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What has a 1 in a million chance? (2010)

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Re: What has a 1 in a million chance? (2010)

#151

Earlier quoted context omitted.

I don’t know if I’ve ever seen it investigated as a mathematical puzzle but there’s probably some interesting number stuff to be found in investigating the mathematics of an idealized swiss cheese risk model. If you take a series of unit squares and from each one remove a random circle (ah, the origin of every protracted probability argument among mathematicians: a random circle selected from which distribution ?), t…

No, you get axis-aligned square holes when you get your milk from cubical cows.

Cows are spherical

Re: What has a 1 in a million chance? (2010)

#152
post #92

Found a fun CgpGrey video on 1 in a million experience. [here]( https://youtu.be/PmWQmZXYd74?si=BDBkrfxEXgAgeRfw )

Is there a word for what he's doing with his voice in this video? Vsauce does the same thing. It's a strange cadence that would make me lift an eyebrow if someone was speaking to me like that in real life. It's like if captain Kirk removed emotion from his voice and began to lecture you.

Wendover Productions is another major offender.

Re: What has a 1 in a million chance? (2010)

#153
post #104
post #80

Earlier quoted context omitted.

The cheese-loving aviators have the Swiss-cheese-model to visualize how small unimportant errors can stack up to a catastrophic outcome. Though in my opinion there's a flaw in this thinking as no sane cheese seller would shuffle their layers of cheese after cutting them: Hence 1-in-million chances happen all the time. https://www.aviationfile.com/swiss-cheese-model/

You'd think that but the Toledo fondue flood of 1973 says otherwise. I can't find the wiki link, but Ronald O'Sullivan, who'd just taken over his father's cheese shop, was attempting to make a single block of swiss after a long week of selling the first 80% of several blocks to different restaurants. He took those cheese tails and stacked them up, not realizing the dangers he was putting everyone else in. It was late…

Need a source on this, please. It sounds real at first look, but I cant find any links and it's very similar to the boston molasses flood of 1918 story, especially that last bit -

"The event entered local folklore and residents reported for decades afterwards that the area still smelled of molasses on hot summer days."

https://en.m.wikipedia.org/wiki/Great_Molasses_Flood

Re: What has a 1 in a million chance? (2010)

#154
It's all availability heuristic. If you can think of an example, you think it's more likely.

“Hundreds of children die every year in drowning accidents,” he says. “We need lifeguards at pools more than armed guards at schools.”

https://www.city-journal.org/article/sorrow-and-precaution-n...

https://news.gallup.com/poll/266681/nearly-half-fear-victim-...

Re: What has a 1 in a million chance? (2010)

#155

The following are all ~ 1 in a million chance of death, or 1 micromort: Travelling 6 miles (9.7 km) by motorcycle Travelling 17 miles (27 km) by walking Travelling 20 miles (32 km) by bicycle Travelling 230 miles (370 km) by car Travelling 1,000 miles (1,600 km) by jet Travelling 6,000 miles (9,656 km) by train But switching from car to bicycle for short trips still increases life expectancy due to health effects. So…

As a cyclist that’s trying to not die, I also have to assume this heavily depends on where you’re cycling. Along a stroad? You’re dead. Country road with more bikes than cars? Much safer.

Re: What has a 1 in a million chance? (2010)

#156
post #4

Picking a random integer between 1 and 1 million.

That depends on the quality of your randomness. If it's a person picking the number that definitely isn't a 1 in a million chance for most numbers. You need to get pretty specialized hardware before you can confidently say it's definitely an equal chance for every number every time.

It would be interesting what kind of clustering (if any) there would be if 1 million people were asked to pick a number between 1 and a million.

Re: What has a 1 in a million chance? (2010)

#157
post #104

Earlier quoted context omitted.

You'd think that but the Toledo fondue flood of 1973 says otherwise. I can't find the wiki link, but Ronald O'Sullivan, who'd just taken over his father's cheese shop, was attempting to make a single block of swiss after a long week of selling the first 80% of several blocks to different restaurants. He took those cheese tails and stacked them up, not realizing the dangers he was putting everyone else in. It was late…

Need a source on this, please. It sounds real at first look, but I cant find any links and it's very similar to the boston molasses flood of 1918 story, especially that last bit - "The event entered local folklore and residents reported for decades afterwards that the area still smelled of molasses on hot summer days." https://en.m.wikipedia.org/wiki/Great_Molasses_Flood

It's 100% made up. It's an attempt to make fun of people who would consider it unlikely that anyone would ever stack cheese as a way to mitigate safety risks.

Re: What has a 1 in a million chance? (2010)

#158
My favorite mental visualization I came up with: imagine driving from New Jersey to Florida (substitute with a long drive you had). Mine was about 1,200 miles which at 60 miles per hour is 20 hours. That's 72,000 seconds of mind-numbing driving.

Now if during the entire, exhausting, 20 hours of driving, you press a button, and it falls within the "danger zone" that lasts 15 seconds, you lose.

The above example is better when looking at lottery winning chances (worse than 1 in million) - where you can imagine having to throw a quarter out of the window, hoping for it to land within the proper 1 inch section of the road.

I like this example because it gives you visceral feeling - allowing you to think in terms of lengths of road or length of time to compare various odds.

Re: What has a 1 in a million chance? (2010)

#159
post #104

Earlier quoted context omitted.

You'd think that but the Toledo fondue flood of 1973 says otherwise. I can't find the wiki link, but Ronald O'Sullivan, who'd just taken over his father's cheese shop, was attempting to make a single block of swiss after a long week of selling the first 80% of several blocks to different restaurants. He took those cheese tails and stacked them up, not realizing the dangers he was putting everyone else in. It was late…

Need a source on this, please. It sounds real at first look, but I cant find any links and it's very similar to the boston molasses flood of 1918 story, especially that last bit - "The event entered local folklore and residents reported for decades afterwards that the area still smelled of molasses on hot summer days." https://en.m.wikipedia.org/wiki/Great_Molasses_Flood

Fondue can't cause a flood like the Great Molasses Flood because it's not capable of truly fully laminar flows.

Fondue is a colloidal suspension of cheese solids in a mixture of wine and melting agents and it shows complex rheological behavior. Unlike Newtonian fluids, where viscosity remains constant regardless of the applied shear rate, fondue demonstrates non-Newtonian features, especially shear-thinning. As the shear rate increases, its viscosity decreases, a phenomenon attributed to the alignment of colloidal particles in the direction of flow, interfering with the fluid and preventing it from filling every nook and cranny like a flood would.

Fondue's inability to achieve truly laminar flow is rooted in its viscoelastic properties. When subjected to stress, fondue exhibits both viscous and elastic characteristics, a behavior modeled by the Maxwell model in rheology. This model combines a viscous damper and an elastic spring to describe the material's response to applied stress. As fondue is subjected to shear stress, its structure becomes disrupted, leading to a breakdown in its ability to maintain a cohesive flow front. This disruption manifests as a turbulent flow, preventing the formation of a flood-like scenario similar to that caused by molasses.

Re: What has a 1 in a million chance? (2010)

#160

Earlier quoted context omitted.

Why is the 20 multiplied by the million? Why not 0.95 multiplied by million? Using the same argument I would accept infinite odds that my username is quickthrower2 so there is infinite information?

It's important to understand that when they said "bits" they didn't mean information in the Shannon entropy sense, but rather in the log-odds evidence sense. Gaining a Shannon entropy bit means learning the answer to a yes-no question that had 1:1 odds. Gaining a log-odds evidence bit means doubling your best-guess odds on a question you are uncertain about, from X:Y to (2X):Y. One Shannon bit is worth arbitrarily ma…

This isn't how the mathematics of odds works, as the GP correctly pointed out. An event which is 20:1 on is not 20 times more likely than certainty.

Going from 1:4 to 1:2 means that the event has become twice as likely. But going from 2:1 to 4:1 does not: it means that the complementary event has become half as likely.

Based on this, we can't do math with odds treating them identically to ratios.

If you do the math correctly, the two types of information measure are basically the same thing.

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