Mathematics and counting is central to human nature. If we were to start from scratch again, as a civilisation, we would have developed the number system same as we have done now. Do this an uncountable number of times and you will find not a single iteration where this rule doesn’t follow. We need numbers. We need them for barter, for security and for effective allocation of resources to our massive, hungry, populations. The development of functions directly follows the development of numbers and counting, be it a hundred or a thousand years, it is inevitable.
Now, one could argue that instead of our number system, we could have developed a different method of calculation and counting. Taking inspiration from the geometric algebra the Greeks made, it is possible one of our imaginary cousin civilisations uses volumes of liquids or grains such as water or sacks of rice to quantify ideas. However, as we have seen with geometric algebra, despite it using numbers thus being a step ahead of our fictional brothers (and sisters), it did eventually develop equations and we can now describe a system of variables in a line and easily understand its significance. Another issue with this water calculation system is that it still, fundamentally uses functions, just in another manner. Therefore, a world without functions must not need the use of mathematics or calculation of any sort. A world with a severe deficiency of video games and twitter.
By now you must have assumed that there is no possible world without functions. This is incorrect. We can find many examples within our own planet. In fact, if you observe closely and with no bias, the usage of functions is actually very, very rare. The slice of organisms who use it is so terrifyingly small on a pi chart that even an optical microscope wouldnt be enough to see it. Most organisms living on earth have no need to develop mathematics. They inherit desirable features that may have elements of mathematical logic to them, gifted to them by evolution, but they do not need to do the mathematics themselves. They get along just fine without knowing how many apples bob bought from the supermarket for his breakfast (answer: 537).
“But”, I hear the reader say, “they are not as dominant or technologically advanced as us, so they should be omitted from this discussion”. I agree. This essay prompt was designed with the thought of a world as technologically advanced as ours, without the need for functions. To not address this would be criminal. In my unqualified opinion, this is possible. Such a situation is difficult to imagine and incredibly speculative in nature. One cannot know for sure if something is possible unless it has been experimentally verified (atleast in this context). This is very much in the realm of science fiction and I have drawn a lot of ideas from one book in particular. The name of the book is “All Tomorrows” and despite my immense regret of having had read it, there is a section of the book devoted to a species that has the potential to not use functions.
The species described in the book is unimaginatively named “Tool Breeders”. They were aquatic animals without opposable thumbs and since there was no possibility of crafting fire under water, these inventive beings made use of the next best resource available to them — other beings. The Tool Breeders would breed other aquatic animals over many generations, to eventually be of use to them. An example of this is the oxygen filtering crustaceans they would place in their blowholes. Over time such a species can master such genetic engineering without the need of mathematics at all. Possibly creating massive factories powered by gentically altered living tools and designing solid, living spaceships that can survive the harshness of vacuum.
I’d like to remind the reader here that, I, myself have no idea about how genetic engineering works. I dropped biology after 10th grade. I am speaking from absolutely no experience and its very probable that everything I’ve written here is complete and utter nonsense with no basis whatsoever. Take whatever you read here with a pinch, no a jar of salt. Sorry.
