*Behold, a brief historical synopsis first*

In the first decade of the 19th century, a couple of years after the wave of revolution in France had settled, Joseph Fourier, priorly an active member of the revolution, joined the group of scholars that accompanied Napoleon to his campaign to Egypt. Fourier eventually became the governor of southern Egypt but he returned to France in a few years. He then started working on one of the then active research areas, the characterization of the the flow of heat in a material.

*Okay now something to chew*

As water naturally flows between two points only when there is a difference in height between them, heat also flows between two points when there is a difference in temperature between two bodies. Now imagine a table: If I ask you to tell me the temperature of the table what you would do is put a thermometer at a random position on the surface of the table, read the temperature there, assume the temperature across the table would approximately be the same and tell me that value, end of story. (You would also probably warn me not to ask you such moronic questions but that’s not the point 🙂 ). Such an approximation isn’t harsh in the grand scheme of things but in the quantum level it wouldn’t hold water.

The distribution of temperature on the surface of the table and its variation over time is modeled by what is called a heat equation. Simply stated the heat equation is the expression of the distribution of difference of temperature across the surface of a material over time. (At this point you are asking yourself “what’s with the freshman science lecture biruk, get to the point.” But bear with me for a second okay 🙂 ). The heat equation is a partial differential equation (partial differential equation or PDE is an equation used to determine the value of something, in this case heat or temperature, in relation to other variables such as the heat source, position etc… and the variation of these variables over time and/or space.)

Before Fourier’s contribution, there had been quite a remarkable progress in the determination of the heat equation. What was missing was an appropriate model of the complex characteristic of the heat source. Since the heat source was part of the equation, it had to have a proper mathematical representation but it was impossible to come up with some simple equation/model because of the complex(messy) nature of nature. Here comes the light bulb moment. Fourier’s idea basically was that any complex mathematical model of something, as messy as it gets, is the sum of many (infinite) but very simple equations known as basis functions. It’s sort of decomposition of the composite but in a clever way. baam…

Let us take a simple example. Consider a simple pasta sauce. My pasta sauce usually contains, among other things tomatoes, onions, garlic, olive oil, basil & black olives. In between the utter orgasm of their taste buds after devouring my pasta (you guessed it, my pasta is delicious 🙂 ), if someone were to ask me what my sauce is made of, a usual answer would be 100g of tomato paste, 65g of onion, 20g of garlic, 30ml of olive oil, 2g of basil and 45g of black olives and I cooked it for 15 minutes. An amalgam such as a tomato sauce can now be represented by a bunch of basis functions (the ingredients, their amount & time it took to cook them). In other words [100, 65, 20, 30, 2, 45, 15] would be a code for my sauce. The index (position) of each number in the list (vector) is associated to each ingredient (in this case position 0 is tomato paste, position 1 is onion etc..) and the numbers represent the amount of ingredient associated to that position/index in the vector This is the sheer brilliance of Fourier transform: Changing the representation of something from one domain to another (in our case from organic ingredients to bunch of numbers).

Fourier transform has a wide range of applications in engineering but we aren’t interested about that today. Rather we are gonna stretch our imagination to what it would be like to have a Fourier transform of more subjective concepts such as love, intelligence, happiness, fear etc… Meaning understanding subjective emotions using an objective frame work.

For example the human brain has been studied by being broken down into different regions. Neuroscientists are always mapping particular states of emotions with different regions of the brain. You are familiar with expressions such as “when you are happy there is some activity in this part of your brain, when you are in love it’s like a fire works in this and that part of your brain, when you are meditating for a long time such and such parts of your brain which are associated with stress shrink, if you are good in math this part of your brain has a 5% larger size than an average person’s brain etc… ” Now this is a case of an unadulterated Fourier transform: mapping of organic emotions to brain activities and sizes. Here the basis functions are the different brain regions and the transformation involves some sort of representation (electrical, chemical etc…) of the states of these regions. It is now almost possible to tell your state of emotion by looking at the chemical content of each section of your brain. Some other domain such as the electrical state of a person, can also be chosen as a basis function to represent these states and understand them from a different light.

Now if the complete mapping of abstract emotions, which have long been considered subjective, to a different, perhaps more objective form were to become possible then one question should definitely be raised. Will this mark the end for these states to be considered personal i.e specific to each person or will the subjective endure and perhaps lead us to a third previously unknown dimension i.e subjective of the objective.