Discreteness Vs Continuity

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Reply Wed 21 Apr, 2010 04:45 am
Firstly, according to my rationale, discreteness is solely related to particulars, meaning them as artificial and naming them as objects,things and artifacts.
On the other hand, the continuum is related solely to compounds, that are the only found in the unspoiled nature - or nature itself as a whole - as opposed to artificial.
Finally, the continuum can be defined as a compound comprised of infinitesimals.
 
jgweed
 
Reply Wed 21 Apr, 2010 08:45 am
@diamantis,
1. Isn't a continuum composed of discrete events?
2. Doesn't a continuum imply that there is more than one event, say two or more for there to be a continuum OF?
3. The difference between unspoiled nature and artificial nature may be obvious in a very general sense, but isn't it necessary to clarify the difference?
4. Are you saying that infinitesimals (whatever that means) are only found in unspoiled nature?

I think I understand what you are getting at, but without clarification, I can only guess and ask questions.
 
GoshisDead
 
Reply Wed 21 Apr, 2010 11:11 am
@jgweed,
I think Bergson's duration applies to this that we experience a duration of but we can only recall discrete events 'moment'. Also this works in lingusitcs among dialect continuums.

The general breakdown is X dialect has {set of} features, at some geographic boundary a feature in the set changes, which is fairly indistinguishable except to those who speak a very similar dialect. The feature is called an isogloss. Thus a person on the north side of a river can tell someone from the south side of it, but someone from another part of the country entirely would not be able to tell the difference between the two side of the river. So while technically these dialects are discrete they are homogenous at the same time.

In the U.S. these phenomena are most easily documented in metropolitan areas of the east coast like Boston, Philly, and NY. However it happens elsewhere. Person from Salt Lake can tell the difference between a person from American Fork and Spanish Fork just by hearing them say the word fork.

When a significant number of these isoglosses change over a geographic space they tend to group into bundles, which make it easier for an outside observer to tell the difference between larger geographic areas, however they still have significant overlap. So take for example the Iberian continuum that goes from the south west tip of Portugal up through the northeast tip of france and the south east tip of Italy. The same thing happens from town to town, geographic separating featur to feature, with the added isogloss bundler geopolitical boundaries, which on a border such as that between Portugal and Spain are less of a separation feature than one might think. Although the political structure of the countries makes the language spoken on the borders grammatically seperate the phonemic structures tend to meld.

So what I'm saying with this is that seen as a whole a continuum from one end to the other shows a kline of indistinguishable isolates. One can easily tell French from Italian without knowing the languages. One cannot however easily distinguish the difference between a person in Faro Portugal from a person from Portemao. The continuum is an experience of sorts seen as a whole, like Bergson's duration. One end and the other of the continuum is arbitraily marked off in order to easily categorize the continuum as its own discrete thing. While the distrete markers in the continuum are only visible from within the continuum. Thus we are working both with the ideals of relative perspective, how we process experience, and cognitive categorization. So a continnum is simultaneously a discrete thing and an indistinguishable experiential whole.
 
Reconstructo
 
Reply Wed 21 Apr, 2010 01:37 pm
@diamantis,
Can we handle a continuum except as a discrete whole? I think Zeno paradox's remains significant. We can work around them, of course, and the issue is boring perhaps to nonphilosophers, but have they really been answered? I think not. We can live continuity, and have no choice perhaps, but can we think it? Oh, we have our words for it. Just as we have a phrase like "round square."
 
prothero
 
Reply Wed 21 Apr, 2010 05:09 pm
@diamantis,
What sorts of things are discrete?
and
What sorts of things are continous in your view?
Personally I think continuity is an imposed mental construct and that reality is composed of discrete events, but that is another subject.
In consciousness we merge discrete events into continuity.
In calculus we divide the continuous into the discrete.
 
GoshisDead
 
Reply Wed 21 Apr, 2010 05:26 pm
@prothero,
Proth:
That is a lot of what we may be saying, assuming we even have a real thing to say about this. Its likely one or the other, everything is continuous and we simply make note of the specific discrete points we can, which may be a physical explanation or everything is discrete and we percieve a bunch of tiny discretes as a continuous because we cannot differentiate. Maybe a mathematical solution. I tend to lean to the former.
One universe/strings/M/multiverse versus atomism.
 
Reconstructo
 
Reply Wed 21 Apr, 2010 07:41 pm
@prothero,
prothero;155019 wrote:
What sorts of things are discrete?
and
What sorts of things are continous in your view?
Personally I think continuity is an imposed mental construct and that reality is composed of discrete events, but that is another subject.
In consciousness we merge discrete events into continuity.
In calculus we divide the continuous into the discrete.


I personally think that humans think in unities. We break the world automatically into separate objects. We can put individual objects into classes, but these classes are just more inclusive unities. And we can also zoom in and break the world into atoms, quarks, etc., but still these are unities. Of course this is just my opinion.

As far as continuous, think of the number line. There are an infinite number of numbers between any two numbers. Of course I have said that we cannot think the infinite, so I should say that we can find as many numbers as we try to between any two numbers. Also we can imagine perfect circles (can we?) and thin-as-air ultra-straight lines. And it fascinates me the way we conceive of volume. Our formula for the volume of a cube assumes that space is equally dense. I guess this is Kantian. Our transcendental intuition of space. Is this continuous?

I just bumped into this little piece of thought poetry. Grandi's series - Wikipedia, the free encyclopedia
And here is a Zeno link. Zeno's paradoxes - Wikipedia, the free encyclopedia

I'm curious what others will make of this. Continuum hypothesis - Wikipedia, the free encyclopedia

---------- Post added 04-21-2010 at 08:56 PM ----------

prothero;155019 wrote:

In calculus we divide the continuous into the discrete.


But do we really? I feel there is a sort of brilliant dodge. We put a tangent line up to the curve and use an infinitesimal dressed up as a limit to get the derivative. What is this infinitesimal? Then a definite integral is at its simplest just one calculation with the anti-derivative. (Zero as the inferior limit.)
 
prothero
 
Reply Wed 21 Apr, 2010 08:40 pm
@GoshisDead,
GoshisDead;155023 wrote:
Proth:
That is a lot of what we may be saying, assuming we even have a real thing to say about this. Its likely one or the other, everything is continuous and we simply make note of the specific discrete points we can, which may be a physical explanation or everything is discrete and we percieve a bunch of tiny discretes as a continuous because we cannot differentiate. Maybe a mathematical solution. I tend to lean to the former.
One universe/strings/M/multiverse versus atomism.
It is interesting you say that because 3 of the 4 fundamental forces have quantum (discontinous and discrete) mathematical forms and M theory which is basically an effort to incorporate general relativity (continuous and point particle) into the already unified (strong, weak and EM theories) seems more likely to be discontinous and quantitized. (Rational speculation).
So our mathematical representation of nature anyway is likely to be discrete not continous and lumpy not point particle.

---------- Post added 04-21-2010 at 07:53 PM ----------

Reconstructo;155061 wrote:
I personally think that humans think in unities. We break the world automatically into separate objects. We can put individual objects into classes, but these classes are just more inclusive unities. And we can also zoom in and break the world into atoms, quarks, etc., but still these are unities. Of course this is just my opinion.
I quess in some ways for me reality is dipolar (not Cartesian dualism but neutral monism). The mental aspect is continuous and point particle as well as unity. The objective material aspect is discrete, discontinous. These two aspects are not separate things which interact mysteriously in some supernatural manner but inseparable components of "ultimate reality". This of course is a reflection of my process philosophy orientation and of my process theological notion about the relationship between the transcendent "the ideal" and the "real"(the material). Its really very platonic (forms being continous and point particle for instance) but actualities (the material manifestations of the ideal, the mental, the transcendent) being discrete, lumpy and imperfect emanations of the "transcendent, the sacred, the spirit, the divine". Hard to express clearly in words.
 
Reconstructo
 
Reply Wed 21 Apr, 2010 09:02 pm
@prothero,
prothero;155094 wrote:

I quess in some ways for me reality is dipolar (not Cartesian dualism but neutral monism). The mental aspect is continuous and point particle as well as unity. The objective material aspect is discrete, discontinous. These two aspects are not separate things which interact mysteriously in some supernatural manner but inseparable components of "ultimate reality". This of course is a reflection of my process philosophy orientation and of my process theological notion about the relationship between the transcendent "the ideal" and the "real"(the material). Its really very platonic (forms being continous and point particle for instance) but actualities (the material manifestations of the ideal, the mental, the transcendent) being discrete, lumpy and imperfect emanations of the "transcendent, the sacred, the spirit, the divine". Hard to express clearly in words.

I think I see what you mean. For me, ideal geometry would be perfectly continuous. Whereas shapes in nature/experience would be always be jagged and lumpy in comparison. I also think we experience music as a continuity. I suppose I see human experience as including both. I think that number shows the discrete side and geometry the continuous. For me, pi is a great symbol of this.

Here's another thing. If I imagine the number one, or pure unity, I am imaging the perfectly discrete. But I because this is pure thought, it has no jagged "incarnation...spacetime position." It exists as a perfectly polished/"continuous" notion of the discrete. As you say, we are dealing with a tricky subject. Our words can only do so much. Smile
 
 

 
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