The Enchanted Isle: A Quest for the Realms of Telepathy

Ahoy, brave explorer! Picture this: you're on a daring voyage across the vast, untamed seas when, suddenly, a mysterious island materializes on the horizon. It's eerily familiar as if it's been calling out to you in dreams. Could it be the legendary Treasure Island? Your adventurous spirit flares up, and you decide to investigate, convinced that hidden riches await beneath its lush canopy.

As you delve deeper into the island's heart, a strange sound pierces the air. Your heart races—is it a sign of danger or perhaps a clue to the treasure's location? You turn to your fellow adventurers, your trusted crew, and ask, "Did you hear that?" It's a natural reaction, but why? Why not just take charge and declare, "This is what we will do!"? But something tells you to check with the team first.

Imagine if the group hadn't heard a thing. "Ahh, OK, I must have imagined it," you might think. But what if they did hear it too? Suddenly, that sound isn't just in your head; it's real, shared, and possibly significant. This leads us to ponder: does collective hearing validate reality? Can we quantify this? What are the odds?

What happens on the island

does not stay on the island!

Let's break it down with a bit of fun math. We have two main possibilities: the sound happened, or it was imagined. For your treasure-hunting team, there are three scenarios: everyone hears it, only a few hear it, or no one hears it. That's six potential cases in total. Let's simplify with a cheat sheet: only two cases truly matter. Either multiple people hear the sound, and it's real, or they all imagined it.

Now, let's assume you're the one who heard the sound. It narrows our focus to four relevant cases, assuming your crew is honest (a fair assumption for treasure hunters, right?). Starting with the scenario where the sound is natural, but only you heard it—the chances are slim. It's unlikely an event occurs without being noticed by the group.

Consider you and a friend in a room, listening to a podcast. The volume's up, and everyone's focused. You'd unlikely hear the podcast while your friend doesn't. Apply this logic to Treasure Island—if the sound is real, everyone should hear it.

Let's explore the next intriguing scenario. You imagined a sound. What are the odds you perceived an event? It is a bit trickier, but fear not. We'll navigate through it together.

To truly understand, we must explore the vast realm of potential sounds and events one could imagine. Imagine the auditory universe: every conceivable sound, from the whisper of the wind to the roar of a distant beast—each unique, each a possibility. Narrow it down to something more tangible—words. Words are great since they are distinct sounds with specific meanings.

Consider the linguistic diversity across the globe. There are countless words in hundreds of languages, each with a unique sound. Let's simplify and say there are about 20,000 common words in each 100 languages. A staggering 2,000,000 distinct word sounds! The odds of you conjuring up one specific word from vast lexicons purely by imagination are about 1 in 2,000,000—a minuscule chance.

The number doesn't tell us whether you heard something or not. It only quantifies the likelihood of imagining a specific word. If you claim you heard a word, we take your word for it. We're focusing on the probability of hearing a specific word here.

If you did hear a word, assuming it's one of those 2,000,000 possibilities, the chance is 1 in 2,000,000. It's a small number but a crucial piece of the puzzle. The calculation helps us understand the boundary between reality and imagination in the auditory realm.

Congratulations, we've tackled another complex case! It wasn't so daunting after all. Now, armed with this knowledge, we can better assess the authenticity of sounds in our treasure hunt or any other adventure. Onward to the next challenge!

The fascinating scenario where others hear as you did. We're faced with two intriguing possibilities: either you and your friends conjured the same auditory illusion, or the sound was real and shared. Let's start by exploring the latter.

Imagine a cozy living room where a couple listens attentively to a radio program. Thus both hear the radio. It's a given. People hear the radio. The probability here is 1 in 1.

Let's transpose this scenario to our adventurous escapade on Treasure Island. If a sound is genuinely present, logic dictates that everyone in the group should perceive it, making the likelihood of collective hearing a solid 100%. This insight helps us dismiss one case, leaving just one more to unravel. Well done!

Alright, let's tackle the final intriguing case: the possibility that everyone imagined the same sound. The odds of this happening are staggeringly low. The sound was likely natural if you and your friends all reported hearing the same thing. It's plausible to theorize that the sound had a tangible source, and you were all receivers of this shared auditory experience, even if the source didn't intend for you to hear it.

Even if your team had indulged in some peculiar island mushrooms, the chances of everyone imagining the same sound simultaneously are next to zero. You have a better chance of winning the lottery. Let's put some numbers to it. The probability of two people imagining the same sound is about 1 in 4,000,000,000,000 or 0.000,000,000,025%. We haven't even factored in the simultaneous aspect, which would make these odds even tinier.

Hold onto your hats because things are about to get even more interesting. If you ask another person, and they also confirmed hearing the same sound, the probability all three of you imagined drops to about 0.000,000,000,025%. Why stop there? If you ask two more people, and they too hear the same thing, the odds all five of you imagined it would be 1 in 8,000,000,000,000,000,000 or 0.000,000,000,000,000,000,012,5%.

And what if 20 people heard the same thing? The odds would be so infinitesimal that it couldn't be a collective imagination. I am highlighting the importance of seeking confirmation from others, especially those you trust, to discern reality from imagination. So, remember to ask around the next time you're in a similar situation. It could be the key to uncovering the truth.

Probabilities for human telepathic communication

 It is perceived or "heard" as sound, but significant differences exist. 

• Telepathy travels more. You could talk to a person on the other side of the planet.

• It seems not to reflect the stuff on Earth (or other planets, if that's a thing). There are no echoes I hear.

• It is "heard" from awkward angles. When I talk to you, my voice comes from where I am. Instead, if I talk to you telepathically, you might hear me from a side, underground, or above. 

• I don't need to turn my head to be heard from a different point. 

• The person in front of me and on my back "hears" me from the same place, up, down, or the side. 

And dozens of people started playing with it in only the past few months.