I started reading the book "Data Structures and Network Algorithms" by Robert Tarjan, which is a classic (but a bit outdated - 1983) and I am a bit perplexed by the paragraph in the first chapter, Page 3, first paragraph. I have attached the paragraph below:
An important caveat concerning random-access and pointer machines is that if the machine can manipulate numbers of arbitrary size in constant time, it can perform hidden parallel computation by encoding several numbers into one. There are two ways to prevent this. Instead of counting each operation as one step (the uniform cost measure), we can charge for an operation a time proportional to the number of bits needed to represent the operands (the logarithmic cost measure). Alternatively we can limit the size of the integers we allow to those representable in a constant times log n bits, where n is a measure of the input size, and restrict the operations we allow on real numbers. We shall generally use the latter approach; all our algorithms are implementable on a random-access or pointer machine with integers of size at most n for some small constant c with only comparison, addition, and sometimes multiplication of input values allowed as operations on real numbers, with no clever encoding.
Would somebody be able to explain this paragraph or point me to some references that elaborates it better?