The reason lies in the concept of the Weber-Fechner law. This law explains the relationship between the magnitude of a stimulus and our ability to perceive changes in that stimulus.
Here's the detailed reasoning:
1. Weber-Fechner Law: This principle states that the smallest detectable change in a stimulus is proportional to the magnitude of the original stimulus. Essentially, as the weight of an object increases, the ability to perceive small differences in weight decreases.
2. Small Weights (1 ounce and 2 ounces):
- The difference between a package that weighs 1 ounce and one that weighs 2 ounces is 1 ounce.
- This difference is relatively large when compared to the total weight. In percentage terms, the difference (1 ounce) is 100% of the smaller package's weight (1 ounce). This large relative difference is easily noticeable.
3. Larger Weights (3 pounds 1 ounce and 3 pounds 2 ounces):
- First, let's convert the weights to a common unit. There are 16 ounces in a pound. So:
- 3 pounds 1 ounce = 3 16 + 1 = 49 ounces
- 3 pounds 2 ounces = 3 16 + 2 = 50 ounces
- The difference between 49 ounces and 50 ounces is still 1 ounce.
- However, this difference is much smaller relative to the total weight. In percentage terms, the difference (1 ounce) is only about 2% of the smaller package's weight (49 ounces). This small relative difference is much harder to perceive.
In conclusion, even though the absolute difference in weight is the same (1 ounce) in both cases, our ability to detect this difference diminishes as the overall weight increases. This perceptual phenomenon is due to the Weber-Fechner law, which indicates that larger absolute weights require proportionally larger differences to be noticeable.
