Distinguishing between Issues and Solutions
This book discusses two parts of the algorithmic view of the real world. On the one hand, you have issues, which are problems that you need to solve. An issue can describe the desired output of an algorithm, or it can describe a hurdle you must overcome to obtain the desired output. Solutions are the methods, or steps, used to address the issues. A solution can relate to just one step or many steps within the algorithm. In fact, the output of an algorithm, the response to the last step, is a solution. The following sections help you understand some of the important aspects of issues and solutions.
Being correct and efficient
Using algorithms is all about getting an acceptable answer. The reason you look for an acceptable answer is that some algorithms generate more than one answer in response to fuzzy input data. Life often makes precise answers impossible to get. Of course, getting a precise answer is always the goal, but often you end up with an acceptable answer instead.
Getting the most precise answer possible may take too much time. When you seek a precise answer that takes too long to obtain, the information becomes useless and you’ve wasted your time. Choosing between two algorithms that address the same issue may come down to a choice between speed and precision. A fast algorithm may not generate a precise answer, but the answer may still work well enough to provide useful output.
Wrong answers can be a problem. Creating a lot of wrong answers fast is just as bad as creating a lot of precisely correct answers slowly. Part of the focus of this book is helping you find the middle ground between too fast and too slow, and between inaccurate and too accurate. Even though your math teacher stressed the need for providing the correct answer in the way expressed by the book you used at the time, real-world math often involves weighing choices and making middle-ground decisions that affect you in ways you might not think possible.
Discovering there is no free lunch
You may have heard the common myth that you can have everything in the way of computer output without putting much effort into deriving the solution. Unfortunately, no absolute solution exists to any problem, and better answers are often quite costly. When working with algorithms, you quickly discover the need to provide additional resources when you require precise answers quickly. The size and complexity of the data sources you use greatly affect the solution resolution as well. As size and complexity increase, you find that the need to add resources increases as well.
Adapting the strategy to the problem
Part 5 of this book looks at strategies you can use to decrease the cost of working with algorithms. The best mathematicians use tricks to get more output from less computing. For example, you can create an ultimate algorithm to solve an issue, or you can use a host of simpler algorithms to solve the same issue, but using multiple processors. The host of simple algorithms will usually work faster and better than the single, complex algorithm, even though this approach seems counterintuitive.
Describing algorithms in a lingua franca
Algorithms do provide a basis for communication between people, even when those individuals have different perspectives and speak different languages. For example, Bayes’ Theorem (the probability of an event occurring given certain premises; see https://betterexplained.com/articles/an-intuitive-and-short-explanation-of-bayes-theorem/ for a quick explanation of this amazing theorem)
P(B|E) = P(E|B)*P(B)/P(E)
appears the same whether you speak English, Spanish, Chinese, German, French, or any other language. Regardless what language you speak, the algorithm looks the same and acts the same given the same data. Algorithms help cross all sorts of divides that serve to separate humans from each other by expressing ideas in a form that anyone can prove. As you go through this book, you discover the beauty and magic that algorithms can provide in communicating even subtle thoughts to others.
Facing problems that are like brick walls, only harder
An important consideration when working with algorithms is that you can use them to solve issues of any complexity. The algorithm doesn’t think, have emotion, or care how you use it (or even abuse it). You can use algorithms in any way required to solve an issue. For example, the same group of algorithms used to perform facial recognition to act as an alternative to computer passwords (for security purposes) can find terrorists lurking in an airport or recognize a lost child wandering the streets. The same algorithm has different uses; how to use it depends on the interests of the user. Part of the reason you want to read this book carefully is to help you solve those hard problems that may require only a simple algorithm to address.
Structuring Data to Obtain a Solution
Humans think about data in nonspecific ways and apply various rules to the same data to understand it in ways that computers never can. A computer’s view of data is structured, simple, uncompromising, and most definitely not creative. When humans prepare data for a computer to use, the data often interacts with the algorithms in unexpected ways and produces undesirable output. The problem is one in which the human fails to appreciate the limited view of data that a computer has. The following sections describe two aspects of data that you see illustrated in many of the chapters to follow.
Understanding a computer’s point of view
A computer has a simple view of data, but it’s also a view that humans typically don’t understand. For one thing, everything is a number to a computer because computers aren’t designed to work with any other kind of data. Humans see characters on the computer display and assume that the computer interacts with the data in that manner, but the computer doesn’t understand the data or its implications. The letter A is simply the number 65 to the computer. In fact, it’s not truly even the number 65. The computer sees a series of electrical impulses that equate to a binary value of 0100 0001.
Computers also don’t understand the whole concept of uppercase and lowercase. To a human, the lowercase a is simply another form of the uppercase A, but to a computer they’re two different values. A lowercase a appears as the number 97 (a binary value of 0110 0001).
If these simple sorts of single letter comparisons could cause such problems between humans and computers, it isn’t hard to imagine what happens when humans start assuming too much about other kinds of data. For example, a computer can’t hear or appreciate music. Yet,
