The Thib Paradox

A Mathematical Framework for Investigating Anomalous Interstellar Objects

Executive Summary

The Thib Paradox identifies a fundamental cognitive bias in the scientific approach to anomalous interstellar objects. When faced with characteristics unknown in our solar system, the scientific community systematically favors hypothetical natural explanations rather than rigorously investigating the artificial hypothesis. This paradox reveals a critical asymmetry in error costs: missing an authentic technosignature represents an irreversible civilizational loss, while investigating a false alarm only incurs temporary and recoverable costs.

1. Context and Motivation

1.1 The 3I/ATLAS Case

The interstellar object 3I/ATLAS presents a major spectroscopic anomaly: a Ni/Fe ratio > 1, never observed naturally in our solar system. VLT observations reveal:

• Nickel detected: Q(Ni) = 10^22.67 atoms/s
• Iron absent: Below detection threshold
• Ni/Fe ratio: > 1 (vs 0.05-0.43 for all known natural bodies)

1.2 Current Scientific Response

The scientific community is actively investigating 3I/ATLAS with considerable resources, exploring various hypotheses including:

• Formation in different galactic environments (thick disk regions)
• Selective nickel carbonylation processes
• Novel physicochemical conditions in other stellar systems

While the artificial hypothesis receives some consideration (notably by researchers like Avi Loeb), resource allocation could benefit from a more systematic framework that accounts for the asymmetry in error costs when investigating potentially revolutionary discoveries.

1.3 The Opportunity for Optimization

According to Drake's equation, civilizations capable of interstellar travel represent a non-negligible probability in our galaxy. The Thib Paradox proposes that a systematic framework for resource allocation could help optimize investigation priorities, particularly when dealing with objects exhibiting characteristics unprecedented in our solar system experience.

2. Formulation of the Thib Paradox

2.1 Main Statement

2.2 The Fundamental Asymmetry

Type I Error: Ignoring an authentic technosignature

Type II Error: Investigating a false alarm

2.3 Application Conditions

The Thib Paradox applies when the following four criteria are met:

1. Object of interstellar origin ✓
2. Characteristics unknown in our solar system ✓
3. Significant asymmetry of error costs ✓
4. Temporally limited observation window ✓

3. Mathematical Formalization

3.1 Fundamental Variables

• A = Anomaly level (0-10, unknown characteristics)
• I = Potential impact of a discovery (civilizational value)
• C = Cost of thorough investigation (normalized)
• P_n = A priori probability of an unknown natural process
• R = Rarity factor in our solar system
• U = Urgency factor (1/temporal window)

3.2 The Thib Equation

Complete Version:

Simplified Version:

Decision Rule:

3.3 Interpretation

The equation formalizes the intuition that:

• Higher anomaly → More investigation needed
• Higher potential impact → More investigation needed
• Lower natural explanation probability → More investigation needed
• Higher required resources → Less investigation needed

4. Application to 3I/ATLAS

4.1 Estimated Parameters

4.2 Threshold Calculation

4.3 Sensitivity Analysis

Even with very conservative parameters:

• A = 3, I = 100, R = 10, U = 2, C = 5, P_n = 0.5
• S = (3×100×10×2)/(5×0.5) = 2400 >> 1

5. Validation on Historical Cases

5.1 Consistency Test: 2I/Borisov

Parameters:

• A = 2 (interstellar origin but normal composition)
• I = 50 (important but not revolutionary)
• C = 1, P_n = 0.8, R = 2, U = 3

Calculation: S = (2×50×2×3)/(1×0.8) = 750

Result: Investigation justified ✓ (indeed studied intensively)

5.2 Consistency Test: Standard Asteroid

Parameters:

• A = 0.5 (standard composition)
• I = 1 (minor discovery)
• C = 1, P_n = 0.95, R = 0.1, U = 1

Calculation: S = (0.5×1×0.1×1)/(1×0.95) = 0.05

Result: No special investigation ✓ (observed behavior)

6. Practical Action Scale

6.1 Operational Thresholds

6.2 Protocol for 3I/ATLAS (S = 45M, Loeb-4)

Consistency with Loeb-4:

• Critical threshold for technosignature investigation crossed ✓
• Intensive observation protocols activated ✓
• Preparation for escalation to higher levels ✓

7. Integration with the Loeb Scale

7.1 Loeb Scale Reminder (0-10)

The Loeb scale classifies interstellar objects according to their anomalies:

7.2 Loeb-Thib Correspondence

7.3 Application: 3I/ATLAS

According to the original Loeb scale, 3I/ATLAS would be classified Level 4:

• Multiple anomalies (Level 3) ✓
• Characteristics weakly compatible with artificial origin ✓
• Critical threshold crossed → Technosignature investigation justified

This Loeb-4 classification perfectly corresponds to our Thib calculation (S = 45M >> 1).

7.4 Unified Framework

Integrated process:

1. Classify with Loeb scale (0-10)
2. Map to Thib parameters (A, I, P_n)
3. Calculate threshold S
4. Decide investigation level
5. Apply appropriate protocols

8. Implications and Applications

8.1 Methodological Enhancement

The Thib Paradox suggests complementing current scientific approaches with:

1. Systematic cost-benefit analysis for resource allocation decisions
2. Explicit consideration of error cost asymmetries
3. Quantitative frameworks for investigation priority setting
4. Integration of impact assessment in research planning

8.2 Future Applications

For interstellar objects:

• Automatic Thib evaluation protocol
• Systematic mapping to Loeb scale (0-10)
• Progressive escalation of investigation protocols

For SETI research:

• Detection threshold readjustment based on cost asymmetry
• Integration with Rio scale for signals
• Resource optimization according to potential impact

For astronomical anomalies:

• Systematic inclusion of artificial hypothesis
• Graduated application according to anomaly level (0-10)
• Independent confirmation protocols

For space missions:

• Prioritization based on S calculation
• Resource allocation proportional to impact
• Rapid interception mission preparation

8.3 Research Impact

The framework could:

• Avoid missing civilizational contacts
• Optimize scientific resource allocation
• Standardize investigation protocols
• Reduce institutional cognitive biases

9. Limitations and Considerations

9.1 Estimation Challenges

• Subjectivity of parameters (A, I, P_n)
• Variability according to experts and contexts
• Evolution of values with new data

9.2 Potential Risks

• Over-investigation of rare natural objects
• Excessive allocation of resources
• Uncontrolled media noise

9.3 Mitigation Measures

• Calibration on historical corpus
• Validation by expert committees
• Periodic revision of parameters
• Rigorous scientific communication

10. Proposed Empirical Validation

10.1 Retrospective Test

Apply the Thib equation to historical discoveries and verify consistency with decisions made.

10.2 Prospective Validation

Use the framework for next interstellar objects and measure effectiveness of resulting protocols.

10.3 Success Metrics

• Detection rate of genuine anomalies
• Optimization of allocated resources
• Reduction of confirmation biases
• Improvement of SETI protocols

11. Conclusions

11.1 Main Contributions

1. Identification of a major cognitive bias in scientific approach
2. Mathematical formalization of error cost asymmetry
3. Practical framework for decision-making
4. Integration with existing classification systems

11.2 Expected Impact

The Thib Paradox proposes a complementary analytical tool: enhancing existing scientific approaches with systematic cost-benefit analysis for resource allocation. Rather than replacing current methodologies, this framework could help optimize investigation priorities based on error cost asymmetries, potentially improving the efficiency of detecting genuinely revolutionary discoveries.

11.3 Guiding Principle

The framework recognizes that current scientific investigations of anomalous interstellar objects like 3I/ATLAS demonstrate appropriate resource allocation. The Thib Paradox provides a systematic method to validate and optimize such decisions.

References and Sources

1. Rahatgaonkar et al. (2025). "Spectroscopic observations of 3I/ATLAS". ArXiv.
2. CATA Press Release (2025). "Unusual nickel detection in interstellar comet".
3. Loeb, A. (2025). "The Loeb Scale for Interstellar Objects". Medium.
4. Drake, F. (1961). "Project Ozma and the Search for Extraterrestrial Intelligence".
5. Micheli et al. (2018). "Non-gravitational acceleration in 1I/'Oumuamua". Nature.

Contact:
Pascal Thibodeau
Sorel-Tracy, Quebec, Canada
Website: https://kshiotsn.gensparkspace.com/