I'd say the same for oboe--if the teacher is not close to pro level on oboe. Bad oboe players are never moderately bad. I recall the pro oboist who sits in front of me having a bad day once. He didn't sound that bad, but he didn't sound pro either that one day--but you had to hear him every day to really notice something was off.

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Todd (Bowie, MD, US, North America, Earth, Sol System, Vega region, Local Bubble, Orion arm, Milky Way Galaxy, Local Group, Virgo A Cluster, Virgo supercluster, the universe in which spock is clean shaven)

Quidquid latine dictum sit, altum sonatur.

personal page: http://blog.astrosketches.info

At the conservatory we only studied our main instrument and had mandatory piano lessons. Only the people going into teaching had general instrument instruction.

However, nobody sits around in hundreds of hours of orchestra rehearsals without at least involuntarily picking up lots on how other instruments work. Even we brass players knew lots of the finer points of the strings' bowing technique, just from listening to what the conductors and concert masters told the string section to do. Not to mention exchanging instruments with friends just to try to get a noise out of them.

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Ach, mein Sinn, wo willst du endlich hin, wo soll ich mich erquicken? Bleib' ich hier, oder wünsch' ich mir Berg und Hügel auf den Rücken?
Bei der Welt ist gar kein Rat, und im Herzen steh'n die Schmerzen meiner Missetat, weil der Knecht den Herrn verleugnet hat.

Yes I know the damping is currently a waste. And the idea still has some potential. The damping could be provided by the 'armature reaction. of the generator. I was only using the initial understanding of a conservative force to demonstrate how maths moved me from a speculation to a deeper understanding.

The energy put into the system is available to be pulled out again electrically. But what about pre detection of a bump? The car's suspension could lift the wheel a little prior to impact saving the work of a greater portion of the whole car's mass impact via the wheel. Then there would not be as much energy available for damping/generating but a more efficient and comfortable ride. So the maths takes the initial idea (a good band aid) and raises it to a very good idea perhaps.

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"You can't talk to a brick wall but you can do Graffiti"

Was there math presented about this idea, in this thread?

That was my thought exactly. No math was presented in the thread.
The regenerative shock absorber idea was analyzed qualitatively, not
quantiatively.

A lot of things can be figured out without using any math at all.

-- Jeff, in Minneapolis

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http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

You are confusing mathematics with arithmetic.

Very little has been discussed without mathematics (except music). There has been little use of arithmetic and specific numbers, but there has been quite a bit of discussion of and application of mathematical theorems. Applying conservation of energy, qualitatively is an application of mathematics.

Mathematics is quite a bit more than "finding the answer" to some equation. Mathematics is about inequalities, topological structures, geometry, ....

There are entire books, rather advanced books, written on the qualitiative theory of differential equations, for instance, and that is how one handles problems like stability. There are more problems that are not completely solvable than problems that are, but that does not stop one from applying deep mathematics to understand features of those problems -- in fact this sort of thing is what modern mathematics is all about.

Thank you DrRocket my thoughts exactly! I think also my intent has been misunderstood. The shock absorber idea was only an example of how I had used my understanding of the maths to get somewhere better. My post was not about the idea itself. If I start doing the arithmetic I might begin designing the system but that would be inappropiate here. I took for granted that the calibre of those on this forum who like to see the math had a similar veiew to that of DrRocket. I.e. I should be able to assume that we all undrstand that the ennergy of a spring system is the intergration of F.dr and that when x1=x0 there has been no change of energy. Of course a real system will have had some energy put in for however many cycles and will have to lose it via heat, sound, or perhaps electricity.

Now that last sentance has been put in to stop those who could 'pounce' on the flaw.

I wonder if perhaps Tommac had a point with "How much do I need to know?" Perhaps it is a case of how much you all need to know of what I know before you have a level of trust?

Many papers make similar assumptions of their readers. Remember if I started throwing figures into my statements I prove nothing but a single case. See now I am assuming the worst of the knowledge level of other readers. We should, i think assume the best of anyones level here until they prove otherwise. I mean car suspension is hardly ATM . Perhaps if I start saying I can run the car forever on the energy derived from the suspension THEN ask me for the maths...OK?

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"You can't talk to a brick wall but you can do Graffiti"

Here's something else to think about while pondering the question, "What good is math?"

Well, for one, our computers, monitors, and networks would be utterly impossible without math, to the point where we wouldn't be having this conversation, at least not over the Internet. Everything from the complex shrinkage patterns that result when the plastic frames surrounding your monitors cool after they're released from the mold, to the complex interactions of the millions of nodes within the various PCUs and other integrated circuits in your computer, monitor, network card, printer, router, etc., all require math, both to be understood, but also to design and manufacture!

No math --> no computers.

I find it interesting in that even the earliest computers, such as the Antikythera mechanism (c. 150-100 BC), the equitorium ((1015 AD), the castle clock (1206 AD), and Wilhelm Schickard's calculating machine (1623) all required math for their design and constuctrion. Indeed, John Napier's observation that multiplication and division could be done by adding and subtracting the numbers' logs lead to his Napier's bones, a device he used in the production of his logarithmic tables.

Through the 1800s, however, all of these machines were based on the relatively simple maths of addition, subtraction, multiplication, division. Babbage's Difference Engine took these a step further, as it could do more than multiply and divide. It solved polynomials, which are approximators of logarithmic and trigonometric functions.

Notice how there's a lot of mathematical terms, here? And our timeline is still half a century before the Civil War!

About the time Babbage was working on the design for his difference engine, Charles Xavier Thomas created a successful mechnical calculator capable of adding, subtracting, multiplying, and dividing. That was nearly 200 years ago, and many followed, remaining in use throughout the 1970s, and even into the 1980s, as mechanical cash registers. I know, as I used one, a rather elaborate and powerful one, complete with pull-handle as a source of its computational energy, in the early 1980s! Other uses of these machines include the Mark I Fire Control Computer used throughout World War II.

The earliest digital electronic computers used vacuum tubes, which were designed using math. The knowledge for designing magnetic tape (indeed all magnic storage devices) requires advanced mathematics. Error-detection and correction, critical in all applications of modern computing, require different branches of mathematics, as does encryption.

So where would we be without math? At best, discussing a need for math over scones and tea at a local pub. More than likely, however, we'd be under a mud-walled, thatched-roofed hut somewhere in a forest.

But this isn't the issue in my mind. tommac thinks that he can have a great understanding of physics without math.

Sure someone, like me, can learn a few pieces of music without the underlying theory. They'll never master the field and in many cases won't even understand most of it. While there will always be savants that don't need to learn underlying principals in a given area we should not use that as a rule to not learn.

Music is probably a bad example because most people have a good enough ear to appreciate good music. Physics isn't always intuitive. Probably why we don't see idiot savants in the fields of things like particle physics.

I can play a handful of songs on the piano quiet well but I can assure you that I wouldn't claim to have any real understanding of music as a whole beyond "knowing what I like". The songs I can play sound good and to me, and my friends, when I play them they also sound good. I'm sure that if someone with real training in music came along and heard me play they might cringe a fair bit.

3000 BC--math needed to design and build the pyramids. You could make and use levers without math, but to plan in advance how big a lever you need to do a certain job....nope. To plan much of anything, for that matter, you need math. Cities could not exist without math. The earliest cities had to take into consideration inflow of food and water and outflow of waste.

Trade without math means the other tribe that has math will get rich off the suckers who can't do accounting.

Given natural selection, this seems to imply a law of nature:

If a species can develop math, it will.

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Todd (Bowie, MD, US, North America, Earth, Sol System, Vega region, Local Bubble, Orion arm, Milky Way Galaxy, Local Group, Virgo A Cluster, Virgo supercluster, the universe in which spock is clean shaven)

Quidquid latine dictum sit, altum sonatur.

personal page: http://blog.astrosketches.info

This reminds me of one of the most, um, interesting things I've ever seen online. A poster on another forum went off on a rant about how math should be banned and no one should ever have to learn it. This rant about how useless and inconvenient math is was made on an internet forum using a computer. The sheer ignorance in that post is still mind boggling.

And we'd have to barter for it, since the cashier couldn't make change.

Good point. Much of the reason why the Medici family managed to amass so much wealth and power is that the dynasty's founder is the guy who introduced double-entry bookkeeping to Florence.

I wonder though if the average level of wealth of forum members with some mathematical competence is higher than those with lower mathematical prowess? Anecdotaly I doubt it.

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"You can't talk to a brick wall but you can do Graffiti"

You can read books for the layman, like those written by Brian Greene on string theory, and manage to gain some understanding about what the theory claims, without having a knowledge of math.

However, in order to say "I don't believe it", or come up with an ATM theory contesting say, Quantum Mechanics, you need to have a solid mastery of math to both understand it and to formulate the ATM theory.

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“He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever”
Chinese proverb
"All you need in this life is ignorance and confidence - and then success is sure." - Mark Twain.

Not that this has much to do about this threads subject... but I agree with Sirius0... Money and your brains efficiency are not a given... Its who you know and what doors that you open... life's like that...
As to the subject at hand... Yes mathematics, arithmetic, algebra, calculus. are very important... so is spelling...
and I can't get that right all to often. You can not avoid these things. They are facts. That in this society we need to be educated. A working knowledge, or at minimum a understanding of basic arithmetic and language skills will assist you in your life. Some very clever people have designed the modern cell phone, computer, mp3, gps and and all those must have objects. None of them are possible without a great deal of math.... If you are not an achiever and can live with lower levels of income or stability. Then follow this no math path... but. Be warned. Its a rocky path.

Or... you can let some other cleaver clogs do all your math for you. I have noted a trend for that to happen.
You can get by on very little actual application of mathematics. A good general knowledge can get you through. With maturity will come the realisation that. You could have done better.... if only you stayed switched on at school.

I agree. Having spend some miserable years coaching teenagers in maths who clearly had no mathematics braincells at all, I have concluded that the vast majority of our society can manage quite well with basic arithmetic only.

The only aspect of maths which ever comes into the lives of most people is in connection with mortgage payments, and the banks do this calculation anyway, with virtually no customer really understanding it.

The problem these days seems to me to be a failure even to train people in basic arithmetic. I have just this minute returned from a shop having bought an item for 11.15 euros. Not having a 10 euro note, I placed 21.15 euros on the till, waited for the cashier to fiddle with his calculator, and he finally gave me something like 7.56 euros change. I challenged this, but he was puzzled because I disagreed with his calculator.

I think the pocket calculator has had a disasterous effect on the ability of the general public to be able to cope even with the simplest of calculations. They should be banned from schools.

In my opinion banning calculators in schools would be a mistake, but it would be appropriate to occasionally give a test where calculators, slide rules and abacus were not allowed, to make sure the students were not over dependent. I typically use a calculator to confirm the mental estimate or manual calculation. When they disagree significantly, I try both again. Failing that, I try a different approach or order of steps. Neil

Maths as used in the natural sciences is reductionist. Equations always have to make simplifying assumptions and assume this that and the other are negligible. An equation is an attempt at a model, usually derived long before the age of computer models.

I believe the maths as used in physics/chemistry courses represents a certain psychology of looking at the world, one that will slowly be replaced.

That's nonsense. Your anecdote there doesn't even support your belief...it was misuse of a calculator that caused the problem, not use of one. Forcing students to slog through pages of arithmetic by hand if they want to try an idea out only discourages exploration, reinforces the impression that math is boring, and teaches nothing about math.

That cashier apparently did not understand what he was putting into the calculator. As early as 3rd grade, meaning age 9, I would have seen instantly that the change would be exactly 10 euros (or whatever currency your country used in 1957). My teacher did an excellent job in explaining how the decimal system worked in doing multiple-column arithmetic.

The calculator is a two-edged sword. It eases the drudgery of crunching big numbers the old way, but it enables one to bypass the learning of techniques that are valuable error catchers. I think we should continue teaching kids how to do the arithmetic the old way, with periodic tests to make sure they do not forget, and to admit calculators for crunching big, messy numbers in applications.

Calculators have their place in the classroom, and there's nothing wrong with using them in appropriate situations. Your statement is overreacting.

There's a point at which forcing students to do all the calculation by hand is simply exposing them to the risk of losing points due to arithmetic mistakes in courses where arithmetic is really not what's being taught. That doesn't seem particularly fair. The fact of the matter is, arithmetic calculation is notoriously time-consuming and error-prone, which is the whole reason why people whose job is to do math have relied on calculation aids since more or less immediately after the dawn of time.

When I was taking linear algebra, for example, we did the entire exam in Mathematica and submitted our answers electronically in the form of a Mathematica notebook. This wasn't about giving us a crutch, it was because if the purpose of the exam is to make sure that the student understands the mathematical concepts involved then it's a stupid and useless waste of time to force them to do the thousands of calculations that might be involved in solving one of the exam questions by hand.

With what? ESP? A bunch of new age touchy-feelie holistic dogma?

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Microsoft is over if you want it.

The bar has been lowered for the promotion of ATM ideas; the bar for the acceptance of ATM ideas must remain high.

Yeah, this is basically the fallacy of the antecedent.

Calculators can work very well, but the important thing is to make sure people understand the structure of math. Once you understand the structure, you can figure anything else out.

I was never good at arithmetic as a kid. It wasn't until much later, when I learned why arithmetic works as it does did I get any good at it. And then I could figure out all by myself all the neat tricks to doing math in my head; adding to find change instead of subtracting, approximating results, adding 0 / multiplying by 1 to simplify, etc.

In fact, playing with calculators in middle school is what lead me to learn some of this structure (gods know it was not taught to me in school).

When I was in high school I got a TI-89, and that taught me a lot more algebra and complex number stuff and calculus than anything else until I read books about junior and senior college math classes!

Calculators can really enhance understanding and curiosity for students who're curious enough, or for teachers who're good enough to know to focus on big ideas and how those lead to specific calculations, rather than just making kids do menial problems, or thinking about things too abstract for them.

I taught arithmetic to calculus at a community college when I was 16, at a "study center" where students could learn stuff on their own from books, watch taped lectures, or talk to us, and then take tests that we'd grade for them (so more involved than a TA/tutor, but less than an instructor).

Teaching there, where most students were in their mid 30s, was really interesting. A lot of the students there really liked me, because I was one of the only people who would talk about thinking about how to solve the problem, instead of just applying rules without thinking. People who I saw really try to do the former did really well, and people who did the latter would be solving "2x+1=3" for practice, take a test, turn it in blank, then complain that nothing like "-2x-1=-3" was in the assignments. (Well, they also liked be because, as I was told / overheard several times, "if that kid can do this, so can I!")

But reading most books, they tend to focus not on thinking about structure or ideas, but about solving specific problems over and over again, which is really sad. Not that problems aren't helpful, but they're hardly everything.

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This isn't right, this isn't even wrong.
- Wolfgang Pauli

What has that to do with anything? Someone I know suggested that the true value of a school was judged in how much its graduates made, suggesting five years down the line as a starting point. Well, of course, my alma mater turns out a lot of teachers and so forth, and of course med school students haven't even finished school five years after graduation with a Bachelor's. And I expect a lot of people with higher "mathematical competence" ("prowess" and "competence" are very different things) are also doing what they love, not to mention that which benefits society, no matter what they're making.

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Gillian

"Now everyone was giving her that kind of look UFOlogists get when they suddenly say, 'Hey, if you shade your eyes you can see it is just a flock of geese after all.'"

"You can't erase icing."

"I can't believe it doesn't work! I found it on the internet, man!"

Completely disagree. Sorry!

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"Science is physics and astronomy." -Me
"There is absolutely no law in physics that prevents time travel." -Dr. Michio Kaku

Of course it is, and the anecdote shows it. But a student will always choose the path of least resistance, so if he has a calculator he will use it for the simplest calculation. I have seen it time and time again. The misuse cannot be controlled. Do you think that it is acceptable for a child to use a calculator to multiply 6 by 7? I've seen it many times.

The calculator also prevents the child from gaining a feel for numbers. I have experienced asking a child I was coaching the product of something like 6 and 7 and getting an answer like 698.4563, because there is no feeling for the impossibility. You cannot restrict the use of calculators without banning them.

Yes, this is why kids always lay comatose in bed all day, instead of doing difficult things, like sports, computer games, or socialization.

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This isn't right, this isn't even wrong.
- Wolfgang Pauli

I agree with the general feeling on this thread that simply banning calculators misses the opportunity they present. Your objections to them are certainly valid as far as they go, but your conclusions about the source of the problem may miss the mark, and so your solution may not be the best one. Indeed, behind every problem there is an opportunity to use that problem for some good purpose.

For example, it's not very clear to me that memorizing multiplication tables is that much different than learning to use a calculator, so to me, the problem with 6 X 7 = 42 is not so much the method used to solve it, but rather, the lack of understanding what it means. It's true that you'll always have your brain, and you won't always have access to a calculator, but I echo cfgauss' point that math is above all a way of thinking about things, and neither memorizing multiplication tables, nor using calculators, by itself can substitute. It's nice to know the tables, it's nice to have a calculator, but neither are mathematics. Perhaps the problem you allude to is actually an entry point to address this much more important lesson?
Why isn't that anecdote a perfect opportunity to teach the feeling for that impossibility? Note that memorizing a multiplication table also doesn't teach rules about how numbers have to work, unless you take the next step and notice things about the numbers you are memorizing. The same "next step" can be applied to using calculators too. So the problem is not the calculator, it is the way we teach people to use them-- we say, "here, take this, follow these steps, and you won't have to think". The exact same attitude can be taken with memorizing multiplication tables, with the same bad outcome. It's all an entry point for learning a lesson about what a calculation is, that transcends the medium for performing the calculation.