Profile

Cover photo
michael livshits
Lives in Cambridge MA
23 followers|4,741 views
AboutPostsPhotosVideos

Stream

michael livshits

Shared publicly  - 
 
 
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
1
Add a comment...

michael livshits

Shared publicly  - 
1
Add a comment...

michael livshits

Shared publicly  - 
 
Low sodium myth busted. Another funnu thing about this article:
<<"I am not sure the best way to convert this odds ratio into a risk ratio," Yang says, but if he had to guess, the risk would probably be lower than the odds.>>  while risk=odds/(1+odds) and odds=risk/(1-risk). It looks like a good idea to take everything with a grain of salt. It's probably not the pounds, but the sugar and other refined junk carbs that get you.
1
Add a comment...

michael livshits

Shared publicly  - 
 
Via aldaily.com: "When Hofstadter finally turns to education, his indignation occasionally merges into jeremiad. He outlines how regularly the United States has failed our children's intellectual development.."
1
Add a comment...
Have him in circles
23 people
Arvald Karp's profile photo
Justin Grosslight's profile photo
Michael Becker's profile photo
Mary Pat Campbell's profile photo
Kristien Creamer's profile photo
Daniel Zaharopol's profile photo
John Klein's profile photo
Gary Zhang's profile photo
闫旗军's profile photo

michael livshits

Shared publicly  - 
 
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  
1
Add a comment...

michael livshits

Shared publicly  - 
 
 
The Costa Concordia emerges from the sea after 19-hour salvage battle.

dailym.ai/16ARivW 
1
michael livshits's profile photo

michael livshits

Shared publicly  - 
 
 
#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."
1
Add a comment...

michael livshits

Shared publicly  - 
 
After conducting the largest online intelligence study on record, a Western University-led research team has concluded that the notion of measuring one's intelligence quotient or IQ by a singular, sta...
1
Add a comment...

michael livshits

Shared publicly  - 
 
 

How Many Engineers does it take to Change a Light Bulb?
1
Add a comment...
People
Have him in circles
23 people
Arvald Karp's profile photo
Justin Grosslight's profile photo
Michael Becker's profile photo
Mary Pat Campbell's profile photo
Kristien Creamer's profile photo
Daniel Zaharopol's profile photo
John Klein's profile photo
Gary Zhang's profile photo
闫旗军's profile photo
Places
Map of the places this user has livedMap of the places this user has livedMap of the places this user has lived
Currently
Cambridge MA
Previously
Iowa City - Ames Iowa - Houston TX - Brighton MA - Leningrad USSR
Story
Bragging rights
I have developed an elementary approach to calculus, it is summarized in my article "You could simplify calculus" on arxiv.org see my home page and my blog for further details.
Basic Information
Gender
Male