Why Does Infinity Break Computers?

Infinity has been one of every mathematician’s and philosopher’s most exciting puzzle for centuries, but when it comes to computers, it’s their biggest nightmare.

My first encounter with this issue was back when our professor gave us the assignment of calculating large factorials. Impatient to test its limits, I inputted 100!, expecting my computer to be on the verge of causing a fire, but instead, I was met with a kind error message and a frozen screen. It was a humbling reminder that we still cannot fully comprehend these complex concepts. To infinity and beyond!

Photo by Angely Acevedo on Unsplash

“Two things are infinite: the universe and human stupidity; and I’m not sure about the universe.” — Albert Einstein

What is infinity?

Infinity represents an immeasurable expanse or “a vast amount of something”. While this abstract definition can be confusing, the concept of infinity finds itself in various fields, from mathematics and physics to the popular Marvel Cinematic Universe.

However, computers don’t find this term half as exciting as we do. The sad truth is, no matter how advanced we are today or will be in 10 years, our beloved machines will not get a single glance at infinity. This limitation poses unique challenges when the systems are met with an infinite number of tasks but have a finite memory cap.

At the most basic level, computers represent numbers using binary (0s and 1s) like in the Matrix. The size of the number is determined by the amount of bits allocated to that task. For example, an 8-bit system can represent numbers from 0 to 2⁸-1, so from 0 to 255. A 64-bit system being commonly used these days has a range from: 0 to 18,446,744,073,709,551,616. But that is not remotely close to infinity, is it?

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Common Scenarios Involving Infinity Issues

Young programmers tend to create the most amount of infinity issues, a faulty loop, recursive functions calling themselves for eternity, and the best one, dividing by 0.

Calculating the logarithm of a non-positive number can lead to undefined or infinite results, causing potential issues in computations.

When visualizing data, encountering an infinite value can destroy the entire plot or graph, making it misleading.

Understanding how computers manage large numbers and infinity is crucial for both software developers and those interested in the intersection of mathematics and computing.

8 Tips to avoid infinite loops:

1. Always define when a loop should stop.
2. Ensure loop counters or conditions are updated within the loop.
3. Use break and continue Wisely, these can control loop flow but use them judiciously.
4. Set a maximum iteration count as a safety measure.
5. Challenge your loops with unexpected inputs or conditions.
6. Set timeouts or fallbacks for loops waiting on external data.
7. Periodically check your code for potential loop issues.
8. Use tools to spot and stop potential infinite loops.

Between the abstract concept of infinity and the tangible limitations of computer systems, programmers stand at the forefront. To navigate this complex terrain, adopting best practices becomes essential. Firstly, good error handling is a must. By anticipating and managing potential errors related to big numbers or infinite processes, developers can ensure that applications remain stable and user-friendly.

Boundary checks, too, are obligatory. By frequently checking that data remains within acceptable limits, programmers can forestall overflow or underflow issues, ensuring accurate and reliable programs. The recourses provided can make our lives easier, providing optimized solutions that have been approved by many developers.

In essence, while infinity poses unique challenges in the realm of computing, a proactive approach grounded in best practices can turn potential pitfalls into opportunities for innovation and precision.