What are the implication if there is no algebra?

Answer 1

I want to answer this question at a deeper level and a shallow level. At a shallow level it is very easy to answer. All that is required is to list the applications of mathematics and to put a big cross over it. Algebra is as fundamental to the whole field of mathematics as letters, words and grammar are fundamental to language and literature. So, at a shallow level, your question is really asking what the applications of mathematics in society are.

In a civilised society nearly everything has required mathematics at one point. Things like computers, washing machines and radios (basically everything that requires electricity) all require mathematics. Things like chairs, carpet, glass, concrete, and plastic (basically everything manufactured and/or built) all require mathematics. Things like cars, boats, trains and airplanes (basically all vehicles) all exist because of mathematics. Mathematics has other more continuous applications in society that are not "objects" such as the transport system, the economy, the medical system, Immigration and communications. These are only a fraction of the applications of mathematics. Essentially you could not have a civilised society without mathematics.

Now I want to answer this question at a deeper level. Algebra is a natural consequence of a normal human thought process. Because of this the only way algebra wouldn't exist is if we were just like the monkeys in the trees. Algebra essentially represents our intelligence as humans.

Algebra represents a thought process called deductive reasoning. Deductive reasoning (or deduction) is a process where you find a definite consequence of a known fact or facts. Let me show you an example. Say there are two kids and a broken vase. They both accuse the other of breaking the vase. We know for a fact that both these kids are making contradictory statements (contradictory meaning cannot be true at the same time). Because of this fact we also know that at least one kid must be lying. So here our known fact is that the kids contradict each other and our definite consequence is that at least one must be lying (it's also possible that both are lying, something else may have broken the vase). In algebra our known fact might be that three plus an unknown number equals six (3+x=6). We also know that because these equal each other we can subtract three from both (3-3+x=6-3). So therefore our definite consequence is that our unknown number equals three (x=3).

My point is that if we didn't have algebra then we wouldn't have deductive reasoning. Deductive reasoning is very similar to another thought process called inductive reasoning. Inductive reasoning is a process where you find a PROBABLE consequence of a known fact or facts. Let's look at an example. You know that every time you go to your friend's house they have white walls. They have not told you that they are going to paint the walls so you assume that next time you go to their house their walls will still be white. This is probably going to be true but it's still possible that something will happen and the walls won't be white.

We are constantly using inductive and deductive reasoning all the time. 99% of the time we don't think about it. Because algebra (and the rest of mathematics) is a natural consequence of our normal thought processes its absence would only be possible if humankind was much more animal like. That's why I say the only way algebra wouldn't exist is if we were just like the moneys in the trees.