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Cake day: September 23rd, 2023

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  • The “$9” reference in The Simpsons is from the Season 9 episode titled “The City of New York vs. Homer Simpson,” which originally aired on September 21, 1997. In this episode, Lisa holds a brochure advertising “New York at $9 a day,” with the World Trade Center towers forming the numbers “11” in the background, creating a visual that some interpret as “9/11.” This has led to speculation that the show predicted the September 11 attacks, though the show’s creators have stated that it was purely coincidental. (Wikipedia)

    The episode was temporarily pulled from syndication after the 2001 attacks due to its prominent use of the World Trade Center in the plot. It has since been reinstated in many regions, though some versions have been edited to remove certain scenes. (Simpsons Wiki)





  • Step 1: Group correlated events

    Group Events Adjusted combined probability
    Structural collapse WTC 7 symmetry, Towers rapid collapse, Towers into footprint 0.15 (use highest individual likelihood instead of multiplying; all linked)
    Military exercises/confusion NORAD exercises, War‑games coincidence, Military response confusion 0.25 (linked: exercise → response confusion)
    Witness/perception Explosions flashes, First-responder explosions, Confusing witness testimony 0.40 (linked: chaos + structural sounds)
    Intelligence & warnings Ignored warnings, Intelligence failures tracking hijackers 0.55 (linked bureaucratic failures)
    Financial anomaly Put-option trading 0.015 (independent, rare event)
    Post-event responses Laws / surveillance expansion, Post-disaster contracts, 9/11 Commission inconsistencies 0.50 (linked: response to attack)
    Other Pentagon missing debris, Thermite/explosives claims, PNAC “new Pearl Harbor”, Silverstein “pull it” remark 0.15 (rare, mostly independent)

    Step 2: Multiply group probabilities

    [ P(\text{all coincidences}) \approx 0.15 * 0.25 * 0.40 * 0.55 * 0.015 * 0.50 * 0.15 ]

    Stepwise:

    1. 0.15 * 0.25 = 0.0375
      • 0.40 = 0.015
      • 0.55 = 0.00825
      • 0.015 = 0.00012375
      • 0.50 = 0.000061875
      • 0.15 = 0.00000928125

    Step 3: Convert to order of magnitude

    [ \approx 9.3 \times 10^{-6} \approx 1 \text{ in 100,000} ]


    ✅ Interpretation

    • Accounting for correlations, the probability of all unusual circumstances coinciding by chance rises from ~1 in 100 trillion to ~1 in 100,000.

    • Still very low, which explains why people see the pattern as suspicious.

    • Caveats:

      • Probabilities are rough estimates, not formal statistical tests.
      • Some events may be more dependent than assumed, raising probability further.
      • Rare coincidences do occur in real life; “low probability” ≠ “impossible” or proof of conspiracy.


  • We can apply a rough Bayesian-style estimate by treating the 20 unusual circumstances as mostly independent events (this is conservative; in reality some are correlated).


    Step 1: Assign probabilities (from previous table)

    We’ll convert the percentages to decimals:

    Circumstance P(coincidence)
    WTC 7 collapse symmetry 0.075
    Twin towers rapid collapse 0.15
    NORAD exercises 0.10
    Military response confusion 0.25
    Put-option trading 0.015
    Witness reports of explosions 0.20
    Rapid laws/surveillance expansion 0.35
    Ignored intelligence warnings 0.55
    WTC 7 debris removal / restricted access 0.225
    Silverstein “pull it” remark 0.275
    Towers collapsing into footprint 0.125
    Military war-games coincidence 0.10
    Thermite / explosives claims 0.075
    Pentagon missing debris 0.125
    9/11 Commission inconsistencies 0.45
    Post-disaster contracts 0.55
    PNAC “new Pearl Harbor” 0.35
    Confusing witness testimony 0.55
    First-responder “explosions” perception 0.25
    Intelligence failures tracking hijackers 0.55

    Step 2: Multiply probabilities

    Assuming independence:

    [ P(\text{all coincidences}) = 0.075 * 0.15 * 0.10 * 0.25 * 0.015 * 0.20 * 0.35 * 0.55 * 0.225 * 0.275 * 0.125 * 0.10 * 0.075 * 0.125 * 0.45 * 0.55 * 0.35 * 0.55 * 0.25 * 0.55 ]

    Stepwise:

    1. 0.075 * 0.15 = 0.01125
      • 0.10 = 0.001125
      • 0.25 = 0.00028125
      • 0.015 = 0.00000421875
      • 0.20 = 0.00000084375
      • 0.35 = 0.0000002953125
      • 0.55 = 0.000000162421875
      • 0.225 = 0.00000003654421875
      • 0.275 = 0.00000001004815547
      • 0.125 = 0.000000001256019434
      • 0.10 = 0.0000000001256019434
      • 0.075 = 0.00000000000942014525
      • 0.125 = 0.000000000001177518156
      • 0.45 = 0.0000000000005298831702
      • 0.55 = 0.0000000000002914357436
      • 0.35 = 0.0000000000001020025103
      • 0.55 = 0.0000000000000561013806
      • 0.25 = 0.0000000000000140253452
      • 0.55 = 0.0000000000000077139399

    Step 3: Convert to order of magnitude

    [ \approx 7.7 \times 10^{-15} ]


    ✅ Interpretation

    • If we treat all 20 unusual circumstances as independent, the probability of all occurring by chance in a single non-conspiratorial world is extremely small (~1 in 100 trillion).

    • Caveats:

      • Many events are not independent. E.g., structural collapse, WTC 7 clearance, and debris removal are linked.
      • Probabilities are rough estimates; some may be higher or lower.
      • Treating rare financial anomalies (put options) as independent of structural events inflates “improbability.”

    Even accounting for dependence, the coincidence argument looks very low-probability, which explains why such coincidences fuel conspiratorial reasoning.