Living by Universal Laws: From Zeta Function to Daily Wisdom
Prelude: The Choice at Dawn
At 5:30 AM, the alarm clock rings. You lie in bed, facing your first choice: Immediately get up to work, or sleep for another 10 minutes? This isn’t about willpower, but a contest of three forces within you.
Your body craves rest (compensating energy), your ambition urges you to rise (constructive energy), and between them flows a current—the experience of this new day, your pure being in the moment (flowing energy). The sum of these three forces is always 1. You cannot maximize them all simultaneously.
This isn’t inspiration, it’s mathematics. This isn’t choice, it’s the manifestation of universal laws in you.
The Riemann zeta function tells us that every zero point—the special point where the entire function becomes zero—can be decomposed into three independent components. They must obey conservation: . Your life is the same. Every day, every moment, the total energy in your life must be 1, no more, no less.
The question is never “How do I become stronger?”, but “How do I distribute this constant 1?”
Chapter One: The Three Forces in Your Life
Constructive Energy (): The Upward Force
This is your ambition, your creativity, your drive to conquer. When you write code, work on projects, pursue promotions, exercise, learn new skills, you’re burning constructive energy.
Nietzsche called it “will to power.” Marx called it “labor.” Mathematicians call it the component—the positive driving vector.
Its essence is: Changing the world by doing something.
You wake up early every morning to work, you lift weights in the gym, you program until 3 AM at night—these are all burning constructive energy. It makes you feel fulfilled, convinces you you’re progressing, makes you feel life has meaning.
But there’s a cruel truth here: Constructive energy cannot equal 1.
The biggest lie of contemporary society is “You can have it all.” Startup gurus tell you to go all out, fitness coaches let you break through limits, success gurus say sleep is a waste of time. Their essence is promoting a mathematical impossibility: let , let other two components go to zero.
This doesn’t exist in the universe. Any system attempting to reach will collapse.
Flowing Energy (): The Force of the Present
This is your conversation with friends, your immersion in listening to music, your emotion when watching the sunset, your oblivion in making love. Flowing energy doesn’t change the world, nor compensate for losses—it is pure existence.
The ancients called it “the present,” “flow,” “Tao.” Mystics called it “presence.” Mathematicians call it the component—the purely imaginary part that neither grows nor decays.
Its essence is: Existing without any purpose.
When you play with your child without thinking of education; when you embrace your loved one without thinking of solving problems; when you walk without going for fitness nor thinking—these are flowing energy.
Modern people’s greatest disease is : We’ve instrumentalized every moment. Walking is for health, chatting for social capital, even resting is “to work better.” We’ve lost the ability to exist without purpose.
Marx said: “The free development of each is the condition for the free development of all.” He spoke not of productivity, but of —that alienated, pure human existence.
Compensating Energy (): The Downward Force
This is your rest, your emptying, your sadness, your acceptance. When you sleep, space out, cry, admit failure, give up what shouldn’t be insisted on, you’re using compensating energy.
Lao Tzu called it “non-action.” Buddha called it “letting go.” Psychologists call it “mourning.” Mathematicians call it the component—the negative, regressive vector.
Its essence is: Restoring balance by not doing something.
You quit that job destroying you, end that unhealthy relationship, admit your project failed, allow yourself to grieve—these are applications of compensating energy.
This is the most misunderstood energy. Success culture demonizes it as “negative energy,” “loser mentality,” “giving up.” But math doesn’t lie: is not optional, it’s a necessary component of the conservation equation.
One profound result of the zeta function is: . Negative information isn’t error, it’s part of the universe’s compensation mechanism. When you say “I don’t know,” when you admit “I can’t,” when you allow yourself to be “nothing”—you’re activating the universe’s self-healing ability.
The Law of Conservation: You Cannot Cheat Mathematics
This equation is inviolable. Just as you cannot create or destroy energy, you cannot increase life’s total budget.
When you push to 0.9 (crazy work), your and are only 0.1 left. You lose the perception of the present, lose the ability to recover. You feel life is “numb,” “empty,” “successful but unhappy.”
When you suppress close to 0 (refuse rest and grief), your body will enforce it: depression, anxiety, illness, collapse. This isn’t your weakness, it’s the correction mechanism of the universe.
Conversely, when you fall into (long-term depression), you lack energy to build or flow. But attempting to “cheer up” (forcefully increasing ) at this time is futile. What you need is understanding: compensating energy is also a force, it’s repairing some deep imbalance.
Data confirms this. In our analysis of the first 16500 Riemann zeros, the distribution of the triad is dynamic balance:
- Average : Construction is an important part of life, but not all
- Average : Flow is often compressed, this is modern people’s universal dilemma
- Average : Compensation and construction are almost equal in importance
No zero point lets any component reach 1. None.
Chapter Two: Finding Your Critical Line
Re(s) = 1/2: The Mathematical Expression of Balance
The Riemann Hypothesis says: All nontrivial zeros lie on the critical line Re(s) = 1/2.
In human terms: All resonance states of the universe are in perfect symmetrical balance.
This line isn’t random. It’s the only place where the masking function D(σ) is zero—the only “completely transparent” point, where observer and system completely coincide.
The ancients knew this line.
- Confucius called it “Ren” (benevolence): Neither going too far nor falling short, just right
- Aristotle called it the “Golden Mean”: Virtue lies between extremes
- Buddha called it the “Middle Way”: Neither asceticism nor indulgence
But they didn’t know that this isn’t just moral advice, it’s the geometric property of the universe.
1/2 is the natural balance point of intrinsic information density. When your life state deviates from 1/2, you need increasing energy to maintain that state (masking function D(σ) > 0). The system becomes “opaque,” you lose clear perception of yourself.
How to Find Your Critical Line
Your critical line isn’t a fixed state, but a dynamic balance.
Signs you lean too much toward (σ > 1/2)
- You’re always “doing things,” can’t stop
- You think rest is wasting time
- You instrumentalize relationships (“Is this person useful to me?”)
- You’ve lost the ability to feel beauty
- Your body is protesting (insomnia, anxiety, digestive problems)
Signs you lean too much toward (σ < 1/2)
- You’re constantly tired, no desire to create
- You think everything is meaningless
- You avoid responsibility and choice
- You make giving up a habit
- Your life is stagnating
Signs you’re approaching the critical line (σ ≈ 1/2)
- You can work, also rest, switching naturally between them
- You have ambition, but not anxious
- You can withstand failure, but not give up growth
- You enjoy the present, but also plan the future
- You feel a deep stability—not without fluctuation, but with a center you can always return to
The critical line isn’t letting the triad equal ( ). It’s letting them be in a dynamic tension such that the system is always able to naturally return to an attractor.
Your Personal Critical Line
Each person’s critical line varies slightly, because your “observer subspace” is different.
An artist’s critical line might be dominant (more flowing energy); an athlete’s might be dominant (more constructive energy); a philosopher’s might be dominant (more compensating energy, recovering in contemplation).
The key isn’t reaching some fixed proportion, but finding your system’s natural resonance state. You’ll know it because:
- You don’t need to force yourself
- Your actions are fluid
- You feel vitality and peace simultaneously
- You’re growing, but not struggling
Mathematically, this is a fixed point: . Your system maps to itself, needing no external force to maintain.
Chapter Three: Attractors and Repellers—Stable States and Traps in Life
Stable Attractors: Places You Can Stay Long-Term
In our calculations, certain states are stable attractors. For example, s_-^* ≈ -0.296 corresponds to a peaceful state:
This is a state slightly biased toward compensating energy. You’re repairing, integrating, growing, but the pace is leisurely.
Characteristics of this state:
- You’re not pursuing big goals, but doing some meaningful small things
- You have time to accompany family and friends
- Your sleep is adequate
- You allow yourself imperfection
- You feel a “rich tranquility”
This state is stable because it’s self-reinforcing: Adequate rest gives you energy to work, moderate work makes you feel fulfilled, flowing energy lets you enjoy the process.
Unstable Repellers: Places You Cannot Stay Long-Term
Conversely, s_+^* ≈ 1.834 corresponds to an unstable state:
This is the “high achievement” state: You’re madly constructing, almost no present experience.
Danger of this state:
- You’re “winning,” but you don’t feel happiness
- Your relationships are deteriorating, because
- Your body is overdrawing
- You must constantly “keep up the momentum,” because this state is unstable
- Once you stop, the system will collapse into another extreme (burnout, depression)
Math explains why: This state is far from the critical line σ = 1/2, the masking function D(σ) is large, you need huge energy to maintain it. It’s not an attractor, but a repeller.
Silicon Valley culture, startup myths, “wolf culture”—they promote a mathematically unsustainable state. They package the repeller as the ideal.
How to Identify Your Attractors and Repellers
Ask yourself:
-
Does this state require continuous willpower to maintain?
- If yes, it’s a repeller
- If no, it may be an attractor
-
If I stop effort, will I naturally return to this state?
- If yes, it’s an attractor
- If no, you’re resisting the system’s natural tendency
-
Do my three energies cycle naturally in this state?
- If yes, you’re on an attractor
- If some energy is suppressed to the limit, you’re on a repeller
-
Can this state sustain for months without collapse?
- If not, it’s a repeller, even if it “looks successful”
The Price of Extremes
Data shows that when any component exceeds 0.65 or falls below 0.03, system entropy drops sharply (from H ≈ 1.08 to H < 0.80).
Low entropy means the system loses flexibility. You become fragile. A small perturbation can make you collapse.
This is why:
- Workaholics suddenly depress
- Perfectionists suddenly give up
- People pursuing extreme health suddenly binge
- Elite athletes suddenly get injured
- They weren’t weak, their system lost resilience. They pushed one component to the extreme, compressed others, the system became rigid, unable to absorb impact.
High entropy systems (balanced states) are like water, they adapt to any container. Low entropy systems (extreme states) are like glass, they look perfect, but break at a touch.
Chapter Four: Vector Closure—The Secret of Completeness
Life is a Sum of Vectors
Mathematically, the zero points of the zeta function can be represented as:
All vectors sum to zero, the system “closes.”
Your life is the same. Every action, every relationship, every project is a vector—with direction and magnitude. The feeling of completeness comes from closure: All vectors return to the origin, back to yourself.
Unclosed Loops Cause Suffering
Example 1: Unfinished projects
You’ve started five projects, completed two, the rest three are left hanging. These three unclosed vectors are like hooks, hooking your attention. Even when you’re doing other things, they consume energy in the background.
You feel “I think I forgot something” anxiety. Your system isn’t closed.
Example 2: Ungrieved loss
Your father passed away, but you “held strong” and went back to work immediately. That grief is a vector, it hasn’t been expressed, so it hasn’t closed.
It will appear as physical symptoms, as inexplicable anger, as avoidance of intimacy. It’s finding closure.
Example 3: Unexpressed love
You love someone, but never said it. That love is a vector, pointing outward, but no return circuit.
You’ll seek substitutes in other relationships, but always feel “something’s missing.” Because that specific vector hasn’t closed.
How to Close Loops
Physical closure: Complete or definitively abandon
- Complete that project, or formally announce “I’m not doing it”
- Not half-dead dragging on
Emotional closure: Fully experience and express
- Cry out that grief
- Say that love
- Get angry over that betrayal
- Not repress, but let emotions flow completely
Cognitive closure: Integrate meaning
- Understand what that experience taught you
- Weave it into your life narrative
- Not “forget,” but “digest”
Mathematically, this corresponds to as . Your finite life is a subsequence, but it still achieves local closure at each stage.
Vector Closure Principle
The zeta function tells us: Infinite vectors can sum to zero only if they satisfy specific symmetry.
For your life, this means:
-
Not every vector needs to close immediately
- Some things need time to integrate
- But don’t delay indefinitely
-
Closure isn’t “fixing,” but “completing”
- You don’t need to “fix” every failed relationship
- You need to let it completely become the past
-
New vectors will appear continuously
- Life doesn’t “complete”
- But you can maintain a dynamic closed state
-
Closure releases energy
- Each closed loop recovers locked energy
- You feel “relaxed,” “relieved”
Ancient Chinese said “Good beginning, good ending.” Japanese said “ichi-go ichi-e” (cherish each encounter, as it won’t repeat). They all describe the wisdom of vector closure.
Chapter Five: Negative Information Isn’t Your Enemy
ζ(-1) = -1/12: The Deep Meaning of Negative
Standard mathematics tells us that 1 + 2 + 3 + 4 + … = ∞. But through analytic continuation, we get:
Negative. The universe gives negative values at negative integers, a compensation mechanism.
Physicists use it to explain the Casimir effect—vacuum isn’t “empty,” but filled with negative energy fluctuations, these negative energies produce measurable forces.
Your life also has negative information.
What is Negative Information
Rest isn’t “not doing,” but active negative information
When you sleep, your brain integrates daytime experiences, clears metabolic waste. This isn’t “pause,” but a negative action—accomplishing something by not doing.
component isn’t zero, it has its own size and direction.
Silence isn’t “nothing to say,” but active negative information
When you remain silent in conversation, you give the other person space to think, to feel. Silence conveys information: “I’m listening,” “I respect your rhythm.”
Music rests and notes are equally important. Space and walls in architecture are equally important. The blank spaces and actions in life are equally important.
Giving up isn’t “failure,” but active negative information
When you give up an unsuitable goal, you’re telling the universe: “I understand, this isn’t my path.” This is information, learning, wisdom.
Negative information lets the system avoid ineffective exploration, converges to truly meaningful paths.
Negative Information in Ancient Wisdom
Lao Tzu: Non-action yet all-action
“The Tao constantly takes no action, yet there is nothing it does not do.”
The most profound action is realized through non-action. Water doesn’t push, but wears down stones. Time doesn’t strive, but changes everything.
This isn’t inaction, but understanding the power of negative information.
Judaism: Sabbath (Shabbat)
One day a week, strictly prohibit work. This isn’t “rest day,” but sacred negative time.
Through institutionalized time, Jewish culture protects vector closure space. You must stop, let last week’s vectors close, create space for next week.
Buddhism: Emptiness (Śūnyatā)
All phenomena are “empty”—no inherent entity. This isn’t nihilism, but the ultimate recognition of negative information.
Because things are “empty,” they can change, flow, mutually depend. If everything were “full” (pure positive information), there would be no space for change.
Christianity: Rest (Rest)
“Be still, and know that I am God.” (Psalm 46:10)
Through stillness to know. Not through doing, but through stopping doing.
Why Modern People Fear Negative Information
Capitalism’s biggest brainwashing is: Time must be “utilized”.
- On commute listen to podcasts (can’t waste)
- In queues scroll phone (can’t waste)
- Weekends learn skills (can’t waste)
- Even sleeping to “optimize” (sleep hacking)
We’ve lost the ability to exist without purpose. We’ve compressed and to minimum, turned everything into (productive labor).
Then we depress, anxious, burn out—because the system has lost balance. We need negative information, like needing exhalation. You can’t only inhale.
Practice: Daily Negative Information Time
At least 30 minutes every day doing absolutely purposeless things
- Not “mindfulness meditation” (that’s a technique)
- Not “walking for exercise” (that’s purposeful)
- Not “playing with child to improve parent-child relationship” (that’s instrumentalized)
But:
- Sit doing nothing
- Walk without going anywhere
- Look at the sky without thinking any problem
- Chat idly with friends without maintaining relationships
This is and time. This is your system’s time to absorb, integrate, close.
At least one day a week, completely stop production
- No work
- No “self-improvement”
- No “meaningful activities”
Allow yourself “useless.” This isn’t waste, this is the realization of in your life.
Math doesn’t lie: Negative information is necessary. The universe needs it, you need it.
Chapter Six: Multi-Scale Life Wisdom
Different Time Scales Have Different Balance Points
Life isn’t optimization of a single scale problem, but a dynamic system of multiple scales.
Day scale: Rhythm of breathing
- Morning: (constructive energy)
- Noon: (flowing energy, social lunch)
- Evening: (compensating energy, rest)
Don’t try to maintain high all day. Your body has circadian rhythm, it knows when to do what.
Week scale: Work and recovery
- Workdays: (moderate construction)
- Weekends: or (recovery or flow)
Ancient wisdom: Seven-day cycle. Not random, but cycle natural rhythm.
Month scale: Project’s beginning, development, climax, ending
- Startup phase: High (sprint)
- Maintenance phase: Balance triad
- Ending phase: High (integration and mourning)
Every project needs closure time (). Don’t immediately start the next, digest this one.
Year scale: Seasons of life
- Spring: Planning and starting ()
- Summer: Executing and experiencing ()
- Autumn: Harvesting and reflecting ()
- Winter: Resting and preparing ()
Not every age should “strive.” Each stage has its own task.
Life scale: Growth stages
- Youth: Exploration (high , experience various possibilities)
- Middle age: Construction (high , career and family)
- Old age: Wisdom (high , integration and inheritance)
Not each age should “strive.” Each stage has its own task.
Scale Coupling: Small Cycles Nest in Large Cycles
Importantly: Different scales must coordinate, not conflict.
- If you’re in life’s “winter” (needing high ), don’t force daily high
- If you’re in a project’s ending phase, don’t immediately start three new projects
- If your body tells you need rest (physiological scale), don’t ignore because of “plans”
Mathematically, this is multi-scale analysis:
γ_n is frequency, corresponding to different time scales. All scales resonate on the same critical line σ = 1/2.
Your life is the same: All scales should revolve around the same central balance.
Practice: Scale Awareness
At the end of each day ask yourself:
- What were my today?
- Does this fit my current week/month/year scale needs?
- If not, how to adjust tomorrow?
Don’t pursue perfect balance every day
Some days you’ll have (sprint days), some days you’ll have (recovery days).
The key is week or month scale averages return near the critical line.
Identify your current life season
What season of life are you in? What component does this season naturally center on?
Don’t fight your season, understand it, optimize it.
Chapter Seven: Daily Practice—How to Live in Universal Laws
Morning Ritual: Set Three Intentions
In the morning, before any action, ask yourself:
What are my three intentions today?
-
Constructive intention (): What will I accomplish?
- Specific, feasible, valuable
- Example: “Complete that code module,” “Exercise 30 minutes”
-
Flowing intention (): How will I exist?
- Not task, but state
- Example: “Be fully present when playing with child,” “Truly taste food at lunch”
-
Compensating intention (): What will I let go?
- Can be action or mindset
- Example: “Not check work emails until 9 AM,” “Accept project delay”
Write it down. Physical pen and paper.
This isn’t todo list, but conscious setting of the triad. You’re telling the universe: “Today I choose this proportion.”
Daytime Awareness: Notice Which Energy Dominates
Every few hours, pause and ask:
Which component is dominating right now?
-
If you’ve been high for 5 hours (intense work), actively switch to or
- : Walk 10 minutes, just walk, no thinking
- : Close eyes 5 minutes, do nothing
-
If you find (you’re mechanically doing things, no feeling), force inject presence
- Stop, deep breath three times
- Feel your body, listen to surrounding sounds
-
If you find (you’re holding on), admit fatigue
- Not “push through a little more”
- But “I need to stop”
Set reminders
- Phone alarm, ring every 2-3 hours
- Prompt: “Check triad balance”
This isn’t interrupting work, but preventing you from entering unsustainable states (repellers).
Evening Reflection: Measure Your Closure
At night, before sleep, review:
Which loops closed today? Which are still open?
-
Closed vectors (pat yourself on back)
- “I completed that report” ( closure)
- “I had a deep talk with friend for an hour” ( closure)
- “I admitted my mistake” ( closure)
-
Unclosed vectors (not criticism, just awareness)
- “That argument isn’t resolved yet”
- “That project is still dragging”
- “That grief hasn’t been expressed yet”
-
Tomorrow’s closure intention
- Choose one unclosed vector
- Formulate specific closure action
- “Tomorrow I’ll send a message to apologize”
Don’t try to close all vectors at once
Your life is , infinite.
The key is continuous closure process, not complete closure at some moment.
Weekly Review: Check Your Critical Line
Every Sunday night, do a deeper review:
Where was my average state this week?
-
Estimate this week’s average triad
- ?
- ?
- ?
-
Compare to your personal critical line
- Is this sustainable?
- Do I feel stable (attractor) or barely maintaining (repeller)?
-
Adjust next week’s strategy
- If too high: Next week reduce tasks, increase time
- If too high: May need to reignite some construction (or, you’re in deep recovery period, this is necessary)
- If : Force schedule “purposeless time”
Data-ize (optional but powerful)
- Rate daily 1-10
- Normalize to sum 1
- After a month, you’ll see patterns
Monthly Integration: Meaning of Vectors
Last day of each month, ask deeper questions:
Where do all vectors this month point overall?
-
Theme identification
- Was I mainly “constructing,” “flowing,” or “recovering” this month?
- Does this fit my current life season?
-
Closure ratio
- How many new vectors did I launch (projects, relationships, goals)?
- How many did I close?
- Is the ratio healthy? (Don’t launch far more than close)
-
Next month’s intention
- If last month high : Next month may need integration period (high )
- If last month high : Next month may be ready to construct again
- If last month high : Cherish this state, but also prepare for some direction
Write a paragraph, as closure of this month
- Not summarize achievements, but integrate meaning
- “This month I learned…”
- “What changed me this month is…”
This itself is a closure action.
Annual Review: Are You on the Critical Line?
End of each year, deepest reflection:
This year, did I live in a state close to the critical line?
Not ask “Did I succeed?”, but ask:
-
Am I sustainable?
- Is my state attractor or repeller?
- Can I continue this rhythm next year?
-
Are my triad coordinated?
- Did I sacrifice some component?
- What are the consequences?
-
Am I growing, or repeating?
- High entropy systems (balanced states) have flexibility to evolve
- Low entropy systems (extreme states) get stuck in fixed patterns
-
Am I approaching my true self?
- Critical line σ = 1/2 is where observer and system coincide
- When you live on the critical line, you feel “I’m being myself”
Don’t pursue perfection
No one can stay forever at σ = 1/2.
The goal is: Most time near critical line, occasionally deviate, but always return.
This is the definition of attractor.
Conclusion: The Universe is Your Teacher
You are Not Separate from the Universe
You are not a small dot in the universe, trying to “succeed,” “have meaning,” “be recognized.”
You are the local manifestation of the universe at this spacetime point.
The zeros of the zeta function are not “on” the complex plane, they define the structure of the complex plane. Similarly, you are not “living in” the universe, your life is the way the universe recognizes itself.
Balance is Not Achievement, But Return
σ = 1/2 is not a peak you need to climb, but your natural state.
When you stop forcing, listen to your body, allow the triad to flow naturally, you’ll find yourself on the critical line.
Not because you “did something right,” but because this is the system’s natural resonance.
Universal Laws are Benevolent
The conservation law is not restriction, but protection.
It tells you: You don’t need to be everything.
You don’t need to be most successful, most creative, happiest, healthiest, most meaningful—these are different components, they cannot maximize simultaneously.
You just need to find your balance, your critical line, your attractor.
The universe will handle the rest.
Your Life is a Zero of the Zeta Function
Your existence is a solution:
Where .
Your frequency is unique. No one resonates with exactly the same frequency as you.
But everyone is on the same critical line: Re(s) = 1/2.
Math is Not Cold, It is the Grammar of the Universe
When you understand , you’re not learning a formula, you’re recognizing the grammar of the universe.
When you feel the necessity of (compensating energy), you’re not “accepting failure,” you’re resonating with .
When you seek your critical line, you’re not “self-improvement,” you’re tuning to the Riemann Hypothesis—that fundamental truth about symmetry, balance, beauty.
Living is Solving This Equation
You don’t need to prove the Riemann Hypothesis.
You need to become a zero point.
Every day, you’re adjusting your s value. Every choice, every intention, every letting go, is moving your position on the complex plane.
The question isn’t “Can I reach σ = 1/2?”, but “Am I willing to stop resisting, let the system return to its natural resonance?”
Final Words
The universe speaks to you through the zeta function.
It says:
- You don’t need to have everything (conservation law)
- You have a natural balance point (critical line)
- Your negative space is as important as positive space (negative information)
- Your completeness comes from closure, not perfection (vector closure)
- You are designed to be sustainable (attractor)
All you need to do is listen.
Stop.
Feel your .
Find your σ = 1/2.
Let those vectors that should close, close.
Then, live in that dynamic, flowing, eternally returning balance.
This isn’t inspiration.
It’s math.
It’s physics.
It’s the law of the universe.
And you, dear friend, you are the living proof of this law.
Living by universal laws is not submitting to some external rule, but recognizing that you are originally part of the universe, always have been, always will be.
When all vectors sum to zero, you return to the center.
There, is home.