Dominion Strategy Forum
Miscellaneous => General Discussion => Topic started by: Kuildeous on January 25, 2014, 06:51:29 pm
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I have to shake my head sometimes. I saw someone post on Facebook that there is a 40% chance of snowstorms. Sure enough there are snowstorms that day. He wondered lamentedly why couldn't he have such great luck with the lottery.
I'm going to tell him that the snowstorm just needed a 13+ for its saving throw. That should remind him that 40% is not that unlikely.
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This is less an issue with maths and more that people are just naturally VERY bad with probability.
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The amount of people that answer 7 – 4 + 3 x 0 + 1 (http://forum.dominionstrategy.com/index.php?topic=3437.0) incorrectly (and other similar order of operations problems) still amazes me.
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The amount of people that answer 7 – 4 + 3 x 0 + 1 (http://forum.dominionstrategy.com/index.php?topic=3437.0) incorrectly (and other similar order of operations problems) still amazes me.
It doesn't help that most people don't know BIDMAS (or BODMAS, or PIDMAS/PODMAS which I think you Americans prefer) should actually be applied as B I (DM) (AS), not B I D M A S. This only really matters for addition/subtraction problems, such as 7 - 4 + 3 (=6) as you do the addition/subtractions in the order written, not addition first.
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The amount of people that answer 7 – 4 + 3 x 0 + 1 (http://forum.dominionstrategy.com/index.php?topic=3437.0) incorrectly (and other similar order of operations problems) still amazes me.
The fact that I originated that thread and this one indicates that I'm a really intolerant person.
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I have to shake my head sometimes. I saw someone post on Facebook that there is a 40% chance of snowstorms. Sure enough there are snowstorms that day. He wondered lamentedly why couldn't he have such great luck with the lottery.
I'm going to tell him that the snowstorm just needed a 13+ for its saving throw. That should remind him that 40% is not that unlikely.
Another thing you could mention is that it's more likely that you will die on your way to the lottery than it is for you to win it.
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The amount of people that answer 7 – 4 + 3 x 0 + 1 (http://forum.dominionstrategy.com/index.php?topic=3437.0) incorrectly (and other similar order of operations problems) still amazes me.
It doesn't help that most people don't know BIDMAS (or BODMAS, or PIDMAS/PODMAS which I think you Americans prefer) should actually be applied as B I (DM) (AS), not B I D M A S. This only really matters for addition/subtraction problems, such as 7 - 4 + 3 (=6) as you do the addition/subtractions in the order written, not addition first.
I never learned order of operations as one of those acronyms, and I speak out against those acronyms exactly for the reason you posted, Tables. They can lead someone to the wrong conclusion. When I learned order of operations, I was also taught that subtraction is really adding a negative number and that dividing is just multiplying an inverse. So, yeah, the acronym should really be BOMA or PEMA or some such. We need to teach kids that subtraction is not really different from addition.
Reason for edit: Can't arrange text for some reason.
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Reason for edit: Can't arrange text for some reason.
Perhaps a misleading acronym about the order to arrange text in would help?
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Strange, the acronym I learned was "BEDMAS" (E for Exponent), not BODMAS. Is the O for order or something?
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O stands for Orders [of power], yeah. It's either Indicies, Orders, Exponents as the second letter, and Brackets or Parenthesis first. And it always should have ended SA, not AS, if even used at all. But that doesn't roll off the tongue quite so well.
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Strange, the acronym I learned was "BEDMAS" (E for Exponent), not BODMAS. Is the O for order or something?
Meanwhile for me is wasn't an acronym but a mnemonic: Please Pardon My Dear Aunt Sally. (The second P was for Power.)
I was incredibly surprised to see acronyms with DMAS instead of MDAS because it instantly loses the parallelism of multiplication being repeated addition and division being repeated subtraction.
As always, though, order of operations can be decided entirely by parens; I don't actually know why we worry about order when any otherwise-ambiguous mathematical expression can be made unambiguous.
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(or BODMAS, or PIDMAS/PODMAS which I think you Americans prefer)
It's PEMDAS ;D
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Please Pardon Excuse My Dear Aunt Sally.
FIFY
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As always, though, order of operations can be decided entirely by parens; I don't actually know why we worry about order when any otherwise-ambiguous mathematical expression can be made unambiguous.
This. The whole "7 – 4 + 3 x 0 + 1 (http://forum.dominionstrategy.com/index.php?topic=3437.0)" thing is totally ridiculous to me because I feel like being ornery and putting parenthesis wherever I want just to make you wrong. No self-respecting mathematician would ever put a string of numbers and operations together like that without parenthesis. I also despise using the whole "x" symbol for multiplication, and that is another reason that the above problem was written by some pre-algebra student who was feeling clever but instead just displayed his own ignorance. When writing multiplication on a computer I always use * (unless I am using LaTeX or some other program)
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I kind of feel like expressions such as the one in the other thread don't really matter..... order of operations isn't really THAT important, worst comes to worst you use unnecessary parenthenses. You never really see silly expressions such as 7 - 4 + 3 x 0 + 1, and in general expressions represent something. e.i., the value of the expression is something else in the word problem your doing, or some real life application. If you knew how to translate the problem into an expression, you know what order it is supposed to be evaluated in. And in general, it is more clear because multiplication isn't usually represented by an 'x', it is quite often just nothing. Division isn't usually a line with dots above and below it, it's often just a horizontal line. In cases like this it is clear what order it is meant to be done in, because if the division line has something with operators in it on either the top or the bottom, obviously those are supposed to be evaluated first, and if it's something like x + y/z (except the line is horizontal), you aren't going to be adding x and y before dividing by z. For multiplication, if it's something like x + yz it is clear you are supposed to multiply first, and if it's z(x + y) it is clear you are supposed to add first.
So the point is that in practice, it doesn't matter a whole lot if you know the order of operations. Just don't write things ambiguously.
PPE: e pretty much nailed it. Heh, I would hope so, with a name like e.
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When writing multiplication on a computer I always use * (unless I am using LaTeX or some other program)
In non-TeX software, you can still insert a real multiplication sign with Alt-0215: × This is a pixel or so higher, and is rotationally symmerical, which the small letter "x" is not in most typefaces.
But yes, the 7 - 2 + 5 x 0 - 4 or whatever boils down to this:
(http://imgs.xkcd.com/comics/words_that_end_in_gry.png)
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Please Pardon Excuse My Dear Aunt Sally.
FIFY FTFY
FTFY
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man, there's an xkcd for everything.
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man, there's an xkcd for everything.
xkcd is a gift that keeps on giving. Well, it gives three days a week at least.
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As always, though, order of operations can be decided entirely by parens; I don't actually know why we worry about order when any otherwise-ambiguous mathematical expression can be made unambiguous.
This. The whole "7 – 4 + 3 x 0 + 1 (http://forum.dominionstrategy.com/index.php?topic=3437.0)" thing is totally ridiculous to me because I feel like being ornery and putting parenthesis wherever I want just to make you wrong. No self-respecting mathematician would ever put a string of numbers and operations together like that without parenthesis. I also despise using the whole "x" symbol for multiplication, and that is another reason that the above problem was written by some pre-algebra student who was feeling clever but instead just displayed his own ignorance. When writing multiplication on a computer I always use * (unless I am using LaTeX or some other program)
On a computer, I'll expect to see * for multiplication. Written, I'll sometimes just see a dot in midair for multiplication. Even better, 3(2+5) is understood to mean 3*(2+5).
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No self-respecting mathematician would ever put a string of numbers and operations together like that without parenthesis.
Depending on what you mean exactly with "like that", this is wrong. Of course, a mathematician wouldn't write this specific example, but there are enough examples which would be written without parentheses, because it's easier readable when you know how it works:
polynomials: a*x^2+b*x+c instead of (a*(x^2))+((b*x)+c) -- (*)
logic: ¬A∧¬B→C→D∨E instead of ((¬A)∧(¬B))→(C→(D∨E))
lambda calculus: λx.λy.λz.xz(yz) instead of λx.(λy.(λz.((xz)(yz))))
and there are other examples
So there is definitely a good reason to omit parentheses when it's clear what you mean. I agree with others that it's not important to memorize the order of operations at a young age, but it's not an arbitrary rule just made to confuse people, either.
(*) [okay, usually this is written as ax2+bx+c which makes it easier to see what the order of operations is, but still there can be examples when you prefer the first one, for example when you have to write pure ASCII (e.g. in a e-mail) or when you have variables which might consist of more than one letter, like in computer science]
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I have to shake my head sometimes. I saw someone post on Facebook that there is a 40% chance of snowstorms. Sure enough there are snowstorms that day. He wondered lamentedly why couldn't he have such great luck with the lottery.
I'm going to tell him that the snowstorm just needed a 13+ for its saving throw. That should remind him that 40% is not that unlikely.
That's a really good idea. There is a lot of psych and cognitive work out there showing people are really bad at interpreting percentages, but much better at interpreting the same information presented as frequencies. Percentages just aren't "natural". And compare that to winning the lottery is like rolling 20s on 6/6 dice in one shot.
Also, why was he lamenting that he WON the snow lottery?
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On a tangent, the percentage for the forecast isn't all that meaningful, anyway. The percentage chance of precipitation = percentage chance precipitation will form TIMES the estimated coverage area.
So, it could be that a 40% chance of snow means there is a 100% chance just the north side of town gets snow. If that's the way storms usually blow through town, and you live on the south side, then your personal forecast of snow could be a much lower number.
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On a tangent, the percentage for the forecast isn't all that meaningful, anyway. The percentage chance of precipitation = percentage chance precipitation will form TIMES the estimated coverage area.
Given a large enough area this would in many cases entail a violation of a Kolmogorov axiom.
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In the Netherlands I believe the rain percentage is based on this simple formula:
(Number of times it rained on days with similar conditions / total # of days with similar conditions) * 100%
I don't know exactly what they mean with "similar conditions", but they're probably looking at pressure, temperature and a few other things.
So if there is a 40% chance of rain, it just means that it out of every 10 days in the past with similar conditions, it rained on 4 of them. The Netherlands are small enough that we don't really need to factor in coverage area for our national percentages; we just take averages and it's close enough.
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man, there's an xkcd for everything.
xkcd is a gift that keeps on giving. Well, it gives three days a week at least.
Whenever Randall isn't sick.
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In the Netherlands I believe the rain percentage is based on this simple formula:
They might do something like that for collecting monthly averages etc, but the percentages they report as part of the forecasts go well beyond that.
Weather forecasts are in general made with extremely sophisticated models (actually simulators) that use a lot of local sensor data but also take into account very large-scale weather patterns. The probability of rain in Netherlands depends naturally on whether it was raining yesterday across the border but more generally also on the pressure distribution (and other things) around the whole Europe and large parts of the Atlantic, and all of these are factored into the numbers they report. The resulting predictions are dramatically more accurate than simply looking at what usually happens in "similar conditions".
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The Netherlands are small enough that we don't really need to factor in coverage area for our national percentages; we just take averages and it's close enough.
So I just looked up land areas; I don't think I'd ever realized how tiny the Netherlands is (are?). It's the size of Massachusetts, Connecticut, and Rhode Island together... three of the smallest states in the US.
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The Netherlands are small enough that we don't really need to factor in coverage area for our national percentages; we just take averages and it's close enough.
So I just looked up land areas; I don't think I'd ever realized how tiny the Netherlands is (are?). It's the size of Massachusetts, Connecticut, and Rhode Island together... three of the smallest states in the US.
You can drive top to bottom in about 3 hours.
And west to east in about 1.5.
So whenever I have to drive for more than 1 hour, it feels like a long drive while it's not uncommon for Germans (used to driving long distances) to visit our coastline, which is often a 2+ hour drive.
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The Netherlands are small enough that we don't really need to factor in coverage area for our national percentages; we just take averages and it's close enough.
So I just looked up land areas; I don't think I'd ever realized how tiny the Netherlands is (are?). It's the size of Massachusetts, Connecticut, and Rhode Island together... three of the smallest states in the US.
You can drive top to bottom in about 3 hours.
And west to east in about 1.5.
So whenever I have to drive for more than 1 hour, it feels like a long drive while it's not uncommon for Germans (used to driving long distances) to visit our coastline, which is often a 2+ hour drive.
I am just getting into stride after 2 hours on the road. To visit my parents from where I am right now is 17 hours. To visit my grandparents is 21 hours. I do have a brother that lives relatively close to me (5.5 hours). Getting to the beach is between 3-5 hours (depending on which beach I want).
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When writing multiplication on a computer I always use * (unless I am using LaTeX or some other program)
In non-TeX software, you can still insert a real multiplication sign with Alt-0215: × This is a pixel or so higher, and is rotationally symmerical, which the small letter "x" is not in most typefaces.
But yes, the 7 - 2 + 5 x 0 - 4 or whatever boils down to this:
(xkcd image)
I'm not convinced the statement of this "riddle" is grammatically ambiguous in any way.. it's merely wrong. Dude deserved to have his hand chopped off.
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Anyone ever read Nate Silver's The Signal and the Noise? He has a chapter on weather forecasting which is quite interesting. But the most interesting part of it for me was that most local weather reports purposefully overstate the chance of inclement weather as people are more likely to remember times when the report was for good weather and they got bad (ruining their picnic or whatever) than the opposite. So in order to make people feel more confident in the weather predictions, they purposefully give worse predictions. Aren't humans great!
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But the most interesting part of it for me was that most local weather reports purposefully overstate the chance of inclement weather as people are more likely to remember times when the report was for good weather and they got bad (ruining their picnic or whatever) than the opposite. So in order to make people feel more confident in the weather predictions, they purposefully give worse predictions. Aren't humans great!
True, it's generally advantageous for the forecaster to overstate the severity of weather.
Then there's this guy:
http://abcnews.go.com/WNT/story?id=130551
But that's clearly a case of the mayor not knowing how weather forecasts work.
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But the most interesting part of it for me was that most local weather reports purposefully overstate the chance of inclement weather as people are more likely to remember times when the report was for good weather and they got bad (ruining their picnic or whatever) than the opposite. So in order to make people feel more confident in the weather predictions, they purposefully give worse predictions. Aren't humans great!
True, it's generally advantageous for the forecaster to overstate the severity of weather.
Then there's this guy:
http://abcnews.go.com/WNT/story?id=130551
But that's clearly a case of the mayor not knowing how weather forecasts work.
Still not as bad as turning seismologists into criminals.
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So whenever I have to drive for more than 1 hour, it feels like a long drive while it's not uncommon for Germans (used to driving long distances) to visit our coastline, which is often a 2+ hour drive.
For me, the Dutch coast is closer than the German. But then, for me (as for ~35 per cent of the German populace) Brussels is closer than Berlin.
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So whenever I have to drive for more than 1 hour, it feels like a long drive while it's not uncommon for Germans (used to driving long distances) to visit our coastline, which is often a 2+ hour drive.
For me, the Dutch coast is closer than the German. But then, for me (as for ~35 per cent of the German populace) Brussels is closer than Berlin.
And for 100% of the US population!
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Edge Case: American ambassador in the Belgian embassy?
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Edge Case: American ambassador in the Belgian embassy?
Ambassador/Embassy seems like a nombo to me.
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Edge Case: American ambassador in the Belgian embassy?
Ambassador/Embassy seems like a nombo to me.
Not by themselves, but embassies are typically found in large cities, and ambassador/embassy/city would work quite well together.
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Anyone ever read Nate Silver's The Signal and the Noise? He has a chapter on weather forecasting which is quite interesting. But the most interesting part of it for me was that most local weather reports purposefully overstate the chance of inclement weather as people are more likely to remember times when the report was for good weather and they got bad (ruining their picnic or whatever) than the opposite. So in order to make people feel more confident in the weather predictions, they purposefully give worse predictions. Aren't humans great!
I really enjoyed this book. I'm glad that fivethirtyeight is starting up again this year.
Edit: It was more than that, jonts. The finding was the local weather reports overstated the chance of inclement weather when the forecasted chance was low. If the models predicted a 70% chance, they tended to report a 70% chance. But when the model predicted a 10% chance, they inflated it. Viewers don't internalize probabilities well. If they report a 10% chance of rain, viewers will think "the weather guy says it won't rain". If they report a 70% chance of rain, viewers will think "the weather guy says it will rain". If the weather model forecasts a 10% chance of rain, then 1 out of 10 days it really should rain.