Crash course im mathematics: Lesson 3 - The hunter and the cook
This lesson is about mathematical thinking. If it is the first lesson of this crash course you encounter, or you missed some lessons, please go back to the beginning and follow the course trough, by using the framework and index, at the end of the introduction
Herzel street is the place to go, to buy cheap furniture in Tel Aviv. When I lived in a rented apartment downtown, and wanted to buy one of these sofas that turn into a double bed, my flatmate told me this: “Go to the south end of Herzel street, and start entering the shops one by one, checking the prices and payment terms of appropriate sofas in each, and when you get to the other side of the street, consider all your options and only then decide”. I follow her advice, and as I started entering the shops, I quickly understood why it was such a good one. The further I went down the street, the better were the deals I could get. As you can probably understand, the shop owners at the beginning Herzel street, can ask for higher prices because most shoppers would not bother going through all the shops and check all their possibilities, but would settle for looking just at the few first ones.
Not checking all the relevant possibilities, may seem like a stupid or lazy thing to do, but in fact, this is the way our instinctive decisions process works, and for a good reason. Our minds have to make an enormous amount of decisions all the time. Most of this decision making process happens subconsciously, and even when it seems to us that we are consciously choosing between several possibilities, our minds have already ruled out many other possibilities in the subconscious level. Because this process has to happen so fast, it is usually worthwhile to sacrifice it's accuracy for speed. You must have heard and read many times about how this was a necessary survival strategy for our gatherer-hunter ancestors because it was better to mistakenly think that that sound in the forest is a bear, than to think it is something else and then discover too late that it is a bear.
But how does all of this has to do with mathematics? Well, long before humans did basic arithmetics or even had names for numbers, the first use of mathematical thinking by our ancestors, was to simply sit in a group and discuss their possibilities. Why did they have to do that all of the sudden? We don't know for sure, but the answer may be that they had to learn to cook.
About 10 minutes drive from where I live, there is a small cave, called “Qesem cave”. It is one of many sites of human habitats from the Acheulo-Yabrudian period (Between 400,000 - 200,000 years ago) that are spread throughout the mountains of the Levant. But the Qesem cave is different, because it includes the first kitchen that we know of. It turns out that the residents of this cave at the end of the Acheulo-Yabrudian period, which means that they were not yet Homo Sapiens, but rather Homo Erectus, had a dedicated area of the cave for preparing their food. There was fire burning their constantly and the tools that were used in this area were different and specialized for the preparation of the meat of small animals. Other evidence found in the site indicate that the residents of the cave were very thoughtful about how they prepared their meals, beyond what was needed for them to simply survive. It seems that the reason for that was that they had to quickly adapt to a change in their diet because the large animals that were their major source of food were gone. Adapting so quickly by creating new tools and working methods, required considering many different possibilities in a methodological manner. It required team effort for coming with new ideas, considering and testing them. In other words, it required a level of thinking that goes beyond the instinctive level.
Were these the first seeds of mathematical thinking? Of course we don't know for sure. But it goes to show that the ability to stop and consider a large variety of options before making a decision, is deeply rooted into our humanity. So if not for any other reason (although there are in fact, many), we should learn at least basic math, in order to allow this part of our human mentality to develop. Not teaching human children basic math, or even just not doing so correctly would be like birds not teaching their chicklings to fly.
In the next lesson, we will finally start talking about something that you can recognize as mathematics, when we will talk about numbers.