Quote:Explore some of the most famous arguments in the ancient debate: is math a human construct or part of the fabric of the universe? -- Would mathematics exist if people didn't? Did we create mathematical concepts to help us understand the world around us, or is math the native language of the universe itself?
Jeff Dekofsky traces some famous arguments in this ancient and hotly debated question. Lesson by Jeff Dekofsky, animation by The Tremendousness Collective.
'Historically, we may regard materialism as a system of dogma set up to combat orthodox dogma...Accordingly we find that, as ancient orthodoxies disintegrate, materialism more and more gives way to scepticism.'
Quote:Did Plato have secret, unwritten doctrines (ἄγραφα δόγματα) deeply influenced by the mathematical esotericism of Pythagoras? From his works, comments by Aristotle, the philosophical project of the Old Academy and later Neo-Pythagorean teachings of Nicomachus of Gerasa and Iamblichus, there is substantial, though controversial evidence, that Plato's deepest teachings are not only to be found in the Dialogues as we know them. What might have these "unwritten doctrines" taught? It may be that a small 4th century ce digest of Arithmology, the intersection of ancient Metaphysics and Mathematics, attributed to Iamblichus might give us insight into these esoteric Platonic teachings and their survival into contemporary philosophy and physics. Join me as we explore this fascinating topic, at the heart of the origins of western philosophy!
'Historically, we may regard materialism as a system of dogma set up to combat orthodox dogma...Accordingly we find that, as ancient orthodoxies disintegrate, materialism more and more gives way to scepticism.'
Quote:...Mathematics gives us shining proof that understanding some aspect of the world does not always come down to uncovering some intricate causal web, not even in principle. Determination is not explanation. And mathematics, rightly understood, demonstrates this in a manner that lets us clearly see the mutual dependency of mind and nature...
'Historically, we may regard materialism as a system of dogma set up to combat orthodox dogma...Accordingly we find that, as ancient orthodoxies disintegrate, materialism more and more gives way to scepticism.'
'Historically, we may regard materialism as a system of dogma set up to combat orthodox dogma...Accordingly we find that, as ancient orthodoxies disintegrate, materialism more and more gives way to scepticism.'
Quote:Brian Fang discusses the many instances in which mathematics developed without empirical motivation turned out to precisely describe the physical patterns of nature. Why would primates evolved to hunt and gather develop the cognitive ability to unveil the underlying mathematical structure of the cosmos? He argues that the most plausible explanation is that nature is itself the expression of mind-like structures also directly present in the human intellect. Mathematical introspection is thus an exploration of the underlying mental landscapes of the cosmos as a whole.
Quote:Consider the timeline. In 1854, Riemann explored a radically general geometry where the rules for measuring distance could vary from point to point. Pure imagination—no experiment suggested space worked this way. Sixty years later, Einstein realized Riemann’s mathematics perfectly described gravity as curved spacetime. He didn’t invent new geometry; he recognized a structure that was waiting.
This pattern repeats with uncanny regularity:
Group theory (abstract algebra) → backbone of particle physics
Hilbert spaces (functional analysis) → natural language of quantum states
Topology (rubber-sheet geometry) → describes phases of matter
Category theory (mathematics of mathematics) → appears in quantum foundations
The key point: mathematical structures typically emerge decades before physicists need them. We’re not curve-fitting data; we’re discovering a prepared architecture.
Quote:It is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena.
Eugene Wigner
'Historically, we may regard materialism as a system of dogma set up to combat orthodox dogma...Accordingly we find that, as ancient orthodoxies disintegrate, materialism more and more gives way to scepticism.'
- Bertrand Russell
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(This post was last modified: 2025-10-25, 05:44 PM by Sci. Edited 1 time in total.)
Quote:This is a brief (~17 minute) introduction to my argument about Platonic space in biology, using a 1-page simplified argument format and then a quick overview of the research program entailed by it.
'Historically, we may regard materialism as a system of dogma set up to combat orthodox dogma...Accordingly we find that, as ancient orthodoxies disintegrate, materialism more and more gives way to scepticism.'
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