The correlation between a dimensionless point and a line

[Erk]

I see no correlation between a dimensionless point and a line although it appears that math has made one. I'm just a philosopher so it's quite possible that I've got it all wrong.

It seems as though any location along a line is always the same location. If a location has no size then it can't be can't be added or multiplied to create a length.

So if a line is a distance between two dimensionless points and there is only one dimensionless point between them (see paragraph above) then all I see at first glance is three dimensionless points and (see paragraph above) I ultimately only see one.

So could someone enlighten me (in plain english) as to how to arrive at a line?

 

[fresh_42]

I see no correlation between a dimensionless point and a line although it appears that math has made one. I'm just a philosopher so it's quite possible that I've got it all wrong.

Correlation is misleading here, as it has a certain and different mathematical meaning. Philosophy on the other hand is a taboo on PF, as we had to make the experience, that it leads to endless and meaningless discussions, which rarely deserves the qualifier philosophical. Therefore we had to decide to exclude it from the list of allowable topics.

It seems as though any location along a line is always the same location. If a location has no size then it can't be can't be added or multiplied to create a length.

You basically rediscovered a version of Zeno's paradox.

So if a line is a distance between two dimensionless points and there is only one dimensionless point between them (see paragraph above) then all I see at first glance is three dimensionless points and (see paragraph above) I ultimately only see one.

So could someone enlighten me (in plain english) as to how to arrive at a line?

There is a fundamental misunderstanding here, because neither a point nor a line do actually exist in a material meaning of existence. They are both constructions which help to solve problems. A similar question would be: How can we have all real numbers, if we cannot construct them? We can't even list all numbers between 0 and 1. So there are a lot of metaphysical problems with the way we do mathematics. Nevertheless, we found out that those concepts are suited to perform accounting and tax calculations, which in my opinion had been the origin of doing math. Those concepts are tools, used to solve problems, make predictions and describe connections. They do not request to be real in a material sense. Plato described it as a world of ideas and placed the existence at this location. Most mathematicians and I assume also physicists are Platonists. My favorite example is a circle: we all have an idea of what it is, but in the end, it does not exist. And before you fetch your compass, be aware that it will have to compete with my electron microscope! Personally I support the point of view, that even art isn't invented or built, but discovered. To me your drawn circle is a kind of projection of Plato's circle as an idea.

So I can only refer to Zeno's paradoxes and Plato. I'm not sure, but I think Wittgenstein found a different approach. However, whatever philosophers had come up with, it didn't really influence the way we balance or tax.

As this is clearly a philosophical subject, I 'll close this thread.