43-594: Jeffrey Hawkins is an American businessman, computer scientist , neuroscientist and engineer. He co-founded Palm Computing — where he co-created the PalmPilot and Treo — and Handspring . He subsequently turned to work on neuroscience, founding in 2002 the Redwood Neuroscience Institute . In 2005 he co-founded Numenta, where he leads a team in efforts to reverse-engineer the neocortex and enable machine intelligence technology based on brain theory. He
86-652: A PhD , M.S. , Bachelor's degree in computer science, or other similar fields like Information and Computer Science (CIS), or a closely related discipline such as mathematics or physics . Computer scientists are often hired by software publishing firms, scientific research and development organizations where they develop the theories and computer model that allow new technologies to be developed. Computer scientists are also employed by educational institutions such as universities . Computer scientists can follow more practical applications of their knowledge, doing things such as software engineering. They can also be found in
129-595: A binary search algorithm (with cost O ( log n ) {\displaystyle O(\log n)} ) outperforms a sequential search (cost O ( n ) {\displaystyle O(n)} ) when used for table lookups on sorted lists or arrays. The analysis, and study of algorithms is a discipline of computer science . Algorithms are often studied abstractly, without referencing any specific programming language or implementation. Algorithm analysis resembles other mathematical disciplines as it focuses on
172-468: A flowchart offers a way to describe and document an algorithm (and a computer program corresponding to it). It has four primary symbols: arrows showing program flow, rectangles (SEQUENCE, GOTO), diamonds (IF-THEN-ELSE), and dots (OR-tie). Sub-structures can "nest" in rectangles, but only if a single exit occurs from the superstructure. It is often important to know how much time, storage, or other cost an algorithm may require. Methods have been developed for
215-506: A computer, Babbage's analytical engine, which is the first device considered a real Turing-complete computer instead of just a calculator . Although a full implementation of Babbage's second device was not realized for decades after her lifetime, Lovelace has been called "history's first programmer". Bell and Newell (1971) write that the Jacquard loom , a precursor to Hollerith cards (punch cards), and "telephone switching technologies" led to
258-680: A computer-executable form, but are also used to define or document algorithms. There are many possible representations and Turing machine programs can be expressed as a sequence of machine tables (see finite-state machine , state-transition table , and control table for more), as flowcharts and drakon-charts (see state diagram for more), as a form of rudimentary machine code or assembly code called "sets of quadruples", and more. Algorithm representations can also be classified into three accepted levels of Turing machine description: high-level description, implementation description, and formal description. A high-level description describes qualities of
301-713: A computing machine or a human who could only carry out specific elementary operations on symbols . Most algorithms are intended to be implemented as computer programs . However, algorithms are also implemented by other means, such as in a biological neural network (for example, the human brain performing arithmetic or an insect looking for food), in an electrical circuit , or a mechanical device. Step-by-step procedures for solving mathematical problems have been recorded since antiquity. This includes in Babylonian mathematics (around 2500 BC), Egyptian mathematics (around 1550 BC), Indian mathematics (around 800 BC and later),
344-475: A final ending state. The transition from one state to the next is not necessarily deterministic ; some algorithms, known as randomized algorithms , incorporate random input. Around 825 AD, Persian scientist and polymath Muḥammad ibn Mūsā al-Khwārizmī wrote kitāb al-ḥisāb al-hindī ("Book of Indian computation") and kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī ("Addition and subtraction in Indian arithmetic"). In
387-997: A hand-held computing device." He also served on the Advisory Board of the Secular Coalition for America where he has advised on the acceptance and inclusion of nontheism in American life. Computer scientist A computer scientist is a scientist who specializes in the academic study of computer science . Computer scientists typically work on the theoretical side of computation. Although computer scientists can also focus their work and research on specific areas (such as algorithm and data structure development and design, software engineering , information theory , database theory , theoretical computer science , numerical analysis , programming language theory , compiler , computer graphics , computer vision , robotics , computer architecture , operating system ), their foundation
430-525: A programmer can write structured programs using only these instructions; on the other hand "it is also possible, and not too hard, to write badly structured programs in a structured language". Tausworthe augments the three Böhm-Jacopini canonical structures : SEQUENCE, IF-THEN-ELSE, and WHILE-DO, with two more: DO-WHILE and CASE. An additional benefit of a structured program is that it lends itself to proofs of correctness using mathematical induction . By themselves, algorithms are not usually patentable. In
473-477: A sequence of operations", which would include all computer programs (including programs that do not perform numeric calculations), and any prescribed bureaucratic procedure or cook-book recipe . In general, a program is an algorithm only if it stops eventually —even though infinite loops may sometimes prove desirable. Boolos, Jeffrey & 1974, 1999 define an algorithm to be an explicit set of instructions for determining an output, that can be followed by
SECTION 10
#1732863066026516-569: A stake in, Hawkins founded the Redwood Neuroscience Institute in Menlo Park , California. In 2004, he co-authored On Intelligence with Sandra Blakeslee , laying out a theory on his " memory-prediction framework " of how the brain works. One of Hawkins' areas of interest is cortical columns . In 2016, he hypothesized that cortical columns did not capture just a sensation, but also the relative location of that sensation, in three dimensions rather than two ( situated capture ), in relation to what
559-416: Is a method or mathematical process for problem-solving and engineering algorithms. The design of algorithms is part of many solution theories, such as divide-and-conquer or dynamic programming within operation research . Techniques for designing and implementing algorithm designs are also called algorithm design patterns, with examples including the template method pattern and the decorator pattern. One of
602-576: Is a more specific classification of algorithms; an algorithm for such problems may fall into one or more of the general categories described above as well as into one of the following: One of the simplest algorithms finds the largest number in a list of numbers of random order. Finding the solution requires looking at every number in the list. From this follows a simple algorithm, which can be described in plain English as: High-level description: (Quasi-)formal description: Written in prose but much closer to
645-460: Is no truly "correct" recommendation. As an effective method , an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function . Starting from an initial state and initial input (perhaps empty ), the instructions describe a computation that, when executed , proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at
688-424: Is the co-author of On Intelligence (2004), which explains his memory-prediction framework theory of the brain, and the author of A Thousand Brains: A New Theory of Intelligence (2021). Hawkins attended Cornell University , where he received a Bachelor of Science with a major in electrical engineering in 1979. His interest in pattern recognition for speech and text input to computers led him to enroll in
731-507: Is the theoretical study of computing from which these other fields derive. A primary goal of computer scientists is to develop or validate models, often mathematical, to describe the properties of computational systems ( processors , programs, computers interacting with people, computers interacting with other computers, etc.) with an overall objective of discovering designs that yield useful benefits (faster, smaller, cheaper, more precise, etc.). Most computer scientists are required to possess
774-453: Is useful for uncovering unexpected interactions that affect performance. Benchmarks may be used to compare before/after potential improvements to an algorithm after program optimization. Empirical tests cannot replace formal analysis, though, and are non-trivial to perform fairly. To illustrate the potential improvements possible even in well-established algorithms, a recent significant innovation, relating to FFT algorithms (used heavily in
817-1094: The Entscheidungsproblem (decision problem) posed by David Hilbert . Later formalizations were framed as attempts to define " effective calculability " or "effective method". Those formalizations included the Gödel – Herbrand – Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church 's lambda calculus of 1936, Emil Post 's Formulation 1 of 1936, and Alan Turing 's Turing machines of 1936–37 and 1939. Algorithms can be expressed in many kinds of notation, including natural languages , pseudocode , flowcharts , drakon-charts , programming languages or control tables (processed by interpreters ). Natural language expressions of algorithms tend to be verbose and ambiguous and are rarely used for complex or technical algorithms. Pseudocode, flowcharts, drakon-charts, and control tables are structured expressions of algorithms that avoid common ambiguities of natural language. Programming languages are primarily for expressing algorithms in
860-532: The GRiDPad , one of the first tablet computers . Hawkins founded Palm Inc. , in January 1992. In 1998 he left the company along with Palm co-founders Donna Dubinsky and Ed Colligan to start Handspring . In March 2005, Hawkins, together with Dubinsky (Palm's original CEO) and Dileep George , founded Numenta, Inc. In 2002, after two decades of finding little interest from neuroscience institutions that he did not have
903-471: The Hammurabi dynasty c. 1800 – c. 1600 BC , Babylonian clay tablets described algorithms for computing formulas. Algorithms were also used in Babylonian astronomy . Babylonian clay tablets describe and employ algorithmic procedures to compute the time and place of significant astronomical events. Algorithms for arithmetic are also found in ancient Egyptian mathematics , dating back to
SECTION 20
#1732863066026946-567: The Kerala School , and the Brāhmasphuṭasiddhānta . The first cryptographic algorithm for deciphering encrypted code was developed by Al-Kindi , a 9th-century Arab mathematician, in A Manuscript On Deciphering Cryptographic Messages . He gave the first description of cryptanalysis by frequency analysis , the earliest codebreaking algorithm. Bolter credits the invention of the weight-driven clock as "the key invention [of Europe in
989-740: The Rhind Mathematical Papyrus c. 1550 BC . Algorithms were later used in ancient Hellenistic mathematics . Two examples are the Sieve of Eratosthenes , which was described in the Introduction to Arithmetic by Nicomachus , and the Euclidean algorithm , which was first described in Euclid's Elements ( c. 300 BC ). Examples of ancient Indian mathematics included the Shulba Sutras ,
1032-521: The biophysics program at the University of California, Berkeley in 1986. While there he patented a "pattern classifier" for handwritten text, but his PhD proposal on developing a theory of the neocortex was rejected. Hawkins joined GRiD Systems in 1982, where he developed rapid application development (RAD) software called GRiDtask . As vice president of research from 1988 to 1992, he developed their pen-based computing initiative that in 1989 spawned
1075-472: The "thousand brains" theory can affect machine intelligence, and how an understanding of the brain impacts the threats and opportunities facing humanity. It also offers a theory of what's missing in current AI. In 2003, Hawkins was elected as a member of the National Academy of Engineering "for the creation of the hand-held computing paradigm and the creation of the first commercially successful example of
1118-504: The Ifa Oracle (around 500 BC), Greek mathematics (around 240 BC), Chinese mathematics (around 200 BC and later) , and Arabic mathematics (around 800 AD). The earliest evidence of algorithms is found in ancient Mesopotamian mathematics. A Sumerian clay tablet found in Shuruppak near Baghdad and dated to c. 2500 BC describes the earliest division algorithm . During
1161-470: The Middle Ages ]," specifically the verge escapement mechanism producing the tick and tock of a mechanical clock. "The accurate automatic machine" led immediately to "mechanical automata " in the 13th century and "computational machines"—the difference and analytical engines of Charles Babbage and Ada Lovelace in the mid-19th century. Lovelace designed the first algorithm intended for processing on
1204-578: The United States, a claim consisting solely of simple manipulations of abstract concepts, numbers, or signals does not constitute "processes" (USPTO 2006), so algorithms are not patentable (as in Gottschalk v. Benson ). However practical applications of algorithms are sometimes patentable. For example, in Diamond v. Diehr , the application of a simple feedback algorithm to aid in the curing of synthetic rubber
1247-450: The algorithm itself, ignoring how it is implemented on the Turing machine. An implementation description describes the general manner in which the machine moves its head and stores data in order to carry out the algorithm, but does not give exact states. In the most detail, a formal description gives the exact state table and list of transitions of the Turing machine. The graphical aid called
1290-588: The algorithm's properties, not implementation. Pseudocode is typical for analysis as it is a simple and general representation. Most algorithms are implemented on particular hardware/software platforms and their algorithmic efficiency is tested using real code. The efficiency of a particular algorithm may be insignificant for many "one-off" problems but it may be critical for algorithms designed for fast interactive, commercial or long life scientific usage. Scaling from small n to large n frequently exposes inefficient algorithms that are otherwise benign. Empirical testing
1333-403: The analysis of algorithms to obtain such quantitative answers (estimates); for example, an algorithm that adds up the elements of a list of n numbers would have a time requirement of O ( n ) {\displaystyle O(n)} , using big O notation . The algorithm only needs to remember two values: the sum of all the elements so far, and its current position in
Jeff Hawkins - Misplaced Pages Continue
1376-413: The code execution through various routes (referred to as automated decision-making ) and deduce valid inferences (referred to as automated reasoning ). In contrast, a heuristic is an approach to solving problems that do not have well-defined correct or optimal results. For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there
1419-459: The development of the first computers. By the mid-19th century, the telegraph , the precursor of the telephone, was in use throughout the world. By the late 19th century, the ticker tape ( c. 1870s ) was in use, as were Hollerith cards (c. 1890). Then came the teleprinter ( c. 1910 ) with its punched-paper use of Baudot code on tape. Telephone-switching networks of electromechanical relays were invented in 1835. These led to
1462-517: The early 12th century, Latin translations of said al-Khwarizmi texts involving the Hindu–Arabic numeral system and arithmetic appeared, for example Liber Alghoarismi de practica arismetrice , attributed to John of Seville , and Liber Algorismi de numero Indorum , attributed to Adelard of Bath . Hereby, alghoarismi or algorismi is the Latinization of Al-Khwarizmi's name; the text starts with
1505-463: The field of information technology consulting , and may be seen as a type of mathematician, given how much of the field depends on mathematics. Computer scientists employed in industry may eventually advance into managerial or project leadership positions. Employment prospects for computer scientists are said to be excellent. Such prospects seem to be attributed, in part, to very rapid growth in computer systems design and related services industry, and
1548-427: The field of image processing), can decrease processing time up to 1,000 times for applications like medical imaging. In general, speed improvements depend on special properties of the problem, which are very common in practical applications. Speedups of this magnitude enable computing devices that make extensive use of image processing (like digital cameras and medical equipment) to consume less power. Algorithm design
1591-450: The input list. If the space required to store the input numbers is not counted, it has a space requirement of O ( 1 ) {\displaystyle O(1)} , otherwise O ( n ) {\displaystyle O(n)} is required. Different algorithms may complete the same task with a different set of instructions in less or more time, space, or ' effort ' than others. For example,
1634-482: The invention of the digital adding device by George Stibitz in 1937. While working in Bell Laboratories, he observed the "burdensome" use of mechanical calculators with gears. "He went home one evening in 1937 intending to test his idea... When the tinkering was over, Stibitz had constructed a binary adding device". In 1928, a partial formalization of the modern concept of algorithms began with attempts to solve
1677-627: The most important aspects of algorithm design is resource (run-time, memory usage) efficiency; the big O notation is used to describe e.g., an algorithm's run-time growth as the size of its input increases. Per the Church–Turing thesis , any algorithm can be computed by any Turing complete model. Turing completeness only requires four instruction types—conditional GOTO, unconditional GOTO, assignment, HALT. However, Kemeny and Kurtz observe that, while "undisciplined" use of unconditional GOTOs and conditional IF-THEN GOTOs can result in " spaghetti code ",
1720-552: The phrase Dixit Algorismi , or "Thus spoke Al-Khwarizmi". Around 1230, the English word algorism is attested and then by Chaucer in 1391, English adopted the French term. In the 15th century, under the influence of the Greek word ἀριθμός ( arithmos , "number"; cf. "arithmetic"), the Latin word was altered to algorithmus . One informal definition is "a set of rules that precisely defines
1763-547: The software publishing industry, which are projected to be among the fastest growing industries in the U.S. economy. Algorithm In mathematics and computer science , an algorithm ( / ˈ æ l ɡ ə r ɪ ð əm / ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation . Algorithms are used as specifications for performing calculations and data processing . More advanced algorithms can use conditionals to divert
Jeff Hawkins - Misplaced Pages Continue
1806-503: Was around it. Hawkins explains, "When the brain builds a model of the world, everything has a location relative to everything else". In 2021, he published A Thousand Brains: A New Theory of Intelligence , a framework for intelligence and cortical computation. The book details the advances he and the Numenta team made in the development of their theory of how the brain understands the world and what it means to be intelligent. It also details how
1849-449: Was deemed patentable. The patenting of software is controversial, and there are criticized patents involving algorithms, especially data compression algorithms, such as Unisys 's LZW patent . Additionally, some cryptographic algorithms have export restrictions (see export of cryptography ). Another way of classifying algorithms is by their design methodology or paradigm . Some common paradigms are: For optimization problems there
#25974