The Gold Coin Analogy

 The Gold Coin Analogy:

If you've watched my earlier videos on Bible Codes, or read those blog posts, you know that my name occurs three times in the Torah. My first and last name in Hebrew are eight characters long. There are different methods of encoding a text, and the method used in this example is an ELS code -- or Equidistant Letter Sequence code. It is an found by picking up letters that are equally spaced apart. If you start looking for a word at a skip sequence of 50, you continue with a skip of 50. The odds of finding the three occurrences of my name by chance alone were less than one in a million according to the software's odds calculator, and I have gone over the specific odds of such a thing occurring randomly before. However, I thought of an analogy that might be helpful in understanding the rarity of this and asked ChatGPT 4 to help me with it. Here is that conversation.

Me: If I go for a drive, and I get out of my car and walk 50 paces and find a gold coin, face up; then walk another 50 paces and find another gold coin, face up; then walk another 50 paces and find another gold coin, face up; is it more likely that this is deliberate design or a lucky fluke? Is it possible to calculate the odds of something like that happening?

ChatGPT 4: The scenario you're describing—finding gold coins face up at regular intervals—is certainly intriguing. To assess whether this situation is more likely due to deliberate design or just a lucky fluke, we can try to calculate the odds of such an event under the assumption of random chance. While we can't know the true intention behind it (design vs. fluke), calculating the odds will help us assess just how unlikely the event might be if it were purely random.

Steps to Approach the Problem:

1. Assume the Coin Finds are Random Events:

   • We'll first need to consider the probability of finding a gold coin at all. Let's say finding a gold coin is a rare event (since gold coins are not lying around everywhere).
   • We also need to factor in the probability of the coin being face up, which would be 50%, as there are two sides to the coin.

2. Probability of Finding the First Coin:

   • Let’s denote the probability of finding one gold coin at random in any given location as $p_{\text{coin}}$. This will be a very small number because gold coins are rare.
   • The probability of that coin being face up is 0.5.

   Therefore, the probability of finding one gold coin face up at a random location would be:

   $$P_1 = p_{\text{coin}} \times 0.5$$

3. Probability of Repeating the Event Three Times:

   • To find three gold coins, each 50 paces apart, all face up, we would need to cube the probability of finding one face-up gold coin.
   $$P_3 = (p_{\text{coin}} \times 0.5)^3$$

4. Calculating the Odds:

   • If $p_{\text{coin}}$ is extremely small (for example, one in a million, or $10^{-6}$), then the odds of finding three gold coins, all face up, would be:
   $$P_3 = (10^{-6} \times 0.5)^3 = (5 \times 10^{-7})^3 = 1.25 \times 10^{-19}$$

   This is an astronomically small probability, suggesting that it is exceedingly unlikely that such a sequence would happen by random chance alone.

Deliberate Design vs. Lucky Fluke:

• Given the minuscule probability of this happening randomly, the event seems highly unlikely to be a mere fluke. Therefore, if such an event occurred, one would typically suspect deliberate design over random chance, as the odds are so low.

However, this conclusion is based on the rarity of finding gold coins. If there were a more mundane explanation (e.g., the coins were placed there intentionally by someone), it would align with the idea of deliberate design.

Does this method of calculating the odds make sense to you, or would you like a more detailed breakdown?

Me: What if they are quarters or pennies instead of gold coins? 

ChatGPT 4: If the coins in your scenario were quarters or pennies instead of rare gold coins, the probability calculation changes because finding quarters or pennies lying around is far more common. Let’s break it down:

Step-by-Step Calculation:

1. Assume the Coins are Common (Quarters or Pennies):

   • Finding a quarter or a penny on the ground is far less rare than finding a gold coin. We would need to estimate the probability of encountering a quarter or penny in a random location. For this, let’s assume that the probability of finding a quarter or penny at any given location, $p_{\text{coin}}$, is much higher than for a gold coin.
   • The probability of the coin being face up is still 50%, or 0.5.

2. Probability of Finding the First Coin (Quarter or Penny) Face Up:

   • If $p_{\text{coin}}$ is, say, 1 in 1,000 (i.e., 0.001), then the probability of finding one face-up quarter or penny is:
   $$P_1 = p_{\text{coin}} \times 0.5 = 0.001 \times 0.5 = 0.0005$$

3. Probability of Repeating the Event Three Times:

   • To find three quarters or pennies, each face up, spaced 50 paces apart, you would cube the probability, just as before:
   $$P_3 = (p_{\text{coin}} \times 0.5)^3 = (0.001 \times 0.5)^3 = (0.0005)^3 = 1.25 \times 10^{-10}$$

   So, the probability of finding three quarters or pennies, all face up, spaced exactly 50 paces apart, by pure chance is about $1.25 \times 10^{-10}$, or 1 in 8 billion.

Interpretation:

• Quarters or Pennies: While it’s more likely to come across quarters or pennies compared to gold coins, the chance of finding three coins in such a specific sequence (face up, evenly spaced) remains incredibly low, though not as astronomically unlikely as with gold coins.

  If this event occurred in real life, it would still seem improbable enough that one might suspect design over random chance. It's possible that someone placed the coins deliberately.

Would you like to explore other factors or adjustments in this calculation?

Me: OK. I thought of another wild scenario. What if I take a walk again and this time I find a series of eight letters, and each letter is a letter from my name? At the end, the letters spell my name. Like the first scenario, each letter is equally spaced apart, let's say every thousand steps. How likely is it for that to happen by chance?  

ChatGPT 4: That is a wild scenario! Finding a series of 8 letters, each spaced equally apart, that spell your name certainly seems extraordinary. Let's break down the probability of this happening by random chance, assuming all letters in the alphabet are equally likely.

Steps to Calculate the Odds:

1. Assume the Alphabet is Randomly Distributed:

   • There are 26 letters in the English alphabet, so the probability of randomly encountering any specific letter (such as the first letter of your name) is $\frac{1}{26}$.

2. Finding 8 Specific Letters in a Row:

   • To spell out your entire 8-letter name, you would need to find the right letter at each of the 8 positions.
   • The probability of finding the correct letter at any given position is $\frac{1}{26}$.
   • The probability of finding all 8 letters, in the correct order, is:
   $$P_{\text{name}} = \left( \frac{1}{26} \right)^8 = \frac{1}{26^8}$$

3. Calculating the Probability:

   • Let’s calculate $26^8$:
   $$26^8 = 208,827,064,576$$

   So, the probability of encountering 8 letters, each spaced 1,000 steps apart, that spell out your name by random chance is:

   $$P_{\text{name}} = \frac{1}{208,827,064,576}$$

   This means the odds are about 1 in 209 billion.

Interpretation:

• Improbability of Random Chance: The odds of finding 8 specific letters in order, each spaced 1,000 steps apart, are astronomically low if the letters are distributed randomly. Such a scenario would strongly suggest either extreme luck or deliberate design.

In real life, such an event would almost certainly be considered more than a fluke. The low probability makes random chance highly unlikely.

Would you like to explore variations of this, or does this answer satisfy your curiosity?

Me: Does it make a difference if the letters are farther apart, say every 5,000 steps? Does the wider skip between letters make it less likely?

ChatGPT 4: The distance between the letters (whether every 1,000 steps or every 5,000 steps) does not affect the probability of the letters themselves being found in a specific order, as long as you're still finding the correct letters. In other words, the likelihood of finding 8 specific letters in the right sequence remains the same regardless of the physical distance between the letters.

Key Points:

• The probability of encountering each letter randomly depends on how often letters appear, not the physical distance between them. Since the odds of each letter being the one you need are still $\frac{1}{26}$, the distance between letters doesn't change the calculation.

• The core probability remains:

  $$P_{\text{name}} = \left( \frac{1}{26} \right)^8 = \frac{1}{208,827,064,576}$$

When Distance Might Matter:

While the pure probability of finding the letters in the correct sequence doesn't depend on the distance, the wider spacing might affect:

• Search fatigue: You’d have to walk much farther to find each letter, which could be practically harder or less likely to attempt in real life.
• Other patterns: If the letters are spaced farther apart, it may feel more significant or designed, simply because of the greater distance covered between each correct letter.

However, mathematically speaking, the distance between the letters doesn’t make the event more or less likely as long as the letters still appear in the correct sequence.

Does that clear things up?

Me: Does it make a difference if the letters that spell out my name are from Japanese Katakana alphabet and I am a native English speaker? Assume that I have studied the alphabet and know a little of the language, but it is not my native tongue.  

ChatGPT 4: The fact that the letters are from the Japanese Katakana alphabet instead of the English alphabet adds an interesting layer, but it doesn’t fundamentally change the way we calculate the probability of finding the letters in sequence. However, we need to adjust for the size of the alphabet and your familiarity with the language. Let's break it down:

1. Katakana Alphabet Size:

• The Japanese Katakana alphabet has 46 basic characters, unlike the 26 letters in the English alphabet. Therefore, instead of $\frac{1}{26}$, each character has a probability of $\frac{1}{46}$ of being randomly found.

2. Probability Calculation:

• To spell out your name in Katakana (assuming an 8-character name), the probability of randomly encountering each correct Katakana letter is now:

$$P_{\text{name}} = \left( \frac{1}{46} \right)^8 = \frac{1}{46^8}$$

• Let’s calculate $46^8$:

$$46^8 = 208,827,064,576$$

So, the probability becomes:

$$P_{\text{name}} = \frac{1}{208,827,064,576}$$

3. Your Familiarity with Katakana:

• Even though you know a little of the Katakana alphabet, this doesn't change the probability of finding the letters by chance, since the calculation is based purely on the likelihood of random letters appearing. Your familiarity would come into play if, for instance, you were consciously interpreting or searching for these letters rather than stumbling upon them by random chance.

Conclusion:

Switching from the English alphabet to Katakana alters the probability slightly due to the larger alphabet size, but otherwise, the logic of the scenario stays the same. The event remains extremely unlikely, with odds now depending on the 46-character set of Katakana.

Let me know if you'd like to explore this further!

Me: Would it change if the alphabet had only 24 letters? 

ChatGPT 4: Yes, if the alphabet had only 24 letters, it would change the probability slightly, making the event more likely because there are fewer possible characters to choose from. Let's go through the new calculation.

Probability Calculation with 24 Letters:

1. New Alphabet Size:

   • If the alphabet has 24 letters, the probability of finding any specific letter would be $\frac{1}{24}$.

2. Finding 8 Specific Letters:

   • The probability of finding the correct 8 letters in sequence (spelling out your name) becomes:
   $$P_{\text{name}} = \left( \frac{1}{24} \right)^8 = \frac{1}{24^8}$$

3. Calculating $24^8$:

   $$24^8 = 110,075,314,176$$

   So, the probability of finding 8 specific letters in a row, randomly from a 24-letter alphabet, would be:

   $$P_{\text{name}} = \frac{1}{110,075,314,176}$$

Comparison with 26 or 46 Letters:

• 26 Letters (English alphabet): $\frac{1}{208,827,064,576}$
• 46 Letters (Katakana alphabet): $\frac{1}{208,827,064,576}$
• 24 Letters (Hypothetical alphabet): $\frac{1}{110,075,314,176}$

As you can see, the probability is higher with fewer letters, though still extremely small. A 24-letter alphabet makes it almost twice as likely as with 26 or 46 letters.

Let me know if you'd like to tweak this further!

Me:  Both would be extremely unlikely, but the fewer letters make the event more likely to occur randomly. Is that correct?

ChatGPT 4: Yes, that's absolutely correct! While both scenarios remain extremely unlikely, having fewer letters in the alphabet makes the event slightly more likely to occur randomly. This is because there are fewer possible characters to choose from, so the odds of finding each specific letter increase.

In summary:

• Fewer letters = higher probability, but still an overall rare event.

You're right on target with your understanding!