Outliers

outlier

 

Today's lecture included the topic of outliers. How is a graph changed when and outlier is included or excluded? Since outliers deal with extremes they often bring up political and social issues. The example from class was of salaries at a hypothetical company where the CEO made more then three times as much as the highest paid employee.

I noticed this graph in the New York Times and wanted to save it for future reference.

Video links for STAT students.

Dear class,
Not all YouTube math videos are created equal!! I will post links to the most useful ones here:

 

Confidence Intervals:

 

Central Limit Theorem:

 

If you want me to post more post a comment about the topic that you need and I will find the best (and mathematically correct) videos for the topic.

Young, cheap tuo cha showdown!

toucha5Can a cheap pu'erh be good? Is it possible to buy cheap tea and age it in to something amazing? Most say "no" --but that won't put me off from trying. The first step is to taste young teas so that one can better understand the aging process.

I put three teas (all inexpensive young pu'erh) in to three teapots without looking much then mixed them up. Who will win the blind tea taste test?

 

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Tea #1

Astringency, Dryness, nice Hui gan, rather sweet and slightly sour like white grapes. This one needed a longer steep than the other two. Nice back of throat feeling. The leaves are big and plump and young.

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Tea #2

Heavy mouth-feel, Astringency, Dryness, some Hui gan... I swear this has this flavor like older tea or shu... it's not strong but its there. Steeps dark very quickly. Thick. This is easiest to drink in some ways.

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Tea #3

Astringency, yet wonderful Hui gan, thick, flavors lasts, just a little biter also smoky? why is raw puerh smoky? Love the after-taste.

Overall
I think in their current young state #2 is the most "drinkable" -- yet it isn't my favorite. I like #3 a bit more ... in fact I like #2 least since it isn't really what I expect from sheng. I suspect it is blended. Not that that is "bad" I just like things that are less contrived.

How will these age? Damned if I know. I have two of each tuocha, one to nibble on and one to keep for a long time. I don't have an special storage arrangements, by my in NYC apartment I never use AC-- so I'm not too worried. In any case, if they start to dry out I'll seek new arrangements. But, If I had to guess,I'd guess that #1 will end up too sweet and plain with age, #2 won't really age much since it's so unstable, and #3 has a shot at be good in a few years.

WINNER: #3

Let's see what happens!

And now....

The Reveal

Xia Guan Yellow Ribbon

Xia Guan Yellow Ribbon Tuo Cha 2010 100g Raw ($9)

Jia Ji Tuo Cha * Menghai Dayi Pu-erh Tea

Jia Ji Tuo Cha * Menghai Dayi Pu-erh Tea 2009 100g Raw ($7)   RUNNER-UP

Mystery Tea From ebay

"2012yr Yunnan Wild Old Tea Pu'er Cake tea 100g" Mystery Tea From ebay ($6) WINNER!

 

And there you have it!

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Living with worms in a small apartment

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(This is the view on our roof in the South Bronx, we have a small garden out here already but I dream of covering it with plants. The worms are helping me generate the soil that I need. Dirt is expensive!)

Earthworms like the common "red wriggler" composting worm can live for up to 6 years. They reproduce every 7 days laying a "pod" with 3-6 baby worms. Hence, a long-lived worm that's highly reproductive can produce 1,000-2,000 babies. That seems like a small number after all of those ads about the danger of un-spayed and un-neutered cats, but those ads use the trick of counting up all of the offspring of the offspring-- I'm not even going to go there with worms. Use your imagination! They are surging with life!

An indoor composting system that is 1'x1'x4' can house 4,000-6,000 worms. Once, the food supply is balanced with the population worms naturally stop having so many babies. Either that or worm college is just more expensive in large thriving worm societies, so who wants 6 kids in the big city?

1,000 worms can eat half a pound of garbage (junk mail, newspaper, kitchen scraps) every day turning it in to worm castings which can be sold to desparte gardeners at surprisingly high prices at your local farmer's market! Or just hoard it yourself and grow freakishly large plants!

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(24 hours of growth. Mixed greens in old potting soil mixed with vermicompost.)

 

Worms can be sold too they don't mind as long as it's not to a fisherperson. They are easy to trick, though, (since they don't have eyes) so you can sell them to fisherpeople anyway, just tell them they are going to a nice garden.

Think of all the pounds of trash we could keep out of landfills if everyone had worms? You would not get as much for selling them, then, so maybe it's not as nice of an idea as I first thought. Hmm.

All of the dirt that you see in the world everywhere just about all of it was made by worms!

Oh-- you can go on vacation for up to two months and the worms need no feeding or care. Easier than cats. The perfect pet for lazy people! Are they much fun? Well, more than you expect, it's fun to watch them making their way through the bin, eating this and that, mating laying "pods" and being born. You come to like them.

And then walking around town it hits you: All of the dirt that you see in the world everywhere just about all of it was made by worms! Without them we'd have much less pleasant forest floors and parks. Darwin was one of the first to make note of this fact. He wrote a paper about the way that old ruins are slowly enveloped by dirt through the action of worms. Worms over time can move move great stone monuments by digging holes underneath, they slowly sink into the earth.

They are a quiet and powerful force.

There is a learning curve for getting set up with your own worms. But it is worth it. The easiest way is to buy an overpriced "worm farm" but a farm can also be made much more cheaply, but it won't look as good, and you're not that handy anyway, right? You can dig your own starter worms or buy them as well. (just buy them, who are you kidding here?) Either way it's very satisfying to feed the worms bills, campaign funds solicitation notices, and bad news articles -- though they refused to touch the one from Anthony Wiener. I wonder why? I guess even worms draw the line somewhere.

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(Hard-working worm devouring some junk mail and wilted spring onion from the garden.)

 

Of course, they like kitchen scraps too-- though, one must be careful not to give them too much of one thing at once.

They smell divine, you know the smell of fresh dirt after the rain, well if you get close to the worms after they've worked through your scraps and unwanted mail you can smell nature in all her glory-- maybe that's why their castings are so valued?

eau de earth

Worms! I'm not obsessed at all!

South Bronx Running Club

The SOUTH BRONX RUNNING CLUB is taking off, I've put these flyers everywhere. What are some other ideas to get people on board?

Life is complicated, running is simple.

Garden of lost feathers: Highbridge park, 1978

Highbridge Park

Bundles clustered in the flickering head,
in the light-weight feathered-skull they multiply.
In this he saw hope for the hair-twirlers,
for muttering mad shufflers in day-lit hallways
shaking (his) tethered, floppy long-sleeved hands.

Once, in the green, when the graffiti was different,
once, under a hundred or so brushed layers of paint,
from The City in brick red and from the lost boys
in green and gold and rainbows spilling over,
daddy died looking for the caves under Manhattan.

Where the Indians once lived
where the junkies shot up and the cars rusted
or burst into flames as he ran from a million voices
where the birds always will sing and fly it turned out
father was right, not paranoid

Demons in the dark do multiply.

O-check and other rare brands from overseas... and Portland.

Ever since notebookstories mentioned an Ellie magazine article about trendy notebooks I have been desparte to get something... anything from o-check. I mean, just look at these notebooks:

o-check notebooks. (click to enlarge)

This is really good advertising for someone like me, they capture photographically the mood of using a nice notebook. Sadly, o-check is not easy to get in the US at all. They are headquartered in Seoul, Korea. After attempting to order from the Korea website (without knowing any Korean!) I finally found an Australian distributor that sold them, Plain, Ruled Graph. (Is it just me or are all the cool notebook companies and stationary stores outside of the US?) I really loved the website, but I do not love the $33 shipping fee to the US.

But I wanted one of the notebooks... badly. So I found a few things that I liked and placed an order. It just came today! I'm really happy with most of it. Take a look:

My O-check Notebook

The o-check notebooks was everything I dreamed it would be. The quality is exquisite.

It feels just like a library book.

I also ordered a small graph paper notebook from Red Horseshoe Paper. Only after did I realize that they are in Portland, so I can get them without the hassle of ordering from Australia!

Red Horseshoe Graph Notebook: it has both metric and Imperial sized grids.

A nice touch on this notebook is the red thread used to stich it together. Lovely!

A nice touch.

The paper is *very* good for fountain pens.

I also bought these darling envelops made by Midori (of the famous travler's notebooks, I may try those some day as well).

Midori Envlopes

So why did I say I was only happy with "most" of it? Well, I saw this ruler on Plain, Ruled Graph, it's made by o-check so I thought: Hey, why not?

O-Check Desk Wooden Ruler (as seem on the website)

I have quite a few slide rules, compasses and other drafting instruments. (I will do a post in the future on that.) So maybe my expectations were just too high, based on the photo I expected high quality, plastic edges (but the nice kind of plastic they use for slide-rules) and a darling little brass knob to hold it. Sadly, this is what I got:

It arrived broken, and the wood is so soft you can mark it witha fingernail.

It is made of very soft wood almost like balsa, it's unfinished, the numbers are painted on and the little knob falls right out if you so much as touch it. Now it was only $6, so maybe I'm expecting too much. I will be cautious about non-notebook items from o-check. I'll write Plain Ruled Graph and see what they can do about this. Since everything else was very nice this isn't such a big deal.

What are all those notebooks FOR: Phases in the life of a notebook.

I have shared my blank notebook collection over the course of three posts: part one, part two, part three.

Now I'd like to say a little about what's inside my *used* notebooks.

One of many shelves in our home filled with full notebooks.

PHASES IN THE LIFE OF A NOTEBOOK

Reverence: It's often a little hard to make my first mark in a notebook, the blank pages are filled with so much promise and possibility. This is how I have ended up saving blank notebooks for years before deciding to use them. In addition the proper purpose must be found for a notebook. Thin notebooks for small tasks, thick ones for big ones.

Christening: When a notebook enters service it's named. I'm certain we all have little rituals that go along with starting a new notebook. I like to leave the first few pages blank, as I hope to add a title page and table of contents later, a hope not always realized...but, I still can't stop myself from doing it. Most of my notebooks get labels for their covers, I also collect nice labels, for this purpose-- I especially like vintage labels. (Though finding a way to revive the paste can be challenging.)

Breaking in: The first entry in a new notebook is done with great care, but as the notebook rides in the bag, gets dropped on the sidewalk, is written in on subways and escalators, it gains a few less-than-perfect entries and a few dog-eared pages. It is this stage that determines what happens next, and once the notebook is half-filled it's time to decide:

Accention to book-like status, or demotion to scrap paper: The great notebooks get page numbers and indices, title pages and a revival in the quality of the entries. The poorer notebooks become my "scratch" notebooks, filled with all of the calculations, random notes and lists that no sane person would ever care to read again. (Especially me) The notebook then earns a place on the book-shelf, or a place in the rubbish bin at this stage.

Second lives: Some of the time I try to give a "scratch" notebook a second life. I carefully remove all of the pages with writing, take off the title tag and place it back on the shelf with the other blanks. Now with fewer pages it's better suited to small projects. Perhaps it will "ascend" in its next life time.

These notebooks acceded to book-like status, earning a place on the shelf.

Notebooks from classes I have taught and taken.

Drawings and color add so much to note books, I rarely throw away a notebook with good drawings. Some of the time I'm surprised by the work that I did. It's fun to spend an evening reading old notebooks. My oldest notebooks are from 2nd grade. I was laughing so hard I was crying at some of the stories (and spelling) in them. Some notebooks are time machines.

Notebook Collection Part 3

This is my third post on my extensive collection of notebooks. You can find part one here and part two here.

Japanese Notebooks

I have a lot of notebooks that are manufactured in Japan. Shown here are several of these from Kinokuniya Bookstore near Bryant park and from Mitsuwa Marketplace in New Jersey. I also have a few of the Japanese-style Molskine notebooks, which are not really from Japan, but pay hommage to a very useful binding method. (I wish Molskine made extra large versions of these notebooks.)

The quality of pens and paper goods from Japan tends to be quite high, they seem to have a better selection of pens that write with a very fine lines. The notebooks often have english phrases on the cover, mostly as decoration, the words don't make much sense. So that seems to suggest that in Japan some western things can be desirable or fashionable. In the US Japanese things are fashionable. And I find Japanese things that go for a western "feel" fascinating. Take "campus" notebooks, they try to evoke the classic leafy green American (or maybe British) college campus with their name and designs. I, in turn, buy notebooks that evoke a Japanese paper company evoking an idyllic campus. Soon in Japan, no doubt, it will be fashionable to get American things that are trying to be like Japanese things that are trying to be like American things. This will create an infinite loop and collapse into a notebook perfection cross-Pacific cultural black hole.

What was I saying? Notebooks. From Japan. (Mostly) Let's look inside!

Pure, white pages.

The pages are smooth and "fountain pen friendly" as they say over at The Fountain Pen Network a great online community with it's own collection of notebook lovers! One of the last courses I took for my masters degree was Topology. It was a lovely course and I used one of these as my "final" notebook. (I always reorganize my notes from class in to a neater, more comprehensive format in my own words and a means of studying. I call this the "final" notebook, since to study for the final I only need to sit down and read it.) At any rate the notebook I kept for that course was one of my best ever. Just thinking about it makes me want to go back to take more classes!

Giant mother of a molskine

Would you look at the size of this thing? "The Folio Sketchbook - A3" is just like a regular Molskine (it even has the elastic strap and back pocket!) but it's the size of a movie poster. I saw it and fell in love instantly. I can't quite make up my mind what to put in it yet, but I know something will come to me. What would you use it for?

The vast expanse of pure, white, paper waiting for creation.

Opening this thing is almost emotional. It's like opening the door to a special room that's just waiting for you to shape it in to a wonderful place. There is something about having a book so big that you must turn your head to look around the page that just makes the whole experience more immersive. This is why I love books with big pages so much. Most of my collection is on the larger side, I find I can do more with more space to write.

And speaking of big books. Look at this beast. It's the "The World's Largest Italian Leather Journal" -- due to the leather cover and other fine materials (leather increases in cost rapidly the larger a piece you require) this book costs $2,000. It's mostly used by big hotels and universities as a kind of guest book. At least they don't have to worry about someone wandering off with it!

The World's Largest Italian Leather Journal, I secretly want one.

Wouldn't you love to sit down in front of this with a nice inky pen? What would you create?

This brings to a close post on the collection. But I will continue to review new additions to the collection from time to time. In my next post I'll share what's INSIDE of some of my full notebooks.

Summer courses almost over, "children's" books in the works.

This summer is one I will remember. I taught both differential equations and calculus II for the first time. Seeing these subjects from the instructors side has really opened my eyes to all kinds of details I never noticed before. One of the most striking new insights is how much these two courses have in common. They both rely deeply on sequences and series. Sequences are like a hallway in mathematics, one that connects many many many rooms.

I am working on two math book projects. The first is a Japanese-styled art book on the topic of sine and cosine. It's inspired by many of the lessons I taught this summer.

Japanese-style book about sine and cosine

I want to bring all of the different ways that sine and cosine are presented in elementary and undergraduate mathematics in to one (long) pictorial document. I start with the differential equation, y''+y=0 then solved it (using the series method from differential equations) producing \sin x = \sum^{\infty}_{n=0} \frac{(-1)^n}{(2n+1)!} x^{2n+1} and \cos x = \sum^{\infty}_{n=0} \frac{(-1)^n}{(2n)!} x^{2n}

Next I wanted a pictorial way to relate these power series to the unit circle. I have found it in this spiral (the first image shows how it is constructed as an involution):

Constructing The Involute Pinwheel

a sequence of involutes: the vertical and horizontal components will form the power series for sine and cosine respectively.

The vertical and horizontal components will form the power series for sine and cosine respectively. Take the series of vertical line segments: \sin x = A_1A_2 - A_3A_4 + A_5A_6 - \cdots and so on, the segments repeatedly over and under-shoot the accutal value of sine. The full paper by Leo S. Gurin, "A problem", can be found here.

I'm going to incorporate Gurin's spiral in to my book. I want to show the power series literally flying out of it, like they have come to life. I wonder if I can make it like the famous drawing of the sine curve projecting out of the unit circle?

Naturally, I already have planned to put that diagram in my booklet.

Work in progress

The Japanese-style book is perfect for series and periodic functions It's one long continuous piece of paper:

Yet very compact:

I'm also working on a very silly book about hypercycloids (that's the "math" name for the shapes drawn by spirographs, did I mention I collect spirographs?):

I'm trying to make it like a children's book, fun, light, a little silly:

I can't wait to share the final product.