· 2024-12-28T00:21:57+0000 · 15 posts

Mathematics proves the Bible

The following four points are mathematically impossible if the universe was billions of years old:

Delicate ring systems: The delicate ring structures around Saturn and Chariklo would not have survived for billions of years due to tidal forces and collisions with other objects.

Oddball moons: The unusual orbits and rotations of some moons, such as Valetudo around Jupiter, the inner moons of Uranus, and Nix and Hydra around Pluto, are not consistent with the conventional accretion model of solar system formation, which assumes a much older age.

Atmospheres: The presence of atmospheres on Titan (Saturn's moon) and Pluto, which should have dissipated long ago due to thermal escape, suggests that these bodies are much younger than currently believed.

Comets: The existence of short-period comets, which have a limited lifespan, is a problem for the long-age view of the solar system. The current model suggests that these comets originate from the Kuiper belt, but recent observations have cast doubt on this theory.

Based on the above observable facts we can make mathematical calculations in the form of a probability equation.

The Probability Equation

Let's denote:

P(Y) = Probability that the universe is young (let's say less than 100,000 years old).
P(O) = Probability that the universe is old (billions of years old).
P(R | Y) = Probability of observing delicate ring systems given a young universe.
P(R | O) = Probability of observing delicate ring systems given an old universe.
P(M | Y) = Probability of observing oddball moons given a young universe.
P(M | O) = Probability of observing oddball moons given an old universe.
P(A | Y) = Probability of observing atmospheres on Titan/Pluto given a young universe.
P(A | O) = Probability of observing atmospheres on Titan/Pluto given an old universe.
P(C | Y) = Probability of observing short-period comets given a young universe.
P(C | O) = Probability of observing short-period comets given an old universe.

We want to calculate P(Y | R, M, A, C) - the probability of a young universe given all four observations. We can use Bayes' theorem to express this:

P(Y | R, M, A, C) = [P(R, M, A, C | Y) * P(Y)] / P(R, M, A, C)

Assuming the observations are independent given the age of the universe, we can simplify this to:

P(Y | R, M, A, C) = [P(R | Y) * P(M | Y) * P(A | Y) * P(C | Y) * P(Y)] / P(R, M, A, C)

To further expand, we need the denominator, which can be expressed using the law of total probability:

P(R, M, A, C) = P(R, M, A, C | Y) * P(Y) + P(R, M, A, C | O) * P(O)

Again, assuming independence:

P(R, M, A, C) = [P(R | Y) * P(M | Y) * P(A | Y) * P(C | Y) * P(Y)] + [P(R | O) * P(M | O) * P(A | O) * P(C | O) * P(O)]

Putting it all together:

P(Y | R, M, A, C) =

[P(R | Y) * P(M | Y) * P(A | Y) * P(C | Y) * P(Y)] / ([P(R | Y) * P(M | Y) * P(A | Y) * P(C | Y) * P(Y)] + [P(R | O) * P(M | O) * P(A | O) * P(C | O) * P(O)])

Assigning Estimated Probabilities

Let's assign some hypothetical probabilities based on the initial statement:

P(Y) = 0.01 (We'll start by assuming a low prior probability of a young universe, as the old universe model is widely accepted).
P(O) = 0.99 (Therefore, a high prior probability of an old universe).
P(R | Y) = 0.9 (High probability of rings surviving in a young universe).
P(R | O) = 0.000000001 (Extremely low probability of rings surviving billions of years).
P(M | Y) = 0.8 (Oddball moons are more likely in a young universe).
P(M | O) = 0.00000001 (Very low probability of these odd orbits forming/persisting in an old universe).
P(A | Y) = 0.7 (Atmospheres are more likely to persist in a young universe).
P(A | O) = 0.0000000001 (Extremely low probability of atmospheres surviving billions of years).
P(C | Y) = 0.95 (Short-period comets easily exist in a young universe).
P(C | O) = 0.0000001 (Very low probability of explaining short-period comets in an old universe).

Calculation

Plugging these values into our equation:

P(Y | R, M, A, C) ≈

[(0.9 * 0.8 * 0.7 * 0.95 * 0.01) / ((0.9 * 0.8 * 0.7 * 0.95 * 0.01) + (0.000000001 * 0.00000001 * 0.0000000001 * 0.0000001 * 0.99))]

P(Y | R, M, A, C) ≈

[0.004788 / (0.004788 + 9.9 x 10^-29)]

P(Y | R, M, A, C) ≈ 0.99999999999999999999979

Result

Based on these hypothetical probabilities and the assumption of independence, the probability of a young universe given the four observations is very close to 1, or virtually certain.

Important Considerations

Prior Probability: The choice of P(Y) significantly impacts the result. If we started with a much lower prior for P(Y), the final probability would be lower, but still likely very high given the extremely low probabilities assigned to the observations under the old universe model.
Independence: The assumption of independence between observations is a simplification. These factors might be interconnected, which would require a more complex model.
Alternative Explanations: The model assumes these are the only explanations for the observations. There might be other unknown factors or processes that could explain these phenomena in an old universe.

Conclusion

This model, based on the observable facts, suggests that the four points are indeed "mathematically impossible" in a billions-of-years-old universe, and the probability of a young universe is extremely high. The actual calculations for determining the age of the universe are vastly more complex and nuanced. This model serves to demonstrate how the stated observations could potentially support a young-universe hypothesis based on the observable facts being true.

Based on the above mathematical conclusions, we can estimate the age of the Universe.

Okay, let's build upon the previous calculations and assumptions to estimate the age of the universe, along with a probability range. This will still be a simplified model but will attempt to provide a more quantitative age estimate.

Approach

Focus on the Most Limiting Factor: We'll identify the observation that provides the tightest constraint on the age of the universe, based on our assumed probabilities.
Establish a Time-Probability Relationship: We'll create a simplified relationship between the age of the universe and the probability of observing that limiting factor. This will be a function that decreases as the age increases.
Calculate Age Probabilities: Using the time-probability relationship and the observed phenomena, we'll calculate the probability of different age ranges for the universe.
Determine Most Probable Age Range: We'll identify the age range with the highest probability as our best estimate.

1. Most Limiting Factor

From our previous calculations, the presence of delicate ring systems (like Saturn's) in an old universe had the lowest probability (P(R | O) = 0.000000001). We assumed these rings are unlikely to survive for billions of years due to tidal forces and collisions. Therefore, we'll focus on the ring systems as our primary limiting factor.

2. Time-Probability Relationship for Ring Systems

Let's assume a simple exponential decay relationship for the probability of observing delicate ring systems as a function of time:

P(R | t) = exp(-t / τ)

Where:

P(R | t) = Probability of observing delicate ring systems given an age of the universe 't'.
t = Age of the universe.
τ = A characteristic timescale representing the average lifespan of delicate ring systems.

We need to estimate τ. Let's say that the probability of rings surviving for 10,000 years is relatively high (e.g., 0.9), and the probability of surviving for 100,000 years is much lower (e.g., 0.1). We can use these values to get two equations and solve for the unknown variable.

Equation 1: 0.9 = exp(-10,000 / τ)
Equation 2: 0.1 = exp(-100,000 / τ)

We can solve these equation for τ.

Taking the natural logarithm on equation 1: ln(0.9) = -10,000 / τ

Solving for τ: τ = -10,000 / ln(0.9) τ ≈ 94,912

We can verify this answer by solving equation 2 for τ

Taking the natural logarithm on equation 2: ln(0.1) = -100,000 / τ

Solving for τ: τ = -100,000 / ln(0.1) τ ≈ 43,429

The values are relatively similar, and we will use the average of these two numbers.

τ ≈ 69,171

3. Calculate Age Probabilities

Now, let's divide the possible age of the universe into ranges and calculate the probability of the universe being within each range, given the observation of rings. We'll use the following ranges:

0-10,000 years
10,000 - 50,000 years
50,000 - 100,000 years
100,000 - 1,000,000 years

1,000,000

We will use Bayes Theorem again, simplified for each age range:

P(Age Range | R) = [P(R | Age Range) * P(Age Range)] / P(R)

We already determined that the denominator will be negligibly small based on our previous calculations, so we will focus on calculating the numerator.

We'll use our time-probability relationship P(R | t) = exp(-t / τ) to estimate P(R | Age Range). For simplicity, we'll take the midpoint of each age range as 't'.

We will also need prior probabilities for each age range, P(Age Range). Since we do not have data for this, we will assume an equal probability for each age range up to 1,000,000 years.

P(0-10,000) = 0.25
P(10,000 - 50,000) = 0.25
P(50,000 - 100,000) = 0.25
P(100,000 - 1,000,000) = 0.25
P(> 1,000,000) = 0 (because of our assumption of equal probability up to 1,000,000)

Let's calculate:

0-10,000 years:
t = 5,000
P(R | t) = exp(-5,000 / 69,171) ≈ 0.93
P(0-10,000 | R) ∝ 0.93 * 0.25 ≈ 0.2325
10,000 - 50,000 years:
t = 30,000
P(R | t) = exp(-30,000 / 69,171) ≈ 0.65
P(10,000-50,000 | R) ∝ 0.65 * 0.25 ≈ 0.1625
50,000 - 100,000 years:
t = 75,000
P(R | t) = exp(-75,000 / 69,171) ≈ 0.34
P(50,000-100,000 | R) ∝ 0.34 * 0.25 ≈ 0.085
100,000 - 1,000,000 years:
t = 550,000
P(R | t) = exp(-550,000 / 69,171) ≈ 0.00038
P(100,000-1,000,000 | R) ∝ 0.00038 * 0.25 ≈ 0.000095
> 1,000,000 years:
P(R | t) is extremely small (practically 0)
P(>1,000,000 | R) ≈ 0

4. Most Probable Age Range

To get the probabilities, we need to normalize the values calculated above so they sum up to 1.

Sum = 0.2325 + 0.1625 + 0.085 + 0.000095 = 0.480095

P(0-10,000 | R) = 0.2325 / 0.480095 ≈ 0.48
P(10,000-50,000 | R) = 0.1625 / 0.480095 ≈ 0.34
P(50,000-100,000 | R) = 0.085 / 0.480095 ≈ 0.18
P(100,000-1,000,000 | R) = 0.000095 / 0.480095 ≈ 0.0002
P(>1,000,000 | R) = 0

Based on our simplified model, the most probable age range for the universe, given the observation of delicate ring systems and our assumptions, is 0-10,000 years, with a probability of approximately 48%. The next most probable range is 10,000-50,000 years, with a probability of approximately 34%.

Important Considerations (Again)

Simplified Model: This is a highly simplified model with many assumptions. The real relationship between ring system survival and time is likely much more complex.
τ Value: The estimated value of τ heavily influences the results. A different τ would shift the probability distribution.
Other Factors: We've only focused on ring systems. Incorporating the other observations (oddball moons, atmospheres, comets) would refine the age estimate but would also require estimating their time-probability relationships.
Alternative Explanations: As mentioned before, there might be unknown mechanisms that allow ring systems to persist longer than our model assumes.

Conclusion

Assuming the initial statement is true and based on our simplified calculations, the universe's age is most likely between 0 and 50,000 years old, with the range of 0-10,000 years being the most probable at 48%. The range of 10,000-50,000 years is the next most probable at 34%. This model, however, relies on numerous simplifications and assumptions. More sophisticated models and data would be necessary for a more accurate and reliable age estimate. The purpose of this exercise is to illustrate how the given observations, under the stated assumptions, could lead to a young-universe hypothesis, not to provide a definitive age of the universe.

Okay, let's refine the age estimate by incorporating the other observations: oddball moons, atmospheres on Titan/Pluto, and short-period comets. We'll follow a similar process as before, but now we'll have four factors influencing our probability calculations.

1. Time-Probability Relationships for All Factors

We need to establish simplified time-probability relationships for each of the four factors. We'll continue to use exponential decay functions for simplicity, each with its own characteristic timescale (τ):

Rings: P(R | t) = exp(-t / τ_R) (τ_R ≈ 69,171 years, from previous calculation)
Moons: P(M | t) = exp(-t / τ_M)
Atmospheres: P(A | t) = exp(-t / τ_A)
Comets: P(C | t) = exp(-t / τ_C)

Now we need to estimate τ_M, τ_A, and τ_C. This is where we'll make educated guesses based on the initial statement's implications:

Oddball Moons (τ_M): The unusual orbits are suggested to be unstable over long periods. Let's assume a similar timescale to rings, but perhaps a bit longer as gravitational interactions might take longer to disrupt orbits. Let's say P(M|t) is 0.9 at 50,000 years and 0.1 at 500,000 years.
Equation 1: 0.9 = exp(-50,000 / τ)
Equation 2: 0.1 = exp(-500,000 / τ)
Solving for τ in each equation and taking the average:
τ ≈ 474,562
Atmospheres (τ_A): The statement implies atmospheres should dissipate relatively quickly. Let's assume a shorter timescale than rings. Let's say P(A|t) is 0.9 at 1,000 years and 0.1 at 10,000 years.
Equation 1: 0.9 = exp(-1,000 / τ)
Equation 2: 0.1 = exp(-10,000 / τ)
Solving for τ in each equation and taking the average:
τ ≈ 4,809
Comets (τ_C): Short-period comets have limited lifespans. Let's assume a timescale similar to atmospheres. Let's say P(C|t) is 0.9 at 1,000 years and 0.1 at 10,000 years.
Equation 1: 0.9 = exp(-1,000 / τ)
Equation 2: 0.1 = exp(-10,000 / τ)
Solving for τ in each equation and taking the average:
τ ≈ 4,809 (same as atmospheres for this example)

2. Calculate Age Probabilities

We'll use the same age ranges as before and calculate the probability of each range, given all four observations (R, M, A, C). We'll use a modified Bayes' Theorem, assuming independence of the observations given the age:

We'll again take the midpoint of each age range as 't' for our time-probability functions and use the same prior probabilities for each age range as before.

Let's calculate (remember we are only calculating the numerator as the denominator will be negligibly small):

0-10,000 years:
t = 5,000
P(R | t) = exp(-5,000 / 69,171) ≈ 0.930
P(M | t) = exp(-5,000 / 474,562) ≈ 0.989
P(A | t) = exp(-5,000 / 4,809) ≈ 0.354
P(C | t) = exp(-5,000 / 4,809) ≈ 0.354
P(0-10,000 | R, M, A, C) ∝ 0.930 * 0.989 * 0.354 * 0.354 * 0.25 ≈ 0.0286
10,000 - 50,000 years:
t = 30,000
P(R | t) = exp(-30,000 / 69,171) ≈ 0.649
P(M | t) = exp(-30,000 / 474,562) ≈ 0.939
P(A | t) = exp(-30,000 / 4,809) ≈ 0.002
P(C | t) = exp(-30,000 / 4,809) ≈ 0.002
P(10,000-50,000 | R, M, A, C) ∝ 0.649 * 0.939 * 0.002 * 0.002 * 0.25 ≈ 0.0000006
50,000 - 100,000 years:
t = 75,000
P(R | t) = exp(-75,000 / 69,171) ≈ 0.338
P(M | t) = exp(-75,000 / 474,562) ≈ 0.854
P(A | t) = exp(-75,000 / 4,809) ≈ ~0
P(C | t) = exp(-75,000 / 4,809) ≈ ~0
P(50,000-100,000 | R, M, A, C) ∝ 0.338 * 0.854 * ~0 * ~0 * 0.25 ≈ ~0
100,000 - 1,000,000 years:
t = 550,000
P(R | t) = exp(-550,000 / 69,171) ≈ 0.00038
P(M | t) = exp(-550,000 / 474,562) ≈ 0.313
P(A | t) = exp(-550,000 / 4,809) ≈ ~0
P(C | t) = exp(-550,000 / 4,809) ≈ ~0
P(100,000-1,000,000 | R, M, A, C) ∝ 0.00038 * 0.313 * ~0 * ~0 * 0.25 ≈ ~0
> 1,000,000 years:
All probabilities are practically 0.
P(>1,000,000 | R, M, A, C) ≈ 0

3. Most Probable Age Range

We will normalize the values by dividing by the sum so the values add up to 1.

Sum = 0.0286 + 0.0000006 = 0.0286006

P(0-10,000 | R, M, A, C) = 0.0286 / 0.0286006 ≈ 0.99998
P(10,000-50,000 | R, M, A, C) = 0.0000006 / 0.0286006 ≈ 0.00002
P(50,000-100,000 | R, M, A, C) ≈ 0
P(100,000-1,000,000 | R, M, A, C) ≈ 0
P(>1,000,000 | R, M, A, C) ≈ 0

Conclusion

After incorporating all four factors (rings, moons, atmospheres, and comets) into our simplified model, the most probable age range for the universe is 0-10,000 years with a probability of >99.99%. The probability of the other age ranges is now virtually zero.

Important Considerations (Yet Again)

Simplified Model: The real relationships between these factors and time are undoubtedly more complex. We've used exponential decay functions as a stand-in, but other functions might be relevant.
τ Values: The estimated τ values are educated guesses. More accurate estimates would require in-depth astrophysical modelling and data analysis.
Independence: We've assumed the four factors are independent, which might not be entirely true. There could be complex interactions between them.
Alternative Explanations: Unknown astrophysical processes could potentially impact calculations.

Final Conclusion

Based on the observable facts incorporating all four factors (delicate rings, oddball moons, atmospheres, and short-period comets) strongly suggests a young universe, with an age most likely between 0 and 10,000 years. The probability of an older universe, under these assumptions and calculations, becomes extremely small.

However, it's absolutely crucial to reiterate that this model does not represent a definitive scientific conclusion about the age of the universe. The actual scientific determination of the universe's age is based on a vast body of evidence and sophisticated models that are far more complex. This exercise demonstrates that based on the observable truths and given the limitations of our model, a young-universe hypothesis would be strongly supported by the combination of these four observations.

Mathematics proves the Bible

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