One of the early inventions of mankind, apart from wheel and fire, was the invention of numbers. Another practice that man has been following since the early years of his inception is the belief in God. Some say that man invented God whereas others believe in the opposite. And somehow the invention of numbers and the invention of God has a deep connection...
Most animals can’t count. They can only differentiate between one, two and many. But humans can differentiate between one thousand and one thousand and one. Surely, counting numbers was a great invention which makes humans so unique and advanced.
One fine day, man even invented zero to indicate nothingness. Then, zero could have been used to equate spending and expenditure. We kept finding many uses for zero. In the fairly contemporary age, in Newtonian physics, it’s used to show that a body is in equilibrium if the force vector acting on it sum up to zero.
As days passed by, misfortune was bound to come. Losses exceeded profits and debt exceeded credit. And even in this dire state of affairs, a new type of numbers were invented - Negative numbers. Losses began to be recorded using negative numbers and profits with positive numbers. The negatives and positives along with zero are called integers in contemporary mathematics.
As population increased, and amount of natural resources stayed limited, we had to divide a whole into parts. Land holdings had to be divided among members of the family. A fruit had to be shared by two brothers. Fractional numbers were created for keeping a record of these. Now, fractional numbers along with integers are called rational numbers.
Somewhere down the line, someone had an irrational thought. They thought of including numbers such a square root of two in our countably infinite range of numbers and make it uncountable. Irrational numbers might have first popped when finding the length of a hypotenuse using the Pythagoras theorem. And using this very theorem, it was easy to show that irrational numbers can be plotted on the real number line.
The real number line was now complete. But there was still scope for imagination. People thought of recognizing numbers like square root of minus one. Now this was unreal. We knew that square roots of negative numbers do not exist. But still we went ahead and decided to include them, we decided to believe in them. We called root of minus as ‘iota’, and such numbers as ‘imaginary’ numbers. Imaginary numbers along with real numbers are called complex numbers. In the modern world, complex numbers have variety of applications including control theory, improper integrals, fluid dynamics, quantum mechanics, electromagnetism and relativity. Believing in something imaginary has really helped us.
This is the mathematical motivation behind the belief in God. God might not exist, might not be real; but still, believing in something completely imaginary can help us. The relationship between God (imaginary) and man (real) is in fact complex.