability of a purchase as a nonlinear function of the features (age, lattitude) and the parameters (the β values). The function is known as the sigmoid or logistic function, thus the name logistic regression.

$$ p(\text{bought}) = \sigmoid{\beta_0 + \beta_1 \text{age} + \beta_2 \text{latitude}}.$$
In the case where we have features to help us predict, we sometimes denote such features as a vector, $\inputVector$, and we then use an inner product between the features and the parameters, $\boldsymbol{\beta}^\top \inputVector = \beta_1 \inputScalar_1 + \beta_2 \inputScalar_2 + \beta_3 \inputScalar_3 ...$, to represent the argument of the sigmoid.

$$ p(\text{bought}) = \sigmoid{\boldsymbol{\beta}^\top \inputVector}.$$
More generally, we aim to predict some aspect of our data, $\dataScalar$, by relating it through a mathematical function, $\mappingFunction(\cdot)$, to the parameters, β and the data, $\inputVector$.

$$ \dataScalar = \mappingFunction\left(\inputVector, \boldsymbol{\beta}\right).$$
We call $\mappingFunction(\cdot)$ the prediction function.

To obtain the fit to data, we use a separate function called the objective function that gives us a mathematical representation of the difference between our predictions and the real data.

$$\errorFunction(\boldsymbol{\beta}, \dataMatrix, \inputMatrix)$$
A commonly used examples (for example in a regression problem) is least squares,
$$\errorFunction(\boldsymbol{\beta}, \dataMatrix, \inputMatrix) = \sum_{i=1}^\numData \left(\dataScalar_i - \mappingFunction(\inputVector_i, \boldsymbol{\beta})\right)^2.$$

If a linear prediction function is combined with the least squares objective function then that gives us a classical linear regression, another classical statistical model. Statistics often focusses on linear models because it makes interpretation of the model easier. Interpretation is key in statistics because the aim is normally to validate questions by analysis of data. Machine learning has typically focussed more on the prediction function itself and worried less about the interpretation of parameters, which are normally denoted by w instead of β. As a result non-linear functions are explored more often as they tend to improve quality of predictions but at the expense of interpretability.

Deep Learning [edit]

Classical statistical models and simple machine learning models have a great deal in common. The main difference between the fields is philosophical. Machine learning practitioners are typically more concerned with the quality of prediciton (e.g. measured by ROC curve) while statisticians tend to focus more on the interpretability of the model and the validity of any decisions drawn from that interpretation. For example, a statistical model may be used to validate whether a large scale intervention (such as the mass provision of mosquito nets) has had a long term effect on disease (such as malaria). In this case one of the covariates is likely to be the provision level of nets in a particular region. The response variable would be the rate of malaria disease in the region. The parmaeter, β₁ associated with that covariate will demonstrate a positive or negative effect which would be validated in answering the question. The focus in statistics would be less on the accuracy of the response variable and more on the validity of the interpretation of the effect variable, β₁.

A machine learning practitioner on the other hand would typically denote the parameter w₁, instead of β₁ and would only be interested in the output of the prediction function, $\mappingFunction(\cdot)$ rather than the parameter itself. The general formalism of the prediction function allows for non-linear models. In machine learning, the emphasis on prediction over interpretability means that non-linear models are often used. The parameters, w, are a means to an end (good prediction) rather than an end in themselves (interpretable).

DeepFace [edit]

Figure: The DeepFace architecture (Taigman et al. 2014), visualized through colors to represent the functional mappings at each layer. There are 120 million parameters in the model.

The DeepFace architecture (Taigman et al. 2014) consists of layers that deal with translation and rotational invariances. These layers are followed by three locally-connected layers and two fully-connected layers. Color illustrates feature maps produced at each layer. The neural network includes more than 120 million parameters, where more than 95% come from the local and fully connected layers.

Deep Learning as Pinball [edit]

Figure: Deep learning models are composition of simple functions. We can think of a pinball machine as an analogy. Each layer of pins corresponds to one of the layers of functions in the model. Input data is represented by the location of the ball from left to right when it is dropped in from the top. Output class comes from the position of the ball as it leaves the pins at the bottom.

Sometimes deep learning models are described as being like the brain, or too complex to understand, but one analogy I find useful to help the gist of these models is to think of them as being similar to early pin ball machines.

In a deep neural network, we input a number (or numbers), whereas in pinball, we input a ball.

Think of the location of the ball on the left-right axis as a single number. Our simple pinball machine can only take one number at a time. As the ball falls through the machine, each layer of pins can be thought of as a different layer of ‘neurons’. Each layer acts to move the ball from left to right.

In a pinball machine, when the ball gets to the bottom it might fall into a hole defining a score, in a neural network, that is equivalent to the decision: a classification of the input object.

An image has more than one number associated with it, so it is like playing pinball in a hyper-space.

import pods
from ipywidgets import IntSlider

pods.notebook.display_plots('pinball{sample:0>3}.svg', 
                            '../slides/diagrams',
                            sample=IntSlider(1, 1, 2, 1))

Learning involves moving all the pins to be in the correct position, so that the ball ends up in the right place when it’s fallen through the machine. But moving all these pins in hyperspace can be difficult.

In a hyper-space you have to put a lot of data through the machine for to explore the positions of all the pins. Even when you feed many millions of data points through the machine, there are likely to be regions in the hyper-space where no ball has passed. When future test data passes through the machine in a new route unusual things can happen.

Adversarial examples exploit this high dimensional space. If you have access to the pinball machine, you can use gradient methods to find a position for the ball in the hyper space where the image looks like one thing, but will be classified as another.

Probabilistic methods explore more of the space by considering a range of possible paths for the ball through the machine. This helps to make them more data efficient and gives some robustness to adversarial examples.

Embodiment Factors [edit]

compute	≈ 100 gigaflops	≈ 16 petaflops
communicate	1 gigbit/s	100 bit/s
(compute/communicate)	104	1014

There is a fundamental limit placed on our intelligence based on our ability to communicate. Claude Shannon founded the field of information theory. The clever part of this theory is it allows us to separate our measurement of information from what the information pertains to².

Shannon measured information in bits. One bit of information is the amount of information I pass to you when I give you the result of a coin toss. Shannon was also interested in the amount of information in the English language. He estimated that on average a word in the English language contains 12 bits of information.

Given typical speaking rates, that gives us an estimate of our ability to communicate of around 100 bits per second (Reed and Durlach 1998). Computers on the other hand can communicate much more rapidly. Current wired network speeds are around a billion bits per second, ten million times faster.

When it comes to compute though, our best estimates indicate our computers are slower. A typical modern computer can process make around 100 billion floating point operations per second, each floating point operation involves a 64 bit number. So the computer is processing around 6,400 billion bits per second.

It’s difficult to get similar estimates for humans, but by some estimates the amount of compute we would require to simulate a human brain is equivalent to that in the UK’s fastest computer (Ananthanarayanan et al. 2009), the MET office machine in Exeter, which in 2018 ranks as the 11th fastest computer in the world. That machine simulates the world’s weather each morning, and then simulates the world’s climate in the afternoon. It is a 16 petaflop machine, processing around 1,000 trillion bits per second.

Figure: The Lotus 49, view from the rear. The Lotus 49 was one of the last Formula One cars before the introduction of aerodynamic aids.

So when it comes to our ability to compute we are extraordinary, not compute in our conscious mind, but the underlying neuron firings that underpin both our consciousness, our subconsciousness as well as our motor control etc.

If we think of ourselves as vehicles, then we are massively overpowered. Our ability to generate derived information from raw fuel is extraordinary. Intellectually we have formula one engines.

But in terms of our ability to deploy that computation in actual use, to share the results of what we have inferred, we are very limited. So when you imagine the F1 car that represents a psyche, think of an F1 car with bicycle wheels.

Figure: Marcel Renault races a Renault 40 cv during the Paris-Madrid race, an early Grand Prix, in 1903. Marcel died later in the race after missing a warning flag for a sharp corner at Couhé Vérac, likely due to dust reducing visibility.

Just think of the control a driver would have to have to deploy such power through such a narrow channel of traction. That is the beauty and the skill of the human mind.

In contrast, our computers are more like go-karts. Underpowered, but with well-matched tires. They can communicate far more fluidly. They are more efficient, but somehow less extraordinary, less beautiful.

Figure: Caleb McDuff driving for WIX Silence Racing.

For humans, that means much of our computation should be dedicated to considering what we should compute. To do that efficiently we need to model the world around us. The most complex thing in the world around us is other humans. So it is no surprise that we model them. We second guess what their intentions are, and our communication is only necessary when they are departing from how we model them. Naturally, for this to work well, we need to understand those we work closely with. So it is no surprise that social communication, social bonding, forms so much of a part of our use of our limited bandwidth.

There is a second effect here, our need to anthropomorphise objects around us. Our tendency to model our fellow humans extends to when we interact with other entities in our environment. To our pets as well as inanimate objects around us, such as computers or even our cars. This tendency to over interpret could be a consequence of our limited ability to communicate.

For more details see this paper “Living Together: Mind and Machine Intelligence”, and this TEDx talk.

Human Communication [edit]

For human conversation to work, we require an internal model of who we are speaking to. We model each other, and combine our sense of who they are, who they think we are, and what has been said. This is our approach to dealing with the limited bandwidth connection we have. Empathy and understanding of intent. Mental dispositional concepts are used to augment our limited communication bandwidth.

Fritz Heider referred to the important point of a conversation as being that they are happenings that are “psychologically represented in each of the participants” (his emphasis) (Heider 1958)

Bandwidth Constrained Conversations

import pods
from ipywidgets import IntSlider

pods.notebook.display_plots('anne-bob-conversation{sample:0>3}.svg', 
                            '../slides/diagrams',  sample=IntSlider(0, 0, 7, 1))

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.

A Six Word Novel [edit]

For sale: baby shoes, never worn

Figure: Consider the six word novel, apocraphally credited to Ernest Hemingway, “For sale: baby shoes, never worn”. To understand what that means to a human, you need a great deal of additional context. Context that is not directly accessible to a machine that has not got both the evolved and contextual understanding of our own condition to realize both the implication of the advert and what that implication means emotionally to the previous owner.

But this is a very different kind of intelligence than ours. A computer cannot understand the depth of the Ernest Hemingway’s apocryphal six word novel: “For Sale, Baby Shoes, Never worn”, because it isn’t equipped with that ability to model the complexity of humanity that underlies that statement.

Heider and Simmel (1944) [edit]

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.

Faith and AI [edit]

There would seem to be at least three ways in which artificial intelligence and religion interconnect.

1. Artificial Intelligence as Cartoon Religion
2. Artificial Intelligence and Introspection
3. Independence of thought and Control: A Systemic Catch 22

Singularianism: AI as Cartoon Religion

The first parallels one can find between artificial intelligence and religion come in somewhat of a cartoon doomsday scenario form. The publically hyped fears of superintelligence and singularity can equally be placed within the framework of the simpler questions that religion can try to answer. The parallels are

1. Superintelligence as god
2. Demi-god status achievable through transhumanism
3. Immortality through uploading the connectome
4. The day of judgement as the “singularity”

Ultraintelligence (Good 1966) is similar to the notion of an interventionist god, with omniscience in the past, present and the future. This notion was described by Pierre Simon Laplace.

Pierre-Simon Laplace [edit]

Figure: Pierre-Simon Laplace 1749-1827.

Famously, Laplace considered the idea of a deterministic Universe, one in which the model is known, or as the below translation refers to it, “an intelligence which could comprehend all the forces by which nature is animated”. He speculates on an “intelligence” that can submit this vast data to analysis and propsoses that such an entity would be able to predict the future.

Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data to analysis—it would embrace in the same formulate the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present in its eyes.

This notion is known as Laplace’s demon or Laplace’s superman.

Figure: Laplace’s determinsim in English translation.

Unfortunately, most analyses of his ideas stop at that point, whereas his real point is that such a notion is unreachable. Not so much superman as strawman. Just three pages later in the “Philosophical Essay on Probabilities” (Laplace 1814), Laplace goes on to observe:

The curve described by a simple molecule of air or vapor is regulated in a manner just as certain as the planetary orbits; the only difference between them is that which comes from our ignorance.

Probability is relative, in part to this ignorance, in part to our knowledge.

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

In other words, we can never make use of the idealistic deterministc Universe due to our ignorance about the world, Laplace’s suggestion, and focus in this essay is that we turn to probability to deal with this uncertainty. This is also our inspiration for using probability in machine learning.

The “forces by which nature is animated” is our model, the “situation of beings that compose it” is our data and the “intelligence sufficiently vast enough to submit these data to analysis” is our compute. The fly in the ointment is our ignorance about these aspects. And probability is the tool we use to incorporate this ignorance leading to uncertainty or doubt in our predictions.

The notion of Superintelligence in, e.g. Nick Bostrom’s book (Bostrom 2014), is that of an infallible omniscience. A major narrative of the book is that the challenge of Superintelligence according is to constrain the power of such an entity. In practice, this narrative is strongly related to Laplace’s “straw superman”. No such intelligence could exist due to our ignorance, in practice any real intelligence must express doubt.

Elon Musk has proposed that the only way to defeat the inevitable omniscience would be to augment ourselves with machine like capabilities. Ray Kurzweil has pushed the notion of developing ourselves by augmenting our existing cortex with direct connection to the internet.

Within Silicon Valley there seems to be a particular obsession with ‘uploading’. The idea is that once the brain is connected, we can achieve immortality by continuing to exist digitally in an artificial environment of our own creation while our physical body is left behind us. They want to remove the individual bandwidth limitation we place on ourselves.

But embodiment factors (Lawrence 2017) imply that we are defined by our limitations. Removing the bandwidth limitation removes what it means to be human.

{In Singularianism doomsday is the ‘technological singularity’, the moment at which computers rapidly outstrip our capabilities and take over our world. The high priests are the scientists, and the aim is to bring about the latter while restraining the former.

Singularianism is to religion what scientology is to science. Scientology is religion expressing itself as science and Singularism is science expressing itself as religion.

You can read this blog post on Singularianism..

See also this paper by Luciano Floridi

You can see a review of this book in this blog post on Superintelligence (Bostrom 2014).

Artificial Intelligence and Introspection [edit]

Ignoring the cartoon view of religion we’ve outlined above and focussing more on how religion can bring strength to people in their day-to-day living, religious environments bring a place to self reflect and meditate on our existence, and the wider cosmos. How are we here? What is our role? What makes us different?

Creating machine intelligences characterizes the manner in which we are different, helps us understand what is special about us rather than the machine.

I have in the past argued strongly against the term artificial intelligence but there is a sense in which it is a good term. If we think of artificial plants, then we have the right sense in which we are creating an artificial intelligence. An artificial plant is fundamentally different from a real plant, but can appear similar, or from a distance identical. However, a creator of an artificial plant gains a greater appreciation for the complexity of a natural plant.

In a similar way, we might expect that attempts to emulate human intelligence would lead to a deeper appreciation of that intelligence. This type of reflection on who we are has a lot in common with many of the (to me) most endearing characteristics of religion.

The Digital Catch 22

Figure: A digital Catch 22: for systems to watch over us they have to watch us.

A final parallel between the world of AI and that of religion is the conundrums they raise for us. In particular the tradeoffs between a paternalistic society and individual freedoms. Two models for artificial intelligence that may be realistic are the “Big Brother” and the “Big Mother” models.

Big Brother refers to the surveillance society and the control of populations that can be achieved with a greater understanding of the individual self. A perceptual understanding of the individual that conceivably be of better than the individual’s self perception. This scenario was most famously explored by George Orwell, but also came into being in Communist East Germany where it is estimated that one in 66 citizens acted as an informants, (Stasi: The Untold Story of the East German Secret Police 1999).

Figure: The Big Brother to Big Mother dilemma. As computers help us they constrain us, leading to a form of dys-utopia.

But for a system to watch over us it first has to watch us. So the same understanding of individual is also necessary for the “Big Mother” scenario, where intelligent agents provide for us in the manner in which our parents did for us when we were young. Both scenarios are disempowering in terms of individual liberties. In a metaphorical sense, this could be seen as a return to Eden, a surrendering of individual liberties for a perceived paradise. But those individual liberties are also what we value. There is a tension between a desire to create the perfect environment, where no evil exists and our individual liberty. Our society chooses a balance between the pros and cons that attempts to sustain a diversity of perspectives and beliefs. Even if it were possible to use AI to organzie society in such a way that particular malevolent behaviours were prevented, doing so may come at the cost of the individual freedom we enjoy. These are difficult trade offs, and the exist both when explaining the nature of religious belief and when considering the nature of either the dystopian Big Brother or the “dys-utopian” Big Mother view of AI.

Figure: The Garden of Eden by Thomas Cole

Conclusion [edit]

We’ve provided an overview of the advances in artificial intelligence from the perspective of machine learning, and tried to give a sense of how machine learning models operate to learn about us.

We’ve highlighted a quintissential difference between humans and computers: the embodiment factor, the relatively restricted ability of human to communicate themselves when compared to computers. We explored how this has effected our evolved relationship with data and the relationship between the human and narrative.

Finally, we explored three parallels between faith and AI, in particular the cartoon nature of religion based on technological promises of the singularity and AI. A more sophisticated relationship occurs when we see the way in which, as artificial intelligences invade our notion of personhood we will need to intrspect about who we are and what we want to be, a characteristic shared with many religions. The final parallel was in the emergent questions of AI, “Should we build an artificial intelligence to eliminate war?” has a strong parallel with the question “Why does God allow war?”. War is a consequence of human choices. Building such a system would likely severely restrict our freedoms to make choices, and there is a tension between how much we wish those freedoms to be impinged versus the potential lives that could be saved.

References