# A way to see Lethe's notation

#### marcus

Gold Member
Dearly Missed
I have been unable to read the differential forms thread but wanted to, and now I have discovered how to make it legible on my browser. Lethe has been using Times Roman font and for some reason most of the symbols come thru as boxes for me in that font. So as an experiment I have quoted a Lethe post and removed the Font specification, setting that back to default. Most of the symbols now come thru for me altho a couple I see here (& sdot , & nabla ) still do not

I'm wondering if anyone else was discouraged earlier by seeing all those boxes and no being able to tell what symbols they stood for.

Originally posted by lethe in diff forms thread

at this point, i will stop using classical vector notation. i will write the directional derivative as v&mu;&part;&mu;&fnof;, where &part;&mu; is shorthand for &part;/&part;x&mu;, and x&mu; is one of the coordinates, and &mu; is a number that ranges over the number of dimensions of the manifold, from 0 to n-1 usually. so there will be n different coordinates for an n dimensional manifold. and v&mu; is going to be associated with the &mu;-th component of the vector, to be defined. and even though i didn t write it, i meant for that to be a summation: v&sdot;&nabla;&fnof; = &sum; v&mu;&part;&mu;&fnof; = v&mu;&part;&mu;&fnof;. i just leave off the &sum; from now on. every time you see an equation with the same letter as a superscript and a subscript, you should sum over that index.

......

we define the vector to be that operator. this is how it operates on a function:
v(&fnof;) = v&mu;&part;&mu;&fnof;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2)
since this is independent of the function that i want to operator on, let me just write the vector operator:
v = v&mu;&part;&mu;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(3)
and this is the point of this post. a tangent vector is defined to be/associated with/thought of as a differential operator. v is the vector, and v&mu; are the coordinate components of the vector, and &part;&mu; are the coordinate basis vectors of the tangent space. the vector itself is coordinate independent, but the components are not, ....

OK, it should be easy to show that the set of tangent vectors, thusly defined, satisfy the axioms of the vector space. i will call this vector space TMp. that is, the tangent space to the manifold M at the point p is TMp. for an n dimensional manifold, the tangent space is always an n dimensional vector space.

......

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#### lethe

so do you think times new roman is poor choice for font? i chose that because certain symbols, like pi, display poorly in the default font. i also upped the size, which might make a difference.

maybe i should change the font/size?

#### marcus

Gold Member
Dearly Missed
Originally posted by lethe
so do you think times new roman is poor choice for font? i chose that because certain symbols, like pi, display poorly in the default font. i also upped the size, which might make a difference.

maybe i should change the font/size?
If I dont change my browser and you dont change your font then when I first open one of your posts I will see a lot of boxes.
This is not the end of the world or even a particularly bad thing.
I can adapt to this situation as I just have in this example by
reposting in the default font!

I am assuming that no one else has the problem I do----everyone else who wants to read the post can do so in your chosen Times New Roman, with things like &nabla; and &sdot; (which I will see as boxes).

BTW I also do not like certain features of the default font----the pi does not look pi-like and the theta looks like an ugly number 8.
But nothing is perfect!

Why not carry on, Lethe, with your chosen font and size, and let me cope by reposting certain passages in the default font so that I can read them? A little occasional repetition in another font seems harmless enough. Or?

I like your style of writing---it could be a really useful thread as originally planned---I would say go for it.
If anyone tries to distract you with some kind of compensatory know-it-all syndrome just put them on the ignore list. The original idea is a basic introductory treatment, right?

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