Potato paradox • Hacker News Board

Re: Potato paradox

#121

Post by escherplex » Thu, Jul 16, 2015, 4:44 PM UTC

gwern wrote: post #106

philh wrote: post #75

Earlier quoted context omitted.

> it takes twice as much evidence to be 99% sure as it is to be 98% sure. Not twice as much evidence. Evidence needs to be measured logarithmically. (Otherwise you'd say it takes twice as much evidence to be 67% sure as 50% sure (2:1 versus 1:1), but the second takes no evidence at all for a binary proposition.) It takes twice as much evidence to be 99% sure as 91% sure. 98% to 99% is 17 decibels to 20 decibels, whic…

This paradox also helps illustrate why you might want to avoid percentages or 0-1 decimal probability in statistics - in some cases, the compression at the end of the range can mask very important phenomenon. (0.01% and 1% look almost the same as percentages or decimals, but can have different implications.) Particularly important if you're doing anything at the tails of the distribution, like thinking about how to i…

Good observations. Look at how much easier it would be to solve this version of the Martian potatoes problem which avoids percentages altogether:

Earth has developed an insatiable appetite for Martian potatoes with their tasty pulp. Yuki runs a successful manufacturing plant on Mars which synthesizes a product called 'Martian Instaspuds'; instant potatoes being more cost effective to ship. Now these red potatoes (it's Mars after all) are processed in lots of 100kg mass which consist of 1kg pulp to 99kg water, 1p:99w. For 'Instaspuds' this ratio must be reduced to 9p:1w. How much water must be boiled-off in solar powered kilns on the Martian equatorial surface to achieve this ratio?

1) posit the pulp mass remains constant at 1kg

2) x = end product mass; 9/10 x = 1kg; x = 10/9 kg; 1/9 kg = final water mass in resulting mixture

3) subtract

Re: Potato paradox

#122

Post by [deleted] » Thu, Jul 16, 2015, 4:50 PM UTC

chestervonwinch wrote: post #115

brobdingnagian wrote: post #49

Earlier quoted context omitted.

This is not an implausible basis with which to start a new list on Wikipedia. It is original research, but it will likely be let in.

"research" is a generous term :) I thought about it, but the qualification to be on my list is pretty subjective. I suppose though, it could be generalized to "ideas inspired by food in STEM fields".

[deleted]

Re: Potato paradox

#123

Post by DanBC » Thu, Jul 16, 2015, 4:55 PM UTC

JoshTriplett wrote: post #17

vecter wrote: post #13

Earlier quoted context omitted.

Although it's somewhat true, if you had started with 14 pounds of potatoes instead, I still think most people at first glance would expect the final weight to be around 14, not half of it.

I agree, but I suspect fewer people would make the mistake. Partly because more people would actually do the math, and partly because there's no immediately attractive wrong answer involving "98/100" and "100 lbs". There's still a somewhat attractive wrong answer of multiplying 98/100 by 14 lbs, but there's one less reason to make that mistake. This seems like the kind of thing that could be tested with a study. Ask…

Gerd Gigerenzer asks roughly similar questions of a wide range of people - mostly medical professionals. It's scary how wrong people are, especially considering that this is information they're using to medicate you or operate on you.

Here's an example from his book:

http://imgur.com/zO4zkl4

Gerd Gigerenzer Reckoning With Risk.

Re: Potato paradox

#124

Post by blacksmythe » Thu, Jul 16, 2015, 5:12 PM UTC

disillusioned wrote: post #43

mhartl wrote: post #36

Earlier quoted context omitted.

45 kg … and 9960 kg You mean 40 kg and 9960 kg (so the sum is 10000 kg)?

Annnnd just spent an hour reading that delightful Colin Percival Putnam thread. Thanks for the reminder on that. Man, people really loved to hate on Tarsnap because of his perceived arrogance.

  >> people really loved to hate on Tarsnap

On the contrary, Colin is highly regarded on HN both for his technical ability, and his success in business (despite breaking from conventional wisdom in how to be successful in business).

Re: Potato paradox

#125

Post by andrewstuart2 » Thu, Jul 16, 2015, 5:23 PM UTC

jfreax wrote: post #70

guelo wrote: post #65

I don't think a simple algebra problem should be called a paradox.

I think it's called a paradox (rightly), because it's not immediately intuitive for most people.

Agreed.

> par·a·dox A statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory.

Re: Potato paradox

#126

Post by vixsomnis » Thu, Jul 16, 2015, 5:41 PM UTC

calinet6 wrote: post #101

netcan wrote: post #89

Earlier quoted context omitted.

Naturally, if you can look at a program which is now twice as fast and be unimpressed you are looking at the wrong metric. It's understandable though in the context of the sequence of actions you might be going through as a tinkerer (as opposed to a scientist). You start with a list of functions and the % of time they take. Improving the top one will have the biggest effect, so this is a good thing to look at when de…

> Naturally, if you can look at a program which is now twice as fast and be unimpressed you are looking at the wrong metric. Or, a computer scientist would say, the right one. The actual speed doesn't matter as much as the complexity. In reality, it does, in the end; but it's also important to consider the type of optimization you're doing, and not just stop at being impressed with twice as fast. For example, a primi…

It's like grocery shopping and coupons, however. If you shouldn't be calling the function, then even a 99% reduction is not useful in that context.

Would you rather call a slow function, a fast function, or skip it altogether?

(A coupon only saves you money if you would buy the item in the first place.)

Re: Potato paradox

#127

Post by juliangregorian » Thu, Jul 16, 2015, 7:22 PM UTC

gjm11 wrote: post #117

perlgeek wrote: post #111

Earlier quoted context omitted.

"What's yellow, normed and complete? A Bananach Space"

Nice! Except it doesn't quite work for me because the vowel sounds don't match. (For me the second and third "a"s in "banana" are like the "a" in "arm", whereas the two in "Banach" are like the "a" in "at", and those are quite different sounds. Other people may differ -- and indeed I may be mispronouncing "Banach".)

As an American, I'll never understand how the English can indiscriminately throw /ɑː/'s into perfectly normal words, yet when faced with a foreign import that actually asks for it, willfully refuse.

Re: Potato paradox

#128

Post by ectoplasm » Thu, Jul 16, 2015, 7:42 PM UTC

calinet6 wrote: post #101

netcan wrote: post #89

Earlier quoted context omitted.

Naturally, if you can look at a program which is now twice as fast and be unimpressed you are looking at the wrong metric. It's understandable though in the context of the sequence of actions you might be going through as a tinkerer (as opposed to a scientist). You start with a list of functions and the % of time they take. Improving the top one will have the biggest effect, so this is a good thing to look at when de…

> Naturally, if you can look at a program which is now twice as fast and be unimpressed you are looking at the wrong metric. Or, a computer scientist would say, the right one. The actual speed doesn't matter as much as the complexity. In reality, it does, in the end; but it's also important to consider the type of optimization you're doing, and not just stop at being impressed with twice as fast. For example, a primi…

> Or, a computer scientist would say, the right one. The actual speed doesn't matter as much as the complexity.

Except, as an engineer would say, in practice the complexity doesn't matter as much as constant factors and the time and cost of design, implementation, and execution.

Re: Potato paradox

#129

Post by jjnoakes » Thu, Jul 16, 2015, 9:40 PM UTC

gjm11 wrote: post #117

perlgeek wrote: post #111

Earlier quoted context omitted.

"What's yellow, normed and complete? A Bananach Space"

Nice! Except it doesn't quite work for me because the vowel sounds don't match. (For me the second and third "a"s in "banana" are like the "a" in "arm", whereas the two in "Banach" are like the "a" in "at", and those are quite different sounds. Other people may differ -- and indeed I may be mispronouncing "Banach".)

Your banana is like arm?

Mine is like umbrella (the u).

Buh-nah-nuh.

Re: Potato paradox

#130

Post by hofstee » Thu, Jul 16, 2015, 9:57 PM UTC

calinet6 wrote: post #101

netcan wrote: post #89

Earlier quoted context omitted.

Naturally, if you can look at a program which is now twice as fast and be unimpressed you are looking at the wrong metric. It's understandable though in the context of the sequence of actions you might be going through as a tinkerer (as opposed to a scientist). You start with a list of functions and the % of time they take. Improving the top one will have the biggest effect, so this is a good thing to look at when de…

> Naturally, if you can look at a program which is now twice as fast and be unimpressed you are looking at the wrong metric. Or, a computer scientist would say, the right one. The actual speed doesn't matter as much as the complexity. In reality, it does, in the end; but it's also important to consider the type of optimization you're doing, and not just stop at being impressed with twice as fast. For example, a primi…

There is a sorting network called AKS which has O(log(n)) depth. Batcher's Odd-Even Mergesort has a depth of O(log^2(n)). Which is better?

In all cases where you can fit n in the total memory capacity of the earth, Batcher's network is vastly superior. Constants matter a whole lot more than you might think.

I'm not arguing against revising algorithms to look for better complexity classes, but if you rewrite your algorithm in a smaller complexity class you had better be sure that your constants are of reasonable size.