1. Euclid’s Elements: 116 votes
2. Turing’s “On Computable Numbers”: 110 votes
3. Gödel’s Incompleteness Theorem: 107 votes
4. Gödel’s P vs. NP Letter to von Neumann: 106 votes
5. George Boole’s Logic: 88 votes
6. Shor’s Algorithm: 88 votes
7. Wikipedia: 85 votes
8. Claude Shannon’s Digital Logic: 82 votes
9. PRIMES in P: 82 votes
10. Cook-Levin Theorem: 80 votes
The rest:
Al-Khwarizmi’s “On the Calculation with Hindu Numerals”: 79 votes
Bardeen, Brattain, and Shockley Invent Transistor: 79 votes
Babbage’s Analytical Engine: 77 votes
Tim Berners-Lee Invents WWW: 75 votes
Fast Fourier Transform: 73 votes
Brin and Page Create Google: 73 votes
von Neumann Architecture: 71 votes
RSA: 70 votes
Hilbert Calls for Mechanization of Mathematical Reasoning: 69 votes
Simplex Algorithm: 69 votes
Claude Shannon Formalizes Cryptography: 68 votes
Dijkstra’s Algorithm: 68 votes
Gaussian Elimination Described in Ancient China: 67 votes
Quicksort: 65 votes
UNIX and C: 65 votes
Newton’s Method: 64 votes
Leibniz Describes Binary Notation, Calculus Ratiocinator: 64 votes
First Program written by Ada Lovelace: 64 votes
Gauss’s Disquisitiones Arithmeticae: 62 votes
Monte Carlo Method: 62 votes
“Bit” Coined: 62 votes
TeX Typesetting: 62 votes
Ginsparg Creates arXiv: 61 votes
Kleene Invents Regular Expressions: 61 votes
McCarthy Invents LISP: 59 votes
“The Art of Computer Programming”: 59 votes
TCP/IP Protocol: 58 votes
Strassen’s Algorithm: 58 votes
PCP Theorem: 56 votes
Turing Test: 55 votes
Randomized Primality Testing: 55 votes
IP=PSPACE: 55 votes
Scott and Rabin’s Paper on Nondeterminism: 54 votes
Jacquard Loom: 54 votes
Colossus Begins Operation at Bletchley Park: 53 votes
Integrated Circuit: 53 votes
Chomsky Hierarchy: 52 votes
Pascal Builds Arithmetic Machine: 51 votes
First Genome Sequenced: 51 votes
Reed-Solomon Codes: 50 votes
Time Hierarchy Theorem: 50 votes
ARPAnet: 49 votes
Four Color Map Theorem Proved: 49 votes
Linux: 49 votes
Diophantine Equations Proved Undecidable: 46 votes
Feynman Suggests Quantum Computing: 46 votes
Deep Blue Defeats Kasparov: 46 votes
Solomonoff-Kolmogorov-Chaitin Complexity: 44 votes
Lempel-Ziv Data Compression: 43 votes
GPS: 42 votes
Marian Rejewski’s “Bombe” + Alan Turing’s Improvements: 41 votes
Diffie-Hellman Public Key Exchange Protocol: 41 votes
Zuse’s Z1: 40 votes
Viterbi Algorithm: 40 votes
First Email Message: 38 votes
Pseudorandom Generators: 37 votes
Oughtred Invents Slide Rule: 36 votes
FORTRAN: 36 votes
ENIAC: 35 votes
Semaphores: 35 votes
Gottlob Frege’s “Begriffsschrift”: 34 votes
Grace Murray Hopper Creates A-O Compiler: 34 votes
Conway’s Game of Life: 34 votes
Xerox Parc’s Alto With First GUI: 33 votes
Kuttaka Algorithm from Ancient India: 32 votes
Scientific Computing During Manhattan Project: 30 votes
Wilkes, Wheeler, and Gill Define Closed Subroutines: 29 votes
Stroustrup creates C++: 28 votes
Zimmermann creates PGP: 28 votes
Dartmouth Conference Popularizes Term “AI”: 27 votes
Moore’s Law: 27 votes
Boosting in Machine Learning: 27 votes
Codd Proposes Relational Databases: 26 votes
Ethernet Invented: 26 votes
Valiant Proposes PAC-Learning: 26 votes
Stallman Writes GNU Manifesto: 25 votes
Wiesner Proposes Quantum Money and Multiplexing: 24 votes
Antikythera Mechanism: 23 votes
BitTorrent: 23 votes
Low-Density Parity Check Codes: 23 votes
McCulloch and Pitts’ “A Logical Calculus Immanent in Nervous Activity”: 22 votes
Engelbart and English Invent Mouse: 22 votes
Dijkstra’s “Go To Statement Considered Harmful”: 22 votes
Back-Propagation: 22 votes
MIT SAGE Creates First Large-Scale Computer Network: 21 votes
Vannevar Bush Creates First Large-Scale Analog Calculator: 20 votes
IBM Introduces Hard Drive: 20 votes
Checkers Solved: 20 votes
First Packet-Switching Network: 20 votes
Atanasoff and Berry’s Vaccum-tube Computer: 19 votes
Vannevar Bush’s “As We May Think”: 19 votes
Hollerith’s Electromechanical Counting Machine: 18 votes
MIT Builds First Time-Sharing System: 18 votes
First Computer Virus: 18 votes
IEEE Floating-Point Standard: 18 votes
IBM PC: 18 votes
“Spacewar!”, First Computer Game: 17 votes
RISC Architecture: 17 votes
Intel’s 8086: 17 votes
al-Jazari’s Water Clocks and Musical Automata: 17 votes
Edward Lorenz (Re)discovers Chaos Theory: 16 votes
Apollo Guidance Computer: 16 votes
CAPTCHAs: 16 votes
VC Dimension: 16 votes
Macsyma Computer Algebra System: 15 votes
Amazon.com: 15 votes
UNIVAC I: 13 votes
DaVinci Surgical Robot: 13 votes
Mark II Incident Popularizes Word “Bug”: 12 votes
Weizenbaum Creates ELIZA: 12 votes
ASCII: 11 votes
TI Handheld Calculator: 11 votes
Simula 67: 11 votes
MIT Whirlwind I Displays Graphics: 10 votes
Sketchpad, First CAD Software: 10 votes
NCSA Mosaic: 10 votes
Robert Morris’ Computer Worm: 9 votes
Pixar Releases “Toy Story”: 9 votes
Stuxnet Worm: 9 votes
IBM System/360: 8 votes
Mac Hack Chess Program: 7 votes
Microsoft Windows: 7 votes
Sojourner on Mars: 7 votes
BASIC: 6 votes
Apple Macintosh: 6 votes
SETI@home: 6 votes
IBM’s Watson Wins At Jeopardy!: 5 votes
Atari’s Pong: 4 votes
Atlas Computer in Manchester: 4 votes
Norbert Wiener Founds Cybernetics: 3 votes
First ATM in Tokyo: 3 votes
Youtube Launched: 3 votes
VisiCalc: 2 votes
Jevon’s Logic Piano: 1 vote
Apple II: 1 vote
Adobe PostScript: 1 vote
SABRE Travel Reservation System: 0 votes
Fischer-Lynch-Paterson Theorem: 0 votes
Facebook, Twitter Use in Egypt Revolution: 0 votes
First Machine Translation Demonstration: -1 vote
Usenet: -1 vote
Akamai: -2 votes
TX-0: -3 votes
CDC 6600: -3 votes
Compact Disc Invented: -3 votes
Aiken’s Mark I: -4 votes
CM-1 Connection Machine: -4 votes
Whirlwind I Displays Graphics: -5 votes
Floppy Disk Invented: -6 votes
MITS Altair Microcomputer and Microsoft BASIC: -6 votes
Axelrod’s “The Evolution of Cooperation”: -7 votes
Microsoft Office: -7 votes
Pentium FDIV Bug: -7 votes
EDSAC: -8 votes
UNIMATE, First Industrial Robot: -9 votes
CLU Programming Language: -9 votes
1ESS Switching System: -11 votes
UNIVAC Predicts Presidential Election: -12 votes
Stanford Arm: -13 votes
“2001 A Space Odyssey” Introduces HAL: -15 votes
“Spam” Coined: -16 votes
First Denial-of-Service Attack: -17 votes
Y2K Bug: -18 votes
Facebook Launched: -18 votes
Nintendo’s Donkey Kong: -19 votes
“Robot” Coined: -21 votes
CSIRAC -21
Apple’s iPhone: -21 votes
Slashdot: -27 votes
Godwin’s Law: -29 votes
Asimov’s Three Laws of Robotics: -32 votes
Match.com: -34 votes
de Vaucanson’s Mechanical Duck: -39 votes
von Kempelen’s Mechanical Turk: -52 votes
A few comments:
It’s (just-barely) conceivable that the results could have been slightly skewed by the quantum- and complexity-loving readership of this blog.
Voters really didn’t like fiction/pop-culture references, mechanical contrivances, or anything that sounded like a publicity stunt. They were much keener on conceptual advances (even to the extent of putting Gödel well ahead of the transistor).
I need to catch a plane to give the Buhl Lecture at Carnegie Mellon tomorrow, so I’ll leave you to draw any further conclusions.
The American Museum of Natural History has two temporary exhibits that are drawing large crowds. One, Brain: The Inside Story, I can attest is worth a visit the next time you’re in NYC. From the New York Times review, I’d been worried that the exhibit would be full of la-de-da generalities: “how marvelously complicated is the brain! how little we understand about it!” But it turned out that was just the review. The exhibit itself does a pretty good job of summarizing what’s known about how the brain is organized, how it develops, how various drugs affect it, and more. One highlight for me was a model brain that you can take apart to see how the brain stem, limbic system, and cerebral cortex fit together—something that 2D images had never successfully conveyed to me. The other exhibit, The World’s Largest Dinosaurs, was sold out for the entire day when we tried to go there, so we had to content ourselves with the smaller dinosaurs in the rest of the museum.
The Mark Twain House and Museum in Hartford, Connecticut, should be avoided at all costs. On a recent visit, I and my family of Twain fans were snidely turned away since we hadn’t booked a tour—a requirement buried in the website, which someone googling for the opening hours would almost certainly miss. (This despite the fact that the museum wasn’t crowded, and we could have easily joined a tour that was starting as we arrived.) So don’t suffer the petty bureaucrats who curate Twain’s legacy, and treat the town of Hartford the way they’d apparently like you to: as a bathroom stop along the highway from New York to Boston. Twain would’ve been amused. Jeffrey Nichols, Executive Director of the Mark Twain House, left me a personal apology in comments section. I thank him warmly for that, and maybe I will visit again sometime—though it will help if I have some way of knowing I won’t just be turned away again! 🙂
The Yad Vashem Holocaust History Museum in Jerusalem has been redesigned since the last time I was there, in 2002. In the old Yad Vashem, you walked around more-or-less randomly looking at the exhibits; in the new one, you proceed in a more linear order (similar to the US Holocaust Memorial Museum in Washington DC): from the rise of Nazism to the first anti-Jewish laws to the ghettoes to the gas chambers and crematoria. The tour ends powerfully, with the Hall of Names (a large circular room with photos of victims and bookshelves of data about 3.8 million of them), followed by a balcony with a spectacular view of West Jerusalem—as if the building itself is trying to explain why the country it’s in exists. I recommend a visit, even if you’ve been to Yad Vashem before its redesign in 2005. But be careful to check the opening hours: the first time my family and guests tried to visit, the museum was closing, we were turned away, and we ended up going instead to a rest stop full of Elvis statues, where people lined up to use the bathroom and bought Elvis t-shirts. (I thought that belonged in some anthology of Jewish humor.)
Summary: While the world’s museums have a great deal to teach us, they ought to devote more of their attention to the fundamental tasks of being open and letting people in. People turned away from a museum are not just lost customers: they’ve often spent hours getting to an unusual place, and may be so annoyed by the wasted trip that they won’t want to return, even if they have the opportunity to do so. In two of the cases above, I checked the website beforehand and that didn’t suffice, since the key information I needed wasn’t there or was buried. Yeah, I suppose I could call ahead before every museum visit, but I hate doing that. If someone wants to start CanIActuallyGetInToTheMuseum.com, it could be a fantastic way to not make any money.
Today I break Shtetl-Optimized‘s long radio silence with a relatively-exciting announcement: you remember my timeline of computer science history? Well, MIT students Jason Zhu and Ammar Ammar have now kindly created a website where you can vote on each of the entries, as well as new entries suggested by commenters. It’s pretty simple: you just register (by entering an email address, username, and password), then upvote each entry you like and downvote each entry you dislike (you can also abstain on any entry).
For reference, here are the 17 new contenders added by popular demand:
150BC Chinese text describes Gaussian elimination
499 Indian mathematician Aryabhata describes the “kuttaka” algorithm for solving Diophantine equations
1206 al-Jazari builds elaborate water clocks and musical automata
1801 The Jacquard loom uses punched cards to control textile manufacturing
1951 Wilkes, Wheeler, and Gill describe the concept of closed subroutines
1956 Stephen Kleene invents regular expressions
1962 The Atlas computer begins operation in Manchester
1962 Robert Gallager introduces low-density parity check codes
1968 First deployed packet-switching network
1969 Strassen’s algorithm for fast matrix multiplication
1969 Stephen Wiesner conceives of quantum money and multiplexing
1971 Vapnik and Chervonenkis introduce VC dimension
1982 PostScript
1992 The PCP Theorem
1999 SETI@home
2006 DaVinci surgical robot performs the first unaided operation
2007 Checkers solved
Update: A new feature has been added that lets you rank four randomly-selected entries—click “Done” on the bottom of the page to access it.
Update: You can now undo a vote by clicking twice on the same arrow.
On Wednesday, Larry Hardesty of the MIT News Office published a nice article about my work with Alex Arkhipov on the computational complexity of linear optics. Although the title—“The quantum singularity”—made me wince a little, I was impressed by the effort Larry put into getting the facts right, and especially laying out the problems that still need to be solved.
Less successful was a story in PC Magazine based on MIT’s press release, which contained the following sentence (let me know if you can decipher what the author meant—I couldn’t):
Aaronson says that he and Arkhipov have not successfully proven that designing a device capable of testing the theory is impossible—which is an important first step, whether to eventually building a quantum computer, or even just laying the initial framework for using the microscopic secrets of the universe to let humans better understand the world that surrounds them.
However, in the competition for Popular Science Article Sentence of the Year, the sentence above will have to contend with a now-classic sentence from the New York Times article about Watson:
More than anything, the contest was a vindication for the academic field of computer science, which began with great promise in the 1960s with the vision of creating a thinking machine and which became the laughingstock of Silicon Valley in the 1980s, when a series of heavily financed start-up companies went bankrupt.
To the NYT’s credit, they quickly posted a correction:
An article last Thursday about the I.B.M. computer Watson misidentified the academic field vindicated by Watson’s besting of two human opponents on “Jeopardy!” It is artificial intelligence — not computer science, a broader field that includes artificial intelligence.
Update (Feb. 14): Thanks so much to the many commenters who offered suggestions—I’ve implemented a large fraction of them! In addition to many clarifications and corrections of existing entries, I’ve added entries for:
Al-Khwarizmi
The slide rule
William Stanley Jevons’s “logic piano”
The Atanasoff-Berry computer
Claude Shannon’s cryptographic work
Reed-Solomon codes (replacing the Hamming code)
Solomonoff-Kolmogorov-Chaitin complexity
The 1ESS switching system
Semaphores
Viterbi’s algorithm
Simula 67
Back-propagation (now sharing an entry with the book “Perceptrons”)
The Solovay-Strassen primality test
Lempel-Ziv compression
PAC-learning
Microsoft Office
Global Positioning System
Slashdot (replacing the entry for the word “blog”)
CAPTCHAs
BitTorrent
Egypt’s “Twitter revolution”
The trouble is that I now have 165 entries, whereas I was told to deliver 150. So, after realizing the infeasibility of simply “choosing” items for deletion, the MIT150 folks and I reached a decision to set up a voting site for the top 150 entries, which should be available within a couple weeks. In the meantime, if you want to suggest even more entries, you can go ahead and do so … thanks!
This year, MIT is celebrating its 150th anniversary—and as part of the birthday festivities, I somehow got roped into creating a timeline of “150 major events in computer science history” (i.e., in the world, not MIT). I understand that the timeline will go up on a wall somewhere.
My first thought was that singling out the “most important events in CS history” was an exercise in futility, and not a particularly original one either. But then, as I spent weekends reading about Konrad Zuse, the UNIVAC, and the IBM 360, I started really getting into my assigned exercise in futility. Sure, there were great CS timelines already on the web—some of which I stole from shamelessly—but none of them had exactly the focus I was looking for. For example, the founding of a company didn’t strike me as a milestone in itself: the question was, what qualitatively new things did the company do? So I decided to take as a starting point the words and concepts that populate the mental landscape of CS: floating-point, compiler, graphics, network, bug. Which events were decisive in loosing these concepts upon the Earth? To clarify, I was just as interested in the demonstration, popularization, and commercialization of existing concepts as in the discovery of new ones: the release of Windows in 1985 brought few new ideas into the world, but it seems hard to argue that Windows hasn’t carved out its place on the mental map. But so, in my opinion, has the Time Hierarchy Theorem, even if only 0.01% as many people have heard of it.
I’m including my current draft list of 152 events below, so that Shtetl-Optimized readers can critique it, nitpick it, and tell me all about the important events I’ve left out and the events I’ve included that shouldn’t be there. I’ll carefully consider all of your suggestions, and will implement the ones that I like.
While you’re sharpening your nitpick-knives, though, let me explain the ground rules I decided to follow:
I adopted a strict policy against listing general trends (“word processing gains widespread acceptance”). To earn inclusion in the list, an event had to be something that happened at a particular time: for example, the release of a product, the publication of a book, or the beginning of a project. Of course, I often chose a specific event to illustrate a trend.
I also adopted a strict policy against arbitrary numerical milestones (“millionth website,” “first processor to break the 1GHz barrier”), since otherwise such milestones would proliferate endlessly.
Even though this was a list of events, I cared a great deal about representing people who played major roles in CS. When—as often happened—the same person was involved in too many significant events to list, I wasn’t shy about picking one or two events to highlight the person.
I wasn’t interested in external “recognition” bestowed on computers, such as TIME Magazine naming the computer its 1982 “Machine of the Year.” Nor was I interested in what you might call “internal housekeeping milestones”: the founding of the ACM or the first CS departments, the establishment of the Turing Award, etc. I felt that, if we’re going to engage in self-congratulation, then at least let it not be self-congratulation over self-congratulation!
Before we get to the list itself, let me give you a breakdown of number of milestones per time period:
From the data, it would appear that the level of intellectual excitement in computer science peaked in the 1960s, and has steadily declined ever since, except for a bump in the 1990s coinciding with the Internet boom. The past decade has been a particularly arid one, producing little of note besides Facebook, Wikipedia, YouTube, and the iPhone. If you don’t like that message—and I’m guessing that many of the MIT150 organizers won’t—then hey, don’t shoot the messenger! The biased, misleading, and unscientific data is what it is.
Without further ado:
300BC Euclid’s Elements describes nontrivial algorithms (for problems such as Greatest Common Divisor) that are still used today
150-100BC The Antikythera mechanism, an astronomical computer, is built in ancient Greece
825 Abu Abdallah Muhammad ibn Musa al-Khwarizmi writes “On the Calculation with Hindu Numerals,” the work primarily responsible for spreading decimal notation in the West. The word “algorithm” will be named for al-Khwarizmi
1622 William Oughtred invents the slide rule, which will remain in use until the 1970s
1642 Blaise Pascal builds an addition and subtraction machine
1669 Isaac Newton describes Newton’s method, an early numerical algorithm for finding roots of equations
1679 Gottfried Wilhelm Leibniz develops binary notation; Leibniz’s writings about a “Calculus Ratiocinator” are among the first to envision a general-purpose computer
1737 Jacques de Vaucanson builds a mechanical duck able to flap its wings, eat grain, and “defecate”
1770 Wolfgang von Kempelen unveils the Mechanical Turk, a “chess-playing automaton” secretly operated by a human. The hoax is only revealed 50 years later
1801 In his “Disquisitiones Arithmeticae,” Carl Friedrich Gauss discusses the computational complexity of factoring and primality testing
1837 Charles Babbage first describes plans for the Analytical Engine
1842 In her notes on the Analytical Engine, Ada Lovelace writes what’s generally considered the first computer program, to calculate Bernoulli numbers
1847 George Boole proposes Boolean logic
1869 William Stanley Jevons recasts Boole’s ideas in algebraic terms, and builds a wooden “logic piano” to construct the truth tables of small Boolean formulas
1879 Gottlob Frege publishes his “Begriffsschrift,” introducing first-order logic as a mathematically-precise language of thought
1890 Herman Hollerith builds the first electromechanical counting machine; the US government buys it to complete the census
1900 In a lecture to the International Congress of Mathematicians, David Hilbert asks for way to mechanize all of mathematical reasoning
1921 Czech author Karel Capek popularizes the term ‘robot’ in his play “R.U.R. (Rossum’s Universal Robots)”
1925 Vannevar Bush and colleagues create the first large-scale analog calculator at MIT
1931 Kurt Gödel publishes his Incompleteness Theorem; the system of “Gödel numbering” used in the proof foreshadows computer programming
1936 Alan Turing publishes “On computable numbers,” often considered the founding document of computer science; the paper gives an explicit construction of a universal Turing machine. Alonzo Church and Emil Post arrive at similar ideas independently
1936 Working alone in Germany, Konrad Zuse builds the Z1, the first working stored-program computer
1937 In his MIT master’s thesis—considered possibly the most influential master’s thesis in history—Claude Shannon proposes the application of Boolean algebra to electrical circuit design
1940 Building on earlier breakthroughs by Polish mathematician Marian Rejewski, Alan Turing builds an improved “Bombe” at Bletchley Park, to break the German Enigma code and help the Allies win WWII
1942 Isaac Asimov introduces his Three Laws of Robotics
1942 At Iowa State College, John Atanasoff and Clifford Berry successfully test a special-purpose vaccum-tube computer able to solve up to 29 simultaneous linear equations; Atanasoff will later spend decades in legal disputes to establish his computer’s priority over Eckert and Mauchly’s ENIAC
1943 Colossus, the world’s first programmable electronic computer, begins operation at Bletchley Park
1943 During the Manhattan Project, Richard Feynman and others pioneer large-scale scientific computing, using humans and later mechanical calculators
1943 In their paper “A Logical Calculus Immanent in Nervous Activity,” Warren McCulloch and Walter Pitts propose neural networks and finite automata
1944 The Mark I, designed by Howard Aiken, begins operations at Harvard
1945 In a 100-page “draft report on the EDVAC”, John von Neumann describes the architecture of a stored-program computer (henceforth called “von Neumann architecture”)
1945 Vannevar Bush publishes “As We May Think” in the Atlantic Monthly, a now-famous article that foresees a global information network based on hypertext
1946 At the University of Pennsylvania, J. Presper Eckert and John Mauchly complete the ENIAC
1946 In Los Alamos, Stanislaw Ulam develops the Monte Carlo method to speed up calculations of neutron diffusion in nuclear weapons
1947 At Bell Labs, John Bardeen, Walter Brattain, and William Shockley invent the transistor
1947 Operators of the Mark II computer trace an error to a moth trapped in a relay. The incident, popularized by Grace Murray Hopper, stimulates wider adoption of the terms “bug” and “debugging”
1947 George Dantzig proposes the simplex algorithm for linear programming
1948 In his landmark paper “A Mathematical Theory of Communication,” Claude Shannon first uses the word “bit,” attributing it to John Tukey
1948 Norbert Wiener publishes “Cybernetics: Or Control and Communication in the Animal and the Machine”
1949 The EDSAC, built by Maurice Wilkes, begins operations at Cambridge University
1949 Claude Shannon initiates the rigorous mathematical study of cryptography, publishing his proof that the one-time pad is unbreakable and that any unbreakable encryption system has the same basic properties
1950 Alan Turing proposes the Turing Test for artificial intelligence; four years later, Turing will commit suicide after being prosecuted for homosexuality
1950 CSIRAC, in Australia, becomes the first computer to play music
1951 J. Presper Eckert and John Mauchly release UNIVAC I, the first commercial electronic computer
1951 Grace Murray Hopper creates A-O, considered the first compiler
1951 MIT’s Whirlwind I computer goes online. Designed by Jay Forrester, Whirlwind features magnetic core memory and vacuum tubes that last 1000 times longer than those previously available
1952 Based on analysis of early returns, a UNIVAC computer borrowed by CBS News predicts that Dwight Eisenhower will defeat Adlai Stevenson in the presidential election
1954 Researchers at Birkbeck College perform the first demonstration of machine translation, with a rudimentary translation of English into French
1955 MIT’s Whirlwind I becomes the first computer to display graphics on a video console
1956 Dartmouth hosts the first conference on artificial intelligence, bringing the term AI into use
1956 In a letter to John von Neumann, Kurt Gödel first poses what will later become known as the P versus NP problem
1956 Edsger Dijkstra conceives his shortest-path algorithm, the basis for modern trip-planning software (Dijkstra also may have been the first person to list his profession as “programmer”)
1956 Noam Chomsky proposes the Chomsky Hierarchy, linking the theory of computing to formal languages
1956 MIT Lincoln Laboratories builds the TX-0, the first general-purpose computer to be built with transistors
1956 Reynold Johnson at IBM introduces the hard drive
1957 A team led by John Backus at IBM delivers a compiler for FORTRAN, the first high-level programming language
1958 John McCarthy proposes the LISP family of functional programming languages
1958 As part of the air-defense project SAGE, MIT Lincoln Labs links hundreds of radar stations in the first large-scale computer network
1958 Jack St. Kilby at Texas Instruments and Robert Noyce at Fairchild Semiconductor propose the integrated circuit
1959 In the seminal paper “Finite Automata and Their Decision Problems,” Dana Scott and Michael Rabin introduce the concept of nondeterminism into computer science
1960 Tony Hoare invents the Quicksort algorithm, while a visiting student at Moscow State University
1960 Irving Reed and Gustave Solomon give a systematic construction of error-correcting codes; later, Elwyn Berlekamp and James Massey will discover an efficient decoding procedure
1960 Ray Solomonoff proposes measuring the complexity of a string by the length of the shortest program that generates it; Andrey Kolmogorov and Gregory Chaitin will later arrive at similar ideas independently
1961 UNIMATE, the first industrial robot, begins work at General Motors
1961 A team led by MIT professor Fernando Corbato demonstrates the first computer time-sharing system
1961 A team led by MIT student Steve Russell creates Spacewar!, the first computer game
1962 While studying computer models of the weather, MIT professor Edward Lorentz discovers the phenomena that would later be popularized as “chaos theory”
1963 At MIT, Joseph Weizenbaum develops ELIZA, the now-famous program that simulates conversation between a Rogerian psychotherapist and a patient
1963 MIT graduate student Ivan Sutherland develops Sketchpad, the first Computer-Aided Design (CAD) software
1963 The first edition of ASCII (American Standard Code for Information Interchange) is published
1964 IBM releases the System/360, one of the first computers based on integrated circuits. Fred Brooks, the lead developer, later describes the lessons learned in his book “The Mythical Man-Month”
1964 At Dartmouth, John Kemeny and Thomas Kurtz create the BASIC programming language
1964 Seymour Cray releases the CDC 6600, the first of many record-breaking supercomputers
1964 American Airlines and IBM debut SABRE, the first computer-based travel reservation system
1965 AT&T debuts 1ESS, the first electronic telephone switching system, in Succasunna, New Jersey
1965 Intel cofounder Gordon Moore enunciates Moore’s Law, that the number of transistors per integrated circuit doubles roughly every two years
1965 At IBM, James Cooley and John Tukey rediscover and popularize the Fast Fourier Transform (versions of which were known to Gauss and others)
1965 Juris Hartmanis and Richard Stearns prove the existence of an infinite hierarchy of harder and harder computational problems
1965 MIT student Richard Greenblatt begins developing Mac Hack, the first computer chess program to succeed in tournament play. Mac Hack also defeats the AI skeptic Hubert Dreyfus, who had famously claimed that computers would never play high-quality chess
1965 Edsger Dijkstra introduces semaphores, which allow multiple concurrently-running programs to share the same resource
1966 Texas Instruments unveils the first electronic handheld calculator
1966 The first cash-dispensing ATM is installed in Tokyo
1967 At SRI, Douglas Engelbart and Bill English apply for a patent for the first computer mouse
1967 Andrew Viterbi invents the Viterbi algorithm for maximum-likelihood estimation in Hidden Markov Models; the algorithm will find major applications in speech recognition, bioinformatics, and both the CDMA and GSM cellular-phone standards
1967 In Norway, Ole-Johan Dahl and Kristen Nygaard develop Simula 67, considered the first object-oriented programming language and a major influence on Smalltalk and later C++
1968 Donald Knuth publishes Volume 1 of “The Art of Computer Programming”
1968 Edsger Dijkstra publishes his now-famous article “Go To Statement Considered Harmful,” igniting an acrimonious debate about programming practices
1968 The movie “2001: A Space Odyssey” introduces the world to HAL
1968 Work begins at MIT on Macsyma, the first computer algebra system
1969 Victor Scheinman builds the Stanford Arm, the first electronic computer-controlled robotic arm
1969 ARPAnet, the precursor of the Internet, links UCLA, SRI, Santa Barbara, and Utah (MIT joins in 1970)
1969 At Bell Labs, Ken Thompson and Dennis Ritchie create UNIX, and begin developing the C programming language
1969 Arthur Bryson and Yu-Chi Ho introduce back-propagation, a learning technique for neural networks that is largely ignored until the 1980s. Meanwhile, Marvin Minsky and Seymour Papert publish “Perceptrons,” a book that introduces important mathematical techniques into computer science, but has also been accused of “killing” neural-net research for more than a decade
1969 The Apollo Guidance Computer plays a crucial role in steering Neil Armstrong and Buzz Aldrin to the lunar surface
1970 John Horton Conway invents the Game of Life cellular automaton; it is estimated that millions of dollars of computer time are wasted watching Lifeforms evolve
1970 E. F. Codd proposes the relational database management system (RDBMS)
1970 Yuri Matiyasevich, building on work of Julia Robinson, Martin Davis, and Hilary Putnam, shows the nonexistence of an algorithm to solve Diophantine equations, negatively resolving Hilbert’s Tenth Problem and demonstrating Turing-universality in one of the oldest parts of mathematics
1971 Stephen Cook and Leonid Levin independently prove that the Satisfiability problem is NP-complete; a paper by Richard Karp a year later demonstrates the pervasiveness of the NP-completeness phenomenon
1971 IBM commercially releases the floppy disk
1971 Ray Tomlinson sends the first email message on ARPANET
1971 Bob Thomas at BBN Technologies creates the first experimental computer virus
1972 Atari releases Pong
1973 At Xerox PARC, Alan Kay and collaborators create the Alto, featuring the first graphical user interface (GUI) with windows, icons, and menus
1973 Robert Metcalfe at Xerox PARC creates Ethernet
1974 MIT professor Barbara Liskov and students begin work on CLU, a predecessor of modern object-oriented programming languages
1976 Kenneth Appel and Wolfgang Haken prove the Four-Color Map Theorem, the first major theorem to be proved using a computer
1975 Bill Gates and Paul Allen adapt BASIC to the MITS Altair microcomputer
1975 Inspired by work of Ralph Merkle, Stanford researchers Whitfield Diffie and Martin Hellman announce the first protocol for public key exchange (which had been discovered previously at the British GCHQ, but kept classified)
1975 Robert Kahn and Vint Cerf test the new TCP/IP protocol between Stanford and University College London
1975 At IBM, John Cocke advocates RISC processor architecture, and begins work on the 801 to implement it
1977 Ronald Rivest, Adi Shamir, and Leonard Adleman develop the public-key encryption system that they call RSA, and announce it via Martin Gardner’s Mathematical Games column in Scientific American
1977 Robert Solovay and Volker Strassen publish an efficient randomized algorithm for primality testing, demonstrating both the feasibility of RSA and the power of randomized algorithm; shortly afterward, Gary Miller and Michael Rabin find a more efficient such algorithm
1977 Steve Jobs and Steve Wozniak release the Apple II
1977 William Kahan puts forward a draft proposal for the IEEE floating-point standard
1977 In Israel, Abraham Lempel and Jacob Ziv propose the data compression algorithm that (after improvements by Terry Welch and others) becomes the basis for PKZIP and most other general-purpose compression software
1978 Intel releases the 8086, the first in the line of x86 processors
1978 Donald Knuth begins developing the TeX computer typesetting system, which will eventually become the lingua franca of science
1979 Dan Bricklin and Bob Frankston release VisiCalc, the first personal spreadsheet program and “killer app” for the Apple II
1980 Duke University graduate students Tom Truscott and Jim Ellis create Usenet
1981 Nintendo achieves its first video game success with Donkey Kong, designed by Shigeru Miyamoto
1981 The IBM PC is released, running Microsoft’s MS-DOS
1981 Richard Feynman points out the exponential difficulty of simulating quantum physics with a conventional computer, and speculates that a quantum-mechanical computer would do better; a few years later; David Deutsch will publish his construction of a universal quantum Turing machine
1982 Work on pseudorandom generators by Manuel Blum, Silvio Micali, Shafi Goldwasser, and Andy Yao begins the modern era of complexity-based cryptography, which will lead over the next decade to notions such as zero-knowledge, interactive proofs, and probabilistically checkable proofs
1982 Sony and Philips commercially release the compact disc
1982 Michael Fischer, Nancy Lynch, and Michael Paterson prove that it’s impossible to reach consensus in an asynchronous distributed system if there’s even a single faulty processor
1983 Bjarne Stroustrup at Bell Labs develops C++, which is to become the dominant object-oriented programming language
1984 With its iconic Super Bowl commercial, Apple announces the Macintosh, the first consumer machine with a mouse/windows interface
1984 Robert Axelrod publishes “The Evolution of Cooperation,” a classic book that uses computer experiments with the Iterated Prisoners’ Dilemma to shed light on human nature
1984 Leslie Valiant at Harvard proposes PAC (Probably Approximately Correct) learning, which becomes the central mathematical framework for machine learning, and helps to explain why Occam’s Razor “works”
1985 Microsoft releases Windows
1985 Richard Stallman publishes his GNU Manifesto, setting out the principles of the free-software movement
1986 Thinking Machines begins shipping the CM-1 Connection Machine, considered the first massively-parallel supercomputer
1988 While a graduate student at Cornell, Robert Morris creates a computer worm that cripples the Internet (though that wasn’t Morris’s intention)
1989 Mike Godwin formulates Godwin’s Law: “As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches 1”
1990 At CERN in Geneva, Switzerland, Tim Berners-Lee creates the World Wide Web
1990 The IP=PSPACE Theorem, proved by Carsten Lund, Lance Fortnow, Howard Karloff, Noam Nisan, and Adi Shamir, shows the unexpected power of interactive protocols and opens a new era in the theory of computing
1990 The discovery of boosting—a technique for combining the predictions of different learning algorithms—by Michael Kearns, Rob Schapire, and Yoav Freund, starts a revolution in the theory and practice of machine learning
1990 Microsoft releases its first Office application suite, consisting of Word, Excel, and PowerPoint
1991 At Los Alamos National Laboratory, Paul Ginsparg founds the arXiv, ushering in the era of rapid online dissemination of scientific research
1991 The Linux kernel is designed by Finnish student Linus Torvalds
1991 Phil Zimmermann releases Pretty Good Privacy (PGP), which makes “military-grade” public-key encryption easily available. After the Customs Service opens a criminal investigation, Zimmermann becomes an Internet folk hero
1993 A team headed by Marc Andreessen at the University of Illinois Urbana-Champaign releases NCSA Mosaic, the browser credited with popularizing the Web
1993 Joel Furr first uses the word “spam” to mean “excessive multiple postings” (in that case, to Usenet newsgroups)
1993 With 24 satellites in orbit, the Global Positioning System achieves “initial operational capability.” Originally designed by the US Department of Defense for military applications, GPS quickly finds numerous civilian uses including computerized car navigation
1994 Peter Shor proves that a quantum computer, if built, would be able to factor numbers efficiently, launching quantum computing as an active research field
1994 Thomas Nicely discovers the Pentium FDIV bug; the ensuing controversy and costly recall by Intel underscore the need for hardware verification
1995 Pixar releases Toy Story, the first feature film made entirely with computer-generated imagery
1995 Lee Zehrer launches Match.com, the first major online dating service
1995 Amazon.com is launched by Jeff Bezos and sells its first book
1995 The Institute for Genomic Research uses whole-genome shotgun sequencing—a technique dependent on massive computer power—to sequence the genome of the first free-living organism, the bacterium Haemophilus influenzae
1996 Stanford graduate students Larry Page and Sergey Brin begin developing Google
1997 IBM’s Deep Blue computer defeats human world champion Garry Kasparov
1997 Rob “Commander Taco” Malda founds Slashdot, which hosts freewheeling web-based conversations of the sort that would later be commonplace on blogs
1997 NASA’s Sojourner robotic rover moves semi-autonomously across the surface of Mars for 83 days, sending spectacular images back to Earth
1999 Widespread fear of the “Y2K millennium bug” underscores society’s dependence on legacy computer systems. Later, many will argue the fears were overblown
2000 The first major denial-of-service (DoS) attack is launched against CNN, Yahoo, and eBay
2000 Putting an unexpected practical twist on Alan Turing’s ideas from 1950, Manuel Blum, Luis von Ahn, and John Langford at Carnegie Mellon articulate the notion of CAPTCHAs (Completely Automated Public Turing tests to tell Computers and Humans Apart), the challenges—usually involving reading distorted text—that are used by numerous websites to discourage spam-bots
2001 Larry Sanger and Jimmy Wales launch Wikipedia
2001 Bram Cohen develops BitTorrent, the controversial peer-to-peer file sharing protocol now estimated to account for 27-55% of all Internet traffic
2001 In the wake of the 9/11 attacks, news websites continue running smoothly in part because of routing algorithms designed by Akamai Technologies. Meanwhile, former MIT student Danny Lewin, who cofounded Akamai with Professor Tom Leighton, is on American Airlines flight 11 when it crashes into the World Trade Center
2002 At IIT Kanpur, Manindra Agrawal and his students Neeraj Kayal and Nitin Saxena announce a deterministic polynomial-time algorithm for primality testing
2004 Harvard sophomore Mark Zuckerberg launches Thefacebook.com
2005 YouTube is launched, beginning an era of online video-sharing
2007 Apple releases the iPhone
2010 Some of Iran’s centrifuges for uranium enrichment are destroyed by the Stuxnet worm, in the first known large-scale cyberattack to target physical infrastructure
2011 Making essential use of Facebook and Twitter as organizing tools, protesters in Egypt force the resignation of President Hosni Mubarak after 30 years of rule
2011 IBM’s Watson computer defeats all-time human champions Ken Jennings and Brad Rutter on Jeopardy
Five years ago, not long after the founding of Shtetl-Optimized, I blogged about Alex Halderman: my best friend since seventh grade at Newtown Junior High School, now a famous security researcher and a computer science professor at the University of Michigan, and someone whose exploits seem to be worrying at least one government as much as Julian Assange’s.
In the past, Alex has demonstrated the futility of copy-protection schemes for music CDs, helped force the state of California to change its standards for electronic voting machines, and led a spectacular attack against an Internet voting pilot in Washington DC. But Alex’s latest project is probably his most important and politically-riskiest yet. Alex, Hari Prasad of India, and Rop Gonggrijp of the Netherlands demonstrated massive security problems with electronic voting machines in India (which are used by about 400 million people in each election, making them the most widely-used voting system on earth). As a result of this work, Hari was arrested in his home and jailed by the Indian authorities, who threatened not to release him until he revealed the source of the voting machine that he, Alex, and Rop had analyzed. After finally being released by a sympathetic judge, Hari flew to the United States, where he received the Electronic Frontier Foundation’s 2010 Pioneer Award. I had the honor of meeting Hari at MIT during his and Alex’s subsequent US lecture tour.
But the story continues. Earlier this week, after flying into India to give a talk at the International Conference on Information Systems Security (ICISS’2010) in Gandhinagar, Alex and Rop were detained at the New Delhi airport and threatened with deportation from India. No explanation was given, even though the story became front-page news in India. Finally, after refusing to board planes out of New Delhi without being given a reason in writing for their deportation, Alex and Rop were allowed to enter India, but only on the condition that they did so as “tourists.” In particular, they were banned from presenting their research on electronic voting machines, and the relevant conference session was cancelled.
To those in the Indian government responsible for the harassment of Alex Halderman and Rop Gonggrijp and (more seriously) the imprisonment of Hari Prasad: shame on you! And to Alex, Hari, and Rop: let the well-wishes of this blog be like a small, nerdy wind beneath your wings.
WARNING: This post makes (what turned out in retrospect to be) advanced use of sarcasm, irony, and absurdism. Indeed, even after I added a disclaimer explaining the sarcasm, many commenters still responded as if I actually favored gutting the National Science Foundation. (Unless, of course, those commenters were also being sarcastic—in which case, touche!)
The confusion is completely my fault. When I write a post, I have in my mind a reader who’s read this blog for a while, and knows that obviously I don’t favor gutting the fraction of a percentage of the Federal budget devoted to the progress of human understanding and American leadership thereof; obviously the NSF wastes plenty of money, but if it didn’t, then it would be doing a terrible job, because research is all about trying stuff that has a good chance of failure; obviously if you were seriously looking for waste, you could find orders of magnitude more of it in the military and elsewhere. So then the only remaining question is: how can we best have fun with a disgusting and contemptible situation? I forgot how many people come to this blog not having any idea who I am or why I’m writing—and for that, I sincerely apologize.
Now, if you’d like a sarcasm-detection challenge, I did leave lots of hints in the following post that I didn’t actually agree with Congressman Smith. See how many of them you can find!
As some of you may have heard, the incoming Republican majority in Congress has a new initiative called YouCut, which lets ordinary Americans like me propose government programs for termination. So imagine how excited I was to learn that YouCut’s first target—yes, its first target—was that notoriously bloated white elephant, the National Science Foundation. Admittedly, I’ve already tried to save NSF from some wasteful expenditures, in my occasional role as an NSF panel member. But this is my first chance to join in as a plain US citizen.
In a video explaining the new initiative, Congressman Adrian Smith concedes that the NSF supports “worthy research in the hard sciences,” but then gives two examples of NSF grants that strike him as wasteful: one involving collaboration among soccer players, the other involving modeling the sound of breaking objects. This article gives some more detail about the projects in question.
While I can’t wait to participate, I have a few questions before I start:
Exactly which sciences count as “hard”? Once the pitchforks are raised, how far do we go? Is math fair game? What about economics, cosmology, evolutionary biology?
Has there ever been a research project that couldn’t be described in such a way as to sound absurd? (“Even in the middle of a war, university academics in Chicago are spending taxpayer dollars in a quixotic attempt to smash teeny-tiny uranium atoms underneath a football field…”)
Years ago, several commenters on my and Lance’s blogs eloquently argued that science funding isn’t a traditional left vs. right issue, that Republicans are at least as friendly to science as Democrats, and that viewing the modern GOP as the “party of ignorance” is inaccurate, simplistic, and offensive. Would any of those commenters kindly help us understand what’s going on?
Let me end this post with a request: I want all of my readers to visit the YouCut page, and propose that quantum computing and theoretical computer science research be completely eliminated. Here’s my own CAREER Award; go ahead and cite it by number as a particularly egregious example of government waste.
See, I’m hungry for the honor (not to mention the free publicity) of seeing my own favorite research topics attacked on the floor of the House. As we all know, it’s child’s play to make fun of theoretical computer science: its abstruseness, its obvious irrelevance to national goals—however infinitesimal the cost is compared to (say) corn subsidies or defense contracts for stuff the military doesn’t want, however gargantuan the payoffs of such research have been in the past. So what are Reps. Eric Cantor and Adrian Smith waiting for? I dare them to do it!
Obviously, though, before the House Republicans end American participation in theoretical computer science, they’ll want to familiarize themselves with what our tiny little field actually is. To that end, let me humbly offer the links on the sidebar to the right as one place to get started.
Update (12/18): When a friend read this post, his first reaction was that the sarcasm would be lost on most readers. I didn’t believe him. See, I exist in a frame of reference wherein, when the mob shows up at your house with torches, you don’t argue with them. Instead you say: “Oh, so you’re the ones here to burn me? Then please, let’s get started! There’s plenty of flammable fat around my torso area. Do you prefer rare, medium, or well done?” That way, at least history will record you as having gone down with your middle finger proudly aloft, rather than cowering in a corner. However, it’s now obvious that my friend was right. So, for the literal-minded: I think reacting to our country’s debt crisis by looking for NSF grants to ridicule is a really terrible idea, for reasons that are so self-evident I’ll simply provide some blank space for you to fill them in yourself: _______________________________. And, having devoted my whole career to quantum computing and theoretical computer science research, I don’t wish to see them eliminated. On the other hand, if science in United States were going to be dismantled (which, despite the efforts of some politicians, I don’t think it will be), then I’d consider it an honor for theoretical computer science to be the first in the crosshairs.
Throughout the day, Dick Lipton’s blog has hosted a phenomenal discussion of Vinay Deolalikar’s attempted proof of P≠NP (of which a new draft appeared as this blog entry was going to press). As of this writing, the discussion seems to have led to the following two conclusions:
Deolalikar deserves our gratitude; he did a wonderful thing by bringing the TCS community together, in “Stone Soup” fashion, to talk about the P vs. NP problem, and also to stimulate public interest in this fascinating problem.
For those of you who just arrived from Mars, I’d recommend starting with a BBC News piece by Victoria Gill, which by the standards of articles about P vs. NP in major news outlets, bears an amazingly close relation to reality. Indeed, the only thing about the article that I disagreed with was the headline: “Million dollar maths puzzle sparks row.” It’s not a row, a spat, or even a squabble: at most it’s a friendly scientific disagreement among friends.
As many others have already said, and as the BBC News piece hints at, the clearest reason for skepticism is (basically) that Deolalikar hasn’t convincingly explained why his approach doesn’t also prove problems are hard that are already known to be easy. This is the simplest sanity check for any attempted proof of P≠NP: if you’re showing that an NP-complete problem like 3SAT is not in P, then your proof had better fail for related problems like 2SAT and XOR-SAT, which are known to be in P. Everyone agrees that, if Deolalikar can’t answer this objection, the proof is toast.Unfortunately, Deolalikar has responded to pointed questions about this issue with vague promises to address it in a later draft (together with worries that the manuscript is already too long!). This doesn’t inspire confidence: if one had really proved P≠NP, one should be able to explain immediately why the proof fails for XOR-SAT.This is far from the only problem with the writeup, but it’s a good example of the sort of basic question that Deolalikar needs to answer and hasn’t.
I feel incredible gratitude that Terry Tao, Timothy Gowers, Russell Impagliazzo, Avi Wigderson, Dick Lipton, Cris Moore, Ryan Williams, and other heavy-hitters of the math and CS worlds are hot on the case, and will quickly converge on what (if anything) is interesting and worthy of further study in Deolalikar’s writeup. What that means is that those of us trying to enjoy our “summer vacations” are free to debate other issues raised in the past few days—issues that don’t involve quite so much, y’know, actual thinking.And thus I’d like to propose a blog-roundtable about the following question:
Under what circumstances, if any, is it desirable to bet publicly on scientific questions?
The responses to my $200,000 offer made it obvious that people I like and respect have wildly different views on the above question.
On one side, Bayesians and economic rationalists of all stripes seemed ecstatic. The economist James Miller wrote:
I talk about prizes in the introductory microeconomics class I teach. I will definitely include what you have just done the next time I teach the course. If more scientists were willing to bet their beliefs we would know a lot more about the world than we currently do.
Several complexity theorists also wrote in privately to express their gratitude:
dear scott, have you heard? there is a P≠NP proof! what do you think of it? please let me know! just kidding. actually, this email is to thank you. my emailbox has been flooded with emails like the above lines, and thanks to your blog, i can now reply by mentioning your blog posting (the “I’ve literally bet my house on it” one—which nonetheless may be most remembered for being the only correct use of “literally” on the internet in the past 5-10 years).
On the other side, one distinguished colleague warned that my bet might hurt the image of theoretical computer science, by focusing attention on superficial snap-judgments rather than the technical evaluation of proofs. On this view, it’s my professional duty to make only scientific arguments in public: I should keep any personal guesses about a proof’s “probability of correctness” to myself. Sure, if I can pinpoint the fatal flaw in Deolalikar’s paper, I should say so. But if I can’t, I should just grin and bear it, even if journalists brush aside the experts’ boring, hard-to-explain technical reservations, and write article after cringe-inducing article exclaiming that “P≠NP HAS (APPARENTLY) BEEN PROVED!!!”
A different criticism—one that I confess took me by surprise—was that my $200,000 offer was “nasty” and “elitist,” something that eats disabled orphans for breakfast. On reflection, though, I think I understand where this was coming from. I felt like I was offering Deolalikar a damn sweet deal: he gets 200 grand if he’s right, and pays zilch if he’s wrong. However, the act of offering those odds might be interpreted as a perpetual “vote of no confidence” in Deolalikar’s personal ability to prove P≠NP.
By analogy, it would be reprehensible if I offered $200,000 to any member of a particular race or gender who proved P≠NP, with the implication being that I didn’t think that race or gender was up to the challenge. (And it would remain reprehensible, regardless of whether I eventually had to pay.) Of course, it’s relevant that that’s nothing like what I did: instead, spurred on by a barrage of emails, I spent a sleepless night with Deolalikar’s manuscript, weighed what I understood of his arguments on one hand and what I knew of the titanic obstacles to proving P≠NP on the other, and (may Merlin help me) cast a prediction accordingly.
Nevertheless, to deal with the “nastiness” issue, I’ve decided to clarify that my $200,000 offer remains in effect until January 1, 2019. That gives Deolalikar a couple more years to finish his current proof (plus more years for the journal refereeing and Clay prize processes), but it also makes clear that my bet is against a specific claim to have proved P≠NP, not against a person for all eternity.
(To answer the other question people kept asking me: no, my offer doesn’t extend to any potential P≠NP prover, much less to the other Clay Problems! I’m hopeful that, within my lifetime, theoretical computer science will have advanced to the point where statements like P≠NP can be proved, and I’ll of course be elated, but not so catatonic as to make giving up my house seem completely immaterial by comparison.)
So: is it the duty of a scientist to express, in public and as a scientist, only what he or she can articulate reasons for? Or is it sometimes appropriate or even desirable for scientists to go beyond what they can verbalize, using such mechanisms as bets? Now it’s your turn to weigh in! I’ll be following the discussion by iPhone during a road trip through northern Israel, to the enormous annoyance of my traveling companions.
Update (8/12): I was hoping for some enlightening discussion about the ethics of scientific betting in general, not more comments on the real or imagined motives behind my bet. However, the actual comments I woke up to have convinced me that the critics of my bet were right. In principle, the bet seemed like a good way to answer the flood of queries about Deolalikar’s paper, and then get back to enjoying my trip. In practice, however, the way people respond to the bet depends entirely on what they think about my motives. If you don’t care about my motives, or consider them benign, then the bet probably provided a useful piece of information or (if you already knew the information) a useful corrective to hype. If, on the other hand, you think I’m arrogant, a media whore, etc., then the bet served no purpose except to confirm your beliefs. Given the number of commenters on this blog who wish to ascribe the worst motives to me, it seems like the bet was counterproductive.PS. Arrogant I can see, but media whore? Really? Is it relevant that curious, well-meaning folks were pestering me to react to this announcement, that they clearly wouldn’t stop until I did, and that I was just trying to answer them while otherwise getting as little involved as I reasonably could?PPS. I’ve said this before, but let me say it again: I am unbelievably grateful to the “rapid response team” of mathematicians and computer scientists who dropped whatever else they were doing to delve into Deolalikar’s paper, and to report what they found on Lipton’s blog and elsewhere. Precisely because of their excellent work, there seemed to me to be little point in canceling my travel plans in order to try and duplicate their efforts.
I’m leaving tomorrow for a grand tour of Banff, then Israel, then Greece, then Princeton. Blogging may be even lighter than usual.
In the meantime, my friend Michael Vassar has asked me to advertise the 2010 Singularity Summit, to be held August 14-15 in San Francisco. Register now, because the summit is approaching so rapidly that meaningful extrapolation is all but impossible.
While I’m traveling, here’s a fun Singularity-related topic to discuss in the comments section: have you signed up to have your head (and possibly body) frozen in liquid nitrogen after you die, for possible Futurama-style resuscitation in the not-a-priori-impossible event that technology advances to the point where such things become possible? Whatever your answer, how do you defend yourself against the charge of irrationality?
If you like math, and you don’t yet have a Math Overflow account, stop reading this post now (not right now, but by the end of the sentence) and set one up, before returning here to finish reading the post. Math Overflow is the real deal: something that I’ve missed, dreamed about, and told my friends someone ought to set up for the last fifteen years, and that now finally actually exists. (It was founded by Berkeley grad students and postdocs Anton Geraschenko, David Brown, and Scott Morrison.) If you have a research-related math problem you can’t solve, you can post it there and there’s a nontrivial chance someone will solve it (or at least tell you something new), possibly within eleven minutes. If you’re an ambitious student looking for a problem to solve, you can go there and find one (or a hundred).
To take one example, here’s a terrific complexity question asked by Timothy Gowers, about a notion of “average-case NP-completeness” different from the usual notions (if you think he’s asking about a well-studied topic, read the question more carefully). I didn’t have a good answer, so I wrote a long, irrelevant non-answer summarizing what’s known about whether there are average-case NP-complete problems in the conventional sense.
But my real topic today is the sensitivity versus block-sensitivity problem, which I recently posted to MO in a disguised (and, dare I say, improved) form.
For non-Boolean-function-nerds, sensitivity vs. block-sensitivity is a frustrating and elusive combinatorial problem, first asked (as far as I know) by Noam Nisan and by Nisan-Szegedy around 1991. Here’s a lovely paper by Claire Kenyon and Samuel Kutin that gives background and motivation as well as partial results.
Briefly, let f:{0,1}n→{0,1} be a Boolean function, with n input bits and 1 output bit. Then given an input x=x1…xn to f, the sensitivity of x, or sx(f), is the number of bits of x that you can flip to change the value of f. The sensitivity of f is s(f) = maxx sx(f). Also, the block-sensitivity of an input x, or bsx(f), is the maximum number of disjoint sets of bits of x (called “blocks”) that you can flip to change the value of f, and the block sensitivity of f is bs(f) = maxx bsx(f). Clearly 1 ≤ s(f) ≤ bs(f) ≤ n for every non-constant Boolean function f. (bs(f) is at least s(f) since you could always just take each block to have size 1.)
To give some examples, the n-bit OR function satisfies s(OR)=bs(OR)=n, since the all-zeroes input is sensitive to flipping any of the n input bits. Likewise s(AND)=bs(AND)=n, since the all-ones input is sensitive to flipping any of the bits. Indeed, it’s not hard to see that s(f)=bs(f) for every monotone Boolean function f. For non-monotone Boolean functions, on the other hand, the block-sensitivity can be bigger. For example, consider the “sortedness function”, a 4-input Boolean function f that outputs 1 if the input is 0000, 0001, 0011, 0111, 1111, 1110, 1100, or 1000, and 0 otherwise. Then you can check that bs(f) is 3, whereas s(f) is only 2.
Here’s the question: What’s the largest possible gap between s(f) and bs(f)? Are they always polynomially related?
What makes this interesting is that block-sensitivity is known to be polynomially related to a huge number of other interesting complexity measures: the decision-tree complexity of f, the certificate complexity of f, the randomized query complexity of f, the quantum query complexity of f, the degree of f as a real polynomial, you name it. So if, as is conjectured, sensitivity and block-sensitivity are polynomially related, then sensitivity—arguably the most basic of all Boolean function complexity measures—ceases to be an outlier and joins a large and happy flock.
The largest known gap between sensitivity and block-sensitivity is quadratic, and is achieved by “Rubinstein’s function.” To define this function, assume for simplicity that n is an even perfect square, and arrange the input bits into a √n-by-√n square grid. Then we’ll set f(x)=1, if and only if there exists a row that has two consecutive 1’s and all other entries equal to 0. You can check that bs(f)=n/2 (for consider the all-zeroes input), whereas s(f)=2√n (the worst case is when every row contains exactly one 1).
It’s a reasonable guess that Rubinstein’s function gives pretty much the largest gap possible, and how hard could that possibly be to prove? Well, how hard could a white rabbit in front of a cave possibly be to kill?
I’ll confess to going on sensitivity versus block-sensitivity binges every couple of years since I first learned about this problem as an undergraduate at Cornell. The last binge occurred this weekend, triggered by the strange block-sensitivity properties of my counterexample to the GLN Conjecture. And that’s when it occurred to me to use the hyper-inter-network tools of Web 2.0, together with my power and influence here at Shtetl-Optimized, to unleash a new flood of activity on the problem. There are at least four factors that make this problem well-suited to a collaborative math project:
The statement can be understood by almost anyone. I could explain it to my parents.
It seems unlikely (though not impossible) that the solution will require any heavy-duty math. What seems needed, rather, is lots of creativity to come up with new ideas specific to the problem at hand, as well as diabolical examples of Boolean functions that refute those ideas.
Even though the problem has been around for 20 years, the relevant literature is very small (maybe half a dozen papers); it would take at most a day to learn everything known about the problem.
Despite 1-3, this is a real problem that a significant number of people would care about the answer to.
If you feel like you want a new angle on the problem—something that hasn’t already been explored to death, or even to serious injury—you can try my “geometric variant” of sensitivity vs. block sensitivity described on Math Overflow.
I’m calling this a “philomath project,” a term that pays tribute to the successful polymath projects popularized by (and carried out on) Timothy Gowers’ wonderful blog, but that avoids infringing on a registered trademark of GowersCorp.
So, here are the philomath project rules: do you have an idea about sensitivity vs. block sensitivity? Or a vague pseudo-idea? Or a proposal for an easier variant? Then post it here! Or go over to Math Overflow and post it there. Let’s see if a block of us acting in unison can flip this problem.
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