Equivalent: There Are Multiple Ways To Be Right

Two different things can be equal. Equivalence is the concept that two expressions, processes, or systems, can yield the same result. Even if they appear different at first glance. 2 plus 2 and 1 plus 3 are both 4. More broadly, it’s a mental model that helps us understand how different approaches can be equal in value or effect. There is more than one way to do things: to solve a problem, make a decision, start a business, remain fit, have a healthy lifestyle, and so on.

Different formulations and/or approaches can lead to the same end result. Recognizing this truth allows us to see diverse methods, strategies, or perspectives that are equally valid. In problem-solving, you can arrive to the same conclusion via different methods. By definition, when two things are equivalent, one can be substituted for the other without altering the outcome. Different algorithms in programming can produce the same results, hence choosing between them boils down to efficiency, speed, and readability. Equivalence extends beyond numbers: to ideas, strategies, and even products. In decision-making, two distinct business strategies can be equivalent in terms of projected profitability, even if one sells adult diapers while the other furnishes kids with lemonade-flavored electrolytes.

Real-world instances of equivalence:

• Mathematics: the elementary equations 2 plus 2 and 1 plus 3 both yield 4. Comprehending this equivalence drills it into your head that different numerical expressions can represent the same underlying truth.

• Business Strategy: a company can choose between two marketing strategies, (1) to focus on social media advertising, or (2) on influencer partnerships. If both strategies are projected to generate the same level of customer engagement and revenue, they are equivalent. The company can then choose based on factors like cost and brand alignment.

• Legal: two different regulatory approaches might aim to reduce overall pollution. One imposes strict emissions limits. The other offers tax incentives for green technology. If both approaches achieve equal reductions in emissions, policymakers can pick one based on public acceptance, upfront investment, and administrative feasibility.

• Day-to-day Decisions: when buying a product, you could compare two items that appear different in design but have equivalent functionality and quality. Recognizing this equivalence in what genuinely matters, you can concentrate on other factors, like price and aesthetics, in lieu of overanalyzing features that ultimately serve the same purpose.

• Software and Algorithms: in computer science, two different sorting algorithms can produce the same exact list. Their equivalence in terms of output gives developers the option to choose the algorithm that best suits criteria like speed and memory consumption.

How you might use equivalence as a mental model: (1) find the equals sign — figure out where different methods, choices, or approaches result in the same outcome; (2) let your brain catch a break — once you recognize that essential results are equivalent between a few options, you can step back and make a choice based on your second-order priorities; (3) stay flexible — where approaches are equivalent, you can experiment with new niches and ideas, knowing that they will result in the same outcome but give you the opportunity to experience something novel; (4) not black, not white, gray — use equivalence to find common ground in negotiations and collaborative projects, demonstrating that different proposals lead to the same endpoint; (5) equal but not really — recognize that if two approaches are equivalent in output, one can be more resource-efficient, and you ought to pick that path.