What’s This Algorithm Stuff About Then

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The use of algorithms is spreading as massive amounts of data are being created, captured and analyzed by businesses and governments. Some are calling this the Age of Algorithms and predicting that the future of algorithms is tied to machine learning and deep learning that will get better and better at an ever-faster pace.

A number of respondents noted the many ways in which algorithms will help make sense of massive amounts of data, noting that this will spark breakthroughs in science, new conveniences and human capacities in everyday life, and an ever-better capacity to link people to the information that will help them. They perform seemingly miraculous tasks humans cannot and they will continue to greatly augment human intelligence and assist in accomplishing great things. A representative proponent of this view is Stephen Downes, a researcher at the National Research Council of Canada, who listed the following as positive changes:

Participants in this study were in substantial agreement that the abundant positives of accelerating code-dependency will continue to drive the spread of algorithms; however, as with all great technological revolutions, this trend has a dark side. Most respondents pointed out concerns, chief among them the final five overarching themes of this report; all have subthemes.

The respondents to this canvassing offered a variety of ideas about how individuals and the broader culture might respond to the algorithm-ization of life. They argued for public education to instill literacy about how algorithms function in the general public. They also noted that those who create and evolve algorithms are not held accountable to society and argued there should be some method by which they are. Representative comments:

However, through experimentation and trial-and-error we can sniff out changes to any given algorithm. For example, some marketers suspect that the Instagram algorithm is starting to crack down on brands that are too explicit about social selling and transaction-specific posts.

Between trial-and-error and what we know about the current crop of social media algorithms, there are actionable steps marketers can take to optimize their posts. The key is finding a balance between what an algorithm wants and creating compelling content for your audience.

Understanding your most valuable subculture can also help you create content that connects authentically with TikTokers, creating greater credibility, brand loyalty, and even more exposure. TikTok users want brands to take this approach: 76% say they like it when brands are a part of special interest groups on the platform.

The default settings on TikTok allow others to create Duets and Stitch videos using your content. If you want to change this for any particular video, tap the three dots icon on the video to open Privacy Settings, then adjust as needed.

The concept of algorithms has existed since antiquity. Arithmetic algorithms, such as a division algorithm, were used by ancient Babylonian mathematicians c. 2500 BC and Egyptian mathematicians c. 1550 BC.[11] Greek mathematicians later used algorithms in 240 BC in the sieve of Eratosthenes for finding prime numbers, and the Euclidean algorithm for finding the greatest common divisor of two numbers.[12] Arabic mathematicians such as al-Kindi in the 9th century used cryptographic algorithms for code-breaking, based on frequency analysis.[13]

In English, the word algorithm was first used in about 1230 and then by Chaucer in 1391. English adopted the French term, but it was not until the late 19th century that "algorithm" took on the meaning that it has in modern English.[25]

An "enumerably infinite set" is one whose elements can be put into one-to-one correspondence with the integers. Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an arbitrary "input" integer or integers that, in theory, can be arbitrarily large. For example, an algorithm can be an algebraic equation such as y = m + n (i.e., two arbitrary "input variables" m and n that produce an output y), but various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of (for the addition example):

Simulation of an algorithm: computer (computor) language: Knuth advises the reader that "the best way to learn an algorithm is to try it . . . immediately take pen and paper and work through an example".[55] But what about a simulation or execution of the real thing? The programmer must translate the algorithm into a language that the simulator/computer/computor can effectively execute. Stone gives an example of this: when computing the roots of a quadratic equation the computer must know how to take a square root. If they don't, then the algorithm, to be effective, must provide a set of rules for extracting a square root.[56]

But what model should be used for the simulation? Van Emde Boas observes "even if we base complexity theory on abstract instead of concrete machines, the arbitrariness of the choice of a model remains. It is at this point that the notion of simulation enters".[57] When speed is being measured, the instruction set matters. For example, the subprogram in Euclid's algorithm to compute the remainder would execute much faster if the programmer had a "modulus" instruction available rather than just subtraction (or worse: just Minsky's "decrement").

One of the simplest algorithms is to find 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 stated in a high-level description in English prose, as:

Euclid's original proof adds a third requirement: the two lengths must not be prime to one another. Euclid stipulated this so that he could construct a reductio ad absurdum proof that the two numbers' common measure is in fact the greatest.[66] While Nicomachus' algorithm is the same as Euclid's, when the numbers are prime to one another, it yields the number "1" for their common measure. So, to be precise, the following is really Nicomachus' algorithm.

Does an algorithm do what its author wants it to do? A few test cases usually give some confidence in the core functionality. But tests are not enough. For test cases, one source[67] uses 3009 and 884. Knuth suggested 40902, 24140. Another interesting case is the two relatively prime numbers 14157 and 5950.

But "exceptional cases"[68] must be identified and tested. Will "Inelegant" perform properly when R > S, S > R, R = S? Ditto for "Elegant": B > A, A > B, A = B? (Yes to all). What happens when one number is zero, both numbers are zero? ("Inelegant" computes forever in all cases; "Elegant" computes forever when A = 0.) What happens if negative numbers are entered? Fractional numbers? If the input numbers, i.e. the domain of the function computed by the algorithm/program, is to include only positive integers including zero, then the failures at zero indicate that the algorithm (and the program that instantiates it) is a partial function rather than a total function. A notable failure due to exceptions is the Ariane 5 Flight 501 rocket failure (June 4, 1996).

Elegance (compactness) versus goodness (speed): With only six core instructions, "Elegant" is the clear winner, compared to "Inelegant" at thirteen instructions. However, "Inelegant" is faster (it arrives at HALT in fewer steps). Algorithm analysis[71] indicates why this is the case: "Elegant" does two conditional tests in every subtraction loop, whereas "Inelegant" only does one. As the algorithm (usually) requires many loop-throughs, on average much time is wasted doing a "B = 0?" test that is needed only after the remainder is computed.

The analysis, and study of algorithms is a discipline of computer science, and is often practiced abstractly without the use of a specific programming language or implementation. In this sense, algorithm analysis resembles other mathematical disciplines in that it focuses on the underlying properties of the algorithm and not on the specifics of any particular implementation. Usually pseudocode is used for analysis as it is the simplest and most general representation. However, ultimately, most algorithms are usually implemented on particular hardware/software platforms and their algorithmic efficiency is eventually put to the test using real code. For the solution of a "one off" problem, the efficiency of a particular algorithm may not have significant consequences (unless n is extremely large) but for algorithms designed for fast interactive, commercial or long life scientific usage it may be critical. Scaling from small n to large n frequently exposes inefficient algorithms that are otherwise benign.

To illustrate the potential improvements possible even in well-established algorithms, a recent significant innovation, relating to FFT algorithms (used heavily in the field of image processing), can decrease processing time up to 1,000 times for applications like medical imaging.[74] In general, speed improvements depend on special properties of the problem, which are very common in practical applications.[75] Speedups of this magnitude enable computing devices that make extensive use of image processing (like digital cameras and medical equipment) to consume less power.

Some problems may have multiple algorithms of differing complexity, while other problems might have no algorithms or no known efficient algorithms. There are also mappings from some problems to other problems. Owing to this, it was found to be more suitable to classify the problems themselves instead of the algorithms into equivalence classes based on the complexity of the best possible algorithms for them.

This machine he displayed in 1870 before the Fellows of the Royal Society.[90] Another logician John Venn, however, in his 1881 Symbolic Logic, turned a jaundiced eye to this effort: "I have no high estimate myself of the interest or importance of what are sometimes called logical machines ... it does not seem to me that any contrivances at present known or likely to be discovered really deserve the name of logical machines"; see more at Algorithm characterizations. But not to be outdone he too presented "a plan somewhat analogous, I apprehend, to Prof. Jevon's abacus ... [And] [a]gain, corresponding to Prof. Jevons's logical machine, the following contrivance may be described. I prefer to call it merely a logical-diagram machine ... but I suppose that it could do very completely all that can be rationally expected of any logical machine".[91] 2b1af7f3a8