Posted on Categories:Computational physics, 物理代写, 计算物理

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## 物理代写|计算物理代写Computational physics代考|Abstractness

There appears to be a disparity between algorithms (i.e., effective procedures), Turing machines, and computable functions – all of which are abstract, mathematical objects-and human computers, which are concrete or non-abstract. ${ }^{35}$ This disparity is evident in the first premise of the analysis, where “the computer” equates the notion of algorithm with that of calculation. It also arises in the second premise, where the restrictions on computers are compared with those of Turing machines.

One way to reconcile this disparity was implicitly suggested by Gandy (1980), and more explicitly by Sieg $(2008,2009)$. They think about the restrictive conditions 1-5 as mathematical constraints or axioms that abstract from the limitations imposed on the human computer. The idea is that these mathematical axioms precisely capture the notion of algorithm (or effective procedure, or effective/algorithmic computation). This is because these conditions model a human computer. The human computer, one might say, is an implementation or concretization of the mathematical axioms (and by extension, human calculation is an implementation of a specific algorithm). ${ }^{36}$

One advantage of this approach is that it does not limit effective computation to human computers, but rather allows it to be executed by non-humans as well-or even by machines. This is simply because the mathematical axioms can be applied to (or model or implemented by) a variety of different systems. The systems in question may be tangible (e.g., human computers) or abstract (e.g., Turing machines); they may be human or non-human. In other words, the axioms define a particular class of (computing) systems – namely, those that satisfy the restrictions, irrespective of whether or not they are human. They can be seen calculation rather than machine computation in mind). Nevertheless, the human interpretation itself invokes real issues about the nature of the human computer that have yet to be resolved. A full discussion of these issues is beyond the scope of the present work; for now, I will make a few pertinent comments that will later be expanded in the context of physical computation (the impatient reader can skip to Section 2.4).

## 物理代写|计算物理代写Computational physics代考|Idealization: Competence and Performance

One may rightly argue that no real human can have unlimited time and space to complete the computation; in this sense, the restrictive conditions are perhaps too liberal. ${ }^{37}$ But the human computer is an idealized entity. ${ }^{38}$ The idealization can take one of two very different forms. One is an idealization in terms of the practical, real-world limitations of space, time, and material aids (e.g., pencils and paper). In principle, the human can use as much time and space as it takes to complete the computation. One might define this kind of idealization in terms of the competence/performance distinction (Chomsky 1965): performance is always limited by the amount of paper potentially available in the universe and by a given time span (e.g., the lifetime of a person, planet, or universe). Competence, however, goes beyond this: under ideal conditions, the human could, in principle, transcend these limitations. This kind of idealization appears to be required if computation is associated with surveyability-since there is no upper limit on the length of a formal proof, other than that it must be finite. ${ }^{39}$

The second sort of idealization concerns normativity. When the human follows an algorithm for addition, the assumption is that he or she is following it “properly”-calculation mistakes, inattention, forgetfulness, distractions,and so forth are immaterial to the computation process. These mistakes are of a different kind from the previous ones. In the preceding cases, real humans will never be able to add very large numbers: they will die or run out of material aids beforehand. This is not the claim here. When asked to calculate ” $67+58$,” even in the actual world, the human computer usually replies ” 125 .” The problem is that occasionally the human-when tired, distracted, or the like-might sometimes reply “126.” Idealization is therefore required to tell which reply is the correct one. Here too, one can describe the difference in terms of the competence/ performance distinction. Competence is associated with the correct application of the (specific) set of instructions, whereas performance is associated with the actual application, which might involve all kinds of faults. ${ }^{40}$

## 物理代写|计算物理代写Computational physics代考|Abstractness

Gandy (1980) 含蓄地提出了一种调和这种差异的方法，而 Sieg 则更明确地提出了一种方法。(2008,2009). 他们将限制条件 1-5 视为数学约束或公理，从强加于人机的限制中抽象出来。这个想法是这些数学公理精确地捕捉了算法（或有效过程，或有效/算法计算）的概念。这是因为这些条件模拟了人机。有人可能会说，人类计算机是数学公理的一种实现或具体化（并且通过扩展，人类计算是一种特定算法的实现）。36

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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## 物理代写|计算物理代写Computational physics代考|Turing’s Computability

Many philosophical accounts of computing subscribe, in one way or another, to the notion that “to compute” is to follow or to execute an effective procedure or an algorithm. I use the terms effective computation, effective calculation, and algorithmic computation interchangeably in reference to any computation (calculation) performed by means of an effective procedure or an algorithm of this sort (in Chapter 3, however, I consider drawing a distinction between effective procedures and algorithms). Similarly, a function (of positive numbers) is deemed effectively computable (calculable) if, as Church puts it, “there exists an algorithm for the calculation of its values” (1936a: 102). In the following chapters, my aim is to cut through the tight relationship between algorithms and physical computation. The first step, made in this chapter, is to separate the notions of algorithmic computation, as studied by Church, Turing, and the other founders of computability, and that of machine computation (at this point I will use the more general term machine; however, I will gradually disambiguate it to distinguish between physical systems and other kinds of machines).

This chapter focuses on Turing’s analysis, which reduces effective computability to Turing machine computability (Turing 1936: sec. 9). Turing’s analysis is of interest for several reasons. First, Turing provided a precise characterization of what is effectively computable (in terms of Turing machine computability). Second, while there were others who offered a precise characterization of effective computability around the same time, Turing’s characterization stands out in that it involves an analysis of the process of computing. Third, Turing introduced the notion of an automatic machine (now known as a Turing machine). ${ }^{1}$ This notion lies at the heart of computability theory and automata theory even today. Turing also introduced the notion of a universal Turing machine: a Turing machine that can simulate the operations of any particular Turing machine, and can thereby compute any function that is computable by any Turing machine. This notion has inspired the development of general-purpose digital electronic computers that now dominate virtually every activity in daily life.

## 物理代写|计算物理代写Computational physics代考|The 1936 Affair

Four pioneering papers were published in 1936 , each of which provides a precise mathematical characterization of effective computability. Alonzo Church (1936a) characterized the effectively computable functions (over the positives) in terms of lambda-definability – an undertaking he began in the early 1930s (Church 1933), and which was carried on by Stephen Kleene and Barkley Rosser. Kleene (1936) characterized the general recursive functions, based on the expansion of primitive recursiveness by Herbrand (1931) and Gödel (1934). ${ }^{3}$ Emil Post (1936) in New York described “finite combinatory processes” carried out by a “problem solver or worker” (p. 289). Meanwhile, young Alan Turing in Cambridge provided a somewhat similar characterization, but offere the precise characterization in terms of Turing machines. Although Turing was referring to the computability of real numbers, he remarked that “it is almost equally easy to define and investigate computable functions” (p. 58) of countable domains. ${ }^{4}$ All these precise characterizations were quickly proven to be extensionally equivalent, as they all define the same class of functions. ${ }^{5}$

Church and Turing-and to some degree Post-formulated versions of what is now known as the Church-Turing thesis (CTT). Church’s classic formulation was as follows:
We now define the notion, already discussed, of an effectively calculable function of positive integers by identifying it with the notion of a recursive function of positive integers (or of a $\lambda$-definable function of positive integers). (Church 1936a: 100)
Kleene coined the term thesis and formulated the thesis as follows:
Thesis I. Every effectively calculable function (effectively decidable predicate) is general recursive. (Kleene 1943: 60) ${ }^{6}$
In this book, we will adhere to Kleene’s formulation. The statement is called a “thesis” because it links a pre-theoretical notion-that of effective (algorithmic) calculability-with the precise notion of general recursiveness, or Turing machine computability. ${ }^{7}$ Arguably, due to the pre-theoretical notion, such a statement is not subject to mathematical proof. ${ }^{8}$ But we will leave aside questions of provability and focus on what is meant by “effective computation.” To address this, we should first explicate the motives that prompted the attempts to characterize computability, which culminated in the so-called 1936 Affair.

## 物理代写|计算物理代写Computational physics代考|The 1936 Affair

1936 年发表了四篇开创性的论文，每一篇都提供了有效可计算性的精确数学表征。Alonzo Church (1936a) 用 lambda 可定义性来描述有效可计算函数（超过正数）——他在 1930 年代初期开始了这项工作（Church 1933），由 Stephen Kleene 和 Barkley Rosser 进行。Kleene (1936) 基于 Herbrand (1931) 和 Gödel (1934) 对原始递归性的扩展描述了一般递归函数。3纽约的 Emil Post (1936) 描述了由“问题解决者或工人”执行的“有限组合过程”（第 289 页）。与此同时，剑桥的年轻艾伦图灵提供了一些类似的表征，但提供了图灵机方面的精确表征。虽然图灵指的是实数的可计算性，但他表示“定义和研究可计算函数几乎同样容易”（第 58 页）可数域。4所有这些精确的表征很快就被证明是外延等价的，因为它们都定义了同一类函数。5

Church 和 Turing——以及在某种程度上是现在被称为 Church-Turing 论文 (CTT) 的后制定版本。Church 的经典表述如下：

Kleene 创造了术语论文并将论文表述如下：

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Computational physics, 物理代写, 计算物理

## avatest™帮您通过考试

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## 物理代写|计算物理代写Computational physics代考|Features

Piccinini (2015: 11-15) lists six desired features of an account of computing: $o b$ jectivity, explanation, the right things compute, the wrong things don’t compute, miscomputation is explained, and taxonomy. I will discuss these features in a somewhat wider perspective, labeling the desiderata a bit differently. The meaning desideratum, as I will call it, is to explain what it means to say that a physical system computes (Section 1.2.1). The ontological desideratum is to explain the objectivity status of computing systems (Section 1.2.2). The utility desideratum is to elucidate the role (such as an explanatory role) of computational descriptions (Section 1.2.3). While this book is mainly concerned with fulfilling the first desideratum, I will also say something about the others.

## 物理代写|计算物理代写Computational physics代考|Meaning

When we say that certain systems, modules, processes, or mechanisms compute, we mean that they are similar in certain respects to each other. Even more importantly, we want to emphasize that they are different in some respects from other, non-computing systems. Thus, the meaning desideratum boils down to classification conditions that correctly classify cases of computation as well as noncomputation. Piccinini formulates this demand in terms of two criteria:
The right things compute. A good account of computing mechanisms should entail that paradigmatic examples of computing mechanisms, such as digital computers, calculators, both universal and non-universal Turing machines, and finite state automata, compute. (2015: 12)

As Piccinini implies, it is unrealistic to have a precise formulation of necessary and sufficient conditions that will clearly classify every system into one of the two classes. There are disputable and borderline cases, such as lookup tables. We would be extremely pleased if our conditions were to correctly classify “paradigmatic examples” of computing and non-computing cases.

Now, what you include in the class of computing systems-and, even more importantly, in the contrast class of non-computing systems-pretty much determines the account of computing you end up with. Changing the context, that is, the systems included in each class, can lead to very different accounts of computing. To illustrate the point about the relationships between the inclusive (things-that-compute) and contrast (things-that-don’t-compute) classes that you start with, on the one hand, and the account of computation you end up with, on the other, we must digress a little and compare two characterizations of computation.

Gödel characterizes computation procedures as being “mechanical,” which he describes as “purely formal, i.e., refer only to the outward structure of the formulas, not to their meaning, so that they could be applied by someone who knew nothing about mathematics, or by a machine” (1933: 45). Jack Copeland provides a somewhat similar characterization of a mechanical computation procedure, saying that it is one that “demands no insight or ingenuity on the part of the human being carrying it out” (Copeland 2015). ${ }^{9}$ In contrast, Sejnowski, Koch, and Churchland claim that “mechanical and causal explanations of chemical and electrical signals in the brain are different from computational explanations. The chief difference is that a computational explanation refers to the information content of the physical signals” (1988: 1300). These two characterizations are blind to content, while Sejnowski, Koch, and Churchland argue that computational explanations refer to informational content, while mechanical ones do not. Leaving aside the validity of these characterizations, it is worth noting that they arrive at very different, and indeed contrasting, characterizations (assuming, of course, that computational explanations and computational procedures are related). I would like to suggest that the characterizations are different partly because they are made in very different contexts.

## 物理代写|计算物理代写Computational physics代考|Features

Piccinini (2015: 11-15) 列出了计算帐户的六个所需特征：○b客观性，解释，正确的事情计算，错误的事情不计算，错误计算得到解释，分类学。我将从更广泛的角度讨论这些特征，对需求的标签略有不同。我将称它为“desideratum”的意思是解释说物理系统进行计算意味着什么（第 1.2.1 节）。本体论的需要是解释计算系统的客观性状态（第 1.2.2 节）。实用需求是阐明计算描述的作用（例如解释作用）（第 1.2.3 节）。虽然这本书主要关注的是实现第一个愿望，但我也会谈谈其他的。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。