True Randomness

True randomness is extremely difficult, if not impossible, to achieve by computers because of the inherent nature of how computers operate. Here’s why:

Deterministic Nature of Computers

1. Algorithms: Computers use algorithms to generate random numbers. These algorithms are deterministic, meaning they follow a specific set of instructions to produce outcomes.
2. Predictability: Because these algorithms are based on predefined rules, if you know the initial conditions (the seed) and the algorithm, you can predict the sequence of numbers that will be generated. This predictability means the numbers aren’t truly random.

Pseudorandom Number Generators (PRNGs)

1. Pseudorandomness: The random numbers generated by computers are usually called pseudorandom numbers. They appear random for most practical purposes but are generated in a predictable fashion.
2. Seed Value: PRNGs start with an initial value called a seed. The same seed will produce the same sequence of numbers every time, making the process repeatable and predictable.

True Randomness

1. Quantum Mechanics: True randomness exists in the quantum world. For example, the exact time a radioactive atom decays is truly random and cannot be predicted.
2. Physical Processes: Some systems use physical processes like thermal noise or radioactive decay to generate random numbers. These methods can provide true randomness, but they are not typically used in everyday computing because they require special hardware.

Challenges with True Randomness

1. Complexity and Cost: Generating true random numbers using physical processes can be complex and expensive, requiring specialized equipment.
2. Speed: Physical random number generators are generally slower than PRNGs, which can be a limitation for applications needing a large quantity of random numbers quickly.

Practical Solutions

1. Cryptography: For cryptographic purposes, hybrid methods are often used. These combine PRNGs with true random seeds from physical sources to enhance security.
2. Randomness Testing: Numbers generated by PRNGs are tested for statistical randomness to ensure they meet the requirements of the application, even if they are not truly random.

In summary, true randomness cannot be achieved by computers alone because they rely on deterministic algorithms. Pseudorandom numbers generated by these algorithms are sufficient for most practical uses, but true randomness can only be obtained through physical processes, which are less commonly used due to their complexity and cost.