Philosophical mode ... on.
Many centuries ago, Friday afternoon, somebody was playing with rectangles and diagonals, and suddenly in that person's mind the correlation a²+b²=c² occurred. Was this correlation a human discovery or was it a human invention?
Some centuries ago, Sunday evening, Mozart was improvising on the piano, and suddenly a graceful melody occurred. He was surprised and excited. Was this graceful melody a discovery or an invention?
If it was an invention, there must've been a plan in his mind before the piano started to sound; and if there was such a plan, the result couldn't have been surprising. So, was it a discovery?
Or: Are there any inventions at all? I don't mean fictional things. Yes, there are invented stories and pictures. I mean inventions that do something in real life, like helpful math formulas or stimulant melodies or the electric light. Are such inventions discoveries? Is it absurd to say that the "Figaro" opera was discovered by Mozart?
|-|
Add the concept of serendipity. That is stumbling unexpectedly on something that was always there, but never recognized as interesting or relevant, until the right combination of knowledge and luck came together.
Wikipedia states:
"Serendipity is an unplanned fortunate discovery. Serendipity is a common occurrence throughout the history of product invention and scientific discovery."
Maybe these words hold the key: product and scientific. A product definitely did not exist before it was invented (electric light). But the number pi did exist before it was discovered. What did not necessarily exist was a representation of pi. The example of a melody is still difficult, as it is not bound to a particular representation (notation, performance, instrument, scale, ...). But a melody in this sense may be in the same area as a story or image.
With discovery, you dis-cover something, you take the cover off and reveal what's beneath. You discover something that was previously in existence, but hidden from view. You enter a room that is dark, you turn the lights on, and you then discover what is in the room.
With invention, from the Latin in (meaning into) and veniere (meaning come), something comes into existence, something that did not previously exist.
In the case of a²+b²=c², the relationship existed, but was not known until it was discovered. But with Figaro, that particular series of notes, in that particular order, with those particular words, did not yet exist as an entity until Mozart brought it into existence.
That said, in colloquial usage, the word "invent" usually applies to a device, not art. We don't say that Leonardo invented the Mona Lisa, but we would say that Lilienthal invented his glider.
Quote from: Hardysuddenly in that person's mind the correlation a²+b²=c² occurred. Was this correlation a human discovery or was it a human invention?
It's a resonance between two elements of the same system.
So who's to say which one is the resonator and which one the resonee?
((((( :P ()()()()()
e=mcc )))))
Cheers,
M=r*tin(I can't possibly speak for Mozart, though.)
Good points.
If the correlation a²+b²=c² is an existence, is this existence mathematical or empirical?
If a²+b²=c² is empirical, it could be an illusion. But a²+b²=c² is independent of natural senses and resonances.
If a²+b²=c² is an existence, when did it start to exist? Was it born with the big bang (assuming the theory is valid), or was it one of the many timeless conditions that enabled the big bang to be the first acausal event on the time line? I would say a²+b²=c² is timeless, and therefore not an existence. It's not a thing per se. It's something metaphysical.
Is the score of the Figaro an existence? It's a sequence of intervals, of correlations. Correlations are correlations even when human resonators are absent.
What makes a melody beautiful? Certain correlations trigger certain emotions in the mind of humans, dogs, cats, birds and so on. The so-called "golden ratio" is a good example of such a correlation; it occurs in visual and acoustical media. It's "just beautiful".
So, beauty seems to be based on mathematical correlations that are not invented by humans. One cannot ask when these laws started to exist, because in this case "existence" is not a category at all.
If the correlation a²+b²=c² has always been there, timeless, independent of the world, then Mozart's Figaro correlations have always been there too, timeless, independent of the world.
Perhaps.
|-|ardy
A little analogy:
Christopher Columbus discovered America, they say. "Discovered", because in the mind of the Europeans of the 15th century, America did not exist.
In the mind of the native Americans of the 15th century, America did exist. From their point of view, Christopher Columbus invented America. In fact, he re-invented India :-)
With Figaro, the building blocks were always there... the intervals between the notes were always there, waiting for people to discover and describe.
But Figaro itself didn't always exist, because it is an assembly of those intervals in a particular order. That took creativity, and without Mozart, we wouldn't have it to listen to. I find it helpful to think of Mozart's activity in composing music to be creating something that didn't exist before, as opposed to uncovering something that was always there: pre-Mozart, nobody had ever assembled notes and intervals in a way that was Figaro.
Just like wood, canvas, leather, and metal existed, but it took Lilienthal to make a glider out of them.
I think so too, and the word "composer" is an ideal description in this case. He assembled components.
I think the work of a composer is a mix of two actions:
1. Discovering emotional functions (that are not invented by humans).
2. Composing a mosaic of such functions (partially planned, partially by accident).
In (software) engineering, there is a concept of pattern.
What the engineer, or composer, discovers is a pattern. If this general pattern is followed, something seems to happen -- like an evocation of an emotion, or a flexible yet maintainable software component. You can learn patterns from a teacher. You can learn that they work, and maybe understand why. You can write books about patterns.
The construction of a particular kind of this pattern, is the creative work of art. Although a teacher can help, it isn't typically material to write a book about.
And then comes the lick.
Quote from: HardyIf the correlation a²+b²=c² is an existence, is this existence mathematical or empirical?
Define "empirical".
E.g. your mind deciding that something exists outside and independent of your mind?
Cheers,
Martin (I think)
By "empirical" I mean one of two ways to gain knowledge: "Empirical" knowledge comes from sensory inputs (eyes, ears etc.) and it's never certain that these inputs represent the sensed object correctly. The other way is rational knowledge; that is about logic and math, independent of the sensed things per se. Rational knowledge may also contain errors.
I mean all this in the philosophical context. When the "Age of Enlightment" began some 400 years ago, more and more people asked themselves what is really true and what's wrong. Is the moon really round or do my senses distort the view? Do I exist at all? René Descartes eventuallly said to himself: The only thing that certainly exists is my thinking. My thoughts may be wrong, but they obviously exist. So, therefore I am. -- That is pure rationalism; it claims, on the way to find the absolute truth, sensory inputs are completely useless.
Then came the empiricists like John Locke, David Hume etc.; they preferred the sensory inputs on their search for the truth.
Some years later Immanuel Kant found that both rationalism and empiricsm have their advantages; so he combined them.
Karl Popper advanced that combination further to the scientific method of today. It recognizes that humans can never find the absolute truth; they can only try to approach the truth -- by continuous testing, open minded publication and continuous error isolation. The theories get finer and finer, but never reach 100% certainty. But it's the best method to find answers and to solve problems.
Cheers,
|-|ardy
As a start on empiricism, here's a good Wiki article, I think: https://en.wikipedia.org/wiki/Empiricism
Well the Bible says:
What has been will be again, what has been done will be done again; there is nothing new under the sun.
Quote from: Walktall on Sat, 28 Nov 2020 07:35
Well the Bible says:
What has been will be again, what has been done will be done again; there is nothing new under the sun.
The Bible also says: O sing a new song to the Lord. :-)
Quote from: Hardy Heinlin on Thu, 26 Nov 2020 17:46
Some centuries ago, Sunday evening, Mozart was improvising on the piano, and suddenly a graceful melody occurred. He was surprised and excited. Was this graceful melody a discovery or an invention?
If it was an invention, there must've been a plan in his mind before the piano started to sound; and if there was such a plan, the result couldn't have been surprising. So, was it a discovery?
Or: Are there any inventions at all? I don't mean fictional things. Yes, there are invented stories and pictures. I mean inventions that do something in real life, like helpful math formulas or stimulant melodies or the electric light. Are such inventions discoveries? Is it absurd to say that the "Figaro" opera was discovered by Mozart?
I doubt Mozart would have been surprised by his creation of a graceful melody - that was his default.
The basis of Western music - the scale - contains a scientific imperfection: the Pythagorean comma. So I think it is difficult to argue that music somehow pre-exists.
The nature of music also needs some thought: how does it exist? On paper in the composer's score? I would argue that it doesn't - notation is a limited code used to convey something much more complex. Music (Figaro, for instance) only truly exists when it is turned into sound by the performer*. So the process begins in the composer's imagination, is transferred to paper in code, then the performer is tasked with recreating the sounds originally imagined by the composer but imperfectly notated. In doing so, the result is a collaboration between composer and performer - the performer is not a humble servant but an equal partner in the process.
It is interesting that composers who choose to perform their own music often take liberties with the notated information. There is a modern trend in performance which espouses "authenticity" in which authenticity is defined as total fidelity to the score. One might describe these performers in aviation terms as "Children of the Magenta"! :-)
M.
* One might argue the same of a Shakespeare play, for example, but most of us are able to imagine a play's performance in our heads while we are reading. Very few people, however, could aurally construct a performance while looking at the score of The Rite of Spring.
Quote from: Martin Baker on Sat, 28 Nov 2020 11:07
I doubt Mozart would have been surprised by his creation of a graceful melody - that was his default.
You're probably right. And my original question was too general. To be more precise, I'd say composers, during their childhood at least,
discover various musical-emotional effects, and
create mosaics of such effects. So the work of composers is a mix of both discoveries and creations. For example, Mozarts "Turkish Marsh" contains oriental phrases. You're a professional musician; you probalby know every note of it :-) These oriental phrases existed before Mozart wrote that piece. He discovered them, and composed a new mosaic out of them.
My original point is this: I think that some basic emotional trigger functions need not be learned but are already programmed in our brains when we are born. Language ist taught by language. But when a newborn doesn't know any language, it won't understand the teaching language either. So there must be a starting point at which some emotional symbols for the initial communication are already available, intuitively. I mean visual and acoustical symbols. For instance, a pair of eyebrows that are formed like this ^^ may trigger a feeling of happiness, while a form like this ´` may trigger a feeling of sadness. These intuitiv symbols are probably a million years old and genetically implemented in our neuronal systems. When a tooth hurts, the muscles in the face will shape a certain visual symbol. The mirror neurons in the external observer will cause that observer to understand the pain.
An acoustical example: As you know, of course, a major chord like d-e-f# sounds happier than a minor like d-e-f. I don't think that this emotional effect has been developed by some human masters in the past centuries; I guess the trigger functions for these effects are already in our brains when we're born. And it's probably intercultural. There are many cultural nuances and fine differences, but some basic acoustic symbols work everywhere, just like ^^ and ´` shaped eyebrows.
Or take certain rhythmic effects. A three-four time sounds rolling, while a two-four time sounds like a stable walk. I guess this has to do with the fact that we have two legs. When the number of beats within a bar is even, every bar ends with the same leg position. But when the number is odd like in a 3/4 waltz or swing, the dual left-right motion at the end of the bar is always incomplete. It never comes to an end. Thus it keeps rolling and floating and flying. Same for Brubeck's "Take Five". -- Also visually: Even numbers look more stable than odd numbers. A square looks more stable than a triangle. A horizontal line looks more stable than a vertical line.
Aesthetical laws that cannot be invented.
What do you think?
Cheers,
|-|ardy
Hardy, this is a fascinating subject - thanks for raising it and making me think about it.
Quote from: Hardy Heinlin on Sun, 29 Nov 2020 08:09
To be more precise, I'd say composers, during their childhood at least, discover various musical-emotional effects, and create mosaics of such effects. So the work of composers is a mix of both discoveries and creations. For example, Mozarts "Turkish Marsh" contains oriental phrases. You're a professional musician; you probalby know every note of it :-) These oriental phrases existed before Mozart wrote that piece. He discovered them, and composed a new mosaic out of them.
Yes, I agree with this. Music is a non-verbal language. When we speak or write, we don't (usually) invent words - we use an existing vocabulary and arrange the words using grammatical conventions to express ourselves. Music is the same - it's a language made up of definable components [indeed, it was very common for older composers to use each others' material freely - the modern understanding of copyright or plagiarism didn't exist] and composers assemble these pre-defined building-blocks to construct something original. As with great authors, the great composers push the boundaries - the rules are always made
post hoc by lesser mortals!
Do we need to learn and use a specific musical vocabulary to convey emotions? I don't think so. When we are babies, we don't remain silent, study language and grammar, then one day suddenly say, "Mummy, would you mind awfully exposing your breast so I can have a delicious meal?" :-) A baby communicates its need for food by more basic means, such as screaming. It's not very refined, but the intention is strongly expressed, and I believe the same is possible in music. Musical language is a tool for expression, not the expression itself.
Thinking further about how music conveys emotions, I think it's necessary to consider the performer and listener. The performer can adjust the message. For example, Oscar Peterson might have chosen to play Albinoni's Adagio in a way that conveys light-heartedness, or Alfred Brendel might play the Blue Danube waltz and make it sound sad. Then the listener: perhaps Schopenhauer might have heard Beethoven's 7th Symphony and found it depressing, while Joe Bloggs might hear Bach's B minor Mass and dismiss it as meaningless rubbish!
Quote from: Hardy Heinlin on Sun, 29 Nov 2020 08:09
My original point is this: I think that some basic emotional trigger functions need not be learned but are already programmed in our brains when we are born. Language ist taught by language. But when a newborn doesn't know any language, it won't understand the teaching language either. So there must be a starting point at which some emotional symbols for the initial communication are already available, intuitively. I mean visual and acoustical symbols. For instance, a pair of eyebrows that are formed like this ^^ may trigger a feeling of happiness, while a form like this ´` may trigger a feeling of sadness. These intuitiv symbols are probably a million years old and genetically implemented in our neuronal systems. When a tooth hurts, the muscles in the face will shape a certain visual symbol. The mirror neurons in the external observer will cause that observer to understand the pain.
An acoustical example: As you know, of course, a major chord like d-e-f# sounds happier than a minor like d-e-f. I don't think that this emotional effect has been developed by some human masters in the past centuries; I guess the trigger functions for these effects are already in our brains when we're born. And it's probably intercultural. There are many cultural nuances and fine differences, but some basic acoustic symbols work everywhere, just like ^^ and ´` shaped eyebrows.
Major and minor chords: you are right, at least to a degree. My experience with children who have no formal musical tuition shows that if one plays a major chord they will say it is happy, and a minor chord they will describe as sad.
This is the case today, and has probably held true from at least the classical period onwards, perhaps even for the baroque. But if you go further back in time, major and minor didn't exist in the way we define them now - music was modal. And if you examine this music, (e.g. gregorian chant, mediaeval or renaissance music) the connection between major sounding modes (modes 5 to 8) and minor sounding modes (modes 1 to 4) no longer accords with the emotions we assign to them now. Music expressing joy can be in a minor mode and vice versa. Some chants expressing the joy of the resurrection sound "minor" to modern ears, and some chants connected with death sound "major". It's not a total reverse of the current situation, but it's different enough that one can argue that the connections we hear today were not made by listeners 500 or 1,000 years ago. [Indeed, thinking about it, even today, sad music can be in a "happy" key: Romeo and Juliet by Dire Straits is in F major, as is the Adagietto from Mahler's 5th.]
Which leaves us with a problem. If these connections appear instinctive today, they have not been so forever, which makes me think that - unlike an angry facial expression - there must be some kind of formation involved in musical tastes. Our reaction to music is caused by some kind of conditioning, but what?
I suppose it is impossible to go anywhere without hearing music these days, even as an infant - supermarkets play music, your parents use the tv/radio/ipad - music (muzak?) is everywhere, so perhaps by the time a child is old enough to speak, a sense of emotional connection with major/minor has already been instilled?
Sorry for the length of this, but in turn I'd love to know what you think.
All best,
Martin
Very interesting thoughts, Martin. Thank you.
QuoteDo we need to learn and use a specific musical vocabulary to convey emotions? I don't think so. When we are babies, we don't remain silent, study language and grammar, then one day suddenly say, "Mummy, would you mind awfully exposing your breast so I can have a delicious meal?" :-)
Great picture!
(I'm seeing a baby reading the newspaper before breakfast.)
QuoteA baby communicates its need for food by more basic means, such as screaming.
I agree. In this discussion I think of
basic symbols anyway. If Schopenhauer's feelings disagree with Beethoven's, I would consider that a discrepancy at a higher, more finely nuanced level, far above the basic level. For example, the emotional difference between a major and a minor chord is something I consider basic, like the difference between, say, laughing and crying. However, the difference between the Mixolydian and the Aeolian modes, for instance, sounds to me like the difference between two long stories -- much more room for interpretations, much more complex than the shape of eyebrows, or squares and triangles.
QuoteBut if you go further back in time, major and minor didn't exist in the way we define them now - music was modal. And if you examine this music, (e.g. gregorian chant, mediaeval or renaissance music) the connection between major sounding modes (modes 5 to 8) and minor sounding modes (modes 1 to 4) no longer accords with the emotions we assign to them now. Music expressing joy can be in a minor mode and vice versa. Some chants expressing the joy of the resurrection sound "minor" to modern ears, and some chants connected with death sound "major".
Yes, that's an important point. That means, the evolution of emotional languages progress faster. On the other hand, it could be that just the
symbology got more precise, while the
basic emotions haven't changed much. For example, a human may think a rainbow consists of just five or so colors. When that same human looks through a telescope (technical evolution), the rainbow reveals its endless number of colors because the color transitions are gradual. Nevertheless, the color "red" keeps symbolizing basic things like fire, blood etc. But now, having discovered an extended color palette, with more nuanced redish tones from orange to wine-red, it's possible to express complex stories of fire, blood etc.
Speaking of fine-tunings. On YouTube I discovered these
microtonal guitars, as they call them. Very fascinating. While a normal guitar fret is a straight bar across all six strings, such a microtonal bar is split into six fragments, each positioned differently. Interestingly, to my "well-tempered" ears, it doesn't sound mistuned at all:
https://youtu.be/iRsSjh5TTqI?t=185
Speaking of Bach: In the following video that microtonal expert demonstrates four different historic tunings on a microtonal guitar. I'm not sure if I really hear any differences or if I just imagine them:
https://youtu.be/kyQaSFgnVI8?t=212
Anyway, what I'm trying to say is that the basic emotional roots, through the centuries, probably haven't changed as fast as the number of tools to express that emotions. -- But I may be wrong.
QuoteWhich leaves us with a problem. If these connections appear instinctive today, they have not been so forever, which makes me think that - unlike an angry facial expression - there must be some kind of formation involved in musical tastes. Our reaction to music is caused by some kind of conditioning, but what?
That's the hot question I've been wondering about for a long time.
I think fashion involves some kind of "gravity law". It starts with a tiny core, a small dust particle that attracts other dust particles. The core gets bigger and thus its gravity increases, therefore attracting even more particles. It grows exponentially. In other words, a famous person -- an influencer! -- sings, for example, a simple two-tone melody though an autotune-yodel-machine, and three fans of that influencer like it because they admire their idol's attitude. That is, the new song symbolizes that special attitude. Those three fans attract more fans and so on. Luck is the biggest parameter in this process. Once a new fashion has started to roll, it keeps rolling.
The logic, to that point, seems plausible.
But the fans won't eat everything the influencer serves. There are limits. So there must be a certain programmed common palette of style elements where the influencer can chose from, and that will generate a resonance among the fans. And that's the big question. Why do special styles at special times have such a great resonance around the world? There are classic fans on all continents. Same for jazz, soul, rock, hip hop etc. for pentatonic scales and so on. I understand that the technical evolution brought new instruments. But only some of them got popular. I think a new instrument can only be successful if it can be used to express the current local life style. So the core lies again in the human itself, in the mood of the people at a certain place at a certain time.
Perhaps :-)
Cheers,
|-|ardy
In pipe organ tuning, there is a plethora of tunings that are not equally tempered. When I still had my big organ, it had various selections that would instantly retune the whole array. When you start playing a familiar piece in one of those, it instantly sounds more interesting, familiar, but not the same. All intervals are just that tiny bit off and all harmonies are just that tiny bit different. For me, with no perfect pitch ears and barely interval ears, it wears off in about a minute, and then you get the same shock when you switch back.
I'll see whether I can find an example somewhere. It's hard because most examples are the same piece played twice, which is (with my ears) very difficult to really compare. You need that one/two/one switch option during the playing of the piece.
Hoppie
Mathematically: http://tonalsoft.com/enc/w/werckmeister.aspx
Quote from: Jeroen Hoppenbrouwers on Wed, 2 Dec 2020 10:08
In pipe organ tuning, there is a plethora of tunings that are not equally tempered. When I still had my big organ, it had various selections that would instantly retune the whole array. When you start playing a familiar piece in one of those, it instantly sounds more interesting, familiar, but not the same. All intervals are just that tiny bit off and all harmonies are just that tiny bit different. For me, with no perfect pitch ears and barely interval ears, it wears off in about a minute, and then you get the same shock when you switch back.
I'll see whether I can find an example somewhere. It's hard because most examples are the same piece played twice, which is (with my ears) very difficult to really compare. You need that one/two/one switch option during the playing of the piece
Hoppie - yes, this is correct. The equal-tempered scale is "out of tune". Major chords are particular offenders - the 3rd is too high above the root and the 5th is too low. The reason for all these temperaments is that they try to get a more perfect tuning in some keys - which brings me back to my first post: music is scientifically imperfect because of the Pythagorean comma. Unequal temperament works in some keys, and equal temperament works in none!
Of course this problem is avoided completely if one sticks to monody - the world is your oyster there - and music originated in monody...
[I need longer to respond to Hardy :-) ]
M
Quote from: Hardy"Empirical" knowledge comes from sensory inputs
Elaboration here; aviation-related, too! (first comment on the page).
Cheers,
martin
(the other one)
As far as taste goes, it wouldn't surprise me if all human cultures have some attraction to rhythm of some kind, because rhythmical sounds are so common in nature, and human beings like to find meaning in things and imitate things. Animals make noises too, and mimicry there is also a basis for human vocalization. And its a short step from there to create tools to make sounds with.
But what direction these experiments take are certainly informed by past experiences and the surrounding culture. I read somewhere once that the ancient Greeks found the major third to be so unpleasant that they avoided it, and now the major third is your prototypical backbone of chords that sound "happy."
Speaking of culture, it occurred to me the other day that the musical Grease (remember it?) was set in 1958, but written in 1971. That means only 13 years passed from the era in which it was set to the era in which it was performed, and yet the whole esthetic of the musical is the whimsey of theatrical travel to a bygone era: poodle skirts, sock hops, hot rod cars, and other 50's tropes. And yet that was only 13 years ago. Look at what 13 years did to pop music:
1958 Billboard top musicians: Everly Brothers, Elvis Presley, Perry Como, Dean Martin, the Coasters, Chuck Berry, Buddy Holly.
1971 Billboard top musicians: Three Dog Night, Bee Gees, Al Greene, Janis Joplin, James Taylor, the Rolling Stones, Joan Baez, Tom Jones.
It's like two completely different universes. So it would make sense that a musical in 1971 about a story in 1958 would seem nostalgic and otherworldly.
But still, that's only 13 years. If we were to make a musical now, set it 13 years ago in 2007, would it seem so far away in time? Is musical innovation moving at the same pace now as it was then? I feel like the answer is no, but is that just because I'm older? Or has the Internet slowed innovation?
Without mass communication, talented "inventors" could more easily achieve critical cultural influence, because there wasn't as much to choose from. So one band could become a trendsetter fairly easily. But in the era of the Internet, when the world's content is at your fingertips and in your headphones, it's harder for one "inventor" to influence great swaths of culture. So trends don't develop as quickly, and cultural transformation slows.
Or maybe I've got that completely wrong, and maybe it's an artifact of time dilation: when you look backwards in time, eras seem more compressed the farther back you go?
Quote from: Will on Wed, 2 Dec 2020 20:37
I read somewhere once that the ancient Greeks found the major third to be so unpleasant that they avoided it, and now the major third is your prototypical backbone of chords that sound "happy."
Hardrock guitarists also avoid that third -- it just sounds too happy :-) Just play the other two notes, and your chord becomes a
power chord.
Quote from: Will on Wed, 2 Dec 2020 20:37
Look at what 13 years did to pop music:
...
Or maybe I've got that completely wrong, and maybe it's an artifact of time dilation: when you look backwards in time, eras seem more compressed the farther back you go?
I think it's both, time dilation and also an accelerated cultural progress in the past 70 years.
All in all, it's nice that new music styles don't replace existing ones. During all this musical progress in the last 500 years, the style palette just gets larger. It's not a single timeline but many timelines in parallel. Classic is still there. Rock ist still there. Folk, jazz etc. No style dies out.
Some pop music composers, however, haven't been particularly innovative in the past two decades. Melodies, nowadays, almost consist of just one pitch. They compensate this boredom by unusual sound effects. Today it's the sound, not the melody, that makes the hit. I can't hear that. Unfortunately, I
have to hear it when I go shopping in the supermarket. I always try to get out as quickly as possible.
Cheers,
|-|ardy
Another time lapse from 1959 to 2009: https://youtu.be/Sb5aq5HcS1A
Hi all,
I regard mathematics as a process of discovery rather than invention for the simple reason that to be logically self-consistent, there can't be alternative choices that one could have made in deriving the system from a given set of axioms. This is the utility of math.
You can make up nonsensical axioms, sure, some that are even logically self-consistent, but unlike math they don't tend to accurately reflect the 'world' we find ourselves in.
Bessy is an elephant
All elephants are pink
Therefore, Bessy is pink
Perhaps one can argue that symbolic expression is an invention. There are choices one can make about how ideas can be represented.
Does math have an existence? That depends on what you mean by 'exist'. Like the word 'reality' it is context-dependent. I would agree that math exists but that its existence is mind-dependent.
Regards Steve.
I might be very black/white here but... To me it sounds like a "definition of words" thing.
Discovery: the finding of the surprise, the outcome was unforeseen. The outcome was different from the goal of the excercise.
Invention: the outcome matches the goal of the excercise. The first car was an invention, because the purpose was to build a car.
In music terms, yes there is a set of notes/frequencies/timing to play around with. If Mozart had an idea in his mind and the outcome matched the idea in his head, it was an invention. If in the process he found another trajectory to follow by "randomness" (a combination of words that created a new "aha?" feeling never experienced before), it's a discovery.
So by definition... discoveries are always an "accident". I discovered my life, I didn't invent anything. So by definition my life is a series of big accidents :-)
Quote from: IefCooreman on Mon, 14 Dec 2020 07:58
So by definition... discoveries are always an "accident".
Certain old seafarers would definitely disagree. But I believe that is a different kind of discovery. Now we get into semantics...
I agree with Steve; mathematical laws are discovered, not invented.
Attributes like "Bessy", "elephant", "pink" themselves are not mathematical functions. They are just symbols that can be counted like any other symbols. They are replaceable; they won't touch any universal mathematical function. Whether Bessy is really an elephant is a matter of empirical sensors and political agreements, i.e. the answer is highly variable and lies outside the mathematical scope. But this human-made variable doesn't change that human-discovered deductive logic. (I'm now putting math and logic into the same pot; some may say logic is yet another extra aside from math.)
My current definitions of the words "discovery" and "invention":
A discovery is a new knowledge element that occured by empirical or rational activity.
An invention is a composition of multiple memorized knowledge elements; the composition is constructed rationally and tested empirically.
There is no memorized "pre-math" knowledge which could be used to invent math. Math itself is already a priori.
Cheers,
|-|ardy
Here's a musing on discovery vs. invention: Imagine you could record every word ever written by humanity in one long string variable. You come up with a scheme for cataloging this, maybe alphabetical by author, by country, and then in chronological order after that, and then represent all of this information as numbers. In base 2 for binary, or base 26 for the English language alphabet, or base 10,000 for all the alphabets in the world... but it's really arbitrary. You just need a way to code it from start to finish, as a value somewhere between 0 and 1.
Then take a gold bar (gold is chosen purely for aesthetic reasons), of one unit length, and make a tiny slice at the correct spot to record that value.
And the result is that you have all the literature of all of humanity coded in a single tick.
But obviously, there could be other ticks, had humanity written different books. In fact, you could just make a random tick on the bar, and come up with an entirely different literature: plays that Shakespeare didn't write, novels by authors who don't exist, songs that have never been written.
Is that discovery or invention?
Hi Will,
I would say the method of encoding the information would fall more in the 'invention' category given free choices can be made by an 'inventor' in assembling an encoding algorithm from available sub-processes.
The decoding of the knowledge itself I would say sounds more like an act of discovery.
But perhaps I'm misunderstanding the question!
Regards Steve.
QuoteAnd the result is that you have all the literature of all of humanity coded in a single tick.
I don't understand your idea, Will. I can't see how a
single value could contain every word ever written by humanity.
Is that
single value just another metaphor for "house"? "Imagine you could build a house that stores every book ever written by humanity; is that house a discovery or an invention?"
Or do you mean "coded in" in the sense of "symbolized by"?
(I'm a coder. For me, a code contains encoded information that can be decoded to get the original information. If the code of all literature can't be decoded to restore all literature then it's not a code.)
Cheers,
|-|ardy
Your code is a one-way hash with extremely high collision risk. It does not encode anything. It compresses extremely with loss of nearly all information. The construction of the code algorithm is an invention (you could patent it); but you cannot link it to discovery of literature, I believe.
Hoppie
Sorry Hardy, having dismantled my 747 sim in June and being on the move for 6 months, I have spent the last couple of weeks getting it set up again - so have been distracted from this thread, hopefully for reasons you understand. :-)
Quote from: Hardy Heinlin on Wed, 2 Dec 2020 04:29
For example, the emotional difference between a major and a minor chord is something I consider basic, like the difference between, say, laughing and crying. However, the difference between the Mixolydian and the Aeolian modes, for instance, sounds to me like the difference between two long stories -- much more room for interpretations, much more complex than the shape of eyebrows, or squares and triangles.
I understand this view, and I certainly think it is true for the majority of us, in Western culture. However, I'm not sure I can go so far as to agree that the emotional expressions we derive from major/minor chords are as innate or instinctive to the human race as laughing/crying, or eyebrow expressions.
Whilst it is the case that, to those of us accustomed to "normal" musical language, mixolydian and aeolian modes (for example) sound less obvious or innate, I have spent a large section of my career teaching young people non-standard Western musical languages and notations. What seems to us adults to be complicated and unusual can seem very simple and intuitive to children who have yet to learn a particular notation, and whose ears - despite several years of subconscious "normal" musical formation - approach modal languages with an ease and understanding that eludes the trained adult ear. I have encountered such young people who, when asked of a major and minor chord, which is happy and which is sad, just look confused and can't answer!
I suspect this may also be the case for people formed in Eastern (i.e. non-Western) musical cultures, but I have no experience of this so cannot comment with any certainty.
Quote from: Hardy Heinlin on Wed, 2 Dec 2020 04:29
On the other hand, it could be that just the symbology got more precise, while the basic emotions haven't changed much. For example, a human may think a rainbow consists of just five or so colors.
It's possible to argue that the reverse of this applies to music: the language of tonality developed from a multi-modal spectrum to just two colours - major and minor - over several centuries, hence the invention of the Second Viennese School (12 tone music) to get composers out of a very confining musical rut! Might it also explain the start of the early music movement, whose origins go back to the mid nineteenth century - musicians looking for ways out of what they perceived as an increasingly narrow path?
Quote from: Hardy Heinlin on Wed, 2 Dec 2020 04:29I think fashion involves some kind of "gravity law". It starts with a tiny core, a small dust particle that attracts other dust particles. The core gets bigger and thus its gravity increases, therefore attracting even more particles. It grows exponentially. In other words, a famous person -- an influencer! -- sings, for example, a simple two-tone melody though an autotune-yodel-machine, and three fans of that influencer like it because they admire their idol's attitude. That is, the new song symbolizes that special attitude. Those three fans attract more fans and so on. Luck is the biggest parameter in this process. Once a new fashion has started to roll, it keeps rolling.
I like this analogy!
Quote from: Hardy Heinlin on Wed, 2 Dec 2020 04:29But the fans won't eat everything the influencer serves. There are limits. So there must be a certain programmed common palette of style elements where the influencer can chose from, and that will generate a resonance among the fans. And that's the big question. Why do special styles at special times have such a great resonance around the world? There are classic fans on all continents. Same for jazz, soul, rock, hip hop etc. for pentatonic scales and so on. I understand that the technical evolution brought new instruments. But only some of them got popular. I think a new instrument can only be successful if it can be used to express the current local life style. So the core lies again in the human itself, in the mood of the people at a certain place at a certain time.
I suppose, thanks mainly to the internet, each individual now has a plethora of choices in musical taste, so perhaps we are seeing a new mediaevalism - a break from the orthodox canon of western musical tradition - where everyone's musical views/tastes are equally valid and anything can be described as good or valid?
A fascinating subject. But, to come full circle, thanks for the amazing 747 software - it's great to have it back! :-)
Martin