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@ -2,40 +2,40 @@ The Kindelia Manifesto |
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====================== |
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What is the true nature of computation? A hundred years ago, humanity answered that very question, twice. In 1936, Alan |
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invented the Turing Machine, which, highly inspired by the mechanical trend of the 20th century, distillated the common |
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invented the Turing Machine, which, highly inspired by the mechanical trend of the 20th century, distilled the common |
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components of early computers into a single universal machine that, despite its simplicity, was capable of performing |
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every computation conceivable. From simple numerical calculations to entire operating systems, this small machine could |
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compute anything. Thanks to its elegance and simplicity, the Turing Machine became the most popular model of |
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computation, and served as the main inspiration behind every modern processor and programming language. C, Fortran, |
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Java, Python are languages based on a procedural mindset, which is highly inspired by Turing's invention. |
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Java and Python, are languages based on a procedural mindset, which is highly inspired by Turing's invention. |
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Yet, the Turing Machine wasn't the only model of computation that humanity invented. Albeit a less known history, also |
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in 1936, and in a completely independent way, Alonzo Church invented the Lambda Calculus, which distillated the common |
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in 1936, and in a completely independent way, Alonzo Church invented the Lambda Calculus, which distilled the common |
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components - not of machines, but of different branches of math - into a single universal language that was capable of |
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modeling every mathematical theory. What was surprising, though, is that this language, unexpectedly, could also perform |
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computations. The same algorithms that could be computed by Turing Machines procedurally, could also be computed by the |
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Lambda Calculus, through symbolic manipulations. The idea of using the Lambda Calculus for computations inspired the |
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creation of an entire new branch of programming, which we call the functional paradigm. Haskell, Clojure, Elixir, Agda |
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creation of an entire new branch of programming, which we call the functional paradigm. Haskell, Clojure, Elixir and Agda, |
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are languages based on the functional mindset, which is highly inspired by Church's invention. |
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If both Turing Machines (and procedural languages), and the Lambda Calculus (and functional languages), are capable of |
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computation, which mindset is the "right one"? When it comes to raw capabilities, neither. Still on the 20th century, it |
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If both, Turing Machines (procedural languages) and the Lambda Calculus (functional languages), are capable of doing |
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computations, then which mindset is the "right one"? When it comes to raw capabilities, neither. Still on the 20th century, it |
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was proven that, when it comes to computability, Turing Machines and the Lambda Calculus are equivalent. Every problem |
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that one can solve, can also be solved by the other. That insight is known as the Church-Turing thesis, which |
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essentially states that computers are capable of emulating each-other. If that was completely true, then the choice |
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wouldn't matter. After all, if, for example, every programming language is capable of solving the same set of problems, |
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wouldn't matter. After all, if, for example, every programming language is capable of solving the same set of problems, |
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then what is the point in making a choice? |
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Yet, while the Church-Turing hypothesis makes a statement about computability, it says nothing about computation. In |
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other words, a model can be inherently less efficient than other. Historically, procedural languages such as C and |
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Fortran have have consistently outperformed the fastest functional languages, such as Haskell and Ocaml. Yet, languages |
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Fortran have consistently outperformed the fastest functional languages, such as Haskell and Ocaml. Yet, languages |
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like Haskell and Agda provide abstractions that make entire classes of bugs unrepresentable. Historically, the |
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functional paradigm has been more secure. Of course, these factors can vary greatly, but the point is that this notion |
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of equivalence is limited, and there are impactiful differences. |
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of equivalence is limited, and there are impactful differences. |
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In 1983, Stephen Wolfram introduced the Rule 110, an elementary cellular automaton that has been shown to be as capable |
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as both. Wolfram argues that this model is of fundamental importance for math and physics, and that a new kind of science should emerge from |
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its study. These claims were met with harsh scepticism; after all, if all models are equivalent, what is the point? |
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its study. These claims were met with harsh skepticism; after all, if all models are equivalent, what is the point? |
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Yet, we've just stablished that, while equal in capacity, different models result in different practical outcomes. |
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Perhaps there isn't a new branch of science to emerge from the study of alternative models of computation, but what |
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about the design of processors and programming languages? |
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