Is Beauty a Measure of Scientific Progress?

[ryokan]

When a mathematical or a physical theory can be considered as beautiful?
It is currently admitted that beauty is an important criterion to construct a physical theory, and symmetry is recognised as an element of beauty. How could we measure the aesthetic value of a theory? Or, at experimental level, there are lists of "elegant experiments". When an experiment es elegant?
I think these questions are related to dilemma "invention vs. discovery" and the Plato's Philosophy.

 

[selfAdjoint]

When a mathematical or a physical theory can be considered as beautiful?
It is currently admitted that beauty is an important criterion to construct a physical theory, and symmetry is recognised as an element of beauty. How could we measure the aesthetic value of a theory? Or, at experimental level, there are lists of "elegant experiments". When an experiment es elegant?
I think these questions are related to dilemma "invention vs. discovery" and the Plato's Philosophy.

Mathematicians have spent (maybe wasted) a lot of time trying to develop a quantitative theory of "beauty" or "elegance" in a theory. It's clear that doing much with little is a big component, the slick trick that solves the big problem. Unifying distant theories is always good, as is breaking new ground.

For example the Tamiyama-Shimura conjecture is beautiful; is posits a significant and 'nifty' relationship between algebraic curves and number theory. But I don't think the proofs of it are beautiful, because they are nitty-gritty.

 

[ryokan]

Beauty as usefulness

Mathematicians have spent (maybe wasted) a lot of time trying to develop a quantitative theory of "beauty" or "elegance" in a theory. It's clear that doing much with little is a big component, the slick trick that solves the big problem. Unifying distant theories is always good, as is breaking new ground.

For example the Tamiyama-Shimura conjecture is beautiful; is posits a significant and 'nifty' relationship between algebraic curves and number theory. But I don't think the proofs of it are beautiful, because they are nitty-gritty.

If so, beauty in Science can be reduced to a criterion of efficiency: by minimizing the cost of the experimental method or, alternatively, with an interdisciplinary approach. In the case of an experiment, its simplicity seems a good argument. It would be beauty in the research work. But, how could we measure the intrinsic beauty of a theory with independence of the method involved in its development? Alternatively, Is such question trivial?

 

[selfAdjoint]

I have seen experiments called beautiful on the same basis as theorems. Not only efficiency - getting a big or difficult result from a small input - but above all "cleverness" of the small input. That's what I tried to capture with the word "nifty". Striking, original, ingenious are other words for this quality. Hard to quantify but you know it when you see it.

 

[marcus]

Striking, original, ingenious are other words for this quality. Hard to quantify but you know it when you see it.

if it is not in your blood to instinctively and immediately recognize mathematical beauty

then do not worry about it and do not bother to try to get people to reduce it to false synonyms

the first person to use a bow and arrow, the first person to sail a boat

the ability to recognize elegant tools must have been bred into all or most humans

survival, reproductive success, crafty genes benefit the tribe

if you can say "ahah!" about a cleverly designed and beautiful physical tool and do not have the same recognition with mathematical ones then it must simply be unfamiliarity with mathematics

there is no difference (except the context)

Dante said:

Considerate le vostre semenza
Fatti no foste a viver come brutti
Ma per sequir' virtute e conoscenza

[consider your breeding
You were not made to live as animals
But to understand mathematical beauty]

 

[balkan]

as long as it works...

 

[wuliheron]

When a mathematical or a physical theory can be considered as beautiful?
It is currently admitted that beauty is an important criterion to construct a physical theory, and symmetry is recognised as an element of beauty. How could we measure the aesthetic value of a theory? Or, at experimental level, there are lists of "elegant experiments". When an experiment es elegant?
I think these questions are related to dilemma "invention vs. discovery" and the Plato's Philosophy.

By definition, elegance refers to simplicity and symmetry, especially when discussing scientific theories.

For example, Einstein's theory of Relativity is widely considered the most beautiful physical theory ever developed. It possesses what physicists call supersymmetry (a recursive and global kind of symmetry) and the entire theory boils down to a simple equation: E=MCC.

Likewise, experiments are considered elegant when they appear to go straight to point and possesses a degree of symmetry. For example, Galileo dropping balls off buildings is considered a classic elegant experiment. By simply dropping balls of different weights he created the foundation by which modern physics was eventually created, the so called "weak equivalancy principle."

Yes, the idea of elegant simplicity is related to Plato's philosophy. If you go back further, it is related to any number of philosophies. Elegant simplicity is simply not a new idea by any stretch of the imagination.

 

[marcus]

By definition, elegance refers to simplicity and symmetry, especially when discussing scientific theories.

...

fascinating discussion

I don't believe one can define elegant

It wouldn't be very satisfying to have a special meaning just for "discussing scientific theories" which was different from what the word means in general.
scientific theories are part of nature like the song of birds
they come out of people's heads and people are a part of nature

a gazelle can be elegant
the way a horse gallops or a fish swims can be elegant
the way a mathematician describes a proportion in nature can be elegant

the bones in a woman's face can be elegant

many words do not have definitions
and one must just look at how they are used
that is, they don't have synonyms

"simple and symmetric" is not a synonym for elegant, at least for me.
It just does not work, even though it intersects elegant it doesn't capture it.

sometimes it helps to look at the derivation of a word

maybe elegant has the same root as elect
I will look in the dictionary
sometimes that helps

 

[marcus]

Yes!

elegance comes from the Latin "elegere" to select

it has the root idea of "correctly chosen"

and the dictionary gives its first definition as "refined gracefulness"


------------

that was where my image of the gazelle must have come from

a gazelle is graceful
and the body-plan of the gazelle has been refined by evolution
because she has to outrun predators in open grassland

so there is this sense of grace and having been correctly selected: a perfect choice

 

[wuliheron]

I don't believe one can define elegant

Curious, first you say it cannot be defined, which is of course, a definition in itself! Then you proceed to define elegance!

The definition I gave is a common one among physicists, not the broader definition of the word. The distinction is that physicists are not simply describing common perceptions, but quantifiable physical phenomena. Here is the second half of the definition you so conviently ignored.

Restraint and grace of style.
Scientific exactness and precision.

Among other things that scientists have managed to discover, is the impact of symmetry on conventional ideas of beauty and elegance. Of course, a lay person may object to the idea of reducing the concepts to a specific quality that can be quantified, but that is precisely what the sciences endevor to achieve.

 

[marcus]

but there is no synonym for grace


none of these words really have synonyms, i suspect

it does not help to say

elegant means graceful and graceful, in turn, means fee-fo, and fee-fo means fum, and so on (this doesn't seem to help at all)

So what I like, wuliheron, is that you are not just trying synonyms but you are showing by example.

you say Gen Rel is an example of an elegant model

that is a very well-chosen example IMHO

I can't recall anything more graceful and elegant that happened in the 20th century (of course my judgement is personal and based on very limited knowledge of course of course).

But I can't recall anything more graceful and elegant---unless maybe it was the woman I saw dancing at new york civic center ballet under Balanchine around 1960---or the flight of swallows.

And moreover, Gen Rel was highly original

(I think you may be wrong about E = MCC. I don't think Gen Rel has anything to do with E = Mc² which comes in a different
much less elegant theory that Einstein produced 10 years before Gen Rel)

General Relativity models gravity (with exquisite accuracy) by means of the geometric shape of the world. It models gravity with shape, instead of force. this is impressively original. I do not think anyone before Einstein thought to do this (but I am not a science history buff and can't speak with certainty)

Maybe the originality and the remarkable accuracy of its predictions are even more impressive features than the elegance---in the case of General Relativity. Also the fruitfulness: it is telling us now 90 years later about all these things we are finding so exciting: quasars, black holes, gravitational lensing, dark energy, cosmological origins, collapse of stars, pairs of pulsars radiating gravity waves, hypernova gammaray bursts. Nearly everything that seems new and wonderful in astronomy these days seems to be coming out of Gen Rel or have something to do with it.

So we should not stop with the idea of elegance, we should say
elegant, graceful, original, and also something like "fertile"----able to go on revealing new wonders even after 90 years, able to keep on suggesting to us things we didnt know and that amazing keep on turning out true---and finally, and perhaps most important, precise.

Gen rel keeps on being verfied to more and more decimal places of precision. (but who knows, that may stop and some needful correction may be found)

sorry, these things make my head spin. Anyway it is a very good example of elegance wuliheron. Certain sonnets are also elegant, I forgot about them for a moment.

 

[marcus]

I humbly beg to disagree with Dictionary.com

You say that according to Dictionary.com
elegance has a special meaning of "scientific exactness and precision"
.

I don't think that is right.

We all use words differently I guess so i have a right to disagree and
Dictionary.com has a right to say that, if that is what he thinks.

But I have to say that from my point of view Dictionary.com is just plain wrong.

Elegance and precision are two very different matters.

Well it looks like we can't discuss anymore because we use words differently and have no means of bridging the difference! thanks for raising a stimulating issue like this!

 

[ryokan]

if it is not in your blood to instinctively and immediately recognize mathematical beauty

then do not worry about it and do not bother to try to get people to reduce it to false synonyms]

If the aesthetic convictions held by scientists are of value in the development of their theories, such as Steven Weinberg sustains in “Dreams of a final Theory”, the concept of beauty in Science would need be discussed from a philosophical perspective, searching the objectivable aesthetic components of a scientific theory.

If we can recognize the beauty of a theory (when our genes allow it), but such recognition is subjective and ineffable, as you suggest, the discussion on the beauty of scientific theories lacks of value. We would be ithen in a mystic region. On the contrary, if we can discuss about the aesthetic aspects of a theory, we can made a more rich approach to the historical development of Science.

 

[marcus]

If we can recognize the beauty of a theory (when our genes allow it), but such recognition is subjective and ineffable, as you suggest, the discussion on the beauty of scientific theories lacks of value. We would be ithen in a mystic region. On the contrary, if we can discuss about the aesthetic aspects of a theory, we can made a more rich approach to the historical development of Science.

ryokan I like your style
although we think differently

I sense in you a strong optimism
You take seriously the idea that grace can be objectified
and since it is part of what has guided the search for mathematical theorems and physical models----since beauty has been a guiding light to some good scientists---this objectified elegance can help in understanding history.

I don't approve of mysticism---it is a vile ugly business. But I am
very pessimistic about these things.
I believe it is of urgent importance to understand history and to
understand science and to preserve scientific values---objectivity,
empiricism, openness, transparency, tolerance of difference, discipline
of rigorous testing etc etc.
But I am very pessimistic about a lot of things, including the possibility
of objectifying what i think may be a highly unreliable gut feeling that is maybe half a million years old.

the sense of beauty is (make no mistake) inconsistent, unreliable, mysterious, entangled with emotion, and all that prickly hairball stuff
but in a certain department it is all we got
there is no algoritmic substitute for it
Alas/Hurrah

 

[ryokan]

although we think differently

Really, we do not think so differently.

 

[wuliheron]

I humbly beg to disagree with Dictionary.com

You are of course free to disagree with whatever you choose, but this is a scholarly bulletin board, not an opinion poll. Alternative definitions and sources are not only welcome, but necessary for cogent conversation to continue.

but there is no synonym for grace

none of these words really have synonyms, i suspect

it does not help to say

elegant means graceful and graceful, in turn, means fee-fo, and fee-fo means fum, and so on (this doesn't seem to help at all)

So what I like, wuliheron, is that you are not just trying synonyms but you are showing by example.

Of course I use examples. Words have no demonstrable meaning outside of specific contexts. Understandly, the dictionary as well often provides examples precisely for this reason. If all a dictionary ever did was define words in terms of each other, there would be no real world reference from which non-native language speakers might use one. Not to mention the ensuing confusion among the rest of us as people attempt to split semantic hairs endlessly.

 

[metacristi]

When a mathematical or a physical theory can be considered as beautiful?
It is currently admitted that beauty is an important criterion to construct a physical theory, and symmetry is recognised as an element of beauty. How could we measure the aesthetic value of a theory? Or, at experimental level, there are lists of "elegant experiments". When an experiment es elegant?
I think these questions are related to dilemma "invention vs. discovery" and the Plato's Philosophy.

The 'beauty' part might play an important role indeed when 'devising=inventing' (I am not a platonist or a mathematical realist) a scientific hypothesis (I consider only hypotheses which respect the minimum criterions of sciencificity) but what really count is how such hypotheses become part of science (are preferred to all other existing hypotheses at a certain moment).Here the emprical corroboration is crucial,no matter how ugly or complex a scientific hypothesis is (the standard formalism of QM is rather ugly,for example).

But when more hypotheses,more or less equally supported empirically,are available the 'aesthetics' part could play a role,sometimes.The definiton of 'beauty' in science depend upon the designated goals of science,or science is intrinsically pragmatic.As Popper (Einstein too) wrote once the first goal of science is to give an account of observed facts based on the minimum number of assumptions,thus we should prefer the hypotheses which proceeds from unifying principles,stable in time,in cases when more,approximatively equal empirically,hypotheses exist (one of the most accepted definitions of 'simplicity' among scientists even now).

Thus 'beauty' is virtually identified with 'simplicity' (including also the ease to use it for all our practical purposes).Kepler's (an improvment over Copernicus') system is the paradigm here;it is an elegant,simple and stable,hypothesis unlike Ptolemy's,which could basically explain equally well the observed facts (at the time),but with the expense of adding new epicicles and equants,basically on a daily basis.

 

[ryokan]

Kepler's (an improvment over Copernicus') system is the paradigm here.

Besides the “a posteriori” recognized beauty of some theories, such as Kepler’s system, there is the power of beauty in the development of the theories. In this respect, we can remember the platonic substrate of the Kepler’s Mysterium Cosmographicum, a theory later refuted by the observational evidence.
I think interesting to see the role that Aesthetics plays in the development of Science, in both senses: towards a predictive, simple and consistent theory, or, on the contrary, towards a construct whitout empirical basis. Kepler is a good example of both situations.

 

[Philocrat]

A theory is beautiful when it can cause any progress...and it is perfect when it can explain everything.

 

[ryokan]

A theory is beautiful when it can cause any progress...and it is perfect when it can explain everything.

Progress isn't synonimous of beauty.
What is progress? There are advances in discovery and advances in explanation.
Discovery in many fields of knowledge is facilitated merely by using new methods, without need of new theories. For example, in Biology with the use of the PCR (Polymerase chain reaction), or in Particle Physics with the advances in technology.
I believe that beauty in a theory is associated, in part at least, to its power of prediction, but not imperiously to progress. Progress can be quantified in some cases. Beauty perhaps never.

 

[marcus]

Besides the “a posteriori” recognized beauty of some theories, such as Kepler’s system, there is the power of beauty in the development of the theories. In this respect, we can remember the platonic substrate of the Kepler’s Mysterium Cosmographicum, a theory later refuted by the observational evidence.
I think interesting to see the role that Aesthetics plays in the development of Science, in both senses: towards a predictive, simple and consistent theory, or, on the contrary, towards a construct whitout empirical basis. Kepler is a good example of both situations.

here is a quote from one of Kepler's prefaces, I have forgotten which

perhaps it is from the Mysterium Cosmographicum which you mention, perhaps it is from Harmonice Mundi (which I think more likely)
this was tacked up on the kitchen wall where we used to live: the paper turned brown with age, or perhaps with burger and bacon smoke.


"Since I have attested it as true in my deepest soul,
and since I contemplate its beauty
with incredible and ravishing delight,
I should also defend it to my readers
with all the forces at my command."

Well ryokan I was not intending to revisit these philosophical discussions, but you see what your reference to Kepler did.

 

[marcus]

Here is from Kepler's preface to Book V of harmonice mundi
in which he presents the 3rd law:

"Having perceived the first glimmer of dawn eighteen months ago,
the light of day three months ago,
but only a few days ago the plain sun of a most wonderful vision---
nothing now shall hold me back.

Yes, I give myself up to sacred madness, I mockingly defy all mortals
with this open confession:
I have robbed the golden vessels of the Egyptians to make out of them
a tabernacle for my God, far from the frontiers of Egypt.

If you forgive me, i shall rejoice.
If you are angry, I shall bear it.
Behold, I have cast the dice, and I am writing
a book either for my contemporaries, or for posterity.

It is all the same to me. It may wait a hundred years for a reader,
since God has also waited six thousand years for a witness..."

It is Book V where he says:

"The ratio which exists between the periodic times of any two planets is precisely the ratio of the 3/2 power of their mean distances from the sun..."

Both Galileo and Kepler, two contemporaries who started a process that resulted in mathematical-empirical science (the discovery of subtle algebraic laws in nature), were skillful writers, and both had interesting, though quite different, styles.

 

[metacristi]

Besides the “a posteriori” recognized beauty of some theories, such as Kepler’s system, there is the power of beauty in the development of the theories. In this respect, we can remember the platonic substrate of the Kepler’s Mysterium Cosmographicum, a theory later refuted by the observational evidence.
I think interesting to see the role that Aesthetics plays in the development of Science, in both senses: towards a predictive, simple and consistent theory, or, on the contrary, towards a construct whitout empirical basis. Kepler is a good example of both situations.

Personally I do not consider the pure 'aesthetical' part very important in the process of devising new hypotheses,outside the 'simplicity' part I talked about before (when choosing among many,more or less equal empirically,candidates).The best example coming to my mind now is that the artificial programs used to devise electronic circuits produced some very ugly architectures but which proved to be slightly more efficient than the 'beautifully' devised circuits by human designers.Basically 'everything goes' as much as the minimum criterions of sciencificity are respected.It even deserve to devise hypotheses which are inferior empirically to other candidates,at a certain moment at least,for history proves that such hypotheses could win potentially,on long term,the 'empirical battle' with its rivals (the heliocentric hypothesis,as Copernicus devised it,is a good example).

What really count is that eventually only the correspondence with facts remain crucial,on medium and long term at least.Thus the pure 'beauty' part is not crucial,even in this process of designing.Of course seeking elegance,symmetry and so on is worth following,since humans have a developed sense of beauty intrinsically,but basically there is no good reason to follow mainly the 'art' part,as I said science is intrinsically pragmatic even in the process of theory making.

Indeed there is no good reason now to think that the laws governing nature should be simple,elegant and beautiful (under human aesthetical standards).This mystical belief might have 'worked' in some cases but there is no reason to think that it 'hints' that the (true) laws of nature are 'beautiful',exactly how the fact that we use now in physical sciences mathematical formalisms elaborated hundreds of years ago cannot constitute a sound evidence for platonism (Kepler invoked mystical causes for prefering his heliocentric system;the dream of alchemists,at least a part of it,has become reality in our days and so on-unfortunately there are very few such cases in practice).

Finally since basically we can never establish that a theory,notwithstanding very successful at a certain moment,is the best possible theory (not to mention an exact model of reality) there is no good reason to follow the 'aesthetical' part with priority.

 

[marcus]

...Indeed there is no good reason now to think that the laws governing nature should be simple,elegant and beautiful (under human aesthetical standards).This mystical belief might have 'worked' in some cases but there is no reason to think that it 'hints' that the (true) laws of nature are 'beautiful',exactly how the fact that we use now in physical sciences mathematical formalisms elaborated hundreds of years ago cannot constitute a sound evidence for platonism (Kepler invoked mystical causes for prefering his heliocentric system;the dream of alchemists,at least a part of it,has become reality in our days and so on-unfortunately there are very few such cases in practice).
...

this issue of whether the laws governing nature are beautiful or will appear so, to humans, when they are discovered---this "platonism" issue that you raise---is an interesting side issue.

I hope you understand that I personally was not talking about this, if you read my posts (but perhaps you do not read what I post and are responding solely to others like ryokan)

My point is not prescriptive. I am not saying how Science should be or should not be done. I am not postulating what strategy will be most successful or efficient. I think somehow that what I am trying to say is more fundamental than that.

theoretical physics and cosmology as initiated by Galileo and Kepler (but also going back to greeks etc) is primarily motivated by desire and passionate curiosity

why are there these particles and not others
why is the sky blue
why are there these notes in the musical scale and not other notes
why does the hydrogen atom, heated, make these colors and not other colors
why are there these forces and not some other forces
what is space made of
what is time made of
why are there these planets and these moons and not some others
is the sun bigger than the Earth or is it smaller than the earth
what makes the speed of sound be what it is and not faster or slower
is there a finite speed of light (galileo asked) or is it instantaneous
and what is the speed of light (roemer asked)
and why is it that and not some other speed (maxwell wondered)
and what makes a rainbow
and why does light reflect off of water so that it sparkles
and moonlight makes a track

As far as tax dollars go, we support a theoretical physics establishment that does a lot of string theory. The justifications given are mystical and aesthetic---there are "signs" that it is deeply right or will lead to something that is deeply right, it is very beautiful, it will lead to something deep and beautiful. One has to listen. Indeed they may be wrong! Indeed the mystical and aesthetic motivations may not be guiding them well. but that is how the tax dollars are allocated.

I don't want to consider already whether "nature is platonic" or if we discover the next law whether that law will be beautiful

I just say how it is, people are driven in this enterprise by desire and passion which are ultimately like those desires and passions of kepler, archimedes, whatever
and it does (I have no doubt) influence the kind of laws which they find.
for good or ill

 

[ryokan]

primarily motivated by desire and passionate curiosity

Yes. Curiosity is the basic motive to do Science. I think that curiosity may be the only motive to do Science.

I regret that other considerations, including the aesthetics, may influence the financial support to scientific research.

But we can also discuss about all the aspects related with Science and its development, including the aesthetic considerations.

And about Aesthetics and Science... I only inquired !

 

[marcus]

Yes. Curiosity is the basic motive to do Science. I think that curiosity may be the only motive to do Science.
...

And about Aesthetics and Science... I only answered !

If you were merely answering, then from my viewpoint you answered well because it maintained my interest. I do not know whether you were answering something I said or someone else.

I think you take too narrow a view of curiosity. Curiosity and the sense of beauty are entangled. In my preceding post i listed some questions and my feeling about them is that they are beautiful questions about nature.
Some also had a certain originality at the time.

It might be difficult to program a machine to ask such questions (other than by accident) because the sense of beauty and curiosity---though trainable---rest on a primitive basis given us by evolution, and have pre-rational antecedents.


I would conjecture that every species has a distinct evolutionary experience and is shaped by that to discover and appreciate certain laws and not others. Intelligent birds might find other laws of physics, because they were excited by different relationships. Intelligent squid a still different set of laws.

It is beyond question that the laws of physics are beautiful to human sensibility. However this is not because there is a Platonic Mathematician Creator who arranges things so as to delight Mr. Pythagoras, rather it's because our species found those particular laws----we only would have found them if they were beautiful to us----only an intense and passionate curiosity drawing on lively intuition will discover a deep law.

Another species might find an alternative relationship (perhaps equivalent in its predictions) which satisfied them---their aesthetic taste and curiosity.
-----

To a significant degree, one knows the quality of a scientist by the quality of the questions he asks. And it is hard to explain how people come up with really original questions---not to mention insights. Maybe they come in dreams, maybe there is visual processing.

Evolution has somehow prepared us to be curious about the hypoteneuse of a right triangle and to consider some proof of the pythagorean theorem to be beautiful.

this is not a test of whether the laws of nature are, in some absolute sense, beautiful (as if the universe were the work of an Artistic Clockmaker) it is a test of us the human animals----did we evolve in a way that adequately prepares us to appreciate the working of this universe. Or would we be better off trying to understand some kindergarten version.

Our sense of beauty (an evolutionary accident with no absolute validity on its own) is being tested to see whether it will be adequate to drive us to understand, for instance, how gravity works and how space is made at a microscopic level. the quantum law of gravity will not be found unless it is beautiful----because the man looking for it is ultimately not all that different from Johannes Kepler---and it will not be found unless it fits the orbit of Mars too. Kepler sweat blood to fit the orbit of Mars and the one who finds quantum gravity law will too, in his or her way.

You may think when you first see it that the law is very ugly, but wait and see what happens. mathematicians create mathematics so that laws may be reformulated elegantly and then everyone says "oh that was the real meaning of the law" and "oh see what a beautiful law was hidden from us untll so and so found it" The fact that certain laws take a beautiful appearance in a certain mathematical context shows that that is the right mathematical context. You see what is happening? The major laws people have found are all stunningly beautiful, think of Carnot's heat engine!

Example of Bohr and the Atom:
Evolution prepared us to be curious about the colors of glowing hydrogen and to consider beautiful the pattern Bohr found in those colors.
The wavelengths are like the notes in a scale. At what point in the Neolithic did the hunt-gather people start playing the musical scale. I have seen photos an ivory carved flute carbondated at 40,000 years old. At what point were people prepared to be fascinated by the colors of glowing hydrogen?

 

[Philocrat]

Progress isn't synonimous of beauty.
What is progress? There are advances in discovery and advances in explanation.
Discovery in many fields of knowledge is facilitated merely by using new methods, without need of new theories. For example, in Biology with the use of the PCR (Polymerase chain reaction), or in Particle Physics with the advances in technology.
I believe that beauty in a theory is associated, in part at least, to its power of prediction, but not imperiously to progress. Progress can be quantified in some cases. Beauty perhaps never.

Well, I do not want to fall into the trap of going with the flow, joining the bandwagon or forces with those who claim that 'beauty is in the eye of the beholder'. Thank heavens that the majority of the people that I have come across know what beauty amounts to..at the same time not denying the fact that there is equally a huge population of people out there that self-deceive themselves on this subject (those who pretend to be happy with what is clearly ugly). I ague that the ability to make preferences, disntinguish between things, makes beauty wholly qauntitative. Even a robbot can make such quantitative distinctions.


Progress cannot only be quantified but also is by itself an accurate measure of beauty. The ugly seems to me to be always labouring under the cuasal and relational deffects of nature. In my opinion, anything that takes us a step out of this originally deffective state of nature is not only progressive but also is beauty itself.

 

[Philocrat]

Well, I do not want to fall into the trap of going with the flow, joining the bandwagon or forces with those who claim that 'beauty is in the eye of the beholder'. Thank heavens that the majority of the people that I have come across know what beauty amounts to..at the same time not denying the fact that there is equally a huge population of people out there that self-deceive themselves on this subject (those who pretend to be happy with what is clearly ugly). I ague that the ability to make preferences, disntinguish between things, makes beauty wholly qauntitative. Even a robbot can make such quantitative distinctions.


Progress cannot only be quantified but also is by itself an accurate measure of beauty. The ugly seems to me to be always labouring under the cuasal and relational deffects of nature. In my opinion, anything that takes us a step out of this originally deffective state of nature is not only progressive but also is beauty itself.

Ok, let me take this controversy a step further:

Beauty, by definition, is an ability to overcome, or raise oneself above, all causal and relational laws of nature. And any theory that permits such an ability to be physically realized is not only quantitative and progressive but also is beauty itself.

 

[ryokan]

If you were merely answeringQUOTE]

A mistake occurred. I have now edited my previous post. Unintentionally I wrote "answered". Because of my problems with English and perhaps a Freudian mistake, I converted "ask" to "answer".

So, ... And about Aesthetics and Science ... "I only questioned"

 

[ryokan]

I think you take too narrow a view of curiosity. Curiosity and the sense of beauty are entangled.

No!. I also think that curiosity and beauty are profundly entangled. I believe that curiosity can arise from an aesthetic contemplation (admiration) of Nature. Its correct scientific explanation in a theory may be also beautiful at short or long term.
But I continue thinking that it is interesting the evaluation of the importance of philosophical ideology, including aestetics, in the History of Science and in the actual consideration of Science.
Is there today a lot of admiration to Nature among scientists?
Today admiration, curiosity, beauty, and all the entangled related concepts seem frequently to be neglected by other most "professional" motives: scientific status, financial support, impact index...
As you see, I don't answer. I only ask.

 

[marcus]

No!.
But I continue thinking that it is interesting the evaluation of the importance of philosophical ideology, including aestetics, in the History of Science and in the actual consideration of Science.
...

History is the mirror in which Perseus can see the Medusa of his own mind

(without being dessicated and paralyzed by introspection)

the history of science must be the most enlightening of all forms of scholarship---or so I suspect.

Do you have a University where you live, which I see is in Spain.
I suppose Madrid is very good.

Do they have a History of Science department where you live?

Unfortunately i do not seem to have enough time to read the biographies of the important scientists of the 20th century. I only meet little parts of the picture by accident
(in Rovelli's textbook of Quantum Gravity there is an enlightening historical account of Einstein thinking 1912-1915 as he was finding Gen Rel,
and a historical appendix at the end-----and also by accident I happened to be reading Artur Koestler's book "the Watershed" about Kepler----and again by accident I had some strong impressions of what Feynman was like from reading a memoir of his---but it is sporadic and accidental, not systematic study)

meeting you, in our brief encounters, is another accident that reminds me how much is to be learned from the ancient and modern history of science.

I also like the book by Timothy Ferris called "Coming of Age in the Milky Way"-----this is what it's all about and why reading the history of humans is really to see the destiny of humans

 

[Imparcticle]

the history of science must be the most enlightening of all forms of scholarship---or so I suspect.

Isn't that an opinion?

 

[ryokan]

Do they have a History of Science department where you live?

Unfortunately, there isn’t any History of Science Department where I live.

My scarce knowledge on this topic arises from casual encounters with books in bookshops and through the information of scientific journals. So, it was, it is, sporadic, anarchic. Recently, Internet was for me a both fascinating and frustrating method to confirm to me that I don’t know nothing on nothing.

From my scant lectures on History of Science, I remember with pleasure older books such as the Astronomy of Fred Hoyle or the autobiographic notes of Max Born, the book of Abraham Pais about Einstein, and of Thomas Kuhn on the copernican revolution, and so on.

I am fascinated by the Physics of the early years of the 20th century and by the biographies of the scientists that have make it possible, with their greatness and their miseries. Unfortunately, my severe limits in mathematics and physics hamper to me enjoy more recent changes. From advances in cosmology, string theories... I only know that they exists and that at a very low divulgative level.

I am reading now the spanish version of "From here to infinity" by Ian Stewart.

For me, meeting you, this accident as you say, was really interesting. This forum reminded to me that there is a world out there.

 

[ryokan]

Beauty, by definition, is an ability to overcome, or raise oneself above, all causal and relational laws of nature. And any theory that permits such an ability to be physically realized is not only quantitative and progressive but also is beauty itself.

By definition?
Of course, progress is independent of previous aesthetic considerations. Nevertheless, I think that personal aesthetic judgements can influence the form in that some scientist perform their theories. My question is best related to the final result. I ask only how can be judge the beauty of a theory or a scientific discovery.
I would reformulate my first question in this thread with a particular case: Is the Mandelbrot set beautiful? Why?

 

[Philocrat]

By definition?
Of course, progress is independent of previous aesthetic considerations. Nevertheless, I think that personal aesthetic judgements can influence the form in that some scientist perform their theories. My question is best related to the final result. I ask only how can be judge the beauty of a theory or a scientific discovery.
I would reformulate my first question in this thread with a particular case: Is the Mandelbrot set beautiful? Why?

Mandelbrot is undisputedly beautiful in that it provides a sophisticated yet very convenient departure from bi-valent quantificational and logical madness. It is progressive and the beauty is in the progress. As you know, for the first time we are able to depart from the macro-world and take a cool trip into a fuzzy world. Before Mandelbrot fractals, fuzzy world or fuzzy realism was inaccessible to any logical or mathematical instruments. Mandelbrot blew open that world and provided us with a beautiful train ride into it.

And remember: the beauty is in the progress of this and the totality of it is even more so!

 

[ryokan]

And remember: the beauty is in the progress of this and the totality of it is even more so!

There is a great level of progress in the alimentary industry, but can we relate beauty to such progress? And I don't will talk on the progress in weapons.
Surely, your reference is only to progress in scientific knowledge, with independence of its practical applications. Yet in such case, theories seem differ in beauty in a different form to their distance in the involved scientific advances. And it remains the question that aesthetic considerations can influence the form in that some scientists have elaborated hypotheses and theories. Of course, Science ever will search the progress in all its fields.

 

[ryokan]

What really count is that eventually only the correspondence with facts remain crucial,on medium and long term at least.Thus the pure 'beauty' part is not crucial,even in this process of designing.Of course seeking elegance,symmetry and so on is worth following,since humans have a developed sense of beauty intrinsically,but basically there is no good reason to follow mainly the 'art' part,as I said science is intrinsically pragmatic even in the process of theory making.

I am in accordance:"only the correspondence with facts remains crucial". But I can also be interested on both the grade of beauty of theories and the influence of the aesthetic judgements can have in the development of theories.
On the contrary, I cannot agree with your assertion on the pragmatism of Science. I think that the aim of Science is the answer to questions, both pragmatic and non-pragmatic. To see if petals of some flowers are related to Fibonacci numbers semms to lack of any practical sense. Are Mathematics ever pragmatic?

 

[selfAdjoint]

I am in accordance:"only the correspondence with facts remains crucial". But I can also be interested on both the grade of beauty of theories and the influence of the aesthetic judgements can have in the development of theories.
On the contrary, I cannot agree with your assertion on the pragmatism of Science. I think that the aim of Science is the answer to questions, both pragmatic and non-pragmatic. To see if petals of some flowers are related to Fibonacci numbers semms to lack of any practical sense. Are Mathematics ever pragmatic?

Pragmatic doesn't mean narrowly utilitarian. Mathematicians are very pragmatic; everything is in the service of getting the answer, or proof, or whatever designated outcome.

Flower petals and seeds show Fibonacci patterns because of the rates of growth they stem from.

 

[ryokan]

Pragmatic doesn't mean narrowly utilitarian. Mathematicians are very pragmatic; everything is in the service of getting the answer, or proof, or whatever designated outcome.
QUOTE]
I don't know if you and metacristi use the term pragmatic in the same sense. I agree with the pragmatism of Science in your's wide sense, not in utilitarian sense. Yet, I think that beauty and pragmatism in Science are different concepts. Pragmatism in wide sense (answer to questions) is essential. Aesthetics can be interesting.

 

[marcus]

hello selfAdjoint and ryokan,
I am posting simply for the pleasure of participating in the discussion.
I have a kind of fascination with the role of beauty in mathematical science (or with the human sense of beauty which I think is partly trainable but also partly a genetic inheritance)
But I do not have a stable consistent ideology about this. So what i say today might be different from yesterday.


If in 1903 the Wrights started out to design a flying machine so it would be beautiful this would have been impractical probably and even dangerous. But they were good engineers and they designed it to be buildable and to function---that is to fly and be controllable.

however even in 1903 one could have had a kind of Faith, almost a fanatical confidence, that if one could build it and then keep improving it year after year that eventually the airplanes would be beautiful

one would not know how it would be beautiful and one could not
use one's preconception of what beauty "is" to guide one in designing, necessarily, but one would be absolutely sure with a fanatical belief that one day one would look at the refined improved designs and realize that they are beautiful.

and they are

and I think it is cross-cultural-----that the kid in LA or Inuit kid or Bushman kid or Cambodian kid whether they live in arctic or outback or jungle or next door to LAX airport they will with some high probability think the airplanes are beautiful. Maybe that's wrong and maybe it has non-genetic explanations too. But I think its in the human bloodline, bred into us by millennia of knowing a wellmade weapon or tool.

 

[selfAdjoint]

hello selfAdjoint and ryokan,
I am posting simply for the pleasure of participating in the discussion.
I have a kind of fascination with the role of beauty in mathematical science (or with the human sense of beauty which I think is partly trainable but also partly a genetic inheritance)
But I do not have a stable consistent ideology about this. So what i say today might be different from yesterday.


If in 1903 the Wrights started out to design a flying machine so it would be beautiful this would have been impractical probably and even dangerous. But they were good engineers and they designed it to be buildable and to function---that is to fly and be controllable.

however even in 1903 one could have had a kind of Faith, almost a fanatical confidence, that if one could build it and then keep improving it year after year that eventually the airplanes would be beautiful

one would not know how it would be beautiful and one could not
use one's preconception of what beauty "is" to guide one in designing, necessarily, but one would be absolutely sure with a fanatical belief that one day one would look at the refined improved designs and realize that they are beautiful.

and they are

and I think it is cross-cultural-----that the kid in LA or Inuit kid or Bushman kid or Cambodian kid whether they live in arctic or outback or jungle or next door to LAX airport they will with some high probability think the airplanes are beautiful. Maybe that's wrong and maybe it has non-genetic explanations too. But I think its in the human bloodline, bred into us by millennia of knowing a wellmade weapon or tool.

Well, I for one find the Wright Flyer beautiful. Graceful, minimally designed for its purpose, "Less is More."

Ted Sturgeon once wrote a short story in which an alien walks down an American street, seeing the cars, which he can see through with his X-ray vision. And he wonders why they streamlined the cars on the outside, but not down in the engine.

 

[ryokan]

but one would be absolutely sure with a fanatical belief that one day one would look at the refined improved designs and realize that they are beautiful.
I think its in the human bloodline, bred into us by millennia of knowing a wellmade weapon or tool.

Yes. That is perhaps the question with Philocrat.
There was progress in the Wrights plane, but not yet refinement.
Beauty would be associated in some form to evolution of theories towards ... Simplicity? Power of prediction? Unification? I don't know, but this evolution and its final result would be perceived as aesthetic pleasure.
In the Aristotle's Poetics art is imitation, mimesis. It is possible that the beauty of a scientific theory express its mimesis, its fitness to Nature.

 

[ryokan]

Godfrey Harold Hardy wrote:
The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.
A Mathematician's Apology. London 1941.

What do you think about this "test"?

 

[marcus]

both these last two posts are pretty good, ryokan

also they are short, which is nice

I don't think of anything to add

 

[Philocrat]

And a theory that helps find or discover the 'Best or Perfect Convergence formula' for structional and functional perfection would be the most beautiful of them all. Perfect Convergence formula is any theory that allows things and what are left of their final properties to survive physical destruction. Scientists should stop being demoralised and start finding this formula!

 

[ryokan]

Scientists should stop being demoralised and start finding this formula![/B]

I don't think that scientists be demoralised. On the contrary, I believe that Science is optimistic in the search of knowledge.
I see that again you identifies beauty with progress.