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Cuchulainn
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Re: Universe Tea - Blog 2018

December 8th, 2018, 12:21 pm

the [$]n[$]th-term test for divergence:

If [$]\lim_{n\to\infty}a_{n}\ne 0[$] or if the limit does not exist, then [$]\sum _{n=1}^{\infty }a_{n}[$] diverges
Which is what we've got here
The theory of dynamical systems (Lotka-Voltera model, strange attractors, etc.) and practically all modern theories in economy, sociology or biology would not exist if Cauchy's descendants (Poincaré?) dropped the problem at that point - vide limit sets. (I agree that the S=1/2 makes no sense, though.)
1/2 = (1 + 0)/2 and it is used to smooth out Gibbs thingies at points of discontinuity/incompatibility.

If S = 1/2 is not to your liking you can have 

S = 0 = (1-1) + (1-1)+...

or

S = 1 = 1 + (-1+1) + (-1+1)+ ...
 
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ppauper
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Re: Universe Tea - Blog 2018

December 8th, 2018, 12:58 pm

or S alternates between 0 and 1
 
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katastrofa
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Re: Universe Tea - Blog 2018

December 8th, 2018, 2:34 pm

S is a limit which is divergent as everybody can see / doesn't exist in the standard limit sense. In the context of dynamical systems, it has a limit set. Either way, it doesn't make sense to write "S-1".
 
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Cuchulainn
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Re: Universe Tea - Blog 2018

December 8th, 2018, 3:18 pm

S is a limit which is divergent as everybody can see / doesn't exist in the standard limit sense. In the context of dynamical systems, it has a limit set. Either way, it doesn't make sense to write "S-1".
I'm not 'everybody'. Can you try again?
 
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katastrofa
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Re: Universe Tea - Blog 2018

December 8th, 2018, 3:52 pm

You surely are very special to me. I meant that Ppauper has already explained it:
the [$]n[$]th-term test for divergence:

If [$]\lim_{n\to\infty}a_{n}\ne 0[$] or if the limit does not exist, then [$]\sum _{n=1}^{\infty }a_{n}[$] diverges
Which is what we've got here
 
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trackstar
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Re: Universe Tea - Blog 2018

December 24th, 2018, 1:55 pm

Well, it's hard not to stop by around the holidays... 

I have a few things for your Solstice/Christmas/Hanukkah/Kwanza stockings and fair enough to say that almost *everyone* in the OT this year has been naughty and "nice" and naughty and... ahem, since people who live in glass castles shouldn't throw stones, I'll let you figure out the ratios.  : D

Here are your gifts - 1-5 tastefully wrapped and placed in a large picnic hamper from F&M:

1) One lump of clean coal - Burn it, trade it, save it in a little jar. Whatever you want, but it is very well-deserved! 
2) One bitcoin (physical) - you can make a cool necklace, or a keychain out of it.
3) One floquet time crystal - have fun with that, but please do not attempt to move me into any other dimension - I'm fine right where I am!
4) One of the warmest, softest cashmere scarves you can imagine - your choice of color(s) and pattern.
5) One sumptuous meal just for you - your most favorite foods. Vegan, Vegetarian, Paleo, all good on this occasion. If you ask for horse meat, I will be disappointed though. ; )
6) Peace, Creativity, and your own special version of "Happiness" to all for the new year.

I'm going back to my little corner of the wilderness now, but Gruss vom Krampus!

TS
trees and light.JPG
Edit: typo corrected, but no gifts were rescinded. : D
Last edited by trackstar on December 25th, 2018, 12:13 am, edited 1 time in total.
 
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bearish
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Re: Universe Tea - Blog 2018

December 24th, 2018, 2:55 pm

Thank you, trackstar, and a peaceful and prosperous winter to you too! I'm about to go wrangle up some lobsters for a festive evening meal.
 
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katastrofa
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Re: Universe Tea - Blog 2018

December 24th, 2018, 3:20 pm

And 7) a lot of vodka! They stopped selling (officially) this Christmas basics in Ukraine  - the martial law. Suddenly it's become too risky to visit the family.
 
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trackstar
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Re: Universe Tea - Blog 2018

December 24th, 2018, 7:15 pm

8) not to forget, a gift of Music.

something for a gray afternoon with snow flurries drifting down

White candles lit, a glass of *cognac, and Anonymous 4. 

*Can substitute a fifth of vodka, a flask of Glögg, a pint of Guinness... as you wish. ; )
To light and darkness.
 
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Cuchulainn
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Re: Universe Tea - Blog 2018

December 24th, 2018, 8:26 pm

Image
 
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katastrofa
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Re: Universe Tea - Blog 2018

December 24th, 2018, 8:37 pm

Cheers to you, Lady Trackstar! I also wanted to add that I, among all those callous savages, miss you the most... Not from your list, but also a nice present I got today - a very old hair comb worn by 5 already dead people, I'm 6th. The other half of a bottle of Syrah to go! To your health, as my people say :-)
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trackstar
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Re: Universe Tea - Blog 2018

December 24th, 2018, 9:51 pm

an extended break has been very refreshing. a holiday visit is fine though.

your cats are so funny, they called me back in here, and I admired the intricate hair comb as well. unfortunate you could not make the trip home right now.

Here just cooking and thinking about some art work for the new year. Recently, I bought a book on illuminated manuscripts and one on calligraphy, so when I have a little time, I will create some texts in the old style.

Have also been looking at stained glass.  Here is Joan of Arc - look at the armor!
joan of arc.jpg
and I also plan to plant trees this spring - will raise some in the house for now.
littlebalsamtree.JPG
hope you will enjoy the holiday - if i were stuck in England, I would rent a car and go up to the Cotswolds.  Beautiful land up there and not too far to drive in a day.  Further north into Scotland is even better.
 
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trackstar
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Re: Universe Tea - Blog 2018

December 24th, 2018, 10:06 pm

10) More music (always!)
Never mind the image's reference to "The Bridegroom" - that is irrelevant.  ; ) 

Just listen to the floating polyphonies on a dark winter night.
 
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trackstar
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Re: Universe Tea - Blog 2018

December 25th, 2018, 11:48 pm

A newly discovered forest trail - goes for many miles.
foresttrail.JPG
 
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katastrofa
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Re: Universe Tea - Blog 2018

December 26th, 2018, 1:02 am

Stunning! Is that photo from today? Has the snow melted? I remember a song about being in love with a snowman, and the spring coming... :'-(
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