Think-a-Dot
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Think-a-Dot
The Think-a-Dot was a mathematical toy invented by Joseph Weisbecker and manufactured by E.S.R., Inc. during the 1960s that demonstrated automata theory. It had eight coloured disks on its front, and three holes on its top – left, right, and center – through which a ball bearing could be dropped. Each disk would display either a yellow or blue face, depending on whether the mechanism behind it was tipped to the right or the left. The Think-a-Dot thus had 28=256 internal states. When the ball fell to the bottom it would exit either to a hole on the left or the right of the device. As the ball passed through the Think-a-Dot, it would flip the disk mechanisms that it passed, and they in turn would determine whether the ball would be deflected to the left or to the right. Various puzzles and games were possible with the Think-a-Dot, such as flipping the colours of all cells in the minimum number of moves, or reaching a given state from a monochrome state or vice versa. S ...
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Joseph Weisbecker
Joseph A. Weisbecker (September 4, 1932 – November 15, 1990) was an early microprocessor and microcomputer researcher, as well as a gifted writer and designer of toys and games. He was a recipient of the David Sarnoff award for outstanding technical achievement, recipient of IEEE ''Computer'' magazine's "Best Paper" award, as well as several RCA lab awards for his work. His designs include the RCA 1800 and 1802 processors, the 1861 "Pixie" graphics chip, the RCA Microtutor, the COSMAC ELF, RCA Studio II, and COSMAC VIP computers. His daughter Joyce Weisbecker took to programming his prototypes, becoming the first female video game designer in the process, using his language called CHIP-8. Early career Professionally, Weisbecker began working with digital logic and computer systems in 1951. It was also his hobby, however, and even his early work is marked by designs that are intended for educational or hobbyist use. These include a hobby tic-tac-toe computer built from ...
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Think A Dot Mechanism
In their most common sense, the terms thought and thinking refer to conscious cognitive processes that can happen independently of sensory stimulation. Their most paradigmatic forms are judging, reasoning, concept formation, problem solving, and deliberation. But other mental processes, like considering an idea, memory, or imagination, are also often included. These processes can happen internally independent of the sensory organs, unlike perception. But when understood in the widest sense, any mental event may be understood as a form of thinking, including perception and unconscious mental processes. In a slightly different sense, the term ''thought'' refers not to the mental processes themselves but to mental states or systems of ideas brought about by these processes. Various theories of thinking have been proposed, some of which aim to capture the characteristic features of thought. '' Platonists'' hold that thinking consists in discerning and inspecting Platonic forms and ...
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Mathematical Toy
Educational toys (sometimes also called "instructive toys") are objects of play, generally designed for children, which are expected to stimulate learning. They are often intended to meet an educational purpose such as helping a child develop a particular skill or teaching a child about a particular subject. They often simplify, miniaturize, or even model activities and objects used by adults. Although children are constantly interacting with and learning about the world, many of the objects they interact with and learn from are not toys. Toys are generally considered to be specifically built for children's use. A child might play with and learn from a rock or a stick, but it would not be considered an educational toy because 1) it is a natural object, not a designed one, and 2) it has no expected educational purpose. The difference lies in perception or reality of the toy's intention and value. An educational toy is expected to educate. It is expected to instruct, promot ...
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Automata Theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word ''automata'' comes from the Greek word αὐτόματος, which means "self-acting, self-willed, self-moving". An automaton (automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a Finite Automaton (FA) or Finite-State Machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type of automaton. This automaton consists of states (represented in the figure by circles) and transitions (represented by arrows). As the automaton sees a symbol of input, it makes a transition (or jump) to another state, according to its transition function, which takes the previous state and current input symbol as its arguments. Automata theo ...
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Digi-Comp I
The Digi-Comp I was a functioning, mechanical digital computer sold in kit form. It was originally manufactured from polystyrene parts by E.S.R., Inc. starting in 1963 and sold as an educational toy for US$4.99. A successor, the Digi-Comp II, was not programmable, but in effect a visible calculator. A two-level masonite platform with guides served as the medium for a supply of marbles that rolled down an inclined plane, moving plastic cams as they fell. Operation In essence, the Digi-Comp I contained three mechanical flip-flops, providing an ability to connect them together in a programmable way using thin vertical wires that are either pushed, or blocked from moving, by a number of cylindrical pegs. The whole arrangement was 'clocked' by moving a lever back and forth. Different configurations of these cylinders caused the Digi-Comp to compute different boolean logic operations. With a three binary digit (3-bit) readout of the state of the flip-flops, it could be programmed to ...
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Digi-Comp II
The Digi-Comp II was a toy computer invented by John "Jack" Thomas Godfrey (1924–2009) in 1965 and manufactured by E.S.R., Inc. in the late 1960s that used marbles rolling down a ramp to perform basic calculations. A two-level masonite platform with blue plastic guides served as the medium for a supply of marbles that rolled down an inclined plane moving plastic cams as they went. The red plastic cams played the part of flip-flops in an electronic computer - as a marble passed one of the cams, it would flip the cam around - in one position, the cam would allow the marble to pass in one direction, in the other position, it would cause the marble to drop through a hole and roll to the bottom of the ramp. The Digi-Comp II platform measures . The Digi-Comp II was not programmable, unlike the Digi-Comp I, an earlier offering in the E.S.R. product line that used an assortment of plastic slides, tubes, and bent metal wires to solve simple logic problems. Computational power Compu ...
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Mathematics Magazine
''Mathematics Magazine'' is a refereed bimonthly publication of the Mathematical Association of America. Its intended audience is teachers of collegiate mathematics, especially at the junior/senior level, and their students. It is explicitly a journal of mathematics rather than pedagogy. Rather than articles in the terse "theorem-proof" style of research journals, it seeks articles which provide a context for the mathematics they deliver, with examples, applications, illustrations, and historical background. Paid circulation in 2008 was 9,500 and total circulation was 10,000. ''Mathematics Magazine'' is a continuation of ''Mathematics News Letter'' (1926-1934) and ''National Mathematics Magazine'' (1934-1945.) Doris Schattschneider became the first female editor of ''Mathematics Magazine'' in 1981. .. The MAA gives the Carl B. Allendoerfer Awards annually "for articles of expository excellence" published in ''Mathematics Magazine''. See also *''American Mathematical Mont ...
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