| THEORIES WITH PROBLEMS - IS INFINITY REAL? -> "Point"and"Exactness"or"Continuum"and"Fuzziness" ? | Start A New Topic | Reply |
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| Posted By: laurus Posted On: Apr 7, 2006 Views: 1236 | "Point"and"Exactness"or"Continuum"and"Fuzziness" ? The following came out of the interesting(?)0.999' ~1 debates on this site. From them,it seemed quite"clear"to me that it's impossible to resolve a continuum into separate, neighbouring points,by no mathemathical means whatsoever.Would it then be unjustified to assume that exclusive points are meanigless(not useless!) or even non-existant in a continuum;and that a continuum is nothing more or less than some kind of"one-ness",and the only "action" we can perform upon it is to divide(or"brake")it up into arbitra- ry bounded regions,which are as continuus as their "mother-"continuum ? So we might say: A continuum is not made up out of (exclusive) points. Then the"exactness"of a point could be replaced by the"fuzziness" of infinitesimal bounded regions in a continuum. (no boundery-or endpoints,only fuzzy boundery- or endregions) A continuum is an unhandable and uninteresting mathematical object.It is only when we set up ar- bitrary bounderies,and thereby dividing it into regions that it becomes handable.(orderrelations, chosing a region as "unit",defining"size","distan- ce",...)Thesame has been done and is done with the notion of "points" ofcourse. Something special about continua might be that they cannot be made to vanish (into a zerodimen- sional point),but always remain thesame apart from "relative size" or eventual deformations. Compare it to a circle viewed from very close and from very far away.It might seem as if it becomes a point,but it still remains thesame unchanged circle. If we assume that continua and points exclude eachother then"zerodimensional points" would be- come a"zerodimensional continuum"(Keith's infini- te void ?) I think that's enough for the time being. All opinions,constructive or destructive,are wel- come.It's just a speculative idea to think or dis- cuss about. Don't take it all too seriously.I don't. |
| Posted By: Keith Mayes Posted On: Apr 7, 2006 Views: 1233 | RE: "Point"and"Exactness"or"Continuum"and"Fuzziness" ? I think that you are getting the real world i.e. the space-time continuum, mixed up with the abstract world of mathematics. It has to be remembered that maths is man made and is therefore what we made it. Therefore we have our man made values which can be either single whole numbers, parts of a whole number, infinitely long numbers or imaginary numbers. We can do what we like with maths as long as we remain within the boundaries that we set when we invented maths. Although we can and do use maths to describe the real world, the laws and values that we apply to maths do not have to apply to the real world. Simply because we can have infinitely long numbers for example does not mean that we can have infinity in the real world. Maths is just a tool that helps us describe the real world, but maths are only an abstraction. |
| Posted By: laurus Posted On: Apr 8, 2006 Views: 1228 | RE: "Point"and"Exactness"or"Continuum"and"Fuzziness" ? I don't share that opinion with you,Keith. Like I said in a previous board,I don't believe mathematics is nothing more than a descriptive tool,a product of our imagination. I think mathematics is the underlying reality of the real physical world. Ofcourse,not all of mathematics needs to have its roots into the real world. The real mathematics might have certain constraints in it where w're not yet aware of, while in our imagination there is no absolute obligation to take contraints into consideration. To give a simple example.In geometry it is not forbidden to have two coinciding lines. In physics it is well known that the "time"con- tinuum can never be made to coincide with the "space"continuum.It's just another way to say that a material particle never can propagate with the speed of light. I'm not saying it's that way!I'm only giving it as an example for a possible mathematical constraint. |
| Posted By: Keith Mayes Posted On: Apr 9, 2006 Views: 1223 | RE: "Point"and"Exactness"or"Continuum"and"Fuzziness" ? laurus, You said..."I think mathematics is the underlying reality of the real physical world..." That thought is very much a Roger Penrose statement. He believes that maths trancends the physical world and is the true Platonic world of perfection. We however, inhabit the real world where people starve to death on one continent and eat themselves to death on another. Maths is a useful tool, but does not have any impact on how the world is. You can create the most beautiful and perfect equation ever, but it will not put food into a single starving baby's mouth. I prefer to discuss the real world, because that's where I live. |
| Posted By: laurus Posted On: Apr 11, 2006 Views: 1214 | RE: "Point"and"Exactness"or"Continuum"and"Fuzziness" ? You're absolutly right,Keith. There are a lot of problems in this world that needs our attention more urgently than anything else.But the question is,what much can we do about it as indivuduals? Having a few people living in harmony is already tricky,let stand having billions living in harmony with eachother and nature. Anyway,I'm glad I like to wonder about the universe and other"interesting" things. It's some kind'a way out of the absurd reality on this planet,even if it's only momentarily. I know this world can be an enerving place for people with common sense(not that I want to count myself among them !)and that it can drive them plain crazy if they would think too much about it,especially when they are not in a position to change something about it. |
| Posted By: Keith Mayes Posted On: Apr 11, 2006 Views: 1212 | RE: "Point"and"Exactness"or"Continuum"and"Fuzziness" ? On those thoughts laurus we do agree. This world is indeed a crazy place and is riddled with injusticies. I reckon I throw out enough food from my fridge each week to keep someone alive. It really ****** me off. |
| Posted By: laurus Posted On: Apr 12, 2006 Views: 1208 | RE: "Point"and"Exactness"or"Continuum"and"Fuzziness" ? Me also,Keith. |