Da gebt der Natur die Ehre/ Froh, an Aug' und Herz gesund/ Und erkennt der Farbenlehre/ Allgemeinen ewigen Grund!

August 15, 2008 6:27 AM

Goethe's Theory of Colors: example of a "research style" that has "played a crucial role in the history of physics", or "tedious heap of mythical, uninformed or impressionistic color anecdotes"? Learn more about "Goethian science", then miss the point entirely by viewing a PDF recreating his experiments photographically, or playing with his triangle online.

Recently inspired by Goethe's Zur Farbenlehre: a drawing machine, an experimental film, and an acupuncture lecture.

posted by No-sword (16 comments total)

heh. thanks for this. i've been wondering about it ever since the "polymath" askme question.
posted by not sure this is a good idea at 7:01 AM on August 15, 2008

I read that as "Goatse's Theory of Colors", which is mostly red, as I (unfortunately) recall.
posted by LordSludge at 8:33 AM on August 15, 2008 [1 favorite has favorites]

I tend to sympathize with Goethe's assertion that 2+2 is only 2+2 and referred to as 4 only because we say it is so; and that 2+2=4 in math is provable only by laws that are accepted in math, and as such are indeed tautological.

The fact that in practice mathematics works pretty well is just dumb luck.

Think about it this way. We all learn as kids that 2 apples plus 2 apples is 4 apples. But when we look at each apple more closely, looking at the little dots on the skin, or one may be missing a stem, and they definitely all have a different number of atoms composing them - then adding two apples to two apples yields a quantity that is different if you add four entirely different apples.

I know that's logically wrong, that we deal with integers, and integers are equal. But the point is that integers are equal only because we say so. It's logical and it works because we wrote the laws in a way that works. A far more obvious comparison is to take the Bible or Koran and to say that logically, they work, because they are the Law of The Universe - or Word of God, rather. Despite the fact that we know there are inconsistencies, contradictions, and fallacies, our failure to abide by the Word of God is our failure, and not It's failure. We fail to understand God, and therefore, we fail.

I was told by a man who has studied this far more than I have - he had a PhD in logic and divinity - that it has never been proven that [~no=yes]. In other words, mathematically it has not been proven that -1(-1)=1. I personally don't know if this is true, but it seems to be one of those things that is so simple it has never been properly challenged, and if it were, would set math and physics back by 10,000 years. It's a ridiculous proposition.

However - it's true only if you accept that the number line only has one axis that extends from it's middle in two directions, negative and positive. This is almost ridiculous, given that there are more than two dimensions, and everybody knows this. Even lawyers note this in one of the fundamental aspects of law - you do not plead "guilty" or "innocent". You plead "guilty" or "not guilty". The tacit logic behind this is that innocent /= not guilty. While this does accept that -g/=g, it implies that -g/=-g, given that innocent=-g.

It's illogical. And logical. Doh!

Nevertheless, Newton was right and it's plain to see, and I feel sorry for Goethe all wrapped up in being right more than seeing right.

BTW, I'd love to know that -1(-1)=1 has been proven by someone. I would sleep better at night.
posted by Xoebe at 8:41 AM on August 15, 2008

Xoebe:
-1(-1) = 1 hasn't been proven. But what has arguably been proven is that it's is impossible to prove.
posted by Zarkonnen at 8:57 AM on August 15, 2008

I don't know whether or not there's been a proof that -1*-1=1, but it's my understanding that there doesn't necessarily have to be. Math is a formal system, and so you can say that -1*-1=1 is an axiom, and move from there. Sure, you can argue that it's all only true because we say it's true, but it's a useful system, and it produces useful results.

Is this Phillips screwdriver really 'true'? Who cares, if it works for its purpose?
posted by echo target at 8:57 AM on August 15, 2008 [1 favorite has favorites]

Is this Phillips screwdriver really 'true'? Who cares, if it works for its purpose?

Yeah, exactly. However, studying religion, one of the common threads is that - despite all our efforts to the contrary - there is a seed of failure that one day, or every day even - comes back to bite us. In Christianity, it's doubt, fear, or sin.

I really don't intend to inject religion into the discussion, but since the Church held the keys to logic for almost the last two thousand years, well, it makes for some good metaphors.

As for being impossible to prove, I kinda figured that, but I am not a "math gizzard" (as my once 8 year old daughter said - she, being a "math gizzard" is much smarter than me and Mom combined).

Oh, and back to the Phillips screwdriver thing. I think one of the most important things I have ever heard was in -of all things - a Woody Allen movie. He related that a rabbi once said, "If I had to choose between the Truth and God, I'd choose God.".

That makes a LOT of sense. I am not religious, probably closer to atheism than agnosticism, but nevertheless, I tend to agree. Recognize that the truth is one thing, and paradoxically, doing the right thing sometimes means being less than honest. Oh, this human condition! Who ever said it was gonna hurt so much! I just want my damn screwdriver to work when I need it. :)
posted by Xoebe at 9:51 AM on August 15, 2008

I tend to sympathize with Goethe's assertion that 2+2 is only 2+2 and referred to as 4 only because we say it is so; and that 2+2=4 in math is provable only by laws that are accepted in math, and as such are indeed tautological.

can you explain why being tautological is a bad thing, and what being "true" might mean otherwise? it's not at all clear what you're "only" is doing there. how would you improve the definition of 2+2? do you expect god to tap you on the shoulder and assure you that it "really is" true?

in other words: if you're going to diss tautology and act like there's something better, you better explain what better is. because it seems to me that you're laughing at the best you've got.
posted by not sure this is a good idea at 10:16 AM on August 15, 2008 [2 favorites has favorites]

Thanks so much for posting this.

I am a great devotee of Goethe's scientific work.

For a positive re-appraisal of his work on color, see this paper. And here is a good reference page.

Goethe also made important contributions to biology that guided the work of prominent scientists like Agnes Arber and Adolf Portmann.

See also these recent monographs:

Goethe as a scientist / Rudolf Magnus
The Wholeness of Nature: Goethe’s Way of Science / Henri Bortoft
The Will to Create: Goethe's Philosophy of Nature / Astrida Tantillo
Goethe, Chaos, and Complexity / Herbert Rowland
The Romantic Conception of Life: Science and Philosophy in the Age of Goethe / Robert J. Richards

Goethe's answer to the critics of his scientific work is "Venetian Epigram," No. 77 (see Goethe, Selected Poems, 127):

So you dabble in botany, optics?
How can you, a poet? Don't you feel better employed touching a sensitive heart?
Oh, those sensitive hearts. Any charlatan knows how to touch them.
No, let my one joy be this, Nature, to touch upon you!

posted by No Robots at 10:47 AM on August 15, 2008

ugh: "your", not you're. made me wince to read that... sorry.
posted by not sure this is a good idea at 11:30 AM on August 15, 2008

Xoebe, you should know about Wigner's essay on the unreasonable effectiveness of mathematics.

If your logician friend tied me to a chair and demanded I prove that -1 is a square root of unity, I would probably put on my geometer hat and talk about scaling, rotation, and translation, not tying the number line in until the end. I can imagine several ways that argument could go. You're right, though, that "guilty" and "innocent" are almost-but-not-quite opposites.
posted by fantabulous timewaster at 12:10 PM on August 15, 2008

You trichromats are so cute with your 3 primary colors. I kid.
posted by BrotherCaine at 12:42 PM on August 15, 2008

Every thinker paints his world in fewer colors than are actually there, and is blind to certain individual colors. This is not merely a deficiency. By virtue of this approximation and simplification he introduces harmonies of colors into the things themselves, and these harmonies possess great charm and can constitute an enrichment of nature. Perhaps it was in this way that mankind first learned to take pleasure in the sight of existence... —Nietzsche, Daybreak §426

posted by RogerB at 1:02 PM on August 15, 2008 [1 favorite has favorites]

Good example of a guy good with words who can't think through a problem clearly, even when the solution is available for the reading.
posted by Mental Wimp at 2:24 PM on August 15, 2008

Good post. A few more links:

Goethe's Theory of Colours (Introduction to/and a translation of Goethe's Introduction to ToC)
Exploratory Experimentation: Goethe, Land, and Color Theory - Physics Today July 2002
posted by psyche7 at 4:10 PM on August 15, 2008

Dang, sorry for the double scitattion, thought the link was different.
posted by psyche7 at 4:12 PM on August 15, 2008

Stop fucking with me you guys. STOP IT!
posted by tkchrist at 5:24 PM on August 15, 2008