We humans have some innate amazing capabilities. However, intuitively grasping mathematical principles, including statistics and probability theory, isn't one of them. Or at least, this is very rare.
That's why almost everybody mistakenly overestimates the rarity of unusual events. I wrote about this in a 2014 post, "Miracles" happen all the time. Mathematics demands them. In that post I included this question from a book I was reading:
How many people must be in a room to make it more likely than not that two of them share the same birthday?
The answer is 23. I would have thought the answer was many more. Even after I've read the reason why 23 people is the answer (it has to do with exponents, basically), I still have difficulty understanding that reason.
The December 2024 issue of New Scientist has a story by mathematician Sarah Hart, "The surprising maths that explains why coincidences are so common." (It's a British magazine, so they say maths.)
Download The surprising maths that explains why coincidences are so common | New Scientist
Hart starts off by relating an experience.
I had a strange experience in a cafe recently. When paying for coffee, I asked to use the toilet. After I tapped my PIN into the card reader, the barista handed me a slip of paper that was blank apart from a single number – the same one I had just tapped into the keypad! It turned out that this was also the entry code for the bathroom door.
Was this evidence of a shadowy plot by the agents of Big Caffeine? No, it was just a fluke, but the event got me thinking about coincidences more generally. Occasionally, we are faced with events that seem so improbable we can’t help but feel the universe is sending us a message. As a mathematician, I know that coincidences are often far more likely to occur than we think – and this fact can have serious consequences everywhere from the science lab to lottery kiosks and the law courts.
My coffee shop experience is a good place to start because we can calculate the exact probability of it happening by chance. There are 10,000 possible four-digit numbers, meaning a 1 in 10,000 probability that the door code matches my PIN. Unlikely, yes, but let us put it in context. The cafe was in York, UK – a popular tourist destination with 8.9 million visitors annually. If each visitor has one bank card, we would expect around 890 cards each year to have the same PIN as that cafe’s bathroom door code. I don’t feel so special now.
Looking more broadly, there are so many events happening to every person each day, coincidences are bound to happen frequently. But we aren't aware of all those seemingly unusual events. Usually we only know about them when they happen to us or a close friend.
Or when they're so unusual, they become a news story, as was the case with the Bulgarian National Lottery when the same six winning numbers came up on two consecutive draws. Hart explains why this actually was to be expected.
Such analyses can help explain some of history’s most breathtaking coincidences, such as the curious case of the Bulgarian national lottery. In September 2009, the same numbers – 4, 15, 23, 24, 35 and 42 – came out in two consecutive draws.
It sounds like a fix, but the statistician David Hand calculated that the game would only have to run for 43 years before it becomes more likely than not for the same numbers to be drawn at least twice. (The lottery had, by this point, been running for 52 years.)
So when someone says of a seemingly unlikely event, "It was a miracle," almost certainly it wasn't. (I was inclined to omit almost, but science tells us that nothing is absolutely certain, just extremely likely.)
Coincidences appear to share with miracles this psychological phenomenon: it's all about us. This was pointed out in the explanation of why it only takes 23 people in a room for it to be more likely than not that two of those people share the same birthday.
Skeptical about how this could be true, we picture ourselves going up to the other 22 people and asking them if their birthday was the same as ours, July 18, say. What we don't picture is each of those 22 people doing the same thing with everybody else in the room. The author of the explanation says:
Take a look at the news. Notice how much of the negative news is the result of acting without considering others. I’m an optimist and do have hope for mankind, but that’s a separate discussion :).
In a room of 23, do you think of the 22 comparisons where your birthday is being compared against someone else’s? Probably.
Do you think of the 231 comparisons where someone who is not you is being checked against someone else who is not you? Do you realize there are so many? Probably not.
The fact that we neglect the 10 times as many comparisons that don’t include us helps us see why the “paradox” can happen.
It's natural to feel that the world revolves around us. After all, the only person who we're in direct intimate contact with as a subject rather than an object is ourself. But statistics and mathematics shows us that we're less important in the grand scheme of things than we typically view ourselves as being.
Having someone call us just when we're thinking of contacting them may seem miraculous from our personal point of view (which happened to me), yet isn't at all surprising when we look at things from a broader perspective where billions of people are contacting each other.
We like to think that the universe is sending us meaningful messages through rare or unexpected events. Actually, laws of probability are sending us non-meaningful messages.
I'm not impressed with NotebookLM or weird notions of oneness
I do my best to accept the diversity of opinions expressed by people who leave comments on this blog. Diversity is good. If we all believed in the same things, life would be super boring.
However, I'm also big on coherent conversations. While I understand that it is difficult to accomplish this via blog post comments, there's much more value in comments that can be understood by other people, as understanding is the foundation for agreements or disagreements.
Here's an example.
A few days ago I wrote "Some thoughts about what oneness is, and isn't." It wasn't one of my best blog posts. Adequate, but not more than that. I was hoping that someone else would have something wiser to say about oneness.
Because I've found that Osho Robbins, a regular commenter on this blog, often makes good sense, I did my best to understand what he was getting at in his comments on my oneness post. I failed. Here's quotes from his comments that seem to summarize his position on oneness.
I have not claimed the existence of ONENESS.
What I have done is shown that ONENESS cannot be known or experienced.
ONENESS is non-existent because it ticks all the boxes for a non-existent thing.
ONENESS has NO CHARACTERISTICS hence it does NOT exist.
OK. I can understand those statements. Oneness doesn't exist and, not surprisingly, it can't be known or experienced. What I can't understand is how Robbins says a whole lot of other stuff in his comments that apparently he considers to be related to nonexistent and unknowable oneness.
Look, over the years I've been fond of saying that existence exists, and wow, isn't that amazing, that there's something rather than nothing. I readily admit that in one sense, existence can't be known or experienced, since all we can know or experience are entities that exist.
So when I say that existence exists, I'm not claiming that existence is something that stands apart from what exists. This appears to be similar to Robbins' statement that oneness can't be known or experienced, just the unity of things that can be known or experienced.
However, the difference is that Robbins seems to have a lot of fondness for oneness that doesn't exist. He isn't expressing admiration for love and other manifestations of the unity that undergirds reality, as manifested in universal laws of nature, ecological interconnectedness, and such.
And that's what I don't get. His take on oneness isn't that it is beyond speech, reason, perception, and other human ways of knowing and communicating. That would put oneness in the sphere of Zen. Rather, it is that somehow we should care about oneness even though it doesn't exist in any fashion.
I can understand the appeal of mysticism, even though I've fallen away from embracing it. What I don't understand is talk about oneness that doesn't exist.
I also don't understand the appeal of NotebookLM, which is capable of fashioning "podcasts" from videos, recordings, or writings, creating two personalities from the thoughts communicated by a single person.
Previously I shared a NotebookLM podcast from Osho Robbins. Then Jim Sutherland, another regular commenter on this blog, emailed me about a NotebookLM podcast fashioned from reports of his about a 2017 visit to the Dera, the headquarters of Radha Soami Satsang Beas in India.
I listened to about a third of the 17 minute audio podcast. I guess I have a low tolerance for NotebookLM, because I found the artificial intelligence generated voices so irritating, I wished that Sutherland that simply shared a written version of what the podcast is about, rather than having those reports filtered through Notebook LM.
The way I see it, NotebookLM simply is regurgitating a communication that already exists in a podcast form. Nothing new is added by NotebookLM. It merely fashions a pseudo-dialogue between two AI generated "people," each of whom reflects the content of the original communication.
Sure, I can understand the appeal of having the NotebookLM personalities gush over the wisdom contained in something a person has created, be it a video, audio recording, or document. But for me, the listener/watcher of NotebookLM, I don't see what benefit there is in having the original communication fashioned into a "podcast" with the same content.
If I'm wrong about NotebookLM, I'll be pleased to be corrected. That's just how I see it at the moment.
Posted at 10:10 PM in Comments, Reality | Permalink | Comments (50)
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