"Marcus du Sautoy is professor of mathematics at Oxford University and a fellow of New College he has recently been named as the next Simonyi Professor for the Public Understanding of Science." He is also very musical. I heard him being interviewed on radio and there was discussion around the connections between music and mathematics.
He goes way beyond obvious patterns and can feel prime numbers in music. It was mentioned that some Messiaen pieces are composed around prime numbers.
We have some mathematicans here. I was wondering if they could give their fix on where they see or feel the connections between the science and the art form. Is there something instinctual for some people in that they can feel the mathematical patterns in say Bach beyond the clear patterns.
What other composers seem to have been influenced by maths in their writing?
Mike
If you can read French, Xenakis has the whole book of Formalized music on his website. But you need to be a math expert, too, if you want to be able to even understand it.
Quote from: knight on December 13, 2008, 01:46:33 AM
It was mentioned that some Messiaen pieces are composed around prime numbers.
It's in the beats, and requires no understanding of higher mathematics--
QuoteThis last element is especially important. Indeed, Messiaen referred to Turangalîla-symphonie as "a vast polyphony of rhythm." As he explained in The Technique of My Musical Language, a treatise explaining his compositional methods, Messiaen thought of rhythm independently of pitch. Rhythmic figures had for him as much integrity and interest as melodic shapes, and over the years he developed a stock of favored rhythmic figures that include not only Classical Greek patterns and Hindu tâlas, but also such original conceits as rhythmic palindromes and figures whose durations yield prime numbers (11, 17, or 23 beats, for example), which Messiaen regarded as having quasi-magical significance.
from http://www.carnegiehall.org/article/box_office/events/evt_8118_pn.html?selecteddate=02152008 (http://www.carnegiehall.org/article/box_office/events/evt_8118_pn.html?selecteddate=02152008)
:)
David, Thank you for the link, it is useful to the extent that this week I bought the Turangalîla, a work I have not heard before. The programme notes on the link are much more detailed than the ones from my discs.
However, saying that 'it's the beats', is like telling me that maths is about numbers.
Thanks ' for the note of other composers who incorporate maths into their music.
I have a feeling we can now just watch this topic drop like a stone down the list.
Mike
Quote from: James on December 13, 2008, 11:57:58 AM
Math can be applied to anything, but who wants to hear math when they listen to music, defeats the purpose me thinks.
Excellent point! *claps*
I major in mathematics but somehow do not feel justified to talk for math in music. My first calculus teacher (her husband is a conductor, btw!) told once that when mathematicians try produce some music using math, it is usually a very lousy kind of music. Schoenberg is a nice illustration to that opinion. The more composers think mathematically and analyze music, disintegrate it into pieces, the more unnatural it becomes.
I like Mozart's mathematical precision in music, though it has nothing to do with math - just classicism style. And fortunately I do not hear prime or imaginary numbers, transcendental functions or matrices in music, though such analogies are tempting. (and Queen's of the Night passage in the second aria can be represented as a sine or cosine function! ;D :D )
One thing they share in common, I think, is that they both are imaginary and created by humans. Mathematics, as well as music, is very powerful, but only in people's minds. They both do not exist in nature, they are artificially created and very well fitted in the perception of the world around us. Mathematicians create rules of the game called "math", as well as composers make up scales for the game called "music". Music is the world of organized sounds and mathematics is the world of organized theories and symbols. So I think the reason some people try to realte them is just because they are part of our imagination and somehow exist only there.
I think you will find disagreement that maths does not appear in nature. My understanding is that it does, the movement of the planets is in part a mathematical expression. Maths is also claimed as being the basis of all science.
Mike
I disagree; maths is not invented, it is discovered. Tied to physics, it tells us about our world.
However, my hope was to prompt any members here to provide insight into the remarks in my initial posting. Perhaps another time when some posters happen by who can relate to that statement.
Mike
Quote from: James on December 13, 2008, 10:40:46 PM
no Sarastro is correct, math is just another abstract language created by us, it's used in an attempt to explain things...but it hardly does any explaining, more describing in a very limited way, there is probably so much more to the larger picture, far beyond what our tiny brains are capable of understanding....
Sounds religious crap to me. The way that math explains things is not "very limited". Perhaps our tiny brains are too tiny to understand everything but that's a stupid excuse not to try our best.
Quote from: knight on December 13, 2008, 10:05:26 PM
the movement of the planets is in part a mathematical expression
But who has expressed this expression? Planets themselves? The Sun? A squirrel? Initially it is not a mathematical expression, it is just the things are. Mathematics is the way we try to describe it, and it works. Sometimes it does not work, and we seek other ways...
Physics, what I have to study as a math major as well, is so quite different... Even mathematics in physics and in pure math is different. For instance, in physics "infinity" is considered to be the approximate number of stars in the Universe and is placed nowhere. In mathematics "infinity" is NOT a number and is a mathematical idealization, as well as the differential and the concept of limits. There are closed and open forms, imaginary numbers that can not exist physically (square root of negative one) or the base of natural log.
Quote from: Sarastro on December 13, 2008, 10:00:27 PMMy first calculus teacher (her husband is a conductor, btw!) told once that when mathematicians try produce some music using math, it is usually a very lousy kind of music.
Of course it's lousy because they use WAY too simple (but somewhat deceptive) algorithms. Science does not know yet enough about human brain. Maybe 50 years from now it does (and computers are powerful enough to run brain simulations in realtime). Computer composer sounds funny to us as an concept but just imagine how much the world will change during the next 50 years! Computers and robots will be able to do almost anything so why not compose too!
We must always be careful about what we are actually doing with math and computers and make the right conclusions.
Quote from: Sarastro on December 14, 2008, 12:10:59 AM
But who has expressed this expression? Planets themselves? The Sun? A squirrel? Initially it is not a mathematical expression, it is just the things are. Mathematics is the way we try to describe it, and it works. Sometimes it does not work, and we seek other ways...
No, I don't see it this way. Of course the planets do not not move in a specific way
in order to describe maths. But they move according to physical laws and those laws are mathmetical in part. Sorry, I stick by my remark that maths is there and is being discovered, not; an invented language or a mere descriptor.
Mike
Quote from: 71 dB on December 14, 2008, 12:12:50 AM
just imagine how much the world will change during the next 50 years!
Yeah - global warming, air pollution, energy depletion, robot revolution, possible vanishing of the human race. :) :D
Actually, all the mathematicians I know who like classical music say that math people should not touch music, as well as computer people. Music is not just a set of meaningless sounds but consists of whole pieces that possess an idea. Putting it into calculations is killing anything live in it. And I don't think computers can ever replace the human soul and brain. The difference is that the computer has a finite set of operations, and it is not organic; human intelligence depends on the area of the gray matter of our brain, it may increase as well as decrease. Of course it can not increase infinitely, but even very small changes bring immense results. And the ability of living creatures is to learn from experience and feel other living beings. How can you imagine electronic music touch a living soul? There have always been tales about that, such as a tale about a mechanical and a live nightingale - for instance in Stravinsky's Le Rossignol (I'm being on topic :D).
Quote from: knight on December 14, 2008, 12:22:55 AM
that maths is there
Well, gravity is there, not math. :D What you are saying is that Jupiter was always there, I mean, called
Jupiter, and we just discovered its name in English. And this also implies that we did not invent English - we discovered it, it was always there, as well as other languages.
Quote from: Sarastro on December 14, 2008, 12:35:47 AM
Well, gravity is there, not math. :D What you are saying is that Jupiter was always there, I mean, called Jupiter, and we just discovered its name in English. And this also implies that we did not invent English - we discovered it, it was always there, as well as other languages.
No that is not what I am saying.
Quote from: Sarastro on December 14, 2008, 12:10:59 AMFor instance, in physics "infinity" is considered to be the approximate number of stars in the Universe
You have misunderstood the idea. The estimated number of stars in the universe is 7*10^22. In many calculations we can use infinity instead of this very large number because the result is the same with "more-than-enough" decimals. That's the main difference between math and physics. In math we can (in most cases) use infinite precision while in physics we have to play with finite presicion because of physical measurements of finite presicion.
Quote from: Sarastro on December 14, 2008, 12:10:59 AMIn mathematics "infinity" is NOT a number and is a mathematical idealization
However, math is able to set rules for infinity. In many cases infinity is not a problem at all. For example the infinity sum 1+1/2+1/4+1/8+...+1/2^n = 2, n E R -> infinity.
Quote from: Sarastro on December 14, 2008, 12:10:59 AMThere are closed and open forms, imaginary numbers that can not exist physically (square root of negative one) or the base of natural log.
Imaginary numbers does not need to exist physically to be mathematically meaningful.
Quote from: knight on December 14, 2008, 12:47:30 AM
No that is not what I am saying.
So what are you saying?
That tangent line to the graph, or integrals, or derivatives, or polar system of coordinates, or Fourier analysis, or infinite polynomials were always there? That right triangles filled the space? That linear transformation existed on the Earth long before?
Quote from: 71 dB on December 14, 2008, 12:52:41 AM
You have misunderstood the idea.
No, I haven't. I am just in math camp. And I didn't get your point in showing a geometric series problem. What infinity? This geometric series converges absolutely and can be very easily explained on a piece of paper - geometrically.
Sarastro, I am not in interested in going there and wrestling about this. My interest is in the coinnection between music and maths, by all means have a discussion about what maths means divorced from music, but not with me.
Mike
Quote from: Sarastro on December 14, 2008, 12:28:11 AM
Actually, all the mathematicians I know who like classical music say that math people should not touch music, as well as computer people.
I agree. We need to know a lot more about human brain, but let's not deny the right to compose for the math/computer people, ok?
Quote from: Sarastro on December 14, 2008, 12:28:11 AMMusic is not just a set of meaningless sounds but consists of whole pieces that possess an idea.
Someday computers will be able to come up with ideas.
Quote from: Sarastro on December 14, 2008, 12:28:11 AMPutting it into calculations is killing anything live in it.
What kind of calculations? The creative prosess of a composer is in fact about VERY complex calculations, so complex that we don't recognise them as calculations but as a creative prosess. There is no reasons why computers could not do that someday. It takes fuzzy logic, neural nets and other things to be invented but it's doable. We already can teach computers to do simple things like control a complex manufacturing process in a factory or recognice sounds/images. The commersical applications are increasing and so is the attraction to finance this kind of scientific research.
Quote from: Sarastro on December 14, 2008, 12:28:11 AMAnd I don't think computers can ever replace the human soul and brain.
Soul does not exist. Computers should be build to
complement human brain rather than replace.
Quote from: Sarastro on December 14, 2008, 12:28:11 AMThe difference is that the computer has a finite set of operations, and it is not organic;
Infinite calculations can be do with finite set of operations. Simple operations are used to have simple algorithms which are used to build little more advanced algorithms which are... ...finally we have extremely sophisticated algorithms. If "organic operations" are needed then we simply make computers simulate organic structures.
Quote from: Sarastro on December 14, 2008, 12:28:11 AMhuman intelligence depends on the area of the gray matter of our brain, it may increase as well as decrease. Of course it can not increase infinitely, but even very small changes bring immense results. And the ability of living creatures is to learn from experience and feel other living beings. How can you imagine electronic music touch a living soul? There have always been tales about that, such as a tale about a mechanical and a live nightingale - for instance in Stravinsky's Le Rossignol (I'm being on topic :D).
What do you mean by electronic music here? Is acoustically played (by human players) but computer composed music electronic?
Today computers can't compose like humans. Someday computers are intelligent "creatures" with self-consciousness. They learn new things by observing their environment. They feel sadness, joy, fear, etc. When computers are that capable (human), there is no reason why they could not compose like humans.
Quote from: Sarastro on December 14, 2008, 01:07:02 AM
No, I haven't. I am just in math camp. And I didn't get your point in showing a geometric series problem. What infinity? This geometric series converges absolutely and can be very easily explained on a piece of paper - geometrically.
The geometric series showed that infinity isn't a problem for math. Not a number? So what?
Quote from: knight on December 13, 2008, 09:20:37 PM
However, saying that 'it's the beats', is like telling me that maths is about numbers.
Math is not about numbers actually. In elementary mathematics courses that might be true, but abstract mathematics is much broader in scope.
Quote from: Sarastro on December 13, 2008, 10:00:27 PM
told once that when mathematicians try produce some music using math, it is usually a very lousy kind of music. Schoenberg is a nice illustration to that opinion. The more composers think mathematically and analyze music, disintegrate it into pieces, the more unnatural it becomes.
Schoenberg didn't use math to write music, and I think you'll find that the consensus has been for quite along time now that he is a first rate artist, one of the greatest composers of the 20th century thank you very much.
Quote from: knight on December 13, 2008, 10:55:39 PM
I disagree; maths is not invented, it is discovered. Tied to physics, it tells us about our world.
Platonic view of mathematics, the others posit the view shared by Aristotle. And I can't believe people still debate this issue to this day! :D
Yes, now is there any chance of discussing music in relation to maths, or is this now really about the origin of maths?
Quote from: knight on December 14, 2008, 06:53:19 AM
Yes, now is there any chance of discussing music in relation to maths, or is this now really about the origin of maths?
If it wasn't clear to you we're talking about the meaning and origins of math because we don't know the answer to your question. ;D
Though I really don't know why prime number beats is not a satisfactory answer. ??? I don't think it goes deeper than that because the claims of the math in Messiaen are highly inflated because the prof is just trying to do a pr job for his field-- math. Though my friends say that I'm cynical now. $:)
Well, take it any way you like, I am out of it for a few days.
Mike
Quote from: DavidW on December 14, 2008, 06:44:03 AM
Platonic view of mathematics
QuotePlatonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the view most people have of numbers. The term Platonism is used because such a view is seen to parallel Plato's belief in a "World of Ideas" (typified by Plato's cave): the everyday world can only imperfectly approximate of an unchanging, ultimate reality. Both Plato's cave and Platonism have meaningful, not just superficial connections, because Plato's ideas were preceded and probably influenced by the hugely popular Pythagoreans of ancient Greece, who believed that the world was, quite literally, generated by numbers.
The major problem of mathematical platonism is this: precisely where and how do the mathematical entities exist, and how do we know about them? Is there a world, completely separate from our physical one, which is occupied by the mathematical entities? How can we gain access to this separate world and discover truths about the entities? One answer might be Ultimate ensemble, which is a theory that postulates all structures that exist mathematically also exist physically in their own universe.
I admit that there might be a heavenly realm of mathematics, as well as a realm of music, or Ideas, and great composers and mathematicians just somehow get access to it. But unless the existence of such realms is scientifically proven, I can not believe in it.
Moreover, the Greeks believed in many things we consider nonsense nowadays. They believed in Gods, monsters, half-divine creatures. They believed that Helios rode his sun chariot during the day and at night traveled through the kingdom of shadows - Hades. They thought that an arrow can fly because its biggest in volume part's, feathers', element is air. Correspondingly they thought that a bigger stone falls into earth and makes a deeper print because its natural element is earth, it "wants" to be closer to it. But my major concern is their belief in gods and their kingdoms which could affect also beliefs in mathematics and other worlds.
Quote from: DavidW on December 14, 2008, 06:40:33 AM
Schoenberg didn't use math to write music
I know he didn't. It was a metaphor. Speaking about being the greatest, I always remember Malevich's joke - black square, and how people rushed to find the organization of the Universe in there. Like
The Emperor's New Clothes tale.
Quote from: James on December 14, 2008, 03:39:26 AM
Well, electronic music is very popular now and does touch many people, where have you been?
Electronic music is music that employs electronic musical instruments and electronic music technology in its production. As far as I understand, it means that instead of using traditional instruments, people just use such devices to create patterns and mix them. That is what DJ's do in clubs, if you have been to one. I personally do not like such kind of music, and always resist when friends try to scoop me in such places.
Quote from: 71 dB on December 14, 2008, 01:43:58 AM
The geometric series showed that infinity isn't a problem for math. Not a number? So what?
I still don't get your point. I was talking about
concepts, and all of a sudden you threw a particular problem. And what if the ratio were bigger than one?
Quote from: 71 dB on December 14, 2008, 01:40:34 AM
Computers should be build to complement human brain rather than replace.
When they start thinking they will absolutely sure start thinking how to replace the humans and be independent. >:D Heard anything about Isaac Asimov?
I'm not religious at all, but there are things that are better not to be touched. Rutherford, after having discovered the model of the atom and having done some work, later regretted of his discoveries, as he very well understood that we are too small and would never be able to control atoms. Moreover, he knew that the sneaky people would not hesitate to use it as a weapon, and he was bitterly correct, in both cases. We've already experienced atomic bombs (not including experiments with them) and the Chernobyl' explosion. The more we advance in technology, the more retarded we become. Apparently, there will be no life in a while. And computers can not exist separately. Unlike organic life, which continued for millions of years, reproducing itself, sources to build mechanical devices are limited.
"There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy." (c) :P
Quote from: Sarastro on December 14, 2008, 04:02:01 PM
I know he didn't. It was a metaphor.
Um do you know what a metaphor is? That was not a metaphor. You were using Schoenberg as an example as your wording clearly indicates.
QuoteSpeaking about being the greatest, I always remember Malevich's joke - black square, and how people rushed to find the organization of the Universe in there. Like The Emperor's New Clothes tale.
Was that supposed to be a pithy way to mock me for believing that there is some kind of meaning to critical consensus? Well excuse me for not being a nihilist. ::)
Quotes and allusions to literature that you enjoy might make you sound witty in your mind, but the rest of us grew out of that phase in high school, and frankly it sounds condescending and trite. Say what you mean, and if it's well argued it will have an impact regardless of the flowery speech you couch it in.
My opinion on the subject is stated in my first post here. As for Schoenberg (as well as for Webern and Berg), I find his music highly mathematical, in a sense that it is mechanical - that is for the metaphor. If a mathematician were to compose a piece, something alike would come out. I think I am entitled to my own opinion regardless of what the consensus decides. By the consensus even Britney Spears is one of the greatest singers of our time.
Quote from: 71 dB on December 14, 2008, 12:12:50 AM
Computers and robots will be able to do almost anything
Making love is one of the exceptions. ;D
Quote from: 71 dB on December 14, 2008, 01:40:34 AM
Soul does not exist.
Proof?
Quote from: 71 dB on December 14, 2008, 01:40:34 AM
Someday computers will be able to come up with ideas.
Your ideas certainly look like they've been programmed. ;D
Quote from: Sarastro on December 14, 2008, 12:10:59 AMIn mathematics "infinity" is NOT a number and is a mathematical idealization
"Number" is an ambiguous term in mathematics, but it usually refers to an element of the real or natural numbers, for example. Infinity is a "number" in the one-point-compactification of the reals, and defined conveniently in many other situations. Don't know what you mean by "idealization" however
A professor came to my university two weeks ago and gave a talk on mathematics and music. He tries to frame the common rules of tonality (which I think was a controversial point) into the language of geometry via quotient spaces and stuff like that. The beginnings of his talk were quite accessible but (what are supposed to be) his substantial results use rather difficult math. I had mixed feelings about it, but thought it was interesting. The pictures were nice. I'll find his name out when I get a chance. He's currently writing a book to be published as well.
Doesn´t math mean, the well defined language of everything? It´s not the point, that math is still very limited and even full of mistakes, if the idea was to describe the truth, math is telling the truth - even if the truth is only local, I think the local coexists with everything else, like individual minds should all be respected, no matter how f..... up they are, and that our universe coexists with parallel universes (in some sence).
Language will always be primitive, but not necessary the understanding of it. The way we use the language of math is, that we generate it from logic, which is the very light of commonness of an observation. And the way we read it is a reflection into ourselfes, so it is no longer a language but the truth itself. Now the reason, that mistakes still appears, especially in excersises made by students, is that we are too lazy to keep focusing on that light of logic, so that it is not always perfectly executed.
Math is supposed to be dealing with the truth, I think, as far as possible, even in order to describe beauty!
Quote from: Sarastro on December 14, 2008, 04:02:01 PMI still don't get your point. I was talking about concepts, and all of a sudden you threw a particular problem. And what if the ratio were bigger than one?
The sum becomes infinite. I never got your point, it seems.
Quote from: Sarastro on December 14, 2008, 04:02:01 PMWhen they start thinking they will absolutely sure start thinking how to replace the humans and be independent. >:D Heard anything about Isaac Asimov?
Why? Perhaps if they were created in evolution. All the emotions must be teached. Why teach machines to hate us? Well, in evil hands of course... ::)
Quote from: Sarastro on December 14, 2008, 04:02:01 PMI'm not religious at all, but there are things that are better not to be touched. Rutherford, after having discovered the model of the atom and having done some work, later regretted of his discoveries, as he very well understood that we are too small and would never be able to control atoms. Moreover, he knew that the sneaky people would not hesitate to use it as a weapon, and he was bitterly correct, in both cases. We've already experienced atomic bombs (not including experiments with them) and the Chernobyl' explosion. The more we advance in technology, the more retarded we become. Apparently, there will be no life in a while. And computers can not exist separately. Unlike organic life, which continued for millions of years, reproducing itself, sources to build mechanical devices are limited.
Ever heard of the benefits of progress? They usually outweight the negative aspects. We can't draw a line when to stop. That's just not possible. It's like trying to "freeze" evolution.
Quote from: Florestan on December 14, 2008, 11:24:40 PM
Making love is one of the exceptions. ;D
You perv... ::)
Quote from: Florestan on December 14, 2008, 11:24:40 PMProof?
I don't need to prove that. You have to proof soul exists. If I claim I am 1000 years old you don't need to prove I am not, I must prove I am. That's the way the burden of proof goes. Frankly, I am surprised some people believe in the existence of soul in 21th century.
Quote from: Florestan on December 14, 2008, 11:24:40 PM
Your ideas certainly look like they've been programmed. ;D
What ideas of mine are you preferring to?
Quote from: 71 dB on December 15, 2008, 08:17:59 AM
The sum becomes infinite. I never got your point, it seems.
I think he was being inconsistent. He was trying to argue that mathematics is not tangible or real, but then when you discussed infinity he said that it was not a number, merely an abstraction and so forth... as if real numbers are "real" and not abstractions, which contradicts his thesis.
I agree with you Elgar, infinity is a well defined notion, and has just as much claim to being "real" as real or complex numbers would.
Arvo Part - Fratres - wasn't this formed from numbers?
Twelve-tone technique - mathematically 'even' music, or at least it's supposed to be.
Quote from: DavidW on December 15, 2008, 09:07:03 AM
infinity is a well defined notion
Did I say it was not? I was just saying that infinity is not a number in a common sense we put in the word "number." Infinity by the formal definition means charging forever, boundlessness, the unlimited. I tutor calculus and know that many students here have problems with understanding the concept, that is why I mentioned it. And I've never said anything about real numbers. They are just called "real" which does not necessarily mean they are real. Numbers are in your head.
Quote from: Sarastro on December 15, 2008, 04:59:31 PM
know that many students here have problems with understanding the concept, that is why I mentioned it.
Suggestion: know your audience. You were discussing the matter with 71 dB, an experienced engineer, not one of your students.
Quote from: 71 dB on December 15, 2008, 08:17:59 AM
Frankly, I am surprised some people believe in the existence of soul in 21th century.
Wonder is the beginning of wisdom...
Quote from: Sarastro on December 15, 2008, 04:59:31 PM
Numbers are in your head.
that's the way I tend to think as well, but then there is an objective measure that goes by the name of "less" or "more" which only makes sense in the presence of numbers. And that does exist in nature:
A pack of 40 wolves will most likely defeat an opposing pack of 5. The main, if not the only, reason for the outcome is the number of wolves in each pack. Even if wolves do not know how to count, the numbers will determine the result.
Quote from: orbital on December 16, 2008, 02:44:31 AM
but then there is an objective measure that goes by the name of "less" or "more" which only makes sense in the presence of numbers.
Real numbers certainly can be made into an ordered field, and we almost always consider them as such (most of analysis is built on presuming the existence of a least element in subsets of the reals), but I don't there is a unique ordering, I think there are others that also work, perhaps CS can comment. Complex numbers on the other hand do not form an ordered field. You can order it, or you can make it a field, but you can't do both.
Anyway I don't think ordering is an absolute, it's merely a restriction that we've applied to our favorite field (albeit a very meaningful restriction). :)
Numbers cannot be in your head because it seems that consciousness does not exist. I know this because it is impossible to prove its existence.
On the subject, I'm not sure it was Schoenberg who was criticized for being mathematical. Rather it was Scriabin who was said to be writing paper music that was merely mathematical formulae. I don't think anyone argues that now.
I must say that I am very sceptical of the value of the golden mean in music. It is a valuable spatial tool that should not be applied to temporal duration.
Quote from: Sarastro on December 15, 2008, 04:59:31 PM
Did I say it was not? I was just saying that infinity is not a number in a common sense we put in the word "number." Infinity by the formal definition means charging forever, boundlessness, the unlimited. I tutor calculus and know that many students here have problems with understanding the concept, that is why I mentioned it. And I've never said anything about real numbers. They are just called "real" which does not necessarily mean they are real. Numbers are in your head.
Ok, this sounds good to me. ;)
Infinity is indeed a difficult concept for many. For example, people have difficulties to believe that 0.99... = 1.
Quote from: DavidW on December 15, 2008, 05:59:25 PM
You were discussing the matter with 71 dB, an experienced engineer, not one of your students.
Thanks! :)
Quote from: Ten thumbs on December 16, 2008, 08:43:01 AM
Numbers cannot be in your head because it seems that consciousness does not exist. I know this because it is impossible to prove its existence.
Many things can't be proven 100 %, at least not yet. We must believe in the most probable, logical and obvious answers for now and revise our believes if knew knowledge/evidence suggests that. That's how science works.
Consciousness most probably exists because that's the best explanation for what we do. Other explanations like the ones were we are just parts of a simulation program of a higher being are less believable and probable. There are not much people who deny consciousness but there are many who deny soul.
Quote from: 71 dB on December 16, 2008, 10:11:35 AM
There are not much people who deny consciousness but there are many who deny soul.
Could you please define "soul"?
Quote from: Florestan on December 17, 2008, 01:22:27 AM
Could you please define "soul"?
I think it's pretty pointless to define something that doesn't exist. Hey wait! Soul
music exists. ;D
The principal and probably the only difference between consciousness and soul is that soul is supposed to continue in existence after death. To some that seems highly improbable but for matter to be conscious is also highly improbable so accepting either is at present a matter of faith.
Quote from: 71 dB on December 17, 2008, 10:41:10 AM
something that doesn't exist.
I think you do not exist. I see an image... a signature, the number of posts. Hey, maybe it's a highly intelligent computer!
Quote from: 71 dB on December 17, 2008, 10:41:10 AM
I think it's pretty pointless to define something that doesn't exist.
I think it's pretty pointless to engage someone who doesn't think. Bye-bye! ;D
Quote from: Ten thumbs on December 17, 2008, 02:07:03 PM
The principal and probably the only difference between consciousness and soul is that soul is supposed to continue in existence after death. To some that seems highly improbable but for matter to be conscious is also highly improbable so accepting either is at present a matter of faith.
Not exactly. The difference between consciousness and soul is that consciousness is bound to the physical world and can only perceive things through the limited senses of the body, while the soul exists in the realm where things are true and immutable, and that is why the soul is immortal, while consciousness isn't.
Quote from: Sarastro on December 14, 2008, 04:02:01 PM
I admit that there might be a heavenly realm of mathematics, as well as a realm of music, or Ideas, and great composers and mathematicians just somehow get access to it. But unless the existence of such realms is scientifically proven, I can not believe in it.
Is there scientific proof for morality and ethics? For good and evil? For beauty and ugliness? For greatness and genius? Or do you mean to say that you have never believed in any of those either, not even for an instance? What an odd concept anyway, to demand that the metaphysical ought to be subject to physical scrutiny. Even if such a thing was possible, what sense would there to bring something from the world that isn't seen to the one that is where the metaphysical would essentially cease to be metaphysical?
This excessive reliance to science, an inferior discipline to philosophy, is one of the reasons why ''genius'' is such a rare commodity this days. A sad state of affairs which, curiously enough, isn't stirring much regret. It seems that the fish is really content to be a fish, even though it manages to step out of the water from time to time to see the sun.