John Von Neumann
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October 22, 2013 1 NEWS FROM COMPUTER SCIENCE AND ENGINEERING Written by the Beta Team of CSESoc Beta Issue # 87 Produced by Wen Di LIM Xi edition Edited by Anne GWYNNE-ROBSON, Week 12 Session 2, 2013 Beth CRANE and Tim WILEY. bETA Free as in speech and our awesome BBQs. FEATURED,HISTORY John von Neumann So, bit of history for you today. I’m instructions and data are contained in He also created the field of cellular going to be talking about American a single memory block. This general- automata, which have many interesting polymath John von Neumann - without purpose, stored-program computer is the applications as discrete models. A cellular him, computer science (along with many basis of modern computing. automaton consists of a grid of cells, other things) might be radically different. which can each be in one of a finite So I thought I’d write an article about him. number of states. These cell states evolve according to a rule, which considers each First, an introduction. He was a cell state and the state of neighbouring Hungarian-born American polymath, cells. living between 1903 and 1957, who made fundamental contributions to One popular example amongst computer mathematics, physics and economics. science students (and others) is Conway’s In fact, he was involved in pretty much Game of Life. This is a simple cellular every technically complex field. He automaton involving a two-dimensional was a child prodigy; at 6 years old grid of cells, which can each be either he could divide 8 digit numbers in his “alive” or “dead”. At each time step, the head. At 8 years old he was familiar cells are updated based on a set of exactly with differential and integral calculus. Neumann also, casually, founded the field 4 simple rules. These rules cause a given At 15 years old he entered the tutelage of game theory. In particular, he came up cell to be alive or dead in the next time step of renowned mathematician Gbor Szeg, with the minimax theorem. The minimax based on that cell’s state and the number who was reduced to tears by Neumann’s theorem establishes an optimal strategy of alive neighbours. Despite the simplicity abilities. Probably like my maths teachers for players in a perfect information zero- of the rules, many complex patterns can in high school, but for different reasons. sum game (one player’s losses equal the emerge in the game. It is therefore widely other’s gains). This strategy allows a used to illustrate that perceived design So he clearly had mad skills. But why player to minimize his maximum loss can emerge spontaneously from simple, are we talking about him? Well, aside by considering possible moves by the deterministic rules. In other words, from all his l337 maths stuff, he was opponent. For anyone that has done an the principles of emergence and self- a founding figure in computer science. Artificial Intelligence course where you organization. In 1945, he described the von Neumann had to program adversarial games, you computer architecture, wherein program can thank John von Neumann. CONTINUED ON NEXT PAGE. UNRA2 - page2 Bits in a Bunch - page6 EB Games Expo - page7 Crossword -3 It’s Election Time!4-5 iLounge 2 -6 http://beta.csesoc.unsw.edu.au Computer Science and Engineering October 22, 2013 2 HISTORY John von Neumann - contd. Oh yeah, and Neumann invented merge atomic bombs. When fellow physicist intellectual brilliance doesn’t imply moral sort. And made key contributions to linear Robert Oppenheimer declared he and goodness. We tend to afford great thinkers programming. I could go on, but I think other scientists involved had “known sin”, with not only intellectual but moral you get the point. John von Neumann responded “sometimes authority. This blind respect is misplaced someone confesses a sin in order to take and needs to be moderated by the reality. On a more morbid note, however, he was credit for it”. So, he was a bit of a tool. Not all geniuses are top blokes (or top a key figure in the Manhattan Project, lasses, don’t mean to be heteronormative). the US-led project that developed the What are the take-away lessons? First, atomic bombs in World War II. Having John von Neumann was a beast. We are developed an expertise in explosions he all the beneficiaries of his insanely broad- NELSON RIGBY was a key figure in the design of the first ranging and important work. Second, OPINION UNRA2: Thinking Fourth Dimensionally It’s likely that everyone has encountered person who witnessed this could attempt 3D analog. a work of fiction involving an extra to describe the shape that passed through dimension at some point. Be it time their world, by thinking of the shapes When drawing with perspective travel or trans-dimensional beings, “extra they saw as 2D slices of some 3D shape, projection, things in the distance appear dimensions” is a very popular topic. But and theoretically reconstruct the 3D shape smaller than things in the foreground. what does it actually mean? by “stacking” these slices through some Perspective projection requires some inconceivable 3rd dimension. concept of an “eye” which represents Think of the word “dimension” as the point from which the image is being referring to “a place for a number to go in What if we - 3D beings - were to “captured”. Things closer to the eye a coordinate”. That is, to specify a point in experience a similar phenomena but this appear larger than things further from the a particular space, for each dimension that time with a cube. We could apply the eyer. When taking a cube - a 3D shape - space has, one must specify one number. same approach to describe the 4D shape and projecting it onto a 2D sheet of paper, To specify a point in a 1-dimensional that could have just been pushed through the back of the cube (ie. the face furthest space, only a single number is required. To our world. We could think of the shape from the eye) appears smaller than the imagine a 1D space, think of an infinitely as represented by a small cube, with lines front. One could draw a cube by simply long line. The number specifies how far projected from each vertex through some drawing a small square inside a larger along the line the point is. Similarly, in inconceivable 4th dimension, where they square with the corresponding vertices a 2D space a point must be specified by meet the corresponding vertices of a larger connected. a pair of numbers and in a 3D space 3 cube. numbers are required. So what would it When taking a tesseract - a 4D shape - and mean if we were in a space that required 4 The Tesseract projecting it onto a 2D page, one must first numbers to specify a point? Take a straight line, and project project the 4D shape into a 3D space, and orthogonally from each end the length then project the resulting 3D shape onto Analogies of the line, and you get a square. Take the page. In the projection from 4D to 3D, A good way to understand the jump from the square, and project orthogonally from the “eye” is a point in 4D space. In the 3D to 4D is to look at analogs from the each vertex the length of one of its sides, resulting 3D shape, parts of the tesseract jump from 2D to 3D. Suppose some and you get a cube. Take the cube, and that were closer to the eye appear larger. 2D people lived in a 2D world, that project orthogonally from each vertex the Thinking of a tesseract as a pair of cubes unbeknown to them, was just a cross length of one of its sides, and you get with the corresponding vertices connected section of some 3D world. If some a tesseract. This is a 4D shape with 16 by edges of length equal to an edge of one 3D being was to push a square frustum vertices, 32 edges and 24 faces. of the cubes, the cube nearer to the eye through the 2D world, what would the 2D will appear larger in the projection than people experience? A square frustum is a Conventionally, when drawn in wireframe the cube further from the eye. Hence the 3D shape resembling a square prism, with using perspective projection, a tesseract resulting 3D shape resembles a small cube one of the square ends being smaller than resembles a small wireframe cube inside a larger cube. This shape is not a the other. inside a larger wireframe cube with the tesseract, in the same sense that an image corresponding vertices connected with of a cube is not a cube. The resulting 3D Assuming it was pushed through small edges. Technically this resemblance is shape is then draw onto the page using end first, the 2D people would see a only apparent when then viewed from the regular perspective projection. small square appear, which would then correct angle. To understand why it looks grow larger, and then disappear. A 2D the way it does, once again, consider the STEPHEN SHERRATT http://beta.csesoc.unsw.edu.au Computer Science and Engineering October 22, 2013 3 ENTERTAINMENT Crossword 1 2 3 4 5 6 7 8 9 10 Down 1. Crypto: ??? Curve Cryptography 11 2. Combination of two sets 4. OO: Data members 12 5. Estimated based on known data 6. Format converter 7. Ballet skirt 13 14 15 8. Confirmation of identity 12.