michael livshits
24 followers
24 followers
michael's posts
Post has attachment
Post has attachment
Post has attachment
Post has shared content
the story of looking up math.
so today, i want to lookup ultra-filter.
“…an ultrafilter on a poset P is a maximal filter on P, …”
so, i have to lookup filter:
“filter is a special subset of a partially ordered set.”
but don't remember what's “partially ordered set” so, lookup it is:
“A poset consists of a set together with a binary relation that indicates that, for certain pairs of elements in the set, one of the elements precedes the other.”
ok, but i want to lookup “total order” to see if that's something i recall:
“a linear order, total order, simple order, or (non-strict) ordering is a binary relation (here denoted by infix ≤) on some set X which is transitive, antisymmetric, and total.”

great, i remember having worked out this. That's total satisfaction.
(actually, i discovered the properties equivalence the http://en.wikipedia.org/wiki/Equivalence_relation when around 1997 i was writing code to decide if 2 polygons in 3d are equivalent, and discovered inconsistancies in my code, namely a==b, b==c, yet my code a≠c. And, i discovered, to great happiness, that to define equivalence is equivalent to partition of a set.)

well, that's a bit excursion. But i was writing about my typical trip to math these days. When trying to understand one thing, involves some 10 or 20 other Wikipedia articles.

by the way, also, some'd suggest math books instead. But no, i prefer dictionary style learning, esp for math. I prefer, the cold, logical, senseless, definition. The human touch of “motivation”, i want after the fact. (side note: sometimes, the human touch are often mis-leading, and there are many different takes, depending on the author. The human touch is often necessary though. But, i've been thinking, it is possible to do without entirely, because, math  (defined as the essence of something), is how things are. And, to some degree (perhaps 100%), you really just need to know that gist, anything else is fluff, and possibly even harmful. But why do we have the need for the human touch? i gather possibly it's pure habit. As in, new thinking usually happens with newer generation (as is, only older generation have problems with imaginary number, whereas newer generation who are taught its definitions directly never have this problem and moves on)) (the gist of this thought is that, what happens, when people learned math ONLY by their logical definitions and never the story behind it.)

(side note: xah's edu corner: linguistics: by the way, in math lingo, often you'll encounter the phrase “Motivation” as a section title. It is a idiom among math texts. The context is that, math becomes so abstract, that just definining something seems out of the blue. So, one needs to provide a context, so that readers can see how the definition came to be. And that, is often called “Motivation”, which is kinda a math idiom. I can't help but finding it funny, when reading math papers (the “formal” type), you encounter a section titled “Motivation” pro forma)

after writing all these, i haven't understood ultra-filter yet. Now, back to procrastination…

#math #education﻿
Post has shared content
Fun, but where is the problem book?﻿
All three volumes of 'The Feynman Lectures on Physics' now free online!

Richard #feynman is nothing short of a legend.  Partly so because of these very lectures!

http://feynmanlectures.caltech.edu/

Tip of the hat to Caltech, Michael Gottlieb and Rudolf Pfeiffer for putting this together!

Go #openaccess and #physics  ﻿
Post has shared content
Post has shared content
The Costa Concordia emerges from the sea after 19-hour salvage battle.

dailym.ai/16ARivW ﻿
Post has attachment
Post has attachment
Superbugs r here: http://www.usatoday.com/story/news/nation/2013/03/05/superbugs-infections-hospitals/1965133/
And they share their antibiotic resistance with other bugs.﻿
Post has shared content
#humour   #joke
A man named Juan comes up to the Mexican border on his bicycle with two large bags over his shoulders.  The guard stops him and asks, "What's in the bags?"

"Sand," answers Juan, to which the guard replies, "We'll just see about that..."

The guard takes the bags, rips them apart, empties them out and finds nothing but sand.  He detains Juan overnight and has the sand analyzed, but discovers that it really is nothing but pure sand.  Finally, the guard releases Juan, puts the sand into new bags, hefts them onto the man's shoulders and lets him cross the border.

The next day, the same thing happens - Juan approaches the border on his bicycle with two bags of sand.  The guard asks him, "What have you got?" and Juan replies, "Sand."  Again the guard does a thorough examination and discovers that the bags contain nothing but sand.  He gives the sand back to Juan, who crosses the border.

This sequence is repeated every day for several months until finally the guard is sitting in a Cantina in Mexico and Juan walks in.

"Hey, Buddy," says the guard to Juan, "I know you're smuggling something...  It's been driving me crazy.  It's all I think about!  I can't sleep.  Just between you and me, what are you smuggling?"

Juan sips his drink and says, "Bicycles."﻿