An explanation of Turing machines—the foundations of digital algorithms and computers

Turing machines consist of an infinite tape, a read-write mechanism and instructions

Based on the information the mechanism reads on the tape, the machine follows the applicable instruction (e.g., if you read a 1, write a 0) and may proceed to the next cell of data. Given enough time and memory, Alan Turing proposed such a machine could perform any computation.

Computational and biological systems share fundamental principles, like randomness

Proposed by Alan Turing and John von Neumann, the concept originates from how DNA and computers run by executing encoded instructions in parallel. The advent of AI and the temperature parameter has seen neural networks mimic the randomness of protein encoding.

Logic gates—digital versions of conditional statements, such as 'if 0 and 1, then 1'—are specialized circuits that combine multiple digital signals, like the binary code representing numbers, into a single output, thereby allowing machines to perform math.

All computers are defined by their ability to input, store, process, and output data

From wooden machines to wearable tech, computers have changed a lot in appearance, but they all still perform the same essential tasks. Early computers were made of wood and metal—some were so big that they filled entire rooms just to solve simple math problems.

A breakdown of algorithms, how they are constructed, and their applications

Algorithms are instructions for accomplishing a goal and typically take the form of a step-by-step procedure. Given the conditions, these procedures can take various paths, increasing an algorithm's complexity. While traditional computer algorithms are programmed to account for all possible scenarios within a given process, machine learning systems build their own rules from data-driven patterns.

See how computer memory really works—from binary bits to modern RAM

The video explains how computers store information as 1s and 0s, how RAM functions as fast working memory, and why systems utilize different types of storage. The video demonstrates how this process enables computers to operate.

Before transistors, which regulate the flow of electricity, vacuum tubes—glass tubes containing no gas that resemble light bulbs—served as the electronic switches in computers.

A simple explanation of semiconductors

Semiconductor chips are electronic devices that store and process information. Today they can contain billions of microscopic switches on a chip smaller than a fingernail. The article provides a quick overview of how the devices work and how they've provided the backbone of the computer age.

The work of Claude Shannon, for whom Anthropic's AI chatbot is named

Known as the father of information theory, Claude Shannon applied Boolean algebra—a subset of mathematics that quantifies true or false statements as 1 or 0, respectively—to circuit design to develop the concept of a binary digit. His paper "A Mathematical Theory of Communication" (1948) laid the groundwork for all modern digital systems.

Transistors in traditional computers are physically limited to atomic scales

As computer parts shrink, transistors—tiny switches that control the path of electrical signals—become obsolete because electrons can quantum tunnel through switch barriers. This makes quantum computers, which take advantage of quantum effects, an enticing alternative.

An overview of 12 fundamental types of algorithms and the uses for each

These include search algorithms to quickly process and find important information, cryptographic algorithms to secure communications, randomized algorithms—such as Monte Carlo simulations for estimating probabilities of outcomes—and greedy algorithms, which make optimal choices based on available data in a step-by-step fashion, as seen in navigation apps.

Computer pioneer Alan Turing was also an elite runner

Alan Turing is credited with helping to found modern computer science, in addition to cracking the Nazi code known as Enigma. Beyond these world-historical achievements, the British mathematician also nearly represented his country in the Olympics in the marathon, running just 11 minutes slower than the eventual gold recipient at the 1948 games. Read more on this lesser-known aspect of the man here.

Transistors are the foundational components of integrated circuits and microchips and manage the processing of electronic signals by controlling the flow of electricity.

More than 2,000 years ago, a hand-powered model of the solar system called the Antikythera mechanism—the oldest example of an analog computer—could predict solar eclipses.

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

Quantum computers harness weird physics to explore unsolvable problems

Classical computers manipulate bits as either 0 or 1, but quantum computers use qubits to hold combinations of both, enabling new algorithms. This new approach could one day help with breakthroughs in medicine, chemistry, and AI.

Semiconductor chips are electronic devices that store and process information

They can contain billions of microscopic switches on a chip smaller than a fingernail. An article provides a quick overview of how the devices work and how they’ve provided the backbone of the computer age.

Algorithms can be designed to train themselves and self-improve without human input, to the point where the optimized code is too complex for programmers to understand.

The first compiler to facilitate communication with computers was developed by Grace Hopper

The A-0 program linker automatically translated mathematical symbols into machine-readable binary code. Although it took two years for computer executives to get on board with the idea, the technology was foundational to future programming languages that allowed computers to understand commands written in word-based languages.

A brief history of artificial intelligence

The concept of artificial intelligence and what it may mean for humanity has evolved as computer technologies have grown increasingly powerful through the decades. Beginning with the first (massive) computers in the 1940s, scientists have sought to make the machines as intelligent as humans. But it wasn't until computing power made exponential gains have computers begun to imitate human behavior.

A timeline of computer history

The earliest computers bear little resemblance to the computing devices that most people rely on today. This timeline graphic from the Computer History Museum tracks their evolution, from the early days of bulky mainframes that only experts generally used through to the personal computing revolution and on to the modern mobile era. Readers will learn important context ahead of the next major computing platform shift.

The Model K—named for its construction on a kitchen table—was the first electromechanical digital binary adder, which used an electric circuit to provide the sum of a pair of zeroes and ones in binary.

The foundation for computer viruses was published after its creator's death

In the late 1940s, Hungarian American mathematician, scientist, and engineer John von Neumann gave a series of lectures where he explained the theoretical framework for a computer program that could replicate itself—the von Neumann Universal Constructor. His lectures were later compiled and published in 1966, nine years after his death from cancer.

The internet explained at five levels of difficulty, from protocols to internet flattening

Resembling a roadway with traffic laws that all cars must follow, the internet is the hardware that connects a source to a destination, and these connections must follow specific software rules. Although data had to travel through about 10 networks to reach a destination in the past, data centers increasingly consolidate traffic, just as a highway does for cars, to improve data speeds.

A simple visual explanation of how blockchains work

Blockchains are decentralized, distributed, and digital methods to record transactions and prevent alterations and tampering of the record. That's a simplified definition. This easy-to-understand six-minute video further and better explains what blockchains are and how they work using colorful illustrations and clear, concise clarifications on their processes and what makes them so special.

Understanding how Claude Code and other AI coding agents function

Under human oversight, a supervising large language model interprets user tasks and delegates work to subordinate LLMs, which can generate code, fix bugs, and run tests, often most effectively for proofs of concept. Incremental backups and versioning are crucial when using such agents, which can lose details during their work as a result of compressing context history to work around memory limitations.

Quantum computers use qubits to solve problems much faster than classical machines

Unlike regular computers, where each bit is either 0 or 1, quantum computers use qubits, which can simultaneously be both—allowing for massive parallel processing power. Google’s quantum processor once solved a problem in seconds that would have taken a supercomputer 47 years.

Since computers rely on the distribution of electrons in microchips to represent binary code, cosmic rays and ionizing radiation from radioactive elements can introduce software errors by detaching electrons from atoms.

What does it mean for AI to "understand" something?

This Quanta article discusses how programmers are working to create a reliable test for the depth and extent of the knowledge of machines. What does AI know and how does it know it, if it knows anything at all? There's been progress, but it hasn't been easy. Even humans can still be fooled some of the time.

A visual guide to how bitcoin transactions work and rely on cryptography

The "crypto-" in cryptocurrencies like bitcoin refers to the mathematical functions that generate pairs of public and private keys and encrypt data in blocks. When combined, these systems secure transactions on the network, verify digital asset and token transfers, and contribute to end-user anonymity.

With many smaller computing cores, graphics processing units process many identical tasks in parallel, whereas central processing units have fewer, larger cores built to handle a wide variety of more complex tasks sequentially.

Machine learning lets computers learn from data instead of relying on programming

ML is a core part of artificial intelligence and is foundational to applications like chatbots, fraud detection, and self-driving cars. Businesses are also adopting it to improve efficiency and identify patterns in data, though the latter may be inaccurate.

Compression algorithms can reduce file sizes without losing quality by consolidating repeated data or replacing blocks of code with more compact representations, thereby reducing storage demands and improving data transmission rates.

In the 1950s, Alan Turing developed a mathematical model to explain why animals have stripes, spots, and other patterns based on differences in how quickly two interacting chemicals spread throughout a developing organism.

Qubits let quantum computers process massive datasets all at once

The quantum phenomena of superposition and entanglement enable qubits to act in 0 and 1 binary states simultaneously and influence each other instantly. These features give quantum computers incredible power, though keeping them stable is a major challenge.

The science of cryptography, including methods to encrypt data and how to break encryption

Monoalphabetic ciphers use a set of rules to replace each letter with another consistently, making them susceptible to brute force attacks that try every kind of replacement. While more complex ciphers can transform text in less obvious ways, because certain letters are used more often than others, an analysis of letter frequency may reveal patterns that help uncover the rules that make up a cipher.

Explore (digitally) the Computer History Museum

When IBM’s Deep Blue supercomputer won its famous chess rematch with then world champion Garry Kasparov in May 1997, the victory was hailed far and wide as a triumph of artificial intelligence. But John McCarthy—the man who coined the term and pioneered the field of AI research—didn’t see it that way. An obituary about McCarthy—who passed in 2001—and his ideas.

Misunderstandings about how quantum computing works may have overhyped their ability

Quantum computers are often viewed as machines that can solve all problems instantly by trying every solution simultaneously. Instead, they amplify correct answers and cancel out wrong ones, which only works for specific kinds of problems with special structures.

When you complete a CAPTCHA on a website to prove you are human, you may be unknowingly training algorithms for self-driving cars, whose systems require training data to help identify crosswalks, bicycles, and other outdoor objects.

Logic bomb viruses can awaken from a dormant phase without human input

Theoretically, computer viruses can remain idle indefinitely while awaiting specific user actions, as instructed by their code. However, logic bombs—embedded code that triggers when specific conditions are met—can automatically execute viruses, such as when a certain date or time is reached.

Visualize how transformer architecture generates a large language model's outputs by running words and subwords assigned to specific numbers through multiple rounds of mathematical processing.

The story of two female programmers running the simulations behind chaos theory's discovery

Margaret Hamilton and Ellen Fetter worked on MIT's 800-pound Royal McBee LGP-30 computer, which was fed binary code on paper tape to perform computations. Among the computations performed were those involving equations describing the motion of gas in a circulating fluid for Edward Lorenz, widely considered the father of chaos theory.

How quantum computers can empower Shor's algorithm to break digital encryption

Secure communications largely rely on numeric keys generated by multiplying two enormous prime numbers together, and it is computationally impractical to determine these primes by trying to divide by every possible one. While Shor's algorithm can provide better guesses for this brute-force approach, it relies on a number that is difficult to determine on classical computers but much easier to calculate using the simultaneous computations enabled by quantum superposition.

Bias can manifest in algorithmic decisions because the program follows rules that may have been written by individuals unaware of their own biases.

Quantum computers can simulate nature more effectively than classical computers

Ordinary computers struggle to simulate quantum fields due to entanglement, but systems built from those elements can model the complexity. Systems using particle in more than two states—qudits—have successfully modeled 2D electromagnetic fields and done so more efficiently.

Watch how the Enigma machine encrypts messages and learn about its critical design flaw

Using settings selected from a series of rotors and a plugboard that let operators swap letters with any of their choosing, the machine lit up the output letter for each letter typed. While this system could generate messages requiring any of 150 quintillion potential keys, the machine's reflector never encrypted a letter as itself, providing an entry point for exploiting the system.

Tokens—numbers assigned to words and subwords—are the basic units of data that AI tools process to generate outputs that mimic language without understanding the text itself.

DNA computing allows for storage and processing of massive amounts of data

Although costly and less efficient for simpler tasks, as of 2025, DNA could hold 455 exabytes of data with near limitless parallel computation potential in small data centers. Every movie ever made would fit inside the volume of a single sugar cube.

FLOW-MATIC was the first programming language resembling the English language

As part of the team working on UNIVAC—the first commercially produced electronic digital computer in the US—Grace Hopper helped develop the system that enabled nonprogrammers and businesspeople without a strong mathematics background to use the machine effectively, thereby enhancing the computer's commercial viability.

An explanation of TCP/IP, which helps transmit data across the internet like a club sandwich

The system consists of several layers—application, transport, internet, and network—each responsible for specific tasks. These include interacting with a web browser, checking for errors, sending packets of data across various networks to avoid congestion on their way to a destination address, and managing the transmission of information across hardware, such as an Ethernet cable.