What makes something timeless?
The celebrated mathematical physicist Roger Penrose wrote about computing and consciousness in 1989 and argued that consciousness is non-computational. The force of his arguments applies today and will continue to apply to the foreseeable future. The ideas put forward will always be relevant to the topic of computability and artificial intelligence. How can this be possible when computers are evolving at an ever-increasing rate, and when our technological capacity completely outperforms anything that existed thirty years ago?
If Penrose were talking about specific hardware or software from the 80s, then it may not have much predictive power even if we might find it interesting. If he were imagining the future based on his present, it still wouldn't hold because most people aren't great at predicting the future in a meaningful way. Instead, he talks about the logical principles behind computability itself, which greatly extend the unyielding nature of his arguments.
In The Emperor's New Mind, Penrose shows that a Turing machine—an idealized mechanical device that can perform an algorithm, the heart of all digital computers today—can answer any standard calculation by reading one number at a time on an infinite roll of tape. He explains that even if the process is slow or clunky, the answer will eventually be produced by the machine as long as it operates by a functional algorithm. At this slow enough computing rate, we can wonder whether or not a computer can understand what it is that it's doing, even if it may convince us it does in fact understand.
Penrose teaches us that some mathematical questions cannot be answered with an algorithm. I was surprised to learn that mathematics itself shows that not all mathematical questions can be solved algorithmically. In the book, Penrose shows us that even if a calculating machine uses two rolls of tape in parallel, or has two hundred rolls going, or reads information stored in three dimensions instead of one, or has trillions of lightning-fast readers and internal states coordinating at the same time, the process is no different fundamentally and the conclusions from the same proof hold true. Even though digital computers will continue to become more and more magical with what their software and hardware can do, their logical limitations will remain the same.
The cohesiveness of a thought or an object can make it timeless. But there is often more to it than that. Insight allows us to transcend the logical, algorithmic way of being in the world.
A logical argument consists of a list of statements and an order that they follow (similar to the algorithms discussed by Penrose). Each premise contained within the argument is believed to be true. And each step furthers the argument while staying c o n n e c t e d to the premise that came before. The connectedness is most interesting to me. The flow and interconnectedness of a logical line of reasoning give an argument a beautiful dimension to it. Our feelings of interconnection coincide with our perception of inherent beauty. The truth appears to us with its companions the good and the beautiful. Penrose's reasoning, which is an example of good thinking, seems to withstand the tests of time. We attribute goodness to thought by the success of its predictive power, and also because of its connections to truth and beauty. When we ask ourselves what makes something timeless, we find ourselves approaching the three concepts of beauty, goodness, and truth, which are often felt to coexist with an eternal reality that is bound to this world. Intuition and insight allow our sentient mind to perceive a permanent, ceaseless reality.
In many ways, timeless truths can be non-mathematical as well. Essential thinking is often expressed as first-principles thinking. So many examples are industrial: Elon Musk's reusable rockets, Henry Ford's assembly line, and even the concept of mise en place that organizes well-run professional kitchens come to mind. But how about teaching in an elementary school classroom—are there any timeless truths to be found in there? In my experience, learning about the principles of leadership helped keep a lot of chaos at bay. To know yourself really well, to have a strong living vision, to be empathic. These concepts make a world of difference when spending a day being seriously outnumbered by nine-year-olds.
Thinking from first principles helps us navigate the world as seasoned pros. The fundamental principles they rest on have that timelessness about them.
In the mathematical world, as surprising and rich as it is, there are no appeals to passionate rhetoric. We instead find a remote clarity. One that can be discerned through logic and appreciated for its beauty. There are chaotic regions of mathematics, but perhaps only in the sense that logic and beauty haven't yet been found in the patterns of its numbers and interrelations. And when discovering how mathematics corresponds to the physical world, we can get a glimpse of something truly timeless, something that was always there emerging out from our own world of continuous change.
Bibliography
Penrose, R. (1989). The Emperor's New Mind. Oxford University Press.
Clear, J. (2017, November). First Principles: Elon Musk on the Power of Thinking for Yourself. James Clear.