What breathes life into the equations?

PearKrill

The current understanding of Science is shown to prove its limits by its very own methods. This doesn't diminish its validity, by contrast, it shows that its domain extends by making fundamental metaphysical questions about consciousness falsifiable, and therefore a part of Science. As a result, sentient experience is shown to be fundamental and intimately connected with Quantum Physics. This naturally suggests a unitary one-world no-conspiracy understanding of Quantum Physics and connects it with sentient life.

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PearKrill

Endnotes (because in the Technical Endnotes PDF File they are messed up)

A mathematical structure consists of a collection of sets and relations between these sets (subsets of Cartesian products of these sets), see Universal Algebra [10] and Model Theory [4].
The possible values of an observable is the spectrum of the operator representing it.
For a state vector $\ket{\psi}$ and the position eigenvectors \ket{x}, the wavefunction is \psi(x):=\braket{x,\psi}.
The dimension of the unitary group U(n) is n^2. The dimension of the subgroup of unitary transformations preserving the Hamiltonian is between n and n^2.
The unitary group acts transitively on the space of unit vectors.
Transformations preserving the form of the dynamical law must commute with the Hamiltonian. In the \emph{standard measurement model} (see [2]}, §II.3.4, and §VII for real-world examples) the Hamiltonian is, during the measurement, H = -g A\otimes p_{\mathbf{Z}} where A is the observable and p_{\mathbf{Z}} is the canonical conjugate of the pointer observable Z.
Then, if for any eigenvalue \lambda of A -\lambda is an eigenvalue of equal degeneracy, the transformation \ket{\lambda,a}\ket{\text{outcome}=\lambda}\mapsto\ket{-\lambda,a}\ket{\text{outcome}=-\lambda} is unitary and commutes with H. If the spectrum of A is \R and the degeneracy is the same for all eigenvalues, the transformation \ket{\lambda,a}\ket{\zeta}\mapsto|\frac{\lambda_2}{\lambda_1}|\ket{\frac{\lambda_2}{\lambda_1}\lambda,a}\ket{\frac{\lambda_2}{\lambda_1}\zeta} swaps the two worlds and commutes with H.
These symmetries relabel a world in which the measurement has an outcome as a world in which the measurement has any other outcome, for a previously unknown observed state.
These observables can be obtained by unitary transformations that commute with the Hamiltonian.
It is often believed that a preferred decomposition into subsystems emerges from conditions like the locality of the interactions [6]. But even for relabelings that don't change the dynamical law and preserve this kind of locality, for a 2^n-dimensional vector space, the ways to decompose it into n qubits (vector spaces with 2 complex dimensions) form a space whose number of dimensions grows exponentially with n (to see this, factor the group of unitary transformations that preserve H through the group of local unitary transformations on the factor spaces).
The Kochen-Specker theorem shows that, at least for three or more dimensions, the observed property could not have a definite value before the quantum measurement [14].
Unlike value-indefiniteness (9), in our approach (5.9-5.1), not the state was indefinite, but the observable associated to the measured physical property. This can avoid the superposition of different outcomes.
We call the measurements of a system by its environment decoherence [12,18].
It is hoped to explain the emergence of classicality at the macro level and resolve the measurement problem. There are serious unsolved questions in the decoherence program, but in any case it can't resolve the measurement problem by itself, but only combined with one of the proposals (5.7-5.10).

Ulla Mattfolk

PearKrill You've hit on the mathematical conflict that the living system is engineered to solve!
Ulla.

EmeraldRaccoon

The essay offers an ambitious and intellectually bold attempt to transcend a purely structural view of reality and to challenge the position that mathematical description alone exhausts the essence of life and consciousness, adopting a relational perspective which convincingly highlights that life and awareness may be understood as processes emerging from interactions rather than as properties of isolated entities. Nevertheless, the essay lacks a clear distinction between metaphor and scientific argument, which makes it difficult to evaluate which claims are intended descriptively and which aspire to ontological validity, and the reasoning remains largely speculative due to the absence of empirical cohesion: references to quantum biology do not lead to explicit, testable conclusions. The text frequently transitions from intuitive observations to strong ontological assertions such as the introduction of “stuff-in-itself,” which weakens logical continuity, and the absence of mathematical or formal structure, even in sections concerning physical processes, causes much of the argumentation to rely solely on intuition without demonstrable grounding. Furthermore, the assumption that consciousness may emerge exclusively from internal relationality, disregarding the role of external data and environment, remains debatable and insufficiently justified. Finally, the essay presupposes the existence of a non-mathematical aspect of reality, whereas one could argue that any coherent universe — enabling stability, evolution, and causal relations — must be structured and describable through formal principles, implying that mathematical organization is not optional but rather a necessary condition for order and, consequently, for life itself.

PearKrill

EmeraldRaccoon

The essay offers an ambitious and intellectually bold attempt to transcend a purely structural view of reality and to challenge the position that mathematical description alone exhausts the essence of life and consciousness,

It is not "an attempt". I start with the claim that structure, relations are sufficient for consciousness, and show, based on mainstream physics, how this leads to a contradiction. It's a no-go theorem.

adopting a relational perspective which convincingly highlights that life and awareness may be understood as processes emerging from interactions rather than as properties of isolated entities.

In any proof by contradiction, you start by assuming that what you will disprove in the end, and show that it leads to contradictions.

Nevertheless, the essay lacks a clear distinction between metaphor and scientific argument,

I did not use metaphors in the proof. I avoided equations as much as possible, leaving the main ones for the endnotes, and I tried to be concise because of the rules of the contest. An AI asked to summarize an essay can't know these things if you don't tell it.

the reasoning remains largely speculative due to the absence of empirical cohesion

The proof by contradiction refutes the belief that consciousness is reducible to the structure, the relations, and not the nature of the stuff in itself. This one: "empirical cohesion" 😃

The text frequently transitions from intuitive observations to strong ontological assertions such as the introduction of “stuff-in-itself,” which weakens logical continuity, and the absence of mathematical or formal structure, even in sections concerning physical processes, causes much of the argumentation to rely solely on intuition without demonstrable grounding.

The proof shows that whatever is that stuff having the structure, without it having certain features that can't be captured by the structure/relations alone, we would know nothing. It follows from the proof, i.e. it is its logical conclusion (not an "intuition"), so I don't see how it "weakens logical continuity" or how it relies on intuition at all.

Furthermore, the assumption that consciousness may emerge exclusively from internal relationality, disregarding the role of external data and environment, remains debatable and insufficiently justified.

I didn't make this assumption.

Finally, the essay presupposes the existence of a non-mathematical aspect of reality, whereas one could argue that any coherent universe — enabling stability, evolution, and causal relations — must be structured and describable through formal principles, implying that mathematical organization is not optional but rather a necessary condition for order and, consequently, for life itself.

First, it does not "presuppose the existence of a non-mathematical aspect of reality", it proves it. But even if it would presuppose it (which it doesn't), from this it doesn't follow that it claims that "mathematical organization is optional", and nowhere in the essay is said or implied anything of this sort.

marcovici alexandru

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EmeraldRaccoon
Nevertheless, the essay lacks a clear distinction between metaphor and scientific argument,

I did not use metaphors in the proof. I avoided equations as much as possible, leaving the main ones for the endnotes, and I tried to be concise because of the rules of the contest. An AI asked to summarize an essay can't know these things if you don't tell it.
...
-----------------------------------------------------------------------------------------------------------------------PearKrill

toughs are always metaphors
at some point a small sets of those educationally speaking gets to be standardized and grounded recognized unanimously

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EmeraldRaccoon
adopting a relational perspective which convincingly highlights that life and awareness may be understood as processes emerging from interactions rather than as properties of isolated entities.

In any proof by contradiction, you start by assuming that what you will disprove in the end, and show that it leads to contradictions.
....
-----------------------------------------------------------------------------------------------------------------------PearKrill

proof by contradictions are slightly more temporal

true false binary-or multivalued logic ?

for primes for examples lets say the proof for infinitude of primes is false

applying some themes/variations on the standard proof (drawing each word)
the proof starts by suppose there are finitely many .. .. and ends by going back to the start
the proof gives the receipt to obtain a new prime

one can challenge or melt the meaning of each of the assumptions for example, what does it mean for a number to be prime graphically , is the multiplication commutative ,or what does it mean to be finite, or what going back means , such that there can be obtained pseudo primes, or nonprimes alternate primes, finitely many primes

the proof by contradiction loads , install itself than it cycles false true false true false true
are there proof by multi contradiction that lets say they have a more complex topology than a circle ?

PearKrill

marcovici alexandru

the proof by contradiction loads , install itself than it cycles false true false true false true

no.