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Why brute force decisions are impossible in principle
Executive Summary
We deliberately make extremely favorable assumptions that are almost impossible to achieve in practice. Nevertheless, the result remains clear: The complete search space of 2300 options cannot be calculated by brute force - not "too slow", but in principle. It follows from this: Value is not created through faster calculation, but through mathematical Optimization (bounding, reduction, intelligent search space control).
Now calculate the entire space and find the optimal decision route
Assumptions (deliberately optimistic, not polemical)
- Decision space:2300 possible combinations (binary decisions over 300 projects)
- Evaluation of an option (portfolio / path): 1 µs = 10-6 seconds (incl. target value calculation, constraints, evaluation - unrealistically fast)
- Computing power: 1,000,000 cores in parallel (greater than realistically exclusively available supercomputer capacities)
Step 1: Size of the problem
2300 ≈ 2,037 × 1090
→ Number of possible portfolios: ~1090
Step 2: Effective computing power
- 1 evaluation = 10-6 seconds
- 1.000,000 cores ⇒106 evaluations in parallel
- ⇒ Effective speed: 1012 evaluations per second
Step 3: Total computing time
T = (2.037 × 1090) / (1012) = 2.037 × 1078 seconds
Conversion to years:
(2.037 × 1078) / (3.154 ×107) ≈ 6.46 × 1070 years
Step 4: Cosmic classification
Age of the universe: ≈ 1.38 × 1010 years
Ratio:
(6,46 × 1070) / (1,38 × 1010) ≈ 4,7 × 1060
→ 4.7 trillion universe ages
Result (clear & unambiguous)
A computer cannot fully calculate2300 options. Not slow. Not expensive. But not in principle.
Even with unrealistically fast evaluation, massive parallelization and perfect scaling, the problem remains physically and cosmologically unsolvable by brute force.
Strategic consequence (the crucial point)
- Brute force: impossible
- Excel & scenarios: meaningless (compared to the size of the room)
- Intuition: systematically wrong
→ Only mathematical optimization with bounding, reduction and intelligent search space control delivers practicable and reliable decisions.