Murphy's law is NOT simply an adage

It can be downright scary (a) how much people trust Wikipedia and (b) how unreliable it can be. Looking to find a simple statement of Murphy's law to cut and paste into a post, I find this gem: 

- Murphy's law is simply an adage and is not grounded on logic or scientific laws.

That is not only incorrect, it is a profound misunderstanding of what the adage means in context and what necessary actions it implies. Software that does not account for edge cases and corner cases (that can go wrong) will inevitably fail (will go wrong). To the extent that you leave an avenue to failure in your software, whatever it may be, you have a defect that in the fullness of time *MUST* be encountered. This article does a disservice to starting and even journeyman programmers by incorrectly framing it as a sort of 'figure of speech'. It means they won't know what it really means in terms of implementation and importance. It also means, if this is their source of information, they won't even understand it or be able to explain it to anyone else. I am, in this regard, a primary source, so I won't change the article, but hopefully, if you are someone who always goes to the talk page (as I do, and as you should do), you will at least be aware that a professional production programmer with more than forty years experience learning the reality of Murphy's Law in practice has a different point of view and this additional explanation.

Murphy's law is true, deep, and somewhat subtle in its implications. It is a simple statement of tautological fact. By definition if it is something that *can* go wrong, it *must* go wrong eventually.

Note: The misspelling in the image, "If it can go wong", is an authentic example of Murphy's Law in practice, perfectly illustrating the principle itself. Even in a text about preventing errors, an error has crept in, demonstrating that anything that can go wrong, will go wrong. ChatGPT that generated the image confessed that it made the mistake honestly. 

Explanation with Probability[edit]

Edge Case Probability[edit]

• Consider an event with two edge cases: E₁ and E₂.
• Let P(E₁) and P(E₂) represent the probabilities of these edge cases occurring.
• Suppose P(E₁) = p and P(E₂) = q.

Corner Case Probability[edit]

• A corner case C occurs at the intersection of two or more conditions.
• If the corner case depends on both E₁ and E₂ happening simultaneously, then:

 ${\displaystyle 𝑃(𝐶)=𝑃({𝐸}_1\cap {𝐸}_2)}$

• Assuming E₁ and E₂ are independent:

 ${\displaystyle 𝑃(𝐶)=𝑃({𝐸}_1)\cdot 𝑃({𝐸}_2)=𝑝\cdot 𝑞}$

Visualization and Interpretation[edit]

Probability of Edge Cases[edit]

• Let's assume ${\displaystyle 𝑝=0.05}$ (5% chance) and ${\displaystyle 𝑞=0.05}$ (5% chance).
• These probabilities might seem low, but they are significant enough to consider in testing.

Probability of Corner Case[edit]

• The probability of the corner case C occurring, given ${\displaystyle 𝑝=0.05}$ and ${\displaystyle 𝑞=0.05}$:

 ${\displaystyle 𝑃(𝐶)=𝑝\cdot 𝑞=0.05\cdot 0.05=0.0025}$

• This is 0.25% chance, much lower than the individual edge cases.

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Murphy's Law Illustration[edit]

Murphy's Law states that if something can go wrong, it will. Applied to our scenario:

• Edge Cases: Each edge case has a 5% chance of occurring. These are already rare, but still within the realm of expected events.
• Corner Cases: The probability of a corner case is much lower (0.25%). Due to its rarity, it might be overlooked during testing.

Mathematical Picture[edit]

Imagine a grid where:

• The x-axis represents one condition (e.g., E₁).
• The y-axis represents another condition (e.g., E₂).

Each condition has a small probability of occurrence. The intersection (corner) where both conditions meet has an even smaller probability.

	Condition Not Met (¬E2)	Condition Met (E2)
Condition Not Met (¬E1)	Common Scenario	Edge Case (q)
Condition Met (E1)	Edge Case (p)	Corner Case (p \cdot q)

Summary[edit]

• Edge Cases: ${\displaystyle 𝑃({𝐸}_1)=0.05}$, ${\displaystyle 𝑃({𝐸}_2)=0.05}$
• Corner Case: ${\displaystyle 𝑃(𝐶)=0.0025}$

Implication[edit]

• While edge cases are relatively rare, corner cases are even rarer.
• According to Murphy's Law, despite the low probabilities, over a large number of trials, even these rare corner cases will eventually occur.
• Because of their rarity, corner cases might not be adequately tested, leading to unexpected failures in real-world scenarios.

This illustration helps in understanding why it's crucial to consider both edge and corner cases during testing and why Murphy's Law suggests that these cases will inevitably manifest over time.