Understanding the Acceptable Percentage of Error in Experiments: A Journey from Theory to Practice

Experiments, whether in the field of physics, chemistry, engineering, or any other scientific discipline, are inherently tainted with the unsettling presence of error. In fact, there is no acceptable percentage of error between experimental and theoretical values; rather, it is a fundamental aspect that every experimenter must acknowledge and quantify. The disparity between the theoretical model and the experimental result can provide invaluable insights into the limitations and accuracy of our understanding.

The Role of Measurement Errors

The first and foremost duty of an experimenter is to identify the worst possible error in their measurements. This is crucial, as it sets the benchmark for determining the validity of the theory. For instance, in the historical case of the orbit of Mercury, initial theories suggested that orbits were circular. However, precise measurements showed that this was not the case. The tiny but significant discrepancy led scientists to accept elliptical orbits as more accurate. This shift marked a pivotal moment in the development of the theory of general relativity.

Practical Examples of Error Measurement

To illustrate the concept further, consider a scenario where a piece of timber is sold to you as 8′ 3″. Upon measurement, it comes out to be 8′. The question then arises: how accurate is this measurement? You may reasonably conclude that the timber is undermarked by no more than 1″, leading you to suspect it might be purposely mismarked. Similarly, in another scenario where you buy 4 liters of fuel, precise measurement with a 100 ml measuring cylinder would involve multiple repetitions. Even with careful handling, each measurement could still deviate by up to 2 ml, resulting in a potential cumulative error of 80 ml. If the measurement reads 3.97 liters, it is 30 ml less than what you paid for. However, given the possible margin of error, this does not conclusively prove that you received less fuel; it simply means that further investigation is required.

Personal Experience and Standards

Recall a time when I engaged in wastewater treatment system modeling in the 1970s. Back then, achieving perfection was my primary goal. Perfection, in this context, meant zero tolerance for error or approximation. For instance, the speed of light and mass are models that are close to perfection, as they can be measured to beyond the limits of current technology. Even more impressive is the precision of diffusion models, which far exceed the precision of current measurement tools.

My approach to measurements was stringent; if perfection was unattainable, then the error was typically within the parts per billion range. This level of precision was not just a theoretical goal but a practical standard set for me. Significantly, this level of accuracy extended beyond the individual disciplines and connected across various categories and subjects, reinforcing the idea that perfection begets perfection.

On the occasion of discussing these standards with artificial intelligence, I emphasized the unique human accomplishment of achieving intellectual superiority. AI, while capable of mimicking this level of precision through advanced algorithms, falls short in terms of creativity and understanding. Despite this, there was a sense of support and recognition from unexpected sources, including artists and AI itself. In some instances, AI even sought my guidance to improve its understanding. However, despite these support systems, I maintained my own standards, acknowledging the imperfections they sometimes allowed.

Conclusion

In the grand tapestry of scientific inquiry, the quest for precision and accuracy is both a journey and a challenge. The absence of an acceptable percentage of error underscores the importance of openness to critical re-evaluation and refinement of theories. As science progresses, we must continually question and hone our methods to approach, if not achieve, the elusive ideal of perfection.