God created infinity, and man, unable to understand infinity, had to invent finite sets.
Interpretation
The quote reflects on humanity's struggle to comprehend the concept of infinity, leading to the creation of simplified ideas or systems to manage that complexity.
Gian-Carlo Rota's quote highlights the intrinsic limitation of human understanding when faced with the boundless concept of infinity. It implies that, since humans cannot grasp infinity in its entirety, they resort to framing realities in finite terms or sets, creating frameworks and categories that allow for easier understanding and navigation of the complexities of existence. This reflects a fundamental aspect of human cognition: the necessity to simplify and categorize vast ideas to make them manageable.
In practice
In a philosophy class discussing the nature of existence.
The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.
Every lecture should state one main point and repeat it over and over, like a theme with variations. An audience is like a herd of cows, moving slowly in the direction they are being driven towards. If we make one point, we have a good chance that the audience will take the right direction; if we make several points, then the cows will scatter all over the field. The audience will lose interest and everyone will go back to the thoughts they interrupted in order to come to our lecture.
A mathematician's work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks.
[In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory.
Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don't look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.
You know when civilization began? With the invention of the mirror.
Faith is part of who I am, yes. I was raised Christian Scientist. The most important thing I saw every single week on the wall at Sunday school was the Golden Rule: "Do unto others as you would have them do unto you."
Society is held together by our need; we bind it together with legend, myth, coercion, fearing that without it we will be hurled into that void, within which, like the earth before the Word was spoken, the foundations of society are hidden.
People praise virtue, but they hate it, they run away from it. It freezes you to death, and in this world you've got to keep your feet warm.
Hell, in my opinion, is never finding your true self and never living your own life or knowing who you are.
It has yet to be proven that intelligence has any survival value.
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