At this moment, I don’t think there’s a single nation contemplating a reduction in its military budget. We may be on the brink of World War III, yet here I am, writing an article about something as seemingly trivial as a mathematical formalism.
Why does this feel so frivolous, even bordering on obscene? The reason lies in the fact that while my potential contribution to preventing future international conflicts is minuscule, I am in a unique position to alleviate some of the suffering caused by such conflicts. As part of the research community, I’m working on genetic therapies that aim to deactivate the subjective experience of intense pain. These therapies are based on well-known mutations that have already demonstrated the ability to reduce pain in certain contexts.
In other words, while I can’t stop us from engaging in wars, I can contribute to ensuring that those who face death in these conflicts don’t have to endure excruciating suffering. Imagine being trapped inside a tank, burning, enduring pain akin to torture. Through advancements in genetic science, we could potentially build a shield against that torture-like agony, making the concept of torture seem as outdated and barbaric as medieval practices. To further develop this, we need a visionary leader willing to make a transformative impact on history. But instead, here I am, immersed in the frivolity of mathematical nuances.
Let’s dive into that frivolity. If you’ve ever worked on developing a compiler, you’ve probably noticed that the minus symbol (–) is used to represent two different meanings.
As a student, I often used symbols without paying much attention to their inconsistencies, valuing formalisms for their practical utility, with my priorities focused elsewhere. But as a teacher, I scrutinize everything I teach, developing an obsession with thoroughly understanding every concept within the subject I’m presenting.
That’s how, while preparing Computer Science contents for the Immune Technology Institute, I ended up reading A Spiral Workbook for Discrete Mathematics by Harris Kwong, a book I highly recommend. I’ve read many excellent books on Discrete Mathematics, but none so clear and approachable as Kwong’s. His methodical approach not only explains what is but also what is not, warning the reader of potential logical pitfalls and correcting common misconceptions. In this way, Dr. Kwong facilitates both learning and unlearning—two essential components of mastering any subject.
One of the key lessons Kwong highlights is the polysemy of the minus symbol (–), which can serve as both a unary operator representing negativity (e.g., –7) and a binary operator for subtraction (e.g., 5–2). My students and I encountered this issue while designing a small compiler for mathematical expressions. This ambiguity proved frustrating, and I wished we could simply use distinct symbols for each meaning.
I see a similar problem with the equals sign (=) in mathematics. The same symbol is used both to represent the correlation between variables in an equation and to indicate the equivalence of two expressions, such as in factorization.
Equation:
Y=2X
Factorization:
(2x+3)(3x-2) = 6×2+5x-6
A parallel issue is addressed in Logic with the symbol ≡, which has three horizontal lines rather than two. This is used to indicate the logical equivalence of two expressions.
In short, we could reserve the equals sign (=) for equations like Y = 2X and use the triple-bar symbol (≡) to indicate equivalence between expressions.
We could also use genetic therapies based on FAAH and FAAH-OUT so that if our soldiers have to lose their lives defending us, at least they do so without suffering.
References:
[1] A Spiral Workbook for Discrete Mathematics (Harris Kwong). https://www.amazon.es/Spiral-Workbook-Discrete-Mathematics/dp/1956862013
1 Comment