S.B. 152 and H.B. 311, collectively known as the Utah Social Media Regulation Act, were social media regulation bills that were passed by the Utah State Legislature in March 2023. The bills would have collectively imposed restrictions on how social networking services serve minors in the state of Utah, including mandatory age verification and age restrictions, as well as restrictions on data collection and on algorithmic recommendations. The Act was intended to take effect in March 2024. However, following a lawsuit over the Act by NetChoice, a tech industry lobby group, the Utah attorney general stated in January 2024 that its implementation had been delayed to October 2024, but was likely to be repealed and amended. On September 10, 2024 Chief Judge Robert J. Shelby issued a written order granting a request from NetChoice for a preliminary injunction, meaning that Utah will be unable to enforce its social media law as litigation plays out. The law was appealed to the 10th Circuit on October 11, 2024 and is awaiting a decision. == Provisions == The Act comprises two bills, S.B. 152 and H.B. 311, which respectively regulate access to social network accounts registered to minors, and impose obligations on social networking services to follow design practices that protect the privacy of minors. The bills would apply to social networks with more than 5 million active users in the United States. Social networking services would've verified the age of all users in the state of Utah, or else their account must've been deleted. The Act does not specify a specific method of age verification. Users who are under 18 must have consent from a parent or guardian to open an account, and the parent must be able to have access to the account and its data for monitoring. Unless required to comply with state or federal law, social networks were prohibited from collecting data based on the activity of minors, and may've not displayed targeted advertising or algorithmic recommendations of content, users, or groups to minors. A social network must not allow minors to access the service between the hours of 10:30 p.m., and 6:30 a.m. without parental consent. H.B. 311 prohibits social networks from exposing features to minors that cause them to have an "addiction" to the platform; the service must perform quarterly audits, and may be sued by users for harms caused by providing "addictive" features; there is a rebuttable presumption of harm if the plaintiff is 16 or younger. The bills prescribed fines of $2,500 per-violation for violations of the provisions of S.B. 152, and up to $250,000 in liabilities (plus fines of $2,500 per-user) for violations of the addiction rules. == History == The two bills were passed in early-March 2023, and signed by Governor Spencer Cox on March 23, 2023. Cox cited studies linking social media addiction to increases in depression and suicide among youth. They were originally intended to take effect on March 1, 2024. In the wake of a lawsuit in Arkansas by the trade association NetChoice over a similar bill, state senator and bill author Mike McKell stated that he planned to introduce amendments when the legislature resumed in 2024. In December 2023, NetChoice filed a lawsuit in Utah seeking to block the Act, citing that its definition of a social network was too vague, and that it "restricts who can express themselves, what can be said, and when and how speech on covered websites can occur, down to the very hours of the day minors can use covered websites. The First Amendment, reinforced by decades of precedent, allows none of this." In regards to its age verification requirements, NetChoice argued that "it may not be enough to simply verify the age of whatever person may be listed on a form of identification (even if they have such a record) because that record may not accurately reflect who the individual actually is." The office of the attorney general stated that the state was "reviewing the lawsuit but remains intently focused on the goal of this legislation: Protecting young people from negative and harmful effects of social media use." In January 2024, Attorney General Sean Reyes asked the court to delay a hearing over the bill, stating that its effective date had been delayed to October 2024, and that the legislature planned to repeal and replace the bills. On September 10, 2024, Federal Chief Judge Robert Shelby granted a preliminary injunction to stop enforcement of the law as litigation continues. The law was later appealed on October 11, 2024, by the state of Utah and had a court hearing on the appeal on November 20, 2025.
Learning curve (machine learning)
In machine learning (ML), a learning curve (or training curve) is a graphical representation that shows how a model's performance on a training set (and usually a validation set) changes with the number of training iterations (epochs) or the amount of training data. Typically, the number of training epochs or training set size is plotted on the x-axis, and the value of the loss function (and possibly some other metric such as the cross-validation score) on the y-axis. Synonyms include error curve, experience curve, improvement curve and generalization curve. More abstractly, learning curves plot the difference between learning effort and predictive performance, where "learning effort" usually means the number of training samples, and "predictive performance" means accuracy on testing samples. Learning curves have many useful purposes in ML, including: choosing model parameters during design, adjusting optimization to improve convergence, and diagnosing problems such as overfitting (or underfitting). Learning curves can also be tools for determining how much a model benefits from adding more training data, and whether the model suffers more from a variance error or a bias error. If both the validation score and the training score converge to a certain value, then the model will no longer significantly benefit from more training data. == Formal definition == When creating a function to approximate the distribution of some data, it is necessary to define a loss function L ( f θ ( X ) , Y ) {\displaystyle L(f_{\theta }(X),Y)} to measure how good the model output is (e.g., accuracy for classification tasks or mean squared error for regression). We then define an optimization process which finds model parameters θ {\displaystyle \theta } such that L ( f θ ( X ) , Y ) {\displaystyle L(f_{\theta }(X),Y)} is minimized, referred to as θ ∗ {\displaystyle \theta ^{}} . === Training curve for amount of data === If the training data is { x 1 , x 2 , … , x n } , { y 1 , y 2 , … y n } {\displaystyle \{x_{1},x_{2},\dots ,x_{n}\},\{y_{1},y_{2},\dots y_{n}\}} and the validation data is { x 1 ′ , x 2 ′ , … x m ′ } , { y 1 ′ , y 2 ′ , … y m ′ } {\displaystyle \{x_{1}',x_{2}',\dots x_{m}'\},\{y_{1}',y_{2}',\dots y_{m}'\}} , a learning curve is the plot of the two curves i ↦ L ( f θ ∗ ( X i , Y i ) ( X i ) , Y i ) {\displaystyle i\mapsto L(f_{\theta ^{}(X_{i},Y_{i})}(X_{i}),Y_{i})} i ↦ L ( f θ ∗ ( X i , Y i ) ( X i ′ ) , Y i ′ ) {\displaystyle i\mapsto L(f_{\theta ^{}(X_{i},Y_{i})}(X_{i}'),Y_{i}')} where X i = { x 1 , x 2 , … x i } {\displaystyle X_{i}=\{x_{1},x_{2},\dots x_{i}\}} === Training curve for number of iterations === Many optimization algorithms are iterative, repeating the same step (such as backpropagation) until the process converges to an optimal value. Gradient descent is one such algorithm. If θ i ∗ {\displaystyle \theta _{i}^{}} is the approximation of the optimal θ {\displaystyle \theta } after i {\displaystyle i} steps, a learning curve is the plot of i ↦ L ( f θ i ∗ ( X , Y ) ( X ) , Y ) {\displaystyle i\mapsto L(f_{\theta _{i}^{}(X,Y)}(X),Y)} i ↦ L ( f θ i ∗ ( X , Y ) ( X ′ ) , Y ′ ) {\displaystyle i\mapsto L(f_{\theta _{i}^{}(X,Y)}(X'),Y')}
Data management plan
A data management plan or DMP is a formal document that outlines how data are to be handled both during a research project, and after the project is completed. The goal of a data management plan is to consider the many aspects of data management, metadata generation, data preservation, and analysis before the project begins; this may lead to data being well-managed in the present, and prepared for preservation in the future. DMPs were originally used in 1966 to manage aeronautical and engineering projects' data collection and analysis, and expanded across engineering and scientific disciplines in the 1970s and 1980s. Up until the early 2000s, DMPs were used "for projects of great technical complexity, and for limited mid-study data collection and processing purposes". In the 2000s and later, E-research and economic policies drove the development and uptake of DMPs. == Importance == Preparing a data management plan before data are collected is claimed to ensure that data are in the correct format, organized well, and better annotated. This could arguably save time in the long term because there is no need to re-organize, re-format, or try to remember details about data. It is also claimed to increase research efficiency since both the data collector and other researchers might be able to understand and use well-annotated data in the future. One component of a data management plan is data archiving and preservation. By deciding on an archive ahead of time, the data collector can format data during collection to make its future submission to a database easier. If data are preserved, they are more relevant since they can be re-used by other researchers. It also allows the data collector to direct requests for data to the database, rather than address requests individually. A frequent argument in favor of preservation is that data that are preserved have the potential to lead to new, unanticipated discoveries, and they prevent duplication of scientific studies that have already been conducted. Data archiving also provides insurance against loss by the data collector. In the 2010s, funding agencies increasingly required data management plans as part of the proposal and evaluation process, despite little or no evidence of their efficacy. == Major components == "There is no general and definitive list of topics that should be covered in a DMP for a research project", and researchers are often left to their own devices as to how to fill out a DMP. === Information about data and data format === A description of data to be produced by the project. This might include (but is not limited to) data that are: Experimental Observational Raw or derived Physical collections Models Simulations Curriculum materials Software Images How will the data be acquired? When and where will they be acquired? After collection, how will the data be processed? Include information about Software used Algorithms Scientific workflows File formats that will be used, justify those formats, and describe the naming conventions used. Quality assurance & quality control measures that will be taken during sample collection, analysis, and processing. If existing data are used, what are their origins? How will the data collected be combined with existing data? What is the relationship between the data collected and existing data? How will the data be managed in the short-term? Consider the following: Version control for files Backing up data and data products Security & protection of data and data products Who will be responsible for management === Metadata content and format === Metadata are the contextual details, including any information important for using data. This may include descriptions of temporal and spatial details, instruments, parameters, units, files, etc. Metadata is commonly referred to as "data about data". Issues to be considered include: How detailed has the metadata to be in order to make the data meaningful? How will the metadata be created and/or captured? Examples include lab notebooks, GPS hand-held units, Auto-saved files on instruments, etc. What format will be used for the metadata? What are the metadata standards commonly used in the respective scientific discipline? There should be justification for the format chosen. === Policies for access, sharing, and re-use === Describe any obligations that exist for sharing data collected. These may include obligations from funding agencies, institutions, other professional organizations, and legal requirements. Include information about how data will be shared, including when the data will be accessible, how long the data will be available, how access can be gained, and any rights that the data collector reserves for using data. Address any ethical or privacy issues with data sharing Address intellectual property & copyright issues. Who owns the copyright? What are the institutional, publisher, and/or funding agency policies associated with intellectual property? Are there embargoes for political, commercial, or patent reasons? Describe the intended future uses/users for the data Indicate how the data should be cited by others. How will the issue of persistent citation be addressed? For example, if the data will be deposited in a public archive, will the dataset have a persistent identifier (e.g., ARK, DOI, Handle, PURL, URN) assigned to it? === Long-term storage and data management === Researchers should identify an appropriate archive for the long-term preservation of their data. By identifying the archive early in the project, the data can be formatted, transformed, and documented appropriately to meet the requirements of the archive. Researchers should consult colleagues and professional societies in their discipline to determine the most appropriate database, and include a backup archive in their data management plan in case their first choice goes out of existence. Early in the project, the primary researcher should identify what data will be preserved in an archive. Usually, preserving the data in its most raw form is desirable, although data derivatives and products can also be preserved. An individual should be identified as the primary contact person for archived data, and ensure contact information is always kept up-to-date in case there are requests for data or information about data. === Budget === Data management and preservation costs may be considerable, depending on the nature of the project. By anticipating costs ahead of time, researchers ensure that the data will be properly managed and archived. Potential expenses that should be considered are Human resources and staff as they handle data preparation, management, documentation, and preservation Hardware and/or software needed for data management, backing up, security, documentation, and preservation Costs associated with submitting the data to an archive The data management plan should include how these costs will be paid. == NSF Data Management Plan == All grant proposals submitted to National Science Foundation (NSF) must include a Data Management Plan that is no more than two pages. This is a supplement (not part of the 15-page proposal) and should describe how the proposal will conform to the Award and Administration Guide policy (see below). It may include the following: The types of data The standards to be used for data and metadata format and content Policies for access and sharing Policies and provisions for re-use Plans for archiving data Policy summarized from the NSF Award and Administration Guide, Section 4 (Dissemination and Sharing of Research Results): Promptly publish with appropriate authorship Share data, samples, physical collections, and supporting materials with others, within a reasonable time frame Share software and inventions Investigators can keep their legal rights over their intellectual property, but they still have to make their results, data, and collections available to others Policies will be implemented via Proposal review Award negotiations and conditions Support/incentives == ESRC Data Management Plan == Since 1995, the UK's Economic and Social Research Council (ESRC) have had a research data policy in place. The current ESRC Research Data Policy states that research data created as a result of ESRC-funded research should be openly available to the scientific community to the maximum extent possible, through long-term preservation and high-quality data management. ESRC requires a data management plan for all research award applications where new data are being created. Such plans are designed to promote a structured approach to data management throughout the data lifecycle, resulting in better quality data that is ready to archive for sharing and re-use. The UK Data Service, the ESRC's flagship data service, provides practical guidance on research data management planning suitable for social science researchers in the UK and around the world. ESRC has a longstanding arrangement with the UK Data A
Ordered key–value store
An ordered key–value store (OKVS) is a type of data storage paradigm that can support multi-model databases. An OKVS is an ordered mapping of bytes to bytes. An OKVS will keep the key–value pairs sorted by the key lexicographic order. OKVS systems provides different set of features and performance trade-offs. Most of them are shipped as a library without network interfaces, in order to be embedded in another process. Most OKVS support ACID guarantees. Some OKVS are distributed databases. Ordered key–value stores found their way into many modern database systems including NewSQL database systems. == History == The origin of ordered key–value store stems from the work of Ken Thompson on dbm in 1979. Later in 1991, Berkeley DB was released that featured a B-Tree backend that allowed the keys to stay sorted. Berkeley DB was said to be very fast and made its way into various commercial product. It was included in Python standard library until 2.7. In 2009, Tokyo Cabinet was released that was superseded by Kyoto Cabinet that support both transaction and ordered keys. In 2011, LMDB was created to replace Berkeley DB in OpenLDAP. There is also Google's LevelDB that was forked by Facebook in 2012 as RocksDB. In 2014, WiredTiger, successor of Berkeley DB was acquired by MongoDB and is since 2019 the primary backend of MongoDB database. Other notable implementation of the OKVS paradigm are Sophia and SQLite3 LSM extension. Another notable use of OKVS paradigm is the multi-model database system called ArangoDB based on RocksDB. Some NewSQL databases are supported by ordered key–value stores. JanusGraph, a property graph database, has both a Berkeley DB backend and FoundationDB backend. == Key concepts == === Lexicographic encoding === There are algorithms that encode basic data types (boolean, string, number) and composition of those data types inside sorted containers (tuple, list, vector) that preserve their natural ordering. It is possible to work with an ordered key–value store without having to work directly with bytes. In FoundationDB, it is called the tuple layer. === Range query === Inside an OKVS, keys are ordered, and because of that it is possible to do range queries. A range query retrieves all keys between two specified keys, ensuring that the fetched keys are returned in a sorted order. === Subspaces === === Key composition === One can construct key spaces to build higher level abstractions. The idea is to construct keys, that takes advantage of the ordered nature of the top level key space. When taking advantage of the ordered nature of the key space, one can query ranges of keys that have particular pattern. === Denormalization === Denormalization, as in, repeating the same piece of data in multiple subspace is common practice. It allows to create secondary representation, also called indices, that will allow to speed up queries. == Higher level abstractions == The following abstraction or databases were built on top ordered key–value stores: Timeseries database, Record Database, also known as Row store databases, they behave similarly to what is dubbed RDBMS, Tuple Stores, also known as Triple Store or Quad Store but also Generic Tuple Store, Document database, that mimics MongoDB API, Full-text search Geographic Information Systems Property Graph Versioned Data Vector space database for Approximate Nearest Neighbor All those abstraction can co-exist with the same OKVS database and when ACID is supported, the operations happens with the guarantees offered by the transaction system. == Feature matrix == == Use-cases == OKVS are useful to implement two strategies: optimize a small feature e.g. to make a 10% improvement in read or write latency; the second strategy is to take advantage of the distributed nature of FoundationDB, and TiKV, for which there is no equivalent at very large scale in resilience. Both users need to re-implement the needed high level abstractions, because there are no portable ready-to-use libraries of high-level abstraction. There is still a complex balance, of complexity, maintainability, fine-tuning, and readily available features that makes it still a choice of experts. Sometime more specialized data-structures can be faster than a high-level abstraction on top of an OKVS. Another interest of OKVS paradigm stems from it simple, and versatile interface, that makes it an interesting target for experimental storage algorithms, and data structures.
Wearable computer
A wearable computer, also known as a body-borne computer or wearable, is a computing device worn on the body. The definition of 'wearable computer' may be narrow or broad, extending to smartphones or even ordinary wristwatches. Wearables may be for general use, in which case they are just a particularly small example of mobile computing. Alternatively, they may be for specialized purposes such as fitness trackers. They may incorporate special sensors such as accelerometers, heart rate monitors, or on the more advanced side, electrocardiogram (ECG) and blood oxygen saturation (SpO2) monitors. Under the definition of wearable computers, we also include novel user interfaces such as Google Glass, an optical head-mounted display controlled by gestures. It may be that specialized wearables will evolve into general all-in-one devices, as happened with the convergence of PDAs and mobile phones into smartphones. Wearables are typically worn on the wrist (e.g. fitness trackers), hung from the neck (like a necklace), strapped to the arm or leg (electronic tagging), or on the head (as glasses or a helmet), though some have been located elsewhere (e.g. on a finger or in a shoe). Devices carried in a pocket or bag – such as smartphones and before them, pocket calculators and PDAs, may or may not be regarded as 'worn'. Wearable computers have various technical issues common to other mobile computing, such as batteries, heat dissipation, software architectures, wireless and personal area networks, and data management. Many wearable computers are active all the time, e.g. processing or recording data continuously. == Applications == Wearable computers are not only limited to computers such as fitness trackers that are worn on wrists; they also include wearables such as heart pacemakers and other prosthetics. They are used most often in research that focuses on behavioral modeling, health monitoring systems, IT and media development, where the person wearing the computer actually moves or is otherwise engaged with his or her surroundings. Wearable computers have been used for the following: general-purpose computing (e.g. smartphones and smartwatches) sensory integration, e.g. to help people see better or understand the world better (whether in task-specific applications like camera-based welding helmets or for everyday use like Google Glass) behavioral modeling health care monitoring systems service management electronic textiles and fashion design, e.g. Microsoft's 2011 prototype "The Printing Dress". Wearable computing is the subject of active research, especially the form-factor and location on the body, with areas of study including user interface design, augmented reality, and pattern recognition. The use of wearables for specific applications, for compensating disabilities or supporting elderly people steadily increases. == Operating systems == The dominant operating systems for wearable computing are: FreeRTOS is a real-time operating system kernel for embedded devices; most of the Smartbands that are currently available in the market are based on FreeRTOS, which include Huawei, Honor, Lenovo, realme, TCL and Xiaomi smartbands. LiteOS is a lightweight open source real-time operating system that is part of Huawei's "1+8+N" Internet of Things solution. Tizen OS from Samsung (there was an announcement in May 2021 that Wear OS and Tizen OS will merge and will be called simply Wear.) watchOS watchOS is a proprietary mobile operating system developed by Apple Inc. to run on the Apple Watch. Wear OS Wear OS (previously known as Android Wear) is a smartwatch operating system developed by Google Inc. == History == Due to the varied definitions of wearable and computer, the first wearable computer could be as early as the first abacus on a necklace, a 16th-century abacus ring, a wristwatch and 'finger-watch' owned by Queen Elizabeth I of England, or the covert timing devices hidden in shoes to cheat at roulette by Thorp and Shannon in the 1960s and 1970s. However, a general-purpose computer is not merely a time-keeping or calculating device, but rather a user-programmable item for arbitrary complex algorithms, interfacing, and data management. By this definition, the wearable computer was invented by Steve Mann, in the late 1970s: Steve Mann, a professor at the University of Toronto, was hailed as the father of the wearable computer and the ISSCC's first virtual panelist, by moderator Woodward Yang of Harvard University (Cambridge Mass.). The development of wearable items has taken several steps of miniaturization from discrete electronics over hybrid designs to fully integrated designs, where just one processor chip, a battery, and some interface conditioning items make the whole unit. === 1500s === Queen Elizabeth I of England received a watch from Robert Dudley in 1571, as a New Year's present; it may have been worn on the forearm rather than the wrist. She also possessed a 'finger-watch' set in a ring, with an alarm that prodded her finger. === 1600s === The Qing dynasty saw the introduction of a fully functional abacus on a ring, which could be used while it was being worn. === 1960s === In 1961, mathematicians Edward O. Thorp and Claude Shannon built some computerized timing devices to help them win a game of roulette. One such timer was concealed in a shoe and another in a pack of cigarettes. Various versions of this apparatus were built in the 1960s and 1970s. Thorp refers to himself as the inventor of the first "wearable computer". In other variations, the system was a concealed cigarette-pack-sized analog computer designed to predict the motion of roulette wheels. A data-taker would use microswitches hidden in his shoes to indicate the speed of the roulette wheel, and the computer would indicate an octant of the roulette wheel to bet on by sending musical tones via radio to a miniature speaker hidden in a collaborator's ear canal. The system was successfully tested in Las Vegas in June 1961, but hardware issues with the speaker wires prevented it from being used beyond test runs. This was not a wearable computer because it could not be re-purposed during use; rather it was an example of task-specific hardware. This work was kept secret until it was first mentioned in Thorp's book Beat the Dealer (revised ed.) in 1966 and later published in detail in 1969. === 1970s === Pocket calculators became mass-market devices in 1970, starting in Japan. Programmable calculators followed in the late 1970s, being somewhat more general-purpose computers. The HP-01 algebraic calculator watch by Hewlett-Packard was released in 1977. A camera-to-tactile vest for the blind, launched by C.C. Collins in 1977, converted images into a 1024-point, ten-inch square tactile grid on a vest. === 1980s === The 1980s saw the rise of more general-purpose wearable computers. In 1981, Steve Mann designed and built a backpack-mounted 6502-based wearable multimedia computer with text, graphics, and multimedia capability, as well as video capability (cameras and other photographic systems). Mann went on to be an early and active researcher in the wearables field, especially known for his 1994 creation of the Wearable Wireless Webcam, the first example of lifelogging. Seiko Epson released the RC-20 Wrist Computer in 1984. It was an early smartwatch, powered by a computer on a chip. In 1989, Reflection Technology marketed the Private Eye head-mounted display, which scans a vertical array of LEDs across the visual field using a vibrating mirror. This display gave rise to several hobbyist and research wearables, including Gerald "Chip" Maguire's IBM/Columbia University Student Electronic Notebook, Doug Platt's Hip-PC, and Carnegie Mellon University's VuMan 1 in 1991. The Student Electronic Notebook consisted of the Private Eye, Toshiba diskless AIX notebook computers (prototypes), a stylus based input system and a virtual keyboard. It used direct-sequence spread spectrum radio links to provide all the usual TCP/IP based services, including NFS mounted file systems and X11, which all ran in the Andrew Project environment. The Hip-PC included an Agenda palmtop used as a chording keyboard attached to the belt and a 1.44 megabyte floppy drive. Later versions incorporated additional equipment from Park Engineering. The system debuted at "The Lap and Palmtop Expo" on 16 April 1991. VuMan 1 was developed as part of a Summer-term course at Carnegie Mellon's Engineering Design Research Center, and was intended for viewing house blueprints. Input was through a three-button unit worn on the belt, and output was through Reflection Tech's Private Eye. The CPU was an 8 MHz 80188 processor with 0.5 MB ROM. === 1990s === In the 1990s PDAs became widely used, and in 1999 were combined with mobile phones in Japan to produce the first mass-market smartphone. In 1993, the Private Eye was used in Thad Starner's wearable, based on Doug Platt's system and built from a kit from Park Enterprises, a Pri
Microsoft Forms
Microsoft Forms (formerly Office 365 Forms) is an online survey creator, part of Microsoft 365. == Usage == Forms allows users to create surveys and quizzes with automatic marking. The data can be exported to Microsoft Excel, Power BI dashboards and viewed live using the Present feature. == Phishing and fraud == Due to a wave of phishing attacks utilizing Microsoft 365 in early 2021, Microsoft uses algorithms to automatically detect and block phishing attempts with Microsoft Forms. Also, Microsoft advises Forms users not to submit personal information, such as passwords, in a form or survey. It also place a similar advisory underneath the “Submit” button in every form created with Forms, warning users not to give out their password.
Kunstweg
Bürgi's Kunstweg is a set of algorithms developed by Jost Bürgi in the late 16th century. They are used to calculate sines to arbitrary precision.. Bürgi used these algorithms to calculate a Canon Sinuum, a sine table in increments of 2 arc seconds. It is believed that the table featured values accurate to eight sexagesimal places. Some authors have speculated that the table only covered the range from 0° to 45°, although there is no evidence supporting this claim. Such tables were crucial for maritime navigation. Johannes Kepler described the Canon Sinuum as the most precise sine table known at the time. Bürgi explained his algorithms in his work Fundamentum Astronomiae, which he presented to Emperor Rudolf II in 1592. The Kunstweg algorithm calculates sine values iteratively. In each step, the value of a cell is the sum of the two preceding cells in the same column. The final cell's value is halved before beginning the next iteration. Ultimately, the values in the last column are normalized. Accurate sine approximations are achieved after only a few iterations. In 2015, Menso Folkerts and coworkers demonstrated that this iterative process does indeed converge toward the true sine values. According to them this was the first step towards differential calculus.