There are a lot of people who often state that they like math because it is absolute. The equation 1 + 1 = 2 will always be absolutely true. Is it? That it will be universal, eternal and true for all time, regardless of context and application?
Suppose you have 1 teaspoon of powdered milk and you have 1 teaspoon of water, will it yield to 2 teaspoons of the milk mix? Try that experiment on your own. My bet is that, depending on the absorptive quality of your powdered milk, that you will get something that is less than 2 teaspoons or more than 2 teaspoons, but not absolutely 2 teaspoons.
Technically, 1 + 1 = 2 is not really an absolute. It is an abstraction. More so, it is called an abstract equation. But when you apply it in concretized real-world settings, that seemingly “absolute” equation may not always hold true.
(Note that I used the same units of measurement, which relieves you for arguing that i did not follow additive logical rules. Plus if the equation were truly absolute, then it should be devoid of having to set conditions or rules for it.)
Then again, what are abstract numbers? I shall spare you from the more technical definition and simply use a dictionary-based meaning :
Abstract numbers are numbers used without application to things, as 6, 8, 10; but when applied to anything like 6 feet or 10 men, they become concrete.
It can also be said that abstract numbers and equations are reduced of its context.
Let me give you another example. Say, statistical averages. Three families have 8, 6 and 3 kids respectively. To compute for the average number of children in the family, you would need to divide the sum of all children by the number of families.
The equation would look like this: (8 + 6 + 3) / 3 = 5.67. The equation is valid, but may not be absolutely true given context and application. The reality is you are not going find a family that will have 5.67 children (where 5 are whole persons and 1 of the kids is less a person!)
A Matter of Semantics?
Abstracts cannot be facts because facts are grounded on concrete reality. Abstracts cannot be “absolute” because if permanence, immutability, totality and universal applicability are functions of being absolute, then abstracts should always hold true even if they are applied. Facts are not absolute either because they are not universal all the time. Fact is i have 5 notebooks today, but it doesn’t mean i will still have 5 notebooks tomorrow. A fact today does not guarantee permanence. However, both abstracts and facts are logically valid. Abstracts are validated by algebraic proofs while facts are validated through actual observation, or expert corroboration. The validity of facts though are limited to a specific period in time. That’s why if i say 10 years from now that: “I had 5 notebooks in 2011”, i am stating a fact that is limited by my use of the past tense.
The Misnomer of Absolute Value: Modulus, Magnitude and Norm
In math, absolute value generally means the distance of a number from its origin regardless of its sign. (That distance can be either be length or size.) It is also called a modulus or the neutral value of the size/extent of a real number. Absolute values are used to denote magnitude. Magnitude is the property of a measurement which signifies the relative size, extent or importance.
In essence when we say absolute in technical mathematical terms, we do not necessarily mean absolute in the truest sense of the word. But it takes into consideration the property or modality of a measure.
Hiding Behind False Certainties
People in my line of work, and generally in everyday life, take comfort in the certainty numbers bring. It’s how people make sense of what can be at times an unpredictable world. But numbers by themselves don’t mean anything. When devoid of context, people fall into a trap of seeing the trees instead of the forest. At some point, number fanatics tend to dehumanize stories and fall into this mechanized analysis of trivialities. Math is an exercise in logic and a philosophical vehicle to understand better. It aids towards the solution, but is not the solution. The trick is knowing when to use it as a tool, and not as a substitute for a decision.
So the next time you hear people regurgitate numbers in a presentation, ask them the question – so what does it mean? If they answer you without further boggling your mind, then good! But if they tell you another equation, then you better ask them if they were born a textbook.