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Main article: History of experiments

One of the first methodical approaches to experiments in the modern sense is visible in the works of the arab mathematician and scholar Ibn al-Haytham . He conducted his experiments in the field of optics - going back to optical and mathematical problems in the works of Ptolemy - by controlling his experiments due to factors such as self-criticality, reliance on visible results of the experiments as well as a criticality in terms of earlier results. He counts as one of the first scientists/ philosophers using an inductive-experimental method for achieving results [7] [8] . In his book "Optics" he describes the fundamentally new approach to knowledge and research in an experimental sense:

“We should, that is, recommence the inquiry into its principles and premisses, beginning our investigation with an inspection of the things that exist and a survey of the conditions of visible objects. We should distinguish the properties of particulars, and gather by induction what pertains to the eye when vision takes place and what is found in the manner of sensation to be uniform, unchanging, manifest and not subject to doubt. After which we should ascend in our inquiry and reasonings, gradually and orderly, criticizing premisses and exercising caution in regard to conclusions – our aim in all that we make subject to inspection and review being to employ justice, not to follow prejudice, and to take care in all that we judge and criticize that we seek the truth and not to be swayed by opinion. We may in this way eventually come to the truth that gratifies the heart and gradually and carefully reach the end at which certainty appears; while through criticism and caution we may seize the truth that dispels disagreement and resolves doubtful matters. For all that, we are not free from that human turbidity which is in the nature of man; but we must do our best with what we possess of human power. From God we derive support in all things.“ [9]

According to his explanation, a strictly controlled test execution with a sensibility for the subjectivity and susceptibility of outcomes due to the nature of man is necessary. Furthermore, a critical view on the results and outcomes of earlier scholars is necessary:

“It is thus the duty of the man who studies the writings of scientists, if learning the truth is his goal, to make himself an enemy of all that he reads, and, applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.” [10]

Thus, a comparison of earlier results with the experimental results is necessary for an objective experiment - the visible results being more important. In the end, this may mean that an experimental researcher must find enough courage to discard traditional opinions or results, especially if these results are not experimental but results from a logical/ mental derivation. In this process of critical consideration, the man himself should not forget that he tends to subjective opinions - through "prejudices" and "leniency" - and thus has to be critical about his own way of building hypotheses.

An algorithm specifies a series of steps that perform a particular computation or task. Algorithms were originally born as part of mathematics – the word “algorithm” comes from the Arabic writer Muḥammad ibn Mūsā al-Khwārizmī, – but currently the word is strongly associated with computer science. Throughout this book we’ll examine a number of different algorithms to perform a variety of tasks.

Algorithms resemble recipes. Recipes tell you how to accomplish a task by performing a number of steps. For example, to bake a cake the steps are: preheat the oven; mix flour, sugar, and eggs throughly; pour into a baking pan; and so forth.

However, “algorithm” is a technical term with a more specific meaning than “recipe”, and calling something an algorithm means that the following properties are all true:

Studying algorithms is a fundamental part of computer science. There are several different characteristics of an algorithm that are useful to know:

Most of these questions will be discussed for the algorithms covered in this book.

An Example Algorithm

Let’s look at a very simple algorithm called find_max() .

Problem: Given a list of positive numbers, return the largest number on the list.

Inputs: A list L of positive numbers. This list must contain at least one number. (Asking for the largest number in a list of no numbers is not a meaningful question.)

Outputs: A number n , which will be the largest number of the list.

Algorithm:

An implementation in Python:

Does this meet the criteria for being an algorithm?

There can be many different algorithms for solving the same problem. Here’s an alternative algorithm for find_max() :

Implementation:

Let’s ask our questions again.

Is it unambiguous? Yes. Each step is simple and easily translated into Python.

Does it have defined inputs and outputs? Yes.

Is it guaranteed to terminate? Yes. The algorithm obviously terminates if L is of length 1. If L has more than one element, find_max() is called with a list that’s one element shorter and the result is used in a computation.

Does the nested call to find_max() always terminate? Yes. Each time, find_max() is called with a list that’s shorter by one element, so eventually the list will be of length 1 and the nested calls will end.

Finally, does it produce the correct result? Yes. Here’s a sketch of a proof. outlet latest collections buy cheap best prices René Caovilla embellished sandals 5PXjI3

Consider a list of length 1. In this case the largest number is also the only number on the list. find_max() returns this number, so it’s correct for lists of length 1.

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