disproving einstein and infinites (Page 3)

MrSteveA67: If we break up sounds into sine waves, a musical note has a fundamental frequency that's the lowest frequency sine wave. The 'timbre' of a sound, such as the difference between hearing a brassy trumpet versus a flute is dependent upon the harmonic frequencies (which are integer multiples of the fundamental frequency) as well as their amplitudes over time.

In Western Music there are 12 tones per octave and they're exponentially spaced. This gives about a 5.95% change in frequency between each half step in a scale. Middle A on a piano is tuned to 440Hz and this gives an octave (an octave is a 2 to 1 ratio in frequencies) of frequencies like this:

A: 440 Hz
A#: 440 * 1.0595 ~= 466.2 Hz
B: 466.2 * 1.0595 ~= 493.9 Hz
C: 493.9 * 1.0595 ~= 523.3 Hz
C#: 523.3 * 1.0595 ~= 554.4 Hz
D: 554.4 * 1.0595 ~= 587.3 Hz
...

If we compare some of the ratios of these, they're close to small fractions. For example, 554.4/440 = 1.26, which is close to 5/4=1/25 and 587.3/440 ~= 1.334, which is close to 4/3=1.333...

Those two ratios are what are used for minor and major chords. They used to tune instruments to play in a specific key and get the ratios closer.

Some ratios that might sound decent in the right context can't be played well using a western scale. I was doing some experiments with skipping a scale altogether and just work with the frequencies directly, though it can send better to have the frequencies off a bit to make it sound more like a chorus, but there could be ways of doing that and having those shifts timed to rhymthic elements.

Anyway, music is definitely something I enjoy and I know there are plenty of things waiting to be done with music.

*******-*******-*******-----

Regarding the 3-D comment, again consider that even if it were somehow possible to see the interiors of objects, the eyes only see a surface anyway - how do you map a 3-D volume to a 2-D surface without losing a dimension?

Consider something like gravity, it would be considered to operate in 3 dimensions (or 4 dimensions if we include time), but consider that an object moving through space is only experiencing an acceleration in a single direction and there are only 2 rotational axises around which that vector could be oriented. The magnitude of the acceleration would then be the 3rd dimension (but the magnitude is only measured over time, so once again it's really just a 3 dimensional force and that's already including time).

Notice also that each eye already has a large number of photoreceptors. Two eyes can double that but both eyes are still just seeing 2-D surfaces. Two, 2-D surfaces doesn't really make a 3-D view anymore than how doubling the the number of photoreceptors of a single eye does.

(Yes, it's not quite as simple as I stated and there are some qualitative differences, but a truely 3-D object has depth and the senses, at any specific moment, only interact with 2-D surfaces. It's the mind/memory that allows us to learn about or create depth components, but that makes conventional "spacetime" 3 dimensional, and 1 dimension is mental and not immediately physically visible - for example, if a ball rolls behind a wall, the mind may know it's there and can make some predictions regarding where it will be but that's not what the immediate physical evidence is - it's just the wall that's seen).

the real slim DEEPy: this is reminding me of the time i dropped acid, and could "see" music floating through the air... thanks to that, i was on an electronica binge for 10 years, what a waste... i could see the organics in synthesized music, and patterns in the tones and waves... well, ill never do that again, i created some of the worst "house" music ever as a result, but perhaps 1 or 2 somewhat remarkable pieces of electronica. i got a good feel of what a good tone was, rich and organic, and spent much time creating custom tones on analog synths. i made a lot of bad songs with some really remarkable tones...



anyway, we see 3 dimensionally by taking two 2 dimensional images and combining them using triangulation. we use triangulation to measure the distances between stars, it is a perfectly acceptable way to recreate the dimension of "depth".

MrSteveA67: Well, yes, there's a depth component to vision but that's like adding another color and doesn't allow something like the interior of a 3-D cube to be seen, but just a visible 2-D surface.

Your comment regarding seeing music is actually rather applicable to the ideas I was working with and yes, some people experience synesthesia and in some of those cases people can see objects associated with sounds.

I've worked with electronics for a long time and had a job with a music company for a while as well. Something fun is to generate "lissajous" images (I think these are closely correlated with properties of atomic orbitals) and then it's easier to "see" what timbres of sounds look like. Here's a quick example:



And another video that's along similar lines of physical resonance and how various ratios of frequencies can be interpreted to create forms:

the real slim DEEPy: not oprganic enough, what i am attemting to explain has movement like a biorhythm, and "breathes" in a sense. there really is no way to explain it, your video is a good way of explaining it, but think, much more boloigical/organic. smoother, rounder, not so jagged. you also have to understand they types of tones i was hearing. this is vco-dominated subtractive synthesys, with rich filter sweeps, and wave pattern layered upon waveform... i believe the album was virus-analog, its impossible to find, very rare, and my coly has not survived time. it is most reminicent of aquamarine or squarepusher- maybe autechre.

heres a sample of the tones with which i came up afterwards..., you need a subwoofer or some large woofers... www.myspace.com/akupuncture/music/songs/lies*******09

um: akupuncture/music/songs/lies*******09 *******09 steve, just open your message box to me, it isnt gonna let me post it...

MrSteveA67: Sounds like something fun to check out. I admit that I don't know how to 'open my message box' on this site. Still rather new and don't know much of the features ...

the real slim DEEPy: just input the www.myspace.com/akupuncture, and look for the song "LIES" in the playlist. its not the best example of organic music, but its a start...

AussieOi: Aheem 12 semi-tones in western music, not 12 tones. And deep not 8. Try to keep accurate fella's.

StuckInTheSixties: There are 7 in most common modes used in "Western" music (not counting the octave).

And 12 in the Chromatic Scale (half tones/steps - again, not counting the octave).

And 6 for the spacey Whole Tone Scale (again not counting the octave - Debussy s!)

Don't bring Harry Partch into this, or the website will probably burst into flame.

By the way ...

deep says:
"the chineese use mostly penatonic (every interval is a note)"

Incorrect, although that statement just makes no sense, so it takes a little bit of guessing about the intent of the statement to define how it's incorrect. An interval is not a note. It's the measured difference between two notes, or said another way, the distance, or space between two notes. It's usually stated as a "minor 2nd, a major 3rd, a perfect 5th, etc. It's a very specific term, which you misused badly, deep.

(shrugs)

It appears that you're trying to say that a pentatonic scale is the same as a chromatic scale, which, as Aussie alluded to, is all 12 notes found within an octave, easily visualized on a piano keyboard, etc. (not counting the octave, of course). There are numerous kinds of pentatonic scales. What they all have in common is having five notes (not counting the octave, of course). Hence the usage of "penta" (five) in the word. A common one is the five black keys on a keyboard.

(shrugs)

But you are correct in that there are pentatonic scales commonly used in traditional music from China, and that certain pentatonic scales have that sort of "oriental" familiarity to them, which is, of course, based on that traditional use.

(shrugs)

That "The Physics Of Sound" vid was pretty interesting. The other less so.

the real slim DEEPy: yes, i did mean to say crhoinmatic, when i said penatonic. and when i said 8 notes, i meant in a scale (doo, ray, mee, fa, soo, la, tee, do) not counting all the half-steps...

yes the chineese tend to use penatonic, but techincally, their scale is chromatic, including all the familiar half steps. what is differrent is they do not use 8 nots scales and the 7 greek modes, as we do in western music. i recognized my mistake about mixingf up chromatic and penatonic last night as i was laying in bed, but didnt have the chance to correct it in time.

AussieOi: this is great, ok now we sing the same tune , we can 'get' music. Who says that mathematically we can only have so many variations of 12 but messily we can create almost infinity songs?

StuckInTheSixties: I was going to continue my thoughts, sparked by AussieOi's above comment, on this thread, but they turned into a self-indulgent long-winded MrStevesque essay. So I thought that rather than imposing that onto someone's thread, particularly since it has nothing whatsoever to do with the initial topic of this thread, I'd rather post it as a separate thread over in the Music Forum.

http://www.wireclub.com/Forums/ViewTopic.aspx?ForumId=647363&ParentId=1196315

the real slim DEEPy: you cant count to infinity, you can always create another number. infinity is impossible mathematically. when can you not just add "and one"?

StuckInTheSixties: Or continuously cut in half.

AussieOi: 'almost infinity' is far easier and less confusing than any attempt by me to guess a really big number that is purely a 'guesstimate'.

the real slim DEEPy: "Or continuously cut in half. "

so you can have an infinitely small fraction, and an infinite amount of whole numbers while NEVER reaching infinity. once again, infinite proves itself impossible.

StuckInTheSixties: I don't know that I'd call those examples proof that infinity doesn't exist.

If you ask me, I'd say that the term "infinity + 1" is facetious. It's just another way of saying "infinity."

Same as saying "infinity/2."

Frankly, it seems pointless.

One Bar: "...you can fit nothing into a pie an infinite amount of times, because nothing will NEVER fill a whole."

If that were the case then nothing times infinity would be one. Which it aint.

One Bar: // I'd say that the term "infinity + 1" is facetious. It's just another way of saying "infinity." //

Correct! Infinity isn't a real number ('real' in the mathematical sense, that is). It's essentially a concept, although there are ways to mathematically 'pin down' infinities and manipulate them algebraically.

Well done for being correct, Sits! )

CoIin: I haven't read through all this, but in response to the original post, I don't think Einstein "proved the existence of black holes". His field equations allowed for their possibility. Just because something is possible doesn't mean it's actually exists.

One Bar: Correct as usual, Col.

Zen Not Zen: As the resident mathematician ....... Infinity is an ABSTRACTION

A set is said to be countably infinite if there exists a bijection between the set and the set of natural numbers.

A set is said to be uncountablly infinite if there is no such bijection.

Viz: the natural numbers (1, 2, 3, ...) are a set with countably infinite cardinality -- there is no largest natural number -- ergo the set is infinite.

The real numbers (integers AND rational numbers AND algebraic numbers (things like square root(2)) AND transcendental numbers (things like pi and e)) are a set with uncountably infinite cardinality -- any attempt to construct a bijection between the real numbers and a natural numbers will leave some real numbers left over -- a proof of this was devised by Gregor Cantor in 1874 and can be found in any textbook on set theory.

Whether or not anything in the physical universe can be said to have an "infinite" property is a matter of further discussion. None the less, as a mathematical abstraction infinity is alive and well and used on regular basis. There is even an area of set theory devoted to categorizing cardinalities -- it has been shown that the "continuum hypothesis" is formally undecidable as a result of these works on the foundation of mathematics.

If in doubt ponder this ... does this series of equalities 1/2 = 2/4 = 4/8 = 8/16 = 16/32 = 32/64 = 64/128 = 128/256 = 256/512 .... terminate?

FYI, 'i' is taken to mean the square root of -1, i.e. i^2 = -1 ... Leonard Euler noted that e^(i*pi) = 0, and that is a calculation that can actually be done, there is nothing imaginary about it; better considered as being complex.

One Bar: Yes, that's what I just said. (Kidding)

What is the largest infinity? And does it have any applications (other than mathematical)?

Zen Not Zen: There is no largest infinity ,,,, if there was a set with the largest possible cardinality, one would just take the power set of that set (the power set is the union of every possible (non-proper) subset) -- and that set (it can be shown) must have a greater cardinality than the original set (Cantor's proof does not work for uncountable sets, but there is a very clever and technical proof used by Russel and others).

So, again, you can go on ad infinitum.

Using the controversial Axiom of Choice one can arrive at uncontable sets whose cardinality cannot be established.

The mathematical application of very large sets is in generalized probability theory -- basically, choice spaces can be very very large.