"Line numbers" finding a number for any symbol

[Elixir]

Note that in Genesis 1 it talks about the waters above vs the waters below - and both the sky and the waters below are bluish/cyan.

Yawn. So does Creatures of Light and Darkness (Zelazny).


“The Prince Who Was A Thousand walks beside the sea and under the sea. The only other intelligent inhabitant of the world within which he walks cannot be sure whether the Prince created it or discovered it. This is because one can never be sure whether wisdom produces or merely locates, and the Prince is wise.

He walks along the beach. His footsteps begin seven paces behind him. High above his head hangs the sea.

The sea hangs above his head because it has no choice in the matter. The world within which he walks is so constructed that if one were to approach it from any direction, it would appear to be a world completely lacking in land masses. If one were to descend far enough beneath that sea which surrounds it, however, one would emerge from the underside of the waters and enter into the planet’s atmosphere. Descending still farther, one would reach dry land. Traversing this land, one might come upon other bodies of water, waters bounded by land, beneath the sea that hangs in the sky.”

The big sea flows perhaps a thousand feet overhead. Bright fish fill its bottom, like mobile constellations. And down here on the land, everything glows.”

 

[Jarhyn]

Math says there are curves that can be defined by bezier curves and that can't.

Bezier curves are curves defined by a set of numbers on points.

Some curves can't be rendered this way.

So there is an infinite family of shapes that can be defined by bezier curves and another infinite family of shapes that can't, and these are uncountably infinite. And there are other shapes still that are even weirder.

This would mean you would start needing signs and symbols to differentiate which parts of the symbol you use.

...So you would really need a whole set of equations with which to construct this stuff.

Just a single number line can't do it.

 

[excreationist]

Math says there are curves that can be defined by bezier curves and that can't.

Bezier curves are curves defined by a set of numbers on points.

Some curves can't be rendered this way.

So there is an infinite family of shapes that can be defined by bezier curves and another infinite family of shapes that can't, and these are uncountably infinite. And there are other shapes still that are even weirder.

This would mean you would start needing signs and symbols to differentiate which parts of the symbol you use.

...So you would really need a whole set of equations with which to construct this stuff.

Just a single number line can't do it.

Now I'm talking about the set of shapes/symbols only going up to 5 lines like I've been showing. Do you have a problem with that? Do individual bezier curves never have a kink in them? Does the count of bezier curves match the number of lines I'm talking about?

 

[excreationist]

Math says there are curves that can be defined by bezier curves and that can't.

Bezier curves are curves defined by a set of numbers on points.

Some curves can't be rendered this way.

Well I want to include all curves so therefore bezier curves aren't sufficient.

This would mean you would start needing signs and symbols to differentiate which parts of the symbol you use.

Each line could just be in a different colour - similar to subtle line boundaries in the dove:

...So you would really need a whole set of equations with which to construct this stuff.

Just a single number line can't do it.

I don't see a problem with what I've done in that image I just included... the line number is the minimum number of lines that can be used to draw it without any kinks.

 

[Jarhyn]

Math says there are curves that can be defined by bezier curves and that can't.

Bezier curves are curves defined by a set of numbers on points.

Some curves can't be rendered this way.

So there is an infinite family of shapes that can be defined by bezier curves and another infinite family of shapes that can't, and these are uncountably infinite. And there are other shapes still that are even weirder.

This would mean you would start needing signs and symbols to differentiate which parts of the symbol you use.

...So you would really need a whole set of equations with which to construct this stuff.

Just a single number line can't do it.

Now I'm talking about the set of shapes/symbols only going up to 5 lines like I've been showing. Do you have a problem with that? Do individual bezier curves never have a kink in them? Does the count of bezier curves match the number of lines I'm talking about?

Some bezier curves have kinks. In fact straight lined geometric shapes are subclasses of bezier curves, and there are an uncountably infinite number of these just in terms of perimeters as a system of equations. You could consider them degenerate in a way, I think.

 

[excreationist]

Some bezier curves have kinks. In fact straight lined geometric shapes are subclasses of bezier curves, and there are an uncountably infinite number of these just in terms of perimeters as a system of equations. You could consider them degenerate in a way, I think.

I consider a bezier curve with kinks to involve two or more straight/curved lines. So bezier curves aren't relevant to what I'm talking about. Also two or more lines that join with no kinks counts as one line. I'm trying to have an objective rather than subjective approach. I mean a person might claim a circle can involve two or more lines but that isn't true in the system like I explained earlier. Or they might say a triangle can involve one line - but it doesn't if you keep the rule about the kinks in mind.

 

[bilby]

Some bezier curves have kinks. In fact straight lined geometric shapes are subclasses of bezier curves, and there are an uncountably infinite number of these just in terms of perimeters as a system of equations. You could consider them degenerate in a way, I think.

I consider a bezier curve with kinks to involve two or more straight/curved lines. So bezier curves aren't relevant to what I'm talking about. Also two or more lines that join with no kinks counts as one line. I'm trying to have an objective rather than subjective approach. I mean a person might claim a circle can involve two or more lines but that isn't true in the system like I explained earlier. Or they might say a triangle can involve one line - but it doesn't if you keep the rule about the kinks in mind.

You don't know what a bezier curve is, do you?

(Full disclosure - nor do I, but I am not afraid to admit my ignorance on that score. Mathematics is very much not my field).

 

[excreationist]

You don't know what a bezier curve is, do you?

(Full disclosure - nor do I, but I am not afraid to admit my ignorance on that score. Mathematics is very much not my field).

Well I used bezier curves in Inkscape to create a lot of the shapes/symbols that I included in this thread...
I know the basics but not every single thing about it. For the trinity symbol in post #8 I couldn't make the curves look exactly like how I wanted and I think that was due to issues in how bezier curves work.

How to Use the Bezier Curve Tool Inkscape | Design Bundles

In this tutorial, learn how to create lines and curves in Inkscape with the Bezier Curve Tool! Use the nodes to create new swirls and waves in your design.

designbundles.net

 

[Jarhyn]

Some bezier curves have kinks. In fact straight lined geometric shapes are subclasses of bezier curves, and there are an uncountably infinite number of these just in terms of perimeters as a system of equations. You could consider them degenerate in a way, I think.

I consider a bezier curve with kinks to involve two or more straight/curved lines. So bezier curves aren't relevant to what I'm talking about. Also two or more lines that join with no kinks counts as one line.

They are absolutely relevant. All closed and non-closed curves created by straight segments up to the segment limit count.

As I said, there's uncountably infinitely many of those, with a discrete value at each vertex.

You could limit it by making a grid and then having pairwise groups for segment ends, up to the maximum, and there would be a (large) number of permutations, with some including dots. This would also make some shapes impossible

 

[excreationist]

They are absolutely relevant. All closed and non-closed curves created by straight segments up to the segment limit count.

As I said, there's uncountably infinitely many of those, with a discrete value at each vertex.

Are you saying that a circle can involve two or more lines and/or bezier curves? BTW what about the case of a cross? Those two lines aren't connected. How is a system saying a circle is made up of an arbitrary number of bezier curves superior to me saying there is objectively only one line? (within the system)

You could limit it by making a grid and then having pairwise groups for segment ends, up to the maximum, and there would be a (large) number of permutations, with some including dots. This would also make some shapes impossible

As far as a maximum goes, I'm mainly only focusing on the first five (up to the pentagram). Then there is the Star of David (6) but other symbols with a lot of lines aren't that interesting.

I think a 10 year old could understand what I'm talking about. I don't see how talking about bezier curves would improve things at all.

 

[Jarhyn]

They are absolutely relevant. All closed and non-closed curves created by straight segments up to the segment limit count.

As I said, there's uncountably infinitely many of those, with a discrete value at each vertex.

Are you saying that a circle can involve two or more lines and/or bezier curves? BTW what about the case of a cross? Those two lines aren't connected. How is a system saying a circle is made up of an arbitrary number of bezier curves superior to me saying there is objectively only one line? (within the system)

You could limit it by making a grid and then having pairwise groups for segment ends, up to the maximum, and there would be a (large) number of permutations, with some including dots. This would also make some shapes impossible

As far as a maximum goes, I'm mainly only focusing on the first five (up to the pentagram). Then there is the Star of David (6) but other symbols with a lot of lines aren't that interesting.

I think a 10 year old could understand what I'm talking about. I don't see how talking about bezier curves would improve things at all.

I'm not saying one system is superior to another. I'm saying that there's no way to make what you want "countable" in a real way, by showing a subset of everything you wish to count is uncountably infinite.

 

[excreationist]

I'm not saying one system is superior to another. I'm saying that there's no way to make what you want "countable" in a real way, by showing a subset of everything you wish to count is uncountably infinite.

This is about historical graphical symbols like those drawn by hand - e.g. post #12 shows cave paintings. There are very complex hand-drawn sigils in post #33 but this system could count the lines - though I think those sigils are very arbitrary and I'm talking about more objective meaning. Though the changes in line thickness in those sigils could create issues in counting the number of lines. Even if the lines in the sigils were counted it is meaningless unlike the 2 line red blood "energy", etc.
What things are you saying are "uncountably infinite"? Circles? Things infinitely more complex than those sigils?
This is about actual examples of esoteric geometry and symbols not theoretical infinite drawings.

 

[excreationist]

This is a thing on eBay that kind of fits the numbers and colours -

"Positive" - 3 lines (vertical, horizontal, outer circle) - green
"Neutral" - 5 lines (square, outer circle) - grey (dark white)
"Negative - 2 lines (horizontal, outer circle) - red