Artificial Intelligence and Machine Learning · Lecture 01 of 16

History of artificial intelligence · Part 1

Foundations and the birth of AI

The first part connects the ideas that made AI possible: probability, computation, artificial neurons and early learning systems.

01Probability and learning from evidence
02Computation, Turing and early neurons
03The birth of AI and early learning systems
Lecture 01 · Concept map

The ideas behind the historical milestones

Follow the story in order, or jump to a concept.

Probability & prediction

Training and evaluationBayes: formula → exampleRegression and least squaresLogistic / probit probabilitiesMarkov and hidden states

Computation & reasoning

What is computation?Computability and efficiencySearch and evaluationBehavior and intelligenceProofs and means–ends analysis

Neurons & learning

Threshold units and logicFeedback loopsHebbian learningPerceptron: rule and limitsLisp and learning from play

Each concept slide links to its explanation in the handout.

Framing the course
Artificial Intelligence

Engineering systems that reason, perceive, plan or learn.

  • AI studies tasks associated with intelligent behavior
  • Evaluate capabilities with explicit tasks and measures
  • Turing shifted the focus: from definition → testable behavior
Machine Learning

Learning from data or experience — one major approach within AI.

  • Learns patterns from examples
  • Requires data or experience and an objective
  • Training updates a model; use need not involve further learning

Also in this course: pattern recognition · computer vision · reinforcement learning · NLP

Concepts · The birth of AI

What actually changes when a machine learns?

1 · Define the task

Example: recognize spam.
Choose what counts as a good prediction.

2 · Train

Use labeled examples to adjust the model’s parameters.

3 · Evaluate

Check predictions on unseen examples to test generalization.

Training: data → parameter updates
Prediction: input + trained model → output

Using a trained model usually leaves its parameters fixed. Further learning needs an update procedure.

The road ahead

Ten eras in the history of AI — at a glance

Chapter I

ERA I: Foundations · Statistics

1763 – 1936

Era I — Foundations Statistics 1763→1936

Before computers, there was probability

1763

Bayes’ Theorem → is about updating uncertainty

Update a prior probability using the likelihood of observed evidence.

1805–86

Linear Regression → is about describing relationships between variables

Least squares: Legendre (1805), Gauss (1809). Galton studied regression toward the mean (1886).

1838–1944

Logistic Curve → Logit

Verhulst modeled continuous population growth; later logit models describe binary probabilities.

1906

Markov Models → are about simplifying sequences

The memorylessness property: the next state depends only on the current one. For sequences — time series, text.

1930s

Logistic and Probit Models → are about predicting categories

A binary-response model using the normal cumulative distribution; an alternative to logit.

Era I — Statistics 1763 · Bayes' Theorem
A graphical representation of Bayes' theorem
Graphical representation of Bayes’ theoremWikimedia Commons · timeline source

Bayes' Theorem

Bayes’ theorem relates a posterior probability to a prior and the likelihood of evidence. Bayes’ essay was published posthumously in 1763.

  • A foundational concept of Bayesian thinking
  • A core tool for developing statistical & machine-learning models
  • The bedrock that the whole era builds upon
Concepts · Statistics

Bayes: reverse the direction of the question

H = hypothesis (“spam”) · E = evidence (“contains ‘prize’”)

P(H | E) = P(H) · P(E | H)P(E)Read P(H | E) as “the probability of H, given E”; assume P(E) > 0.

Prior · P(H)

How plausible is H before seeing E?

Likelihood · P(E | H)

How likely is this evidence if H is true?

Posterior · P(H | E)

How plausible is H after seeing E?

P(E) accounts for the evidence across all hypotheses; it makes the posterior probabilities sum to 1.

Concepts · Statistics

Bayes in numbers: is ‘prize’ enough?

Toy inbox: 1,000 emails. Assume 10% are spam.

Email typeTotalContain ‘prize’Matching emails
Spam10080%80
Not spam90010%90
P(spam | ‘prize’) = 80 / (80 + 90) ≈ 47%P(‘prize’) = 0.8 × 0.1 + 0.1 × 0.9 = 0.17

The evidence raises the probability from 10% to 47% — even though 80% of spam contains ‘prize’.

Concepts · Statistics

What the Bayesian update is telling us

The direction matters

P(‘prize’ | spam) = 80%
P(spam | ‘prize’) ≈ 47%
These answer different questions.

The starting rate matters

There are many more legitimate emails. Even a small matching fraction contributes many examples.

Posterior ∝ likelihood × priorFor the same evidence, compare candidate classes using both ingredients.

Bayes’ theorem is a probability identity. The prior and likelihood must be specified or estimated; the formula does not supply them.

Era I — Statistics 1805–1886 · Linear Regression
Francis Galton's illustration of parent–child height correlation
Galton’s 1886 study of parent–child height correlationWikimedia Commons · timeline source

Linear Regression

Linear regression is one of the simplest models in statistical analysis: it assesses a linear law between two or more variables of interest.

  • Galton’s 1886 height study describes regression toward the mean
  • Least squares: Legendre published in 1805; Gauss gave a probabilistic treatment in 1809
  • Still one of the most widely used models today
Concepts · Statistics

Linear regression: a model you can read

ŷ = w₁x₁ + w₂x₂ + bx = predictors · ŷ = predicted response · w = learned weights · b = intercept

Representation

A weighted sum describes how an output varies with its inputs. The intercept sets a baseline.

Toy example

Predicted score = 40 + 5 × study hours
4 hours → 60 points
The slope is 5 points per extra hour.

A linear relationship is a modeling assumption. Choosing a linear model is not a claim that reality is always linear; it is a choice of representation. Sometimes that simplicity is worth more than perfect accuracy.

Concepts · Statistics

How do we choose the line? Minimize error.

Residual: rᵢ = yᵢ − ŷᵢ
Choose w and b to minimize Σᵢ (yᵢ − ŷᵢ)²yᵢ is an observed response; ŷᵢ is the model’s prediction for that example.
Candidate predictionsResidualsSum of squared errors
Line A−2, +24 + 4 = 8
Line B0, +50 + 25 = 25

Squaring prevents positive and negative errors from canceling, and penalizes large misses more. Line A fits these observations better.

A better fit on training data still needs evaluation on unseen data.

Era I — Statistics 1838–1944 · Logistic Regression
Verhulst’s historical population-growth curves
Verhulst’s historical population-growth curvesWikimedia Commons · timeline source

From the logistic curve to logistic regression

The same sigmoid shape connects two distinct models: continuous population growth and binary-response probabilities.

  • Verhulst’s 1838 work concerns population growth, not binary regression
  • Berkson popularized the logistic alternative to probit and the term logit in 1944
  • Still widely applied to classification problems
Concepts · Statistics

From a score to a probability to a decision

Linear score

z = w₁x₁ + w₂x₂ + b
Can be any real number.

Sigmoid

p = 1 / (1 + e−z)
Maps z into (0, 1).

Decision

Predict class 1 if p ≥ τ.
τ is a chosen threshold.

Score zProbability pDecision if τ = 0.5
−2≈ 0.12Class 0
00.50Class 1
+2≈ 0.88Class 1

Logistic regression models a binary outcome’s probability. Changing the threshold changes decisions, without changing those probabilities.

Era I — Statistics 1906 · Markov Chain
The mathematician Andrey Markov
Andrey Markov · mathematicianWikimedia Commons · timeline source

Markov Chain

Named after its inventor, Andrey Markov, the chain is used in sequential data analysis — time series, sentences, proteic sequences.

  • The Markov (memorylessness) property: the next state depends only on the current one
  • The future is independent of the past, given the present
  • Foundation of Hidden Markov Models, long used in NLP
Concepts · Statistics

A sequence model that keeps one current state

P(next state | entire history) = P(next state | current state)The Markov assumption: earlier history adds no information once the current state is known.
Today ↓ / Tomorrow →SunnyRainy
Sunny0.80.2
Rainy0.40.6

Illustrative transition probabilities. Each row sums to 1.

If today is rainy, this model predicts 60% rain tomorrow, regardless of yesterday. Whether that simplification is useful depends on the chosen state.

Concepts · Statistics

What if we cannot observe the state?

Hidden states

Weather today → weather tomorrow
States evolve through transitions.

Observations

Umbrella today · umbrella tomorrow
Each state can produce observable evidence.

Ordinary Markov chain

We observe the current state and predict the next state.

Hidden Markov model

We observe indirect signals and infer the hidden state sequence.

An umbrella suggests rain, but does not prove it. Combine state transitions + observation probabilities to reason under uncertainty.

Era I — Statistics 1930s · Probit Model
A comparison between logit and probit models
Logit and probit fitted curvesFrancis Smart · timeline source

Probit Model

Like other regression models, the probit model was rediscovered many times and became popular in the 1930s for classification tasks.

  • A sibling of logistic regression — a different link function on the same idea
  • Uses the standard normal CDF to map a linear score to a probability
  • Remains a useful alternative to logistic regression
Concepts · Statistics

Logit and probit: two probability mappings

Start from the same kind of linear score: z = w · x + b.

Logistic model

p = 1 / (1 + e−z)
The logistic sigmoid maps a score to a probability.

Probit model

p = Φ(z)
Φ(z) is the probability that a standard normal variable is ≤ z.

Both: real-valued score → probability in (0, 1)Both give p = 0.5 at z = 0; their scales and tail behavior differ.

The choice expresses different distributional assumptions. Neither mapping is universally best.

Chapter II

ERA II: Computation Theory & Turing

1936 – 1950

Era II — Computation Theory 1936–1950

Before the machine, a definition of computation

1936–37

Computability and Its Limits

Church and Turing formalize effective procedures and prove the general decision problem undecidable.

1940s–50s

Early Chess Algorithms · TuroChamp

Turing and Champernowne specify chess decisions before a practical contemporary implementation.

1950

The Imitation Game (“Turing Test”)

“Computing Machinery and Intelligence”: machine intelligence framed as observable behavior.

Era II — Computation Theory 1936 · Church–Turing Thesis

What counts as a computation?

Mechanical Turing Machine in Wood — video preview
A wooden implementation of a Turing machine · modern demonstrationRichard Ridel · from timeline.md

Watch on YouTube ↗

Can we make “a calculation carried out by precise rules” mathematically exact?

  • Alonzo Church: functions. Lambda calculus expresses computation through functions applied to arguments.
  • Alan Turing: a machine. An unbounded tape, a read/write head and rules for changing symbols and moving.
  • Same computational power. Both formalisms describe exactly the same class of computable functions.

The thesis: Anything that can be computed by a clear, finite, mechanical step-by-step procedure can be computed by a Turing machine. It does not say that every problem is computable.

Concepts · Computation & Turing

A Turing machine: read → apply a rule → move

One step of a Turing machine, connecting its parts to its operations An unbounded tape contains symbols. The read/write head is over a cell containing 1. In the example, the machine is in state q0. Its rule for state q0 and symbol 1 says to write 0, enter state q1, and move the head one cell right. The three connected boxes explain reading, applying the rule, and moving and repeating. Other rules may move left; computation stops if a halting state is reached. Unbounded tape One symbol per cell · □ = blank □01110□□□ R: one cell right Read/write head Next cell,next step 1 · Read2 · Apply a rule3 · Move and repeat Read the symbol under the head.Here: 1; current state: q₀.q₀ is the current control state. Look up (state q₀, symbol 1).Write 0 · enter q₁ · move R.Illustrative entry in the rule table Move the head one cell right.Read again in state q₁.Other rules may move left (L).

Each step depends only on the current state + scanned symbol. Repeat until a halting state is reached; some computations run forever.

Concepts · Computation & Turing

Three different questions about an algorithm

Computability

Does an algorithm exist that always solves the problem?

Efficiency

If it exists, how much time and memory does it require?

Implementation

Can we run it on the hardware available to us?

Undecidable ≠ merely slowExample: no general algorithm can decide whether every arbitrary program/input pair will halt.

Equivalence of formal models and undecidability are mathematical results. The link to informal “effective calculation” is the thesis.

Era II — Computation Theory 1940s–50s · Chess Programs

TuroChamp: a procedure for choosing a move

The 1952 TuroChamp vs Glennie game
TuroChamp (white) vs. Glennie (black), 1952 · animated gameWikimedia Commons · timeline source

Turing and Champernowne faced a useful challenge: clear rules, but far too many possible continuations to explore exhaustively.

  1. 1 · Search. Look ahead at candidate moves and possible replies.
  2. 2 · Evaluate. Score positions using material, mobility and development.
  3. 3 · Choose. Use those estimates to select a promising move.

Search + evaluation turns a huge decision space into a manageable procedure.

1952: execution on paper. Turing carried out the algorithm by hand. Specifying a procedure and running it on available hardware are different milestones.

Concepts · Computation & Turing

Playing chess: search + evaluation

Generate

List legal moves and possible opponent replies.

Look ahead

Explore continuations to a limited depth.

Evaluate

Score resulting positions; use likely replies to choose a move.

10 choices at each step → 10⁴ = 10,000 paths after 4 stepsToy branching example: the number of possibilities grows rapidly with depth.

A heuristic estimates which positions or paths look promising. It makes search practical, but need not identify the best possible move.

Era II — Computation Theory 1950 · The Imitation Game

From “thinking” to an observable test

In his 1950 paper Computing Machinery and Intelligence, Turing reframes “Can machines think?” as a question about conversational behavior. He proposed a way to make the question testable: the imitation game.

Alan Turing
Alan Turing

A human

Identity concealed

A machine

Identity concealed

↕ Typed messages only — no face, voice or body language ↕

A human examiner

Asks questions and tries to identify which respondent is the machine.

The test: can the examiner reliably tell them apart under the chosen protocol?

The shift: evaluate what a machine does. Conversational success alone does not establish consciousness or settle every meaning of intelligence.

Concepts · Computation & Turing

What does the imitation game measure?

An operational test

Specify a text conversation, an examiner and a protocol. Measure how reliably the examiner distinguishes human from machine.

Scope of the evidence

The result concerns conversational behavior under that protocol. It does not, by itself, establish consciousness or inner experience.

A test makes a capability measurable. Its result supports only the claims that the test actually measures.

Discussion: could a system be good at planning or perception but poor at imitating human conversation?

Chapter III

ERA III: Cybernetics & Neurons

1943 – 49

Era III — Cybernetics & Neurons 1943–49

From biology to the first artificial neuron

1943

McCulloch & Pitts Neuron — What does a single processing unit compute?

An influential logical model of idealized neural activity, without a learned-weight rule.

1948

Wiener Publishes “Cybernetics” — How does a whole system regulate its own behavior?

The science of regulatory systems & feedback — a field at AI's root.

1949

Hebb’s Learning Postulate — How do neural connections change with experience?

Correlated neural activity can strengthen connections — inspiration for later learning rules.

Era III — Cybernetics & Neurons 1943 · McCulloch–Pitts Neuron
The structure of an artificial neuron
Generalized artificial-neuron structureWikimedia Commons · timeline source

McCulloch & Pitts · 1943

Designed by cybernetician Warren McCulloch and logician Walter Pitts to model neuronal activity.

  • Binary inputs & output
  • Original model: excitatory and inhibitory inputs; diagram: a generalized teaching abstraction
  • Threshold function decides the firing output (0 / 1)
Concepts · Cybernetics & neurons

A threshold unit can implement logic

s = w₁x₁ + w₂x₂; output = 1 if s ≥ θ, else 0Generalized teaching model · binary inputs · fixed weights w₁ = w₂ = 1
Inputs (x₁, x₂)Sum sAND: θ = 2OR: θ = 1
(0, 0)000
(0, 1) or (1, 0)101
(1, 1)211

Choosing weights and a threshold specifies what the unit computes. We still need a separate procedure to learn suitable parameters.

Era III — Cybernetics & Neurons 1948 · Norbert Wiener
First edition of Norbert Wiener's Cybernetics
Wiener’s Cybernetics · first edition, 1948Wikimedia Commons · timeline source

Cybernetics · 1948 — Norbert Wiener

“Control and Communication in the Animal and the Machine”

  • The science of regulatory systems & feedback
  • A transdisciplinary field that gathers AI, analog computing, neuroscience & communication
Concepts · Cybernetics & neurons

Feedback: observe → compare → adjust

Observe

Thermostat measures
19 °C.

Compare

Target: 21 °C
Error: +2 °C.

Act

Turn on heating.
Measure again.

Action → environment → measurement → next action ↻The loop reacts to disturbances, such as an open window.

Feedback changes the next action. Learning changes the system’s parameters or decision rule; a fixed thermostat can use feedback without learning.

Era III — Cybernetics & Neurons 1949 · Hebb's Rule
Donald Olding Hebb
Donald Hebb · neuropsychologistWikimedia Commons · timeline source

Hebb's Rule · 1949 — Donald Hebb

“The Organization of Behavior. A Neuropsychological Theory”

Neurons that fire together wire together.
Correlated activity can strengthen neural connections.
Concepts · Cybernetics & neurons

Unsupervised learning from co-activity

Δwᵢⱼ = η xᵢ xⱼA simple later mathematical illustration of Hebbian learning; η > 0 sets the update size.

Local signal

When both connected units are active, their connection strengthens. With binary activities, if either is 0, this update is 0.

No target answer

The rule reinforces co-occurrence. It does not compare a prediction with a correct label.

Experience can change a connection without an external teacher. Co-activity alone does not tell us whether a prediction is correct.

Chapter IV

ERA IV: The Birth of AI

1950s

Era IV — The Birth of AI 1950s

A field is born, and names itself

1955–61

Logic Theorist & General Problem Solver

Early demonstrations of automated reasoning, heuristic search and means–ends analysis.

1955–56

Dartmouth Proposal and Workshop

The 1955 proposal uses “artificial intelligence”; the summer study follows in 1956.

1957

The Perceptron

Rosenblatt's neuron learns its weights — a working learning machine.

1958–59

LISP & “Machine Learning”

McCarthy's AI language and Arthur Samuel naming the field.

Era IV — The Birth of AI 1955–56 · Logic Theorist & GPS
Illustrative theorem-proving search tree
A schematic search through goals and known resultsOriginal teaching diagram · Logic Theorist context

Logic Theorist · developed 1955–56

One of the first algorithms able to perform automated reasoning for theorem proving — it explores a search tree from an hypothesis toward the statement to prove.

  • Proved 38 of 52 theorems in chapter 2 of Principia Mathematica
  • For one, found a more elegant proof than the book's own

General Problem Solver · 1957–61

Uses a new search method, means-ends analysis, to solve tasks like theorem proving or the Tower of Hanoi.

Concepts · The birth of AI

Means–ends analysis: work on the gap

General Problem Solver: compare the current state with the goal.

Find a difference

Goal: have a book at home.
Current state: book is at the library.

Choose an operator

Borrow the book.
Precondition: be at the library with a valid card.

Create subgoals

Get the card and reach the library, then borrow the book.

Actions may require subgoals before they can be applied. A useful heuristic organizes search; it does not guarantee that every task is solvable.

Era IV — The Birth of AI 1956 · Dartmouth Workshop
Dartmouth 1956 workshop
Participants in the 1956 Dartmouth summer research project

“Artificial Intelligence” is born

  • The 1955 proposal names “artificial intelligence”; the workshop follows in 1956
  • Proposal authors: McCarthy, Minsky, Rochester and Shannon
  • An organizing milestone connecting existing research traditions
Era IV — The Birth of AI 1957 · Perceptron
Mark I Perceptron machine
Mark I Perceptron · an early learning machineWikimedia Commons · timeline source

Perceptron · 1957 — Frank Rosenblatt

A new kind of artificial neuron, inspired by the McCulloch & Pitts design, that can automatically update its weights from inputs and expected outputs.

  • Supervised mistake-driven updates — distinct from Hebbian learning and the delta rule
  • An important precursor of later neural learning systems
  • Modern MLPs generally use differentiable nonlinear units and backpropagation
Concepts · The birth of AI

The perceptron learns from mistakes

ŷ = 1 if w · x + b ≥ 0, else 0
w ← w + η(y − ŷ)x   ·   b ← b + η(y − ŷ)y ∈ {0, 1} is the target; ŷ is the prediction; η > 0 is the learning rate.

Predict and compare

Show a labeled example.
Compute the prediction and the difference y − ŷ.

Update and repeat

Correct prediction → no update.
Wrong prediction → adjust weights and bias toward the target.

Unlike Hebbian co-activity, this update needs a correct answer. It is a supervised, mistake-driven rule; the delta rule is a different learning algorithm.

Concepts · The birth of AI

What can one perceptron represent?

Decision boundary: w₁x₁ + w₂x₂ + b = 0A straight line in two dimensions; a hyperplane with more inputs.

XOR: opposite corners share a class

0101x₁x₂0011

Geometry limits learning

XOR cannot be separated by one straight line.

More training cannot fix an insufficient representation. Networks of units can represent richer boundaries.

The perceptron converges on linearly separable training data. If no separating boundary exists, mistakes need not stop.

Era IV — The Birth of AI 1958–59 · LISP & “Machine Learning”
John McCarthy
John McCarthy · creator of LispStanford University · EE380

LISP · 1958 — John McCarthy

Inspired by IPL (Newell, Shaw & Simon), McCarthy creates LISP — a high-level language for AI programming that powers algorithms like SHRDLU.

“Machine Learning” · 1959

Arthur Samuel popularizes the term while building a self-learning checkers algorithm.

Concepts · The birth of AI

Lisp: make symbolic structure easy to manipulate

Represent an expression

(OR (NOT A) B)
A logical formula stored as nested lists.

Represent a computation

(+ 1 2)
A list that yields 3 when evaluated as a program.

Build

Create expressions from smaller parts.

Traverse

Use recursion to visit nested structures.

Transform

Rewrite expressions using explicit rules.

A program can manipulate symbolic expressions, including code, as data. The representation makes reasoning procedures easier to express.

Concepts · The birth of AI

Samuel’s checkers: improve through experience

Play

Generate experience through games, including self-play.

Evaluate

Estimate how promising a board position is.

Adapt

Use experience to improve evaluations that guide future moves.

Learning ideaWhat drives change?
Hebbian learningCo-activity of connected units
PerceptronA labeled example and a prediction error
Learning from playExperience with positions and game results

Representation makes a problem computable. Adaptation lets a learning system improve its decisions through experience.

Lecture 01 · Wrap-up

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