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# 物理代写|计算物理代写Computational physics代考|PHYS5640 Abstractness

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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。