Why do some people think 5=2+2

A seemingly simple problem like 2+2 turned into a paradox when real-world contexts came into play, and this sparked Kareem Carr’s discussions about the definitions and principles of the subject. Karim Karr shows how the context can distort the calculation; For example, angles that return to 2π radians or rounding that can turn 2.3+2.3 into 5. The idea extends to statistics and politics, warning that scores like IQ or measuring emotions can be misleading.

On paper, this is one of the easiest math problems in the world. If you’re counting something like screws in a hardware store, the answer is pretty straightforward. But in other contexts, the boundaries are blurred. If you combine 0.48 liters of vinegar with 0.48 liters of baking soda and the resulting reaction produces 1.2 liters of foamy liquid, does that mean that 2+2 equals 5?

We introduce assumptions into the world of mathematics. In this case, simple counting numbers, i.e. integers 1, 2, 3 and the like, show a gap between mathematical abstraction and its application. Using the proposition 2+2=4 as food for thought, mathematicians are exploring situations where 2+2 does not actually equal 4, at least not in a regular way. These interpretations can be extended to larger questions in epistemology, that is, how do we actually know what we know!

A few years ago, Karim Kar, a PhD student in biostatistics at Harvard University, ignited a debate on the social network X about whether 2+2 can equal 5.

In his tweet, he emphasized that counting numbers are abstractions of underlying real things in the world, and as such, we must be careful how these abstractions distort the truth when introduced into real-world scenarios. Arithmetic works well in the textbook, but in practice it is often faced with contextual questions that do not consider parts of a whole, approximations, or more relevant vectors.

For example, if you add whole degrees to an angle, you end up with an angle that measures 2π radians. But an angle with a size of 2π radians has the same orientation as an angle with a size of 0 radians, so whether the angle is 0 radians or 2π radians depends on the context. Similarly, if you turn a screw five full turns instead of four full turns, that is, 8π radians versus 10π radians, the orientation of the screw remains the same, but in one case the screw is driven deeper into the wood.

Replies to Kareem Carr’s tweet showed other examples of real-world account restrictions. Many pointed out that two animals could become three through breeding, or even one depending on the parameters, or that two machines could be turned into three machines using spare parts each and a little manual labor. Others noted that 2.3 rounds to 2, but 2.3 + 2.3 rounds to 5, and so under a certain filter, 2 + 2 = 5.

In general, the notion that we innately learn counting numbers, that is, only integers and not fractions or decimals, is a common misconception among people not trained in mathematics or human development. Young children learn numbers one by one through counting, but only begin to learn more advanced counting, larger numbers, when they can recognize quantities quickly. For example, we find it easier to count to 7 when we can immediately recognize a group of four and then count the fifth, sixth, and seventh. Counting is a learned and unnatural skill; Even non-human animals that can count to four or five, such as dogs and chimpanzees. Therefore, the imposition of abstract numerical numbers on the real world creates an inherent tension.