I dropped my land line over ten years ago, and have never wanted it back. Occasionally I use skype, but only when someone on the other end wants to see my beaming face; the rest of the time it's my cell phone. Why would anyone pay for a land line? Is it because the voice quality is that much better? (My current phone is a Nokia, and the voice quality seems quite good, both send and receive.) Are there other reasons?
I call nonsense. I use my Windows phone, and believe me, I am quite familiar with Here maps, as I suspect anyone else who uses a Windows phone.
BTW, I find Here to be better than any GPS/navigation tool I used on my old Android phone, for the map download ability alone. My wife and I recently drove from Stuttgart to Lindau am Bodensee and back using Here and maps I downloaded before the trip. Given that I didn't have a cellphone plan in Germany, that (or a stand-alone GPS with maps for Europe) was about the only way we could have gotten around.
My experience is analogous to yours. We were required to take a foreign language in Junior High. I was assigned to take Spanish, and hated it. All memorization, no principles (I guess there was a principal...).
Then one day I saw a Spanish paradigm, probably the present indicative of hablar (a regular verb, happens to mean "to speak"). But not only was it the paradigm of hablar, it was the paradigm of every other -ar verb in Spanish. (There are two other conjugation classes, but -ar verbs are the majority.) I was astounded--it was *not* all memorization, there were rules! From that day I grooved on Spanish, figured out all the rules I could. And today I am a "fully papered" (to use your term) linguist, and my special interest is inflectional morphology (which includes paradigms).
BTW, there are lots of irregularities in Spanish verbs...but that was to come, and as it turns out, there are rules for the irregulars too.
I wonder how many kids there are out there who don't have this kind of ah-ha! experience, and who never find the sort of thing that they would be good at.
If you mean "half life", then it all depends. Half life of U-238 is on the order of 4 billion years; C-14, 5730 years; I guess I won't live that long. But half life of Pb-211 is just over half an hour. I'd like to think I have at least that long to live...
The tidal range at this location is two feet (http://tides.willyweather.com/fl/st-lucie-county/hutchinson-island-south.html), a long ways from 3 meters. OTOH, I think your estimate of top swimming speed for a diver is probably pretty good--that would be about 2 mph; I don't think an average diver could keep that up for long.
There's an aerial photo of the power plant, including the cooling lagoons, so you could estimate their surface area.
If he really got sucked in, and didn't intentionally swim in, then something more than tide is making the water flow that fast. I suppose there could be a pump pumping water out of the lagoon.
"Did you know 80 to 90% of the moderators on slashdot wouldn't recognize a troll even if one dragged them under a bridge." Would too! I saw one in Willow.
All seriousness aside, I do believe that understanding things _like_ (not limited to, of course) the concept of statistical significance is important for everyone. That is, we see things all the time like "the percentage of people in favor of candidate A went up by 0.5% last week," but there is often no indication of whether that change is statistically significant, and for most people I'd bet there's no understanding of what it means if the statistical significance is given. Same thing with climate research: "Year X was the Nth warmest year ever recorded"; but the statistical significance is seldom given, and if it is, most people probably ignore it. (5th warmest probably encompasses a range from 8th to 3rd at some level of significance; even "warmest" really means somewhere in the range of 3rd or 4th to 1st)
But IANAS (I Am Not A Statistician), so take my ideas for what they're worth. I just think such things are much more important for most people than knowing how to do integral calculus. And I think that probability and statistics are (or ought to be) fundamental to most real world debates these days.
Won't it? How much algebra do you really need to understand and work statistics problems--the kind of statistics problems that have real world relevance?
BTW, I think I agree with everything you said in your first post (well, I don't know enough to agree or disagree with some of it, but it certainly sounded convincing). And I agree that it would be better to fix those other things; but I was just hopeful that one could understand stats without much algebra.
Wow, and this dates all the way back to Noah: after the flood, he built a table out of logs left over from the ark, so the snakes could climb up on it and sun themselves, and thereby get warm enough to reproduce. That's right: Noah knew that even an adder can multiply if you give him a log table!
There is this thing called a "calculator." And before that there were things called "tables" inside other things called "books."
As for the description, of course it can be described without calculus, at an intuitive level. Someone needed calculus to fill in the tables, or to program the calculator; but you don't need it to use the calculator or tables.
At the risk of starting a flame war (not with you, with someone else), one place a misunderstanding of probability comes up is biological evolution. I've heard calculations of the probability that our DNA arose by chance which are wrong on so many levels. I've also heard the "it's too improbable that we arose by chance" argument, without any calculations. The next time I hear that, I'm going to ask them what the probability is that there will be at least two people in a room of 23 people who have the same birthday...
That calculation requires absolutely no algebra, just plug the # into the formula. Figuring out the formula did, of course, require some algebra (perhaps even calculus, since the rate of absorption varies over time). But the nurse or EMT or pharmacist doesn't need to derive the formula, just use it. (At least in the US, doctors probably don't even use the formula, they let someone else do that.)
"replacing one kind of complex math course with another semi-hard to graph math course that many people won't use isn't going to help much." I guess it depends on what you want to help. If help = increasing the number of people who pass math, I think you're right. But if help = giving people a tool that will actually be useful/ important for the rest of their lives, then my vote is for statistics.
Finance, yes, but statistics has IMO an almost equally broad and important impact. (And fwiw, I found algebra, calculus, trig etc. easy, but probability and statistics comparatively hard. So I'm not saying this because I liked statistics, au contaire!)
"Statistics are an important thing to understand (and I don't even know some of the more advanced statistics information) but I'm not sure that they can't be covered in some sort of critical thinking course - well enough to be functional and not needing to spend a whole year on the subject." I think you're right that critical thinking should be part of the curriculum (although I suspect it would indeed take at least a year).
But there are some statistical concepts that IMO should definitely be covered in such a course. Tests of statistical significance would probably be up near the top of my list; is a x% improvement (or "deprovement") important, or just random noise? You can't tell unless you have a measure of statistical significance, and it requires a bit of statistics to understand that concept. And you should also understand the limits of statistical significance measures, particularly where you throw a bunch of potential dependent variables into the mix and see which of them passes the statistical significance test: a no-no.
Also modeling: making explicit assumptions, and knowing how to test for their effects. For example, I've heard a lot of talk about declining SAT scores over the years. But unless you can model the effect of increasing participation (higher % of students taking SATs), you can't tell whether that decline is caused by poorer teaching/ less prepared students, or simply increased test taking by students at the lower end of achievement.
> you have to wade through a lot of algebra 2 just to get to [exponentiation]
No, you don't; in principle, you can multiply 1.02 (the 2% inflation rate of a post above here) by itself 35 times; no algebra 2 required. But these days you just plug it into a calculator.
"Another item that concerned me is the idea that coders don't need advanced math classes. Apart from financial calculations, anyone doing 3d graphics is likely to need matrix math and trigonometry." I do coding all the time, but I don't do 3d graphics, and I'd bet most coders don't. And even if I did, I'm pretty sure the algorithms are already available in libraries. At best I'd need an intuitive idea.
One can understand that at an intuitive level without being able to do integration by parts, or the reverse chain rule, or integration using trig identities, or any of the other arcana that I had to learn when I took calculus...and yes, forgot in the nearly fifty years since then, precisely because I never had to use it, or even think about it, after the final exam.
No, not necessarily simpler; different. I don't think statistics is any simpler than calculus, just different. I loved and excelled in math up through integral calculus (algebra I, algebra II, linear algebra, trig,...), but I could probably count on my fingers the number of times I've had to use anything more advanced than algebra I, and a very general understanding of trig. Statistics, otoh: I run into it all the time, and I wish I knew more. (I have had two courses in probability and statistics, but neither was terribly practical.)
So yes, I'd love to see them replace anything past maybe algebra I with statistics (except of course for mathematicians, engineers, and so forth). IMNSHO, nearly everyone would benefit from an understanding of things like statistical significance and statistical modeling. And it should be taught in a way that emphasizes real-world issues. (Example: if more students take SATs now than did ten years ago, and SAT scores are lower now than they were ten years ago, can we conclude that students are on the average "dumber"? How can we tell? Or along the same lines, what can SAT scores predict? Success in college, success in career, health,...)
He needs to qualify his statement: he's clearly looking for digital computers. The Navy (and for all I know other services) has long used analog computers (yes, with gears) for controlling their big guns; we had them on my ship, a DDG retired in 1992. I believe the last of the analog gunfire control computers were retired from the US Navy in the early 2000s, but I could be wrong.
I guess he was a bizarre man. There's an entire Wikipedia article on the topic: https://en.wikipedia.org/wiki/.... I haven't read the entire thing, but the consensus appears to be that he was at best opportunistic in his public statements about the church.
Slashdot Mirror
I dropped my land line over ten years ago, and have never wanted it back. Occasionally I use skype, but only when someone on the other end wants to see my beaming face; the rest of the time it's my cell phone. Why would anyone pay for a land line? Is it because the voice quality is that much better? (My current phone is a Nokia, and the voice quality seems quite good, both send and receive.) Are there other reasons?
what provider?
...and now I just need more hours in the day, so I can make my hippocampus grow more.
(It is a causal relation, right? :-)
http://www.rioranchomathcamp.c...
Not to this Windows Phone owner, so N -= N.
I call nonsense. I use my Windows phone, and believe me, I am quite familiar with Here maps, as I suspect anyone else who uses a Windows phone.
BTW, I find Here to be better than any GPS/navigation tool I used on my old Android phone, for the map download ability alone. My wife and I recently drove from Stuttgart to Lindau am Bodensee and back using Here and maps I downloaded before the trip. Given that I didn't have a cellphone plan in Germany, that (or a stand-alone GPS with maps for Europe) was about the only way we could have gotten around.
My experience is analogous to yours. We were required to take a foreign language in Junior High. I was assigned to take Spanish, and hated it. All memorization, no principles (I guess there was a principal...).
Then one day I saw a Spanish paradigm, probably the present indicative of hablar (a regular verb, happens to mean "to speak"). But not only was it the paradigm of hablar, it was the paradigm of every other -ar verb in Spanish. (There are two other conjugation classes, but -ar verbs are the majority.) I was astounded--it was *not* all memorization, there were rules! From that day I grooved on Spanish, figured out all the rules I could. And today I am a "fully papered" (to use your term) linguist, and my special interest is inflectional morphology (which includes paradigms).
BTW, there are lots of irregularities in Spanish verbs...but that was to come, and as it turns out, there are rules for the irregulars too.
I wonder how many kids there are out there who don't have this kind of ah-ha! experience, and who never find the sort of thing that they would be good at.
If you mean "half life", then it all depends. Half life of U-238 is on the order of 4 billion years; C-14, 5730 years; I guess I won't live that long. But half life of Pb-211 is just over half an hour. I'd like to think I have at least that long to live...
Of course, maybe your sig line is for real.
Dunno about the undead, but the dead tend to vote Democrat. At least that's how it used to be in Chicago.
The tidal range at this location is two feet (http://tides.willyweather.com/fl/st-lucie-county/hutchinson-island-south.html), a long ways from 3 meters. OTOH, I think your estimate of top swimming speed for a diver is probably pretty good--that would be about 2 mph; I don't think an average diver could keep that up for long.
There's an aerial photo of the power plant, including the cooling lagoons, so you could estimate their surface area.
If he really got sucked in, and didn't intentionally swim in, then something more than tide is making the water flow that fast. I suppose there could be a pump pumping water out of the lagoon.
"Did you know 80 to 90% of the moderators on slashdot wouldn't recognize a troll even if one dragged them under a bridge." Would too! I saw one in Willow.
Maybe I need a course in critical writing...
All seriousness aside, I do believe that understanding things _like_ (not limited to, of course) the concept of statistical significance is important for everyone. That is, we see things all the time like "the percentage of people in favor of candidate A went up by 0.5% last week," but there is often no indication of whether that change is statistically significant, and for most people I'd bet there's no understanding of what it means if the statistical significance is given. Same thing with climate research: "Year X was the Nth warmest year ever recorded"; but the statistical significance is seldom given, and if it is, most people probably ignore it. (5th warmest probably encompasses a range from 8th to 3rd at some level of significance; even "warmest" really means somewhere in the range of 3rd or 4th to 1st)
But IANAS (I Am Not A Statistician), so take my ideas for what they're worth. I just think such things are much more important for most people than knowing how to do integral calculus. And I think that probability and statistics are (or ought to be) fundamental to most real world debates these days.
Won't it? How much algebra do you really need to understand and work statistics problems--the kind of statistics problems that have real world relevance?
BTW, I think I agree with everything you said in your first post (well, I don't know enough to agree or disagree with some of it, but it certainly sounded convincing). And I agree that it would be better to fix those other things; but I was just hopeful that one could understand stats without much algebra.
Wow, and this dates all the way back to Noah: after the flood, he built a table out of logs left over from the ark, so the snakes could climb up on it and sun themselves, and thereby get warm enough to reproduce. That's right: Noah knew that even an adder can multiply if you give him a log table!
There is this thing called a "calculator." And before that there were things called "tables" inside other things called "books."
As for the description, of course it can be described without calculus, at an intuitive level. Someone needed calculus to fill in the tables, or to program the calculator; but you don't need it to use the calculator or tables.
Go down in your basement and trip all the circuit breakers. Or if you can wait longer, don't pay your electrical bill for six months.
Turning *on* the fan if the remote's batteries die...that's harder.
At the risk of starting a flame war (not with you, with someone else), one place a misunderstanding of probability comes up is biological evolution. I've heard calculations of the probability that our DNA arose by chance which are wrong on so many levels. I've also heard the "it's too improbable that we arose by chance" argument, without any calculations. The next time I hear that, I'm going to ask them what the probability is that there will be at least two people in a room of 23 people who have the same birthday...
That calculation requires absolutely no algebra, just plug the # into the formula. Figuring out the formula did, of course, require some algebra (perhaps even calculus, since the rate of absorption varies over time). But the nurse or EMT or pharmacist doesn't need to derive the formula, just use it. (At least in the US, doctors probably don't even use the formula, they let someone else do that.)
"replacing one kind of complex math course with another semi-hard to graph math course that many people won't use isn't going to help much." I guess it depends on what you want to help. If help = increasing the number of people who pass math, I think you're right. But if help = giving people a tool that will actually be useful/ important for the rest of their lives, then my vote is for statistics.
Finance, yes, but statistics has IMO an almost equally broad and important impact. (And fwiw, I found algebra, calculus, trig etc. easy, but probability and statistics comparatively hard. So I'm not saying this because I liked statistics, au contaire!)
"Statistics are an important thing to understand (and I don't even know some of the more advanced statistics information) but I'm not sure that they can't be covered in some sort of critical thinking course - well enough to be functional and not needing to spend a whole year on the subject." I think you're right that critical thinking should be part of the curriculum (although I suspect it would indeed take at least a year).
But there are some statistical concepts that IMO should definitely be covered in such a course. Tests of statistical significance would probably be up near the top of my list; is a x% improvement (or "deprovement") important, or just random noise? You can't tell unless you have a measure of statistical significance, and it requires a bit of statistics to understand that concept. And you should also understand the limits of statistical significance measures, particularly where you throw a bunch of potential dependent variables into the mix and see which of them passes the statistical significance test: a no-no.
Also modeling: making explicit assumptions, and knowing how to test for their effects. For example, I've heard a lot of talk about declining SAT scores over the years. But unless you can model the effect of increasing participation (higher % of students taking SATs), you can't tell whether that decline is caused by poorer teaching/ less prepared students, or simply increased test taking by students at the lower end of achievement.
> you have to wade through a lot of algebra 2 just to get to [exponentiation]
No, you don't; in principle, you can multiply 1.02 (the 2% inflation rate of a post above here) by itself 35 times; no algebra 2 required. But these days you just plug it into a calculator.
"Another item that concerned me is the idea that coders don't need advanced math classes. Apart from financial calculations, anyone doing 3d graphics is likely to need matrix math and trigonometry." I do coding all the time, but I don't do 3d graphics, and I'd bet most coders don't. And even if I did, I'm pretty sure the algorithms are already available in libraries. At best I'd need an intuitive idea.
One can understand that at an intuitive level without being able to do integration by parts, or the reverse chain rule, or integration using trig identities, or any of the other arcana that I had to learn when I took calculus...and yes, forgot in the nearly fifty years since then, precisely because I never had to use it, or even think about it, after the final exam.
Statistics, otoh, I see all the time.
No, not necessarily simpler; different. I don't think statistics is any simpler than calculus, just different. I loved and excelled in math up through integral calculus (algebra I, algebra II, linear algebra, trig,...), but I could probably count on my fingers the number of times I've had to use anything more advanced than algebra I, and a very general understanding of trig. Statistics, otoh: I run into it all the time, and I wish I knew more. (I have had two courses in probability and statistics, but neither was terribly practical.)
So yes, I'd love to see them replace anything past maybe algebra I with statistics (except of course for mathematicians, engineers, and so forth). IMNSHO, nearly everyone would benefit from an understanding of things like statistical significance and statistical modeling. And it should be taught in a way that emphasizes real-world issues. (Example: if more students take SATs now than did ten years ago, and SAT scores are lower now than they were ten years ago, can we conclude that students are on the average "dumber"? How can we tell? Or along the same lines, what can SAT scores predict? Success in college, success in career, health,...)
He needs to qualify his statement: he's clearly looking for digital computers. The Navy (and for all I know other services) has long used analog computers (yes, with gears) for controlling their big guns; we had them on my ship, a DDG retired in 1992. I believe the last of the analog gunfire control computers were retired from the US Navy in the early 2000s, but I could be wrong.
I guess he was a bizarre man. There's an entire Wikipedia article on the topic: https://en.wikipedia.org/wiki/.... I haven't read the entire thing, but the consensus appears to be that he was at best opportunistic in his public statements about the church.