Numbers and Matrices and Values and the Sun on our Faces

“Hey Mawtchi, I asked my brother to buy twenty-five jars of coconut oil, and each one costs four Euros, how much should I pay him?” she asks me with mischievous eyes.

I interrupt the calculations with matrices I was writing down in a LaTeX file, and since I had not focused enough on her question, my mind engaged in matrix calculation, I ask her, “How much exactly?”

“Twenty-five jars of coconut oil of four Euros each, how much is that?”

“Aha, that’s just one hundred Euro.”

“Really, how coincidental, just one hundred Euro, incredible that you know this so quickly,” she sighs with exaggerated emphasis.

“Four times twenty-five, that’s easy, isn’t it?” I smile, and gently embrace her when she sits down next to me in the sofa.

“No, not four times twenty-five, but twenty-five times four, that’s what I need to know,” she now responds fiercely.

“My love, twenty-five times four, that’s the same amount as four times twenty-five, isn’t it?”

“That’s not the same, nothing my brother bought for us costs twenty-five Euros, I think you’re all wrong now.”

I smile again, “you’re right, you know, twenty-five times four is only equal to four times twenty-five if you consider both the four and the twenty-five as numbers, regardless of what you actually use those numbers for, but when it comes to jars of coconut oil, which cost four Euros each, it could be more complicated, and that’s why you’re wary.”

She looks at me with endearment now that I am showing so much understanding of her awkwardness for all things mathematics.

“By the way,” I continue, “I was just calculating with matrices, which are mathematical entities that are in a sense generalizations of numbers, and there you would be right, one cannot just change the order when multiplying them without affecting the outcome.”

“There, you see,” she says as she gives me a teasing look, “you were just doing math that gets me right.”

“You are even more right than you might suspect this yourself,” I tell her, “you see, the matrices I am calculating with represent magnitudes of microscopic entities, in quantum mechanics, and those magnitudes indeed behave in such a way that swapping order when one multiplies two of them does not lead to the same product.”

“Really,” she says, clearly interested now, and in a combative voice she declares, “I can tell you that I take the side of the matrices then, against the numbers.”

I think she is fantastic, and continue, “that in our human world we use numbers to express the value of jars of coconut oil when they change hands is essentially a very brutal practice, because how could a number express a value in an even slightly correct way. Above all, it shows how primitive our civilization still is. Indeed, numbers are the simplest mathematical notions, if one uses them to replace entities of the real world, one violates the notion of value in an intrinsic way. Values are not numbers, matrices would already be much better, and apparently microscopic entities have understood, they use more sophisticated means to express their values, and indeed, they use matrices.”

She looks at me in silence, with a slightly furrowed brow, “that is what you are working on, among other things, together with your co-workers, isn’t it, a more refined understanding of the dynamics of values in human society, and certainly more refined than the economic one that is so all-important now. Indeed, in that economic dynamics of today, at the interface of exchange, there are mainly quantities of money, expressed in numbers. And in what a disenchanted society that has resulted.”

I marvel at the power and lucidity of her sudden profound remark.

“Yes, well, insights have grown in recent years during the QUARTZ project that make something like this possible, indeed, you sum that up pithily. But, we are just beginning, there is a lot of work ahead, the foundations however are solid, I believe.”

“If you found a political party with the slogan ‘for the matrices and against the numbers’, I will definitely vote for that party,” she smiles.

The sun that we delightfully feel shining on our faces, the nurturing sun, which we know keeps alive, nourishes, cherishes, and will continue to do so for a long time to come. How could a number express this in at least a somewhat faithful way?