A Discussion on the Boundaries of Science, Complex Systems, and Empirical Testing
Fatalism holds that a person’s life is already written; the belief in a personal god posits the existence of a deity with will and emotions who responds to prayers, rewards good deeds, and punishes blasphemy.
These two claims, though seemingly from different domains, share the same logical structure: they both claim to explain reality but fail to offer clear, stable, and repeatedly verifiable predictions about it.
No matter what happens, they can reinterpret the outcome after the fact to prove themselves correct.
If you succeed, it was destined; if you fail, that too was destined.
If a prayer is answered, it’s a response from God; if it’s not, God has other plans.
A theory that cannot fail regardless of the outcome may seem to explain everything, but in reality, it has never been truly tested against reality.
This article aims to argue that, according to a unified scientific standard, neither fatalism nor a personal god are explanations consistent with natural reality. Instead, they are incorrect descriptions that cannot withstand empirical testing.
To complete this argument, we must first answer a more fundamental question: what exactly is science? “Science” is perhaps one of the most abused words in modern society.
Some say a certain health regimen is scientific, others claim an educational method aligns with scientific principles, and still others believe that any view using mathematical formulas, physics terminology, or proposed by a famous scholar is inherently scientific.
But what truly defines science? Is it anything a scientist says? Is it the use of formulas and jargon? Or can any view that finds a few supporting examples be called scientific? None of these.
Science is not an identity, not an authority, and not a set of esoteric-sounding language.
Science is the most reliable and closest description of the natural world we currently have, established through public testing, repeated verification, error control, and the specification of boundaries.
Science is not ultimate truth, but it is also far from being a mere arbitrary opinion.
It may be revised in the future, but it remains the best knowledge system we possess today for understanding the actual workings of the natural world.
Any theory that claims to explain nature, describe reality, or influence objective outcomes must submit itself to the judgment of reality.
I. The Absoluteness of Mathematics and the Relativity of Science
To understand science, one must first distinguish between mathematics and the natural sciences.
Mathematics studies abstract structures.
Within a given set of axioms, definitions, and logical rules, a conclusion that has been rigorously proven possesses logical necessity.
In the standard system of natural number arithmetic, 1+1=2.
This conclusion is not derived from countless experiments with two apples but is rigorously deduced from the definitions of numbers, addition, and their corresponding rules.
Apples can rot, be cut, or be taken away, but these real-world changes do not alter the fact that 1+1=2 in abstract arithmetic.
Of course, the absoluteness of mathematics has a prerequisite: it exists within a given axiomatic system.
Euclidean and non-Euclidean geometries use different premises and arrive at different conclusions. This is not a contradiction within mathematics but a reflection of them studying different formal systems.
Therefore: the certainty of mathematics comes from logic. As long as the premises remain unchanged, what is correct is correct, and what is wrong is wrong.
The natural sciences are entirely different.
Natural science does not study abstract systems defined by humans but the real world that exists independently of human will.
A physical theory, no matter how mathematically elegant or internally consistent, cannot prove that nature must operate according to it on these grounds alone.
It must be subjected to experiment.
Therefore, natural science rarely offers an absolute truth that holds under all conditions and never needs revision.
What it usually provides is: under what conditions it holds; to what degree of precision it is accurate; what margin of error is allowed; and beyond what scope it requires modification.
This is the most fundamental difference between mathematics and natural science: mathematics seeks logical necessity within defined premises; natural science seeks empirical reliability in the real world.
The “relativity” of science does not mean that science is subjective or that everyone can have their own truth.
It means that scientific conclusions are valid relative to specified conditions, scopes, times, precisions, and errors.
Given the same conditions and the same methods, the results should be stable.
Therefore, although science is not absolute truth, it is humanity’s most correct, most reliable, and closest description of the natural world to date.
II. What Kind of Theory Is Scientific?
A theory about the natural world should meet at least the following five conditions: it can be publicly tested; it can be repeatedly experimented on or verified by independent evidence; it holds stably under specified conditions, times, and error margins; it can specify its own scope of applicability, precision, and boundaries; and it cannot interpret all possible outcomes as confirmation of its correctness.
Here, we must limit the scope of our discussion.
The terms “scientific” and “unscientific” in this article apply to factual claims about the natural world and objective reality, such as: how objects move; how diseases spread; whether a drug is effective; how the universe evolves; whether a certain human behavior produces stable consequences; whether a certain force truly exists and affects reality.
Aesthetic judgments, moral choices, and mathematical theorems are not the same type of proposition.
“This piece of music is beautiful” expresses a personal aesthetic preference, not a natural law that requires everyone to reach the same conclusion. Mathematics, on the other hand, establishes certainty through formal proof.
But as soon as a claim asserts that an object truly exists, truly affects nature, or truly changes people’s lives, it enters the realm of scientific evaluation.
Within the scope defined in this article: a claim about nature that cannot be tested, cannot be independently verified, or conflicts with reliable facts cannot be established as correct natural knowledge.
III. Testability Is Only the First Step into Science
The fact that a claim can be tested does not mean it is already reliable scientific knowledge.
Scientific exploration involves at least three stages.
The first stage is a testable hypothesis.
For example, someone might propose: “A certain drug can reduce the mortality rate of a specific type of patient.” As long as it specifies the patient group, dosage, duration, control method, and criteria for effectiveness, it can enter scientific inquiry.
The second stage is a theory that has withstood testing.
A hypothesis gradually becomes reliable scientific knowledge only after undergoing numerous public, rigorous, and repeatable experiments, or being supported by independent evidence from different sources, and consistently holding true under specified conditions and within permissible errors.
The third stage is a hypothesis falsified by experiment.
If a hypothesis is consistently proven to be false by numerous reliable experiments within its claimed scope of applicability, it should be revised or discarded.
Therefore: testability determines if a claim can enter scientific inquiry; withstanding tests determines if it can become reliable scientific knowledge.
Science allows for incorrect conjectures.
But an incorrect conjecture does not automatically become correct knowledge just because it was studied by scientists.
The reliability of science comes not from scientists never making mistakes, but from science’s ability to discover, publicize, correct, and eliminate errors.
IV. What Does “Falsifiability” Really Mean?
When discussing the boundaries of science, many people cite Karl Popper’s concept of “falsifiability.”
In a literal Chinese interpretation, this term can easily be misunderstood to mean: only things that can be proven false are science.
If this were the meaning, it would of course be absurd.
A theory that has been consistently proven false by numerous reliable experiments within its claimed scope of applicability cannot continue to be considered correct scientific knowledge.
What Popper truly wanted to emphasize is that a theory must make a clear judgment and cannot interpret any possible outcome as a confirmation of its correctness.
Therefore, instead of repeatedly explaining the ambiguous term “falsifiability,” it is better to state directly: science must submit to empirical tests with clear criteria for success and failure.
But it must be especially emphasized: a true test must include the possibility of failure.
If a theory claims to be correct when faced with favorable results, and then offers a different explanation to still claim correctness when faced with unfavorable results, it has not truly been tested; it has merely declared victory unilaterally.
A theory that can explain all outcomes often predicts no specific outcome.
V. Anecdotes and Single Successes Don’t Prove Causation
Many people like to use a single personal experience to prove a grand theory.
For example, someone might say: “Last night I prayed to God to find money on my way out today, and I really did find some, so God answered me.”
This only shows that two events occurred in temporal succession: he prayed, and then he found money.
But temporal succession does not automatically prove a causal relationship.
It could have been a coincidence; perhaps people often drop loose change on that road; perhaps he had prayed many times before without success and only remembered this one time; or perhaps after praying, he paid more attention to the ground than usual, thus increasing his probability of finding change.
To turn this into a scientific proposition, it must be rephrased: people who pray in a specified manner have a significantly higher probability of finding money on a specified route at a specified time than people who do not pray.
Then, one would conduct a randomized controlled trial with a sufficiently large sample size, pre-determined criteria for success, and have the experiment repeated by different researchers.
Only if the prayer group consistently shows a stable difference across many experiments, and the results can be repeatedly reproduced by other researchers, have we truly discovered a phenomenon that needs explaining.
Science does not reject a phenomenon in advance just because it involves “God.”
What science rejects is the packaging of a single coincidence as a universal law.
VI. Why Is a Personal God Not a Scientific Explanation?
The gods in most religions have distinct personal characteristics: they can love, get angry, judge, bless, and punish.
Since God is said to influence nature and human life, this influence must produce testable real-world consequences.
However, theology often forms a closed loop that can never fail: if a prayer succeeds, God has answered; if it fails, God has other plans; if you suffer a disaster, God is testing you; if nothing happens, it is because God is invisible.
Thus, any outcome can be used to prove God’s existence.
But a theory that can explain all outcomes, in fact, explains nothing.
When no outcome can truly serve as a referee, it exits the realm of science.
Similarly, some say: “The universe was created by God, the laws of physics were established by God, and the Big Bang was initiated by God.” Whatever science discovers, one can always add at the end: “This too was designed by God.”
However, adding this sentence introduces no new predictions, changes no experimental results, and does not explain what phenomena would not occur if God did not exist.
It merely adds an untestable cause with no predictive power on top of a natural explanation.
A theory that claims to explain reality but cannot accept empirical testing is not profound, but empty.
If one further defines God as having no personality, no will, not responding to prayers, and never intervening in any natural process, then such a God is observationally indistinguishable from “non-existent.”
Assuming it exists, the world operates this way; assuming it doesn’t exist, the world still operates this way.
It is no longer a natural explanation, but merely a renaming of “the universe,” “the laws of nature,” or “existence itself.”
VII. Why Is Newtonian Mechanics Still Science Even Though It Was Revised?
Some might ask: since scientific theories must be tested against reality, and Newtonian mechanics was later revised by relativity, does that mean Newtonian mechanics is not scientific? Not at all.
A mature scientific theory is not simply “absolutely correct” or “completely wrong.”
Newtonian mechanics can describe the motion of objects with extreme accuracy at low speeds, in weak gravitational fields, and for ordinary engineering purposes.
How cars drive, how cannonballs move, how bridges bear loads, how machines operate—a vast number of real-world problems can be stably calculated using Newtonian mechanics.
We don’t need to apply relativistic corrections every time we calculate the motion of an ordinary car.
This is not because we knowingly use a wrong conclusion for convenience, but because under these conditions, the relativistic correction is far smaller than the required precision.
When an object’s speed approaches the speed of light, special relativity is needed; when strong gravity and significant spacetime curvature are involved, general relativity is needed.
What was revised was not the effectiveness of Newtonian mechanics within its low-speed domain, but the overextended claim that “Newtonian mechanics is absolutely precise under all conditions.”
Newtonian mechanics is science precisely because it can: perform quantitative calculations; be repeatedly tested; specify its errors; define its scope of applicability; and indicate where it begins to fail.
True science doesn’t just say, “I am always right.” It honestly tells you: under what conditions I am correct, to what degree of accuracy, and where my boundaries lie.
This also shows that the absence of ultimate truth in science does not mean science is wrong.
Science is the most reliable description of reality we currently have, valid within well-defined boundaries.
When a new theory emerges, the old one often doesn’t disappear entirely but is placed within a more accurately defined scope of applicability.
VIII. A True Prediction Must Meet Three Conditions
Many people believe that as long as a result can eventually be calculated, it means the future is predictable.
This view overlooks the most basic conditions for prediction.
A scientifically meaningful prediction must satisfy at least three points.
First, the prediction must be fixed in advance. The content of the prediction must be recorded before the event occurs and cannot be modified after the result is known.
It can be made public, or it can be encrypted, sealed, or entrusted to an independent third party.
The key is not that everyone sees it immediately, but that an unalterable record exists.
Second, the prediction must be independently verifiable. After the event occurs, others must be able to compare the original prediction with the actual result.
If someone just says, “I knew it all along,” but cannot produce a pre-fixed record, it’s not a prediction, just a post-hoc claim.
Third, the calculation must be completed before the event occurs. Suppose we want to predict the state of a system one hundred years from now, but the calculation itself takes at least one hundred years to complete. Even if the final calculation is correct, it has no predictive value.
The computer is merely running in sync with the system, not obtaining the future in advance.
If expressed symbolically, a true prediction must satisfy: T_computation < T_event
Where “T_computation” is the minimum physical time required to obtain the prediction result, and “T_event” is the time difference between the present moment and the occurrence of the target event.
If the time required for calculation exceeds the waiting time for the event, the prediction loses its practical meaning.
If the calculation result always arrives later than reality, it is not a prediction, but a post-hoc reenactment.
IX. Theoretically Computable Does Not Equal Physically Predictable
Just because a system has clear laws of evolution does not mean its future can be calculated in advance by a real-world computer.
All real computations require time, energy, storage space, and information transfer.
A computer itself is a physical system and cannot escape the laws of physics.
Physicist Seth Lloyd estimated that the total number of elementary operations the observable universe could have performed since its birth is on the order of 10^120, and the amount of information it can register is on the order of 10^90 bits.
These numbers depend on specific physical and cosmological assumptions, but they illustrate a fundamental fact: the computational resources provided by the universe are finite.
If a prediction task requires an amount of information, number of calculations, or completion time that exceeds the physical limits the universe can provide, then even if it can be run step-by-step in abstract mathematics, the prediction cannot be completed in reality.
Furthermore, increasing computing power does not guarantee the solution to all prediction problems.
In 1990, Cristopher Moore proved that it is possible to construct continuous dynamical systems with as few as three degrees of freedom whose motion is equivalent to universal computation.
For such systems, even if the initial conditions are given precisely, certain questions about their long-term evolution are undecidable.
This does not mean that all systems with three degrees of freedom are unpredictable, but it shows that undecidability can appear even in rule-defined dynamical systems with very few degrees of freedom.
This result refutes an overly simplistic notion: that as long as the laws of nature are clear and a computer is given enough resources, it can surely calculate everyone’s future in advance.
This is not the case.
Having rules does not mean a predictive shortcut exists; being theoretically evolvable does not mean it can be completed in advance; and having deterministic rules does not mean all long-term questions have a feasible algorithm.
X. A Thought Experiment on Predicting Human Behavior
Suppose someone claims: “I can accurately predict whether you will choose A or B at 10 a.m. tomorrow.”
According to scientific standards, they must first fix their prediction.
If they tell the prediction directly to the subject, the subject can adopt a very simple rule: if you predict I’ll choose A, I’ll choose B; if you predict B, I’ll choose A.
This shows that for a subject who can understand the prediction and change their behavior based on it, the prediction itself becomes a new input to the system.
A stone will not change its trajectory because you predict it; a person will.
The counterargument might be: “Then I won’t tell you the prediction, I’ll just seal it and give it to a third party.” This does prevent the subject from deliberately doing the opposite, but the prediction must still face empirical testing.
We can strengthen the thought experiment further.
Suppose the person pre-specifies: “At 10 a.m. tomorrow, my action will be determined by a quantum random bit generated at that exact moment. If the result is 0, I choose A; if it’s 1, I choose B.”
The predictor must encrypt, seal, and deliver their prediction to an independent third party before the random bit is generated.
The next day, the random bit is read on-site, the corresponding action is performed, and finally, the prediction record is opened for comparison.
Modern Bell experiments have already ruled out local hidden-variable theories. Furthermore, experiments based on the violation of Bell’s inequality can, under clear assumptions, certify randomness, producing random outputs that cannot be known in advance by the predictor.
At this point, the predictor can no longer explain failure by saying, “You knew the prediction and deliberately changed your behavior,” because the subject did not know the random outcome in advance. The predictor also cannot change their answer after the fact, because the prediction was fixed by a third party.
If the predictor still claims they can be accurate every time, the experiment is very clear: repeat it enough times and check if their success rate significantly exceeds the probability level given by quantum theory.
If the predictions succeed, it becomes significant evidence that needs a new explanation; if they fail, their claim of deterministic prediction is not supported.
This thought experiment does not require that all human behavior depends on quantum randomness.
It only needs to construct a class of well-defined actions: human action can be actively tied to a physical process that, within the current scientific framework, can only provide probabilities, not a definite single outcome in advance.
Thus, the absolute proposition that “every single human action can be precisely predicted in advance” is no longer tenable.
XI. Quantum Processes Are Not Mysterious Stories, but Objects of Experimental Study
Quantum randomness is not an untestable philosophical slogan.
Bell’s inequality experiments can test whether quantum correlations conform to local realistic models. Randomness certification based on Bell violations can turn “unpredictability” into a repeatable, statistically verifiable experimental conclusion.
This suggests that the probabilistic nature of quantum mechanics is not due to our “lack of information (hidden variables),” but is an intrinsic randomness of nature.
Modern experiments can even track the intermediate processes of a quantum jump in real time.
In 2019, Minev et al. continuously monitored a superconducting artificial atom, catching and reversing a quantum jump in progress.
The experiment showed that the evolution of a jump that has started and will eventually complete can be continuous, coherent, and trackable.
This experiment does not single-handedly settle all interpretations of quantum mechanics, but it demonstrates that so-called quantum jumps are not mysterious events to be discussed only in imagination, but physical processes that can be observed, monitored, intervened in, and studied repeatedly.
According to the standards established in this article, within the scope of current evidence, the probabilistic description of standard quantum mechanics—usually expressed in the operational language of the Copenhagen interpretation—directly corresponds to repeatable experiments and can provide precise statistical predictions.
If a deterministic interpretation claims that all single outcomes are in fact predetermined, but cannot propose new predictions that differ from standard quantum theory, nor design independent experiments to test itself, then it cannot scientifically replace the empirically tested probabilistic description.
Within the current evidence and precision, the probabilistic description that directly corresponds to experiments and can be repeatedly verified is the scientific explanation that is currently closer to natural reality.
This is not to say that a more complete theory will never emerge in the future.
Just as Newtonian mechanics is not the ultimate truth but is extremely reliable within its own domain, standard quantum theory can be the most reliable description today while remaining open to future testing and revision.
XII. Why Is a Person’s Future Harder to Predict Than a Simple Mechanical System?
The human brain is not an isolated, closed, and fixed-boundary mechanical device.
A person continuously receives new information, recalls the past, revises judgments, changes goals, and may also choose new behaviors based on others’ predictions about them.
A person’s future depends not only on their current brain state but is also influenced by future encounters, information seen, bodily changes, diseases, social events, environmental changes, and countless feedback processes.
More importantly, the prediction itself can enter the system.
If a prediction is known to a person, it will change their thinking. Even if the prediction is not known to the person, it must be fixed in advance and subjected to independent testing. If human behavior is further tied to a certifiable quantum random result, then a deterministic single-event prediction becomes a claim whose success or failure can be directly tested.
The obstacles to predicting complex systems are not caused by a single factor but by a combination of limitations: initial states cannot be measured with infinite precision; small errors can be amplified by non-linear feedback; the system constantly receives new external information; the prediction can in turn change the system; computation is limited by time, energy, and storage; and some dynamical systems even have mathematically undecidable problems.
Therefore, a person’s long-term future is not a script that can be read in its entirety in advance.
In a scientific sense, a system has operational determinism only if it can be stably predicted in advance under specified conditions, precision, and timeframes.
A “hidden determinism” that cannot produce a verifiable prediction before an event occurs is not a scientific conclusion, but an untestable metaphysical assumption.
XIII. Why Is Fatalism an Incorrect Description of Nature?
Fatalism holds that a person’s life is already destined.
Mechanical determinism, on the other hand, imagines that if one knows the complete state of the universe at a single moment and all its laws, the future is entirely contained within the past.
The two are not identical, but fatalism often borrows from mechanical determinism to cloak the idea that “a person’s life is already written” in a seemingly scientific guise.
Fatalism usually has a “teleological” flavor (i.e., the endpoint is inevitable, regardless of the path taken), whereas mechanical determinism only speaks of “causality” (evolution from initial conditions and equations).
Complex systems and computational limits destroy the foundations of both.
The problem is, this claim cannot answer the most basic questions: What are the variables that determine an individual’s fate? What is the evolutionary formula? How much information is needed? What is the prediction accuracy? How far in advance can it be predicted? What result would prove fatalism wrong?
Fatalism can usually only explain the result after it has happened: if you work hard and succeed, it was destined; if you give up and fail, that too was destined; if you hear about fatalism and decide to resist, your resistance was also destined.
A theory that can accommodate all outcomes has not truly undergone any test.
It provides no new information, nor does it make a prediction that risks failure; it merely re-labels everything that has already happened as “fate.”
Of course, human behavior is influenced by genetics, environment, education, experience, and brain activity.
But: that behavior has causes does not mean life is a single path that has already been written and can be read in advance.
Modern mathematics has proven that rule-defined dynamical systems can contain undecidable long-term problems; physics shows that any real computation is limited by the universe’s resources and time; and quantum experiments provide physical processes that can only be described probabilistically and whose unpredictability can be certified.
Together, this evidence refutes a simple and absolute fantasy: that as long as the universe has causal laws, a sufficiently powerful computer can surely calculate every person’s life in advance.
This is not the conclusion of modern science.
Fatalism can neither provide an operational model nor form a verifiable prediction; and when it fails, it can explain the failure itself as being destined.
Therefore, under the scientific standards established in this article: fatalism is not a valid scientific description of the natural world, but an erroneous explanation arising from the infinite extension of causality.
XIV. The True Boundary of Science
Now, we can offer a more complete definition of science: Science is the most reliable and closest description of the natural world we currently have, established through public testing, repeated experiments or independent evidence, within specified conditions, timeframes, precision, and error margins.
It must allow reality to support, limit, revise, or negate it, and must never interpret all possible outcomes as confirmation of its own correctness.
Each of these components is indispensable.
Testability is the ticket to enter scientific inquiry; repeatability and independent verification are the foundation for building public knowledge and eliminating personal delusion; specified conditions, scope, and error are the honest boundaries of science; predictions must be fixed in advance and completed before the event; and tests must allow for failure, otherwise, the test is merely a performance.
Mathematics establishes necessity through logical proof within given premises.
Natural science establishes empirical reliability about the real world through observation, experiment, measurement, and prediction.
A personal god claims to intervene in reality but cannot provide stable, clear, and verifiable results, and is therefore not a scientific explanation.
Newtonian mechanics can be calculated, tested, and specifies its scope and errors, so even though it is not an ultimate theory, it is still science.
The prediction of complex systems is limited by initial information, feedback, algorithms, time, and physical resources; human behavior can also react to the prediction itself and be actively tied to certifiable quantum random events.
Therefore, a person’s long-term future cannot be treated as a pre-written script that can be deterministically read.
Science never relies on the assertion of an authority, does not depend on how many advanced formulas are used, nor on being cloaked in a sophisticated philosophical or religious guise.
Science ultimately has only one referee: reality.
If reality consistently supports a theory, it can temporarily become reliable knowledge.
If reality shows it is valid only in a limited range, it must acknowledge its boundaries.
If reality consistently refutes it, it must be revised or retired.
Science is not ultimate truth.
But for understanding the natural world, humanity has yet to find a method more reliable and closer to the truth than science.
And a theory that refuses empirical testing, yet claims to explain everything, is nothing more than empty and erroneous soliloquy, no matter how profound it may sound.