How to Make 1 + 1 = 2 Look Scientifically Impressive

By Unknown

Suppose we want to publish something that is as simple as

\[ 1 + 1 = 2 \tag{1} \]

This is not very impressive. If we want our article to be accepted by IEEE reviewers, we have to be more abstract. So, we could complicate the left-hand side of the expression by using

\[ \ln(e) = 1 \]

and

\[ \sin^2 x + \cos^2 x = 1, \]

and the right-hand side can be stated as

\[ 2 = \sum_{n=1}^{\infty}\frac{1}{2^n}. \]

Therefore, Equation (1) can be expressed more scientifically as:

\[ \ln(e) + \left(\sin^2 x + \cos^2 x\right) = \sum_{n=1}^{\infty}\frac{1}{2^n}. \tag{2} \]

which is far more impressive. However, we should not stop here. The expression can be further complicated by using

\[ e = \lim_{z \to \infty}\left(1 + \frac{1}{z}\right)^z \]

and

\[ 1 = \cosh(y)\sqrt{1 - \tanh^2(y)}. \]

Equation (2) may therefore be written as

\[ \ln\left[ \lim_{z \to \infty} \left(1 + \frac{1}{z}\right)^z \right] + \left(\sin^2 x + \cos^2 x\right) = \sum_{n=0}^{\infty} \frac{\cosh(y)\sqrt{1 - \tanh^2(y)}}{2^n}. \tag{3} \]

Note: Other methods of a similar nature could also be used to enhance our prestige, once we grasp the underlying principles.

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