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class="entry-title">Algorithmic How-to</h1> </header> <div class="entry-content"> <ul> <li> </li> </ul> <p>When it comes to the How-to category, it seems that we are in the paradise of algorithms. It has long been known that algorithms rule in mathematics – as a precise set of instructions for solving a problem. Here is just a very simple example of an algorithm: first step: add two random numbers, second step: divide their sum by two. Let’s say you add 4 and 8. Then the result would be 6, i.e.: (4+8) : 2 =6.</p> <figure class="wp-block-image size-full is-resized"><img decoding="async" width="242" height="456" class="wp-image-2558" style="width: 607px;height: auto" src="https://howtobook.hypotheses.org/files/2025/01/1736280465558-8120b1ea-13d4-466b-b0d6-2c78ac7bf623_1.jpg" alt="" srcset="https://howtobook.hypotheses.org/files/2025/01/1736280465558-8120b1ea-13d4-466b-b0d6-2c78ac7bf623_1.jpg 242w, https://howtobook.hypotheses.org/files/2025/01/1736280465558-8120b1ea-13d4-466b-b0d6-2c78ac7bf623_1-159x300.jpg 159w" sizes="(max-width: 242px) 100vw, 242px" /></figure> <p>But a recipe can also be seen as an algorithm. For instructions on how to bake a doughnut [Krapfen], for example, why not turn to the oldest German cookery book <em>Kuchemaistrey</em> [Kitchen Mastering] printed 1490 in Nürnberg (HAB 276 Quod): 1. Take eggs and flour and 2. make a good, smooth dough. 3. Colour it, 4. chop everything finely, knead it with a raw egg, season, salt, yellow (saffron), 5. put the chopped ingredients on the dough, 6. put another sheet of dough on top and 7. brush the edges with egg white, 8. press it on and bake it as a doughnut. Where there’s How-to, there’s algorithm, isn’t there?! Algorithms, of course, are also integral to our postdigital world. Our smartphone apps apparently have their predecessors in the how-to books of the early modern era, in the practical approach laid down in tried and tested rules. There is no doubt that a lot has changed between the 16th and 21st century in the way how-to knowledge is being imparted. Bartolomeo Scappi´s ’Paper Kitchens‘ from the Renaissance are now the apps ’Tasty Recipes‘ or ’tasty.co‘ on our smartphones. <a href="https://howtobook.hypotheses.org/1576">In her blog post recently</a>, Alina Lange makes clear how much the how-to of (online) food preparation has become intertwined with other skills that have nothing to do with it. Once it has been shared with thousands of followers, elements of entertainment come into play. Whether you cook the dishes or not seems to be becoming less and less important. Instead, let´s kill time with the help of similar clips that the algorithm suggests! Everything points to it: No presentation of skills without how-to mechanisms in the shadows. In the end, you certainly won’t become a better cook, but maybe a better clown….</p> <p>What is going on here in terms of how-to? Digital formats rule when it comes to the dissemination of how-to knowledge – text guides, videos, tutorials or apps. Does that make us puppets of machine-generated calculations, or are completely new possibilities for human existence opening up? Which of our senses will be used most in the future? How will our sensory and physical skills evolve? Why have arithmetic operations made such a stunning career? Turbulent times, certainly, but also time to organize our thoughts.</p> <p> </p> <p><strong>The how-to idea and algorithms</strong></p> <p>It is striking that the how-to knowledge of the past and the algorithms of our digital present are based on an almost identical logic of sequence, problem-solving and purpose. An algorithm is a calculation that consists of a series of instructions that are executed step by step, with a result at the end. In our daily lives, we are repeatedly confronted with problems. The challenge may be to treat an illness, repair defective software or bake a muffin. The good thing about these kinds of problems is that they can be solved as long as you follow a disciplined, sequenced guideline. You are always dealing with a clearly defined approach; instructions are followed in a specific order, where the same inputs produce the same results. As Lorraine Daston explains in her latest book <em>Rules</em> (2022), algorithms are two things: in the narrower sense, they express arithmetic calculations using Indian numerals, as we all know them: addition, subtraction, multiplication and division. In the broader sense, they can refer to any step-by-step process for solving problems, as soon as you are „dividing up a complex task into a finite, definite sequence of small steps with precisely defined inputs and outputs. Cookbook recipes, IKEA assembly instructions, and any other procedure spelled out step-by-step resemble algorithms in this extended sense of the term, even if no calculations are involved.“</p> <p>It has now become common practice to use the example of the cooking recipe to illustrate and make comprehensible the ominous way algorithms work. A recipe provides instructions for preparing a dish, while an algorithm does the same for processing a task, such as a product recommendation. The aim is to make a desired result both predictable and reproducible. The logic of an algorithm is sequential, but it can also contain additional conditions, such as loops (‘repeat this until a condition is met’) or branches (‘if X, then do Y’). These rules are equivalent to alternatives in a recipe (‘if you have no sugar, use honey’). Data in an algorithm is like ingredients in a recipe. Nevertheless, a recipe can be adapted through improvisation, while algorithms follow rigid rules set by the programmer, although big data and machine learning have shaken things up – but there remains a difference. Both systems draw on input (ingredients or data) to achieve an optimised result. And both systems communicate with the user in an open way, but while traditional how-to knowledge enables users to act independently, algorithms merely simulate this user-friendly tone by means of personalised addresses or suggestions (most likely to make money). While how-to knowledge promotes the autonomy and expands the skillset of the user, algorithms often take over tasks without explaining how they work. Normally, how-to knowledge has to be transparent, every action and its purpose are comprehensible. Algorithms, on the other hand, are often ‘black boxes’: users see the recommendations, but not the underlying calculations or criteria. The platform operator is concerned with problems like this: How do I find out what the user likes or finds interesting, and how do I manage to keep them on YouTube, Instagram or Tiktok for as long as possible? These platforms are so mighty because they have access to the data of the user’s behaviour, they can create a user profile to make recommendations tailored to them. The interactions of the users with the recommendation systems fuel each other in an endless feedback loop, and the momentum of machine learning is gathering pace. However, the codes on which the algorithms at Google, YouTube and Spotify are based remain the great secret of the operators. Algorithms could be seen as a kind of meta-how-to knowledge that plays virtuously with numbers in the background to provide instructions on how to generate answers to specific questions from data – so much from the engine room of digitisation</p> <p><br /><strong>Practical calculations in earlier times</strong></p> <p>In the virtual space there is so much talk about algorithms – a key term of mathematics. When I was a child, I was given an abacus as a gift. But I was never taught how to use this wooden calculating aid properly. My mental arithmetic skills were usually sufficient until the end of the 1970s, when pocket calculators became affordable for regular people. From then on, they were an indispensable tool in every maths exam, allowing pupils to immediately address the higher questions of maths. Here‘s my original device from 1982:</p> <figure class="wp-block-image size-large is-resized"><img decoding="async" width="375" height="500" class="wp-image-2562" style="width: 591px;height: auto" src="https://howtobook.hypotheses.org/files/2025/01/Taschenrechner-375x500.jpg" alt="" srcset="https://howtobook.hypotheses.org/files/2025/01/Taschenrechner-375x500.jpg 375w, https://howtobook.hypotheses.org/files/2025/01/Taschenrechner-225x300.jpg 225w, https://howtobook.hypotheses.org/files/2025/01/Taschenrechner-768x1024.jpg 768w, https://howtobook.hypotheses.org/files/2025/01/Taschenrechner-1152x1536.jpg 1152w, https://howtobook.hypotheses.org/files/2025/01/Taschenrechner-1536x2048.jpg 1536w, https://howtobook.hypotheses.org/files/2025/01/Taschenrechner-1568x2091.jpg 1568w, https://howtobook.hypotheses.org/files/2025/01/Taschenrechner-scaled.jpg 1920w" sizes="(max-width: 375px) 100vw, 375px" /></figure> <p>The invention marked the modest beginnings of the digital age – of what was soon to become digitisation’s complete penetration of everyday life: few people at the time could have predicted the rapid developments that would happen over the course of the next 40 years, half a lifetime.</p> <p>In remote pasts, there were even more tangible ways of dealing with numbers. For thousands of years, calculating was an operation that had to be demonstrated to others, whether written on clay, papyrus, palm leaves, bamboo strips, parchment or paper. The number system was usually cumbersome, but this began to change in the High Middle Ages. Like many other things that have made our lives easier, this new system, too, came from the Islamic area (such as optics, chemistry and so forth). ‘Algorithm’ is the Latinised version of the Arabic name Muhammad ibn Musa al-Kharizmi. In the first half of the 9th century, the mathematician, astronomer and geographer from Persia wrote an arithmetic work in which he compiled everything known about the new calculations from India. Al-Khwarizmi’s writings no longer exist. But we know about them because later mathematicians quote excerpts from it. In addition, a fragmented version translated into Latin is known from the 12th century (now available in the Cambridge University Library); it begins (without a title) with the words: ‘Dixit Algorizmi’. And what did Al-Khwarizmi say? He explained the advantages of the Indian number system and familiarised his Arab contemporaries with it and its applications. The characters we still use today make it easy for us to add, subtract, multiply and divide. How convenient it is not to have to write MMMDCCCLXXXVIII, but just 3888! Moreover, these numbers are abstract symbols that work independently of language; everyone can understand their meaning immediately, regardless of whether they speak German or Chinese (provided that they have learned the ten number signs, including zero, through education). This mastery of numbers shows an important human ability: the ability to think abstractly. It looks as if numbers are entirely immaterial entitities, they only exist through our thinking, through our brains.</p> <p>What the ‘maître d’algorisme’ was in France, the ‘Rechenmeister’ was in German-speaking countries: ‘Das macht nach Adam Riese…’ [According to Adam Riese, this amounts to…] became a familiar saying in Luther’s time, when trade began to pick up and calculations became increasingly important in everyday life. The saying goes back to the mathematician Adam Ries, who taught maths with genuine how-to books (and bestsellers) such as <em>Rechenung auff der linihen und federn auf allerley handthirung gemacht </em>[Calculation on lines and quills made for handling of all kinds] from1522. It was reprinted a hundred times (!) during his lifetime. Here’s the 1529 edition from the<em> Saxon State and University Library Dresden</em>:</p> <figure class="wp-block-image size-large is-resized"><img decoding="async" width="500" height="320" class="wp-image-2563" style="width: 1005px;height: auto" src="https://howtobook.hypotheses.org/files/2025/01/Ries-500x320.png" alt="" srcset="https://howtobook.hypotheses.org/files/2025/01/Ries-500x320.png 500w, https://howtobook.hypotheses.org/files/2025/01/Ries-300x192.png 300w, https://howtobook.hypotheses.org/files/2025/01/Ries-768x491.png 768w, https://howtobook.hypotheses.org/files/2025/01/Ries.png 1335w" sizes="(max-width: 500px) 100vw, 500px" /></figure> <p>Ries’ publications were widely disseminated thanks to their clear structure, excellent didactic design and the fact that they were all written in German. Ries introduced written calculations and the appropriate methods for doing so, and contributed significantly to the replacement of the cumbersome Roman numerals with Arabic numerals. At that time, calculations were mainly done on calculating boards (abacuses), or simply on tablets with lines drawn on them. The numbers were marked by little metal tags (Rechenpfennige). In Gregor Reisch’s <em>Margarita Philosophica</em> , the first encyclopaedic textbook on the Artes Liberales, first published in Freiburg in 1503 and reprinted many times, an ‘algorist’, who calculates with Indian-Arabic numerals, and an ‘abacist’, who uses a board with lines and little stones (calculi) for the same purpose, compete in the illustration of mathematics (from the 1504-Strasbourg-edition, Munich, Bavarian State Library), watched over by the figure of ‘Arithmetica Speculativa’. The staging of shadows and light and the direction of the female allegory’s gaze indicate that the ‘algorist’ is the winner.</p> <figure class="wp-block-image size-large is-resized"><img loading="lazy" decoding="async" width="408" height="500" class="wp-image-2576" style="width: 599px;height: auto" src="https://howtobook.hypotheses.org/files/2025/01/Reisch_Arithmetik-408x500.jpg" alt="" srcset="https://howtobook.hypotheses.org/files/2025/01/Reisch_Arithmetik-408x500.jpg 408w, https://howtobook.hypotheses.org/files/2025/01/Reisch_Arithmetik-245x300.jpg 245w, https://howtobook.hypotheses.org/files/2025/01/Reisch_Arithmetik-768x941.jpg 768w, https://howtobook.hypotheses.org/files/2025/01/Reisch_Arithmetik.jpg 798w" sizes="auto, (max-width: 408px) 100vw, 408px" /></figure> <p>Two centuries later, as a librarian in Wolfenbüttel, the polymath Gottfried Wilhelm Leibniz, who by the way changed the system of organising books by subject, as had been the practice for decades under the great book collector Duke August the Younger, to alphabetical order by author name – isn’t that also an algorithm in the wider sense?! – went down in history for being the first to realise that all numbers could be represented by only the digits 1 and 0 (binary system). While computer scientists of our time see in ‘1’ and ‘0’ the states of electronic circuits– current is either flowing or it isn’t –, Leibniz saw in 1 and 0 the symbols for ‘to be’ and ‘not to be’, which he associated with creation and divine order ‘Omnibus ex nihilo ducendis sufficit unum.’ [To derive everything from nothing, one is sufficient], as Leibniz wrote in a New Year’s letter to Duke Rudolf August of Wolfenbüttel in 1697. Here is an excerpt from this epochal letter with the emblematic number formation, from the Gottfried Wilhelm Leibniz Library (Hanover). In the left column is the list of decimal numbers, which increase by a factor of 10 from line to line (from 1 to 100 trillion). In the right column are the binary numbers, which are increased by 2 (from 1 to 16384) and which should become crucial in digitisation.</p> <figure class="wp-block-image size-large is-resized"><img loading="lazy" decoding="async" width="500" height="200" class="wp-image-2569" style="width: 773px;height: auto" src="https://howtobook.hypotheses.org/files/2025/01/Leibniz_am_Wolfenbuttel-500x200.jpg" alt="" srcset="https://howtobook.hypotheses.org/files/2025/01/Leibniz_am_Wolfenbuttel-500x200.jpg 500w, https://howtobook.hypotheses.org/files/2025/01/Leibniz_am_Wolfenbuttel-300x120.jpg 300w, https://howtobook.hypotheses.org/files/2025/01/Leibniz_am_Wolfenbuttel-768x308.jpg 768w, https://howtobook.hypotheses.org/files/2025/01/Leibniz_am_Wolfenbuttel.jpg 1176w" sizes="auto, (max-width: 500px) 100vw, 500px" /></figure> <p>The decimal 151 becomes 10010111 digitally. Would you like a little how-to on how to come up with it? First of all, you have to read binary numbers from right to left. Now, all the digits (or places) from the rightmost (zeroth digit) to the leftmost (seventh digit) are raised to the power of 2, with the power increasing by 1 from digit to digit. Let’s get started: 2 to the power of 0 for the right-most digit = 1, so this 1 remains unchanged. Then 2 to the power of 1 (=2), the 1 is also there; the intermediate value increases by 2 (2+1). Then 2 to the power of 2 (= 4), the 1 is also there, the intermediate result increases again (4+2+1). At 2 to the power of 3, we come across 0 for the first time, nothing is added, the intermediate result remains unchanged. Then 2 to the power of 4 (= 16), the 1 is here, the intermediate result is increased by 16 (16+4+2+1). At 2 to the power of 5 and 2 to the power of 6, the 0 is there again, nothing is added. Then 2 to the power of 7 (=128); since we come across a 1 again, 128 must be added, and we arrive at the final result: 128+16+4+2+1=151. In our time, digitisation goes much, much further, also translating analogue information, i.e., not only numbers but also images, sounds, texts into a sequence of ones and zeros. The letter ‘A’, for example, is represented as 65 in ASCII code; in binary numbers, this letter becomes 01000001. Humans would be constantly at a loss, if they tried to read this language; they can no longer identify any specific structure because of all the ones and zeros, but machines can handle such input perfectly – quite magical what can be created with the help of electric energy.</p> <p> </p> <p><strong>The systemic repression of bodily functions</strong></p> <p>Is it useful to put ourselves in the algorithm’s shoes? Why not! It seems as if, in the hands of mere humans, algorithms have had quite an impaired, listless existence. Today, in the age of machine learning, they can develop their full potential, be creative, and develop a momentum that would be alive if they were alive. Within fractions of a hundredth of a second, a massive implementation takes place, which the user in most cases is not even aware of. The knowledge that this algorithm produces is not practical knowledge (as in how-to books), but, rather, knowledge about user behaviour, from which the user’s specific preferences are then derived, according to the motto: if the user has liked five videos with cats, I will show him ten more. Machines make use of the fact that numbers are logically independent of space and time. Algorithms by machines have become largely invisible, and our hands and fingers do no more than swipe across screens or press buttons.</p> <p>When how-to mechanisms disappear into an external black box and humans only see their results on a small screen, they get alienated more and more from their bodies and their multisensory abilities. How-to knowledge used to be closely linked to physical experience and direct interaction with materials, tools and the environment. For example, you felt the consistency of a dough with your hands, smelled the fermentation when brewing beer, heard the hissing of hot metal when forging or observed exactly how the colour of a textile changed when dyeing. Seeing, hearing, smelling, tasting and touching worked together, skill was anchored in the multisensory experience of one’s own body. This experience may not get completely lost with digitisation (as long as you actually implement what is demonstrated), but it does fade into the background (like when the amusement derived from watching a cooking video on YouTube does not lead to imitation but is being followed by the purchase of a frozen ready-made product in the supermarket). Today, we are experiencing a profound change in which physical appropriation is being replaced by digital representations and abstract interactions. Knowledge is consumed as disembodied information, not acquired through physical experience. A YouTube video explains how to bake a loaf of bread, but the learner all too often remains a passive consumer, without directly feeling the physical intricacies of the process. The learner ‘sees’ or ‘reads’, but does not smell, feel or taste. In the computer environment, the learning process is reduced to clicks, inputs and screen interactions. Although there have been attempts to bring back physical dimensions through virtual reality technologies or haptic interfaces, they remain substitute solutions. In contrast, in physical processes, motor skills and sensory knowledge are acquired in a way that is difficult to express in words or numbers. This is called tacit knowledge or implicit knowledge, a kind of knowledge acquired through doing. Those who make jugs, for example, not only learn the theory, but also feel with their fingers whether the clay is just right, whether it is not too moist and muddy, not too firm and dry. In other crafts, too, an interactive symbiosis is established between material, device and human that no screen can even come close to replacing.</p> <p>While we can agree that instructions and algorithms share the logic of sequentiality, purposefulness and pragmatic problem-solving, algorithms represent an automated further development of these principles, which, to a large extent, relegates the ‘how-to’ to the metaphorical closet of mathematical-mechanical processing (and thus to the unconscious of the user). The way algorithms work has disappeared from view; they no longer need to be understood or reproduced in order to be followed. At the same time, they present us with new challenges: While traditional instructions emphasised transparency and autonomy, algorithms seem to do the opposite. They make us act in a certain way without us actually knowing or noticing it. To some extent, they help us solve problems we didn’t know we had. A critical examination of how and based on what their suggestions are being made seems overdue. But who is going to do that, numbed and intoxicated as we all are by the auspicious media promises of the digital world?</p> <p>What remains is a residue of unease in terms of skill: Of what use are our physical and sensory functions in this datafied world? It seems that only a few of today’s ten-year-olds still want to or are able to climb trees, and fewer and fewer adults still feel the need to smell the scent of blooming meadows in spring. On the other hand, today’s digital natives are undoubtedly learning other skills that ‘silver surfers’ like me will never be able to acquire or catch up on retrospectively. I’m not sure, though, how much ‘body work’ is required for that….</p> <hr/><div class="citation"><p><span class="citation-title">OpenEdition suggests that you cite this post as follows:</span><br/>Stefan Laube (January 8, 2025). Algorithmic How-to. <em>How-to</em>. 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