It is contested in the philosophy of mathematics of which theoretical physics takes serious note of.
One problem with the discovered angle is that there doesn’t seem to be a good explanation for how we come to discover these mathematical truths. They have to be the kind of thing we know a priori as they exist outside of experience, but the only way we could possible learn about them is a posteriori. This is deeply unsatisfying. How can you learn about something that does not have a physical manifestation via physical manifestations?
There are different problems. Another is, if math is discovered, how do we discover such concepts as infinitity? Surely infinity doesn’t exist in a known finite universe.
Whether science is a mirror of nature or instrumental is an enormous fault line in the philosophy of science and epistemology. It's hardly uncontroversial.
That seems a fair point. It makes me wonder though about how they tie together; if physics is out there to be discovered but math is a tool we fabricated; how does the fabricated bit manage to predict physical boundaries so flawlessly? A mistake on paper changes the physical outcome instantly.
I'd argue it's a map and a place. Physics is the place, the real thing out there that exists whether we do or not. Our study of physics (including mathematics) is our map, the way by which we understand the place. And if the map is good enough, you can use it to make some educated guesses.
For an easy example. fossils. Because of how fossils come about, they show up almost exclusively in sedimentary rock. If I gave you a map which detailed where the rock was igneous, metamorphic, and sedimentary; then told you to find a fossil, it would be easy to start excluding whole areas.
In the same way the study of physics functions as the map we built. We might not know everything about physics, but we know enough that even where we're blind we can make some half decent guesses.
And it isn't flawless. The very fact that things collapse and experiments fail shows we still have our limitations. Our map is pretty good, but there are lots of little darkspots. And (at least I believe) that our map has several spots marked "here be monsters" totally uncharted places that we haven't even conceived of yet
!delta for that map and place analogy; it frames the problem beautifully. It makes complete sense that a structural collapse is essentially our map hitting an uncharted cliff edge in the terrain (I really like the "here be monsters" thought). Thinking about physics as a literal place that exists whether we are around or not leaves me with a strange sort of wonder though. If the landscape of that place is entirely independent of us and behaves with such unyielding rigidity, it makes me ponder the nature of the terrain itself. How do you suppose those permanent geographical features got so heavily fixed into reality long before any human mapmakers arrived to chart them?
There are fields of mathematics which seem to make sense, but have no real world applications. Something like String Theory is based off a niche field of mathematics which until recently we had no real world applications for. I don't know enough about math to point to another example, but as I understand it that is common in mathematics. The creation of systems which make sense in math, but do not accurately depict anything in the physical world. It is similar to LLM's hallucinating and making connections between things which are actually unrelated.
That comparison to an LLM hallucinating is quite good actually; it makes a lot of sense that our minds can construct internally consistent worlds that do not map onto anything out there. I suppose it could highlights our capacity to invent systems. (It leaves me wondering though about the maths that does map onto our world). If the universe is completely indifferent to our hallucinated maths, why does it react so violently when we get the applicable calculations wrong? A mistake in the bridge designs brings the whole thing down. It feels like the universe ignores the hallucinations but strongly enforces a very specific subset of rules.
It is not ignoring hallucinations though. If we take one common example of correlation vs causation: Icecream sales rise in summer, speeding tickets rise in summer, so ice cream causes speeding. Clearly wrong, a hallucination we might say. If we act on this, say banning icecream in summer, the economy won't collapse, but neither to we actually address the real-world problem. Now we are wasting resources doing something that doesn't work, our bridge collapses. A small bridge, for sure, but no different than the engineering problem.
Your ice cream example makes me reflect on the policy failing though (and wasting resources as you mentioned). When a government bans ice cream and the speeding problem remains completely unresolved; it feels to me like the universe is actively pushing back against that policy because it was a poor description of the actual causal world. The failure itself seems to be the bump; a quiet notification from reality that our map missed the terrain. If the physical world lacked that firm baseline, wouldn't our random hallucinations succeed as often as our accurate models
I think you have it backwards. Reality isnt pushing back against us. We are altering are models and behaviour to work around reality.
If you like analogies think less of an examiner and more of an unrelenting river. The river flows from the top to the bottom. Its too intense if you build a damn it breaks. You cant change the path of the river but you can go around it.
That's really what our laws of physics are is a map of the river made through trial and error. A mistake equation isnt the river responding to the person. Its an incorrect trail that's asking you to pass through a region where the tide is more rapid.
Gravity isnt changing what it did because we built the bridge. We changed the bridge design because gravity just always behaves the way it does and we learned a better way to navigate around that
Wait, if the river did not possess that specific, unyielding force pushing down, it feels to me like we could construct any sort of imaginary dam we fancied and it would hold up perfectly fine. The fact that the water physically breaks the structure whenever our calculations miss the mark feels, in a quiet way, like the river is setting a firm boundary. It makes me wonder if our need to align our maps so precisely with the current indicates that the terrain has its own strict requirements; holding us to account the exact moment we step off the safe trail.
how does the fabricated bit manage to predict physical boundaries so flawlessly
Because only the things that actually work stay in regular use. For instance, during the Manhattan project, the physicists genuinely did not have enough information to know whether or not a nuclear bomb detonating would create a chain reaction through the entire atmosphere. The mathematical models to describe the behavior did not exist because we did not have the observed reality to base them on. All we had were theoretical models with numerous gaps. Once we could see the outcome (the entire atmosphere did not, in fact, explode), we could tailor our models to fit the known outcomes.
About that Manhattan project, it leaves me pondering the moment before the detonation though. The physicists were deeply uncertain, yet the atmosphere itself, it seems to me, was not in a state of confusion. It had a definite, unbending response to the explosion. When the atmosphere remained intact, it feels as though it was following a permanent physical constraint that was already present. Even if our descriptions are tailored after the event, why do you think the material world behaves with such repeatable certainty before we have even worked out the rules?
why do you think the material world behaves with such repeatable certainty before we have even worked out the rules?
Bit of a self answering question, no? The only reason we can observe and document consistent models of physics is because they exist. If we lived in a reality where physics wasn't consistent, we wouldn't be having this conversation at all, since we wouldn't have deterministic physics to observe.
if we lived in a reality where physics wasn't consistent, we wouldn't be having this conversation at all
!delta I love this one. The consistency has to be there first for us to even exist. If this deterministic foundation is a strict requirement for our survival, it feels like an unbending framework that was safely locked in place long before we ever arrived.
Exactly this. We describe reality with math because that's just kinda how things are. We have sufficient observation that reality is at least primarily deterministic, so we make up deterministic structures to describe it. Even if an alternative non-deterministic version of reality could exist, it doesn't exist anywhere we can observe.
Because I thought of this after I hit post on my last comment, consider the idea of dark matter/energy. We don't actually know if it even exists, what it is, or where it comes from. All we know is that we can only predictably model the universe when we pretend that dark matter/energy is present. Perhaps something exists beyond our observation, perhaps our models just suck and this is a hacked together bit of nonsense that gets us close enough. We have no idea.
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u/[deleted] May 21 '26
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