# Is Beauty Quantifiable ?

## 144 posts in this topic

The Golden Ratio is the positive solution to the quadratic equation arising from the ratio 1:x :: x:(x-1) and is (-1 + sqrt(5))/2. This ratio pops up in various length ratios in the human skeleton (and some other mammalian skeletons too). I have a hunch why this keeps happening. It so happens that the characteristic equation of the Fibonnaci[sic] Sequence is non other than the above quadratic x^2 -x +1 = 0. The Fibonnaci[sic] Is ubiquitous in physical processes.

Prof. Peter Schickele has a much simpler formulation:

One millihelen: The amount of beauty required to launch one ship.

And now, back to the regularly scheduled thread.

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Prof. Peter Schickele has a much simpler formulation:

One millihelen: The amount of beauty required to launch one ship.

And now, back to the regularly scheduled thread.

Great! Can you tell me where I can buy a Helenomometer? And what size ship?

Bob Kolker

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There was a great TV special on The Learning Channel (here) that talked about common occurance of a number called the golden section, or the golden ratio in things that are generally accepted are visually appealing. Their examples range from faces, to architecture, to credit cards, to shells. There are also many other occurances and methods that this number pops up in.

I was interested on what peoples opinions were on the idea of esthetics being quantifiable. Generally esthetics is often ascribed personal opinion to a large extent, but if it is in fact quantifiable, personal opinion drops as a criterion to judge beauty and beauty is no longer in the eye of the beholder.

The Golden Ratio is the positive solution to the quadratic equation arising from the ratio 1:x :: x:(x-1) and is (-1 + sqrt(5))/2. This ratio pops up in various length ratios in the human skeleton (and some other mammalian skeletons too). I have a hunch why this keeps happening. It so happens that the characteristic equation of the Fibonnaci Sequence is non other than the above quadratic x^2 -x +1 = 0. The Fibonnaci Is ubiquitous in physical processes.

See the article in Wikipedia on the Fibbonacci Numbers.

http://en.wikipedia.org/wiki/Fibonnaci_Seq...mbers_in_nature

This provides no explanation of the aesthetics. It is pure rationalism.

The "golden ratio" may be a pleasing proportion with an interesting mathematical history tied to it through coincidence and a lot of legend, but is not unique and the mathematics of Fibonnacci sequences provides no explanatory value for the esthetics whatsoever. The ratio, regardless of one set of mathematical machinery that happens to be related to the number, is only an approximate measurement of something that has been observed to be pleasing. Mathematics is not metaphysics, giving mystical insight into the intrinsic nature of the universe and psychology. To try to use it that way is no better than Pythagorean number mysticism. The precision of the physical sciences cannot be copied just by copying the use of mathematics without regard to scientific content.

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[...]The

"golden ratio" may be a pleasing proportion with an interesting

mathematical history tied to it through coincidence and a lot of legend,

but is not unique and the mathematics of Fibonnacci sequences provides

no explanatory value for the esthetics whatsoever. The ratio, regardless of

one set of mathematical machinery that happens to be related to the number,

is only an approximate measurement of something that has been observed to

be pleasing. Mathematics is not metaphysics, giving mystical insight into

the intrinsic nature of the universe and psychology. To try to use it that

way is no better than Pythagorean number mysticism. The precision of the

physical sciences cannot be copied just by copying the use of mathematics

without regard to scientific content.

LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL

I hope that I understand the gist of what you say.

For example, "The "golden ratio" may be a pleasing proportion with an

interesting mathematical history tied to it through coincidence and a lot

of legend,..."

That is true, however, that's where you left truth and started to posit

statements about Pythagoras without sufficient factual basis.

I will concur that to find the Fibonnacci sequence in nature or in man made

designs doesn't explain nature, [although there is underlying locational

geometry in natural structures] nor does it justify nature or esthetic

constructions in and of itself.

You are right that in certain instances of nature, designs, and mathematical

concepts, the Fibonnacci sequence may be found to be pleasing.

Mathematical and geometric principles do not exist in physical reality, and

nor are they physical in the sense that some modern physicists claim; that

for example, they claim that mathematics is what is known as the cause

rather than the measurement of the consequences of gravity. I have

read that some scientists believe that mathematical principles exist as

metaphysical existents and processes in the physical universe; and that

mathematics is not a matter only of epistemological existents and

relationships.

You continue and say, "Mathematics is not metaphysics, giving mystical

insight into the intrinsic nature of the universe and psychology." That's

true.

But you fail to be factual in trying to justify the claim in your next sentence,

that, "To try to use it that way is no better than Pythagorean number

mysticism."

I understand what you are trying to say about the wrong uses of

mathematics, however, you misrepresent the Pythagorean theoretical

system of geometry by calling it mysticism.

Recall that there is only one generation from Thales to Pythagoras, and

that Pythagoras continued Thales' work. Eudoxus work called by his

contemporaries, "Eudoxus famous theory of equiproportionality," was

based upon the discoveries and demonstrations of principles of geometry,

in what they called the subscience of, "ratios," by Pythagoras. Aristotle's

development of the science of deductive logic was based upon Eudoxus'

work with ratios, and Aristotle added his science of definitions to

equiproportionality to make a complete logic. Then there were Euclid with

his formalization of the subscience of logical proof, and also Archimedes,

the latter who used logic and physical quantities in proportional statements

to conceptually found the sciences of algebra and physics calculations.

Recently on The FORUM, and previously on HPO, I have written regarding

the geometrical theory of Pythagoras. One shouldn't claim that the theory

of Pythagoras is all mysticism until the context of geometrical and

mathematical science of the Ancient Greek geometers and the theoretical

exploration work done by Pythagoras is better understood. With those

contexts you will find that his work was not mystical. You will also find that

some bad translations of key scientific and geometry terms resulted in a

gross misunderstanding of his ideas in history.

Just one example is that he discovered the general principles of the

commensurability and incommensurability and solutions of the roots

of rectangles and sides of triangles in both plane and solid constructions.

His less understood work is the development of a complex system of

understanding basic scientific concepts and principles and

demonstrations of geometry. No mysticism there.

Mathematics and its sub-science, or in a different context, its basic

sciences of geometry and logical proof, may be used to create man made

structures that, excluding modern scientific engineering for the time

being, are one of the causes, that when integrated with other causes may

result in the creation of interesting, well ordered, and beautiful man made

things.

Mathematical and geometrical relationships are tools that may be used by

designers to create beautiful, dramatic and well ordered creations. They

don't exist as metaphysical existents, however, they may be used to help

cause and, especially, to demonstrate principles that are given shape in

man-made physical and artistic epistemological creations.

The demonstration of the principles of mathematics in designs and art,

for example, in music and architecture, may result in a type of directly

perceptible reality that may be pleasing and be well worth the finite time

of contemplation.

Simply, the principle of evenly measured intervals is an example.

LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL

Inventor

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[...]

Because there are identical half steps in the chromatic scale, with ratios of the frequencies all the same, you can always do this for any key and any scale. Scales other than the major scale simply use a different distribution of notes in sequence of increasing (or decreasing) frequency. The same holds for chords, in which different distributions of notes are played simultaneously for different "harmonies". Any chord and any scale can be transposed to any key because the frequency ratios between notes are uniform and there are no missing notes. To obtain more harmonies than are available under this system would require using different frequencies than are used in the modern Western scale, which would normally be perceived as dissonances.

You have proposed an interesting question. A repeat demonstration of the claimed discovery is in order, and also the mathematical ratios need to be re-demonstrated in calculations. That different frequences may be called for is an interesting question.

I have found that there are different ways that a piano may be tuned. The numerical ratios on one scale are not the same as those on another scale. I'm no way near being an expert in this area, however, I now don't know what a proper tunimng would be in terms of proper ratios.

I don't have a keyboard at this time to re-check the work. Ideally, I hope to find a programable keyboard to demonstrate the existing and new ratios. Yamaha can't help in the matter due to the fixed physical relationships of their equipment, and Roland won't for other reasons, so time will tell.

Inventor

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[...]

Because there are identical half steps in the chromatic scale, with ratios of the frequencies all the same, you can always do this for any key and any scale. Scales other than the major scale simply use a different distribution of notes in sequence of increasing (or decreasing) frequency. The same holds for chords, in which different distributions of notes are played simultaneously for different "harmonies". Any chord and any scale can be transposed to any key because the frequency ratios between notes are uniform and there are no missing notes. To obtain more harmonies than are available under this system would require using different frequencies than are used in the modern Western scale, which would normally be perceived as dissonances.

You have proposed an interesting question. A repeat demonstration of the claimed discovery is in order, and also the mathematical ratios need to be re-demonstrated in calculations. That different frequences may be called for is an interesting question.

I have found that there are different ways that a piano may be tuned. The numerical ratios on one scale are not the same as those on another scale. I'm no way near being an expert in this area, however, I now don't know what a proper tunimng would be in terms of proper ratios.

The ratios for notes in different scales are the same because they are ratios of frequencies of the same notes that are only at different places in the sequence in different scales. This is only true for the equal temperament system, which is designed for that purpose.

Tuning a piano is more complex. We have been discussing scales in a single octave. A piano keyboard covers multiple octaves, for which the slight deviations between just and equal temperament scales accumulate and become more significant. Piano tuning is therefore based on the equal temperament system, but uses slight adjustments to it so that larger intervals sound right. There are also other factors due to the construction of different pianos in which vibrations physically interact between the strings and the soundboard in different ways, causing differences in tonality and perceived harmonics. These deviations are still much smaller than the spacings between half-tones and do not change the essential features of scales and chords.

I don't have a keyboard at this time to re-check the work. Ideally, I hope to find a programable keyboard to demonstrate the existing and new ratios. Yamaha can't help in the matter due to the fixed physical relationships of their equipment, and Roland won't for other reasons, so time will tell.

It doesn't have to be a keyboard. You need an adjustable tone generator; if you restrict yourself to electronic keyboards intended to be keyboards you won't get that. Experiments are most practical by sending wave forms for the tones to a computer, or generating them in software on the computer, where you then use software to assemble them into scales and chords to systematically evaluate the sound. You are better off using software for the whole thing.

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[...]The "golden ratio" may be a pleasing proportion with an interesting mathematical history tied to it through coincidence and a lot of legend, but is not unique and the mathematics of Fibonnacci sequences provides no explanatory value for the esthetics whatsoever. The ratio, regardless of one set of mathematical machinery that happens to be related to the number, is only an approximate measurement of something that has been observed to be pleasing. Mathematics is not metaphysics, giving mystical insight into the intrinsic nature of the universe and psychology. To try to use it that way is no better than Pythagorean number mysticism. The precision of the physical sciences cannot be copied just by copying the use of mathematics without regard to scientific content.

... "The "golden ratio" may be a pleasing proportion with an interesting mathematical history tied to it through coincidence and a lot of legend,..." That is true, however, that's where you left truth and started to posit statements about Pythagoras without sufficient factual basis.

...You continue and say, "Mathematics is not metaphysics, giving mystical insight into the intrinsic nature of the universe and psychology." That's true. But you fail to be factual in trying to justify the claim in your next sentence, that, "To try to use it that way is no better than Pythagorean number

mysticism."

I did not say anything about Pythagoras, let alone "posit statements about Pythagoras without sufficient factual basis." You have extracted out of context one phrase referring to "Pythagorian number mysticsm" in one sentence about something else and misused it repeatedly in what you imagine that I wrote in sentences about Pythagoras which do not exist.

This hasn't been a discussion about Pythagoras at all. I had simply referred in passing to the well-known philosophical position of "Pythagorean number mysticism". The Pythagoreans were a mystic religious cult started by Pythagoras, about whom very little is known personally. The Pythagoreans over time made some important elementary geometric and numerical discoveries but misused them in their mystical metaphysics incorporating number mysticism. Their reification of numbers was described by Aristotle. Do you deny that? Do you not understand what "Pythagorean number mysticism" means?

There was no "trying to justify", from Pythagoreans, a "claim" that "mathematics is not metaphysics, giving mystical insight into the intrinsic nature of the universe and psychology". I only wrote that it is "no better than Pythagorean number mysticism". What "failure" of what attempted "justification" do you claim to be talking about? I expected Forum readers to know enough to be able to understand the reference.

I understand what you are trying to say about the wrong uses of mathematics, however, you misrepresent the Pythagorean theoretical system of geometry by calling it mysticism.

Where do you claim to find a statement equating any "theoretical system of geometry" with "mysticism"? There are no such statements and no such misrepresentation.

Recall that there is only one generation from Thales to Pythagoras, and that Pythagoras continued Thales' work. Eudoxus work called by his contemporaries, "Eudoxus famous theory of equiproportionality," was based upon the discoveries and demonstrations of principles of geometry, in what they called the subscience of, "ratios," by Pythagoras. Aristotle's development of the science of deductive logic was based upon Eudoxus' work with ratios, and Aristotle added his science of definitions to equiproportionality to make a complete logic. Then there were Euclid with his formalization of the subscience of logical proof, and also Archimedes, the latter who used logic and physical quantities in proportional statements to conceptually found the sciences of algebra and physics calculations.

This doesn't have anything to do with the topic. It is irrelevant that early discoveries in actual elementary mathematics, including those from the Pythagoreans, were as a matter of course passed on and used by later thinkers such as Euclid in his compendium. Eudoxus, Euclid, Archimedes and Aristotle were not Pythagoreans. Nor did later formulations and vast extensions of geometry have anything to do with Pythagorean philosophy. Nor does Aristotle's "science of deductive logic" follow from a single geometric principle of Eudoxus in geometry. Nor does any of this have anything to do with what I originally wrote about the golden mean.

Recently on The FORUM, and previously on HPO, I have written regarding the geometrical theory of Pythagoras.

Pythagoras personally had no geometrical theory. His techniques and discoveries were not systematized until much later and no one knows even what of the early Pythagorean work was actually done by Pythagoras himself. What did you write about

"the geometrical theory of Pythagoras"?

One shouldn't claim that the theory of Pythagoras is all mysticism until the context of geometrical and mathematical science of the Ancient Greek geometers and the theoretical exploration work done by Pythagoras is better understood. With those contexts you will find that his work was not mystical.

Why do you think it appropriate to admonish that no one should claim that mathematical work of Pythagoras or his followers was "all mysticism". No one has said any such thing. A simple reference to their "number mysticism" says nothing about their valid mathematical discoveries, which they misinterpreted in their own philosophy.

You will also find that some bad translations of key scientific and geometry terms resulted in a gross misunderstanding of his ideas in history.

There are no bad translations of Pythagoras. There are no translations at all. If he wrote anything, which is unknown, it did not survive. There is nothing to translate. The relevant translations are all of much later writers. No ambiguities in translations of "key scientific and geometry terms" change the mysticism of the Pythagoreans or obliterate the concept of "Pythagorean number mysticism", which is all I referred to.

Just one example is that he discovered the general principles of the commensurability and incommensurability and solutions of the roots of rectangles and sides of triangles in both plane and solid constructions. His less understood work is the development of a complex system of understanding basic scientific concepts and principles and demonstrations of geometry. No mysticism there.

Whether or not Pythagoras versus his followers did some or all of that -- including an alleged "complex system of understanding basic scientific concepts and principles" in an age of pre-science -- and ignoring that there is no such thing as a "root of a rectangle", who do you claim ever said that the geometry is mysticism? Who and what do you think you are arguing with?

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Whether or not Pythagoras versus his followers did some or all of that -- including an alleged "complex system of understanding basic scientific concepts and principles" in an age of pre-science -- and ignoring that there is no such thing as a "root of a rectangle", who do you claim ever said that the geometry is mysticism? Who and what do you think you are arguing with?

EWV:

You have raised numerous questions in as many as three posts of reply, and I have mostly failed to respond to your remarks. I simply haven't had the time. In due time I hope to get some answers together, and to post them here. Thanks for your thoughts.

Concerning the last paragraph the you've posted, and that is quoted above.

You simply don't have an understanding of Pythagoras' system of geometry and of the specific contributions that he made to science.

Recall that he worked withing the system of Thales to organize concepts into proofs of statments that contained educational logical validations of the concepts. Non-contradiction was the rule. Thales studied they complex relationships of ratios that the priests of Egypt had discovered. Pythagoras organized those principles into a huge system of gemetrical knowledge; principles that identify facts of the universe and that could other wise be used to discover even more facts about the universe. When you find all those books on the topic of proportion, roots and squares, solutions to triangles, basic trigonometry and calculations of triangular ratios, the "Golden Mean, and "dynamic symmetry" you are mostly dealing with the work of Pythagoras. The Parthenon was a building built long after Pythagoras, and it was based upon the principles discovered by Pythagoras. One can justifiably wonder if Iktinos and Kallikrates were members of the Pythagorean cult. Pythagoras wasn't all that mystical. Rather, he was prolific, right, and secretive. He also made money from the intellectual reputation of his school, and that was well known in the world of his time. His world was hardly an era of pre-science. It was the dawn of science, and he, after Thales, the Egyptians, the Babylonians, and many sea captains, who were knowingly putting in place the foundations of all sciences, especially those of proof, validation, inductive discovery, and geometry.

The root of a rectangle, for example, that of a square, is the side of a square. I.e., if the area of a square is 16, the root of the square is 16^.5 or 4. Roots exist, if you will recall.

Geometry to the Ancient Greeks prior to and contemporaneous with Aristotle's work was science. After Aristotle's development and formalization of the principles of proportion [from his contemporary, Eudoxus] and his integration of his own discoveries if the principles and classifications of all knowledge in the form and system of definitions, geometry became one of the several sciences, which were thene capable of being uniquely generated and defined in terms of objective [and not Platonic] postulates.

I have no idea with whom I am arguing, nor do I have the slightest idea of who you are. Who are you, then?

Inventor

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I was interested on what peoples opinions were on the idea of esthetics being quantifiable. Generally aesthetics is often ascribed personal opinion to a large extent, but if it is in fact quantifiable, personal opinion drops as a criterion to judge beauty and beauty is no longer in the eye of the beholder.

I think you've confused some philosophic principles in your question.

Your first question is about aesthetics being quantifiable. Before you can answer this you need to carefully define what "quantify" means.

You then posit that the golden ratio might conflict with subjective aesthetics. To address this kind of problem you need to get to the root of aesthetics. What is beauty? What is the purpose of describing something as beautiful? What is meant by "beauty is in the eye of the beholder"? What is the criterion for judging beauty? Is math related to aesthetics? If so how?

If you consider these questions you can clean up you're conception of aesthetics and answer the proposed conflict between the golden rule and subjective beauty.

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You then posit that the golden ratio might conflict with subjective aesthetics. To address this kind of problem you need to get to the root of aesthetics. What is beauty? What is the purpose of describing something as beautiful? What is meant by "beauty is in the eye of the beholder"? What is the criterion for judging beauty? Is math related to aesthetics? If so how?

I have a hunch. Beauty is related to symmetry or near symmetry which makes it just the thing to analyze mathematically. Group theory, for example. is all about symmetry.

Bob Kolker

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I have a hunch. Beauty is related to symmetry or near symmetry which makes it just the thing to analyze mathematically. Group theory, for example. is all about symmetry.

Beauty is often related to symmetry, but also is often not. Group theory itself is not symmetric, yet it is beautiful.

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I have a hunch. Beauty is related to symmetry or near symmetry which makes it just the thing to analyze mathematically. Group theory, for example. is all about symmetry.

I agree that people find symmetry aesthetically pleasing, but are you agreeing with Alex that this contradicts beauty being in the eye of the beholder?

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I have a hunch. Beauty is related to symmetry or near symmetry which makes it just the thing to analyze mathematically. Group theory, for example. is all about symmetry.

I agree that people find symmetry aesthetically pleasing, but are you agreeing with Alex that this contradicts beauty being in the eye of the beholder?

Different people find different things pleasing depending on their values, which may or may not be rational. Mathematical symmetry can't predict what that will be and isn't nearly enough to predict what it will be and relative rankings for even the most rational people; there are two many other relevant variables. Mathematical symmetry provides a partial measure of what most (sane) people will prefer in geometrical figures, but does not explain or justify it and says nothing about evaluating literature, music, etc.

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Different people find different things pleasing depending on their values, which may or may not be rational. Mathematical symmetry can't predict what that will be and isn't nearly enough to predict what it will be and relative rankings for even the most rational people; there are two many other relevant variables. Mathematical symmetry provides a partial measure of what most (sane) people will prefer in geometrical figures, but does not explain or justify it and says nothing about evaluating literature, music, etc.

Yup. That is exactly my point. Beauty is an evaluation. It is not an intrinsic quality.

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Different people find different things pleasing depending on their values, which may or may not be rational. Mathematical symmetry can't predict what that will be and isn't nearly enough to predict what it will be and relative rankings for even the most rational people; there are two many other relevant variables. Mathematical symmetry provides a partial measure of what most (sane) people will prefer in geometrical figures, but does not explain or justify it and says nothing about evaluating literature, music, etc.

Yup. That is exactly my point. Beauty is an evaluation. It is not an intrinsic quality.

Now, I want to take a try at that.

Beauty is recognized and identified as an esthetic and esthetic-emotional response to the charateristics and qualities of the existing or created object, or scene. You are right in that evaluation plays a significant part in the discussion of beauty. Lets say that beauty is not subjective, e.g., made only of emotional responses without an intellectual basis or causes. Lets also say that beauty is objective. Borrowiing from an Objectivist context beauty requires that there is something out there that one can, or may, respond to, and that there are chracteristics of the object that one may evaluate emotionally and intellectually and respond to. The responses may be direct, emotional, with the evaluations being bio-automatic, or the responses may be a result of learned conditions that enable a cascade of intellectual results that are deemed pleasing, e.g., ordered or dramatic arrangements. Borrowing from what you say, "Beauty is an evaluation," I would then add, "Beauty is an evaluation" of specific characteristics of an object or arrangements of objects or its characteristics.

Is beauty an intrinsic quality? I say not. For reasons that the viewer, listener, appreciator must be a part of the process that engenders a high quality response, and, also, that certain characteristics and relationships of the object must be present. Beauty is objective. Not intrinsic or subjective.

Natural beauty has several characteristics, e.g., sense of life, that one may positively respond to. [No, Christianity is mostly focussed upon death, suffering, wealth destruction and distribution, and inflicted pain. There is no beauty there.] Natural scenes have wonderful characteristics, and I can't hope to describe them here.

Lets substitute the term 'wonderful' for 'positive' in the context of values. Values....another whole realm, e.g., what is the value of 'fields of grain?'

Music composers and musicians, architects, designers, fashion apparel designers, interior decorators, craft object makers, dance choreographers and dancers, and even craftsmen and mathematicians create beauty. They manipute the causes for what objects they create, and the results are integrated into the objects made. The characteristics that they place or engineer into the result are part of the object [here either a singular or plural concept]. Thus, a beautiful object is created, and until an appreciator arrives to be wowed over by the subtleties portrayed the response to beauty remains undemonstrated. The beautiful object functions as it exists, and it exists as a demonstration of its intended, and not haphazard, characteristics. Beauty created by the artist, to name one type of creator, has to link the object, its natural or intended placed characteristics, the appreciator, and the functioning of the characteristics and the appreciator.

Beauty is objective. That, I find here, is to say one humongus quantity of ideas about existence, values, created things, and the individual.

What is the relationship of a value, or values, to beauty?

What is the relationship of market values for beautiful objects to beauty?

Inventor

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Inventor, your preaching to the quire when you say that beauty is objective. But I don't agree with how you interpret 'objective'.

Beauty is recognized and identified as an esthetic and esthetic-emotional response to the charateristics and qualities of the existing or created object, or scene.

This is not true. Beauty is not a response. It is an evaluation of characteristics. You don't say I feel beauty or I am beauty. You say that thing is beautiful.

You are right in that evaluation plays a significant part in the discussion of beauty. Lets say that beauty is not subjective, e.g., made only of emotional responses without an intellectual basis or causes.

Subjective does not mean "made only of emotional responses." In fact, emotional responses are objective. Subjective means subject to the observers interpretation. Because beauty is not an existential property, it does not exist as a characteristic of an entity but is an evaluation of existential properties, it is partially subjective.

Lets also say that beauty is objective. Borrowiing from an Objectivist context beauty requires that there is something out there that one can, or may, respond to, and that there are chracteristics of the object that one may evaluate emotionally and intellectually and respond to. The responses may be direct, emotional, with the evaluations being bio-automatic, or the responses may be a result of learned conditions that enable a cascade of intellectual results that are deemed pleasing, e.g., ordered or dramatic arrangements. Borrowing from what you say, "Beauty is an evaluation," I would then add, "Beauty is an evaluation" of specific characteristics of an object or arrangements of objects or its characteristics.

Is beauty an intrinsic quality? I say not. For reasons that the viewer, listener, appreciator must be a part of the process that engenders a high quality response, and, also, that certain characteristics and relationships of the object must be present. Beauty is objective. Not intrinsic or subjective.

I agree with most of this except the first and last few sentences and how you interpret your argument in the middle. Certainly beauty is an evaluation of existential properties. However, how someone evaluates those properties depends on their context. That context is different from person to person. In that sense beauty is partially objective and partially subjective. It is objective in that the fundamental standard is pro-life, and inside of an individuals context a given artwork has an objective evaluation to that standard. However, beauty is subjective in that there are many ways for art to be aesthetically pro life and people are free prefer one kind to another without contradicting the fundamental standard. Classic music is not objectivly better, from one person to another, than rock. High voices, in singing, are not objectivly better than low voices. Fast paced dramas are no objectivly better than a slow burn dramas. But in each of these choices, one might be objectivly better for an individual.

Natural beauty has several characteristics, e.g., sense of life, that one may positively respond to. [No, Christianity is mostly focussed upon death, suffering, wealth destruction and distribution, and inflicted pain. There is no beauty there.] Natural scenes have wonderful characteristics, and I can't hope to describe them here.

Lets substitute the term 'wonderful' for 'positive' in the context of values. Values....another whole realm, e.g., what is the value of 'fields of grain?'

Music composers and musicians, architects, designers, fashion apparel designers, interior decorators, craft object makers, dance choreographers and dancers, and even craftsmen and mathematicians create beauty. They manipute the causes for what objects they create, and the results are integrated into the objects made. The characteristics that they place or engineer into the result are part of the object [here either a singular or plural concept]. Thus, a beautiful object is created, and until an appreciator arrives to be wowed over by the subtleties portrayed the response to beauty remains undemonstrated. The beautiful object functions as it exists, and it exists as a demonstration of its intended, and not haphazard, characteristics. Beauty created by the artist, to name one type of creator, has to link the object, its natural or intended placed characteristics, the appreciator, and the functioning of the characteristics and the appreciator.

Beauty is objective. That, I find here, is to say one humongus quantity of ideas about existence, values, created things, and the individual.

I do not understand what you are getting at in these paragraphs. You seem to meander and confuse your point.

What is the relationship of a value, or values, to beauty?

Beauty is an evaluation of something according to ones values.

What is the relationship of market values for beautiful objects to beauty?

Inventor

A market value is the summation of many individual evaluations. There is no contradiction between market value and beauty if you properly conceptualize beauty as individually objective but subjective between individuals. For one person, the statue of David might be the most valuable piece of art on earth. For someone else it might be Atlas Shrugged. There is no contradiction between the two.

To sum up my point. Beauty is in the eye of the beholder. It is contextual to an individuals values. Some values are objectively good or bad (happiness and heroism vrs depression and mediocrity) but some are subjectively good or bad (swift brush strokes and red hues vrs careful and precise brush strokes and blue hues).

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HELP!

The author of the piece linked has not read Ayn Rand's works

either, and if he had, he is a determined prosteletizer in opposition

to Objectivism.

I don't have the patience to present a critique of that author's

piece, and I would have to rummage through too many particular

details in order to reformulate and validate the underlying

universal axioms for the concepts for the argument in support of

values.

I also suspect that the piece linked opposes the underlying

premises of the 'adamsmith.org' web site.

Inventor

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Check out the comments - somebody got there first.

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Inventor, your preaching to the quire when you say that beauty is

objective. But I don't agree with how you interpret 'objective'.

Beauty is recognized and identified as an esthetic and esthetic-emotional

response to the characteristics and qualities of the existing or created

object, or scene.

My time is limited, however, I'll try to respond with what may be answers

to what may be questions. If I don't agree with a basic concept of

Objectivism I may bring that concept forward and say why, however, I

don't have disagreements. My remarks are all within the context of the

well validated philosophy of Objectivism. At this point it is appropriate

objectivity, and values. I won't reiterate what she has said.

Beauty is a concept, and it is one that identifies certain specific

properties and characteristics of objects that are deemed to be of value

for the purposes of contemplation.

Contemplation in this sense has the bases of sense-perception, the

emotional and intellectual education of the appreciator, and the evaluation

by the individual.

Beauty, in esthetics, is also a study of the object, its characteristics, of

the function of sense perception, of the education and sensitivities of

the individual appreciator, of the values of the appreciator or objective

student, of the emotional potentials and functioning of the individual,

and of the individual's intellectual functionings regarding the intellectual

equivalents of emotions that Ayn Rand calls esthetic emotions.

I don't say that beauty is only intrinsic within the object, nor do I say that

beauty is a matter only of the responses of feelings of the individual.

Rather, beauty is the recognition and conceptualization of that which

is deemed to be of value by the objective observer who responds in

terms of esthetic emotions, e.g., with respect to stylization, to the

characteristics of the selected object. The study of beauty is an

integrated combination of several causes that result in an appreciation

of values for the purposes and results of happiness.

Objective does not mean "made only of emotional responses." That is

reserved for subjectivity, which exists with respect to emotions without

logic. In fact, most emotional responses of rational, non-impulsive

individuals are objective. Subjective means subject to the observer's

interpretation based upon feelings, illusion, or mysticism.

Beauty is objective. Beauty is a matter of the recognition of the causes

and characteristics of objects that are found to be of value for the

purposes of enjoyment and happiness.

What are those causes and characteristics?

What respects and examples may be selected that demonstrate the

principles that cause beauty?

What are one's favorite works, and why?

BTW, one of the most difficult tasks of writing about esthetics is

Non-Contradiction. The writer cannot say that a thing is black and

non-white at the same place. Just stay with one type of statement,

for example, that a glossy sphere is black, and order everything

in the writing accordingly. That simplifies a work to one-half the

verbiage, and in some cases, when you really had nothing to say,

to nothing at all.

One more problem that scientists have equally with writers of

philosophy or esthetics is logic. For example, if the writer says that

because principle [1] and principle [2] are parts of relationship in a

first premise, and because principle [2] and principle [3] are parts

of a similar relationship in the second premise, that, therefore,

principle [1] and principle [2] logically follow in the appropriate

relationship. That conclusion, if the three principles have no

relationship to the checkable facts of reality, is patently false.

Just because the form of, a=b, b=c, therefore, a=c, is followed,

that does not mean that, in the absence of demonstrated factual

identities for a,b,c, the physical identities are true. That error is

common where demonstrated and proved definitions have not

been identified and set forth.

The writer of esthetics must set forth an array of definitions, and

produce logical demonstrations to validate them. Explanations

with appropriate examples are called for.

Inventor

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Subjective does not mean "made only of emotional responses." In fact, emotional responses are objective. Subjective means subject to the observers interpretation. Because beauty is not an existential property, it does not exist as a characteristic of an entity but is an evaluation of existential properties, it is partially subjective.

I disagree with this and my disagreement is premised on the need to distinguish between "subjective" and "personal."

"Subjective" means of the view that consciousness creates reality. "Personal" means pertaining to one person only. Thus I would say that beauty is not an intrinsic property. It does not exist as a characteristic of an entity but is an evaluation of existential properties by an individual within the context of his own sense of life and hierarchy of values. That evaluation, if based on the facts of the work being evaluated ("It is realistic, well-composed, etc."), will be objective and personal. If not based on those facts ("It focuses the higher energies of the collective unconsciousness"), it will be subjective.

However, how someone evaluates those properties depends on their context. That context is different from person to person. In that sense beauty is partially objective and partially subjective.

I would say that, because an esthetic context varies from person to person, esthetic responses are always personal and may be objective or subjective depending on whether or not the evaluation is based on the facts of what the work being evaluated actually is.

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Subjective does not mean "made only of emotional responses." In fact, emotional responses are objective.

In this context "objective" does not apply to "emotional responses" because emotions are not tools of cognition at all. It is a fact that you have a certain emotional response, but the evaluation inherent in that response must be validated. Reliance on unexamined emotions is subjective.

Subjective means subject to the observers interpretation. Because beauty is not an existential property, it does not exist as a characteristic of an entity but is an evaluation of existential properties, it is partially subjective.

An evaluation is not by its nature "partially subjective". The objective is not a combination of the subjective and the intrinsic, somehow being "partially" both. It is a rejection of both. An evaluation is objective when the object is evaluated in accordance with rational standards.

However, how someone evaluates those properties depends on their context. That context is different from person to person. In that sense beauty is partially objective and partially subjective.

I would say that, because an esthetic context varies from person to person, esthetic responses are always personal and may be objective or subjective depending on whether or not the evaluation is based on the facts of what the work being evaluated actually is.

The evaluation must also be rational. An irrational, subjective assessment of "the facts" is not objective.

Beauty is also not "partially objective and partially subjective". Dependence on context does not make something "partially subjective" and does not limit it to being only "partially objective". The partially objective is not objective.

To sum up my point. Beauty is in the eye of the beholder. It is contextual to an individuals values.

Beauty is not "in the eye of the beholder" any more than it is "in the object". It depends on both the facts and the standards of evaluation.

Better read or reread Leonard Peikoff's Objectivism: The Philosophy of Ayn Rand on the nature of values, the objective vs. the subjective and intrinsic, the role of context, and the standards of evaluation in art in accordance with both esthetic principles and philosophical principles regarding what the art is representing. There is a realm of personal options in art, but beauty is not deuces wild in accordance with arbitrary standards depending only on personal choice. That is not what "context" means in objective evaluation.

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BTW, one of the most difficult tasks of writing about esthetics is

Non-Contradiction. The writer cannot say that a thing is black and

non-white at the same place. Just stay with one type of statement,

for example, that a glossy sphere is black, and order everything

in the writing accordingly. That simplifies a work to one-half the

verbiage, and in some cases, when you really had nothing to say,

to nothing at all.

One more problem that scientists have equally with writers of

philosophy or esthetics is logic. For example, if the writer says that

because principle [1] and principle [2] are parts of relationship in a

first premise, and because principle [2] and principle [3] are parts

of a similar relationship in the second premise, that, therefore,

principle [1] and principle [2] logically follow in the appropriate

relationship. That conclusion, if the three principles have no

relationship to the checkable facts of reality, is patently false.

Just because the form of, a=b, b=c, therefore, a=c, is followed,

that does not mean that, in the absence of demonstrated factual

identities for a,b,c, the physical identities are true. That error is

common where demonstrated and proved definitions have not

been identified and set forth.

This supposed explanation of how the alleged "problem that scientists have equally with writers of philosophy or esthetics" is logic" is itself incomprehensible.

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An evaluation is not by its nature "partially subjective". The objective is not a combination of the subjective and the intrinsic, somehow being "partially" both. It is a rejection of both. An evaluation is objective when the object is evaluated in accordance with rational standards. The evaluation must also be rational. An irrational, subjective assessment of "the facts" is not objective. Beauty is also not "partially objective and partially subjective". Dependence on context does not make something "partially subjective" and does not limit it to being only "partially objective". The partially objective is not objective.
I would say that, because an esthetic context varies from person to person, esthetic responses are always personal and may be objective or subjective depending on whether or not the evaluation is based on the facts of what the work being evaluated actually is.

I realize that my use of the term subjective was confusing. I was responding to the idea that beauty is not in the eye of the beholder. To that end I used the term subjective to mean, as I put it "subject to the observers interpretation" and as Betsy Speicher puts it, "personal". This is a different use than Ayn Rand's in her arguments against subjectivism as primacy of consciousness, but it is not an invalid use of the term. I gave the definition that I was using in my post. I am not implying that the observers interpretation is arbitrary i.e. not based on the facts of reality.

Beauty is not "in the eye of the beholder" any more than it is "in the object". It depends on both the facts and the standards of evaluation.

What do you think "Beauty is in the eye of the beholder" means? It is a distinction between a property like height which has external evaluation (one thing can be intrinsically taller than another) and beauty which has internal evaluation (one thing can not be intrinsically more beautiful than another). It means one person's opinion does not invalidate another. I pointed out in my post that someone's opinion of beauty can be objectively right or wrong but is not necessarily so.

Better read or reread Leonard Peikoff's Objectivism: The Philosophy of Ayn Rand on the nature of values, the objective vs. the subjective and intrinsic, the role of context, and the standards of evaluation in art in accordance with both esthetic principles and philosophical principles regarding what the art is representing.

If you believe that beauty is not in the eye of the beholder than you should not be giving advice about which references need rereading.

There is a realm of personal options in art, but beauty is not deuces wild in accordance with arbitrary standards depending only on personal choice. That is not what "context" means in objective evaluation.

I never implied that beauty is "deuces wild" or "arbitrary". I actually pointed out that it is not. "Some values are objectively good or bad (happiness and heroism vrs depression and mediocrity) but some are subjectively good or bad (swift brush strokes and red hues vrs careful and precise brush strokes and blue hues)...in each of these choices, one might be objectively better for an individual." I am highlighting the difference between what is true for one individual vrs true for everyone. Something can be beautiful for one person, and not beautiful for another without objective contradiction. This is what is meant by "Beauty is in the eye of the beholder."

I am arguing against the original poster's and Inventor's implication that one standard of beauty can be applied to everyone.

The original post:

Generally esthetics is often ascribed personal opinion to a large extent, but if it is in fact quantifiable, personal opinion drops as a criterion to judge beauty and beauty is no longer in the eye of the beholder.

Far too many arguments by Objectivists, I have found, rely upon individual rights at their conclusion. I wasn't able to present a concept of objective beauty, or as an artist, say that one work of mine was more sophisticated and more beautiful than the previous work. The 'rights' proponents say that 'Its my right to have the preferences that I want, and that there are no other types of opinions that can supercede my preferences in type or importance.

and:

What is the relationship of market values for beautiful objects to beauty?

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An evaluation is not by its nature "partially subjective". The objective is not a combination of the subjective and the intrinsic, somehow being "partially" both. It is a rejection of both. An evaluation is objective when the object is evaluated in accordance with rational standards. The evaluation must also be rational. An irrational, subjective assessment of "the facts" is not objective. Beauty is also not "partially objective and partially subjective". Dependence on context does not make something "partially subjective" and does not limit it to being only "partially objective". The partially objective is not objective.
I would say that, because an esthetic context varies from person to person, esthetic responses are always personal and may be objective or subjective depending on whether or not the evaluation is based on the facts of what the work being evaluated actually is.

I realize that my use of the term subjective was confusing.

Confusion of your readers is not the issue. You are at the least misusing the term. Objective evaluations are not "partially subjective". Objectivism stresses that objectivity is an alternative to both subjectivism and intrinsicism. It is not a mixture of them.

I was responding to the idea that beauty is not in the eye of the beholder. To that end I used the term subjective to mean, as I put it "subject to the observers interpretation" and as Betsy Speicher puts it, "personal". This is a different use than Ayn Rand's in her arguments against subjectivism as primacy of consciousness, but it is not an invalid use of the term. I gave the definition that I was using in my post. I am not implying that the observers interpretation is arbitrary i.e. not based on the facts of reality

Subjectivism is not synonymous with primacy of consciousness. We are not talking about metaphysics.

An "observer's interpretation" without regard to relevant facts of what the object is and validation by rational standards is improperly subjectivist in any realm. Such a process is not the same thing as the objectively "personal", i.e., in accordance with one's personal experiences and interests where appropriate.

Beauty is not "in the eye of the beholder" any more than it is "in the object". It depends on both the facts and the standards of evaluation.

What do you think "Beauty is in the eye of the beholder" means? It is a distinction between a property like height which has external evaluation (one thing can be intrinsically taller than another) and beauty which has internal evaluation (one thing can not be intrinsically more beautiful than another). It means one person's opinion does not invalidate another. I pointed out in my post that someone's opinion of beauty can be objectively right or wrong but is not necessarily so.

That alleged distinction is not correct. Measurements, e.g., height, are objective, not intrinsic.See Ayn Rand's Introduction to Objective Epistemology. Proper esthetic evaluation is objective, not intrinsic or subjective.

Better read or reread Leonard Peikoff's Objectivism: The Philosophy of Ayn Rand on the nature of values, the objective vs. the subjective and intrinsic, the role of context, and the standards of evaluation in art in accordance with both esthetic principles and philosophical principles regarding what the art is representing.

If you believe that beauty is not in the eye of the beholder than you should not be giving advice about which references need rereading.

If you would read OPAR on the subject you would see why "beauty is in the eye of the beholder" is not correct. You don't have to read it if you don't want to, but don't contradict it here, apparently without even realizing it, and then in a snide non sequitur like the above statement demand that no one who rejects your position should be "giving advice" on what to read. Look up the subject in the index, or don't, but don't tell anyone not to refer you to OPAR on specified topics as the answer to your post.

There is a realm of personal options in art, but beauty is not deuces wild in accordance with arbitrary standards depending only on personal choice. That is not what "context" means in objective evaluation.

I never implied that beauty is "deuces wild" or "arbitrary". I actually pointed out that it is not. "Some values are objectively good or bad (happiness and heroism vrs depression and mediocrity) but some are subjectively good or bad (swift brush strokes and red hues vrs careful and precise brush strokes and blue hues)...in each of these choices, one might be objectively better for an individual." I am highlighting the difference between what is true for one individual vrs true for everyone. Something can be beautiful for one person, and not beautiful for another without objective contradiction. This is what is meant by "Beauty is in the eye of the beholder."

You relied on each individual's own "context" to claim lack of objectivity in evaluation of art. That is not what dependence on "context" means in pursuing objectivity. Nor are properly optional assessments of inessential features "subjectively good or bad".

"Happiness and heroism vrs depression and mediocrity" are not objects subject to the attribute "beauty" and provide no commensurate distinction with assessment of use of color and texture. You appear to have confused philosophical evaluation with a narrower esthetic evaluation. Again, see OPAR.

I am arguing against the original poster's and Inventor's implication that one standard of beauty can be applied to everyone.

Rational standards on essentials do apply to everyone; even where there are some secondary options dependent on personal factors of one's life. The best possible to man is objective and universal. Rational evaluation, even with relevant personal factors included where appropriate, is not the same thing as personal emotional responses.

The original post:
Generally esthetics is often ascribed personal opinion to a large extent, but if it is in fact quantifiable, personal opinion drops as a criterion to judge beauty and beauty is no longer in the eye of the beholder.

The claim that it is "quantifiable", at least in the present context of advancement of knowledge, is highly dubious, which is not to say that it can't be measured and compared. But measurements alone do not provide justification for a standard or evaluation.

Far too many arguments by Objectivists, I have found, rely upon individual rights at their conclusion. I wasn't able to present a concept of objective beauty, or as an artist, say that one work of mine was more sophisticated and more beautiful than the previous work. The 'rights' proponents say that 'Its my right to have the preferences that I want, and that there are no other types of opinions that can supercede my preferences in type or importance.

and:

What is the relationship of market values for beautiful objects to beauty?

As has been discussed before I have never encountered any Objectivist who confuses political rights with esthetic evaluation.