But a lot of philosophy isn't right or wrong, much like art isn't right or wrong or literature isn't right or wrong, and yet I don't hear you decrying their practice.
There's been at least one of my rants on modern "art" on otd at some point I'm sure. It probably involved a chainsaw and a blowtorch. Otherwise I have nothing against making pretty pictures.
Literature I do have a problem with on the elementary/highschool levels. If its considered "literature" that's a fancy way of saying it bites and you're going to be bored. It turns people, especially boys, off to reading.
But neither of those are claiming to be a path to a higher truth (or if they are thats the point where I mock them mercilessly, *lifts philistine spear on high*) Philosophy (philosophers?) claim to be the ultimate arbiters of truth, going so far as to constrain how science is supposed to make its claims.
But really, this is a conversation for another thread :D
Just showing my consistency on the matter :K (gooey)
He believed that if a crop was exposed to cold enough climates, it would grow cold-resistant.
Actually, he might be right. Question is, how steep can the gradient of temperature per year be for the crop to acclimate?
Interesting comments. Still hate math with a passion. I'm surprised I don't injure one of my first friends just standing near him I hate it so much.
I've used Excel and programs like Access. It's been a long time, but I've set up complicated spreadsheets and databases. I would NOT be able to do the kind of work that Kirth does without explicit instructions. I wouldn't actually understand a lot of what I was doing unless I spent time looking up what it meant and trying to understand it. I can't do it because I don't know the math behind it.And, frankly, that's the issue and why formal math is needed, and the more the better.
Let's return to our little waitress word problem:
The management of a restaurant assigns each waitress between 7 and 15 tables. One waitress finds that when she is assigned seven tables, each table brings in $30 per week in tips. If she is assigned more tables, the amount of attention she gives to each table decreases. Thus, each table brings in less per week in tips. Suppose each additional table causes every table to bring in $2 less per week in tips. Use calculus to determine how many tables she should be assigned to maximize her weekly earnings from tips. Show or explain how you find each formula you use.I assume that she wants to be able to make as much money as possible, and do as little work as possible herself in figuring it out.
With basic arithmetic, she can figure out that if she has 7 tables, she will make $30/table in tips, for a total of $210. She can also figure out, as a separate problem, that if she has 8 tables, she will make $28/table, for a total of 8*28 which is a little more, and so on. But that's a lot of raw number crunching.
If she has algebra skills, she can figure out that she makes (7+x)(30-2x) dollars and can even set this up as a cell calculation in a good spreadsheet, so she need only type the numbers in and see which one gives her the most money. She's solving as many problems but they're easier to solve if you have the skills and more amenable to computational support.
With calculus, she can solve directly for the maximum of...
Note it becomes harder to use the spreadsheet if this can extend to tables that are not integers. As the number of possible points keeps getting larger. Calculus and computational tools are complements not substitutes.
For your edification[/url] a link to my school's forestry school. UW Madison's school of Wildlife Management was the first in the world and it was created (and headed) by none other than Aldo Leopold. It requires no math higher than basic statistics, algebra, and trigonometry. You've been had, sir.
Reasonable requirements AND cheese... why couldn't I have been born in Wisconsin?
As for the other thing, I guess I lucked out. I had a professor for Anthropology of Myth, Magic and Religion who was singularly awesome. Not only did he acknowledge temporal influence on religious thought, but his line of reasoning was that was ALL that it was: all religious thought is either a reaction to external stimuli or navel-gazing.
My Indigenous Lit teacher on the other hand: ** spoiler omitted **...
You're on a college campus. Pop some acid, grab some sculpty and mold what you see. Be sure to use a mobius strip. They'll probably think its a brilliant allegory of a slice of life of coming of age or something.
Or better yet, sculpt the story of your last pathfinder adventure and see what they make of it...
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There's been at least one of my rants on modern "art" on otd at some point I'm sure. It probably involved a chainsaw and a blowtorch. Otherwise I have nothing against making pretty pictures.
Literature I do have a problem with on the elementary/highschool levels. If its considered "literature" that's a fancy way of saying it bites and you're going to be bored. It turns people, especially boys, off to reading.
But neither of those are claiming to be a path to a higher truth (or if they are thats the point where I mock them mercilessly, *lifts philistine spear on high*) Philosophy (philosophers?) claim to be the ultimate arbiters of truth, going so far as to constrain how science is supposed to make its claims.
Of all the things I was forced to read in high school, there were probably 4 that I really liked: Lord of the Flies, Of Mice and Men, 1984 and Brave New World. And I liked them precisely BECAUSE they were a path to a higher truth. What literature and art do that is worthwhile is expose you to peoples' thoughts, both intellectual and emotional, that you would otherwise be geographically isolated from experiencing and helps you to learn empathy for people who are different from you when you are surrounded by people who are just like you. It broadens your horizons.
Philosophy is worthwhile in much the same way. I would not have had the courage to come out as an atheist if I hadn't read Nietzsche, because at the time my school and my social life were all within the "world" of the catholic church. Philosophy is about making arguments, and I found the arguments of Nietzche (as well as Anton LaVey and Harlan Ellison among others) re-christianity to be pretty convincing.
Philosophy doesn't claim to be the arbiter of truth, rather, as a discipline, is a kaleidoscope of lenses through which you can choose to view the truth. Only empiricism, which I've already said is the greatest school of philosophical thought, has any claim to be the arbiter of truth.
Nonetheless, yes, the march of scientific progress is constrained by philosophy such as ethics, in which it is argued that it is not right to use humans as guinea pigs. Also using ethics, it is being argued that it's no more right to use actual guinea pigs...as guinea pigs. What you see as this monolithic school of thought is really a cacophony of dissenting voices.
Philosophy IS debate.
He believed that if a crop was exposed to cold enough climates, it would grow cold-resistant.Actually, he might be right. Question is, how steep can the gradient of temperature per year be for the crop to acclimate?
Well, the environment-people have turned to epigenetics as their holy grail. Thing is, the problem is that the most studied part of epigenetics, the histone loops that "hide away" different stretches of the genome, does not deal with "new" genetic information. In practice, if you set your hopes to epigenetics, you had better hope that some of those seeds ALREADY have genes for cold resistance. If you want NEW genetic information, you will need to rely on new mutations. These take a VERY long time, likely on the scale of thousands of generations.
Reasonable requirements AND cheese... why couldn't I have been born in Wisconsin?
/snip
You're on a college campus. Pop some acid, grab some sculpty and mold what you see. Be sure to use a mobius strip. They'll probably think its a brilliant allegory of a slice of life of coming of age or something.Or better yet, sculpt the story of your last pathfinder adventure and see what they make of it...
1) I dunno man, it's pretty awesome though. Other than the current tectonic shift in politics *grumble*
2) I wish I had the hookup for some LSD. Regardless, since I've already transferred to the 4-year university, and the grade in this class will not have an effect on my GPA, I've decided that I'm going to do the minimum required to just pass.
The main argument for calculus in general education is procedural thinking, i.e. how to figure out an effective step by step process for doing thingsIts main argument bites because it does not in fact do this. It becomes a mindless exercise in translating one set of numbers by multiplying exponents by coefficients and dropping an exponent , or mindlessly plugging equations into that annoying to read f of the g of the f of the x and then trying to multiply them out without an error. There's no thinking going on there, its just a conscientiousness test.
Calculus can provide that, and in most universities today so can statistics and in many cases a computer programming course. In some universities, even algebra will work. The important thing, though, is to demonstrate the ability to deal rationally and procedurally with hard data.I have never seen data in a calculus class or a calculus textbook.
Man, that must have been a terrible Calculus class. It's starting to become clear to me that these views some people have on the subject are mostly due to awful Calculus teachers.
Man, that must have been a terrible Calculus class. It's starting to become clear to me that these views some people have on the subject is mostly due to awful Calculus teachers.
Two of them.
Can you give me a calculus I word problem?
Man, that must have been a terrible Calculus class. It's starting to become clear to me that these views some people have on the subject is mostly due to awful Calculus teachers.Two of them.
Can you give me a calculus I word problem?
Sure, from the top of my head:
A company is designing aluminum packages for one of its products. Each package should be able to contain 100mL of product and must have the shape of a cylinder. What should be the dimensions of the package in order to use the least amount possible of aluminum per unit?
Man, that must have been a terrible Calculus class. It's starting to become clear to me that these views some people have on the subject are mostly due to awful Calculus teachers.
The main argument for calculus in general education is procedural thinking, i.e. how to figure out an effective step by step process for doing thingsIts main argument bites because it does not in fact do this. It becomes a mindless exercise in translating one set of numbers by multiplying exponents by coefficients and dropping an exponent , or mindlessly plugging equations into that annoying to read f of the g of the f of the x and then trying to multiply them out without an error. There's no thinking going on there, its just a conscientiousness test.
Calculus can provide that, and in most universities today so can statistics and in many cases a computer programming course. In some universities, even algebra will work. The important thing, though, is to demonstrate the ability to deal rationally and procedurally with hard data.I have never seen data in a calculus class or a calculus textbook.
I Kee hearing that with respect to math in general.
I Kee hearing that with respect to math in general.
And yet, there are a number of people (who are not mathematicians or math teachers) who swear these topics are interesting and important.Usually, these people either managed to learn the topics by themselves or had the luck of having good teachers.
Being a good teacher is really hard, specially for such an abstract topic as mathematics. I think that better prepared teachers (with the correct career incentives) would be a huge step in the direction of changing this perception.
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I Kee hearing that with respect to math in general.Man, that must have been a terrible Calculus class. It's starting to become clear to me that these views some people have on the subject are mostly due to awful Calculus teachers.
The main argument for calculus in general education is procedural thinking, i.e. how to figure out an effective step by step process for doing thingsIts main argument bites because it does not in fact do this. It becomes a mindless exercise in translating one set of numbers by multiplying exponents by coefficients and dropping an exponent , or mindlessly plugging equations into that annoying to read f of the g of the f of the x and then trying to multiply them out without an error. There's no thinking going on there, its just a conscientiousness test.
Calculus can provide that, and in most universities today so can statistics and in many cases a computer programming course. In some universities, even algebra will work. The important thing, though, is to demonstrate the ability to deal rationally and procedurally with hard data.I have never seen data in a calculus class or a calculus textbook.
Are there subjects taught in school which don't get a bad repution from the very same reason? "No, dude, books are great, you must have had a terrible litreture teacher! besides, the way they teach reading in school makes you hate a subject that's actualy great!"
The only single thing that makes math stand out and call more attention to itself than the other classes is that math is *hard*. The ability to understand it and make all those abstractions is a rare one among humans, and even most of those who are capable of it often achieve it through a great deal of excersie. It's not about being smart or anything, it's just a specific skill, and if you don't have it learning math must feel like banging your hand against the wall. For this very same reason - math is hard - it's also harder to find teachers capable of teaching it well. The direct result of this fact is that most math teachers suck *hard*. I wal lately able to teach my younger brother everything he is expected to learn in math class this year, which puts him monts and months ahead of his class. He got it all easily. One day he returned home, and told me even though he already understood a certain subject, he had no idea what the teacher was talking about when she taught that subject. That didn't surprise me.
Math is hard => less people are good at teaching it + the same amount of math teachers are required as any other kind of teacher => math teachers tend to be really bad at their jobs.
To understand maths, you need to be able to hold a more than trivial number of abstract things in your head. This is what makes it difficult. To my thinking, the best way of dealing with it is programming. It is flat out the best way to practice that specific skill. If you do, you will find that even advanced maths are pretty simple to grasp.
Interestingly enough, one of the reasons that math is hard is that some of the basic functions aren't "natural" to human understanding. A few investigations into the subject of how people do math with zero formal training has suggested that humans naturally think in logarithmic functions.
Example: What is half the distance between 1 and 9.
Formal education: most people will answer with 5. 1+4=5 and 5+4=9, making 5 equidistant from 1 and 9.
No formal education: most people will answer 3. 1x3=3 and 3x3=9, making 3 equidistant from 1 and 9.
Example: Which two numbers are further apart: 1 and 2 or 8 and 9.
Formal education: both set of numbers are the same value apart, 1.
No formal education: 1 and 2 are further apart because 2 is twice as much as 1.
If we focused less on linear math training, people might find it easier to grasp. It seems counter-intuitive to most of us, but most people have also spent a life time learning and using linear math.
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I'd clarify that the WAY it's taught is generally stupid, because it leaves people unaware of what calculus actually is and can actually be used for. Calculus is all about rates of change. Teaching it as such underlines that life and the universe aren't just static things that sit around and wait patiently for us to decide to notice them. Things happen whether we watch them or not, and it's often VERY useful to know the ways in which they're changing, before they bite you in the ass.
If people actually knew what they could do with it, it would be useful for managers, financiers, shopkeepers, farmers, military leaders -- not just mathematicians and scientists. Instead, it's taught as if it were some kind of arcane symbology with no relation to real stuff, so people assume it has no real uses.
All that said, I'm a professional hydrogeologist. I need calculus. Please don't get rid of it!
OK calculus this set of formula descriptions...
1. Time is a consequence of continuous change in possibility.2. The Singularity is the moment of change in possibility.
3. The Universe is Debris of Change in possibility.
OK calculus this set of formula descriptions...
1. Time is a consequence of continuous change in possibility.
2. The Singularity is the moment of change in possibility.
3. The Universe is Debris of Change in possibility.
You've given me no boundary conditions. Am I supposed to pick them at random?
Man, that must have been a terrible Calculus class. It's starting to become clear to me that these views some people have on the subject is mostly due to awful Calculus teachers.Two of them.
Can you give me a calculus I word problem?
A landscape photographer is taking long exposure pictures.
To achieve a blue sky at night, the lens must recieve a luminous exposure of at least 1000 lux seconds. The current luminous emittance of the sky is 5 lux, but its rate of decay is <insert appropriate logrithmic formula> lux/minute. How long must the camera exposure be?The photographer wants the house in the picture to be lit up inside. To appear occupied, the windows must be between 8000 and 10000 lux seconds. Assuming each window produces 300 lux when the lights are on, how long must the lights be turned on durring the camera exposure?
The ambient light from neighbors homes creates 10 lux on a tree in the background. The photo will be washed out if the lux seconds exceeds 15000. What is the latest time the photographer can open his shutter before this light will ruin the image? How long is this exposure?
Every question here can be solved with performing a single integration and using the produced formula. It is a scenareo that I have personally dealt with. It is something photographers should understand, but don't necessarily need to worry about because they can use experience of what levels of lux will cause will cause issues with what exposures. But that baseline had to be developed.
For annother one:
A baseball is thrown from 1.5m above ground level at a 30° angle from the ground at a velocity of 25m/s. Assume wind resistance on the sphere is F=1/2pv^2CA, where F is the force of resistance, p is the density of air, 1 kg/m^3, C is the coeficient of friction, <given constant>, and A is the cross sectional area of the baseball. The baseball's diameter is .075m and weighs .15kg.
How far does the baseball travel?
Supplemental equasions if they have not also taken physics 1:
Force = mass * acceleration
Velocity = integral of aceleration with respect to time
distance = integral of velocity with respect to time
- I had roughly this question on my highschool physics AP exam.
Unfortunately I hadn't taken calculous yet so I had no idea how simple it was.
Can you give me a calculus I word problem?
The waitress who wants to maximize her earnings upthread is one.
Another -- possibly more cool but more challenging one is at
http://www.stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/up files/WebChallengeProblems_3C3.pdf
Specifically, problem 5.6. Summarizing, it's literally rocket science. A rocket that burns so-many kilograms of fuel per second has a specific set of performance characteristics.
How high is it at any point in time, and what's the maximum height it will achieve?
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Math is hard => less people are good at teaching it + the same amount of math teachers are required as any other kind of teacher => math teachers tend to be really bad at their jobs.
Not to mention
Math is hard => few people are good at it + many jobs use math + teachers generally aren't paid well => people who are good at math tend to take higher paying (non-teaching) jobs
A company is designing aluminum packages for one of its products. Each package should be able to contain 100mL of product and must have the shape of a cylinder. What should be the dimensions of the package in order to use the least amount possible of aluminum per unit?
V= pi r^2 H
100= pi* r^2* H
31.83=r^2 h
Excel values of H, get r, calculate surface areas, look at lowest surface area and i get
h=6mm
R= 2.3mm
I could add decimals in for more precision, but i'd imagine there's an upper limit
I don't know how to set the problem up in calculus. Its been a while.
Ummm... if you do go through the proper steps to get a general, exact solution, the height at minimum material use will be exactly twice the radius.
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A company is designing aluminum packages for one of its products. Each package should be able to contain 100mL of product and must have the shape of a cylinder. What should be the dimensions of the package in order to use the least amount possible of aluminum per unit?
V= pi r^2 H
100= pi* r^2* H
31.83=r^2 h
Excel values of H, get r, calculate surface areas, look at lowest surface area and i get
h=6mm
R= 2.3mmI could add decimals in for more precision, but i'd imagine there's an upper limit
I don't know how to set the problem up in calculus. Its been a while.
Surface area (SA) = 2*pi*r*h + 2*pi*r^2
Volume = pi*r^2*h = 100 cm^3h=100/(pi*r^2)
SA = 200/r + 2*pi*r^2
dSA/dr = -200/r^2 +4*pi*r set equal to 0 to find minimum
r=3√(50/pi) (cubic root) = 2.51...~= 2.5cm
h= 5.03... using exact value for r. 2.5cm results in 5.09... or ~5.1 cm.
Yeah, definitely not worth another semester of math.
V= pi r^2 H100= pi* r^2* H
31.83=r^2 h
Excel values of H, get r, calculate surface areas, look at lowest surface area and i get
h=6mm
R= 2.3mmI could add decimals in for more precision, but i'd imagine there's an upper limit
I don't know how to set the problem up in calculus. Its been a while.
Yeah, that's kind of what I mentioned above.
If [the waitress] I has algebra skills, she can figure out that she makes [formula] dollars and can even set this up as a cell calculation in a good spreadsheet, so she need only type the numbers in and see which one gives her the most money. She's solving as many problems but they're easier to solve if you have the skills and more amenable to computational support.
Basically, you're solving this problem over and over again, until you get an answer you like to a degree of precision you're happy with.
If you know calculus, you can solve the general form of the problem once and get an exact answer. (As Syssyl pointed out, the height is twice the radius.) This also helps if the company wants to make not only 100ml containers, but also 50ml, 200ml, and 500ml, because the same setup and formula generalizes.
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Just chiming in... I have never used the Calculus I learned, but eventually I did study far enough in music theory that I had to start applying trigonometry. Every pitch is really a sine wave with a frequency and an amplitude and you have to know how those relate.
(Fun fact: when you convert pitches to frequency [Hz], each octave is a doubling or halving in frequency, but when you use a 3:4 frequency ratio to go around the circle of fifths until you come back to where you started, the other intervals are not tuned properly. The science of tuning is about hiding this mathematical discrepancy, and there are lots of books written on the pros and cons of various approaches to smoothing out the extra Hz.)
There's nothing like studying two subjects so far that they eventually connect with one another.
Further reading: The Syntonic comma and the Quarter-comma meantone.
V= pi r^2 H100= pi* r^2* H
31.83=r^2 h
Excel values of H, get r, calculate surface areas, look at lowest surface area and i get
h=6mm
R= 2.3mmI could add decimals in for more precision, but i'd imagine there's an upper limit
I don't know how to set the problem up in calculus. Its been a while.
Yeah, that's kind of what I mentioned above.
If [the waitress] I has algebra skills, she can figure out that she makes [formula] dollars and can even set this up as a cell calculation in a good spreadsheet, so she need only type the numbers in and see which one gives her the most money. She's solving as many problems but they're easier to solve if you have the skills and more amenable to computational support.Basically, you're solving this problem over and over again, until you get an answer you like to a degree of precision you're happy with.
If you know calculus, you can solve the general form of the problem once and get an exact answer. (As Syssyl pointed out, the height is twice the radius.) This also helps if the company wants to make not only 100ml containers, but also 50ml, 200ml, and 500ml, because the same setup and formula generalizes.
It's also important to point out that small imprecisions can lead to large amounts of wasted material in large scale processes. And that this is one of the simplest problems calculus can help you with.
Yeah, definitely not worth another semester of math.
There is nothing that I did that isn't taught in the first week, assuming your calculous class isn't dumb and spend way too mcuh time on limits first.
.
The forced study of Calculus in school is stupid. No human ever needs to know
such things to live a happy productive life.
As a physicist, I disagree. ;)
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I noticed a few folks up-thread complaining similarly about Trig. Being a Professional Land Surveyor, Trig is perhaps my second most commonly used math (behind arithmetic).
You have a power line you need the sag elevation on to ensure trucks can pass safely onto a job-site. You locate the two power poles on either side of the entrance, the location of the entrance, and then turn a vertical angle from your observation point up to the power lines. You then compute the vertical height of the power lines by solving a tangent (in this case distance_to_crossing*tan(Θ) = height_of_wires). Foresters also use this very simple trig problem to determine heights of trees when they cruise timber to estimate sale yields.
When I'm mentoring our CAD techs and Survey Interns, I have to help them through visualizing things like coordinate geometry and triangle solutions. Once they've figured out what each part of their equations actually represents, their required maths become much easier.
I really think the biggest problem with the disdain of math comes from equations. You're expected to be able to memorize all these things like sin(A)/a = sin(B)/b or even Pythagorean, but the actual science behind what each constituent part of the equations are gets glossed over.
Yeah, definitely not worth another semester of math.There is nothing that I did that isn't taught in the first week, assuming your calculous class isn't dumb and spend way too mcuh time on limits first.
The sky is blue
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You've given me no boundary conditions. Am I supposed to pick them at random?OK calculus this set of formula descriptions...
1. Time is a consequence of continuous change in possibility.
2. The Singularity is the moment of change in possibility.
3. The Universe is Debris of Change in possibility.
Everything you need is there...
OK calculus this set of formula descriptions...
1. Time is a consequence of continuous change in possibility.
2. The Singularity is the moment of change in possibility.
3. The Universe is Debris of Change in possibility.
You've given me no boundary conditions. Am I supposed to pick them at random?
Everything you need is there...
Awesome and sneaky! Indeed, everything is there. The formula is one simple equation that requires over a hundred pages of math. Susskind has a two hour lecture on this in his cosmology course. It's also in his textbook on entropy.