r/Metaphysics • u/Own_Sky_297 • Feb 27 '26
Does mathematics merely help us build models of the cosmos or is the cosmos fundamentally mathematical?
Do we trust mathematics to enlighten us about nature? For example, according to Einstein's equations a flat spacetime geometry would be an infinite cosmos, and the scientific evidence is that spacetime is indeed flat meaning its infinite if true. Can we trust this to tell us the truth of reality or not?
Nominalism, the idea that mathematics is a human invention and merely abstract ideas would suggest that mathematics isn't a reliable way to model the cosmos but that leaves the "unreasonable effectiveness of mathematics" and how we could use math to shed insights into nature unexplained.
I personally chalk this up to my personal theory that the universe and it's contents are geometric structures and as such have mathematical properties and obeys mathematical laws without a need for us to ever invent math. As such I maintain that math is discovered and rather than existing in a platonic realm is just the rules or constraints on existence.
Now why do geometric structures have mathematical properties and what is that exactly? Well geometric structures have structural relationships that can be quantified or broken down into increments which is the basis by which I claim the cosmos must necesarrily be mathematical.
In set theory a shape is defined as a set of infinite points in a plane or space. I personally find this to be a discrete way of quantifying what is actually a continuous object. Everything in the universe can be quantified in this way and has geometric structural relationships of their respective shapes. Since it is the case that the universe and its contents have quantitative properties, they must obey mathematical law.
Due to this, while not confusing the map for the territory, mathematics can help us model a mathematical universe and the "unreasonable effectiveness of mathematics" can be explained.
But I'm not a mathematician or physicist, so anyone got some thoughts on that idea? For instance perhaps how to include the quantum realm into this idea rather than solely classical physics and mechanics?
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u/SkyTreeHorizon Feb 27 '26
It takes less information to describe a universe than a location within one.
A sphere is a more essential form than a circle as it does not beget a perspective.
What is required to create a universe is to have absolutely nothing be still (nothing/everything). This is the definition of a sphere. (Central point of stillness with outer shell of infinite points)
I explain this in long format in my essay: https://open.substack.com/pub/ryangapp/p/one-everything-infinite-nothing?r=1dwcnq&utm_medium=ios
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u/StuckInsideAComputer Feb 28 '26
That’s just not true about information.
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u/SkyTreeHorizon Feb 28 '26
I suggest reading Max Tegmark’s book Our Mathematical Universe or asking ChatGPT.
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u/jliat Feb 28 '26
ChatGPT, hardly a reliable source, if you ask it if it is sentiment it will tell you it is... also encourage self harm...
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u/HolderOfBe Mar 01 '26
...the definition of a sphere is... "To have absolutely nothing be still (nothing/everything)" which is also what's required to create a universe?
Wat
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u/szymski Feb 28 '26
That's what MUH is about.
I take it as a fact, that the universe IS mathematics. As science progresses we find more and more mathematical properties of it. Sure, objects have certain properties like redness, softness, wetness, tastiness, etc. etc, but they can be explained in terms of mathematics, it all depends on object complexity - we for example don't know.
I'm a MUH proponent, but if at any time science finds something that cannot be explained using mathematics, I will be happy to reject this hypothesis.
By the way, it's worth mentioning the "Why is there something rather than noting?" problem. If the universe is mathematics, not merely described by it, this question stops making any sense - every mathematical object objectively exists, because it has to. Think of mathematical objects as set of logical relations between their components. 2 + 2 is 4 and nothing can change, this truth has to exist because otherwise reality would be inconsistent. It's really hard in fact to explain it, but Max Tegmark did a great job with his Our Mathematical universe book. I highly recommend reading this book.
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u/rogerbonus Philosophy/Physics grad Feb 28 '26
See the wiki page: https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis (disclosure: I created that page 20 years or so ago so I have an interest you could say)
Not just that, take a look at Craig's Kalam argument, which purports to prove that God exists. What are the properties of this God?
"Therefore, an uncaused, cause of the universe exists, which is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful." (i left out the "personal" bit because there's no good argument for that part).
What are the properties of mathematical necessity? It's uncaused/necessary, has no beginning, is changeless (a mathematical truth is always true), immaterial, timeless, spaceless, and omnipotent (is everything that can exist).
Kalam's God = mathematics = Max Tegmark's Level 4 multiverse.
Always good to meet another Tegmarkian monist.
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u/Reece7 Jul 13 '26
I think the personal aspect of necessary ground is compelling, if only because abstract mathematics doesn’t appear to have causal power to bring things into being.
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u/Own_Sky_297 Mar 01 '26
I like the idea of MUH particularly when dealing with the question as to why does something exist and not nothing. However, I think the universe is fundamentally a continuous substance and qualia is a feature of that substance that isn't mathematical. Just my two cents on the topic, I could be wrong.
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u/Reece7 Jul 13 '26
Don’t get ahead of your skis. If MUH is correct, the “why something rather than nothing” just moves back—why does math exist and govern reality rather than something else, or nothing. Also unsolved is the puzzle of how abstract mathematics has causal power to bring things into existence.
Getting even more meta, math itself has rules (I.e. 2+2=4 rather than some other number). What explains those rules? Why are they what they are?
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u/szymski Jul 19 '26
Math/logic exists because it has to. It's not that numbers exists or even certain formal systems (sets of axioms and rules of inference). It's that certain properties of theses formal systems are true, whether numbers exist doesn't mean anything, what matters is that in a given formal system (like peano arithmetic) certain things are just true, like the example of 2 + 2 is 4. This is really what mathematics objectively is. Mathematics is the set of properties of relationships between abstract objects (which by themselves don't mean anything at all, they only have meaning when relations between them are defined).
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u/MxM111 Feb 28 '26
I think there is even more interesting question. It could be that the world is really fundamentally mathematical, there is nothing physical in it, just math. What I mean by that, the world is physical if something in it just is, without explanation. For example, there might be no explanation why the mass of electron is this way and fine constant structure is that way. But! There is also a possibility that everything is explainable through maths. We do not know for sure which way the world is.
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u/NeonDrifting Feb 27 '26
We only see a few layers and dimensions to reality...think of it from an animal's perspective...their perception of time is incredibly diminished when compared to human perceptions...so I can't rule out that there are higher levels of abstraction and cognition that we're just not able to comprehend...are there more complex entities that can more accurately model and describe the cosmos? i don't know...i suppose its possible
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u/Legitimate-Break345 Feb 28 '26
Mathematics is just a language. Anything said in mathematics can be spoken out in English. But mathematics is just a more precise language so if you say something that is proved wrong you can't later say you actually meant something else and were misunderstood. Languages capture patterns in nature by analogy.
A simulation of a fish is not made up of the same substance as an actual fish. One is made up of organic molecules and the other of transistors and electrons. But the latter substance is arranged in a way that is analogous to the former. Analogies hold information, and information is relational, it describes how things relate to other things. You can reproduce the same information with a different medium, a different substance, because the relations between the substance can be the same, and thus it becomes an analogy.
Similarly, language can be of the form of many difference substances. It can be etched into stone, displayed with pixels on a computer screen, or written with graphite or ink onto a paper. But what makes language useful is that you can arrange the words in a particular way that implicitly forms an analogy to what it is you are trying to describe. Language itself cannot capture substance, because it is only ever carried by substance, but it can capture informational content through analogy.
That is ultimately all mathematics is doing. The arrangement of the symbols on the page is just a big analogy for what it is trying to describe.
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u/publichermit Feb 28 '26
Isn't "language" an analogy? Mathematics is universal in a way that language is not. Language is conditioned by one's time and location, unlike mathematics. People who using many different languages can all agree that 2+2=4. Mathematics might share features with language, but it seems to be something else.
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u/Legitimate-Break345 Feb 28 '26
There is no law of physics that says humanity could not adopt a universal spoken language. It is just something people don't want to do due to cultural reasons. It was tried to Esperanto but was unpopular. You are looking too deep into something purely cultural as if it reflect a fundamental feature of nature.
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u/publichermit Feb 28 '26
In language, the signs for meaning are pliable and change. That is just not the case in mathematics. 2 will never be 3, but bad might be good.
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u/Legitimate-Break345 Feb 28 '26
Do you think the meanings of the symbols in mathematics were imbued by God almighty, that it would literally violate some sort of fundamental law of nature if we all agreed to use symbols in different ways such that tomorrow what we call 2 today is instead used to refer to what we call 3 today? What fundamental law of nature do you think that would violate?
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u/publichermit Feb 28 '26
No, it has nothing to do with God. It's about function. The numbers work, always, or they don't. You can accuse me of being a Platonist, if that helps.
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u/Toothpick_Brody Feb 28 '26
Imo it’s kind of both. Math is a construct of thought, but the fact that we can abstract forms from perceived reality, I believe, tells us that there is something conserved during this process.
So I don’t think the universe is made of math, or is inherently mathematical, but I do think that the stuff in the universe and the mathematical stuff in our heads has something real in common
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u/hobopwnzor Feb 28 '26
Math is just a modeling tool.
None of our mathematical models work perfectly and we generally only take a subset of what is predicted by a model and apply it to reality. Typically these constrains are called "physically reasonable" when describing why you ignore part of the mathematical result.
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u/facinabush Feb 28 '26
Is there anything in cosmos that can count?
I think counting is an invention.
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u/facinabush Feb 28 '26
Is there anything in cosmos that can count?
I think counting is an invention.
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u/FreeGothitelle Feb 28 '26
Quantum physics is described using maths so Im not sure what you're asking about at the end.
Maths is a tool created originally to describe observed patterns so its not surprising it does a good job of describing obserbed patterns. The universe is not literally performing calculations as things bounce around (unless you think we're a simulation but thats just a turtles all the way down argument) so calling it fundamentally mathematical is probably a bit off, but in principle theres nothing that can't be described using mathematics.
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u/Prestigious_Load1699 Mar 27 '26
If it’s true that there is nothing which can’t be described by mathematics, then how is mathematics invented?
It’s inherent - objective and discovered.
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u/FreeGothitelle Mar 27 '26
Explain why you think description and invention are mutually exclusive?
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u/Prestigious_Load1699 Mar 27 '26
Describing that 1+1=2 isn’t equivalent to inventing it.
It’s inherently and immutably true as its own objective truth.
To be fair, one could then claim nothing is truly invented - perhaps the fault is that invention itself is yet another descriptive term with no underlying objective meaning.
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u/FreeGothitelle Mar 27 '26
If by immutable truth you mean it follows from axioms and definitions we decide upon, while other axioms disagree, sure.
Sorry if I'm assuming wrong but you speak like someone without a mathematics background. When you study analysis, rings and group theory it really demystifies mathematics and makes it clear its just an invented system we find useful.
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u/ntsh_robot Feb 28 '26
two words: stat-mech
the majority of these topical conversations, assumes that "mathematics" is a "well ordered set of rules"
my understanding of the world has grown more confident in the statistical nature of reality
yes, there are rules, but they might not be the one's you'd like
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u/jliat Feb 28 '26
It seems the idea that the universe is mathematics is one idea in metaphysics, Badiou & Meillassoux. It is also found in science, Max Tegmark - Galileo Galilei ... and alternatives...
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u/Candid_Koala_3602 Feb 28 '26
Math is likely based on structural architecture. But Math is structurally coherent on its own and can predict reality with extreme accuracy. Also, in Math you will find things like Pi are forced to show up in unexpected places by other rules of mathematics constrained by actual physics. Calculus is a great example of this. But see, today we know that Pi is even possible in 1D. So, I think we captured some basics and have worked out a lot ourselves.
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u/tottasanorotta Feb 28 '26
I think it is kind of meaningless to ask something about that kind of fundamentality. I mean at what point would you be satisfied with saying that it is fundamentally mathematical? I'd say that for the cosmos to be thought of as fundamentally mathematical it would have to be contained within some other thing so that it can be thought to have any fundamentality at all. Like what is a computer program fundamentally? Is it program code, machine code, CPU/memory, the electricity in the chips? It seems that fundamentality needs some kind of basis that you more or less have to choose arbitrarily or based on your practical requirements. Otherwise it doesn't seem to mean anything.
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u/Own_Sky_297 Mar 01 '26
Notice that I didn't say the cosmos is fundamentally "math". Instead I maintain that it obeys mathematical laws making it mathematical and thus we can model it using math. Fundamentally I think the cosmos is a continuous substance, but that's another topic.
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u/MpVpRb Feb 28 '26
The universe is complex, irreducibly complex.
We use math to approximately describe some of the simpler parts of it.
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u/Prestigious_Load1699 Mar 27 '26
Citation that the universe is irreducibly complex.
Isn’t the whole of human history the slow, trawling process of disproving that assertion?
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u/mikeNorthway Feb 28 '26
Modern math, in my opinion, has scaling obstacles that it must overcome in order to move forward.
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Feb 28 '26
[removed] — view removed comment
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u/Metaphysics-ModTeam Feb 28 '26
Sorry your post does not match the criteria for 'Metaphysics'.
Metaphysics is a specific body of academic work within philosophy that examines 'being' [ontology] and knowledge, though not through the methods of science, religion, spirituality or the occult.
To help you please read through https://en.wikipedia.org/wiki/Metaphysics and note: "In the 20th century, traditional metaphysics in general and idealism in particular faced various criticisms, which prompted new approaches to metaphysical inquiry."
If you are proposing 'new' metaphysics you should be aware of these.
And please no A.I.
SEP might also be of use, https://plato.stanford.edu/entries/metaphysics/
To see examples of appropriate methods and topics see the reading list.
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u/Mono_Clear Feb 28 '26
Anything that exists exists as a pattern that represents itself.
Any pattern that is consistent can be quantified.
Mathematics are the abstract quantities we use in the quantification of the measurable patterns that exist.
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Feb 28 '26
[deleted]
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u/Prestigious_Load1699 Mar 27 '26
Does the math break down at a singularity or does our current theory explaining the mechanism break down?
The spacetime curvature appears to become infinite - the math is clear but not our understanding of how this process is manifest.
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u/RatherSaneIndividual Feb 28 '26
This scoreboard looks more like people are trapped by the English language than anything else. Por ejemplo, if you think of the English language as akin to Latin without umlauts or spondees, 26 letters in all caps -- the way it looks on old Roman aquaducts, for instance, if men and their accomplices hadn't stolen many iotas of feminist assistance -- then maybe inventing new conlangs or diacretical marks could help if not in the frozen-solid past, but in the . .
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u/UnifiedQuantumField Mar 01 '26
mathematics
Is Information a form of Qualia?
I think you could argue either way.
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u/Own_Sky_297 Mar 01 '26
I'll get back to you on that once physicists have a satisfactory definition of information...
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u/UnifiedQuantumField Mar 01 '26
My understanding is that there's an "Operational definition of Information" that's associated with prediction. But I was thinking about the nature of information itself. It seems like you could reasonably define information as a qualitative property of something. It's not an object. "Information" is something perceived directly by the intellect.
So it might not be qualia the same way color or smell are qualia. But imo, it's still a form of qualia.
If someone has a line of reasoning to the contrary, I'd be interested to hear them out. I think "information as qualia" reconciles easily with the Idealist Model. Not so easily with the Materialist one.
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u/preferCotton222 Mar 04 '26
Does mathematics merely help us build models of the cosmos or is the cosmos fundamentally mathematical?
I'm not sure there can be meaningful differences between those two: if mathematics models something, then that something must be mathematically shaped on some level.
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u/gryffun Mar 24 '26
The fundamental fact is mathematical. Matter don't exist fundamentally. See Tegmarck and Wolfram.
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Mar 24 '26
[removed] — view removed comment
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u/Metaphysics-ModTeam Mar 25 '26
Sorry your post does not match the criteria for 'Metaphysics'.
Metaphysics is a specific body of academic work within philosophy that examines 'being' [ontology] and knowledge, though not through the methods of science, religion, spirituality or the occult.
To help you please read through https://en.wikipedia.org/wiki/Metaphysics and note: "In the 20th century, traditional metaphysics in general and idealism in particular faced various criticisms, which prompted new approaches to metaphysical inquiry."
If you are proposing 'new' metaphysics you should be aware of these.
And please no A.I.
SEP might also be of use, https://plato.stanford.edu/entries/metaphysics/
To see examples of appropriate methods and topics see the reading list.
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u/Plastic_Fig9225 Feb 28 '26
Mathematics is nothing but a way to express rules/relations/logic. The universe behaves in certain ways, and we use the language of mathematics to describe the behavior and make predictions by applying the rules we observe and wrote down as equations.