9 ms·

> 16. If you let a 100g strawberry that is 99% water by mass dehydrate such that the water now accounts for 98% of the total mass then its new mass is 50g: http

> 16. If you let a 100g strawberry that is 99% water by mass dehydrate such that the water now accounts for 98% of the total mass then its new mass is 50g: https://en.wikipedia.org/wiki/Potato_paradox https://en.wikipedia.org/wiki/Potato_paradox I really like this one. It's a perfect combo of intuitive from one perspective and mind bending from another. > 18. A one-in-billion event will happen 8 times a month: https://gwern.net/Littlewood https://gwern.net/Littlewood This one, on the other hand, I don't like. Depending on a whole bunch of subjective definitions, a one-in-billion event can happen a million times a second or practically never or whatever else you choose.

lotsofpulp 5y ago
>https://en.wikipedia.org/wiki/Potato_paradox https://en.wikipedia.org/wiki/Potato_paradox The Wikipedia link above says: > Fred brings home 100 kg of potatoes, which (being purely mathematical potatoes) consist of 99% water. He then leaves them outside overnight so that they consist of 98% water. What is their new weight? The surprising answer is 50 kg. It annoys me when mass is used interchangeably with force (weight), so I went to the Wikipedia source, and the source is accurate in using units of force throughout. https://web.archive.org/web/20140202214723/http://www.daviddarling.info/encyclopedia/P/potato_paradox.html https://web.archive.org/web/20140202214723/http://www.davidd... Wonder why the person that wrote the Wikipedia article changed it up when it is supposed to be a direct quote.
- deleted 5y ago
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- jgtrosh 5y ago
  In this situation, the mass and weight are proportional and irrelevant to the problem. Other than proper respect of units, why would it really matter? I would agree that using mass+kg would remain correct and be less unusual, but it doesn't matter a lot.
  - lotsofpulp 5y ago
    It does not matter, it is just a pet peeve of mine. Might be due psychological trauma from when I was a kid and arguing with an older cousin about how pounds and kilograms are not units of the same thing, and the older cousin "winning" the argument in the eyes of the elders because the cousin was quite a few years older than me and considered to be smart in school.
    - version_five 5y ago
      From what I remember from intro physics, we distinguished between pounds and pounds force, the latter having the 32ft/s^2 multiplied in. And wikipedia seems to agree with me, see pound (mass) vs pound (force).
      - lotsofpulp 5y ago
        Oh wow, learning a lot today. I was taught in the US that pounds are a measure of force, and that is how it was always used in physics problems.
        tharkun__ 5y ago
        As a European I learned in metric. When I first learned pounds, it was as the imperial system's equivalent of grams and a conversion factor was given. Force in physics class was taught in Newtons (kg*m/s^2).
        kergonath 5y ago
        Pounds as a mass unit are perverse enough. Things like pound force and psi (pounds per square inch) were used only to make fun of old mechanics papers and textbooks. Also, btu. It is quite amazing actually that someone would see the SI and think “no, too simple; I’ll keep my pounds, ounces, inches, and feet”. Anyway, yes, the proper unit of force is the Newton.
        version_five 5y ago
- mint2 5y ago
  I really don’t like that example because it makes no sense. In no logical circumstance could the potatoes dehydrate so quickly when left out over a single night.
  - tharkun__ 5y ago
    And they also don't consist of 99% water. That is why they called them "purely mathematical potatoes" and they could've chosen any type of fruit or vegetable. Heck, I'm just waiting for a car analogy now! Brake fluid anyone?
    - mint2 5y ago
      But that 99% water simplification is needed for the purpose of the exercise. The left out overnight is basically an absurd statement that is intended to confuse and not really related to the actual question. The statement could be “left in a dry environment until” or simply “left to dry a few weeks”
      - tharkun__ 5y ago
        You definitely could write that but it wouldn't change anything and you could make the same "argument" you are making now. "The left to dry a few weeks is basically an absurd statement that is intended to confuse" and it still wouldn't be true. It's not intended to confuse at all. It's intended to get the point across that you let this imaginary thing dry from 99% to 98%. They could've said "sponge" and let it out to dry any number of minutes. The point isn't to make a 100% accurate example of the drying properties of any actual 'thing'. They just needed something that people intuitively know "has water content" and that "can dry".
        mint2 5y ago
        Wow by the downvotes I learned people react extremely negatively to any critique of math word problems. Spherical cows and 99% water potatoes are fine, those over simplifications are required for the analysis. Saying Leaving the potatoes out overnight to imply they halved in mass, sounds as reasonable as “the potatoes were in the ground for 12 hours and then doubled in amount, what percent of water are they now?” It’s so gratuitous and requires ignoring all other laws of physics, while the goal of the spherical cow type simplification is to only ignore a few key challenging ones.
- syncsynchalt 5y ago
  > Wonder why the person that wrote the Wikipedia article changed it up when it is supposed to be a direct quote. They likely changed it from lb to kg because that would be more friendly to an international audience, without realizing that lb is a measure of weight and kg is a measure of mass. Therefore they didn't know to change "weight" to "mass".
  - lotsofpulp 5y ago
    Oh yes, that would make sense.
  - kergonath 5y ago
    I have been to the US quite regularly, and been living in the UK for a number of years, and I have never seen someone using pounds as a unit of force instead of a unit of mass meaning roughly 500g, give or take. Second meaning was about 1.20€. FWIW, the pound is a proper unit of mass: https://en.m.wikipedia.org/wiki/Pound_(mass) https://en.m.wikipedia.org/wiki/Pound_(mass) .
    - syncsynchalt 5y ago
      I'm a civil engineer. In statute terms pound is the unit of force and slug is the unit of mass. That might have colored my thinking.
- sbakzbsmx 5y ago
  The difference between weight and mass is domain specific to physics. I actually get annoyed at people who are pedantic about these things. Precision is important in some conversations, but just elitist in other. Anyway, the term “weight” to refer to mass outdates its use as a force - its only since Newton that we distinguish the two, after all.
- p1necone 5y ago
  You're being overly pedantic (and I would argue actually incorrect). Kilograms and pounds are both referred to as "weight" in general conversation and nobody is going to be confused by this. Go to any supermarket in a country that uses the metric system, potatoes will be sold by the kilogram - it's the natural way to phrase this outside of America. In a physics context the definition of kilogram might be specifically mass, with newtons referring to weight/force. But words can have different meanings outside of technical contexts. If you go to a metric country, and ask someone how much they "weigh", approximately zero people will say "x newtons", they will say "x kilograms" (or "x pounds" still in a lot of commonwealth countries if we're being pedantic).
  - p1necone 5y ago
    Although the more I think about this the more I think the difference between technical and colloquial is actually that "weight" in colloquial use refers to mass, because force is not commonly relevant.
    - eru 5y ago
      Yes, in colloquial use weight refers to mass _most_ of the time. But can also refer to inertia or mass. Or be used metaphorically.
    - jacobolus 5y ago
      "Weight" historically referred to mass, in common speech dating back forever. It’s the Germanic word which has been used throughout the history of English, whereas "mass" comes from Latin via French, like 5–6 centuries ago. The two words are almost exact synonyms, in historical/colloquial use. Both historically and today, a "pound" (Roman libra) is a unit of mass. People use a pound-force as a unit of force only in somewhat specialized contexts. At some point in the relatively recent past, someone (not sure who) decided that we needed to have 2 separate words for mass vs. force, and we should keep the Latin word for mass and use the Germanic word to mean force. Now pedantic people are constantly insisting that using the standard English word weight to mean mass is "wrong".
- menotyou 5y ago
  When I buy potatoes I am interested to buy 10 kg mass of potatoes, not the amount or potatoes of which has a gravity force of 98,1N. On mars you need to eat 10 kg of potatoes a week, not the amount of which has 98,1N gravity force. The scales in the supermarket on earth automatically convert the weight into mass for my convenience by applying a constant factor of 1/9,81. I am hardly far away enough from earth that the constant changed, so I did not need to distinguish between the two measures so far. When carrying the potatoes home I just use the mass of 10 kg as a proxy for the force I need. And to determine the increased breaking distance of my car, I need to know the mass again.
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pessimizer 5y ago
> > 16. If you let a 100g strawberry that is 99% water by mass dehydrate such that the water now accounts for 98% of the total mass then its new mass is 50g: https://en.wikipedia.org/wiki/Potato_paradox https://en.wikipedia.org/wiki/Potato_paradox >I really like this one. It's a perfect combo of intuitive from one perspective and mind bending from another. Comes up a lot lately because of vaccine effectiveness e.g. 95% is twice as effective as 90%.
- xarope 5y ago
  and sunscreen (SPF) calculations...
- umvi 5y ago
  Wait, how is 95% effective twice as effective as 90%?
  - anandoza 5y ago
    It halves your risk.
  - zbaxrl 5y ago
    90% is 1 in 10, 95% is 1 in 20.
  - fgonzag 5y ago
    just as going from 98% effectiveness to 99% effectiveness halves your risk (you go from 2% chance of falling ill to 1%) its a common concept in games in which armor follows a linear formula (each point of armor is more effective than the last when calculating effective health)
    - anthk 5y ago
      Then there's the polynomial wizard.
- sib 5y ago
  It's probably more intuitive if you say that it's "half as ineffective"
nighthawk454 5y ago
Yes, it doesn't explicitly state the rate or distribution of events. But it is a good reminder of what happens when your whatevers/second are pretty high - see the famous "One in a million is next Tuesday" [1]. "Rare" is soon if you roll the dice fast enough. Any time your service has a high TPS, your API gets a lot of calls, a button in your app gets pressed a lot, ... this applies. Critically, "a lot" is defined relative to your failure tolerance. It may actually be very fast or a lot, or not particularly fast but it really really needs to work. It highlights the fallacy of equating "low probability" and "won't happen". [1] https://docs.microsoft.com/en-us/archive/blogs/larryosterman/one-in-a-million-is-next-tuesday https://docs.microsoft.com/en-us/archive/blogs/larryosterman...
- IIAOPSW 5y ago
  Or everyone's newest favourite, the virus randomly mutating is "rare".
- leeoniya 5y ago
  "Given the scale that Twitter is at, a one-in-a-million chance happens 500 times a day." https://www.ted.com/talks/del_harvey_protecting_twitter_users_sometimes_from_themselves/transcript?language=en https://www.ted.com/talks/del_harvey_protecting_twitter_user...
- curiousgal 5y ago
  > And I’ve seen some absolute doozies in my time – race conditions on MP machines where a non interlocked increment occurred (one variant of Michael Grier’s “i = i + 1” bug) I could not find any info about that bug, anyone got a link or a source?
  - jerf 5y ago
    I assume that bug is referring to the fact that while i = i + 1 may look atomic to you as a human, in the computer it turns into Read i into register. Add one to that register. Write i back to the memory location. And there's a window during that "add one to the register" where you can obviously have something jump in and write something else to that memory location. What happens on your real processor is more complicated since this is going to relate to cache coherency between the processors, not directly writing RAM at that point, and that's a deep rabbit hole. I couldn't describe it all in detail anyhow. But I can observe it doesn't take much at all to turn that one cycle vulnerability into something with a larger target.
kbenson 5y ago
>> 18. A one-in-billion event will happen 8 times a month: https://gwern.net/Littlewood https://gwern.net/Littlewood > This one, on the other hand, I don't like. Depending on a whole bunch of subjective definitions, a one-in-billion event can happen a million times a second or practically never or whatever else you choose. I think this is about events happening to people, the number of people alive (and assuming they all communicate "miracle" occurrences"), and how many things they experience. That is, if I understand if correctly it's not that you can choose a random number between one and a billion and run a CPU to randomly check numbers in that range as fast as possible and get lots of results in seconds, it's that based one how we have roughly 8 billion people all communicating events that things we consider "one in a billion" occurrences will be experienced about 8 times a month across the populate, and we'll all pretty much hear about it, which may not match with our expectations of how often we should see a "one in a billion" event reported. Edit: Here's some relevant info from the paper "Methods for Studying Coincidences"[1]: The Law of Truly Large Numbers. Succinctly put, the law of truly large numbers states: With a large enough sample, any outrageous thing is likely to happen. The point is that truly rare events, say events that occur only once in a million [as the mathematician Littlewood (1953) re- quired for an event to be surprising] are bound to be plentiful in a population of 250 million people. If a coin- cidence occurs to one person in a million each day, then we expect 250 occurrences a day and close to 100,000 such occurrences a year. Going from a year to a lifetime and from the population of the United States to that of the world (5 billion at this writing), we can be absolutely sure that we will see incred- ibly remarkable events. When such events occur, they are often noted and recorded. If they happen to us or someone we know, it is hard to escape that spooky feeling. A Double Lottery Winner. To illustrate the point, we review a front-page story in the New York Times on a "1 in 17 trillion" long shot, speaking of a woman who won the New Jersey lottery twice. The 1 in 17 trillion number is the correct answer to a not-very-relevant question. If you buy one ticket for exactly two New Jersey state lot- teries, this is the chance both would be winners. (The woman actually purchased multiple tickets repeatedly.) We have already explored one facet of this problem in discussing the birthday problem. The important question is What is the chance that some person, out of all of the millions and millions of people who buy lottery tickets in the United States, hits a lottery twice in a lifetime? We must remember that many people buy multiple tickets on each of many lotteries. Stephen Samuels and George McCabe of the Depart- ment of Statistics at Purdue University arrived at some relevant calculations. They called the event "practically a sure thing," calculating that it is better than even odds to have a double winner in seven years someplace in the United States. It is better than 1in 30 that there is a double winner in a four-month period-the time between win- nings of the New Jersey woman. 1: https://www.gwern.net/docs/statistics/bias/1989-diaconis.pdf https://www.gwern.net/docs/statistics/bias/1989-diaconis.pdf
duxup 5y ago
16 is like the money hall problem. I understand the answer, the answer makes sense to me. And yet but when I think of it how I think of it initially ... it still makes no sense.
- pvg 5y ago
  The limit case can be helpful here, a strawberry made of 100% water can be dehydrated to practically nothing and is still made of 100% water.
  - adamleo 5y ago
    What you said makes no sense. If I'm only judged by how much money I have, then even if I have $0 I'm still a billionaire?
- machinelearning 5y ago
  The way to make sense of this is not to think about the water weight but the solid matter. By changing the proportion of water from 99% to 98%, you're also doubling the proportion of solid mass from 1% to 2%.
  - maweki 5y ago
    > you're also doubling the proportion of solid mass from 1% to 2%. And the final step is then, that the solid mass didn't change and therefore the liquid must be halved, instead of the solid doubled.
- lifeplusplus 5y ago
  For me the mistake was 1:1 relation between percentage and weight which didn't remain true after weight loss but I thought it did
- deleted 5y ago
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- silisili 5y ago
  Easiest for me if thinking only in fractions and percentages, and realizing that the dry mass is a constant. The obvious example is 99g water, 1g dry mass. Knowing that 1g cannot change, what do we need water to be to equal 98%? 49g.
Aerroon 5y ago
#16 is something video games taught me, particularly Path of Exile. In PoE resistance are a flat multiplier to incoming damage. Eg monster does 100 damage per attack and you have 60% resistance then you take 40 damage. The interesting thing is that the higher your resistances the more effective each additional percentage point of resistance is. Let's say a monster does 100 damage per attack. If you have 0% resistance and increase it to 5%, then your incoming damage went from 100 to 95. You take 5% less damage than before. If you have 75% resistance and increase it to 80%, then your incoming damage went from 25 to 20. You take 20% less damage than before. It is pretty unintuitive until you realize that you need to focus on the remainder rather than the other part.
- throwaway8451 5y ago
  OK, let's assume you have 75% elemental resistance. You also take 15% reduced damage and 10% less damage. You have 5% chance to avoid elemental damage and 10% to dodge it and are under the effect of Elemental Equilibrium and Gluttony of Elements. How much better is it to just kill everything before it can kill you?
  - BigJono 5y ago
    You joke, but PoE's use of stuff like 'increased/decreased' and 'more/less' to distinguish between additive and multiplicative calculations is one of the smartest game design decisions I've seen. The game has a lot of seemingly arbitrary distinctions and concepts that you just have to learn over time, but once you actually learn them, the consistency of it all makes it very easy to handle the large amounts of complexity in the game. It's completely unbearable going back to other games that just say crap like "+30% to x" without actually distinguishing between the different ways calculations can be done, forcing you to either experiment endlessly, look up every tiny thing on a community wiki, or just wing it. It's a nice contrast to something like WoW where every time you get a new item you just chuck the item code into some ten million LOC simulator and fuck around with limiting permutations until it doesn't take 15 minutes to run, just to find out through some totally opaque process that you have 189 more dps. And then 2 months later you find out there was a bug in the simulation and the item you deleted 1.9 months ago was actually better.
niklasbuschmann 5y ago
The strawberries remind me of the pricing of long-term bonds. Let’s say newly issued 100yr Treasuries pay a 1% coupon today, but tomorrow the coupon will be 2%, how much does the price of the older bond change? The answer is a near 50% loss, simply because this is required to bump the yield of the older bond to 2%. (If we include the discounted principal payment the exact answer becomes a 41.3% loss)
I_complete_me 5y ago
Here's my attempt to understand what's going on: 100g strawberry total weight where the 100% is made up of 99% water and 1% solid matter. 100g strawberry total weight where the 100g is made up of 99g water and 1g solid matter. 99/100 = 0.99 50g strawberry total weight where the 100% is made up of 98% water and 2% solid matter. 50g strawberry total weight where the 50g is made up of 49g water and 1g solid matter. 49/50 = 0.98

lotsofpulp 5y ago

>https://en.wikipedia.org/wiki/Potato_paradox https://en.wikipedia.org/wiki/Potato_paradox The Wikipedia link above says: > Fred brings home 100 kg of potatoes, which (being purely mathematical potatoes) consist of 99% water. He then leaves them outside overnight so that they consist of 98% water. What is their new weight? The surprising answer is 50 kg. It annoys me when mass is used interchangeably with force (weight), so I went to the Wikipedia source, and the source is accurate in using units of force throughout. https://web.archive.org/web/20140202214723/http://www.daviddarling.info/encyclopedia/P/potato_paradox.html https://web.archive.org/web/20140202214723/http://www.davidd... Wonder why the person that wrote the Wikipedia article changed it up when it is supposed to be a direct quote.

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jgtrosh 5y ago
In this situation, the mass and weight are proportional and irrelevant to the problem. Other than proper respect of units, why would it really matter? I would agree that using mass+kg would remain correct and be less unusual, but it doesn't matter a lot.
- lotsofpulp 5y ago
  It does not matter, it is just a pet peeve of mine. Might be due psychological trauma from when I was a kid and arguing with an older cousin about how pounds and kilograms are not units of the same thing, and the older cousin "winning" the argument in the eyes of the elders because the cousin was quite a few years older than me and considered to be smart in school.
  - version_five 5y ago
    From what I remember from intro physics, we distinguished between pounds and pounds force, the latter having the 32ft/s^2 multiplied in. And wikipedia seems to agree with me, see pound (mass) vs pound (force).
    - lotsofpulp 5y ago
      Oh wow, learning a lot today. I was taught in the US that pounds are a measure of force, and that is how it was always used in physics problems.
      - tharkun__ 5y ago
        As a European I learned in metric. When I first learned pounds, it was as the imperial system's equivalent of grams and a conversion factor was given. Force in physics class was taught in Newtons (kg*m/s^2).
        kergonath 5y ago
        Pounds as a mass unit are perverse enough. Things like pound force and psi (pounds per square inch) were used only to make fun of old mechanics papers and textbooks. Also, btu. It is quite amazing actually that someone would see the SI and think “no, too simple; I’ll keep my pounds, ounces, inches, and feet”. Anyway, yes, the proper unit of force is the Newton.
      - version_five 5y ago
mint2 5y ago
I really don’t like that example because it makes no sense. In no logical circumstance could the potatoes dehydrate so quickly when left out over a single night.
- tharkun__ 5y ago
  And they also don't consist of 99% water. That is why they called them "purely mathematical potatoes" and they could've chosen any type of fruit or vegetable. Heck, I'm just waiting for a car analogy now! Brake fluid anyone?
  - mint2 5y ago
    But that 99% water simplification is needed for the purpose of the exercise. The left out overnight is basically an absurd statement that is intended to confuse and not really related to the actual question. The statement could be “left in a dry environment until” or simply “left to dry a few weeks”
    - tharkun__ 5y ago
      You definitely could write that but it wouldn't change anything and you could make the same "argument" you are making now. "The left to dry a few weeks is basically an absurd statement that is intended to confuse" and it still wouldn't be true. It's not intended to confuse at all. It's intended to get the point across that you let this imaginary thing dry from 99% to 98%. They could've said "sponge" and let it out to dry any number of minutes. The point isn't to make a 100% accurate example of the drying properties of any actual 'thing'. They just needed something that people intuitively know "has water content" and that "can dry".
      - mint2 5y ago
        Wow by the downvotes I learned people react extremely negatively to any critique of math word problems. Spherical cows and 99% water potatoes are fine, those over simplifications are required for the analysis. Saying Leaving the potatoes out overnight to imply they halved in mass, sounds as reasonable as “the potatoes were in the ground for 12 hours and then doubled in amount, what percent of water are they now?” It’s so gratuitous and requires ignoring all other laws of physics, while the goal of the spherical cow type simplification is to only ignore a few key challenging ones.
syncsynchalt 5y ago
> Wonder why the person that wrote the Wikipedia article changed it up when it is supposed to be a direct quote. They likely changed it from lb to kg because that would be more friendly to an international audience, without realizing that lb is a measure of weight and kg is a measure of mass. Therefore they didn't know to change "weight" to "mass".
- lotsofpulp 5y ago
  Oh yes, that would make sense.
- kergonath 5y ago
  I have been to the US quite regularly, and been living in the UK for a number of years, and I have never seen someone using pounds as a unit of force instead of a unit of mass meaning roughly 500g, give or take. Second meaning was about 1.20€. FWIW, the pound is a proper unit of mass: https://en.m.wikipedia.org/wiki/Pound_(mass) https://en.m.wikipedia.org/wiki/Pound_(mass) .
  - syncsynchalt 5y ago
    I'm a civil engineer. In statute terms pound is the unit of force and slug is the unit of mass. That might have colored my thinking.
sbakzbsmx 5y ago
The difference between weight and mass is domain specific to physics. I actually get annoyed at people who are pedantic about these things. Precision is important in some conversations, but just elitist in other. Anyway, the term “weight” to refer to mass outdates its use as a force - its only since Newton that we distinguish the two, after all.
p1necone 5y ago
You're being overly pedantic (and I would argue actually incorrect). Kilograms and pounds are both referred to as "weight" in general conversation and nobody is going to be confused by this. Go to any supermarket in a country that uses the metric system, potatoes will be sold by the kilogram - it's the natural way to phrase this outside of America. In a physics context the definition of kilogram might be specifically mass, with newtons referring to weight/force. But words can have different meanings outside of technical contexts. If you go to a metric country, and ask someone how much they "weigh", approximately zero people will say "x newtons", they will say "x kilograms" (or "x pounds" still in a lot of commonwealth countries if we're being pedantic).
- p1necone 5y ago
  Although the more I think about this the more I think the difference between technical and colloquial is actually that "weight" in colloquial use refers to mass, because force is not commonly relevant.
  - eru 5y ago
    Yes, in colloquial use weight refers to mass _most_ of the time. But can also refer to inertia or mass. Or be used metaphorically.
  - jacobolus 5y ago
    "Weight" historically referred to mass, in common speech dating back forever. It’s the Germanic word which has been used throughout the history of English, whereas "mass" comes from Latin via French, like 5–6 centuries ago. The two words are almost exact synonyms, in historical/colloquial use. Both historically and today, a "pound" (Roman libra) is a unit of mass. People use a pound-force as a unit of force only in somewhat specialized contexts. At some point in the relatively recent past, someone (not sure who) decided that we needed to have 2 separate words for mass vs. force, and we should keep the Latin word for mass and use the Germanic word to mean force. Now pedantic people are constantly insisting that using the standard English word weight to mean mass is "wrong".
menotyou 5y ago
When I buy potatoes I am interested to buy 10 kg mass of potatoes, not the amount or potatoes of which has a gravity force of 98,1N. On mars you need to eat 10 kg of potatoes a week, not the amount of which has 98,1N gravity force. The scales in the supermarket on earth automatically convert the weight into mass for my convenience by applying a constant factor of 1/9,81. I am hardly far away enough from earth that the constant changed, so I did not need to distinguish between the two measures so far. When carrying the potatoes home I just use the mass of 10 kg as a proxy for the force I need. And to determine the increased breaking distance of my car, I need to know the mass again.

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pessimizer 5y ago

> > 16. If you let a 100g strawberry that is 99% water by mass dehydrate such that the water now accounts for 98% of the total mass then its new mass is 50g: https://en.wikipedia.org/wiki/Potato_paradox https://en.wikipedia.org/wiki/Potato_paradox >I really like this one. It's a perfect combo of intuitive from one perspective and mind bending from another. Comes up a lot lately because of vaccine effectiveness e.g. 95% is twice as effective as 90%.

xarope 5y ago
and sunscreen (SPF) calculations...
umvi 5y ago
Wait, how is 95% effective twice as effective as 90%?
- anandoza 5y ago
  It halves your risk.
- zbaxrl 5y ago
  90% is 1 in 10, 95% is 1 in 20.
- fgonzag 5y ago
  just as going from 98% effectiveness to 99% effectiveness halves your risk (you go from 2% chance of falling ill to 1%) its a common concept in games in which armor follows a linear formula (each point of armor is more effective than the last when calculating effective health)
  - anthk 5y ago
    Then there's the polynomial wizard.
sib 5y ago
It's probably more intuitive if you say that it's "half as ineffective"

nighthawk454 5y ago

Yes, it doesn't explicitly state the rate or distribution of events. But it is a good reminder of what happens when your whatevers/second are pretty high - see the famous "One in a million is next Tuesday" [1]. "Rare" is soon if you roll the dice fast enough. Any time your service has a high TPS, your API gets a lot of calls, a button in your app gets pressed a lot, ... this applies. Critically, "a lot" is defined relative to your failure tolerance. It may actually be very fast or a lot, or not particularly fast but it really really needs to work. It highlights the fallacy of equating "low probability" and "won't happen". [1] https://docs.microsoft.com/en-us/archive/blogs/larryosterman/one-in-a-million-is-next-tuesday https://docs.microsoft.com/en-us/archive/blogs/larryosterman...

IIAOPSW 5y ago
Or everyone's newest favourite, the virus randomly mutating is "rare".
leeoniya 5y ago
"Given the scale that Twitter is at, a one-in-a-million chance happens 500 times a day." https://www.ted.com/talks/del_harvey_protecting_twitter_users_sometimes_from_themselves/transcript?language=en https://www.ted.com/talks/del_harvey_protecting_twitter_user...
curiousgal 5y ago
> And I’ve seen some absolute doozies in my time – race conditions on MP machines where a non interlocked increment occurred (one variant of Michael Grier’s “i = i + 1” bug) I could not find any info about that bug, anyone got a link or a source?
- jerf 5y ago
  I assume that bug is referring to the fact that while i = i + 1 may look atomic to you as a human, in the computer it turns into Read i into register. Add one to that register. Write i back to the memory location. And there's a window during that "add one to the register" where you can obviously have something jump in and write something else to that memory location. What happens on your real processor is more complicated since this is going to relate to cache coherency between the processors, not directly writing RAM at that point, and that's a deep rabbit hole. I couldn't describe it all in detail anyhow. But I can observe it doesn't take much at all to turn that one cycle vulnerability into something with a larger target.

kbenson 5y ago

>> 18. A one-in-billion event will happen 8 times a month: https://gwern.net/Littlewood https://gwern.net/Littlewood > This one, on the other hand, I don't like. Depending on a whole bunch of subjective definitions, a one-in-billion event can happen a million times a second or practically never or whatever else you choose. I think this is about events happening to people, the number of people alive (and assuming they all communicate "miracle" occurrences"), and how many things they experience. That is, if I understand if correctly it's not that you can choose a random number between one and a billion and run a CPU to randomly check numbers in that range as fast as possible and get lots of results in seconds, it's that based one how we have roughly 8 billion people all communicating events that things we consider "one in a billion" occurrences will be experienced about 8 times a month across the populate, and we'll all pretty much hear about it, which may not match with our expectations of how often we should see a "one in a billion" event reported. Edit: Here's some relevant info from the paper "Methods for Studying Coincidences"[1]: The Law of Truly Large Numbers. Succinctly put, the law of truly large numbers states: With a large enough sample, any outrageous thing is likely to happen. The point is that truly rare events, say events that occur only once in a million [as the mathematician Littlewood (1953) re- quired for an event to be surprising] are bound to be plentiful in a population of 250 million people. If a coin- cidence occurs to one person in a million each day, then we expect 250 occurrences a day and close to 100,000 such occurrences a year. Going from a year to a lifetime and from the population of the United States to that of the world (5 billion at this writing), we can be absolutely sure that we will see incred- ibly remarkable events. When such events occur, they are often noted and recorded. If they happen to us or someone we know, it is hard to escape that spooky feeling. A Double Lottery Winner. To illustrate the point, we review a front-page story in the New York Times on a "1 in 17 trillion" long shot, speaking of a woman who won the New Jersey lottery twice. The 1 in 17 trillion number is the correct answer to a not-very-relevant question. If you buy one ticket for exactly two New Jersey state lot- teries, this is the chance both would be winners. (The woman actually purchased multiple tickets repeatedly.) We have already explored one facet of this problem in discussing the birthday problem. The important question is What is the chance that some person, out of all of the millions and millions of people who buy lottery tickets in the United States, hits a lottery twice in a lifetime? We must remember that many people buy multiple tickets on each of many lotteries. Stephen Samuels and George McCabe of the Depart- ment of Statistics at Purdue University arrived at some relevant calculations. They called the event "practically a sure thing," calculating that it is better than even odds to have a double winner in seven years someplace in the United States. It is better than 1in 30 that there is a double winner in a four-month period-the time between win- nings of the New Jersey woman. 1: https://www.gwern.net/docs/statistics/bias/1989-diaconis.pdf https://www.gwern.net/docs/statistics/bias/1989-diaconis.pdf

duxup 5y ago

16 is like the money hall problem. I understand the answer, the answer makes sense to me. And yet but when I think of it how I think of it initially ... it still makes no sense.

pvg 5y ago
The limit case can be helpful here, a strawberry made of 100% water can be dehydrated to practically nothing and is still made of 100% water.
- adamleo 5y ago
  What you said makes no sense. If I'm only judged by how much money I have, then even if I have $0 I'm still a billionaire?
machinelearning 5y ago
The way to make sense of this is not to think about the water weight but the solid matter. By changing the proportion of water from 99% to 98%, you're also doubling the proportion of solid mass from 1% to 2%.
- maweki 5y ago
  > you're also doubling the proportion of solid mass from 1% to 2%. And the final step is then, that the solid mass didn't change and therefore the liquid must be halved, instead of the solid doubled.
lifeplusplus 5y ago
For me the mistake was 1:1 relation between percentage and weight which didn't remain true after weight loss but I thought it did
deleted 5y ago
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silisili 5y ago
Easiest for me if thinking only in fractions and percentages, and realizing that the dry mass is a constant. The obvious example is 99g water, 1g dry mass. Knowing that 1g cannot change, what do we need water to be to equal 98%? 49g.

Aerroon 5y ago

#16 is something video games taught me, particularly Path of Exile. In PoE resistance are a flat multiplier to incoming damage. Eg monster does 100 damage per attack and you have 60% resistance then you take 40 damage. The interesting thing is that the higher your resistances the more effective each additional percentage point of resistance is. Let's say a monster does 100 damage per attack. If you have 0% resistance and increase it to 5%, then your incoming damage went from 100 to 95. You take 5% less damage than before. If you have 75% resistance and increase it to 80%, then your incoming damage went from 25 to 20. You take 20% less damage than before. It is pretty unintuitive until you realize that you need to focus on the remainder rather than the other part.

throwaway8451 5y ago
OK, let's assume you have 75% elemental resistance. You also take 15% reduced damage and 10% less damage. You have 5% chance to avoid elemental damage and 10% to dodge it and are under the effect of Elemental Equilibrium and Gluttony of Elements. How much better is it to just kill everything before it can kill you?
- BigJono 5y ago
  You joke, but PoE's use of stuff like 'increased/decreased' and 'more/less' to distinguish between additive and multiplicative calculations is one of the smartest game design decisions I've seen. The game has a lot of seemingly arbitrary distinctions and concepts that you just have to learn over time, but once you actually learn them, the consistency of it all makes it very easy to handle the large amounts of complexity in the game. It's completely unbearable going back to other games that just say crap like "+30% to x" without actually distinguishing between the different ways calculations can be done, forcing you to either experiment endlessly, look up every tiny thing on a community wiki, or just wing it. It's a nice contrast to something like WoW where every time you get a new item you just chuck the item code into some ten million LOC simulator and fuck around with limiting permutations until it doesn't take 15 minutes to run, just to find out through some totally opaque process that you have 189 more dps. And then 2 months later you find out there was a bug in the simulation and the item you deleted 1.9 months ago was actually better.

niklasbuschmann 5y ago

The strawberries remind me of the pricing of long-term bonds. Let’s say newly issued 100yr Treasuries pay a 1% coupon today, but tomorrow the coupon will be 2%, how much does the price of the older bond change? The answer is a near 50% loss, simply because this is required to bump the yield of the older bond to 2%. (If we include the discounted principal payment the exact answer becomes a 41.3% loss)

I_complete_me 5y ago

Here's my attempt to understand what's going on: 100g strawberry total weight where the 100% is made up of 99% water and 1% solid matter. 100g strawberry total weight where the 100g is made up of 99g water and 1g solid matter. 99/100 = 0.99 50g strawberry total weight where the 100% is made up of 98% water and 2% solid matter. 50g strawberry total weight where the 50g is made up of 49g water and 1g solid matter. 49/50 = 0.98