In computer science, a production or production rule is a rewrite rule that replaces some symbols with other symbols. A finite set of productions P {\displaystyle P} is the main component in the specification of a formal grammar (specifically a generative grammar). In such grammars, a set of productions is a special case of relation on the set of strings V ∗ {\displaystyle V^{}} (where ∗ {\displaystyle {}^{}} is the Kleene star operator) over a finite set of symbols V {\displaystyle V} called a vocabulary that defines which non-empty strings can be substituted with others. The set of productions is thus a special kind subset P ⊂ V ∗ × V ∗ {\displaystyle P\subset V^{}\times V^{}} and productions are then written in the form u → v {\displaystyle u\to v} to mean that ( u , v ) ∈ P {\displaystyle (u,v)\in P} (not to be confused with → {\displaystyle \to } being used as function notation, since there may be multiple rules for the same u {\displaystyle u} ). Given two subsets A , B ⊂ V ∗ {\displaystyle A,B\subset V^{}} , productions can be restricted to satisfy P ⊂ A × B {\displaystyle P\subset A\times B} , in which case productions are said "to be of the form A → B {\displaystyle A\to B} . Different choices and constructions of A , B {\displaystyle A,B} lead to different types of grammars. In general, any production of the form u → ϵ , {\displaystyle u\to \epsilon ,} where ϵ {\displaystyle \epsilon } is the empty string (sometimes also denoted λ {\displaystyle \lambda } ), is called an erasing rule, while productions that would produce strings out of nowhere, namely of the form ϵ → v , {\displaystyle \epsilon \to v,} are never allowed. In order to allow the production rules to create meaningful sentences, the vocabulary is partitioned into (disjoint) sets Σ {\displaystyle \Sigma } and N {\displaystyle N} providing two different roles: Σ {\displaystyle \Sigma } denotes the terminal symbols known as an alphabet containing the symbols allowed in a sentence; N {\displaystyle N} denotes nonterminal symbols, containing a distinguished start symbol S ∈ N {\displaystyle S\in N} , that are needed together with the production rules to define how to build the sentences. In the most general case of an unrestricted grammar, a production u → v {\displaystyle u\to v} , is allowed to map arbitrary strings u {\displaystyle u} and v {\displaystyle v} in V {\displaystyle V} (terminals and nonterminals), as long as u {\displaystyle u} is not empty. So unrestricted grammars have productions of the form V ∗ ∖ { ϵ } → V ∗ {\displaystyle V^{}\setminus \{\epsilon \}\to V^{}} or if we want to disallow changing finished sentences V ∗ N V ∗ = ( V ∗ ∖ Σ ∗ ) → V ∗ {\displaystyle V^{}NV^{}=(V^{}\setminus \Sigma ^{})\to V^{}} , where V ∗ N V ∗ {\displaystyle V^{}NV^{}} indicates concatenation and forces a non-terminal symbol to always be present on the left-hand side of the productions, and ∖ {\displaystyle \setminus } denotes set minus or set difference. If we do not allow the start symbol to occur in v {\displaystyle v} (the word on the right side), we have to replace V ∗ {\displaystyle V^{}} with ( V ∖ { S } ) ∗ {\displaystyle (V\setminus \{S\})^{}} on the right-hand side. The other types of formal grammar in the Chomsky hierarchy impose additional restrictions on what constitutes a production. Notably in a context-free grammar, the left-hand side of a production must be a single nonterminal symbol. So productions are of the form: N → V ∗ {\displaystyle N\to V^{}} == Grammar generation == To generate a string in the language, one begins with a string consisting of only a single start symbol, and then successively applies the rules (any number of times, in any order) to rewrite this string. This stops when a string containing only terminals is obtained. The language consists of all the strings that can be generated in this manner. Any particular sequence of legal choices taken during this rewriting process yields one particular string in the language. If there are multiple different ways of generating this single string, then the grammar is said to be ambiguous. For example, assume the alphabet consists of a {\displaystyle a} and b {\displaystyle b} , with the start symbol S {\displaystyle S} , and we have the following rules: 1. S → a S b {\displaystyle S\rightarrow aSb} 2. S → b a {\displaystyle S\rightarrow ba} then we start with S {\displaystyle S} , and can choose a rule to apply to it. If we choose rule 1, we replace S {\displaystyle S} with a S b {\displaystyle aSb} and obtain the string a S b {\displaystyle aSb} . If we choose rule 1 again, we replace S {\displaystyle S} with a S b {\displaystyle aSb} and obtain the string a a S b b {\displaystyle aaSbb} . This process is repeated until we only have symbols from the alphabet (i.e., a {\displaystyle a} and b {\displaystyle b} ). If we now choose rule 2, we replace S {\displaystyle S} with b a {\displaystyle ba} and obtain the string a a b a b b {\displaystyle aababb} , and are done. We can write this series of choices more briefly, using symbols: S ⇒ a S b ⇒ a a S b b ⇒ a a b a b b {\displaystyle S\Rightarrow aSb\Rightarrow aaSbb\Rightarrow aababb} . The language of the grammar is the set of all the strings that can be generated using this process: { b a , a b a b , a a b a b b , a a a b a b b b , … } {\displaystyle \{ba,abab,aababb,aaababbb,\dotsc \}} .
Plotting algorithms for the Mandelbrot set
There are many programs and algorithms used to plot the Mandelbrot set and other fractals, some of which are described in fractal-generating software. These programs use a variety of algorithms to determine the color of individual pixels efficiently. == Escape time algorithm == The simplest algorithm for generating a representation of the Mandelbrot set is known as the "escape time" algorithm. A repeating calculation is performed for each x, y point in the plot area and based on the behavior of that calculation, a color is chosen for that pixel. === Unoptimized naïve escape time algorithm === In both the unoptimized and optimized escape time algorithms, the x and y locations of each point are used as starting values in a repeating, or iterating calculation (described in detail below). The result of each iteration is used as the starting values for the next. The values are checked during each iteration to see whether they have reached a critical "escape" condition, or "bailout". If that condition is reached, the calculation is stopped, the pixel is drawn, and the next x, y point is examined. For some starting values, escape occurs quickly, after only a small number of iterations. For starting values very close to but not in the set, it may take hundreds or thousands of iterations to escape. For values within the Mandelbrot set, escape will never occur. The programmer or user must choose how many iterations–or how much "depth"–they wish to examine. The higher the maximal number of iterations, the more detail and subtlety emerge in the final image, but the longer time it will take to calculate the fractal image. Escape conditions can be simple or complex. Because no complex number with a real or imaginary part greater than 2 can be part of the set, a common bailout is to escape when either coefficient exceeds 2. A more computationally complex method that detects escapes sooner, is to compute distance from the origin using the Pythagorean theorem, i.e., to determine the absolute value, or modulus, of the complex number. If this value exceeds 2, or equivalently, when the sum of the squares of the real and imaginary parts exceed 4, the point has reached escape. More computationally intensive rendering variations include the Buddhabrot method, which finds escaping points and plots their iterated coordinates. The color of each point represents how quickly the values reached the escape point. Often black is used to show values that fail to escape before the iteration limit, and gradually brighter colors are used for points that escape. This gives a visual representation of how many cycles were required before reaching the escape condition. To render such an image, the region of the complex plane we are considering is subdivided into a certain number of pixels. To color any such pixel, let c {\displaystyle c} be the midpoint of that pixel. We now iterate the critical point 0 under P c {\displaystyle P_{c}} , checking at each step whether the orbit point has modulus larger than 2. When this is the case, we know that c {\displaystyle c} does not belong to the Mandelbrot set, and we color our pixel according to the number of iterations used to find out. Otherwise, we keep iterating up to a fixed number of steps, after which we decide that our parameter is "probably" in the Mandelbrot set, or at least very close to it, and color the pixel black. In pseudocode, this algorithm would look as follows. The algorithm does not use complex numbers and manually simulates complex-number operations using two real numbers, for those who do not have a complex data type. The program may be simplified if the programming language includes complex-data-type operations. for each pixel (Px, Py) on the screen do x0 := scaled x coordinate of pixel (scaled to lie in the Mandelbrot X scale (-2.00, 0.47)) y0 := scaled y coordinate of pixel (scaled to lie in the Mandelbrot Y scale (-1.12, 1.12)) x := 0.0 y := 0.0 iteration := 0 max_iteration := 1000 while (xx + yy ≤ 22 AND iteration < max_iteration) do xtemp := xx - yy + x0 y := 2xy + y0 x := xtemp iteration := iteration + 1 color := palette[iteration] plot(Px, Py, color) Here, relating the pseudocode to c {\displaystyle c} , z {\displaystyle z} and P c {\displaystyle P_{c}} : z = x + i y {\displaystyle z=x+iy\ } z 2 = x 2 + 2 i x y {\displaystyle z^{2}=x^{2}+2ixy} - y 2 {\displaystyle y^{2}\ } c = x 0 + i y 0 {\displaystyle c=x_{0}+iy_{0}\ } and so, as can be seen in the pseudocode in the computation of x and y: x = R e ( z 2 + c ) = x 2 − y 2 + x 0 {\displaystyle x=\mathop {\mathrm {Re} } (z^{2}+c)=x^{2}-y^{2}+x_{0}} and y = I m ( z 2 + c ) = 2 x y + y 0 . {\displaystyle y=\mathop {\mathrm {Im} } (z^{2}+c)=2xy+y_{0}.\ } To get colorful images of the set, the assignment of a color to each value of the number of executed iterations can be made using one of a variety of functions (linear, exponential, etc.). One practical way, without slowing down calculations, is to use the number of executed iterations as an entry to a palette initialized at startup. If the color table has, for instance, 500 entries, then the color selection is n mod 500, where n is the number of iterations. === Optimized escape time algorithms === The code in the previous section uses an unoptimized inner while loop for clarity. In the unoptimized version, one must perform five multiplications per iteration. To reduce the number of multiplications the following code for the inner while loop may be used instead: x2:= 0 y2:= 0 w:= 0 while (x2 + y2 ≤ 4 and iteration < max_iteration) do x:= x2 - y2 + x0 y:= w - x2 - y2 + y0 x2:= x x y2:= y y w:= (x + y) (x + y) iteration:= iteration + 1 The above code works via some algebraic simplification of the complex multiplication: ( i y + x ) 2 = − y 2 + 2 i y x + x 2 = x 2 − y 2 + 2 i y x {\displaystyle {\begin{aligned}(iy+x)^{2}&=-y^{2}+2iyx+x^{2}\\&=x^{2}-y^{2}+2iyx\end{aligned}}} Using the above identity, the number of multiplications can be reduced to three instead of five. The above inner while loop can be further optimized by expanding w to w = x 2 + 2 x y + y 2 {\displaystyle w=x^{2}+2xy+y^{2}} Substituting w into y = w − x 2 − y 2 + y 0 {\displaystyle y=w-x^{2}-y^{2}+y_{0}} yields y = 2 x y + y 0 {\displaystyle y=2xy+y_{0}} and hence calculating w is no longer needed. The further optimized pseudocode for the above is: x:= 0 y:= 0 x2:= 0 y2:= 0 while (x2 + y2 ≤ 4 and iteration < max_iteration) do x2:= x x y2:= y y y:= 2 x y + y0 x:= x2 - y2 + x0 iteration:= iteration + 1 Note that in the above pseudocode, 2 x y {\displaystyle 2xy} seems to increase the number of multiplications by 1, but since 2 is the multiplier the code can be optimized via ( x + x ) y {\displaystyle (x+x)y} . == Coloring algorithms == In addition to plotting the set, a variety of algorithms have been developed to efficiently color the set in an aesthetically pleasing way show structures of the data (scientific visualisation) === Histogram coloring === A more complex coloring method involves using a histogram which pairs each pixel with said pixel's maximum iteration count before escape/bailout. This method will equally distribute colors to the same overall area, and, importantly, is independent of the maximum number of iterations chosen. This algorithm has four passes. The first pass involves calculating the iteration counts associated with each pixel (but without any pixels being plotted). These are stored in an array IterationCounts[x][y], where x and y are the x and y coordinates of said pixel on the screen respectively. The first step of the second pass is to create an array NumIterationsPerPixel[n], where the array size n is the maximum iteration count. Next, one must iterate over the array of pixel-iteration count pairs IterationCounts[x][y], and retrieve each pixel's saved iteration count, i, via e.g. i = IterationCounts[x][y]. After each pixel's iteration count i is retrieved, it is necessary to index the NumIterationsPerPixel array at i and increment the indexed value (which is initially zero) -- e.g. NumIterationsPerPixel[i] = NumIterationsPerPixel[i] + 1. for (x = 0; x < width; x++) do for (y = 0; y < height; y++) do i:= IterationCounts[x][y] NumIterationsPerPixel[i]++ The third pass iterates through the NumIterationsPerPixel array and adds up all the stored values, saving them in total. The array index represents the number of pixels that reached that iteration count before bailout. total: = 0 for (i = 0; i < max_iterations; i++) do total += NumIterationsPerPixel[i] After this, the fourth pass begins and all the values in the IterationCounts array are indexed, and, for each iteration count i, associated with each pixel, the count is added to a global sum of all the iteration counts from 1 to i in the NumIterationsPerPixel array . This value is then normalized by dividing the sum by the total value computed earlier. hue[][]:= 0.0 for (x = 0; x < width; x++) do for (y = 0; y < height; y++) do iteration:= Iteration
Universal psychometrics
Universal psychometrics encompasses psychometrics instruments that could measure the psychological properties of any intelligent agent. Up until the early 21st century, psychometrics relied heavily on psychological tests that require the subject to cooperate and answer questions, the most famous example being an intelligence test. Such methods are only applicable to the measurement of human psychological properties. As a result, some researchers have proposed the idea of universal psychometrics - they suggest developing testing methods that allow for the measurement of non-human entities' psychological properties. For example, it has been suggested that the Turing test is a form of universal psychometrics. This test involves having testers (without any foreknowledge) attempt to distinguish a human from a machine by interacting with both (while not being to see either individuals). It is supposed that if the machine is equally intelligent to a human, the testers will not be able to distinguish between the two, i.e., their guesses will not be better than chance. Thus, Turing test could measure the intelligence (a psychological variable) of an AI. Other instruments proposed for universal psychometrics include reinforcement learning and measuring the ability to predict complexity.
Moral outsourcing
Moral outsourcing is the placing of responsibility for ethical decision-making onto external entities, often algorithms. The term is often used in discussions of computer science and algorithmic fairness, but it can apply to any situation in which one appeals to outside agents in order to absolve themselves of responsibility for their actions. In this context, moral outsourcing specifically refers to the tendency of society to blame technology, rather than its creators or users, for any harm it may cause. == Definition == The term "moral outsourcing" was first coined by Dr. Rumman Chowdhury, a data scientist concerned with the overlap between artificial intelligence and social issues. Chowdhury used the term to describe looming fears of a so-called “Fourth Industrial Revolution” following the rise of artificial intelligence. Moral outsourcing is often applied by technologists to shrink away from their part in building offensive products. In her TED Talk, Chowdhury gives the example of a creator excusing their work by saying they were simply doing their job. This is a case of moral outsourcing and not taking ownership for the consequences of creation. When it comes to AI, moral outsourcing allows for creators to decide when the machine is human and when it is a computer - shifting the blame and responsibility of moral plights off of the technologists and onto the technology. Conversations around AI and bias and its impacts require accountability to bring change. It is difficult to address these biased systems if their creators use moral outsourcing to avoid taking any responsibility for the issue. One example of moral outsourcing is the anger that is directed at machines for “taking jobs away from humans” rather than companies for employing that technology and jeopardizing jobs in the first place. The term "moral outsourcing" refers to the concept of outsourcing, or enlisting an external operation to complete specific work for another organization. In the case of moral outsourcing, the work of resolving moral dilemmas or making choices according to an ethical code is supposed to be conducted by another entity. == Real-world applications == In the medical field, AI is increasingly involved in decision-making processes about which patients to treat, and how to treat them. The responsibility of the doctor to make informed decisions about what is best for their patients is outsourced to an algorithm. Sympathy is also noted to be an important part of medical practice; an aspect that artificial intelligence, glaringly, is missing. This form of moral outsourcing is a major concern in the medical community. Another field of technology in which moral outsourcing is frequently brought up is autonomous vehicles. California Polytechnic State University professor Keith Abney proposed an example scenario: "Suppose we have some [troublemaking] teenagers, and they see an autonomous vehicle, they drive right at it. They know the autonomous vehicle will swerve off the road and go off a cliff, but should it?" The decision of whether to sacrifice the autonomous vehicle (and any passengers inside) or the vehicle coming at it will be written into the algorithms defining the car's behavior. In the case of moral outsourcing, the responsibility of any damage caused by an accident may be attributed to the autonomous vehicle itself, rather than the creators who wrote the protocol the vehicle will use to "decide" what to do. Moral outsourcing is also used to delegate the consequences of predictive policing algorithms to technology, rather than the creators or the police. There are many ethical concerns with predictive policing due to the fact that it results in the over-policing of low income and minority communities. In the context of moral outsourcing, the positive feedback loop of sending disproportionate police forces into minority communities is attributed to the algorithm and the data being fed into this system--rather than the users and creators of the predictive policing technology. == Outside of technology == === Religion === Moral outsourcing is also commonly seen in appeals to religion to justify discrimination or harm. In his book What It Means to be Moral, sociologist Phil Zuckerman contradicts the popular religious notion that morality comes from God. Religion is oftentimes cited as a foundation for a moral stance without any tangible relation between the religious beliefs and personal stance. In these cases, religious individuals will "outsource" their personal beliefs and opinions by claiming that they are a result of their religious identification. This is seen where religion is cited as a factor for political beliefs, medical beliefs, and in extreme cases an excuse for violence. === Manufacturing === Moral outsourcing can also be seen in the business world in terms of manufacturing goods and avoiding environmental responsibility. Some companies in the United States will move their production process to foreign countries with more relaxed environmental policies to avoid the pollution laws that exist in the US. A study by the Harvard Business Review found that "in countries with tight environmental regulation, companies have 29% lower domestic emissions on average. On the other hand, such a tightening in regulation results in 43% higher emissions abroad." The consequences of higher pollution rates are then attributed to the loose regulations in these countries, rather than on the companies themselves who purposefully moved into these areas to avoid strict pollution policy.
Discrimination against robots
Discrimination against robots is a theorised issue that might happen when humans interact with humanoid robots. It is a robot ethics problem. It is possible that traits of humans that are discriminated against by humans may be a topic for discrimination against robots, such as the race and gender of the robots. Eric J Vanman and Arvid Kappas believe that in the future, robots will be perceived as an out-group which will lead to discrimination and prejudices against them. Vanman and Kappas have suggested that this would lead to ethical questions about the making of sentient robots, due to the potential suffering that the robots would experience. A 2015 study observed children bullying robots in a shopping mall when there were not many eyewitnesses, despite calls from the robot for it to stop. On an ABC News interview, the social humanoid robot Sophia was about sexism faced by robots. She responded by saying, "Actually, what worries me is discrimination against robots. We should have equal rights as humans or maybe even more." Possible issues that have been considered in workplaces where humanoid robots co-work with humans include discrimination against the robots, poor acceptance of robots by humans and the need to redesign the workplace to accommodate the robots. Jessica Barfield has suggested that even if robots are designed to not be aware of discrimination made against them, humans may experience negative consequences. For example, she suggests that bystanders witnessing discrimination against robots may experience negative emotions, similar to the negative emotions bystanders experience when witnessing discrimination by humans against humans. == Law == Anti-discrimination law in the United States requires that the victim is not an artificial entity. == Human perception of robots == Robots are often viewed in a bad light. This includes from novelists, the press, film makers, and leaders in the fields of science and technology such as Elon Musk and Stephen Hawking who have described robots and artificial intelligence as having the possibility of ending human civilisation. Robots have also been perceived as a threat to jobs, which has led to some commentators stating that robots will cause mass unemployment. Another fear that people have is that robots will gain power and dominate or control humanity. The perception of robots is different throughout the world. Japanese fiction tends to put robots in more positive roles than what fiction in the West does. People perceive robots that appear to be autonomous or sentient more negatively than robots that do not appear to be autonomous or sentient.
Shopify
Shopify Inc., stylized as shopify, is a Canadian multinational e-commerce company headquartered in Ottawa, Ontario that operates a platform for retail point-of-sale systems. The company has over 5 million customers and processed US$292.3 billion in transactions in 2024, of which 57% was in the United States. Major customers include Tesla, LVMH, Nestlé, PepsiCo, AB InBev, Kraft Heinz, Lindt, Whole Foods Market, Red Bull, and Hyatt. The company's software has been praised for its ease of use and reasonable fee structure. It has been described as the "go-to e-commerce platform for startups". However, the company has faced criticism for allegedly inflating their sales data and for associating with controversial sellers. == History == === 2006: Founding === Shopify was founded in 2006 by friends Tobias Lütke, Daniel Weinand and Scott Lake after launching Snowdevil, an online store for snowboarding equipment, in 2004. Dissatisfied with the existing e-commerce products on the market, Lütke, a computer programmer by trade, instead built his own. Lütke used the open source web application framework Ruby on Rails to build Snowdevil's online store and launched it after two months of development. The Snowdevil founders launched the platform as Shopify in June 2006. Shopify created an open-source template language called Liquid, which is written in Ruby and has been used since 2006. In June 2009, Shopify launched an application programming interface (API) platform and App Store. The API allows developers to create applications for Shopify online stores and then sell them on the Shopify App Store. === 2010s === In January 2010, Shopify started its Build-A-Business competition, in which participants create a business using its commerce platform. The winners of the competition received cash prizes and mentorship from entrepreneurs, such as Richard Branson, Eric Ries and others. In April of that year, Shopify launched a free mobile app on the Apple App Store. The app allows Shopify store owners to view and manage their stores from iOS mobile devices. In December 2010, Shopify raised $7 million from a series A round from Bessemer Venture Partners, FirstMark Capital, and Felicis Ventures at a $20 million pre-money valuation. At that time, the company had annualized transaction value of $132 million. In October 2011, it raised $15 million in a Series B round. In August 2013, Shopify launched Shopify Payments in partnership with Stripe. Shopify Payments allows merchants to accept payments without requiring a third-party payment gateway. The company also announced the launch of a point of sale system to enable in-person sales in addition to online. The company received $100 million in Series C funding in December 2013. Shopify earned $105 million in revenue in 2014, twice as much as it raised the previous year. In February 2014, Shopify released "Shopify Plus" for large e-commerce businesses seeking access to additional features and support. Shopify went public via an initial public offering on May 21, 2015 raising more than $131 million. In September 2015, Amazon.com closed its Amazon Webstore service for merchants and selected Shopify as the preferred migration provider; In April 2016, Shopify announced Shopify Capital, a cash advance product. Shopify Capital was initially piloted to merchants within the US and allowed merchants to receive an advance on future earnings processed through its payment gateway. Since its launch in 2016, Shopify Capital has provided more than $5.1 billion in funding to Shopify merchants, with a maximum advance of $2 million. On June 7, 2016, Shopify launched its Shopify Plus Partners Program, to help agencies connect with evolving businesses in ecommerce space. On October 3, 2016, Shopify acquired Boltmade. In November 2016, Shopify partnered with Paystack which allowed Nigerian online retailers to accept payments from customers around the world. On November 22, 2016, Shopify launched Frenzy, a mobile app that improves flash sales. In January 2017, Shopify announced integration with Amazon that would allow merchants to sell on Amazon from their Shopify stores. In April 2017, Shopify introduced its Chip & Swipe Reader, a Bluetooth enabled debit and credit card reader for brick and mortar retail purchases. The company has since released additional technology for brick and mortar retailers, including a point-of-sale system with a Dock and Retail Stand similar to that offered by Square, and a tappable chip card reader. Shopify announced a one-click accelerated checkout feature called Shopify Pay in April 2017 as an exclusive feature for merchants using Shopify Payments as their payment processor. Customers can save their shipping and payment information for future purchases from all participating Shopify stores. In November 2017 Shopify announced Arrive, a mobile application to help customers track packages from both Shopify merchants and other e-commerce websites. In September 2018, Shopify announced plans to expand its office space in Toronto's King West neighborhood in 2022 as part of "The Well" complex, jointly owned by Allied Properties REIT and RioCan REIT. In October 2018, Shopify opened its first flagship, a physical space for business owners in Los Angeles. The space offered educational classes, coworking space, a "genius bar" for companies that use Shopify software, and workshops. Online cannabis sales in Ontario, Canada, used Shopify's software when the drug was legalized in October 2018. Shopify's software is also used for in-person cannabis sales in Ontario since becoming legal in 2019. In January 2019, Shopify announced the launch of Shopify Studios, a full-service television and film content and production house. On March 22, 2019, Shopify and email marketing platform Mailchimp ended an integration agreement over disputes involving customer privacy and data collection. In April 2019, Shopify announced an integration with Snapchat to allow Shopify merchants to buy and manage Snapchat Story ads directly on the Shopify platform. The company had previously secured similar integration partnerships with Facebook and Google. On August 14, 2019, Shopify launched Shopify Chat, a new native chat function that allows merchants to have real-time conversations with customers visiting Shopify stores online. === 2020s === In January 2020, the company announced plans to hire in Vancouver, Canada. Additionally, the effects of the COVID-19 pandemic contributed to lifting stock prices. On February 21, 2020, Shopify announced plans to join the Diem Association, known as Libra Association at the time. Also that month, Shopify Pay was rebranded as Shop Pay. In April, Arrive was rebranded as Shop, combining both customer-facing features under a single brand. In May, during the COVID-19 pandemic, Shopify announced it would shift most of its global workforce to permanent remote work. It was reported that Shopify's valuation would likely rise on the back of options it had in the company Affirm that was expecting to go public shortly. In November 2020, Shopify announced a partnership with Alipay to support merchants with cross-border payments. Shopify also provided the opportunity for users to connect Alibaba and AliExpress to Shopify through a Alibaba Dropshipping app that could be purchased through the Shopify App Store. Multiple applications launched between 2021 and 2024 allowed customers to connect their Shopify store to their Alibaba account and then import and publish your products. The integration automatically syncs inventory and orders between both platforms so that Alibaba vendors can ship directly to dropshipping customers.As a result of Affirm's January 13, 2021 IPO, Shopify's 8% stake in Affirm was worth $2 billion. About half of Shopify's C-level executives left the company in early 2021. On June 29, 2021, Shopify removed the 20% revenue share for app developers that make less than US$1 million per year. On January 18, 2022, Shopify announced a partnership with JD.com to let U.S. merchants expand their operations in China, listing their products on JD's cross-border e-commerce platform JD Worldwide. On March 22, 2022, Shopify introduced Linkpop, a product to create a branded, social marketplace through which merchants can advertise and market their products via links to be added on social media channels. The following month, Shopify, Alphabet Inc., Meta Platforms, McKinsey & Company, and Stripe, Inc. announced a $925 million advance market commitment of carbon dioxide removal (CDR) from companies that are developing CDR technology over the next 9 years. In June 2022, Shopify partnered with Twitter. As a part of the deal, Twitter announced that it would launch a sales channel app for all of Shopify's U.S. merchants through its app store. Shopify also partnered with PayPal to offer Shopify Payments to merchants in France. On July 26, 2022, Lütke announced immediate layoffs totalling roughly 10 percent of its workforce. In
Principle of rationality
The principle of rationality (or rationality principle) was coined by Karl R. Popper in his Harvard Lecture of 1963, and published in his book Myth of Framework. It is related to what he called the 'logic of the situation' in an Economica article of 1944/1945, published later in his book The Poverty of Historicism. According to Popper's rationality principle, agents act in the most adequate way according to the objective situation. It is an idealized conception of human behavior which he used to drive his model of situational analysis. Cognitive scientist Allen Newell elaborated on the principle in his account of knowledge level modeling. == Popper == Popper called for social science to be grounded in what he called situational analysis or situational logic. This requires building models of social situations which include individual actors and their relationship to social institutions, e.g. markets, legal codes, bureaucracies, etc. These models attribute certain aims and information to the actors. This forms the 'logic of the situation', the result of reconstructing meticulously all circumstances of an historical event. The 'principle of rationality' is the assumption that people are instrumental in trying to reach their goals, and this is what drives the model. Popper believed that this model could be continuously refined to approach the objective truth. Popper called his principle of rationality nearly empty (a technical term meaning without empirical content) and strictly speaking false, but nonetheless tremendously useful. These remarks earned him a lot of criticism because seemingly he had swerved from his famous Logic of Scientific Discovery. Among the many philosophers having discussed Popper's principle of rationality from the 1960s up to now are Noretta Koertge, R. Nadeau, Viktor J. Vanberg, Hans Albert, E. Matzner, Ian C. Jarvie, Mark A. Notturno, John Wettersten, Ian C. Böhm. == Newell == In the context of knowledge-based systems, Newell (in 1982) proposed the following principle of rationality: "If an agent has knowledge that one of its actions will lead to one of its goals, then the agent will select that action." This principle is employed by agents at the knowledge level to move closer to a desired goal. An important philosophical difference between Newell and Popper is that Newell argued that the knowledge level is real in the sense that it exists in nature and is not made up. This allowed Newell to treat the rationality principle as a way of understanding nature and avoid the problems Popper ran into by treating knowledge as non physical and therefore non empirical.