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Artificial intelligence
From Turing's machine to today's models: what a machine can compute, and what it cannot.
The reading track
- 01
Artificial intelligence can be built through rational agents that perceive the environment and act to achieve goals.
Artificial Intelligence: A Modern Approach · Stuart Russell și Peter Norvig · 1995
Imagine a robot playing chess. It sees the board (perceives), thinks about which move to make (processes), and moves the piece (acts). This is the idea of a rational agent: a program that makes good decisions to win, just like a human player.
Why it matters This book is the modern foundation of artificial intelligence, used in universities to learn how robots and virtual assistants work.
- 02
The brain does not compute in the formal language of mathematics and von Neumann machines; it has its own analog, massively parallel way of processing information.
The Computer and the Brain · John von Neumann · 1958
Von Neumann, the architect of the modern computer, argued in his last work that machines and the brain are fundamentally different kinds of computers. His mechanism: neurons are slow, working in milliseconds rather than nanoseconds, but they operate in parallel across billions of units and learn through the wiring of their connections. That is why the brain solves speech and face recognition on roughly twenty watts, a budget the sequential machines of his era could never approach. His conclusion was that we cannot assume mathematical logic is the language of the nervous system. Neuromorphic chips take that diagnosis seriously.
When we talk mathematics, we may be so naively disposed as to believe that the language of mathematics is actually the language in which nature speaks. But this is very unlikely. The language of the brain is not the language of mathematics.The Computer and the Brain, partea a II-a (Sistemul nervos), ultimul capitol
Why it matters As artificial intelligence strains power grids, the idea that another computing architecture exists stays vital. Neuromorphic chips are the attempt to build silicon on the principle described here, not on separated memory and processor.
- 03
Feynman argues that nature is quantum, not classical, so any machine that wants to process it faithfully must itself use quantum phenomena, not merely classical bits.
Simulating Physics with Computers · Richard Feynman · 1982
Feynman starts from a simple observation. Simulating a physical system on a classical computer grows exponentially with the system's size, because quantum states cannot be represented efficiently with ordinary bits. So he proposes a computer that is itself quantum, one that processes amplitudes and interference rather than mere digits. Light is exactly such a system: photons propagate, interfere and combine according to quantum equations. An optical processor lets light perform the operation directly, through interference, instead of simulating it step by step in silicon. A neural network is, at its core, a chain of matrix multiplications, and an optical matrix performs that multiplication as the beam travels through it.
Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.prelegerea «Simulating Physics with Computers» (1981), publicată în International Journal of Theoretical Physics, vol. 21, 1982
Why it matters Feynman's idea underlies today's photonic computing: if light is a quantum system, then neural networks can be carried and processed by photons rather than electrons, at near light speed and with far lower energy use than classical chips.
- 04
Alan Turing proved that some problems cannot be solved by any computer, no matter how powerful.
The Annotated Turing · Charles Petzold · 2008
Think of an impossible puzzle: you want to know if a program will ever get stuck, but you can't find out for sure. Turing showed there are questions computers can never answer, even if they are very fast. It's like trying to find a treasure that doesn't exist.
Why it matters This limit of computation helps us understand why some problems, like perfect security, are impossible.
- 05
The human mind can do things that no computer can do, because of the limits of computation.
The Emperor's New Mind · Roger Penrose · 1989
Think of a computer that can solve any math problem. Penrose says it's not possible, because some problems are too complex. He believes our brain uses something special, like a superpower, that computers don't have. It's like trying to measure a shadow with a ruler.
Why it matters This book challenges the idea that AI can match the human mind, an important topic in current debates.
- 06
A synapse strengthens when the neuron using it manages to fire the neuron on the far side. Learning is not a program; it is a direct consequence of local activity.
The Organization of Behavior · Donald O. Hebb · 1949
Hebb argued that learning lives in the connections between neurons, not in a central command post. His mechanism is local: when one neuron repeatedly helps fire another, the link between them becomes more effective. No supervisor is needed to tell each cell what to do. This rule, now called the Hebbian rule, became the foundation of learning in neural networks. Neuromorphic chips take it one letter further by putting it into silicon. Carver Mead and Misha Mahowald built analog circuits in which each transistor imitates a neuron, and the connections between them carry a weight that changes exactly like a synapse. In their chips, for instance the silicon retina, pixels talk through pulses, just like biological neurons. Spiking networks run on the same principle: artificial neurons send brief events instead of continuous numbers, and they learn from the coincidence of pulses. The engineering target is clear: the brain runs on roughly 20 watts, so neuromorphic chips chase that same ratio of computation to energy, not raw speed.
When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A's efficiency, as one of the cells firing B, is increased.The Organization of Behavior: A Neuropsychological Theory, cap. 4 («The first stage of the problem: conceptual analysis»)
Why it matters Classical digital chips burn energy on every multiplication, and large models keep hitting that ceiling. Silicon that learns like a synapse promises massive computation at thousands of times less power.
- 07
Penrose argues that conscious understanding cannot be reduced to an algorithm: there are true mathematical judgments that no formal procedure can systematically generate.
Shadows of the Mind: A Search for the Missing Science of Consciousness · Roger Penrose · 1994
Penrose starts from Gödel's incompleteness theorems. They show that for any consistent formal system, there are true statements the system cannot prove. A human mathematician, he says, 'sees' the truth of such a statement from outside the system. So understanding is not computation. From this follows his thesis about consciousness: the mind must rest on a non-computable physical process. He locates it in objective orchestrated quantum reduction, occurring in the microtubules of brain neurons, together with anaesthetist Stuart Hameroff. His favourite example is Gödel's theorem itself: the computer stays trapped inside the system, the human transcends it through understanding.
Consciousness seems to me to be such an important phenomenon that I cannot believe that it is something just 'accidentally' conjured up by a complicated computation.Shadows of the Mind, cap. 1 («Consciousness and computation»)
Why it matters The idea matters because it poses a hard question for artificial intelligence: if understanding is not computation, then no machine that merely runs algorithms has a mind. Even though Orch-OR is a minority view among scientists, the Gödelian challenge remains a test for any theory of minds and machines.
- 08
Consciousness might arise from loops that refer back to themselves, the way a drawing of a hand drawing itself seems impossible, yet makes sense as an idea.
Gödel, Escher, Bach: An Eternal Golden Braid · Douglas Hofstadter · 1979
Hofstadter compared the mind to an Escher drawing, where a staircase seems to keep climbing yet returns to where it started. He linked this to Gödel's discovery: a system complex enough can talk about itself. Perhaps this exact kind of self-referring loop creates our sense of self.
Why it matters The book's ideas still influence research today into how consciousness might emerge in artificial intelligence.
- 09
Writing good code is not just making it work, but finding the most efficient recipe, like a chef searching for the best method, not just one that works.
The Art of Computer Programming · Donald Knuth · 1968
Knuth carefully analyzed thousands of different ways to sort or search data, measuring exactly how many steps and how much memory each method uses. Some recipes look simple but become very slow with much more data. Other, more complicated-looking recipes stay fast even with millions of entries.
Why it matters His books remain, decades later, a standard reference for software engineers.
- 10
People and computers rarely search for the perfect solution to a problem; they settle for one "good enough," because time and available information are always limited.
The Sciences of the Artificial · Herbert A. Simon · 1969
Simon called this bounded rationality: nobody can analyze absolutely every possible option before deciding. When choosing dinner, you do not compare every recipe in the world; you settle on the first reasonable option found quickly. Computer algorithms use the same strategy, searching for good solutions rather than perfect ones.
Why it matters The idea directly influenced how search algorithms used everywhere today are designed.
- 11
An imaginary, extremely simple machine that reads and writes symbols on an infinite tape can, in principle, compute anything any other computing machine ever could.
On Computable Numbers, with an Application to the Entscheidungsproblem · Alan Turing · 1936
Turing imagined a long tape divided into boxes, where a simple machine reads a symbol, decides what to do using fixed rules, then moves left or right. However simple it looks, this Turing machine can, in theory, run any program that today's most powerful supercomputer can run.
Why it matters His idea laid the theoretical foundation for every computer and phone in use today.
- 12
Modern cryptography uses mathematical algorithms to turn messages into unreadable codes, but only if they are implemented correctly.
Applied Cryptography: Protocols, Algorithms, and Source Code in C · Bruce Schneier · 1994
Imagine you have a robot that mixes the letters of a letter according to a secret rule. If the rule is good, no one can read the letter without the key. But if the robot makes a small mistake, a clever enemy can guess the rule and read everything. So it is with computer codes.
Why it matters This book is essential for understanding how online security works today.
- 13
Many systems — animals, machines, even cities — self-regulate by using feedback about their own results, the same way a thermostat shuts off heat once it is warm enough.
Cybernetics: Or Control and Communication in the Animal and the Machine · Norbert Wiener · 1948
Wiener called the study of feedback loops cybernetics: a system measures the effect of its own action and adjusts its behavior based on that effect. A thermostat reads the temperature, compares it to the target, then turns heat on or off. Your body does the same when it shivers.
Why it matters This idea of continuous feedback underlies modern robots and the autopilot systems in aircraft.
- 14
Any message — words, images, music — can be broken down into the smallest possible unit of information, a simple yes-or-no answer called a bit.
A Mathematical Theory of Communication · Claude Shannon · 1948
Shannon showed you can measure information exactly like a weight, in units called bits. One bit equals a single yes-or-no question. String enough bits together and you can describe a photograph, a song, or an entire book, no matter what original language was used to create it.
Why it matters Every file sent over the internet today is, at its core, just a long string of bits.
- 15
Two authors tried to build all of mathematics from pure logic alone, needing hundreds of pages just to prove that 1+1=2.
Principia Mathematica · Bertrand Russell and Alfred North Whitehead · 1910
Russell and Whitehead wanted to show numbers and addition are not just memorized rules but can be built rigorously from basic logical symbols. The work was huge and painstaking, with the proof of 1+1=2 appearing only hundreds of pages in. Their effort revealed how deep simple ideas truly are.
Why it matters The book paved the way for Gödel's later discoveries about the limits of any logical system.
- 16
In any mathematical system powerful enough, there exist true statements that can never be proven using only that system's own rules.
Gödel's Proof · Ernest Nagel and James R. Newman · 1958
Gödel somehow built a mathematical statement that says about itself I cannot be proven here. If the statement were false, the system would prove something wrong, which cannot happen. If it is true, then there exists a truth the system cannot reach on its own. Math has real limits.
Why it matters His discovery directly inspired the ideas behind modern computers and artificial intelligence.
- 17
Starting from just a few simple, clearly true rules, you can build, step by step, all of geometry's truth — without assuming anything else.
Euclid started with rules so simple nobody could disagree, like you can draw a straight line between any two points. From these tiny rules, through clear logical steps, he proved hundreds of truths about triangles, circles, and angles. Each step rests only on the ones that came before it.
Things which are equal to the same thing are also equal to one another.
Why it matters This step-by-step way of proving things underlies all the mathematics taught in schools today.
- 18
Many shapes in nature — a coastline, a snowflake, a lung — repeat the same pattern no matter how much you zoom in or out.
The Fractal Geometry of Nature · Benoit Mandelbrot · 1982
If you measure a country's coastline on a large map, you get one number. Measure it with a much smaller ruler, tracing every little bay, and the number grows. Mandelbrot called these shapes fractals: equally jagged at any scale. Their math can describe mountains, lungs, and even stock market prices.
Why it matters Fractals are used today for image compression and for simulating landscapes in movies.
- 19
Some rules in geometry are not "absolute truth" but conventions chosen because they are the most practical — we could, in theory, have chosen others.
Science and Hypothesis · Henri Poincaré · 1902
Poincaré showed you can describe the same world using different geometries, just like you can map the same city on a flat sheet or on a globe. We pick ordinary geometry not because it is the only true one, but because it makes calculations simplest. The choice matters, even if invisible.
Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house.
Why it matters This idea helped Einstein, a few years later, to think beyond ordinary geometry.
- 20
A true mathematician does math mostly for its beauty, the way a painter paints for the beauty of the picture, not only for usefulness.
A Mathematician's Apology · G. H. Hardy · 1940
Hardy said the most beautiful theorems are like elegant chess moves: surprising, simple, and tightly connected. He preferred pure math with no immediate use, precisely for that purity. Ironically, many ideas he thought useless, like number theory, are today the foundation of internet cryptography and online security.
Why it matters The number theory he loved now protects your passwords and online payments.