John von Neumann: 20th Century Mathematician & Physicist PDF

**John von Neumann** - **A 20th Century mathematician & physicist** considered the **last representative of pure and applied mathematics.** - He did considerable contributions to the following: \- Mathematics \- Functional Analysis \- Topology \- Statistics \- Quan...

**John von Neumann** - **A 20th Century mathematician & physicist** considered the **last representative of pure and applied mathematics.** - He did considerable contributions to the following: \- Mathematics \- Functional Analysis \- Topology \- Statistics \- Quantum Mechanics \- Hydrodynamics \- Nuclear Physics \- The first Atomic Bomb; the Manhattan Project in WW2 \- Game Theory \- Self-Replicating Machines \- Stochastic Computing - He also published 150 books; 120 of those are Mathematics, 20 being Physics, and the remaining are a mixture of non-Mathematics, and Special Mathematical Subjects. - Born on December 28th, 1903, in Budapest, Hungary which was a part of Austria-Hungary at that time. - He was given a nickname of Neumann Janos Lajos, and was born to a wealthy, acculturated, and observant Jewish family. - In **1921**, John von Neumann published two papers, the second paper being about Ordinal Numbers that we used today. - University of Berlin and University of Budapest - Places where Von Neumann studied. - The Axiomatization of Cantor\'s Set Theory - John von Neumann\'s PhD Thesis, and he received a Degree in - In 1927, Von Neumann published twelve Mathematics papers. In the end of 1929, he published thirty-two papers. Chemical Engineering from ETH Zurich in **1926**. - Axiom of Regularity - Every non-empty Set A contains an element that is disjoined from A. - Notion of Class - A class of Sets that can be unambiguously defined by a property that all its members shared. - Russell\'s Paradox - Let A set R be defined as X, such that X does not belong to itself, then the R belongs to itself if and only if R does not belong to itself. - Von Neumann\'s Game Theory & Mini Max Theorem - In zero-sum games with perfect information, there exists a pair of strategies for both players to minimize their maximum losses. He displayed maxes as equal in absolute value and contraries by sign. He later expanded the Game Theory lacking perfect information and account games with more than two players. - 1932 Ergodic Theory - A study of invariant measures in dynamical systems. An invariant measure being a measure is preserved by a function. - Mathematical Foundations of Quantum Mechanics - Published in 1932 by Neumann, it is the first work to establish a mathematical framework for Quantum, which are coined as Dirac-Von Neumann Axioms. - Theory of Games and Economic Behavior - Authored by Von Neumann and Oscar Morgenstern in 1942, It is declared that economic theory needed to use functional analysis rather than traditional differential calculus, emphasizing use of differential topology. - When Alan Turing visited Princeton in 1930s, him and Von Neumann worked on the Philosophy of Artificial Intelligence. And in 1943, Von Neumann wrote a 23-page sorting program for Electronic Discrete Variable Automatic Computer (EDVAC). - Merge Sort Algorithm - The first and second halves of an array are sorted recursively and then merged. - Simulation Theory - Von Neumann developed simulations on his digital computers for hydrodynamic computations when working on the Hydrogen Bomb. This ended up him contributing heavily to the Monte Carlo Method. - Monte Carlo Method - A method used for solving complicated problems to be approximated using random numbers. - Middle Square Method - A pseudo-random generator which was criticized as crude, but Von Neumann knew it already as he justified it being faster than any available method at the time. - Self-Replicating Automata - By creating a field of cellular automata using pencil and a graph paper, Von Neumann constructed the first self-replicating automata. This was later used in 1949 to create the world\'s first computer virus. - Stochastic Computing - Introduced in 1953 by Von Neumann, it is a collection of techniques that represent continuous values by streams of random bits, reducing complex computations to simple bitwise operations of streams. - Climate Modeling Software - Written by Von Neumann in 1946, it is the first climate modeling software. This was used to perform numerical weather forecasts. - Numerical Integration of the Barotropic Vorticity Equation - Published by Von Neumann in 1950 - The Manhattan Project - Started in 1930s where Von Neumann contributed to develop the world\'s first nuclear weapons. One of the bombs known as \"Fat Man\" developed in this project was later dropped in Nagasaki, Japan. - Codename Trinity - An atomic bomb test site where Von Neumann witnessed the first atom bomb explosion. - Mutually Assured Destruction (MAD) - In the height of Cold War, weapons like these were common. If a nation used this weapon, and the other retaliated with one of their own, both sides would be destroyed. - Intercontinental Ballistic Missile (ICBM) - A missile that can fly for hundreds of miles and cause devastating damage upon impact. A common weapon in the Cold War for the two superpowers. - Marietta Kövesi - Von Neumann\'s wife in 1930 to 1937, she studied at University of Budapest, and later became a professor. She and Von Neumann had a daughter named Marina in 1935. They later divorced on November 2nd, 1937 - Klára Dán - Von Neumann\'s second wife in 1937. She was a mathematician, self-taught engineer, and computer scientist. She also made significant contributions to Monte Carlo Method, ENIAC, and MANIAC - John von Neumann\'s Death - In 1955, Von Neumann was diagnosed with cancer. He later died on February 8th, 1957 at Walter Reed Academy Medical Hospital, and was buried at Princeton Cemetery. - it all Started with the **Victorians**, At the very pin of the British empire but the industrial revolution the - Machine age relied on men called computers men who did math\'s with a Pencil - trouble was these men with pencils made Mistakes , get rid of human error the men With pencils needed to be replaced with something more reliable what was needed Was a mechanical brain but to come up with the goods it took a Man with a Pencil **Charles Babbage** - son of a wealthy banker - was Lucian professor of mathematics at Cambridge university - fellow of the royal society - Respected economist and amate playwright the archetypal polymath - he died 130 years ago (153 now 2024) - he was uncelebrated and unloved no one came to his funeral - Babbage was a man who mingled with the glitterati of the Victorian intelligencia - in death he was abandoned by all but his closest relatives - this was a man who once baked himself in an oven at 265°for exactly 4 minutes to find out what would happen then when he cooled down - he invented the Greenwich time signal **what he did:** - one afternoon for fun he went to the London borough of Maryland and encountered all the broken windowpanes - There were 462 and then he drew up a chart detailing the precise cause and type of every single break. - One day he was lowered onto Mount Venus because he wanted to know how hot lava was. - Charles Babbage was a complete junkie, obsessed with order, with tabulation, with math. Every part of his life was needed to put in neat, ordered structure. **inventions:** - What Babbage needed was a machine and he eventually built to fuel his thirst for order, he called his \"difference engine\" it was what we today might call a computer. - his Victorian audience called it a \"miracle\" - Babbage had only built a demonstration piece, a working model of **the difference engine** if he was to complete the project he needed backers. - Charles invention was almost capable of thought. Machine that could change the world in the mid-1800s the British empire. - Marvelous machine offered an end to human error the difference engine would calculate and print out the vital tables eliminating mistakes all the way through the process - Babbage was given 177,000 pounds and that\'s what it would have cost back then to buy two warships, we were at the height of his career **why he wasn\'t able to build the difference engine?** 1. he fell out with the one man in the country capable of making the machine his engineer **\'Joseph Clement\'** 2. next he changed his mind about the design and started from scratch and called it **\"difference engine 2\"** 3. **he ran out of money** **After:** - in 1991 to mark the bent tannery of Babbage\'s birth engineers at the science museum did build the \'cogwheel brain\' and it did work - machine\'s accuracy was down to what Babbage called the unerring certainty of mechanism the idea was that the position of the cog unlike a thought cannot be misinterpreted - The difference engine - ballistic equations they made gunnery tables and calculated where it was going to land. - If Babbage had done it in the 1850\'s the first war would have lasted 25 mins. **other inventions** - Babbage recognized the need for even more powerful machines and continued designing mechanical computers - He came up with an 'analytical engine\' worked almost the same with modern electronic computer but it remained on paper because no one took him seriously. - he gave so much to the world (theater colored lighting, railways with 2 different types of cowcatchers, no brass brain so the chance of a Victorian Information age was extinguished) **WAR** - **Adolf Hitler** who ensured that a computer was needed like never before - **1940 Europe\'s Under the Nazi** jack boot stouthearted east end folk Britain in big trouble defend our island - **they needed to spy to prevent a German evict** - **staying one step ahead of Hitler by listening in to Wireless communications** - for a math Machine a machine that could make sense of all the coded nonsense Alan Turing - **a brilliant young mathematician** - during the way he and his friends were military code breakers - their first success was cracking the German enigma code that meant the opts were defeated and that vital allied shipping was safe once more - who was responsible for cracking the **enigma code** **the Loren\'s cipher** - was the holy grail the almost impenetrable code used by the German high command and Hitler. - now it is simply a mathematical problem - 1930s Turing had proved that something called a \'universal machine\' could solve any mathematical problem on the planet **COLOSSUS** - the world\'s First programmable electronic computer - key to unlock Loren\'s cipher **Tommy Flowers** - was a post office engineer - flowers had been working on automatic telephone exchanges - he needed massive collection of Switches tommy was uniquely placed to offer a groundbreaking solution to the Loren\'s problem - he was working with Max Newman Turing\'s old tutor at Cambridge - Flowers and Newman believed that Turing\'s universal machine has the chance of life - cut all that was needed was the green light from military Intelligence **HOW WILL IT WORK?** - two data streams need to be synchronized - running two teleprinter tapes in perfect time together - new machine will have is the capability of memorizing one particular stream - making the need for synchronized paper tapes a thing of the past - tommy brought new technology to the party tommy brought the \'valve\' - valves work perfectly well so long as you don\'t turn them off - The military didn\'t approve of how long it would take, because they believed that in less than a year the war would be over. but tommy still built the machine using his own money (1000 pounds) **THE MAKING OF COLOSSUS** - his team at the GOP\'s research facility at Dolli\'s hill worked around the clock - it took 10 months to make the machine - it worked with 800 valves glowing reliably - it had taken months to decipher a German message by which time it was out of date colossus could crack the toughest highest level German cipher in hours and sometimes minutes - the top brass was so impressed they immediately ordered 10 - a math machine it used mathematics to break Loren Cipher - world war ii was shortened by at least a year because of the work done at Bletchley Park and Tommy\'s computer Colossus was at the very heart of that work **AFTER THE WAR** - Colossus was dismantled and parts were returned to GOPO stores but 2 of them went permanently to spying community in Cheltenham. - rumored that they were used to crack soviet ciphers during the cold war - that one colossus still exists deep in the bowels of GCHQ - Colossus machines one thing is certainly true subject to a 50-year rule and bound by the official secrets act officially they didn\'t exist. **WHAT HAPPENED TO TURING?** - he was convicted of homosexuality - he was stripped of his security clearance and ostracized by the intelligence community - he committed suicide in 1954 - father of the modern computer - there are seven Academic institutions and even a ring road named after him **THE REAL HERO TOMMY FLOWERS** - He brought Turing\'s idea to life. - he shortened the war - he went back to working on the Telephone exchange trying to get funding but couldn\'t because they don\'t know what he already had done for the country - he was awarded 1000 pounds - Tommy kept his mouth shut about colossus **AMERICANS** - **Thomas Watson confidently predicted the world will probably eventually need five Computers** **SILICON CHIP** - in 1958 gave birth to switch nana the silicon Chip - this chip the brain from a modern pc - tommy flowers could have got his 2,000 switches the entire colossus machine on this silicon chip - silver strip in the middle there has 100 million switches that\'s 50,000 Colossus **GROOVY CALIFORNIANS** - in the early 70s the xerox corporation founded the \'poo alto research center just outside San Francisco the coolest hippiest Scientists on the planet - paperless office - a screen with icons accessed by mice - floppy discs - laser printer - laptops - emails - the web - Computers - The average British home contains about a 100 so instead of there being five Computers - are over 17 million in the UK alone - we\'ve reached the point where there are plenty of things we simply couldn\'t do without computers - euro fighter's onboard computer makes hundreds of tiny alterations a second to the aircraft\'s control surfaces - -1999 NASA\'s mars climate Orbiter was programmed using both metric and imperial units so after 10 long months getting to mars the system got confused by inches here and cm there the \$125 million space probe plowed into the ground which it thought was somewhere else. **ROBOTS** - in computers that run robots would Require at least a modicum of intelligence - very credible scientists out there are pushing ai as the next big thing - to find out whether a computer was intelligent or not Turing devised a test it was very simple he said that if you can have a conversation with it in 1950 Turing predicted that within 100 years we\'d be able to have a conversation like that on any subject with a machine however there are those who say we can do it now 50 years early - Ella the machine but couldn\'t uphold a conversation - Electric Dogs of London that can play football - Doctor Hu (trains the dog) against Matthew Dave and Bo - From Essex university the Essex rovers - robot world cup robo cup - they make their own decisions the idea behind robo cup is that by 2050 a team of robots will be able to beat the human world cup champions already two-legged robots are being developed ready for the challenge and many are said to be cleverer than their human counterparts **KEVIN WARWICK** - one of the ai community\'s leading lights his cyborg comes complete with radar in its nose and an infrared top lip basic instinct programmed to make basic decisions based on that sensory information - **dolphin's chimps** - **50 to 100 brain cell area** - we do have this this the power supply they don\'t have their own batteries they have a basic instinct to go and look for some power somewhere - he went to hospital and had a plug socket surgically implanted in his wrist - best bits of the human brain the best bits of the machine brain link them together give humans extra abilities by linking directly with a machine - electrical plug with 100 points on it that was fired into my nervous system and then that was connected to this hand yeah via we connected via the computer to this hand - fingertip sensors on - thoughts on computer ai we can always turn it off they\'re individual they can\'t protect themselves But think of the internet can you switch the internet off - Within the next 20 years at most that we\'re going to have dangers with it - Clearly for autonomous fighting machines - in the next 20 years the military having machines - Kevin is talking about is this tanks and planes with no one in them just doing their own thing **ELECTROMAGNETIC PULSE** - **if an emp device was exploded here 300m above us anything containing a silicon chip would stop working Europe would in effect be switched off** - England there\'s a secret facility where the emp death ray can be summoned up at the flick of a switch - you can switch the computer back on but there\'s no point it\'s gone mad **Central Processing Unit** - \"brains\" of the computer**.** - Its function is to execute programs that are stored in memory. **All computers can be summarized with just two basic components:** - Primary storage or memory - A central processing unit or CPU. **Control Unit (CU)** - The control unit is also responsible for fetching instructions from the main memory and decoding the instruction. **Arithmetic-Logic Unit (ALU)** - Performs arithmetic operations such as addition and subtraction as well as logical operations such as AND, OR and NOT. **Registers -** smallest units of memory and are located internally within the CPU. Two basic functions: 1. **User-visible registers**: these enable machine/assembly language programs to minimize main memory references by optimizing use of registers. 2. **Control and Status registers:** used by the control unit to control the operation of the CPU and by privileged, operating system programs to control the execution of programs. **Accumulator (AC, DR)** - The contents can be used by the arithmetic-logic unit for arithmetic and logic operations, and by the memory buffer register. **Instruction Register (IR)** - This instruction is now ready to be executed and is accessed by the control unit. **Memory Address Register (MAR)** - This register specifies the address in memory where information can be found and can be also used to point to a memory location where information is to be stored. **Memory Buffer Register (MBR)** - The main purpose of this register is to act as an interface between the central processing unit and memory. **Program Counter (PC)** - The contents of the program counter are copied to the memory address register before an instruction is fetched from memory. **Program Status Word (PSW)** - This register encapsulates key information used by the CPU to record exceptional conditions. **Memory** - Memory is made up of a series of zero\'s (0) and one\'s (1) called bits or binary. **Input Devices** - Accepts outside information - Converts it into digital signals suitable for computation by the CPU **Output Devices** - Communicates data stored in memory or processed data, to the outside world - May be in various forms such as a computer Monitor or a Hardcopy **Bus Interconnection** - A bus is a communication pathway connecting two or more devices **Bus Structure** - Each line is assigned to a particular function **Three functional groupings** 1. **Data lines** - Provides a path for moving data between system modules 2. **Address lines** - Used to designate the source or destination of the data on the data bus 3. **Control lines** - Used to control the access to and the use of data and address lines **Fetch Cycle** to start off the fetch cycle, the address, which is stored in the program counter (PC), is transferred to the memory address register (MAR). The CPU then transfers the instruction located at the address stored in the mar to the memory buffer register (MBR) via the data lines connecting the CPU to memory. The control unit (CU) coordinates this transfer from memory to CPU. To finish the cycle, the newly fetched instruction is transferred to the instruction register (IR) and unless told otherwise, the cu increments the pc to point to the next address location in memory. A screenshot of a computer program Description automatically generated After the CPU has finished fetching an instruction, the CU checks the contents of the IR and determines which type of execution is to be carried out next. This process is known as the decoding phase. The instructions are now ready for the execution cycle. **Execute Cycle** - can comprise some complex operations  **Interrupt Cycle** - An interrupt can be described as a mechanism in which an I/O module etc. can break the normal sequential control of the central processing unit (CPU). - When central processing units (CPU\'s) were first developed they processed the first instruction before starting the second. - Modern processors, on the other hand, have developed what are called pipelines. - **Pipelines** are the most common implementation technique in a CPU today that increases the performance of the system. A diagram of a cycle Description automatically generated