I'm no mathematician so maybe I misunderstand but it seems to me like something in zfc might be arbitrary. I think I understand the concept of a set, where the quantity of 5 is a set of 5 thus numbers are sets. However, let's take the idea of an empty set.

Now my understanding of what an empty set is, is a box of chocolates w/o any chocolate. It's purely a mental overlay of reality when we say the box is an empty set. But the question is does nature deal in empty sets outside of the one's invented by our minds?

It seems to me that if mathematics may be said to exist in some capacity, such as if math is merely the laws or rules of existence, that it would not be meaningful to have an "empty set". As that's saying there is something ontologically more to a set than it being the collection of things in a set. In one instance your saying a set is a thing in and of itself, in the other "set" just refers to the things collectively considered such that an absence of the things leaves you with no set rather than something that's empty.

This "something" that is called a "set" such that it can even be empty seems like something that has no ontological reality and things that have no ontological reality can't be said to exist.

I guess the question is if mathematics exists mind independently can an empty set actually exist also or is it merely invention and if so how can the concept be said to be a "foundation" of math? Thoughts?

Here “observer” means a role inside a formal model: the place where distinction becomes part of the system itself.

The conditions below are proposed as a minimal formalizable scheme. Each of them should allow a stricter expression, and removing any one of them should change the content of the model. The observer appears as the wholeness of the process: the conditions of distinction are held together as a single act.

Below are three minimal structural conditions.

1. A positional condition.
The distinguisher and the distinguished should not coincide. If they collapse into the same point, the act of distinction loses its content: there is no way to draw a distinction, or a boundary, between two coincident positions.

2. A trace.
After the act of distinction, there has to be some recognizable difference: in a state, a record, a correlation, or some other trace. If there is no such difference, the observation is indistinguishable from no observation at all.

3. Self-closure.
The criterion of distinction should be internal to the structure. If the distinction depends only on an external arbiter or external observer, a regress appears: that external observer now needs another basis of validation.

If any one of these conditions is removed, a different kind of failure appears.

Without the positional condition, there is collapse into identity.
Without a trace, there is an act with no distinguishable result.
Without self-closure, there is an infinite regress of grounds.

These three failures seem different to me. None of the three conditions appears to follow from the other two: each blocks its own way in which observation can break down.

In that sense, the structure is similar to a Borromean link: three elements work only together, and removing any one of them breaks the whole. This is not meant as a proof, but as an image of minimality: the observer is not a separate entity added on top, but a bundle of conditions under which distinction becomes stable and checkable inside the structure itself.

Then an “observer” can be understood not as an original subject, but as a formal role: a structure with positional separation, trace, and an internal criterion of distinction.

I’d be grateful for any criticism of the idea.

I am self-learning Mathematics. Here is one question that arised when I was learning about Axioms.

Are there infinite possible theories in Mathematics as there can be an infinite combination of Axioms as long as the Axioms and the whole System is consistent and don't contradict each other?

So this means that Mathematics knowledge is infinite?

When a singular cell goes through the process of mitosis it will divide/multiply 1 time and become 2 cells. Is this not proof that 1x1=2? And 1÷1=(2x0.5)?

-1x1=1 is mapping a map, its not mapping the territory. (true)

-in terryology multiplication is mapping the territory instead of mapping a map/mental concept. (true)

-Mapping a map is self referential delusion and a fallacy for modeling reality. (true)

Lets see you guys try to go up against standard logic. Will be interesting seeing the semantic games that will be played to try and defend this simple point.

>!You cant defend this with utility and consistency because utility and consistency can be found and work inside of a false axiom.!<

>!And you cant defend this by saying math doesnt claim to model reality because we treat math as if it does model reality(physics, engineering)!<

logic is calling your foundational multiplication operation self referential delusion and a fallacy

https://preview.redd.it/vwhyc4hnq5yg1.png?width=1672&format=png&auto=webp&s=9ca9dd9ecb09485596883a90e91f3897e2d05f41

Sometimes, just floating is the prize.Ten papers were dropped into the strange waters of the LLMPhysics Journal Ambitions Contest. Some were elegant. Some were over-engineered. Some looked like vehicles assembled from spare parts of mathematics, philosophy, computational physics, and late-night metaphysics. The rules were simple: each paper would be scored by two large language models — Claude Sonnet 4.6 and GPT-5.2 — across six dimensions: hypothesis, novelty, scientific humility, engagement with prior work, rigor, and citations.

The result was not a podium for the Theory of Everything. It was something more useful: a public test of whether speculative ideas can survive being read by something that is not already on their side.

In other words, a sea trial.

>

Final ranking and rubric breakdown

A final rank tells us who arrived first, but not how each boat floated.

So before turning this into metaphor, here is the score breakdown. The table uses the averaged rubric values from the two model evaluations. The final score is the normalized average used for the contest ranking.

Rank	Author / Entry	Hypothesis	Novelty	Scientific Humility	Engagement	Rigor	Citations	Final Score
1	Düring	8.50	10.50	11.00	11.50	6.00	6.50	63.50
2	Anonymous	9.50	9.00	12.00	10.50	6.50	6.25	63.20
3	Matt Asantz	8.75	8.50	13.25	9.00	6.00	6.50	61.15
4	Guri	5.00	8.50	13.50	9.50	7.00	6.25	58.55
5	Christian	4.00	10.50	8.50	12.50	4.00	6.00	53.50
6	BlackJakey	8.50	8.50	12.25	5.75	5.75	3.50	52.05
7	Shatto	9.25	8.00	6.50	8.00	4.25	6.25	49.75
8	Mosher	5.50	6.50	8.75	6.25	5.25	5.50	44.40
9	Novgorodtsev	4.50	6.00	1.50	2.50	2.25	3.50	23.80
10	aveeageZA	5.00	2.50	4.50	1.00	3.50	0.00	19.45

The breakdown matters because the final ranking hides interesting structure. Düring won overall through balance: strong novelty, strong engagement, and a focused hypothesis. Anonymous was especially strong in hypothesis and formal structure. Matt Asantz had one of the highest scientific humility scores. Guri had the strongest rigor score in the averaged table. Christian scored highly in novelty and engagement, but lost ground on rigor and hypothesis clarity. BlackJakey had strong hypothesis and humility, but weaker citations and engagement.

So the contest was not simply “who had the strangest idea?” or “who wrote the most mathematical-looking paper?” It rewarded something subtler: ideas bold enough to be interesting, but disciplined enough to be inspected.

"Did it float?" beats "Is it true?"

The first instinct, reading speculative physics, is to ask whether it is correct.

That instinct is almost always wrong — not because correctness doesn't matter, but because correctness is unanswerable for ideas that propose new ontologies, new geometries, or new emergent mechanisms. Asking whether a paper has solved quantum gravity is like asking whether a homemade vessel has crossed the ocean. The honest first question is whether it can leave the dock without sinking.

So: did it float?

Did the hypothesis stay coherent under pressure? Did the author know where the leaks were? Did the paper distinguish between what was derived, what was assumed, what was calibrated, and what was speculation? Did it engage with prior work, or did it pretend the rest of physics didn't exist?

These questions can be answered. And they are exactly the questions an LLM rubric is good at probing — not because LLMs are infallible critics, but because they are stubborn, literal, unromantic readers. They notice when a section header promises a derivation that the section does not deliver. They notice when predicted is used for a quantity that was actually calibrated. They notice missing citations.

The contest, in that sense, was less a beauty pageant and more a stress test for honesty.

The fleet, grouped by virtue

The standard way to write this would be in ranking order. I think that's misleading, because rank conflates several different kinds of strength. So instead I'll group the ten entries by what each can teach the next person who tries to build a boat.

The discipline of focus

The two entries that won by narrowness — Düring (#1) and Guri (#4) — share a virtue.

Düring's Quantum Consensus Principle asks one question and only one: how does a definite measurement outcome emerge from the dynamics of a macroscopic apparatus? It treats the apparatus not as a passive witness but as a kind of social arena where one outcome wins by becoming a macroscopic consensus. The framing gives reviewers a single object to inspect, and the paper explicitly compares itself to Copenhagen, Many-Worlds, Bohmian, GRW, and Quantum Darwinism — refusing to operate in a vacuum. Some derivations are deferred to supplements, but the boat has a clear keel.

Guri's Threshold-Activated Dissipation in a Vorticity-Dependent Navier–Stokes Model does something even braver: it refuses to claim a solution to the classical Navier–Stokes problem. Instead it studies a modified system where dissipation activates above a vorticity threshold. That is not a weakness. That is methodological maturity. A smaller claim, well-defended, is a stronger scientific object than a larger claim with frayed edges.

The lesson: a smaller hull is easier to seal.

The discipline of formal structure

Anonymous (#2) wrote the most architecturally disciplined paper in the fleet. Standard Model Structure from the Bundle of Lorentzian Metrics is enormous in ambition — it asks whether structures resembling the Standard Model can emerge from the geometry of metric bundles — but it is staged carefully, with explicit falsifiers listed: outcomes that would seriously damage or kill the proposal.

That matters more than people realize. A speculative framework earns trust when it volunteers the conditions under which it would be wrong. "Here is how I could fail" is the speculative-physics equivalent of a watertight bulkhead.

The risk, of course, is that an ambitious chain of conditional steps creates many places where the chain can break. But the boat was built with the right philosophy.

The risk of ontological reach

Two entries went after deep structure rather than narrow phenomena.

Matt Asantz (#3) — full disclosure, this is my entry — Relational Geometry and the Emergence of Gravity tries to work below the level of equations. It treats distance as relational information, gravity as the reduction of relational phase offset, matter as stabilized informational closure, and harmonic closure as a possible cross-scale organizing principle. Read fairly, the strongest move is the explicit separation of postulates, derived claims, hypotheses, speculative notes, and open problems. Read fairly, the weakest move is scope: gravity, neutron stars, harmonic closure, weak equivalence, E8, and relational ontology in a single piece is too much for one hull. Compartments help, but a future version would be stronger if it presented one central claim at a time, with the rest gestured at as future work.

Christian (#5) — Navier–Stokes Regularity Is Independent of ZFC — moves further out, into the borderlands of PDE theory, computability, logic, and foundational mathematics. The conceptual move is dazzling: maybe the equations are not unsolvable in some technical sense; maybe the framework in which we ask the question cannot decide the answer. The risk is the title. A claim of independence from ZFC creates an enormous burden of proof, and any open bridge in the argument becomes more conspicuous because the door above it is so dramatic.

The general lesson: the larger the claim, the quieter the language must become.

The pitfalls, made visible

The remaining five entries are not failures. They are something more useful: clean exhibits of the specific traps any speculative framework has to navigate. If you are about to write your own paper, read these closely.

**BlackJakey (#6) — **Pressure Gradient Theory is admirable for its workshop-bench transparency: hypotheses sorted, mechanisms proposed, claims labeled as proven, calibrated, open, or rejected. Internal honesty is high. The opportunity is external — stronger engagement with existing literature would harden the framework against critique it hasn't yet faced.

**Shatto (#7) — **Mode Identity Theory earns points for putting cosmological predictions on the line, which is what a falsifiable theory should do. The opportunity is rhetorical: when language outruns derivations, readers begin defending against the tone instead of engaging with the content. A model can be bold without sounding final.

**Mosher (#8) — **Gravitational Phenomena from Medium Flow uses a vivid physical picture: gravitation as the emergent behavior of a medium-flow or tick-rate substrate. Vivid pictures are an asset; they give readers something to hold. The pitfall is circularity. If a constant is used to calibrate the model, it cannot later be presented as a prediction of the model. Calibration is not prediction. Most alternative frameworks fall into this trap somewhere; spotting it in your own draft is half the battle.

**Novgorodtsev (#9) — **Nuclear Structure from Sphere Packing Geometry chases the kind of deep numerical and geometric order that has, historically, sometimes been right: group theory, hidden symmetries, compact structures. The pitfall is the inverse: numerical elegance without dynamics looks like post-hoc pattern matching. The standard is not "the numbers fit" but "the numbers had to fit, because the structure forces them."

**aveeageZA (#10) — **Elastic Vacuum / TUE uses an accessible image: the vacuum as elastic medium. The image is a strength for communication. The opportunity is the basic triad every speculative model needs to put on its hull: citations, comparison with existing frameworks, and explicit falsifiers. Without those, even an appealing intuition struggles to stay afloat.

The part nobody wants to write

This is a contest where ideas about physics, generated with help from LLMs, were judged by other LLMs, and is now being reviewed by yet another LLM. There is no escape from the recursion.

That isn't a reason to dismiss the exercise. It's a reason to be specific about what the exercise can and cannot do.

What it cannot do: tell us whether any of these frameworks is correct. LLM rubrics do not run experiments. They cannot detect a deep insight buried under bad presentation, and they may reward well-organized confusion over poorly-organized truth. The LIGO interferometer is not paying attention.

What it can do, and does well: enforce minimum standards of accountability. An LLM-graded contest will reliably notice when predicted is misused, when citations are missing, when scope is inflated, when a falsifier is described in such a way that nothing could ever falsify it. These are exactly the failure modes that have plagued speculative physics for decades, long before LLMs existed. The contest formalized them and put a number on them.

Whether you trust the number is a separate question. But the kind of number it is — a measure of structural honesty, not metaphysical correctness — is genuinely new, and genuinely useful for a community trying to figure out how to do speculative work in the age of automated assistance.

For science communicators

If you write about physics for a general audience, the LLMPhysics Journal Ambitions Contest is unusually rich material — and not for the reason you might think.

It is not a story about AI discovers new physics. None of the ten papers discovered new physics. Telling that story would be a betrayal of the actual situation.

It is a story about a community of people, working alongside language models, beginning to build the institutional scaffolding for evaluating speculative work in public. That is much more interesting than another AI breakthrough headline. It has tension — the boats either float or they don't — characters, a framework, and an honest meta-layer: LLM critics, with their own limitations, doing the judging. It can be told without overpromising and without dismissing.

The boats want their stories told accurately. They don't want to be sunk and they don't want to be inflated.

For labs and research groups

The reason to pay attention is not that any of these papers is the next paradigm. It is that the contest demonstrates a workable model for vetting speculative work cheaply, transparently, and at scale. A small team running a similar rubric on incoming preprints, internal proposals, or early-stage hypotheses could:

• catch scope inflation before it metastasizes;
• enforce explicit falsifier statements;
• separate calibration from prediction in early-stage modeling;
• make the difference between interesting metaphor and testable hypothesis visible to the author themselves before submission;
• normalize the practice of stating, on paper, the conditions under which one's own model would be wrong.

None of that is glamorous. All of it is useful. The Ambitions Contest is the prototype of a process, not a result. The process is what's worth borrowing.

Closing

Not every boat in the derby was beautiful. Some leaked. Some had odd silhouettes. One or two looked like they might be held together by enthusiasm and electrical tape.

But several stayed up. Some stayed up with elegance. Some stayed up because their builders had carefully marked, in advance, exactly where the leaks would be.

For a community trying to do speculative physics responsibly — with or without language models in the workshop — that is the real result of the contest: not a finish line, but an improvised harbor where unusual vessels can be tested, criticized, repaired, and perhaps made seaworthy.

The next derby won't be far away. If you are building a boat right now, the question is worth asking before you launch:

Where, exactly, are your leaks?

*Repository and full papers: *LLMPhysics-Journal-Ambitions-Contest on GitHub

People are constantly seeing things in the world every day. They see an apple, a tree, a star, or a bacterium. They hear a strong sound, or maybe a thought pops up in their minds, and they start noticing that all these things have something in common.

If I show you a cow, a person, or a planet, your mind already knows what they are. You probably know what these things have in common. It is in your mind: a categorization or a pattern that your mind already uses for surviving and recognizing things across the universe.

You can use any tool you have—a pencil or a reed—and assign a symbol to this. It could be a simple line, a dot, or maybe the symbol “1” to represent this idea on paper or clay (like our ancestors did), and voilà—you have the number 1.

Scroll through the sub. It’s a sea of fucking 0s. Every single post questioning the subjective foundation of math downvote botted into the negative.

Yet a post about aliens, on a philosophy of math subreddit is apparently not too much, but the second you question the foundation of math on a philophsy of math subreddit then that’s too much…

That’s very telling.

This is obviously not organic and getting astroturfed. You’re not allowed to question the subjective foundations of math anywhere. You’ll get censored and suppressed(already got valid epistemic arguments mod removed from several subs) (also other people like Karma penny just get straight removed from everywhere)

I already screen recorded and documented every single post of this subreddit for 10 pages straight so don’t even think of trying to undo it

Tdlr; "red introduces risk" vs "blue introduces risk" are equally valid, but contradictory answers. Attempts to prove one side using analogies or mathematical representations have a host of issues. In either case, the logic is circular, based on presumptions, and despite claims having different answers, the situations are equivalent.

Terms to understand before reading

Terms: Analogous --- when I say "analogous," I don't just mean "comparable." I mean analogous in the sense that, if you come to a conclusion in one scenario, it holds true for the other scenario due to the identical parallel.

Summary & root of issue

I am at an impasse. As I understand it, which button "introduces risk" is a determination that, for either side, depends on how you define "blame"/"introduces risk," relies on circular logic, and the entirety of the question itself is paradoxical in a way. Paradoxical in a sense that you can reach two opposite conclusions that are equally valid. And circular in the sense that, your reason for pressing the button is because other people press the same button.

You press the red button because other people might press the red button and you want to save yourself. You press the blue button because you want to save other people who might also press the blue button. Pressing the button creates the need to press the button.

Also, you can create analogies for the scenario that demonstrate that one choice introduces risk, however, those analogies can be flipped to favor on choice.

Lastly, you can create two different mathematical representations of the problem that are equivalent, but provide different answers as to what introduces risk.

Anologies

I will present four brief hypotheticals to demonstrate why I'm struggling. These hypotheticals will swap the buttons with something else. Then I will go into the math (as best as I can, which isn't that good).

Hypothetical Blue 1 (blue does not introduce risk) --- Imagine there is only a red button. If you do nothing, you and those who made the same choice will die if >50% of people press the red button.

Hypothetical Blue 2 (blue does not introduce risk) --- Imagine everyone has spikes. If >50% of people place their spikes on the ceiling, the spikes will fall and those who did not place spikes will die. If you place a spike, you will live regardless of the outcome.

Hypothetical Red 1 (red does not introduce risk) --- Imagine that there is only a blue button. If you press it, you will die unless >50% of people also press the blue button.

Hypothetical Red 2 (red does not introduce risk) --- Everyone is standing on a platform next to train tracks. If >50% of people jump onto the train tracks, those who are on the train tricks will survive the incoming train.

These hypotheticals seem to be analogous to the original situation. The same function and outcome. And yet, depending on how it is framed, which choice introduces risk is different. I see three options. 1) One sides' hypotheticals are analogous while the other's aren't. 2) They are all analogous and therefore either answer is correct. 3) Or none of them are analogous due to the original question never having an original assumption of which choice introduces risk. 4) (The fourth one is that one side's/none of them are analogous, but not because there aren't any analogous scenario's in which one choice introduces risk for either side, but rather because I simply created flawed hypotheticals. Maybe regardless of them being flawed, they still help convey perspective).

The issue seems to me that: 1) Any analogy created where one choice introduces risk is circular, because it is already based on the presumption that one choice introduces risk, and the analogy is created around that presumption. 2) Any analogy that favors one side can be flipped to favor the other. 3) There is the possibility that no analogy will be perfect because they will always have additional hidden presumptions or elements that deviate from the original scenario.

It seems that in order to prove which choice (if either) introduces risk (at least with certainty), that you have to prove it within the question itself, which I don't know how you do that, or whether it's even provable. However, it hasn't stopped attempts from occurring.

Doing the math

Here is a mathematical representation that I found on reddit that demonstrates that the blue button introduces risk:

>Let's have the total population be represented by the variable "N". Let the number of people choosing red be "R" and the number choosing blue be "B", forming the equation "N = R + B". An individual selecting red possesses a definitive mortality probability of zero. A person selecting blue enters a conditional probability state. If "B >= 0.5N", casualties remain zero. If "B < 0.5N", every blue participant experiences a mortality probability of one.

>Evaluating the extremes isolates the source of fatality. When "R = N" and "B = 0", global casualties are precisely zero. Lethal outcomes manifest exclusively when "B > 0" alongside the specific condition "B < 0.5N". The mathematical formula for death explicitly requires the presence of blue participants failing to satisfy their own internal quota.

So yeah on an objective standard blue is the entity that introduces death. 

I'm still in highschool, and I haven't studied math myself outside of school. So I'm not qualified to determine whether or not this math checks out. However, to me it seems like it works. And I see no flaws in it. Here is my attempt at creating an equivalent, but opposite, mathematical representation that shows that red introduces risk.

>Let the total population be N, where N = B + R. A person choosing blue is the only path toward a collective no-causality state that requires cooperation. A person selecting red enters a saboteur state.

>Casualties (D) occur if and only if the number of people choosing red (R) exceeds a specific threshold. D = 1 if R > 0.5N. When B = N and R = 0, the casualties are zero. Without the presence of red participants, the condition for death (R > 0.5N) can never be met.

>Therefore red is the entity that introduces death. Red participants are betting against the group, and if their number (R) becomes too high, they trigger the mortality of the blue participants.

I'm aware that this is probably very flawed because, again, I don't know math that well. So I tried to flip it and copy the first representation. If this is wrong, is it possible to create a flipped representation that shows red introduces risk? If not, why? If so, can you demonstrate a better example than mine?

The issues here

Again, I don't have a deep understanding of math, but it seems like these mathematical representations themselves have underlying presumptions, or as it is referred to in math, axioms, the answer of which choice introduces risk depends on the axiom. So the question is, how do we prove that these axioms are inherently true? But from what I understand about axioms, they are just assumptions or premises you initially make to go forward. And that they necessarily can't be proven.

Secondly, despite these mathematical representations having different (contradictory?) conclusions, they are equivalent. What holds true for one holds true for the other. It's true that R > 0.5N results in casualties (second representation), just as B < 0.5N results in casualties (first representation).

My bias on this issue

My initial answer to this question was blue. I personally see it as the morally correct question, and the reason I saw it that way was because I thought red was the choice that introduced risk. However, I'm starting to believe that there is actually no correct answer, and that there is no objectively correct answer to this dillemma/problem.

For the first representation, I have a question for "blue enters a conditional probability state." Blue enters a conditional probability state, but why? Is that probability state inherent, or does it only exist because of red? And the question is, even if it is inherent, why would you want to trigger that condition by pressing red? Just like in the earlier analogy, why would you place spikes on the ceiling and create the risk of death in the first place?

Questions

Does the answer depend on how you define "introduce risk" and responsibility/blame? (Does the answer stay the same regardless of how you define anything, and I'm wrong about one side being equally valid)?

Are these mathematical representations correct (was mine)? Are they equivalent?

(In the scenario that either representation is flawed). Is it possible to create correct mathematical representations that show either choice introduces risk, or only one?

Is the relationship between the blue and red button ontological?

Is the danger a physical property of the choice or just a logical consequence of the rules?

Does the blue/red button create ontological risk (Is the risk created as a fundamental, built-in part of the button itself, regardless of how we describe it)?

Does the blue/red button have inherent risk (is it dangerous by its very nature)?

Can it be possible that the answer is both, and that they don't necessarily contradictory to eachother? If so, what does that mean?

Anyways, thank you for reading.

Sorry if it was too long.