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Topic: Mathmatics or "it's all Greek to me" (Read 18009 times) previous topic - next topic
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Mathmatics or "it's all Greek to me"

Folks,

I'm not a math-wiz like many of you. I struggled with algebra 1 (failed it the first time, got a D the second and got an A the third time).

I really, really want to get to the point where i can read scientific papers about things like ambisonics and at least *understand* the math if not create/solve the formulas myself.

Take this for example: http://ambisonics10.ircam.fr/drupal/files/...keynotes/K4.pdf

I donno how advanced that is. It's all Greek to me (because some of it is, in fact Greek).  What "level" of math is that? If i were to go out and buy text books to study would i need to understand upto trigonometry or advanced calculus? 

I can do up to algebra I from a 2 year degree. It got me started and now i have my own computer tech/programming business.  That's all good, but i'm fascinated by sound itself, ambisonics and i really want to be able to understand the blathering..err...i mean in-depth conversations here on HA.

Thanks,

Bearcat
Music lover and recovering high end audiophile

Mathmatics or "it's all Greek to me"

Reply #1 –
If you want to understand the maths regarding music analysis/compression and computer applications, you're going to need AT LEAST a solid grasp of trig/calculus and discrete maths. Most likely some differential equations as well.

Edit: Scratch that. You're going to need a VERY SOLID grasp of calculus and differential equations. In that document alone you have integrals, differentials, matrices, and summations. I think I saw the golden ratio in there a few times as well.

Mathmatics or "it's all Greek to me"

Reply #2 –
I would say that they level of math is the same as what I took back in high school with my pre-cal course.  So any beginning calculus book should give you an idea of what is going on in there.  You have some summations (algebra), integrals (pre-cal), derivatives (pre-cal), fractions (pre-algebra), and matrices (more advanced algebra, they aren't anything special).  Personally, I wouldn't worry about solving or running any of those formulas as that is not the reason as to why they were used in that paper.  Instead, it would be better to understand the concepts of what is going on.

I can give you an example from my college days in my advanced concrete engineering course.  We had a rather large formula that use a derivative, integral (bound by an upper and lower limit), and a couple of other things.  The textbook went into great details when it came to actually formulating this formula.  It explained the reasons why each function was used, the bounds, and everything else.  This is called deriving the formula.  Although it is nice, it didn't mean anything to us as it is not the job of the engineer to actually derive the formula but rather effectively using it.  One could argue that deriving a formula is a nice way of understanding how to use it but I disagree.  Seeing the formula in action through multiple examples is a much better way.

You can actually obtain all of the information you need to know through Wikipedia.  They even have many nice examples expressing integrals, derivatives, matrices, etc.  A college textbook would be an extremely expensive investment (at least $100) for something that is recreational.  Then again, I come from the Bart Simpson point of view in that "oh, it's the weekend, I don't want to learn."

Dang, you bet me by a few minutes.

Mathmatics or "it's all Greek to me"

Reply #3 –
I think that it really depends on what fields you want to concentrate on.

My university studies of electrical engineering here in Serbia included 5 math courses which covered algebra, calculus, functional analysis, discreet mathematics, numerical analysis and probability and statistics.
But you also might also consider doing some physics. So, I agree with kornchild2002, it's much important to understand the underlying concepts.

Good luck!
If age or weaknes doe prohibyte bloudletting you must use boxing

Mathmatics or "it's all Greek to me"

Reply #4 –
Quote from: eevan on
But you also might also consider doing some physics. So, I agree with kornchild2002, it's much important to understand the underlying concepts.

Good luck!


The  paper contains a lot of physical background. The beginnig just decribes a wave equation and how to handle with it. 

In my opinion the "level" of math is very high because things like the Bessel functions or Legendre functions are not trivial.  But to understand the paper it is not necessary to know how to derive the functions.

Mathmatics or "it's all Greek to me"

Reply #5 –
Quote from: BearcatSandor on
Take this for example: http://ambisonics10.ircam.fr/drupal/files/...keynotes/K4.pdf

I donno how advanced that is. It's all Greek to me (because some of it is, in fact Greek).  What "level" of math is that? If i were to go out and buy text books to study would i need to understand upto trigonometry or advanced calculus?
Just look at the pictures. I'm not being flippant. The pictures on page 2 are showing you what the formulae on page one mean.

There is beauty in the formulae too. Some people get it, some people don't. Some people actually think in formulae. I think in pictures.

You can learn - you can learn what the symbols in a formula mean, and then eventually figure out what the formula as a whole means, and then you'll realise that, oh, it means what's in the pictures!

Quote
I can do up to algebra I from a 2 year degree. It got me started and now i have my own computer tech/programming business.  That's all good, but i'm fascinated by sound itself, ambisonics and i really want to be able to understand the blathering..err...i mean in-depth conversations here on HA.
Good grief, which threads am I missing - I've never had to call on this stuff!


I'll give you another nice visual example - 2-D DCTs:
http://en.wikipedia.org/wiki/Discrete_cosi...imensional_DCTs
See the formula? See the picture? Telling you the same thing ish (for n1=n2=8 in the picture).

Understanding what on earth it is and how it's used would be useful for a discussion. I'm not sure understanding the formula itself would be. Not unless you want to implement it from scratch, or you have a real head for maths.

I'm just speaking from my experience - and it sounds like you like maths even less than I do!


EDIT: Here's a nice anecdote, about ambisonics too!
Quote
Record company CBS (later bought by Sony) had hired a large conference room in a Park Lane hotel to demonstrate its SQ system. We heard a demonstration of sound effects rattling round the room and got the chance to pretend we were sitting in the middle of an orchestra. The CBS people then launched into a highly technical explanation of why SQ was better than the systems which their Japanese rivals had developed. They talked a lot of mathematics about "vectors" and it sailed right over our heads.

From the back of the room, a lanky young man stood up, holding a flimsy square cage made out of wire. He turned it inside out to explain vectors in gloriously simple language. Gerzon's point was that although SQ might sound good with some musical material, like that used for the demonstration, mathematical theory proved that there would always be more music that would sound wrong.

In later years I never ceased to marvel at the way Gerzon could make even the most complicated concept easy to understand.
from http://members.tripod.com/martin_leese/Amb...faq_latest.html

Cheers,
David.

Mathmatics or "it's all Greek to me"

Reply #6 –
Beercat:

To address your question first: This particular paper is in the realm of functional analysis. It is what mathematicians would think of as "applied" functional analysis (it is actually applied, as in: has a physical application, but mathematicians would be inclined to call functional analysis "applied" if you apply it to the wave equation, or to wavelets, or to Fourier analysis, regardless of whether there is a real-world physical wave you are considering).
When I was a student, the relevant course in applied functional analysis would require a background of
- a half-semester course of calculus (differentiation, integration, trigs ...) -- before you start on this, you would have what in the US is referred to as "college algebra", and you would usually know what a derivative is.
- a full semester of vector calculus and linear algebra
- about a full semester of ordinary and partial differential equations.
- then you could start on the pallied functional analysis course.
So basically, the courses required to understand this article would require some one and a half years of work. Since the courses would be based on one another, it'd take me two years and a half to get there (we'd usually fill the remaning 3/4 year with preliminaries in physics, stats, programming and general philosophy).
But in an engineering college, they'd probably have less maths before they start doing stuff related to the paper you link to (they'd distill away "less necessary" maths to get to the point earlier on).



The problem (... your problem ...) about these scientific papers, is that they are precisely that -- scientific papers.
They utilize mathematical language and mathematical manipulations.

Although you "could" -- to some extent -- translate the mathematical language, they won't. Because they need this language to formulate the manipulations, which is why they are writing a paper; hence, those who appreciate what they are really doing, already know the Greek. (That said, there are a lot of unnecessary fancy mathematics around, which could be simplified -- indeed, that is usually what happens when mathematicians and practitioners get a better grip on what the Greek really means.)

Mathmatics or "it's all Greek to me"

Reply #7 –
Quote from: BearcatSandor on
Folks,

I'm not a math-wiz like many of you. I struggled with algebra 1 (failed it the first time, got a D the second and got an A the third time).

I really, really want to get to the point where i can read scientific papers about things like ambisonics and at least *understand* the math if not create/solve the formulas myself.

Take this for example: http://ambisonics10.ircam.fr/drupal/files/...keynotes/K4.pdf


I see two parts to your problem. One is as you say, the basic math, which has already been discussed well in my opinion. A couple 4 semesters of calculus would teach you how to read and evaluate the equations in the paper you cite. That's one-two years of engineering school. However, it would also be good to get some education about how the math that you would then know applies to acoustics. Information like that shows up in junior and senior year engineering classes, and postgraduate classes, given that you've found a college or university (e.g. University of Waterloo or Penn State, or some such) that has good faculty strengths in
acoustics.

Back in real life, almost nobody actually uses all the math that they learn. Most of the good you're going to get out of understanding articles like the one you cite is for your brain, not what you do day-to-day in audio if you are an audio professional.  I pretty much finished up a masters degree in engineering, but rarely if ever had to do anything in the real world that I couldn't do with a 4-function calculator. YMMV.

Mathmatics or "it's all Greek to me"

Reply #8 –
An interesting radio program segment on the "Science Friday" show on National Public Radio (NPR):

Calculus Diaries

Sure, the math teacher said this stuff was important -- but why? We'll talk with Jennifer Ouellette, author of "The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse," about using math in everyday life.

http://www.sciencefriday.com/program/archives/201009177
Kevin Graf :: aka Speedskater

Mathmatics or "it's all Greek to me"

Reply #9 –
Quote from: Arnold B. Krueger on
Back in real life, almost nobody actually uses all the math that they learn. Most of the good you're going to get out of understanding articles like the one you cite is for your brain, not what you do day-to-day in audio if you are an audio professional.  I pretty much finished up a masters degree in engineering, but rarely if ever had to do anything in the real world that I couldn't do with a 4-function calculator. YMMV.


That's been my experience as well. Which kinda surprised me, actually, way back when. I kept asking myself "When do I use the math?"

Mathmatics or "it's all Greek to me"

Reply #10 –
Quote from: BearcatSandor on
Folks,

I'm not a math-wiz like many of you. I struggled with algebra 1 (failed it the first time, got a D the second and got an A the third time).

I really, really want to get to the point where i can read scientific papers about things like ambisonics and at least *understand* the math if not create/solve the formulas myself.

Take this for example: http://ambisonics10.ircam.fr/drupal/files/...keynotes/K4.pdf

I donno how advanced that is. It's all Greek to me (because some of it is, in fact Greek).  What "level" of math is that? If i were to go out and buy text books to study would i need to understand upto trigonometry or advanced calculus? 

I can do up to algebra I from a 2 year degree. It got me started and now i have my own computer tech/programming business.  That's all good, but i'm fascinated by sound itself, ambisonics and i really want to be able to understand the blathering..err...i mean in-depth conversations here on HA.

Thanks,

Bearcat


Agree with what everyone said about what you'd have to know. The challenge here is that if you follow the standard course, you'll end up learning much that you don't really need to know, assuming that your goal is to follow the math rather than to do original work.

I wouldn't worry too much about your experience with Algebra I, you're older now and can proceed at your own pace, and with more motivation. The concepts aren't really very hard, although they can seem that way once the mathematicians are done with them, LOL. In fact, as a programmer, you're already familiar with some of what's here, such as the summations and matrices, in different notation.

Mathmatics or "it's all Greek to me"

Reply #11 –
Quote from: Josh358 on
Quote from: Arnold B. Krueger on
Back in real life, almost nobody actually uses all the math that they learn. Most of the good you're going to get out of understanding articles like the one you cite is for your brain, not what you do day-to-day in audio if you are an audio professional.  I pretty much finished up a masters degree in engineering, but rarely if ever had to do anything in the real world that I couldn't do with a 4-function calculator. YMMV.


That's been my experience as well. Which kinda surprised me, actually, way back when. I kept asking myself "When do I use the math?"


On balance, I must admit that learning how to use math to solve problems did pay lasting benefits. Not the math, but the experience with solving problems using logic and relevant facts. 

I took maybe 6 semester-length 4 credit undergraduate and post graduate classes in automatic control systems,. I designed only one feedback loop professionally in the 40 years that followed. I did apply the principles of stability that I learned, but only conceptually, not by using any actual math. The good news is that that one feedback loop design ingratiated me to my bosses for 3-4 years.

I had a lot of fun  designing feedback systems when I was fooling with building power amps, but that was for fun, not business.

Mathmatics or "it's all Greek to me"

Reply #12 –
Quote
I'm not a math-wiz like many of you. I struggled with algebra 1 (failed it the first time, got a D the second and got an A the third time).
I'm not a math whiz either, but I have an engineering degree and that required lots of math classes (as well as math in the engineering courses).   

I found geometry & trigonometry easier than algebra because I could visualize shapes & angles.

I struggled with calculus.  But it “felt” like an entirely different subject, so some people might find it easier than algebra or trig.  The basic concepts of integrals & derivatives were easy enough to understand, but I didn’t always understand how all of the formulas were derived and it seemed like memorization (or attempted memorization  ) of a lot of random stuff.

...I'm just trying to say that just because algebra was difficult for you, that doesn't mean you will automatically fail at higher math.

Mathmatics or "it's all Greek to me"

Reply #13 –
I'll second what most other people have mentioned here - as far as a US curriculum is concerned, all you need to grasp the paper is vector calculus, differential equations, and Fourier analysis - which is at least ~4 semesters right there - and perhaps 3+ semesters of prerequisites behind those. The stuff about spherical harmonics, Bessel functions etc is more or less understandable by that point even though those courses wouldn't have include those in their syllabi.

Calculus is encountered when solving new problems. The result of a calculus problem ultimately winds up being an algebra formula, which explains why it's rarely encountered in "real" life (whatever that means). But when you want to peek behind the curtain, as the OP wants to do, it's more or less required for all sorts of disciplines. And also explains its widespread inclusion in college technical degree-granting programs, even though lord only knows how few engineering graduates actually apply honest-to-god calculus in their careers.

Mathmatics or "it's all Greek to me"

Reply #14 –
Thanks for all the replies. I think i'm understanding that the detailed math work is needed more if you're going to go into the study of the math itself, say if i were to pursue becoming a professor or designing DSP chips.

I find myself at 38 having something like a mid-life crisis, but it's not really a crisis. It's more of a "yeah you've always been interested in music, involved with it in some way so why not use that talent?"  The problem is that i'm interested in sound and psychology/healing, setting up audio systems for people, mixing and recording..just about everything. I've got no direction and no structure to do it in. No one around me does any of this stuff and i don't have a close college or the money to go even if i did.

So, i've taken up reading about it to see what makes me most interested, but i want to understand all that i'm reading. Obviously the higher math present in that paper is not where to start *now*, but i donno. I'll get there eventually and as stated the math itself is not what's important.

I would really enjoy making a secondary business/hobby out of doing ambisonic recordings for people and setting up hometheater/audio systems for folks just like i do with computers now. I have the heart, i just need the brain for it. Thanks to HA i'd be able to set up good systems for people without inadvertently robbing them of their life savings for 'better sound'

I would also like to be able to integrate audio with the computer programming i know. There are plenty of opensource projects looking for volunteers so that's probably my first place to start.

I'll just keep reading and learning. I'm enjoying it and if something comes of it then i'll consider it a bonus i guess.

Besides a good math review would help me in daily life regardless of all this audio stuff.

Quote from: DVDdoug on
I found geometry & trigonometry easier than algebra because I could visualize shapes & angles.
<snip> </snip>

...I'm just trying to say that just because algebra was difficult for you, that doesn't mean you will automatically fail at higher math.

Thanks for the encouragement.  I think it will also be different for me simply because i'm doing it for me rather than being in school.  I had trouble with math because my mind works in little visions, not words or numbers at all.  If i ask someone to pass the salt, i see a vision of them doing so and project an emotion of 'want'. Then i take that and translate it into words.  Conversely, when someone speaks to me the words are translated back into vision form.  I don't know if you're similar but your statement of things making since because you can visualize them is a familiar sentiment.

Math is troublesome as i've only recently figured out that what i need to do to make "2+4" make any sense to my mind is to visualize myself stacking two rocks on top of four of them and count them.  I find i'm *very* fast at that and i can do simple algebra in my head in ways i never could before i started doing this about a year ago.  Calculus? I'll figure out a way to make it work i guess.
Music lover and recovering high end audiophile

Mathmatics or "it's all Greek to me"

Reply #15 –
Quote from: BearcatSandor on
Math is troublesome as i've only recently figured out that what i need to do to make "2+4" make any sense to my mind is to visualize myself stacking two rocks on top of four of them and count them.


Well, can you visualize propagating, reflecting and standing waves?

A fair deal of mathematical concepts -- including those used in this article -- have a "sorta visualizable" interpretation. Which is fairly natural, because a fair share of mathematics did stem from visualizable problems in the first place.

If you look up this article, then you have Abstract, then 1. Introduction, and then begins the substance. Just start with the very first sentence. "Spherical coordinates" means you represent position by distance from the origin, and longitude, and latitude (as opposed to length, width and heigth, which is referred to as "Cartesian" coordinates). That's visualizable. And then there is this "eigenfunctions of the wave equation" (which is a bit sloppy language, but I'll skip that). The wave equation is a partial differential equation modelling the propagation of waves -- although the equation itself might look like goobledegok, then the propagation of waves should be visualizable.

Eigenfunctions. What's that. They are functions which do not change shape under the transformation in question, they only change magnitude. Standing waves between two reflecting walls can be thought of in that way: at a certain frequency, the reflected signal is a copy of the original. Attenuated though, but these attenuated copies add to the original signal and creates a boom.



Oh, and if a handful of mathematical articles can solve your midlife crisis, they are cheaper than a Harley 

Mathmatics or "it's all Greek to me"

Reply #16 –
I think you're much better off starting here for a mathematical grasp of audio, rather than building up the prereqs for understanding ambisonics, which are quite esoteric:

http://www.dspguide.com/

I suspect that book is far too light on the continuous-time side of analysis, but honestly, if you limit yourself to discrete-time systems, a huge amount of calculus goes bye-bye. And that level of knowledge is more than enough to do a lot of very interesting things with computers.

Mathmatics or "it's all Greek to me"

Reply #17 –
Quote from: BearcatSandor on
I had trouble with math because my mind works in little visions, not words or numbers at all.  If i ask someone to pass the salt, i see a vision of them doing so and project an emotion of 'want'. Then i take that and translate it into words.  Conversely, when someone speaks to me the words are translated back into vision form.


You're repeated this a few times now, but please understand that you are not suffering form a unique neurological deformation of some sort for which you need to apologize.  It's nearly fundamental to the human brain to visualize and the oddity in fact lies with those who are bad at visualization but very good at abstract processing. The extreme of that manifests in people to whom you can shout 2846×374! and they'll shout back 1064404! instantly.

Point is, you're not beyond help. What you seem to miss is a proper visual toolset, such as the basic number line, but maybe I'm assuming too much.

Quote from: BearcatSandor on
Math is troublesome as i've only recently figured out that what i need to do to make "2+4" make any sense to my mind is to visualize myself stacking two rocks on top of four of them and count them.  I find i'm *very* fast at that and i can do simple algebra in my head in ways i never could before i started doing this about a year ago.  Calculus? I'll figure out a way to make it work i guess.


Replace the stones with simple bars on a number line, and you're already a leap forward in terms of visualizing the processes of math. For example, here's an approximation of what 3 + 2 looks like in my head:

More complex math just begets a more complex image.

I'm curious why you only began with the rocks so shortly ago. Have you never worked with graphs and functions in highschool? Surely you know what a simple function like x² = y looks like and how to project it in your mind? It's just putting increasingly tall stacks of rocks next to eachother and painting the top rock of each stack red.

If you don't mind another picture (I'm sure you don't):



(I apologize if I perhaps come across a little patronizing with my bright & colourful images, but it's generally difficult to perfectly assess an inquiring mind's total body of knowledge, and one has to start somewhere in getting to the same page. I hope I've been of some assistance.)

Mathmatics or "it's all Greek to me"

Reply #18 –
To learn it you need to love it first. Watch presentations on prime numbers by Terence Tao (UCLA), that'll get you going. Or ask yourself questions like: If all measurements are real, why do we need imaginary numbers? etc. but i don't think any book will teach you math... you need to take a class with a teacher and use books as a reference for further understanding or exercises.

EDIT: Please don't go to wikipedia.

Mathmatics or "it's all Greek to me"

Reply #19 –
WikiBooks is actually pretty damn good for math.

Mathmatics or "it's all Greek to me"

Reply #21 –
Quote from: JapanAudio on
EDIT: Please don't go to wikipedia.
Seconded! The content might be correct, but being taught something by someone who barely understands it themselves is a bad experience. Some wikipedia pages are like this. Sadly some education institutions are like this too!

Cheers,
David.

Mathmatics or "it's all Greek to me"

Reply #22 –
Quote from: kornchild2002 on
I would say that they level of math is the same as what I took back in high school with my pre-cal course.  So any beginning calculus book should give you an idea of what is going on in there.  You have some summations (algebra), integrals (pre-cal), derivatives (pre-cal), fractions (pre-algebra), and matrices (more advanced algebra, they aren't anything special).


If you were doing double integrals in a pre-calc course, what did they save for calculus?

Quote
Although it is nice, it didn't mean anything to us as it is not the job of the engineer to actually derive the formula but rather effectively using it.  One could argue that deriving a formula is a nice way of understanding how to use it but I disagree.  Seeing the formula in action through multiple examples is a much better way.


One advantage of at least understanding the derivation is knowing where the end formula can or can't be applied.
How many threads have we seen where people who are just "given" the Nyquist sampling theorem present us with their counter example of a 20 kHz sine wave that after A/D and D/A would "clearly" come out as an uneven square wave that's nothing like a sine wave, or (with slightly more imagination) an exactly half sample-rate signal whose samples all come out to be zero?


Quote
.  A college textbook would be an extremely expensive investment (at least $100) for something that is recreational.


If you don't need it for a particular course, the cost of a used book that's been superseded by a new edition goes WAY down.
Some publishers are famously coming out with new editions every year or 2 to force students to buy new books, with only minor revisions to the content.   

That's a different issue than whether a single text would teach him what he wants to know.


Mathmatics or "it's all Greek to me"

Reply #24 –
Quote from: Arnold B. Krueger on
Quote from: Josh358 on
Quote from: Arnold B. Krueger on
Back in real life, almost nobody actually uses all the math that they learn. Most of the good you're going to get out of understanding articles like the one you cite is for your brain, not what you do day-to-day in audio if you are an audio professional.  I pretty much finished up a masters degree in engineering, but rarely if ever had to do anything in the real world that I couldn't do with a 4-function calculator. YMMV.


That's been my experience as well. Which kinda surprised me, actually, way back when. I kept asking myself "When do I use the math?"


On balance, I must admit that learning how to use math to solve problems did pay lasting benefits. Not the math, but the experience with solving problems using logic and relevant facts. 

I took maybe 6 semester-length 4 credit undergraduate and post graduate classes in automatic control systems,. I designed only one feedback loop professionally in the 40 years that followed. I did apply the principles of stability that I learned, but only conceptually, not by using any actual math. The good news is that that one feedback loop design ingratiated me to my bosses for 3-4 years.

I had a lot of fun  designing feedback systems when I was fooling with building power amps, but that was for fun, not business.


I'm glad to have the math too, in part because it allowed me to understand technical literature that was valuable for my own work, and in part because like you I found the conceptual understanding useful. The designs I ended up doing from scratch were mostly digital, but since I worked in audio and video there were times when I had to do analog design and interface with analog equipment. In fact, one of the first things I did at my first full time job was to modify the servo loop of an old Ampex VR-2000 so that it could be slewed by an 8080-based synchronizer. I actually had to slave the quad to an old dubber system running off selsyn motors, if you can believe it! Man, those days were fun.

I also enjoy being able to understand the concepts behind something like Ambisonics. It's very beautiful, really, from the perspective of physics. The Kirchhoff-Helmholtz integral may not have had any professional utility for me, but then, my profession was always just an offshoot of my hobby: I like to understand this stuff and to find solutions to challenges in audio engineering, even in subspecialties with which I'll probably never be involved.