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.

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.

Transistors are the foundation of electronic signal processing

Small amounts of voltage can allow or block the flow of electrons across a transistor made from modified layers of semiconducting materials. The conducting (1) and insulating (0) states can be quickly modified as binary code is processed in a computer system.

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.

The first computers performed calculations using lightbulb-like tubes

Before transistors, the first electronic computers relied on vacuum tubes—components that switched signals on and off. Despite machines like ENIAC—the first programmable, general-purpose, electronic computer—utilizing nearly 18,000 tubes that generated massive amounts of heat and frequent failures, they laid the foundation for modern computing hardware.

Binary mathematics represented as switches allows silicon rocks to do math

Each switch is assigned a zero or a one based on whether it is open or closed, and logic gates are built from these switches that let the system perform mathematical operations. Modern software builds upon these operations to perform increasingly complex tasks.

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.

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.

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.

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.

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.

Watch how 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.

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.

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.

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.

LLMs explained simply and quickly

Large language models generate responses by predicting one token at a time, based on patterns they’ve learned from massive datasets. This explainer covers their core components: data, architecture, training, and how transformer models use context to simulate conversation.

Storing data in DNA requires converting binary code into DNA's four-base system

Researchers have suggested that DNA's ability to form compact, dense structures justifies investigating its use for long-term, safe data archiving. This system could fit all of the world's data in a single shoebox, though processing each bit into a nucleotide base takes 2 minutes, as of 2024.

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.

Social media algorithms are shaping real-life language through memes

The evolution of the internet in the early 2000s supercharged the creation and spread of memetic content. Now, highly tuned algorithms on platforms like TikTok and YouTube influence the language, phrasing, and content of creators, which shapes how we use language in the real world.

Explaining computer kernels and what makes monolithic kernels different from microkernels

A kernel is an intermediary piece of software on a device that manages the connection between software programs—the services and processes they perform to run correctly—and the available hardware resources, such as memory and computing bandwidth, including prioritizing resource allocation and managing access to specific hardware. A monolithic kernel manages all of an operating system's services, whereas a microkernel only handles essential services.

Time crystals are systems of atoms organized into periodic patterns of motion

Unlike traditional crystals—whose atomic structures cause them to look identical no matter how you look at them in space—time crystals exhibit this behavior through time, where the motion of atoms will bring them to the same positions relative to one another regularly.

Radioactive elements can introduce software errors because the ionizing radiation they produce can detach electrons from atoms, and computer code relies on the distribution of electrons.

The term 'algorithm' originated from the Latinized name of al-Khwārizmī, a 9th-century mathematician whose works introduced Arabic numerals and the decimal-based numeral system to Europe and whose treatise 'Al-Jabr' gave algebra its name.

The first robot in literature may have been a 'mechanical man' in 1907's 'Ozma of Oz,' a book in L Frank Baum's 'Wizard of Oz' series.

A vending machine run with Anthropic's AI went out of business after it was convinced to give away items for free and sell a video game console.

According to the physics of black holes, our 4D reality may be a hologram—a projection of information coded on a 2D surface on the edge of the universe.

The history of many kitchen appliances involves unexpected discoveries and applications, including wartime radar turned hamster defroster and replacing an 'ice king' with heat-stealing boxes.

Clever Hans was a 1900s horse that was believed to be able to solve math equations, tell time, and read and comprehend German, until a psychology student discovered how he got his answers.

Visualize how CRISPR-Cas9—a type of immune system used by single-celled organisms to attack invasive viruses—targets and makes precise changes to a gene's DNA.

The name 'Silicon Valley' arose from the founding of Shockley Semiconductor Laboratory in Fairchild Semiconductor in 1956-57, founded near Stanford University in Palo Alto

Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

Alzheimer's can lead to brain shrinkage, with an average of around 2% of volume reduction per year

The story of Dollree Mapp, whose legal challenge over her 1957 conviction for possessing "obscene material" led to a major strengthening of the Fourth Amendment

Memecoins are a type of cryptocurrency—a form of digital currency with a wide variety of uses—created around popular 'memes,' or viral internet jokes.

Tattoos remain visible on your skin thanks to immune cells called macrophages

Hear 50 years of iconic hip-hop samples, the genre's foundational looped tracks

To reduce wrinkles in clothing, research recommends gentle wash cycles with more water and tumble drying with smaller loads and longer times.

The United States is one of only around two dozen countries with a fully federal system of government, in which power is divided between national and state governments.

For centuries, it was common to sleep in two shifts: a few hours at the beginning of the night, and a longer period beginning around midnight

The hormonal disorder PCOS was renamed PMOS in 2026, a move designed to improve care and research by shifting the focus to the hormonal causes of this condition that affects 1 in 8 women.

The first steps to rebuilding your credit score include getting to know exactly what's on your credit report and figuring out how far you are from the '700 club,' or 'good score' range.

Explore a list of the 100 best novels of all time, compiled by some of the world's best living writers, including Salman Rushdie, Stephen King, and Jennifer Egan.