Saying you can understand physics without understanding math is like saying you can understand Japanese pop music without understanding Japanese. You may think it sounds nice, but that's it. They could be singing about how the Japanese love to eat babies for all you know.

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

This is dependent of your definition of "understanding". If you assume the essence of pop music in general is found in it's lyrics, then I must say I cannot agree. I can hardly understand some lyrics of Crass or the Exploited, but I can pick up the general themes. And what about Philip Glass's Koyaanisqatsi (title song of the soundtrack of Godfrey Reggio's motion picture of the same name)? It's lyrics are in the Hopi language. Or what about Mike Oldfield's and Tangerine Dream's instrumental compositions? Are all these not pop music?

I'm hardly an expert on the doubtlessly broad range of Japanese Pop Music, but I'm familiar with some albums of Fantastic Plastic Machine which feature songs in English, French and German (and none in Japanese). They are funny. (although I admit my listening experience might differ from the average Japanese listener's).

Fantastic Plastic Machine - Electric Lady Land @ Youtube

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Neptune, Titan, Stars can Frighten...

Precisely.

Many people confuse a "passing acquaintence" with an "understanding". This leads to the altogether too common problem of someone who does not understand that he does not understand.

There are a LOT of baseball pitchers, golfers and NASCAR drivers who have an intimate working knowledge fluid dynamics, lever arms, friction an momentum but only a cursory knowledge of calculus, if any at all. Likewise many gambling odds-makers use their heads to set odds, not actuary tables. As a discriptive qualitative language of physical events, English and other adaptible languages trump math. But if you want to know if the physical laws you are using are close approximations of the real physical world, advanced math is as essential as round cows. ('Round cows' are assumptions, because our mathematical modeling techiques are limited.)

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jwj

It's a big universe out there...is it really unwinding, really burning out?

A classic example of not understanding that one does not understand.

True dat. Saying a race car driver has intimate working knowledge of fluid dynamics is like saying I have an intimate working knowledge of internal medicine.

ETA: which I do. My wife is a physician, and we have relations. Some of them are embarrassing--the ones without serious political afflictions. When we visit them all they talk about is sports--their kids, the result of genetic inbreeding I imagine. One of them looks like a goat. Whenever I start to talk about internal medicine or fluid dynamics, they have to change their diapers, or some other excuse. They're full of excuses, or what passes for excuses. I know this because I'm an expert in internal medicine and fluid dynamics. Fluid mechanics, however, is a different story. Then, they're all over it, wondering whether I know Barry Grant or Stewart Warner or Sandra Bullock, and why is her bacon number now one? I try to explain about Loverboy, but hey who can?

Funny enough this is a great analogy. Many little kids don't know how to read but you swear they could if you saw them with an open book. They've memorized the story and might even recognize the words when in the proper place but give them one of those words outside of the book they won't be able to read it. Likewise if you give them a simple word they have never seen they won't be able to sound it out.

Not understanding the math, and never doing math, means that you will never really come up with valid new idea or be able to relate to concepts together. Sure you can say you understand that 2 concepts are related but that would be just memorizing the story someone else has read to you.

Ummm I think he is banging his head against the wall because of the "the song" as in "one piece" forgive me but off the top of my head I think he has well over 200 known pieces.

So while "song" makes the comment of
sound a bit more naive implying that old Freddy wrote only 1 song is even worse and not the sign of a good debater.

I will have to watch the ramble factor with this one. Math has been such an issue for me.

Recently (two years ago) I had an identity crisis. I had always thought that I was a Physicist (minimally qualified, I completed an BSc Physics approx ten years ago). Anyhow I had a Big Thought about GR. I proceeded to read up on GR, I purchased Sean Carroll's Book Spacetime and Geometry: An Introduction to General Relativity Started to read, the maths looked familiar enough. But then I realised that while I may have understood a fair bit during the degree and I could pass exams and I was well taught, that the understanding was not broad enough. Most proofs did not mean anything.

I was quite capable of having a Big Thought (read Smart speculation) but not a Clever Inspiration. I am not a physicist but a scummy dilettante and I needed to learn.

Since then I have revised all the classical mech of earlier, stepping through all the proofs. Lots of matrices, hermitian, eigen values eigen vectors, forms, transforms, diagonalisation, basis, R^n spaces etc. Soon I will step through differential systems with these tools. Differential calculus at least should be smoother. All these I have stepped through the proofs and I am thoroughly enjoying myself!

Soon I will go through tensors and then(maybe a year off, maybe sooner) I will return to Sean's book.

I think the amount of maths needed to be known is that amount that allows for complete logical thought about the subject at hand. Within that logic could come a well founded inspiration.
I do think speculative thoughts could be very useful but once had have to be rounded out with maths or experimented with until the appropriate maths is known. After all a bubble is only a drip if it doesn't hold air.

Forgive the long post

An example of how math changed an old idea of mine.


I used to think it would be a good idea to integrate a linear generator into a car's suspension. That way the wasted energy of the suspension's compression could be used to charge the battery. But once I really understood Hooke's law as a conservative force I realised that getting any energy out would require the car's engine to put some energy in even though the path for this energy may not be immediately obvious. (of course there may be lossy systems that this would work for but perhaps it would be better to design a better suspension!)

Regards Chris (wish me luck)

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

It can be understood on a basic level and in actuality the math is VERY simple. Yet tommac has demonstrated, multiple times, that he doesn't really understand the curve of that funnel. To be exact he keeps messing up the amount of time dilation someone would experience at different distances from the event horizon of a black hole including once where he stated a time dilation of finding 1 spot of ~1x10^200 would throw off the average space time dilation for a region of ~1x10^200 spot. Which in itself is true but he was implying that the ~1x10^200 spots would be stretched across a solar system. That would be cherry picking your data points first of and second off it doesn't change the average as much as he implies. IE (1x10^200) -1 points with the value of 1 and 1 point with the value of (1x10^200) averaged is only 2 and not some huge number like he tried to imply....because he never even did the maths to check his own claim.

I agree that I, and others, can explain concepts very well with out maths. But that explanation can only be trusted as far as you trust the person doing the explaining. Maths is the independent verifier. Come up with a idea, back it up with math and others can verify your claim. Other than that it is just philosophy.

FYI, in case you don't know, MIT has put their entire course catalog online, free of charge. The media includes video-taped lectures, lab notes, examples, etc.

http://ocw.mit.edu/OcwWeb/web/home/home/index.htm

The math specific courses are here:

http://ocw.mit.edu/OcwWeb/web/course...tm#Mathematics

Although they won't give you a diploma, now *anyone* can get an MIT education. For free!

Rob

That was so trivial that I just ignored it. Either an editing error or
a clumsiness typical of Tom's expression, implying nothing whatever
about his knowledge or lack of knowledge of Chopin's body of work.

I suppose that if it hadn't been for the juxtaposition of two such
peculiar word choices right together, kleindoofy would have let it
pass as well.

Let me go even farther off-topic to clarify my earlier comments
about the word "song". In this case, terms specifically applicable
to classical music are obviously the best choice. My longstanding
problem is to find a word that suits *all* forms of music. The word
"song" is a top contender for that use in the USA.

-- 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

No, it was the basic tone of the whole response, the assumption that one could play virtuoso piano music without ever having practiced the instrument, just by pure will. The comments on Chopin and the word "song" put it over the top.

That's like saying one could land on Jupiter if one only really wanted to and then calling moons planets. It just hurts the ears and demonstrates a certain lack of knowledge.

Which brings us back to moons and planets. Or mathematical terminology. Why differentiate between numerals, integers, digits, etc.? Just call them all "counting thingies."

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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.

That is cool, robross. Thanks.

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Let's put together the pieces of The Grand Puzzle . (website - now revised)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."

Who cares for a diploma... It´s just a piece a paper; a mark of social distinction.

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What brings us together is stronger than what pulls us apart

That is a gross misinterpretation of what he said.

If I may offer my own interpretation, he said that an understanding
of music theory is not needed to play Chopin well. Practice at making
the piano do what you want it to do is obviously required, and Tom
did not say anything to suggest that it isn't. Furthermore, his first
words in the statement lead me to believe that he was describing his
own personal observations, not an assumption. I do not have the
experience to make such a statement myself, but I understand that
many first-rate musicians in different genres were self-taught, and
did not receive instruction in music theory before winning acclaim for
their accomplishments.

What Tom *actually said* is not unreasonable, and fits the facts that
I'm aware of. People who have the innate dexterity and timing can
learn to play music that they hear without knowing anything about
how theory describes that music.

-- Jeff, in Minneapolis

__________________
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

Re-reading what Tom wrote yet again, I don't even think his use of the
definite article was particularly clumsy-- just surprising. It isn't either
factually or grammatically incorrect.

-- 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

As far as my understanding goed, I think you are right about this.

That's probably not untrue too, but I think we should not look down upon of e.g. Democritus's ideas, and recognize the intuitive 'truishness' of several of them.

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Neptune, Titan, Stars can Frighten...

At the thought experiment level, I think you gave up on your regenerative shock absorber idea prematurely.

When a car is bouncing up and down on its suspension after hitting a bump, the energy of that vertical motion did not come from nowhere. It got there at the expense of the kinetic energy of the forward motion. In other words, the car slowed down slightly, and some extra energy from the engine is needed to restore the forward speed.

Shock absorbers as we know them use hydraulic drag to convert the bounce energy into heat, so it continues as wasted energy. In theory we could convert some of it into electricity and use it to recharge the battery. That would reduce the demand on the regular generator and thus lighten the load on the engine.

This thought experiment still shows how mathematical analysis is needed to firm up a bright idea, or to reject it as the case may be.

The trick is they have to hear it first. Without an understanding of the theory and language of music, however, they'll likely never play a score handed to them on paper. They won't understand all those 16th and 32nd notes, the dynamic markings, or the key changes. And with all the work they put into learning a "song" that they've heard (and likely many, many times) they are left with only that song to show for it.

Learn the language, the theory, and even the history of music and you can apply it to a work you've never heard or heard of. You can apply it to music of your own creation...and this is where the analogy really breaks down for for ATM proponents. They're trying to write new "music" without knowing what the notes mean or even how to stay in key.

You can hum a little tune 'til your heart's content but if you want to be taken seriously as a "composer" learn how to write "music".

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Brett
Peters Creek, Alaska
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That's as may be, but it's wrong. "Tune," perhaps. "Song" has words.

No. It isn't.

I do have the experience. Being self-taught is one thing. I've known some self-taught musicians. Some good ones. However, to say that you don't have to know scales or sixteenth or thirty-second notes to know Chopin is flatly wrong, whether you've taught yourself or by someone else. What's more, that's not what I would call music theory. That is an understanding of music itself. You don't have to know the principles of chords. You don't have to know Chopin's history. There are all sorts of things that you don't have to know. But even a self-taught musician must know a great deal about scales and types of notes in order to play Chopin. Even if all you're doing is playing three-chord rock and roll, you still have to know the chords and how to play them.

But scales are not "theory." Scales are an intrinsic part of the music. To claim that you don't have to know sixteenth and thirty-second notes to play Chopin is, bluntly, like saying you don't need to know how to add in order to do physics.

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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!"

That is almost irrelevant. Reading sheet music is an entirely different
skill from being able to play music or being able to compose music.
More than a few musicians never learned to read music. Even some
composers never learned to read or write music. Their compositions
were recorded by other means, or they have been lost. I expect
that a great deal of very good music was never recorded and has
been lost forever, in part because the composer had no way to
record what he composed. A great deal of dreck, too, of course.
And modern technology makes it much easier to record music than
it was two hundred years ago.

It would be dreadful if musicians had to be able to write out their
music in order for it to be taken seriously.

-- Jeff, in Minneapolis

__________________
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

I do not find the comparison of music and physics relevant.

Theoretical physics has to be mathematically consistent. It is not a question of coming up with aesthetically beautiful theories, it is about coming up with theories (which might be beautiful) which are predictive and accurate.

You need math, period.

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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.

Inconvenient, yes...for those without a skill that can be learned (by most). But dreadful? Let's translate that from the analogy to the OP subject:

It would be dreadful if physicists had to be able to write out their theory mathematically in order to be taken seriously.

Doesn't really ring true to my ear.

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Brett
Peters Creek, Alaska
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I'd say this--understanding music theory--at a "I can feel it" level is necessary to play Chopin well--though not knowing the terms involved, like phrasing, agogic, etc. isn't so important--you don't have to know what cadence means, but you have to recognize them to get the phrasing anywhere close to right. There are plenty of people who think they can play piano well because they don't miss any notes and play at full speed, but....that's the easy part (and it's not easy!). This would be like someone who mastered the pronunciation of English words and can read through a speech, but monotone with out any expression, suggesting they might not know the meanings of the sentences.

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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

I am fully in support of mathematical rigor, and this is a nice sentiment.

It would be better if it were true.

The next clear and rigorous definition of the Feynman path integral will be the first one.

QFT is predictive and accurate. It is not known to be mathematically consistent. It is not even well defined from a mathematical perspective.

If theoretical physicists were really required to be truly mathematically rigorous, and theories were required to be demonstrably mathematically consistent, there would be a lot less theoretical physics. Rigor is an appropriate goal. But quite often expediency wins. It is a good thing that there are experiments to help separate the wheat from the chaff.

That hasn't been my experience. At the music school I attended (a state university with an excellent music program) only the music education majors were required to learn to play everything. Everyone else (the performance and musicology/composition majors) only needed to master a primary instrument and show basic proficiency in two others; one of the three had to be piano.

We learned the peculiarities of each instrument and group in orchestration class, but we didn't have to try playing them all.

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“There’s nothing that spells progress in large, friendly letters like trying to combine two totally incompatible technologies.” – David Szondy, Tales of Future Past.

Except for Mendelssohn's "Song without words."

Let's not take the music/physics analogy too far. It's a bit limpy and was only meant as a passing remark for a certain aspect of the main argument: "what is math worth?"

Having said that: practicing scales is to Chopin (more or less) as practicing multiplication tables is to math. The scales help teach you how to move your fingers across the keyboard in a technical manner which you need when playing Chopin, perhaps not so much for Boogy-Woogy. Multiplication tables help train your mind for the relationship of numbers beyond the ten fingers.

@GeorgeLeRoyTirebiter

By "everything" I think Gillian meant different *kinds* of music, not all instruments.

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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.

To be honest, everyone I know who majored in music majored in music education, so the people I know had to learn every instrument. (Though my high school music teacher, on learning the bassoon, was given the instructions to make sure that any kid taking it up could afford private lessons!) However, surely even not-music education majors gets at least the basics in how every instrument works!

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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!"

Well, sort of. Like I mentioned, we covered much of that in the basic orchestration course (which everyone had to take). We didn't need to learn things that would only be important to the players (embouchure, fingerings, etc.), and instead concentrated on details of use to the composer or conductor. It seems like we spent a third of the semester on bowing, even though the string players are just going to ignore the written instructions anyway.

I don't recall spending much time on the basic mechanics of how each instrument works; there wasn't any I blow through here/ and the music goes down and 'round/ whoa-ho-ho-ho ho-ho/ and it comes out here. I think they expected that if we made it into the program, we already knew things like the difference between a woodwind and a brass instrument.

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“There’s nothing that spells progress in large, friendly letters like trying to combine two totally incompatible technologies.” – David Szondy, Tales of Future Past.