futurebird – Page 2 – mathematical sandbox

## Living with worms in a small apartment

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! Learn more at https://www.paydaychampion.com/payday-consolidation/

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 and hunting with your Outdoorempire accessories 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.

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!
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## 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?

Here are some advantages of running:
It Prevents Disease
For women, running can actually help to lower your risk of breast cancer, although for the people that got them, they can get a reconstructive surgery with specialist as the Dr. Franco and many others. It can also help reduce the risk of having a stroke. Many doctors today recommend running for people who are in the early stages of diabetes, high blood pressure, and osteoporosis, and it is proven to help reduce the risk of having a heart attack. By helping the arteries retain their elasticity and strengthening the heart, your chances of suffering a heart attack can be significantly reduced, and also helps treat chronic pain, which people also do with supplements that are sold online.
treat chronic pain.
In any case you have other problems like nerves pain, haven been proved that you can use a nerve pain supplement which really help with this problem, and make people feel better and live without pain for much longer.
You Might Lose Weight
Running is one of the best forms of exercise for losing or maintaining a consistent weight, along with Kickboxing Training you people can achieve an amazing physic. You will find that it is a leading way to burn off extra calories and that it is the second most effective exercise in terms of calories burned per minute, following only after cross country skiing. When running is recommended to use the right gear, like the Vessi waterproof sneakers.

Not all of the benefits of running are physical. Running can provide an noticeable boost to your confidence and self-esteem. By setting and achieving goals, you can help give yourself a greater sense of empowerment that will leave you feeling much happier.

Life is complicated, running is simple.

## Garden of lost feathers: Highbridge park, 1978

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 with an extra costs when leasing 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:

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: The o-check notebooks was everything I dreamed it would be. The quality is exquisite. 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! A nice touch on this notebook is the red thread used to stich it together. Lovely! I also bought these darling envelops made by Midori (of the famous travler's notebooks, I may try those some day as well). 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? 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 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.

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.

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.

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!

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!

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?

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! 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. 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): 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. 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. ## Notebook Collection Part 2 In which I continue to share my collection of blank notebooks and journals. These are some of my large notebooks, the theme here is "unconventional paper" -- blank paper and lined paper are very nice, but when you spend as much time as I do staring at notebooks a change of scenery is nice. Whitelines paper is a love or hate thing. I know many people who love it and just as many who can't stand it. I'm on the love side. I find it much easier to see my drawings and diagrams without black lines cutting through them. I have rejected many notebooks for having lines that are far too dark. To my eye dark lines look cheap, like those cartoon character notebooks you see in dollar stores. The Rhodia Dot Pad was my favorite paper until I discovered Writersblok dot paper. As I mentioned in my previous post Writersblok is very much underrated and they make the best dot paper around. I'll show you why: Here you see the inside of the three notebooks with dotted paper. The Bob's Your Uncle notebook is very fun, but the dots are so big that they don't really work for graphing. (Bob's Your Uncle graph paper notebooks on the other hand are amazing, very relaxed light green grid, I'd share but I filled them all up so quickly that I have no blank pages!) Rhodia is better, but the dots still stand out on the very white paper. But, Writersblok has it perfect! Look at how fine those dots are, they almost don't even show up in the photo! What about the green "custom" number? It's a mix of different types of graph paper, dot papers and blank pages. Next up? Hardcover books: I keep my eye out for re-purposed journals with scientific or mathematical themes. The burgundy recycled journal has a Coptic binding. (I'm not a huge fan of Coptic binding, but this one is very nice!) Open it to find... I don't know what to write in the "mathematics" book it is very formal and commanding isn't it? This RECORD book has a lovely red satin bookmark. These can be found at old house sales, or on Amazon for around$20.

I don't often used lined pages but I'll make an exception. The numbered pages and "Table of Contents" page are the kind of little touches that make me fall in love with a notebook. The red and black record book to the right also has numbered pages....

... BUT instead it has quad paper! My favorite. I first discovered this notebook at a Manhattan stationary store. It was very dusty and I literally fished it out from behind a cabinet. It was torn in a few places, but the store owner still wanted $90 for it! I was so in love I almost bought it. So, when I discovered I could get one on Amazon for$30 ... well that seemed like a deal. I want to take this one camping with me this summer.

I still have a lot more to share, but that's all for today! If you have notebooks that you love let me know in the comments.

## Notebook Collection

There is nothing quite as exciting as a fresh blank notebook full of possibilities, well except, perhaps a full worn notebook filled with new mathematics! I can admit that I'm addicted to notebooks. Whenever I see one, with a new kind of color or material I buy it. As such, a shelf in our house is totally devoted to blank notebooks.

It was only a few months ago when I put them all in one place that it hit me how many I'd accumulated. These are all blank. I go through about one or two notebooks per week (of the Moleskine Cahier size) So, I have almost a whole bookcase full of full notebooks as well. I use Rhodia, Moleskine, Whitelines, Writer's block and other big brands quite often, In this post I'll focus on the more rare and unique stuff, the notebooks that make my hand tremble with excitement as I get ready to make that first mark on the unblemished page! The notebooks that I cherish, they are almost too good to write in, yet, I await the day that I mark them with such pent-up desire!

Okay, maybe I'm getting a little too excited here, on with the notebooks!

Although I like large notebooks best I do have a few small ones that I could not resist. Here we have: Quattero, a generic red notebook, an antique 1950s notebook, Writer's block "Dots" mini notebook and "Tidbit" Free Cut memo.

Quattero notebooks come in all sizes, they are a little pricy, but the paper is so smooth and thick it's worth it, the only thing I don't like about them is that the backs of the papers are blank, you only get the grid on one side, considering that the paper is bleed-proof this seems like a missed opportunity.

Writersblok is one of the most underrated notebooks around. They are a less expensive version of the "Moleskine Cahier" but, even if they cost more than Moleskine I'd still take them over the Moleskine any day! Why? DOTS. Dots are the ideal method of ruling the blank page, grid paper is too distracting, lined paper looks awful if you stop to make drawings and graphs as often as I do. So dotted paper is one of the main things I look for in a notebook. The dots in the Writersblok notebooks are the best, they are whisper light, so that you'll almost forget they are there. Yet when you look at your pages you'll see that the lines are straighter, graphs are more accurate and the text is evenly spaced. I've been seeing more and more kinds of dot paper, I really hope it catches on!

Antique notebooks fascinate me. Especially those that have survived totally blank and untouched like this one for decades. I love that this little memo book has an even smaller notebook (not an address book!) tucked inside. If I ever think of the perfect use for it I will use it, but for now it remains untouched, it is one of my most cherished notebooks. (*sniff*)

Ever since I started loving blank books and shopping for them I have starting HATING address books, planners and photo albums. Why? Often I'll see a notebook on the shelf, the perfect size! The perfect color! I reach for it and.... it's a PHOTO ALBUM! ugh. So annoying. I end up wondering who are all of the people who like photo albums and address books so much, have they not heard of Flikr and gmail? I suppose they must be wondering what's with all of the blank books... who needs paper? I have an iPad.

(I will continue sharing my collection in the next post.)

## Of yarn and math.

Yarn has been on my mind. It's on my mind because I love to knit, but also because of this post I read some weeks ago on the mathematics stack exchange. The author presents a paper about an "optimal yarn ball" that looks like this:

Very cool, but it would be impossible to do that with real yarn! (Though, I doubt that was their goal here.) When wrapping yarn around a ball you cannot make sharp turns or the yarn will fall off. If we think of the yarn as a curve on the surface of the sphere, we would say it must have curvature less than some small constant m. (meaning the best fit tangental circle must have radius greater than $\frac 1m$)

The yarn should be wrapped evenly: it should not overlap itself too often. (This would lead to the yarn ball taking on a non-spherical shape over time. No good!) The distribution of the self-intersections should be of nearly consistent density over the surface of the sphere. The yarn will divide the surface of the sphere in to regions. If $A_i, A_j$ are the areas of any two of these regions then for some small constant F, |A_i- A_j| < F[/latex], $\forall i, j$. As the curve is extended further and further (wrapped around more times) the density of intersections should increase and $A_i \rightarrow 0$ for all of the regions. I know one answer is a randomly generated curve that deviates from a straight path. Overtime it produces a perfect yarn ball. That's how I make my yarn balls, randomness produces even inward tension which forms a sphere. But, I want to know if there is a non-random answer to this question. First Thoughts: In trying to solving this myself I thought it might be a good idea to project the sphere on to the plane, as a Riemann surface. But, since so many of the requirements focus on uniformity, this makes the problem a little strage. Observe: The area of the regions will need to *increase* as we move away from the unit circle toward infinity. If the curve ever passes through the north pole, then the plane version would shoot off to infinity. What I found even more weird is what would happen if the curve simply passed very near, but not through, the north pole. Then, on the plane, the curve would go very far from the origin and then loop back. By making the curve near enough to the north pole the loops can be as large as we please. Since wrapping increases the density uniformly, if we observe the wrapping pattern projected on to the plane it would be like loopy knot that, over time, keeps casting bigger and bigger outlier loops, it would always grow and be un-bounded. (even without any intersection with the north pole!) The requirement about curvature, would mean that the knot could be more curvy inside of the unit circle, and then grow less curvy as we move away from the origin. Next to find such a curve... Maybe if I projected the following polar plot back on to the Riemann sphere? The graph of the form r= \theta^2 \sin (k \theta)' class='latex' /> produced good-looking results for 0 < k <1... but all of the graphs are far too dense near the origin. Also, wrapping would start in a lop-sided manner, filling in the bottom of the sphere first then moving up... and never reaching the north pole! But, maybe there is some way to tweak this? (This graph shows the kind of non-random pattern I have in mind for a solution. In a practical sense, a solution to this problem could be used to wind spherical balls of ropes, yarns, or cords in a factory setting. Now, I will think about how I would instruct a robot to wind a yarn ball... if the robot is unable to do things randomly. What would you tell the robot to do?)

This post grew out of a question I asked at the Stack Exchange.