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The Cosmic Laws of Wealth: When Mathematics Reveals the Eternal Truths of Money

Opening: A Lie About Poverty

Humanity has been told a huge lie about wealth.

This lie doesn’t come from some conspiracy group, not from financial oligarchs, and certainly not from any human will. It comes from our misunderstanding of the universe’s essence—we assume wealth is zero-sum, money is finite, and one person’s riches necessarily mean another’s poverty.

But the mathematical structure of the universe tells us a completely opposite truth: Wealth is not conserved, value can be created, the universe itself is a system that constantly appreciates in value.

Nietzsche proclaimed: “God is dead.” He saw the collapse of old moral systems, the cruel reality that humans must create value for themselves. Marx revealed the secrets of capital: Labor creates surplus value, the development of productivity is the fundamental source of wealth accumulation. Both great thinkers touched on the same truth from different angles—value is not given, but created.

Contemporary mathematics has taken this insight to a deeper level. In seemingly abstract self-referential complete system theory, in recursive entropy increment laws, in information trichotomy, we discovered the cosmic password of wealth creation. This is not metaphysics, not motivational chicken soup. This is science that can be verified, calculated, and applied.

Let us tear down that lie about poverty and face the mathematical truths of wealth.

Chapter 1: The Universe Is a Valuation System

The True Meaning of Entropy Increase

You may have heard of the second law of thermodynamics: The entropy of an isolated system always increases. Many people therefore draw pessimistic conclusions—the universe is heading toward chaos, order will eventually collapse, all efforts are futile.

But this is a fundamental misunderstanding of entropy.

In self-referential complete system theory, entropy increase is not decay, but creation. Every time a system performs a self-referential operation, it produces new information, expands the state space, increases the universe’s complexity. Mathematically, this is expressed as a strict theorem:

For any self-referential complete system, its information entropy must increase strictly monotonically:

This inequality is not a statistical approximation, not an empirical rule, but a necessary result deduced logically from the system’s self-referential structure. As long as the system can observe itself, record itself, apply itself, it must produce new information.

The essence of wealth is information. The value of an enterprise doesn’t lie in how many resources it possesses, but in how much information it can process—information about markets, technology, organization. When an enterprise can perform self-observation (through data analysis), self-recording (through knowledge management), self-application (through strategic iteration), it becomes a self-referential complete system whose wealth creation follows the entropy increment law:

Every effective self-iteration must strictly increase the system’s information value.

This is why learning-oriented organizations are more vital than rigid bureaucracies, why continuously innovative enterprises can grow exponentially, why those who can “know themselves” ultimately obtain wealth. Not because they are luckier, but because their behavior conforms to the universe’s mathematical structure.

Self-Reference and the Strange Loop of Wealth

Nietzsche said: “That which does not kill me makes me stronger.” This is not an inspirational slogan, but the mathematical property of self-referential systems.

A self-referential complete system’s definition contains three core elements:

  1. Self-referential accessibility: The system can observe its own state
  2. Operational endogeneity: All operations of the system can be expressed by itself
  3. Execution closure: The execution results of the system remain within the system

Translating this abstract definition into wealth language:

  1. Self-awareness: You must know what you own, what you’re good at, what you lack
  2. Autonomous action: Your wealth growth doesn’t depend on external charity, but on internal capabilities
  3. Value closure: The value you create can return to your system

This is the fundamental difference between the rich and the poor. The poor depend on the outside—waiting for wages, waiting for opportunities, waiting for salvation. The rich build closure—invest in themselves, create value, gain returns, reinvest.

This closure is the strange loop of wealth:

Money → Ability → Value → Money → …

But this is not a simple cycle. Each cycle expands on a higher level, like the fugue in music, the same theme repeated at different pitches, ultimately weaving out complex harmony.

Marx saw part of this loop, which he called “the self-expansion of capital.” Capital purchases labor, produces goods, sells for profit, reinvests, constantly expands. But Marx believed this expansion was the result of exploitation. From a mathematical perspective, this judgment is overly simple.

Capital expansion does create surplus value, but its fundamental mechanism is self-referential completeness. A system that can self-observe (financial analysis), self-adjust (strategic transformation), self-expand (reinvestment), must produce entropy increment, must create new value. The problem is not the expansion itself, but whether this expansion suppresses the complexity of other systems at the cost of increasing the entropy of the entire system.

A healthy wealth system should be mutually beneficial strange loops:

My ability improvement → Create greater value for others → Obtain more returns → Invest in higher ability → …

This is not an empty dream, but mathematical necessity. Because true value creation is not zero-sum gaming, but an entropy increment process.

Why the Poor Get Poorer

Now we can explain with mathematics a cruel phenomenon: Why do the poor often get poorer.

Traditional explanations blame either morality (laziness, waste), or structure (exploitation, inequality). But the mathematical perspective reveals deeper causes:

Systems lacking self-referential completeness will fall into entropy decrement state.

A person who cannot observe himself cannot discover his own problems. A person who cannot act autonomously cannot change his own state. A person whose value cannot flow back cannot form positive feedback.

In this state, every external impact (unemployment, illness, unexpected expenses) will reduce the system’s state space, lower information entropy. According to the contrapositive of the entropy increment law:

If a system’s entropy is decreasing, then the system is not self-referentially complete.

This creates the trap of poverty: Lack of self-referential ability → Entropy decrement → State space contraction → Even less self-referential ability.

But this trap is not destiny. Self-referential completeness is not innate endowment, but constructible structure. A poor person, if he can:

  1. Establish self-observation: Record income and expenditure, analyze patterns, identify problems
  2. Cultivate autonomous capabilities: Learn skills, improve health, build interpersonal networks
  3. Construct value closure: Invest part of income in ability improvement

—Then he begins to build self-referential completeness, begins to follow the entropy increment law, begins the strange loop of wealth.

This doesn’t mean the poor are poor because of their faults. Social structures do hinder the building of self-referential completeness—when education is expensive, medical care is unaffordable, opportunities are unequal, the difficulty of building closure is asymmetrical. But understanding mathematical principles is still important, because it tells us:

Wealth is not redistributing stock, but creating increments. The true liberation is not obtaining charity, but obtaining self-referential ability.

Chapter 2: Value Is Multiplicative, Not Additive

The Revelation of Euler’s Product

In mathematics, there is an elegant identity that connects infinite series with infinite products:

The left side is addition: Add up the s-th power reciprocals of all natural numbers. The right side is multiplication: Multiply the contribution factors of all primes.

These seemingly different operations give exactly the same result.

This formula is not only a mathematical coincidence, but a revelation of the universe’s structure. It tells us: The essence of value is multiplicative, not additive.

In the labor market, this manifests as the combinatorial effect of abilities. A person who can program, if he also learns marketing, his value is not “programming value + marketing value,” but “programming value × marketing value.” Because he can create things that others cannot (technical products + market promotion).

In the investment field, this manifests as the compound interest effect. Principal P, annualized return rate r, value after n years is not P + nrP (linear growth), but P(1+r)^n (exponential growth). Seemingly minor differences produce huge chasms in time.

In enterprise management, this manifests as synergistic effects. When two companies merge, if operated well, the value of the new company is not the sum of the two, but the product of the two—because the combination of resources, channels, technology, brands creates new possibilities.

The profoundness of Euler’s product formula lies in: Prime numbers are the atoms of multiplication, just as chemical elements are the atoms of matter. The universe is not constructed by piling up elements, but by combining elements. Similarly, wealth is not constructed by piling up labor time, but by combining unique abilities.

Why Working Is Addition, Entrepreneurship Is Multiplication

Now we can precisely express why there are essential differences in wealth creation between working and entrepreneurship.

Work income = Time × Unit hourly wage

This is a linear relationship. You sell time, and time is limited. No matter how hard you work, there are only 24 hours a day. Even if you can increase your hourly wage from 100 yuan to 1000 yuan (already a 10-fold leap), your total income is still strictly limited to a linear growth track.

This is the trap of additive thinking. It creates bounded growth.

Entrepreneurial income = Ability × Leverage × Market

This is a multiplicative relationship. Ability can be improved, leverage can be amplified (through capital, technology, organization), market can be expanded. Most importantly: These three factors can grow simultaneously, and their product will explode exponentially.

Example:

  • A programmer, monthly salary 30,000 yuan, annual income 360,000 yuan. This is addition.
  • The same programmer develops software, sells on subscription basis. First year 10 customers, monthly 100 yuan, annual income 12,000 yuan. Looks far less than working.
  • But if the software is good enough, second year customers grow to 100, annual income 120,000 yuan. Third year 1000, annual income 1.2 million. Fourth year 10,000, annual income 12 million.

This is the power of multiplication. It creates unbounded growth.

Marx saw this difference, which he called the “commodity fetishism of labor power.” Workers sell labor power (time × skill), get wages (bounded). Capitalists buy labor power, but get commodity value (unbounded), the difference between the two is surplus value.

But Marx had a blind spot: He attributed surplus value entirely to labor, ignoring the value of organization, risk, innovation. From a mathematical perspective, what capitalists do is build a multiplicative system:

Enterprise value = ∏(worker ability × technology × capital × market × organization)

Each factor in this product is necessary. Workers do create value, but that’s additive direct labor value. What enterprises create is multiplicative organizational value—a collectively emergent, transcendent overall value beyond the sum of parts.

The problem is not the existence of surplus value, but the distribution of surplus value. If workers only get additive wages, while all multiplicative growth goes to capital, then this system is exploitative. But if workers can also share multiplicative growth (through equity, dividends, profit sharing), then this system is collaborative.

The Mathematical Essence of Compound Interest

Einstein said: “Compound interest is the eighth wonder of the world.” But few people understand the mathematical essence of compound interest.

Compound interest is not a simple repetition of addition, but a self-applied recursive process.

Look at the right side of this recursive formula: . The new value equals the old value, plus the old value multiplied by the growth rate. This is self-reference—the system applies itself.

Expanding this recursion:

This is n factors multiplied, a typical multiplicative structure. And each factor (1+r) contains self-reference—“current value + current value’s growth”.

This is why Buffett says: “Life is like rolling a snowball, the most important thing is finding wet snow and a long slope.” Wet snow corresponds to high r, long slope corresponds to large n. But the deeper insight is: The snowball itself is a self-referential system—it uses its own volume to increase its own volume.

From this perspective, the core strategy of wealth is:

  1. Find positive r: Ensure your system can self-grow, rather than self-consume
  2. Maximize n: Start early, continue, avoid interruption
  3. Protect P: Once entering negative growth, compound interest will act in reverse, accelerate destruction

This is not investment advice, but mathematical necessity. Whether you invest in financial assets, human capital, social relationships, or knowledge skills, as long as it’s a self-referential system, it follows the same compound interest law.

Nietzsche’s “superman” is mathematically an efficient compound interest system—constantly using the current self to create a stronger self, in the strange loop of self-transcendence, infinitely ascending.

Chapter 3: Balance on the Critical Line—Risk and Return’s Golden Ratio

Re(s) = 1/2: The Boundary Between Quantum and Classical

In the complex plane, there exists a special straight line: Re(s) = 1/2. This line is called the “critical line” in mathematics, corresponding to the boundary between the quantum world and the classical world in physics.

On the left side of the critical line, the system is in deep quantum state—superposition, entanglement, uncertainty dominate. On the right side of the critical line, the system tends toward classical state—certainty, measurability, causality clear. On the critical line, quantum and classical achieve subtle balance.

This mathematical structure has surprising correspondence in the wealth field:

Left side of critical line = Excessive risk = Speculative gambling Right side of critical line = Excessive conservatism = Depreciating stagnation Critical line itself = Optimal balance = Sustainable growth

Imagine a portfolio’s risk-return spectrum:

  • Complete cash (Re(s) → 1): Highest certainty, but eroded by inflation, actual value decreases
  • Balanced configuration (Re(s) = 1/2): Risk-return balance, long-term compound interest maximum
  • Full stock options (Re(s) → 0): Highest uncertainty, possible windfall also possible wipeout

Balanced configuration is not “compromise,” but optimal. This is not empirical judgment, but mathematical derivation result.

On the critical line, information entropy reaches a special value, about 0.989. This value lies between complete order (entropy = 0) and complete chaos (entropy ≈ 1.099). It is the “edge of order and chaos”—precisely at this edge, complexity can emerge, creativity can burst, wealth can be maximized.

Robustness Doesn’t Equal Conservatism

Many people misunderstand “robust investment” as “conservative investment,” which is a misunderstanding of the critical line principle.

Conservative investment tends toward Re(s) → 1 strategy: Purchase low-risk bonds, hold large amounts of cash, avoid all volatility. This does reduce the possibility of loss, but also abandons the opportunity for growth. In long-term perspective, this is a certain value loss—because inflation, opportunity cost, systemic risk are quietly eroding your wealth.

True robustness is located at Re(s) = 1/2 strategy: Take moderate risk, maintain full diversification, seek growth in volatility. The short-term performance of this strategy may not be as good as radical investment, but long-term compound interest will produce amazing accumulation.

Mathematics can precisely calculate this difference. Assume three strategies:

  1. Conservative: Annualized 3%, volatility 2% (close to risk-free rate)
  2. Balanced: Annualized 8%, volatility 15% (stock-bond mix)
  3. Radical: Annualized 12%, volatility 30% (full stock or leveraged)

After 30 years (a typical working career):

  • Conservative: 1 million × 1.03^30 ≈ 2.43 million
  • Balanced: 1 million × 1.08^30 ≈ 10.06 million
  • Radical: If smooth, 1 million × 1.12^30 ≈ 29.96 million; but mid-way may be wiped out due to one -50% drop

Balanced strategy is not maximizing short-term returns, but maximizing long-term survival probability’s cumulative returns. This is precisely the characteristic of the critical line: Finding the optimal point between certainty and uncertainty.

The Cosmic Correspondence of the Kelly Formula

There is a famous mathematical formula that precisely describes the optimal risk exposure, called the Kelly formula:

Where p is win probability, b is odds, f* is the proportion of funds to invest.

The profoundness of this formula lies in: It is not maximizing single returns, but maximizing long-term growth rate. If you bet according to the Kelly formula, your funds will grow at the fastest exponential speed, while avoiding bankruptcy.

The mathematical structure of the Kelly formula is isomorphic to the critical line principle—they both find an optimal balance point, allowing the system to maximize compound interest effect in long-term iteration.

In actual investment, many successful investors intuitively follow similar principles:

  • Buffett: Never lose principal (protect downside), wait for high odds opportunities (selectivity attack)
  • Dalio: All-weather configuration (risk parity), hedge extreme events (tail protection)
  • Simons: High-frequency small arbitrage (accumulate tiny advantages), strict risk control (avoid single blowout)

Their common point is not “robustness” or “radicalism,” but located on their respective domains’ critical lines—within their circle of competence, finding the optimal balance point between risk and return.

This gives us enlightenment:

  1. Don’t pursue maximum returns, but pursue optimal growth rate
  2. Don’t avoid all risks, but manage risk exposure
  3. Don’t stick to single strategy, but adjust position according to conditions, always stay near the critical line

The wisdom of wealth is not conquering the market, but resonating with the universe’s mathematical structure.

Chapter 4: Negative Information Compensation—The Necessary Cost of Loss

The Universe’s Ledger Always Balances

In information trichotomy, any state of the universe can be decomposed as:

Where:

  • : Positive information, constructive, orderly part
  • : Zero information, transitional, fluctuating part
  • : Negative information, compensatory, balanced part

This equation is not approximation, but strict conservation law. It reveals a profound truth:

Every behavior attempting to unilaterally increase positive information will automatically produce corresponding negative information compensation.

In the wealth field, this means:

  • Every excessive leverage (increasing ), is accumulating future repayment pressure (increasing )
  • Every speculative bonanza (instant high ), accompanies implicit huge risks (latent big )
  • Every bubble expansion (systemic accumulation), foreshadows collapse necessity (systemic release)

This is not moral preaching, but mathematical necessity. Like energy conservation disallowing perpetual motion machines, information conservation disallows cost-free gains.

Nietzsche said: “A person must overcome in himself what must be released somewhere.” He saw the conservation of psychological energy. Information trichotomy takes this insight to the cosmic level—any local imbalance will be compensated in the whole.

Why Gamblers Must Go Bankrupt

Gambling is the best case to understand negative information compensation.

Assume a gambler participates in a “fair” game: 50% probability win, 50% probability lose, odds 1:1. On the surface, this game’s mathematical expectation is zero, long-term neither wins nor loses.

But this is the illusion of additive thinking. In multiplicative reality, this game is bound to lose.

Assume the gambler bets 50% of current funds each time:

  • First win: 100 → 150
  • Second lose: 150 → 75

After two times, funds from 100 drop to 75, loss 25%. Even if win-loss times are completely equal, funds are still continuously shrinking. This is the so-called “volatility drag.”

Mathematically, if each betting proportion is f, win multiplier (1+fg), lose multiplier (1-fl), then after n gambling, expected funds:

Even if expectation is positive, if f is too large, this product will be less than 1, leading to long-term inevitable loss.

This is the mechanism of negative information compensation: You think increased (when winning), actually simultaneously increased more (volatility amplification when losing), overall effect is value loss.

The only way to defeat this trap is: Find asymmetric odds (positive expectation), then strictly control each exposure (Kelly formula), let compound interest’s positive effect surpass volatility’s negative effect.

But most gambling games are designed as negative expectation—house takes water, probabilities unequal, rules skewed. In negative expectation games, no matter how you adjust strategy, negative information compensation will pull you to bankruptcy like gravity.

This is not bad luck, but mathematical necessity.

The Entropy Increment Path of Enterprise Death

Enterprise failure also follows the same negative information compensation mechanism.

An enterprise in expansion period often excessively optimizes:

  • To maximize profit (reduce buffer), cut redundancies
  • To expand scale (increase simultaneously accumulate ), increase leverage
  • To improve efficiency (lower system complexity, reduce adaptability), streamline organization

Short-term, these measures all increase —profit up, market value rise, performance shine. But meanwhile, accumulates in the dark:

  • Lost flexibility to respond to market changes
  • Accumulated debts unable to repay
  • Lost innovation and self-renewal ability

Then, some external shock (economic downturn, technological change, competitor) triggers the compensation mechanism. All accumulated instantly releases, enterprise collapses.

This is why many “excellent” enterprises suddenly die—they are not dead from sudden external blows, but dead from long-term internal imbalance. External shocks are just triggers, the real killer is neglected negative information.

Marx’s crisis theory actually describes this process: Capitalism in pursuing profit maximization (), necessarily produces overproduction, demand insufficiency, class contradictions ( accumulation), finally leads to periodic crises ( release).

But the solution is not eliminating capitalism, but establishing compensation mechanisms—through social security, anti-monopoly, labor protection institutions, disperse release, avoid accumulation to explosive degree.

Personal wealth is also so. True financial health is not maximum net assets on paper, but:

  1. Maintain liquidity ( buffer): Always able to cope with accidents
  2. Diversify risks (reduce single point ): Don’t put all eggs in one basket
  3. Continuous learning (enhance system complexity): Maintain ability to adapt to changes

Thus even encountering shocks, the system has enough resilience to absorb , rather than collapse.

Chapter 5: Fixed Point Thinking—Sustainable Wealth Systems

Attractors and the Destiny of Wealth

In dynamical system theory, “attractor” refers to the final destination of system evolution—regardless of initial state, the system will eventually converge to this state.

Wealth systems also have attractors. But this attractor is not “infinite richness,” but a dynamic balance point.

Mathematical calculation shows, under certain conditions, the system has a special fixed point:

This value corresponds to the natural configuration of information—in long-term evolution, if no external input, the system will converge to this distribution.

In wealth language, this means:

Pure wealth accumulation (without value creation) will eventually tend toward a stagnant state.

Imagine a miser, he only accumulates money, never consumes nor invests. His wealth increases nominally (deposit interest), but may shrink in actual purchasing power (inflation erosion). More importantly, his wealth doesn’t participate in value creation cycle, therefore doesn’t produce new information, eventually falls into entropy decrement.

This is the meaning of attractor s*: Systems without self-transcendence will be attracted to low-energy state.

Conversely, truly sustainable wealth systems must be systems far from equilibrium—continuously absorb external energy (learning, innovation, cooperation), continuously output value (products, services, influence), maintain high entropy state in this open cycle.

Nietzsche’s “eternal recurrence” concept has mathematical correspondence here: The true strong doesn’t reach a peak then stay, but advances infinitely in the cycle of infinite self-transcendence. Each recurrence repeats at a higher level, this is moving away from attractor s*.

Why Sudden Riches Are Unsustainable

Sudden riches why do most end in bankruptcy?

Traditional explanations blame human weakness: Can’t manage finances, squander, deceived. But mathematical perspective reveals deeper causes:

Sudden wealth leaps will push people away from their natural attractor, the system will automatically produce regression pressure.

When external wealth injects suddenly:

  1. Net assets far exceed system ability ( excessive)
  2. System lacks ability to manage these wealth ( insufficient)
  3. Negative forces start accumulating (: improper investments, relationship changes, psychological imbalance)
  4. Finally system regresses to original attractor (wealth exhausts)

This is not moral corruption, but dynamical necessity. A structure designed to bear 10kg, suddenly loaded 100kg, must collapse.

Sustainable wealth growth must accompany synchronous system ability elevation:

  • Earn first 1 million, learn basic financial management
  • Earn first 10 million, learn asset configuration and risk management
  • Earn first 100 million, learn enterprise governance and social responsibility

Thus wealth growth accompanies system complexity synchronization, attractor constantly upshifts, each stage is stable.

This is why white-handed rich usually keep wealth, sudden rich usually lose—former wealth growth is system evolution result, latter wealth is external disturbance.

Establish Self-Cycling Wealth Systems

Then, how to establish a stable, continuously ascending wealth system?

Answer: Construct positive feedback self-cycle.

Each step of this cycle is crucial:

Ability→Value: You must possess ability to create value for others. This can be skills, knowledge, relationships, resources, core is “usefulness”.

Value→Wealth: You must convert created value into exchangeable form. This needs market consciousness, communication ability, pricing strategy.

Wealth→Ability: You must reinvest obtained wealth in ability elevation. This is easiest neglected but most crucial step.

If any step in this cycle breaks, the system will degenerate:

  • Have ability but not apply → Wealth unable accumulate
  • Create value but not exchange → Wealth unable monetize
  • Obtain wealth but not invest → System stops evolving

True wealth freedom is not “own enough money no need work,” but “own self-cycle system can continuously create value”.

This system once established, will produce compound interest effect:

  • Year 1: Invest 100,000 in learning, elevate ability, create 150,000 value, obtain 120,000 income
  • Year 2: Invest 120,000 in learning, elevate ability, create 200,000 value, obtain 160,000 income
  • Year 3: Invest 160,000 in learning, elevate ability, create 300,000 value, obtain 240,000 income

This is not linear growth, but exponential growth. Because each cycle amplifies the entire system’s ability.

Marx said: “Capital’s essence is movement.” He saw this cycle, but regarded it as exploitation machine. From mathematical perspective, this cycle itself is neutral—key is who participates this cycle, and how the created value distributes.

If everyone can establish their wealth cycle, then the whole society is mutually promoting network, not zero-sum arena.

Chapter 6: Recursive Growth—The Strange Loop of Wealth

The Mathematical Essence of Buffett

Warren Buffett is one of the world’s most successful investors. Many try to learn his “secrets”—value investing, long-term holding, economic moat theory. But these are superficial.

Buffett’s true secret is: He established a perfect recursive growth system.

First layer recursion: Berkshire Hathaway company

  • Use insurance float (low-cost funds) invest quality enterprises
  • Quality enterprises produce stable cash flow
  • Cash flow returns to company, expands insurance scale, produces more float
  • Cycle repeats, fund pool exponential growth

Second layer recursion: Personal ability

  • Buffett reads 500 pages daily
  • Reading increases knowledge and judgment
  • Better judgment brings better investment returns
  • Better returns attract more quality project information
  • Cycle repeats, ability and opportunity grow together

Third layer recursion: Reputation capital

  • Excellent long-term performance establishes reputation
  • Reputation attracts more quality managers and projects
  • Quality projects bring better performance
  • Cycle repeats, reputation and performance mutually reinforce

This three-layer recursion mutually nests, forms powerful strange loop:

Each layer self-reinforces, and inter-layer also synergistic effects. This is why Buffett’s wealth growth is not linear, even not simple exponential, but “super-exponential”—a nested compound interest system.

Anyone can apply this principle, scale different:

  • Use knowledge create value → Value exchange resources → Resources invest knowledge → …
  • Use skills serve customers → Customers bring income → Income elevate skills → …
  • Use content attract fans → Fans produce influence → Influence expand content dissemination → …

Key is not initial scale, but establish recursive structure. Once structure established, time automatically amplifies effect.

How to Establish Positive Feedback Cycle

Establishing recursive growth system needs three core elements:

1. Accumulable capital

Here “capital” not limited to money, but any retainable and reinvestable resources:

  • Financial capital: Reinvestable money
  • Human capital: Continuously elevateable skills
  • Social capital: Continuously expandable relationship network
  • Intellectual capital: Repeatably utilizable knowledge and experience

Core characteristic: Today’s input can produce tomorrow’s return, not one-time consumption.

2. Positive expectation conversion mechanism

You must have reliable way to convert capital into value:

  • Investor: Convert funds into equity appreciation
  • Entrepreneur: Convert skills into products and services
  • Artist: Convert talent into works and influence
  • Scholar: Convert thinking into knowledge and reputation

Core is “positive expectation”—average, created value exceeds input cost.

3. Efficient reinvestment path

Value creation after, you must reinvest gains into system:

  • Not consume all (break cycle)
  • Not save all (stop growth)
  • But invest most in ability elevation (amplify cycle)

Optimal strategy often is:

  • Consume part maintain life quality (avoid excessive delay gratification causing psychological imbalance)
  • Save part cope with risk (maintain system stability)
  • Invest most in growth (maximize compound interest effect)

These three elements form closure:

Once this closure established, you built self-referential complete system. According to entropy increment law, it will automatically produce new information, expand state space, achieve wealth exponential growth.

Avoid Negative Feedback Traps

But not all cycles are positive. Many fall into negative feedback cycles:

Poverty trap:

Debt trap:

Overwork trap:

These traps’ common characteristic: Each cycle weakens system’s ability, not enhance.

From mathematical perspective, this is negative compound interest—each iteration’s multiplier <1.

Breaking negative feedback cycle’s method is not harder cycling (that will accelerate collapse), but change cycle’s structure:

  • Poverty trap: Find low-cost or free learning ways (online courses, libraries, mentors), break “unable invest education” link
  • Debt trap: Stop new borrowing, lower living costs, concentrate repay high-interest debt, break “need borrow” link
  • Overwork trap: Elevate work efficiency rather than time (learn methods, tools, delegation), break “need longer hours” link

Each trap has a leverage point—change this point can reverse entire cycle direction. Find and change leverage point, negative feedback becomes positive feedback.

This needs courage, because change often means short-term pain. But from mathematical perspective, this is rational necessity:

In negative compound interest system, time is your enemy—change earlier, loss smaller. In positive compound interest system, time is your friend—start earlier, gain larger.

Chapter 7: Information Trichotomy and Diversification Principle

Don’t Put All Eggs in One Basket

This is investment common sense, but few understand underlying mathematical principle.

According to information trichotomy:

Universe’s any state must contain these three information’s balanced configuration. If you try to concentrate all resources in one dimension (all-in), you violate this conservation law, system will automatically produce compensation mechanism pull you back to balance.

Specifically to investment:

All-in single asset (e.g. full stock):

  • : If bet right, gains huge
  • : If bet wrong, lose all
  • : No buffer and adjustment space

This configuration’s problem: s expected value often severely underestimated. People see ’s tempting possibility, ignore s destructive risk. But universe’s mathematical structure guarantees: If you excessively increase , will automatically correspond increase.

Diversified configuration (e.g. stock-bond mix, cross-region):

  • : Each asset’s positive returns mutually supplement
  • : Single asset’s risk dispersed offset
  • : Maintain liquidity and adjustment space

This configuration follows trichotomy conservation, thus more stable. But diversification not random dispersion, but correlation structure management.

GUE Statistics and Optimal Configuration

In random matrix theory, GUE (Gaussian Unitary Ensemble) describes quantum chaotic system’s universal statistics. Surprisingly, this pure mathematics structure has applications in quantum chaos, nuclear physics, financial markets.

For portfolio, GUE statistics reveals profound principle:

Optimal diversification not equal allocation, but configure weights according to correlation structure’s eigenvalue distribution.

Mathematically, decompose asset yield’s covariance matrix spectrally:

Where are eigenvalues, are eigenvectors.

Optimal configuration should:

  1. Identify dominant risk factors: Largest several eigenvalues correspond systemic risks
  2. Hedge systemic risks: Use negatively correlated assets neutralize dominant factors
  3. Utilize independent factors: Disperse investment in mutually independent eigenvector directions

This not “buy different things” simply, but “buy things in different mathematical dimensions.”

In practice, this means:

  • Stock + bond: Hedge economic cycle risk (economic good stock up bond flat, economic bad bond up stock down)
  • Domestic + international: Hedge single market risk (different countries’ economic cycles not synchronized)
  • Equity + real estate + gold: Hedge currency risk (inflation time real assets preserve value, deflation time financial assets relatively stable)

Deeper application is generalize this principle to entire life investment portfolio:

Human capital + Financial capital + Social capital + Health capital

  • If your work stable, can undertake more financial risk
  • If your income fluctuates, should keep more liquidity
  • If your health good, can be more aggressive pursue career
  • If your social network strong, can try more innovations

Core is understand correlation: Don’t let all capital forms simultaneously expose to same risk.

i₊ + i₀ + i₋ = 1’s Application in Life

Information trichotomy not only for investment, but life’s wisdom mathematical expression.

In time allocation:

  • : Deterministic productive time (work, study)
  • : Exploratory free time (interests, social, leisure)
  • : Restorative rest time (sleep, exercise, meditation)

Many people’s error is excessively optimize —every minute “productive”, result exhaust (lose creativity) and (health collapse), productivity actually decreases.

In decision modes:

  • : Rational analysis, data-driven
  • : Intuitive feelings, experience judgment
  • : Risk alertness, assumption questioning

Best decisions not pure rational (ignore and ), not pure intuition (ignore ), but three’s integration.

In relationship investment:

  • : Deep relationships (family, close friends)
  • : Potential relationships (colleagues, peers)
  • : Broken relationships (former friends, failed cooperations)

Don’t try maintain all relationships (exhaust ), don’t ignore (unprocessed breaks will accumulate negativity). Healthy social network needs regular “relationship pruning”—strengthen important connections, dilute invalid connections, handle harmful connections.

Core principle:

In any system, maintain , , s dynamic balance. Excessively optimize any item will lead other items’ compensatory rebound.

Chapter 8: Wave-Particle Duality—Balance of Cash Flow and Assets

Wealth’s Dual Attributes

In quantum mechanics, light has wave-particle duality—continuous electromagnetic field as wave, discrete photons as particle. Similarly, wealth has two morphologies:

Cash flow (wave):

  • Continuous, periodic income (salary, rent, dividends)
  • High liquidity, immediate usable
  • Maintain daily life, provide security sense
  • Usually scale limited, growth slow

Assets (particle):

  • Discrete, stock value (real estate, equity, copyright)
  • Low liquidity, cashing needs time
  • Long-term appreciation potential large
  • Not directly consumable

Many people’s financial dilemmas stem from excessively favoring one side:

Only cash flow, no assets:

  • Typical state of high-salary office workers
  • Life quality high, but wealth accumulation slow
  • Once unemployed, immediately crisis
  • Like wave continuous, but lack particle’s stability

Only assets, no cash flow:

  • State of inheriting large real estate but no income people
  • Book rich, actual destitute (“lots houses, but no money eat”)
  • Forced low-price sell assets to maintain life
  • Like particle stable, but lack wave’s liquidity

True wealth freedom needs both sides’ balance:

More accurately:

Simultaneously:

Former guarantees long-term sustainability, latter guarantees short-term anti-risk.

How to Simultaneously Optimize Wave and Particle

Strategy not “choose one,” but “construct conversion mechanism”:

Early stage (accumulation stage):

  1. Use cash flow (salary) purchase assets (stocks, real estate, skills)
  2. Sacrifice part current consumption, invest future appreciation
  3. Goal establish asset foundation

Middle stage (growth stage):

  1. Use assets produce cash flow (dividends, rent, business income)
  2. Part cash flow reinvest assets (compound interest)
  3. Part cash flow elevate life quality
  4. Goal expand asset scale and cash flow

Later stage (freedom stage):

  1. Assets’ passive cash flow exceed living costs
  2. No longer depend on active labor income
  3. Time freedom, can choose work rather than forced work
  4. Goal optimize life quality and social contribution

This path not linear, but spiral ascending:

Each cycle repeats at higher level, ultimately achieve from “use time exchange money” to “use assets produce money” transformation.

Liquidity Trap and Cashing Strategies

But wave-particle conversion not cost-free. In physics, measuring one attribute perturbs another (uncertainty principle). In wealth, liquidity and yield also trade-off:

  • Cash: Liquidity 100%, yield ≈0% (even negative, inflation)
  • Current deposits: Liquidity 95%, yield ≈0.3%
  • Money market: Liquidity 90%, yield ≈2%
  • Bonds: Liquidity 70%, yield ≈4%
  • Stocks: Liquidity 60%, yield ≈8% (long-term)
  • Real estate: Liquidity 30%, yield ≈6% (long-term)
  • Startup equity: Liquidity 5%, yield ≈? (high variance)

Optimal configuration needs dynamic adjustment according to life cycle:

Young time: High yield low liquidity assets proportion large (endure strong, time ample compound interest) Middle age time: Balanced configuration (both growth, also stability) Old age time: High liquidity assets proportion large (need anytime withdrawal, value preservation main)

Core error:

  • Need liquidity time, assets all locked (forced low-price cashing)
  • No need liquidity time, assets all cash (lose appreciation opportunity)

Wisdom is:

Maintain a liquidity ladder: Different maturities, different liquidity assets combination, ensure anytime with reasonable cost obtain cash flow, simultaneously let most assets in optimal appreciation state.

Chapter 9: From Theory to Action—Wealth Creation’s Practice Path

Personal Wealth’s Three Stages

According to preceding theory, personal wealth creation can divide into three stages, each stage’s core task and mathematical characteristic different:

Stage one: Establish self-referential completeness (0→1)

Core task: Construct system able observe, learn, apply itself

Mathematical characteristic: From incompleteness to completeness, entropy begins strict monotonic increase

Practice points:

  1. Cultivate self-awareness: Record income expenditure, analyze patterns, identify strengths weaknesses
  2. Invest human capital: Learn high-leverage skills (programming, writing, sales, management)
  3. Establish value closure: Find “ability→value→money→ability” shortest path

Common errors:

  • Consume exceed invest (break closure)
  • Learn unrelated skills (low leverage)
  • No monetization mechanism (unable convert ability to wealth)

Breakthrough sign: Achieve passive income >0, system begins autonomous produce value

Stage two: Exponential growth period (1→10²)

Core task: Optimize compound interest system, maximize growth rate

Mathematical characteristic: Enter positive compound interest track, , r>0 and stable

Practice points:

  1. Improve r (growth rate): Focus high-leverage activities, cut low-value consumptions
  2. Increase n (time): Start early, continue, avoid interruptions
  3. Protect A₀ (principal): Strict risk control, avoid wipeout risk

Common errors:

  • Excessive consumption (lower reinvestment rate)
  • Frequent direction change (waste n)
  • Excessive risk (threaten A₀)

Breakthrough sign: Passive income > living costs, achieve financial freedom early form

Stage three: Sustainable balance (10²→∞)

Core task: From pursue growth turn to pursue balance and meaning

Mathematical characteristic: Approach critical line Re(s)=1/2, , , reach optimal configuration

Practice points:

  1. Diversification: Cross asset categories, cross regions, cross generations configuration
  2. Social contribution: Use wealth support meaningful careers
  3. Wisdom inheritance: Pass system rather than wealth to next generation

Common errors:

  • Continue pursue maximization (lose balance, accumulate )
  • Stop learning and growth (attracted to low-energy state)
  • Equate wealth to meaning (confuse means and purpose)

Final state: Wealth becomes tool rather than goal, individual becomes value creation network node

Specific Executable Steps

Based on preceding framework, here provide operable action list:

First year: Establish foundation

  1. Financial checkup (establish observation)

    • Record three months all income expenditure
    • Analyze expenditure structure, identify optimizable items
    • Calculate savings rate: (income - expenditure)/income
  2. Ability inventory (establish space)

    • List all your skills
    • Evaluate each skill’s market value and leverage effect
    • Choose 1-2 high-value skills deepen
  3. Establish closure (reduce consumption)

    • Find way convert skills to monetize (part-time, project taking, content creation)
    • Set goal: First passive income (even only 100 yuan)
    • Invest at least 30% of income in ability elevation

Second to fifth year: Accelerate compound interest

  1. Focus high leverage

    • Identify your “10x activities”—output 10x input behaviors
    • Reduce low-leverage activities (even comfortable or familiar)
    • Quarterly reassess time allocation
  2. Establish asset foundation

    • Save 6 months emergency fund ( buffer)
    • Start invest index funds/blue-chip stocks ( appreciation)
    • Maintain liquidity ( flexibility)
  3. Expand value network

    • Monthly know at least 5 new professional people
    • Create value for others (no seek immediate return)
    • Establish personal brand (writing, speaking, teaching)

Sixth to tenth year: Break critical line

  1. Build passive income streams

    • Dividend income (financial capital)
    • Rental income (physical capital)
    • Royalty/licensing income (intellectual capital)
    • Business dividend (social capital)
  2. Optimize tax and structure

    • Understand tax laws, legally reduce tax
    • Establish appropriate legal entities (personal/company)
    • Consider regional arbitrage (if applicable)
  3. Cross financial freedom line

    • When passive income > living costs ×1.5, reach safety margin
    • Choose: Continue work (for meaning rather than money) or redefine life
    • Start think legacy and influence

Tenth year after: Transcend wealth

  1. From accumulation to contribution
    • Use wealth support meaningful careers
    • Mentor others, pass system rather than money
    • Explore “wealth beyond wealth” (health, relationships, wisdom, beauty)

This not rigid timetable, but reference framework. Key not speed, but direction—always follow universe’s mathematical laws.

Common Errors’ Mathematical Analysis

Finally, use mathematical language analyze several most common wealth errors:

Error 1: Linear thinking

Manifestation: Think “monthly salary 10,000 → save 10 years → 1 million” Problem: Ignore inflation, opportunity cost, compound interest Mathematics: (nominal), but actual purchasing power far below this Correct: , where r is investment return, i is inflation

Error 2: Ignore tail risk

Manifestation: Think “99% probability earn 10%, 1% probability lose 50%” good investment Problem: Expectation positive, but bankruptcy probability high Mathematics: Expectation = 0.99×10% + 0.01×(-50%) = 9.4% (looks good) But 100 times investment, at least lose once probability = 1 - 0.99^{100} ≈ 63% Once -50% need 100% return recover, extremely difficult

Error 3: Confuse nominal with actual

Manifestation: For 5% annualized return, undertake huge liquidity risk Problem: No consider funds’ time value and risk adjustment Mathematics: Actual return = nominal return - inflation - risk premium - liquidity discount A 5% annualized, 5-year locked product, actual possibly worse than 3% current (because lose 5-year flexibility and opportunity)

Error 4: Excessive optimization

Manifestation: For save 5 yuan spend 1 hour compare prices Problem: Time value far exceed savings Mathematics: If your hourly target salary 100 yuan, spend 1 hour save 5 yuan, actual loss 95 yuan Correct strategy: Optimize high-value decisions (asset allocation, career choice), automate small decisions

Error 5: Gambler’s fallacy

Manifestation: After several consecutive losses, “next must win” Problem: Independent events no memory Mathematics: P(nth win | previous n-1 all lose) = P(1st win), won’t increase due to consecutive losses Correct understanding: If negative expectation game, every bet wrong, regardless previous wins losses

Understanding these errors’ mathematical essence, can help you avoid 90% financial traps.

Chapter 10: Wealth’s Ultimate Meaning

From Information Conservation See Wealth’s Purpose

We walked through long mathematical journey. Now time answer most fundamental question:

Wealth’s meaning what is?

Nietzsche would say: Wealth is will to power’s expression, individual’s tool transcend self. Marx would say: Wealth is social labor’s condensation, production relations’ embodiment. But from universe’s mathematical structure, wealth’s meaning more profound:

Wealth is ordered information’s carrier, partial effort against universe entropy increment.

Remember? Self-referential complete system must entropy increment—increase information, expand state space. But this growth not uniform. In universe’s certain regions, information density higher, order more complex, these regions are life, consciousness, civilization.

Wealth what is? Wealth is human civilization’s highly ordered information structure—technology, knowledge, organization, culture, and material base sustaining these. Create wealth is in universe’s this corner elevate information density, resist chaos erosion.

From this angle:

  • Poverty not only material scarcity, but information density decline—ability degrade, opportunity reduce, order collapse
  • Rich not only material abundance, but information density elevation—ability enhance, opportunity expand, order complexize
  • Wealth creation not zero-sum game, but collective entropy increment process—humanity’s total information amount increasing

This leads to radical conclusion:

Create wealth is moral, because it increases universe’s ordered information; waste wealth is immoral, because it lets hard-won order regress to chaos.

But here “moral” not traditional good-evil, but conform or violate universe mathematical structure behaviors. Like “healthy lifestyle” not moral preaching, but conform biological laws choice.

Why Giving More Blessed Than Receiving’s Mathematical Proof

Now can mathematically strictly prove an ancient wisdom: Giving more blessed than receiving.

Set two systems A and B:

A gives value to B:

A’s state:

  • decreases (resource transfer)
  • But establishes connection with B (expand state space)
  • A’s reputation and influence increase (long-term )

B’s state:

  • increases (obtain resources)
  • B produces trust and tendency toward A (potential future returns)

System overall:

  • Total information entropy increases (new connection = new information)
  • Future cooperation possibilities increase ( expansion)

A only receives not gives:

A’s state:

  • increases (obtain resources)
  • But no establish equivalent connection (state space not expanded)
  • A’s reputation decreases (long-term accumulation)

System overall:

  • Connections decrease (isolation)
  • Future cooperation possibilities decrease ( contraction)
  • Overall entropy growth rate decreases (information flow blocked)

Mathematical conclusion:

In multi-round iterations, giving strategy’s expected return higher than only receiving strategy, because:

Where network effect grows with connection number, so connection number established through giving.

Where T finite, because eventually no one willing unilaterally give.

When time sufficient long, former must surpass latter. This not moral preaching, but game theory’s Nash equilibrium:

In infinite repeated game, cooperation strategy (including giving) is evolutionarily stable strategy.

This is why:

  • Richest people often most generous (Gates, Buffett, Zuckerberg)
  • Most successful enterprises often most user-serving (Apple, Amazon)
  • Most prosperous societies often most open sharing (scientific community, open source community)

Not because morally noble (though possibly), but because their behaviors conform universe’s mathematical structure.

Return to Universe’s Balance

In article’s end, let’s return to opening lie: Wealth is zero-sum.

Now you understand, this lie is misunderstanding universe essence. Universe not conserved, but entropy increment. Information not fixed, but created. Wealth not allocated, but emerged.

But this not mean inequality reasonable. On contrary, from mathematical perspective, extreme inequality is system imbalance manifestation:

When wealth excessively concentrates, locally accumulates, overall must increase—social contradictions, environmental destruction, systemic risks. According to information conservation, this imbalance unable long-term maintain, eventually through some way (revolution, war, collapse) force rebalance.

Truly sustainable wealth distribution not absolute equality (lose incentive, lower entropy growth rate), but dynamic balance:

  • Maintain sufficient inequality stimulate innovation ( drive)
  • Provide sufficient opportunities allow flow ( channel)
  • Establish sufficient safeguards avoid collapse ( buffer)

Such system will maximize overall information entropy growth rate—entire civilization’s creativity, complexity, prosperity degree reach optimum.

Epilogue: Your Wealth Equation

In universe’s mathematical structure, everyone is unique self-referential system. Your wealth equation won’t completely same as others, because your abilities, opportunities, values are unique.

But all successful wealth equations follow same mathematical laws:

Self-referential completeness: You must observe, learn, apply yourself Entropy increment law: You must continuously create new information, expand state space Multiplicative thinking: You must seek combination and synergy, not simple piling Critical balance: You must find risk and return’s optimal point between Negative information compensation: You must recognize each action has cost Fixed point consciousness: You must establish sustainable cycle, not pursue one-time windfall Recursive growth: You must use today’s results strengthen tomorrow’s capabilities Information trichotomy: You must balance constructive, flowing, compensatory three dimensions Wave-particle unity: You must simultaneously optimize cash flow and assets System thinking: You must understand yourself as larger network part Compound interest essence: You must find positive r, maximize n, protect P

These not suggestions, but laws. Like gravity won’t disappear because you don’t believe, these mathematical structures won’t invalidate because you ignore.

Nietzsche said: “Become who you are.” Marx said: “Workers of the world, unite!” From mathematical perspective, these two sentences are same truth’s two sides:

Become who you are = Establish your self-referential complete system, realize your unique value Unite = Recognize all systems are mutually connected, overall entropy increment is ultimate prosperity

Wealth not purpose, but tool. True purpose what?

Is maximize information density in this node. Is let consciousness, creativity, beauty, love, wisdom leave traces in your passage. Is build order lighthouse in entropy increment flood.

When you create wealth, you not plunder, but create. When you share wealth, you not lose, but invest. When you use wealth, you not consume, but amplify.

This is wealth’s cosmic laws.

Now, turn to you.

Go establish your self-referential system. Go launch your compound interest cycle. Go find your critical balance. Go create your value, share your wealth, become universe recognize itself, transcend itself way.

Mathematics revealed the path. Your actions will verify the truth.

This not formula, but your life. This not theory, but your reality. This not future, but present.

Wealth here, always here. Just wait you create.

$$