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.'
'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:Sergiu Klainerman spent years proving that black holes won’t fly apart; and arguing that maths is not a human invention
Quote:The Kerr result came during the early stages of the COVID-19 pandemic, which brought almost everything else to a halt. Klainerman found himself isolated in Manhattan – a ‘phantom city’, as he put it, of largely emptied streets. With his wife, daughter and son 3,000 miles away in California, and a second daughter 1,500 miles away in Dallas, Klainerman suddenly had more time on his hands than usual – enough, as it turned out, for him to take a deeper look at the Wigner essay that had first seized his imagination nearly 50 years before. The ideas behind the paper that Klainerman eventually wrote in response, ‘Reflections on an Essay by Wigner’ (2022), had been ‘germinating for a long time’.
Quote:...Yet it is hard not to take Plato’s ideas seriously when it comes to mathematics. In a famous passage in his Republic, he points to the fact that mathematical objects, such as the circle, seem to have an objective reality independent of our own.108 We associate objectivity to physical things and processes first, because of our senses. We see a glass of wine, we can touch it, smell and taste the wine within it. We can either drink the wine or hear the sound made by breaking the glass. We can also share our experience with friends and not be at all surprised that they have impressions identical to ours. We can also leave the glass on the table and discover a day later that it is still in the same place. It is this rigorous coherence and consistency between the various ways we experience the glass that gives it its sense of objectivity, that is reality.
It makes sense to attempt to define the objectivity, or reality, of a physical object or process by the coherence and consistency of all our sensory experiences,109 including the exchange of impressions with other people. But what about things we consider real, but which cannot be experienced directly through our senses, such as viruses and bacteria, or stars invisible to the naked eye? Those can be brought within the same definition of reality with the help of instruments, such as a microscope or telescope, which vastly enhance our senses. But it is difficult to extend this definition to even smaller things like atoms, electrons, or quarks, for which microscopes are powerless, or massive things like black holes, which are intrinsically not directly observable.110
To account for their reality we need to extend our notion of objectivity by making a huge stretch. We consider them objective not because they are directly coherent and consistent with our senses, which they are not, but because they have a measurable effect, through an observation or experiment, within the framework of an accepted physical theory. These measurable effects may be quite remote from our senses; they need only be consistent, through logical inference, with all other known facts of the theory. But this is not enough. An acceptable physical theory must not only be consistent with all the measurable effects alluded to above, as well as all previously accepted physical facts, but also with itself—that is, with its entire logical framework. This is a mighty task and one that only mathematics is able to accomplish.111 Mathematics indeed provides an unambiguous and highly efficient language to tie together our various physical experiences into coherent physical laws and use them to make precise measurable predictions which can then be confronted by experiments...112
'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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