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(Main prize page: The Wolfram 2,3 Turing Machine Research Prize)“And although it will no doubt be very difficult to prove, it seems likely that this Turing machine will in the end turn out to be universal.”So I wrote on page 709 of A New Kind of Science (NKS).I had searched the computational universe for the simplest possible universal Turing machine. And I had found a candidate—that my intuition told me was likely to be universal. But I was not sure.And so as part of commemorating the fifth anniversary of A New Kind of Science on May 14 this year, we announced a $25,000 prize for determining whether or not that Turing machine is in fact universal.I had no idea how long it would take before the prize was won. A month? A year? A decade? A century? Perhaps the question was even formally undecidable (say from the usual axioms of mathematics).But today I am thrilled to be able to announce that after only five months the prize is won—and we have the answer: the Turing machine is in fact universal!Alex Smith—a 20-year-old undergraduate from Birmingham, UK—has produced a 40-page proof.I’m pleased that my intuition was correct. But more importantly, we now have another piece of evidence for the very general Principle of Computational Equivalence (PCE) that I introduced in A New Kind of Science.We are also at the end of a quest that has spanned more than half a century to find the very simplest universal Turing machine.Here it is. Involve only a finite number of “nonzero bits”—and that the Turing machine must “halt”.But the 2,3 Turing machine—like modern computers (or systems in nature)—doesn’t “halt”. And in Alex Smith’s construction the Turing machine “tape” (i.e., memory) must be filled with an infinite pattern of bits.But the key point is that the pattern of bits can be set up without doing universal computation. So that means that when we see universal computation, it’s really being done by the 2,3 machine, not somehow by the encoding we’re using.What Alex Smith needed to do to establish universality and win the prize was just to show that there’s some way of programming the 2,3 machine to do any computation. That it’s possible to make a “compiler” that compiles “code” for some known class of universal machines to code for the 2,3 machine.He did that. But his “compiler” doesn’t make terribly compact or efficient code. In fact, for anything but the simplest cases, the code tends to be astronomically large and horrendously inefficient.But that isn’t the point here. The point is one of principle: the 2,3 Turing machine is universal.No doubt it’ll be possible to find much better compilers, that make much better code.And that’ll be interesting. Perhaps one day there’ll even be practical molecular computers built from this very 2,3 Turing machine.With tapes a bit like RNA strands, and heads moving up and down like ribosomes.When we think of nanoscale computers, we usually imagine carefully engineering them to mimic the architecture of the computers

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No. 1393)" (1936) by Reichsdruckerei Berlin (1879 - 1949)Museum for Communication Frankfurt, Museum Foundation Post and TelecommunicationThe encryption process involved code tables as well as the Enigma machine. At the start of every radio message, the starting position of the rotors would be sent (the message key) and the basic setting of the rotors and plugs confirmed (key identification). This information was encrypted manually using tables.Enigma I rotor cipher machine with 3 rotors, in a box made of high-density plywood (1941 - 1945) by Ertel-Werk für Feinmechanik (1921 - 1984)Museum for Communication Frankfurt, Museum Foundation Post and TelecommunicationThe Enigma machine was believed to be unbreakable because of its 100 quadrillion combinations. During the Second World War, the German armed forces had complete faith in the ingenious design of the Enigma machine—even though some of the enemy's unexplained successes should have given rise to doubt.Photograph of Henryk Zygalski, Jerzy Różycki, and Marian Rejewski, mathematicians at the University of Poznan (1932)Museum for Communication Frankfurt, Museum Foundation Post and TelecommunicationEncryption by Enigma had certain weaknesses, including that a letter was never encrypted to itself. That made it possible to guess the position of expected words in the text, and that was how Polish mathematicians were able to decrypt Enigma messages. In 1932, Henryk Zygalski, Jerzy Różycki, and Marian Rejewski succeeded in working out a formula for Enigma's encryption code and reconstructing the wiring of the rotors.Notes by Alan Turing on breaking the Enigma code (1939 - 1942) by Alan Mathison Turing (1912 - 1954)Museum for Communication Frankfurt, Museum Foundation Post and TelecommunicationBritish citizen Alan Turing (1912–54) was an outstanding mathematician and computing pioneer. From 1938, he worked for the GC&CS secret service, which had set up a decryption "factory" at Bletchley Park.Notes by Alan Turing on breaking the Enigma code (1939 - 1942) by Alan Mathison Turing (1912 - 1954)Museum for Communication Frankfurt, Museum Foundation Post and TelecommunicationAt Bletchley Park, Turing developed mathematical models for decrypting Enigma messages. His Turing Bombe automated the decryption process so that the time required was reduced to just a few hours.Enigma M4 rotor cipher machine with 4. Portable Apps; More Home Free Trials Misc. Categories Educational Tools Uber Turing Machine. Uber Turing Machine Download Uber Turing Machine Download. Portable Apps; More Home Free Trials Misc. Categories Educational Tools Uber Turing Machine. Uber Turing Machine Download Uber Turing Machine Download.

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At Go (link resides outside ibm.com).Though these models might represent breakthroughs in artificial superintelligence, they have not achieved artificial "general" intelligence, as such AI systems cannot autonomously learn new tasks or expand their problem-solving capabilities beyond their narrowly defined scope.Furthermore, it’s worth noting that superintelligence is not a prerequisite of AGI. In theory, an AI system that demonstrates consciousness and an intelligence level comparable to that of an average, unremarkable human being would represent both AGI and strong AI—but not artificial superintelligence. Existing definitions of artificial general intelligence There is no consensus among experts regarding what exactly should qualify as AGI, though plenty of definitions have been proposed throughout the history of computer science. These definitions generally focus on the abstract notion of machine intelligence, rather than the specific algorithms or machine learning models that should be used to achieve it.In 2023, a Google Deepmind paper (link resides outside ibm.com) surveyed existing academic literature and identified several categories of frameworks for defining artificial general intelligence:The Turing Test: Machines that can convincingly act like humansStrong AI: Systems possessing consciousnessAnalogies to the human brainHuman-level performance on cognitive tasksAbility to learn new tasksEconomically valuable workFlexible and general capabilities“Artificial Capable Intelligence” (ACI) The Turing Test Alan Turing, a seminal figure in the history of theoretical computer science, published one of the earliest and most influential definitions of machine intelligence in his 1950 paper, “Computer Machinery and Intelligence.” The core of his argument was that intelligence can be defined by behavior, rather than mystical philosophical qualities. Acknowledging the difficulty of pinning down firm definitions of concepts such as machines and thinking, Turing proposed a simple way around the problem based on a party game called the Imitation Game.The “Turing Test” is simple: a human observer must read text samples and determine whether they were generated by a human or by a machine. Turing proposed that if a human cannot distinguish between the program’s output and another human’s output, the program can be said to demonstrate human-like intelligence.Criticisms of the Turing Test Despite its monumental influence, computer scientists today do not consider the Turing Test to be an adequate measure of AGI. Rather than demonstrate the ability of machines to think, the test often simply highlights how easy humans are to fool.For instance, in 1966 Joseph Weizelbaum created a chatbot program called ELIZA that applied simple rules to transform the human language of a user’s input And his work blazed a trail for modern computers as we know them today. Turing introduced the concept of a universal machine, also known as a Turing machine, that could perform thousands of calculations based on predetermine rules/instructions. Also, Turing is credited with helping the Allies to defeat the Nazis in World Word II, when he helped to decode the German Enigma code.Fun Fact: Turing developed a test for artificial intelligence, known as the Turing Test, which evaluates whether or not a machine can trick a human into thinking it is human as well. Famous Mathematicians in History #13: Shakuntala Devi 13.) Shakuntala Devi (1929 - 2013 AD)Devi, an Indian mathematician and mental calculator, is known as the Human Computer. She belongs on our list of famous mathematicians due to her incredible mental math abilities, which have earned her a place in the Guinness Book of World Records!Fun Fact: Known for being able to perform incredibly complex mathematical calculations mentally in mere seconds, Devi famously multiplied two randomly chosen 13-digit numbers in her head in under 30 seconds, which was a world record in 1982. Famous Mathematicians #14: Grigori Perelman 14.) Grigori Perelman (1966 - Present)Perelman, an accomplished Russian mathematician, is famous for solving the Poincaré conjecture, which was one of the 7 Millennium Prize Problems in 2002. The conjecture essentially states that any finite 3D space that has no boundary is the topical equivalent of a 3D sphere.Fun Fact: After Perelman’s solution to the Poincaré conjecture was confirmed in 2002, he was awarded a one million dollar prize in addition to the prestigious Fields Medal. However, he declined to accept either award stating that he did not care about money or fame. Maryam Mirzakhani 15.) Maryam Mirzakhani (1977 - 2017 AD)Mirzakhani, an decorated and celebrated Iranian mathematician, is the first and only woman to ever win the prestigious Fields Medal for her work in mathematics, namely in the fields of Riemann surfaces and hyperbolic geometry.Fun Fact: Mirzakhani becoming the first female to win the Fields Medal in 2014 was no small feat, as the award is often considered the

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Rotors, Navy version (1944) by Olympia Büromaschinenwerke AG (1936 - 1950)Museum for Communication Frankfurt, Museum Foundation Post and TelecommunicationAfter February 1942, the German Navy began to use an improved version of Enigma with 4 rotors instead of 3. This was not broken by the Allies until December 1942. That decryption success led to the Allies' victory in the U-boat war and had a decisive impact on the outcome of the Second World War.Photograph of a Turing Bombe at Bletchley Park (1944)Museum for Communication Frankfurt, Museum Foundation Post and TelecommunicationThe Turing Bombe was used to work out the basic Enigma settings for that day—the sequence of the rotors and their starting positions. Each bombe had 108 rotors, replicating 36 Enigma machines.Photograph of a row of Turing Bombes at Bletchley Park (1944)Museum for Communication Frankfurt, Museum Foundation Post and TelecommunicationBy using a word that was likely to be included in the radio message, the Turing Bombe would try out all the possible settings in succession, at a rate of 60 rotations per minute. This process would often take just 2 hours.Decrypted Enigma message from the Supreme Commander of the Wehrmacht to the surrounded Courland Army Group (12. Feb 45) by Oberkommando der WehrmachtMuseum for Communication Frankfurt, Museum Foundation Post and TelecommunicationListening posts all over the UK were intercepting all German radio traffic. Intercepted messages such as this one were sent to Bletchley Park by teleprinter. The decrypted messages were checked at Bletchley Park for valuable information—such as this message from the Supreme Commander of the Wehrmacht to the surrounded Courland Army Group on February 12, 1945.T 52b telegraphic cipher machine, given the code name "Sturgeon" by the Allies (1941 - 1942) by Siemens & Halske AG (1897 - 1966)Museum for Communication Frankfurt, Museum Foundation Post and TelecommunicationDuring the Second World War, this cipher machine was used at command level in the German Kriegsmarine and Luftwaffe. The T52b encrypted the 5-bit Baudot teleprinter code.The 10 rotors were advanced irregularly and generated pseudo-random digits which were substituted for the plain text. A scrambler would then mix up the 5 encrypted bits.T 52b telegraphic cipher. Portable Apps; More Home Free Trials Misc. Categories Educational Tools Uber Turing Machine. Uber Turing Machine Download Uber Turing Machine Download. Portable Apps; More Home Free Trials Misc. Categories Educational Tools Uber Turing Machine. Uber Turing Machine Download Uber Turing Machine Download.

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Just two states and three colors. And able to do any computation that can be done.We’ve come a long way since Alan Turing’s original 1936 universal Turing machine—taking four pages of dense notation to describe.There were some simpler universal Turing machines constructed in the mid-1900s—the record being a 7-state, 4-color machine from 1962.That record stood for 40 years—until in 2002 I gave a 2,5 universal machine in A New Kind of Science.We know that no 2,2 machine can be universal. So the simplest possibility is 2,3.And from searching the 2,985,984 possible 2,3 machines, I found a candidate. Which as of today we know actually is universal.From our everyday experience with computers, this seems pretty surprising. After all, we’re used to computers whose CPUs have been carefully engineered, with millions of gates.It seems bizarre that we should be able to achieve universal computation with a machine as simple as the one above—that we can find just by doing a little searching in the space of possible machines.But that’s the new intuition that we get from NKS. That in the computational universe, phenomena like universality are actually quite common—even among systems with very simple rules.It’s just that in our normal efforts of engineering, we’ve been too constrained to see with such things.From all my investigation of the computational universe, I came up with the very general principle that I call the Principle of Computational Equivalence.What it says is essentially this: that when one sees behavior that isn’t obviously simple, it’ll essentially always