There is a tendancy to know what you need to know in the context of your task (proffession or hobby). I'm an accountant by profession. I've nearly always worked around engineers and scientists.
As trivial as the math in accounting is, I'm still surprised by how it often bamboozles people whose math ability in other regards is way beyond mine. Oddly, enough the breakdown seems to come most often in something very fundamental: a*(b+c)=a*b + a*c. When encountered in a building a department budget, balancing a checkbook or calculating tax liabilities a lot of people stumble on this concept even though in other contexts is is so hardwired that they don't even think about it.. Actually, most accountants stumble over it if you try to describe it algebraicly but utilize it in the own way many times every day.
A couple of years ago I had never heard of "Nyquist stability" or "dominant pole". At present I know why they are important to what I want to do (recreationally) and may struggle with the math but fully expect to learn enough to enable me to do what I want.
As trivial as the math in accounting is, I'm still surprised by how it often bamboozles people whose math ability in other regards is way beyond mine. Oddly, enough the breakdown seems to come most often in something very fundamental: a*(b+c)=a*b + a*c. When encountered in a building a department budget, balancing a checkbook or calculating tax liabilities a lot of people stumble on this concept even though in other contexts is is so hardwired that they don't even think about it.. Actually, most accountants stumble over it if you try to describe it algebraicly but utilize it in the own way many times every day.
A couple of years ago I had never heard of "Nyquist stability" or "dominant pole". At present I know why they are important to what I want to do (recreationally) and may struggle with the math but fully expect to learn enough to enable me to do what I want.
Jay, I can assure you that as someone with a California mortgage, a low-paying job with a start-up, and a 2 year old with an insatiable appetite, I'm not wealthy!
And I can assure you that I was once 17, and figured out the hard way that I needed to get math proficiency so that I'd stop flailing around and do something productive.
I spent enough years teaching technical subjects to youngsters that it was driven home to me that lack of proficiency in basic math was the number one cause of my students' problems. I rarely had a physics or chemistry student who failed because the physics or chemistry was too hard; the vast majority got hung up because they had to work so hard to do simple math that they had no capability to even start to think about the actual problem at hand.
And I can assure you that I was once 17, and figured out the hard way that I needed to get math proficiency so that I'd stop flailing around and do something productive.
I spent enough years teaching technical subjects to youngsters that it was driven home to me that lack of proficiency in basic math was the number one cause of my students' problems. I rarely had a physics or chemistry student who failed because the physics or chemistry was too hard; the vast majority got hung up because they had to work so hard to do simple math that they had no capability to even start to think about the actual problem at hand.
SY: the complete Pease story continous: "but with a little anti-freeze....."
The only problem I have with math it is when the level of abstraction gets so high that reality is lost, and the mathematics become the subject, not the description of the subject. I never got the hang of quantum mechanics or relativistic electrodynamics.
The only problem I have with math it is when the level of abstraction gets so high that reality is lost, and the mathematics become the subject, not the description of the subject. I never got the hang of quantum mechanics or relativistic electrodynamics.
Depends on the level to which you want to understand those logic circuits!
The word "complex" is unfortunate because it scares people. "Imaginary" is just as bad. But understanding complex numbers and their algebra isn't that difficult, and it makes the understanding of phase issues much simpler. Though I have to say that I buffaloed one of my math teachers in junior high when we were introduced to the concept of i (j to you engineering types); we were taught that i was the square root of one, and I innocently asked, "Well, then, what's the square root of i?" The blank look and rapid subject change was my introduction to how often public school teachers are poorly prepared in their supposed areas of specialty.
The word "complex" is unfortunate because it scares people. "Imaginary" is just as bad. But understanding complex numbers and their algebra isn't that difficult, and it makes the understanding of phase issues much simpler. Though I have to say that I buffaloed one of my math teachers in junior high when we were introduced to the concept of i (j to you engineering types); we were taught that i was the square root of one, and I innocently asked, "Well, then, what's the square root of i?" The blank look and rapid subject change was my introduction to how often public school teachers are poorly prepared in their supposed areas of specialty.
Math is mandatory if you are a designer in electronics. But it is just a handy tool and nothing else. If you finally know what it is all about and how to use it then you can say “Is that all there is”. Many people are stunned when they actually understand how it works and what it is all about. Stunned about the long way it took to discover how simple things sometimes are. But you have to go that long way sometimes to understand. But is understanding necessary to have fun with your hobby?
For DIY math can be handy, just as a ruler is for making your LS boxes. Without it you are indeed left to the math done by others for you. Or go the long way of “trial and error”. On disadvantage of “trial and error” is that you never know when your making become successful or at least converging. If it is, most time it is good luck. Math and deeper knowledge can be of help to keep on track, just like a map.
But many people can live quite happy without a map and find their way by asking other people. That's why there are forums. Nothing wrong with that.
And SY most teachers are bad teachers. Many do not fully understand what they are actually teaching. If you are a teacher you need to know and understand at least ten times more about the subject than what you actually want to teach IMHO. And knowing and understanding means not only theory but experience as well. Many teachers do have the theoretical knowing but they lack the experience of the practical implications of the theory. Not to mention the weak knowledge of the history of the subject they intend to teach.
For DIY math can be handy, just as a ruler is for making your LS boxes. Without it you are indeed left to the math done by others for you. Or go the long way of “trial and error”. On disadvantage of “trial and error” is that you never know when your making become successful or at least converging. If it is, most time it is good luck. Math and deeper knowledge can be of help to keep on track, just like a map.
But many people can live quite happy without a map and find their way by asking other people. That's why there are forums. Nothing wrong with that.
And SY most teachers are bad teachers. Many do not fully understand what they are actually teaching. If you are a teacher you need to know and understand at least ten times more about the subject than what you actually want to teach IMHO. And knowing and understanding means not only theory but experience as well. Many teachers do have the theoretical knowing but they lack the experience of the practical implications of the theory. Not to mention the weak knowledge of the history of the subject they intend to teach.
To have some fun with audio, it isn't necessary to know math. But to gain the deeper satisfaction of having done something on your own, something original and creative, then yes, you need it. And even more so when you're talking about a youngster, for whom the sky is the limit. Kids learn basic things faster and more easily than adults; audio can provide a perfect motivation for a youngster to crack down and do some real mental exercise which, though rewarding in the end, otherwise might be skipped over. As other have said, even though they don't use trigonometry in their daily lives, the process of having to learn it taught them a sort of mental discipline and logic which is universally useful.
Square Root of i
I managed to convince my high school algebra teacher that you actually needed yet another dimension for the square root of i.
But, I had long before become cynical about teachers:
My second grade teacher misspelled "February" on a spelling test.
In third grade we had a student teacher who thought there were 52 states in the USA: the 50 contiguous states plus Alaska and Hawaii.
I managed to convince my high school algebra teacher that you actually needed yet another dimension for the square root of i.
But, I had long before become cynical about teachers:
My second grade teacher misspelled "February" on a spelling test.
In third grade we had a student teacher who thought there were 52 states in the USA: the 50 contiguous states plus Alaska and Hawaii.
Again I don't agree. It seems an obsession this mathematic subject. A hobby is a hobby and I don't see the absolute need to study and study and not having time to actually build something. Life is short enough already.
When you need to calculate you grab a book and search for the needed formula and calculate what's needed. If a hobby should be as fanatical as you seem to describe it I would quit and start reading a book or learn to cook.
Ever thought that studying and wanting to know everything at a high level of your hobby ( including math ) make that it isn't a hobby anymore ? More like your everyday job...
I loved to learn languages for a hobby once because it broadens one's horizon in a great way and with the fifth language my fanatism and perfection actually created so much stress that I simply quit learning them. It wasn't fun anymore.
It is something else when one wants to be or is learning to be an engineer IMO.
Straw man, Jean-Paul. Or should I say, "un homme en paille"? Who says that you should spend so much time studying something that you don't have time to build? Not me.
Formulae in books have their uses, but typically, the one you need for a given problem isn't there. or you don't have theright book available. Or the book formula makes an assumption which isn't true in your case. Go back to my example of the drive current requirement for my ESL. Sorry, that just wasn't in any of the books I have around my house. Yeah, you can ask questions in an Internet forum. But there are going to be a million questions for even a simple project like a preamp, and it's not easy for a person new to an avocation to be able to distinguish answers from wordy blowhards (typehards?) from answers from true experts.
And even if you find the book formula, it will generally take manipulation to get out the variable you're after. That might seem second nature to you or me, but if you haven't gained proficiency in algebra, it can be insurmountable.
Formulae in books have their uses, but typically, the one you need for a given problem isn't there. or you don't have theright book available. Or the book formula makes an assumption which isn't true in your case. Go back to my example of the drive current requirement for my ESL. Sorry, that just wasn't in any of the books I have around my house. Yeah, you can ask questions in an Internet forum. But there are going to be a million questions for even a simple project like a preamp, and it's not easy for a person new to an avocation to be able to distinguish answers from wordy blowhards (typehards?) from answers from true experts.
And even if you find the book formula, it will generally take manipulation to get out the variable you're after. That might seem second nature to you or me, but if you haven't gained proficiency in algebra, it can be insurmountable.
mirlo, I had my epiphany later than you; I'm slow, I guess. It was in college, when as part of my degree requirements I took some courses in the education department. My god! the students around me were, pound-for-pound, the dumbest individuals I ever met. And I say that as someone who taught physics to phys-ed majors. The courses were trivially easy.
I suspect it's not trivially easy to control a goup of sugared-up seven year olds, so there must be SOME talent that these people have. But on an academic level, I don't think I met one person in that department who could count their fingers twice and get the same answer both times. It suddenly became clear to me why my teachers had seemed... oddly non-comprehending of what was going on around them; they were actually stupid.
I suspect it's not trivially easy to control a goup of sugared-up seven year olds, so there must be SOME talent that these people have. But on an academic level, I don't think I met one person in that department who could count their fingers twice and get the same answer both times. It suddenly became clear to me why my teachers had seemed... oddly non-comprehending of what was going on around them; they were actually stupid.
For me it is very simple:
with enough of this: http://www.diyaudio.com/forums/showthread.php?postid=145619#post145619
and enough of what you see on the pic below, i can still hold a soldering iron - but don´t do any math anymore.
with enough of this: http://www.diyaudio.com/forums/showthread.php?postid=145619#post145619
and enough of what you see on the pic below, i can still hold a soldering iron - but don´t do any math anymore.
Attachments
math????
An interesting thread. Interesting to see what all you guys think.
Einstein's Greek grammer teacher. Joseph Degenhart, did tell him that "nothing would ever become of you." He did get rather average grades. His boss refused to promote him to 2nd class patent clerk (from 3rd) "until he has become fully familiar with mechanical engineering." This was in 1902 3 years before he publishes E=mc^2! (hehe)
Anyway, there are more ways than one to skin a cat. I've made an effort on it and think it quite important.
Edison of course was a genius at tinkering w/o math at all. Not like you can't make significant strides without it.
Crowhurst wrote without it. Read the first two paragraphs here:
http://www.audioxpress.com/resource/audioclass/ga699ac.pdf
Morgan Jones book has feed lots of hobbyists. He begins chapter one as follows:
" It is thus with deep sorrow that the author has had to forsake comlex numbers and vectors, whilst the omission of differential calculas is a particularly poignant loss. All that is left (in his book he is saying) is ordinary algebra, and although there are lots of equations, they are timid, miserable creatures and quite defenseless."
It seems you can do good level diy with timid algebra!
If SY is right about the hobby I think it would exclude about 99% of us. On the other hand, I'm glad there are guys doing it and capable, like crowhurst, of writing it simply. The folks who take it to the next level will surely include math wizards with, like someone pointed out, very good intuition and imagination re electronic circuits.
Cheers
Craig ryder
An interesting thread. Interesting to see what all you guys think.
Einstein's Greek grammer teacher. Joseph Degenhart, did tell him that "nothing would ever become of you." He did get rather average grades. His boss refused to promote him to 2nd class patent clerk (from 3rd) "until he has become fully familiar with mechanical engineering." This was in 1902 3 years before he publishes E=mc^2! (hehe)
Anyway, there are more ways than one to skin a cat. I've made an effort on it and think it quite important.
Edison of course was a genius at tinkering w/o math at all. Not like you can't make significant strides without it.
Crowhurst wrote without it. Read the first two paragraphs here:
http://www.audioxpress.com/resource/audioclass/ga699ac.pdf
Morgan Jones book has feed lots of hobbyists. He begins chapter one as follows:
" It is thus with deep sorrow that the author has had to forsake comlex numbers and vectors, whilst the omission of differential calculas is a particularly poignant loss. All that is left (in his book he is saying) is ordinary algebra, and although there are lots of equations, they are timid, miserable creatures and quite defenseless."
It seems you can do good level diy with timid algebra!
If SY is right about the hobby I think it would exclude about 99% of us. On the other hand, I'm glad there are guys doing it and capable, like crowhurst, of writing it simply. The folks who take it to the next level will surely include math wizards with, like someone pointed out, very good intuition and imagination re electronic circuits.
Cheers
Craig ryder
Though Crowhurst eschewed equations, his books and articles were actually full of mathematical concepts. As soon as he says, "Plot the load line for a 1K plate resistor," he assumes you understand Cartesain coordinates and slope/intercept equations.
If I make it sound like I think you need to be a math "wizard" to do the hobby, my writing is even poorer than I think it is. But you do need to be proficient with those timid, miserable equations unless you want to be limited to always following recipes.
Proficiency also mean much less memorization; when I can't remember the gain equation for an inverting versus non-inverting amp, it only takes me a few seconds to derive it.
If I make it sound like I think you need to be a math "wizard" to do the hobby, my writing is even poorer than I think it is. But you do need to be proficient with those timid, miserable equations unless you want to be limited to always following recipes.
Proficiency also mean much less memorization; when I can't remember the gain equation for an inverting versus non-inverting amp, it only takes me a few seconds to derive it.
Math and hobbies
For some people math IS a hobby. If I had more time, it would be my hobby -- I only got into electrical engineering because math was a more difficult way to make a living. Entering grad school, I figured math would be my profession and electronics my hobby; now it is more the other way around, but the math is being forgotten instead of played with :^(
Despite all the less than complimentary things we've said about teachers, I have to give a lot of credit to anyone who can control a room full of 13 year olds. That requires a sort of social genius that I can only dream of.
SY:
I agree. But for some reason too many students don't want to be taught that way. The "Will this be on the exam? No? Then who cares!" mentality is pervasive.
For some people math IS a hobby. If I had more time, it would be my hobby -- I only got into electrical engineering because math was a more difficult way to make a living. Entering grad school, I figured math would be my profession and electronics my hobby; now it is more the other way around, but the math is being forgotten instead of played with :^(
Despite all the less than complimentary things we've said about teachers, I have to give a lot of credit to anyone who can control a room full of 13 year olds. That requires a sort of social genius that I can only dream of.
SY:
I agree. But for some reason too many students don't want to be taught that way. The "Will this be on the exam? No? Then who cares!" mentality is pervasive.
Useful math for electronics
Overlooked I think has been the most useful thing: linear algebra.
If you can solve systems of linear equations, and especially if you can understand them visually, you have a skill a lot more important for electronics than calculus.
For some reason, basic linear algebra is taught in a way that makes it tedious and dull, so people are left without visual ways to think about it. But it is the foundation for all kinds of signal and system theory that is used in engineering.
Overlooked I think has been the most useful thing: linear algebra.
If you can solve systems of linear equations, and especially if you can understand them visually, you have a skill a lot more important for electronics than calculus.
For some reason, basic linear algebra is taught in a way that makes it tedious and dull, so people are left without visual ways to think about it. But it is the foundation for all kinds of signal and system theory that is used in engineering.
I have read the entire thread and thought I would offer my perspective. I am leaning towards agreeing with SY but not completely. There are a number of people arguing against the requirement for using math to participate in audio as a hobby. My area of interest is speaker design so I will draw my analogy by describing three different ways of designing and building a speaker.
1. Absolutely No Math
Buy any mid-bass driver, at random, and with no information stick it in a box and hook it up. Add a tweeter and some of those funny looking parts in a random orientation and do a little more listening. Make more random changes until you find the perfect configuration. Chances of sucess are slim to none.
2. Using Somebody Else's Math
Buy a driver based on some desired Thiele-Small parameters as described in the Loudspeaker Design Cookbook. Based on the T-S parameters select a low frequency alignment and size a box be it closed or ported. Use a crossover design package to help set up the crossover for your tweeter. Maybe make a few computer measurements to see how the impedance or SPL response looks. Make changes to the system to improve your initial results.
For this method, the amount of math that YOU are doing is probably minimal. Maybe some algebra to calculate the approximate box volume or port length and some of the crossover component values. But a lot of calculus was done by somebody else to arrive at the nice and easy alignment tables. A lot more calculus is being done while you are running the programs to design the crossover and make the measurements. While you are not required to understand or do much math you are in effect still performing some significant math and calculus. To say you don't need any math is a little closed minded. The more of the math you understand the better and easier the design will be to complete. My guess is that most of the people above fall into this category even if they do not recognize it.
3. Doing All The Math
This is probably a very small minority of audio hobby types. If you have put in the time studying the math and the methods used for speaker design, then you are able to stray outside the already worked out speaker design alignments. You are able to design and build something a little more cutting edge. This is not just being able to do a lot of fancy math and proofs but is the capability to see into the math and recognize how to apply it in a novel way to the particular physical problem under consideration. I think of this as applied math and engineering. Like I said, there are not as many people interested in this approach.
OK, that is my take. Is any one of these three methods a absolute must follow to build an excellent speaker system? NO. But is I were to rate the probability of building something real nice using the first method, I would say that it is very low. In my opinion the second and third method are the most likely paths to a great sounding speaker. I would also add that any one or the other is not an absolute guarentee of the best result.
So like it or not, my guess is that most people are using math to design audio components even if they did not really recognize it. They are just using the results of somebody else's math skills.
Just my thoughts,
1. Absolutely No Math
Buy any mid-bass driver, at random, and with no information stick it in a box and hook it up. Add a tweeter and some of those funny looking parts in a random orientation and do a little more listening. Make more random changes until you find the perfect configuration. Chances of sucess are slim to none.
2. Using Somebody Else's Math
Buy a driver based on some desired Thiele-Small parameters as described in the Loudspeaker Design Cookbook. Based on the T-S parameters select a low frequency alignment and size a box be it closed or ported. Use a crossover design package to help set up the crossover for your tweeter. Maybe make a few computer measurements to see how the impedance or SPL response looks. Make changes to the system to improve your initial results.
For this method, the amount of math that YOU are doing is probably minimal. Maybe some algebra to calculate the approximate box volume or port length and some of the crossover component values. But a lot of calculus was done by somebody else to arrive at the nice and easy alignment tables. A lot more calculus is being done while you are running the programs to design the crossover and make the measurements. While you are not required to understand or do much math you are in effect still performing some significant math and calculus. To say you don't need any math is a little closed minded. The more of the math you understand the better and easier the design will be to complete. My guess is that most of the people above fall into this category even if they do not recognize it.
3. Doing All The Math
This is probably a very small minority of audio hobby types. If you have put in the time studying the math and the methods used for speaker design, then you are able to stray outside the already worked out speaker design alignments. You are able to design and build something a little more cutting edge. This is not just being able to do a lot of fancy math and proofs but is the capability to see into the math and recognize how to apply it in a novel way to the particular physical problem under consideration. I think of this as applied math and engineering. Like I said, there are not as many people interested in this approach.
OK, that is my take. Is any one of these three methods a absolute must follow to build an excellent speaker system? NO. But is I were to rate the probability of building something real nice using the first method, I would say that it is very low. In my opinion the second and third method are the most likely paths to a great sounding speaker. I would also add that any one or the other is not an absolute guarentee of the best result.
So like it or not, my guess is that most people are using math to design audio components even if they did not really recognize it. They are just using the results of somebody else's math skills.
Just my thoughts,
Re: Math and hobbies
We've had the same experiences. I kept asking my students, "Wouldn't it be just as easy to really understand the material as memorize a bunch of equations for every possible test question?"
Martin:
Interesting points. I think people can get pleasure out of this hobby at all three of the levels you talk about. For the non-genius, the chances of doing something really good probably lie north of #2. If you rely on manufacturers' specs and curves and don't have the wherewithal to get the curves yourself (understanding the measurement you're doing so that the data is actually valid), you'll be not much better off than the #1 guy. They're most often quite inaccurate for the drivers actually purchased off the shelf, and certainly inaccurate for drivers mounted in baffles.
mirlo said:
We've had the same experiences. I kept asking my students, "Wouldn't it be just as easy to really understand the material as memorize a bunch of equations for every possible test question?"
Martin:
Interesting points. I think people can get pleasure out of this hobby at all three of the levels you talk about. For the non-genius, the chances of doing something really good probably lie north of #2. If you rely on manufacturers' specs and curves and don't have the wherewithal to get the curves yourself (understanding the measurement you're doing so that the data is actually valid), you'll be not much better off than the #1 guy. They're most often quite inaccurate for the drivers actually purchased off the shelf, and certainly inaccurate for drivers mounted in baffles.
That's what you get for taking me seriously...
But that is not what I said. Your reading is bad not your writing. (hehe-just kidding!)
I said " The folks who take it to the next level will surely include math wizards" and, I think, it will include them by necessity. I also said (about mathmatics in this hobby) "I've made an effort on it and think it quite important." So I really do not disagree with you much. On the other hand I'm not that good at it so my opinion is moot.
And Hi Martin. I like your site very much. I have been following your Lowther DX project. Thanks for that.
http://www.quarter-wave.com/Project04/Project04.html
" We study electricity not by knowing what it is, but by scrutinizing what it does, and mathmatics is the window."
O.K., who can identify that quote?
Cheers All
Craig Ryder
But that is not what I said. Your reading is bad not your writing. (hehe-just kidding!)
I said " The folks who take it to the next level will surely include math wizards" and, I think, it will include them by necessity. I also said (about mathmatics in this hobby) "I've made an effort on it and think it quite important." So I really do not disagree with you much. On the other hand I'm not that good at it so my opinion is moot.
And Hi Martin. I like your site very much. I have been following your Lowther DX project. Thanks for that.
http://www.quarter-wave.com/Project04/Project04.html
" We study electricity not by knowing what it is, but by scrutinizing what it does, and mathmatics is the window."
O.K., who can identify that quote?
Cheers All
Craig Ryder
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