July 31, 2011
"Love and Tensor Algebra" by Stanislaw Lem

Come, let us hasten to a higher plane
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n
Commingled in an endless Markov chain!

Come, every frustrum longs to be a cone
And every vector dreams of matrices.
Hark to the gentle gradient of the breeze:
It whispers of a more ergodic zone.

In Riemann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.

I’ll grant thee random access to my heart,
Thou’lt tell me all the constants of thy love;
And so we two shall all love’s lemmas prove,
And in our bound partition never part.

For what did Cauchy know, or Christoffel,
Or Fourier, or any Bools or Euler,
Wielding their compasses, their pens and rulers,
Of thy supernal sinusoidal spell?

Cancel me not - for what then shall remain?
Abscissas some mantissas, modules, modes,
A root or two, a torus and a node:
The inverse of my verse, a null domain.

Ellipse of bliss, converge, O lips divine!
the product o four scalars is defines!
Cyberiad draws nigh, and the skew mind
Cuts capers like a happy haversine.

I see the eigenvalue in thine eye,
I hear the tender tensor in thy sigh.
Bernoulli would have been content to die,
Had he but known such a^2 cos 2 phi!

March 20, 2011
xkcd: Fairy Tales

xkcd: Fairy Tales

March 14, 2011
The Venn Piagram (via HungryHungryHippo)

The Venn Piagram (via HungryHungryHippo)

(via tiwyh-deactivated20120503)

February 10, 2011
A Literary Glass Ceiling? Why Magazines Aren't Reviewing More Female Writers. | The New Republic

The first shots were fired last summer, when Jennifer Weiner and Jodi Picoult called the New York Times Book Review a boys’ club. (I weighed in then, too, calling on the Times to respond to statistics posted by Double X regarding the disparity between books by male authors and female authors reviewed in their pages.) Now, the war is on. A few days ago, VIDA, a women’s literary organization, posted on its website a stark illustration of what appears to be gender bias in the book review sections of magazines and literary journals. In 2010, as VIDA illustrated with pie charts, these publications printed vastly more book reviews by men than by women. They also reviewed more books by male authors.

The numbers are startling. At Harper’s, there were 27 male book reviewers and six female; about 69 percent of the books reviewed were by male authors. At the London Review of Books, men wrote 78 percent of the reviews and 74 percent of the books reviewed. Men made up 84 percent of the reviewers for The New York Review of Books and authored 83 percent of the books reviewed. TNR, I’m sorry to say, did not compare well: Of the 62 writers who wrote about books for us last year, only 13 (or 21 percent) were women. We reviewed a total of 64 books, nine of them by women (14.5 percent). “We know women write,” poet Amy King writes on the VIDA website. “We know women read. It’s time to begin asking why the 2010 numbers don’t reflect those facts with any equity.”

But let’s slow down for a moment. There’s some essential data missing from these moan-inducing statistics. What’s the gender breakdown in books published last year? It’s crucial to both of the categories VIDA explores, because freelance book reviewers, who make up the majority of the reviewing population, tend to be authors themselves. If more men than women are publishing books, then it stands to reason that more books by men are getting reviewed and more men are reviewing books. So TNR’s Eliza Gray, Laura Stampler, and I crunched some numbers. Our sample was small and did not pretend to be comprehensive, and it may not represent a cross-section of the industry, because we did not include genre books and others with primarily commercial appeal. But it gave us a snapshot. And what we found helps explain VIDA’s mystery.

We looked at fall 2010 catalogs from 13 publishing houses, big and small. Discarding the books that were unlikely to get reviewed—self-help, cooking, art—we tallied up how many were by men and how many were by women. Only one of the houses we investigated—the boutique Penguin imprint Riverhead—came close to parity, with 55 percent of its books by men and 45 percent by women. Random House came in second, with 37 percent by women. It was downhill from there, with three publishers scoring around 30 percent—Norton, Little Brown, and Harper—and the rest 25 percent and below, including the elite literary houses Knopf (23 percent) and FSG (21 percent). Harvard University Press, the sole academic press we considered, came in at just 15 percent.

I speculated that independents—more iconoclastic, publishing more work in translation, and perhaps less focused on the bottom line—would turn out to be more equitable than the big commercial houses. Boy, was I wrong. Granted, these presses publish a smaller number of books in total, so a difference in one or two books has a larger effect on their percentages. Still, their numbers are dismaying. Graywolf, with 25 percent female authors, was our highest-scoring independent. The cutting-edge Brooklyn publisher Melville House came in at 20 percent. The doggedly leftist house Verso was second-to-last at 11 percent. Our lowest scorer? It pains me to say it, because Dalkey Archive Press publishes some great books that are ignored by the mainstream houses. But it would be nice if more than 10 percent of them were by women. (In the 2011 edition of Dalkey’s much-lauded Best European Fiction series, edited by Aleksandar Hemon, 30 percent of the stories are by women. Last year, at least Zadie Smith wrote the preface.)

Now we can better understand why fewer books by women than men are getting reviewed. In fact, these numbers we found show that the magazines are reviewing female authors in something close to the proportion of books by women published each year. The question now becomes why more books by women are not getting published.

The VIDA numbers provide a start toward an answer: Of the new writing published in Tin House, Granta,and The Paris Review, around one-third of it was by women. For many fiction writers and poets, publishing in these journals is a first step to getting a book contract. Do women submit work to these magazines at a lower rate than men, or are men’s submissions more likely to get accepted? We can’t be sure. But, as Robin Romm writes in Double X, “The gatekeepers of literary culture—at least at magazines—are still primarily male.” If these gatekeepers are showing a gender bias, there’s not much room to make it up later.

Or maybe it’s that we’re not quite as equal as we like to think we are. My colleague Meghan O’Rourke wistfully comments in Slate that “writing isn’t a field historically dominated by men, like theoretical physics … and one might reasonably have assumed that since feminism’s second wave, matters had roughly evened out.” In fact, it’s the rare profession in which the numbers are even. According to a fact sheet published last year by the AFL-CIO’s Department for Professional Employees, in 2008, women constituted 32.4 percent of all lawyers and 32.2 percent of physicians and surgeons. (We’re 68.8 percent of psychologists, 92 percent of nurses, and 50.4 percent of technical writers, the only type of writer included in the report.) Granted, many important numbers have already increased: The proportion of women in law school has gone up from 3.7 percent in 1963 to nearly 50 percent in 2007-08, and women also account for nearly 50 percent of med school students. Yet, while we may have come a long way, in many areas we’re still catching up.

Peter Stothard, editor of the Times Literary Supplement, told The Guardian that he refused to “make a fetish” of having an equal number of male and female contributors. “The TLS is only interested in getting the best reviews of the most important books,” he said. I, too, like to think I choose the books that I review for their inherent interest, their literary quality. But the VIDA statistics made me wonder afresh about the ways we define “best” and “most important” in a field as subjective as literature, which, after all, is deeply influenced by the cultural norms in any given age. As a member of third-wave feminism, growing up in the 1970s and ’80s, I was brought up to believe we lived in a meritocracy, where the battles had been fought and won, with the spoils left for us to gather. It is sobering to realize that we may live and work in a world still held in the grip of unconscious biases, no less damaging for their invisibility. (Meghan has written about this, too.)

Now, I’m contemplating my personal 2010 statistics, which demonstrate how a strict male-female breakdown flattens out the complexities. I reviewed a biography of a female writer (Clarice Lispector) written by a man, but focused the piece on her and her work: Does this count in the male or female column? What about a new translation by a woman (Lydia Davis) of a book by a male author (Madame Bovary)? And, in my columns, I often mentioned new books by female writers and addressed issues of particular interest to women, such as the aforementioned “Franzenfreude” debacle. But, in the end, my bottom line was only a little more equitable than the norm: Of the books I reviewed, around 33 percent were by women.

Ruth Franklin is a senior editor for The New Republic.

October 21, 2010
Benoît Mandelbrot obituary | Science | The Guardian

Mathematician whose fractal geometry helps us find patterns in the irregularities of the natural world

by Nigel Lesmoir-Gordon

A computer-generated fractal image. ‘Why is geometry often described as cold and dry?’ asked Mandelbrot. ‘One reason lies in its inability to describe the shape of a cloud, a mountain or a tree.’ Photograph: © Stocktrek/Corbis

Benoît Mandelbrot, who has died of pancreatic cancer aged 85, enjoyed the rare distinction of having his name applied to a feature of mathematics that has become part of everyday life – the Mandelbrot set. Both a French and an American citizen, though born in Poland, he had a visionary, maverick approach, harnessing computer power to develop a geometry that mirrors the complexity of the natural world, with applications in many practical fields.

At the start of his groundbreaking work, The Fractal Geometry of Nature, he asks: “Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.” The approach that he pioneered helps us to describe nature as we actually see it, and so expand our way of thinking.

The world we live in is not naturally smooth-edged and regularly shaped like the familiar cones, circles, spheres and straight lines of Euclid’s geometry: it is rough-edged, wrinkled, crinkled and irregular. “Fractals” was the name he applied to irregular mathematical shapes similar to those in nature, with structures that are self-similar over many scales, the same pattern being repeated over and over. Fractal geometry offers a systematic way of approaching phenomena that look more elaborate the more they are magnified, and the images it generates are themselves a source of great fascination.

Mandelbrot fingers

Mandelbrot always had a highly developed visual sense: as a boy, he saw chess games in geometrical rather than logical terms, and shared his father’s passion for maps. Photograph: Nigel Lesmoir-Gordon

Mandelbrot first visualised the set on 1 March 1980 at IBM's Thomas J Watson Research Centre at Yorktown Heights, upstate New York. However, the seeds of this discovery were sown in Paris in 1925, when the mathematicians Gaston Julia, a student of Henri Poincaré, and Pierre Fatou published a paper exploring the world of complex numbers – combinations of the usual real numbers, 1, -1 and so on, with imaginary numbers such as the square root of -1, which Gottfried Wilhelm Leibniz had labelled “that amphibian between being and not being”. The results of their endeavours eventually became known as Julia sets, though Julia himself never saw them represented graphically.

It was Mandelbrot’s uncle Szolem who initially directed him to the work of Julia and Fatou on what are termed self-similarity and iterated functions. In my documentary The Colours of Infinity, shown on Channel 4 in 1995, Mandelbrot told me how he set about developing his approach: ‘“For me the first step with any difficult mathematical problem was to programme it, and see what it looked like. We started programming Julia sets of all kinds. It was extraordinarily great fun! And in particular, at one point, we became interested in the Julia set of the simplest possible transformation: Z goes to Z squared plus C [where C is a constant number. So Z times Z plus C, and then the outcome of that becomes a new Z while C stays the same, to give new Z times new Z plus C, and so on]. I made many pictures of it. The first ones were very rough. But the very rough pictures were not the answer. Each rough picture asked a question. So I made another picture, another picture. And after a few weeks we had this very strong, overwhelming impression that this was a kind of big bear we had encountered.”

In his view, the most important implication of this work was that very simple formulas could yield very complicated results: “What is science? We have all this mess around us. Things are totally incomprehensible. And then eventually we find simple laws, simple formulas. In a way, a very simple formula, Newton’s Law, which is just also a few symbols, can by hard work explain the motion of the planets around the sun and many, many other things to the 50th decimal. It’s marvellous: a very simple formula explains all these very complicated things.”

Mandelbrot, born into a Lithuanian-Jewish family living in Warsaw, showed an early love for geometry and excelled at chess: he later admitted that he did not think the game through logically, but geometrically. Maps were another inspiration. His father was crazy about them, and the house was full of them.

In 1936, the rise of nazism in Germany persuaded his family to leave for Paris, and eventually Lyon, in the south of France. A year of studying mathematics there after he left high school brought home to Mandelbrot his extraordinary visual ability.

At the end of the second world war he returned to Paris for college entrance examinations, which he passed with distinction, winning a place at the École Normale and then moving on to the École Polytechnique. From there he went on to the California Institute of Technology, Pasadena, to study turbulence and gain a master’s in aeronautics.

After obtaining a doctorate in mathematics (1952) in Paris, he returned to the US, this time to the Institute for Advanced Study in Princeton, New Jersey. There he came across the idea of the Hausdorff-Besicovitch dimension – the revelation that there were phenomena that existed outside one-dimensional space, but in somewhat less than two dimensions. Mandelbrot took up the concept on the spot: it provided an all-purpose tool and was a special example of his eventual notion of fractal dimension.

Mandelbrot spike

Fractals have structures that are self-similar over many scales, the same pattern being repeated over and over. Photograph: Nigel Lesmoir-Gordon

His interest in computers was immediate, and his use of the new resource grew rapidly. He returned to France, married Aliette Kagan and became a professor at the University of Lille and then at the Centre National de la Recherche Scientifique in Paris. His academic future looked assured. But he felt uncomfortable in that environment, and in 1958 he spent the summer at IBM as a faculty visitor.

The company asked him to work on eliminating the apparently random noise in signal transmissions between computer terminals. The errors were not in fact completely random – they tended to come in bunches. Mandelbrot observed that the degree of bunching remained constant whether he plotted them by the month, the week or by the day. This was another step towards his fractal revelation.

During the 1960s Mandelbrot’s quest led him to study galaxy clusters, applying his ideas on scaling to the structure of the universe itself. He scoured through forgotten and obscure journals. He found the clue he was looking for in the work of the mathematician and meteorologist Lewis Fry Richardson: he took a photocopy, and when he returned to consult the volume further, found it had gone to be pulped. Nonetheless, he knew he had struck a rich seam.

Richardson loved asking questions others considered worthless, and one of his papers, Does the Wind Possess a Velocity? anticipated later work by Edward Lorenz and other founders of Chaos Theory. One of Richardson’s great insights was a model of turbulence as a collection of ever-smaller eddies.

Mandelbrot was struck too by Richardson’s 1961 observations on the lengths of coastlines, and published a paper called How Long is the Coast of Britain? This apparently simple question of geography reveals, on close inspection, some of the essential features of fractal geometry. At IBM in 1973 Mandelbrot developed an algorithm using a very basic, makeshift computer, a typewriter with a minute memory, to generate pictures that imitated natural landforms.

While the ideas behind fractals, iteration and self-similarity are ancient, it took the coining of the term “fractal geometry” in 1975 and the publication of The Fractal Geometry of Nature in French in the same year to give the quest an identity. As Mandelbrot put it, “to have a name is to be” — and the field exploded.

He had bolstered his own presence by adding a middle initial that stood for no particular name, and Benoît B Mandelbrot became a fixture at IBM, with visiting professorships at Harvard and MIT, the Massachusetts Institute of Technology. He started teaching at Yale in 1987, becoming a full professor there in 1999. His many awards included the Wolf prize for physics in 1993.

Fractal geometry is now being used in work with marine organisms, vegetative ecosystems, earthquake data, the behaviour of density-dependent populations, percolation and aggregation in oil research, and in the formation of lightning. Lightning resembles the diffusion patterns left by water as it permeates soft rock such as sandstone: computer simulations of this effect look exactly like the real thing.

Fractals hold a promise for building better roads, for video compression and even for designing ships that are less likely to capsize. The geometry is already being successfully applied in medical imaging, and the forms generated by the discipline are a source of pleasure in their own right, adding to our aesthetic awareness as we observe fractals everywhere in nature.

Their beauty and power are displayed in the just-published book The Colours of Infinity, updating the account given in the film. In the course of making that and a further film with Mandelbrot – Clouds Are Not Spheres (2000, now a DVD) – I became aware of his great kindness and generosity. At the end of Clouds Are Not Spheres he reflects: “My search has brought me to many of the most fundamental issues of science. Some I improved upon, but certainly left very wide open and mysterious. This had been my hope as a young man and has filled my whole life. I feel extremely fortunate.”

He is survived by Aliette and his two sons, Laurent and Didier.

• Benoît Mandelbrot, mathematician, born 20 November 1924; died 14 October 2010

• This article was amended on 20 October 2010. The original referred to the Institute for Advanced Study at Princeton University, New Jersey. This has been corrected.

October 8, 2010
"The axioms of science are not statements of facts. They are rules which single out the classes of problems to which they apply and determine how we are to proceed in the theoretical consideration of these problems."

— Richard von Mises

October 5, 2010
"The shortest distance between two points is often unbearable."

— Charles Bukowski (via aperfectcommotion)

(Source: mythologyofblue)

September 28, 2010
Why thinking of nothing can be so tiring: Brain wolfs energy to stop thinking

Ever wonder why it’s such an effort to forget about work while on vacation or to silence that annoying song that’s playing over and over in your head?

Mathematicians have found that the brain uses a substantial amount of energy to halt the flow of information between neurons. (Credit: iStockphoto/Sebastian Kaulitzki)

Mathematicians at Case Western Reserve University may have part of the answer.

They’ve found that just as thinking burns energy, stopping a thought burns energy — like stopping a truck on a downhill slope.

"Maybe this explains why it is so tiring to relax and think about nothing," said Daniela Calvetti, professor of mathematics, and one of the authors of a new brain study. Their work is published in an advanced online publication of Journal of Cerebral Blood Flow & Metabolism.

Opening up the brain for detailed monitoring isn’t practical. So, to understand energy usage, Calvetti teamed with Erkki Somersalo, professor of mathematics, and Rossana Occhipinti, who used this work to help earn a PhD in math last year and is now a postdoctoral researcher in the department of physiology and biophysics at the Case Western Reserve School of Medicine. They developed equations and statistics and built a computer model of brain metabolism.

The computer simulations for this study were obtained by using Metabolica, a software package that Calvetti and Somersalo have designed to study complex metabolic systems. The software produces a numeric rendering of the pathways linking excitatory neurons that transmit thought or inhibitory neurons that put on the brakes with star-like brain cells called astrocytes. Astrocytes cater essential chemicals and functions to both kinds of neurons.

To stop a thought, the brain uses inhibitory neurons to prevent excitatory neurons from passing information from one to another.

"The inhibitory neurons are like a priest saying, ‘Don’t do it,’" Calvetti said. The "priest neurons" block information by releasing gamma aminobutyric acid, commonly called GABA, which counteracts the effect of the neurotransmitter glutamate by excitatory neurons.

Glutamate opens the synaptic gates. GABA holds the gates closed.

"The astrocytes, which are the Cinderellas of the brain, consume large amounts of oxygen mopping up and recycling the GABA and the glutamate, which is a neurotoxin," Somersalo said.

More oxygen requires more blood flow, although the connection between cerebral metabolism and hemodynamics is not fully understood yet.

All together, “It’s a surprising expense to keep inhibition on,” he said.

The group plans to more closely compare energy use of excitatory and inhibitory neurons by running simultaneous simulations of both processes.

The researchers are plumbing basic science but their goal is to help solve human problems.

Brain disease or damaging conditions are often difficult to diagnose until advanced stages. Most brain maladies, however, are linked to energy metabolism and understanding what is the norm may enable doctors to detect problems earlier.

The toll inhibition takes may, in particular, be relevant to neurodegenerative diseases. “And that is truly exciting” Calvetti said.

Story Source:

The above story is reprinted (with editorial adaptations by ScienceDaily staff) from materials provided by Case Western Reserve University, via EurekAlert!, a service of AAAS.

Journal Reference:

Rossana Occhipinti, Erkki Somersalo, Daniela Calvetti. Energetics of inhibition: insights with a computational model of the human GABAergic neuron–astrocyte cellular complex. Journal of Cerebral Blood Flow & Metabolism, 2010; DOI: 10.1038/jcbfm.2010.107

September 18, 2010
New pi record exploits Yahoo's computers - physics-math - 17 September 2010 - New Scientist

by David Shiga

A Yahoo researcher has made a record-breaking calculation of the digits of pi using his company’s computers. The feat comes hot on the heels of a breakthrough Rubik’s cube result that used Google’s computers. Together, the results highlight the growing power of internet search giants to make mathematical breakthroughs.

One way to show off computing power is to calculate pi to as many digits as possible, creating a string that starts with 3.14 and continues to the nth digit. The more digits one wants, the more computations it takes.

But it is also possible to skip ahead to the nth digit without calculating the preceding ones – for example, determining that the 10th digit is 3, without having to find the first 9 digits: 3.14159265. This is another way of testing computing power, since more computations are required to find higher values of n.

Now, Tsz-Wo Sze, a computer scientist at Yahoo in Sunnyvale, California, has used the company’s computers to calculate the most distant digits yet.

Pushing pi to 9 trillion digits (Image: Mykl Roventine)

(Image: Mykl Roventine)

Downtime

His computer program represents pi in binary notation, and calculated the 2 quadrillionth (2 x 1015) binary digit, or bit, of pi. It is twice as distant as the previous record, which found a string of bits around the 1 quadrillionth bit.

Calculations that do not skip any digits have come nowhere near this remote territory. The latest record for that kind of calculation is 2.7 trillion digits in decimal notation, which works out to around 9 trillion (9 x 1012) bits.

Sze’s program was installed on 1000 Yahoo computers, each equipped with eight processors. They ran the calculations in July, when they were in low demand for regular work, doing in 23 days what would have taken half a millennium using just one processor.

The computation was made possible by open-source software called Hadoop that allows thousands of networked computers to be used as if they constituted a single extremely powerful machine, a concept called cloud computing. Yahoo programmers have done much of the work to develop Hadoop, though it draws on ideas first published by Google.

Web data

Yahoo is not the only internet giant delving into abstruse mathematics calculations. A recent result showing that any configuration of a Rubik’s cube can be solved in 20 moves or less relied on distributing calculations across many computers at Google, completing in a few weeks what would have taken a single computer 35 years.

Sze says the computing power that companies like Yahoo and Google can bring to bear on these problems is a by-product of their need to speedily process vast amounts of web-related data. “That is why we are building large-scale computation systems,” he says.

"As a technology company with big data at its core, we are excited by the possibilities of distributed software systems, most notably, Hadoop," says Eric Baldeschwieler, vice president of Hadoop engineering at Yahoo.

Easily divided

Calculations of pi are especially suited to distributed computing because they are easily broken into smaller parts, says David Bailey of the Lawrence Berkeley National Laboratory in California, which is setting up cloud-computing facilities to run such problems.

"They can be divided into sections and assigned to separate computational processors, which can then operate almost completely independently of the others," says Bailey, who in 1996 co-discovered the first formula allowing one to skip ahead to compute distant digits of pi.

Distributed computing is also being used in a project called the Great Internet Mersenne Prime Search. It searches for large examples of a special class of prime numbers using computing power donated by individual volunteers via the internet.

March 7, 2010
RP 4: More on the movie Up! (or Upper)

Up is a great movie (with the dubious distinction of being the Only Film To Have Ever Made Me Cry), so I’m willing to grant it a bit of poetic latitude. That said, the balloon-flown house immediately reminded me of a Mythbusters episode in which they have a really difficult time lifting a child in a similar manner. Allain incorporates estimates from several other sources in his discussion of the mechanics involved, and does a fairly comprehensive job laying out just how difficult it’d be to make this work:

The most important thing to estimate is the mass of the house. I am going to completely ignore the buoyancy of the house. I figure this will be insignificant next to the buoyancy needed. Anyway, let me go ahead and recap what has already been done on this in the blogosphere.

Wired Science - How Pixar’s Up House Could Really Fly - from that post:

  • First, they calculated (seemingly correct) that the buoyancy of helium is 0.067 pounds per cubic foot of helium. This does not include the mass of a balloon holding this, nor any strings on the balloon.
  • The weight of the house is 100,000 pounds. I like how they got this - they had a house mover estimate it. Seems legit.
  • It would take 1,500,000 cubic feet of helium to lift the house. This would require 112,000 balloons (3 foot diameter balloons)

Slate Explainer: How Many Balloons Would it Take to Lift a House - from that post:

  • If using party balloons, (11 inches in diameter) they would have a lift equivalent to 4.8 grams.
  • The dude would need 9.4 million party balloons to lift his house.
  • Pixar estimated it would take 23.5 million balloons to lift a 1,800 square foot house.
  • Pixar used 20,622 balloons in the animation of the lift off and 10,297 balloons from the floating sequences

Physics and Physicists looked at Up also. ZapperZ looked at how the balloons were deployed. He assumed that the balloons were originally attached to the house before being released (this would have the same buoyancy as if they were deployed). However, it seems like the balloons may have been attached outside the house to the ground or something.

Swans on Tea looked at the problem with precision in the calculations. I am guilty of this sin also. Basically, if you estimate that the house is 100,000 pounds and convert that to Newtons or something, you should keep the same level of precision. He (Tom) is correct.

Finally, here is stuff on buoyancy and floating things. That is from a post on the MythBusters making a lead balloon float. Oh, and here is my last post about Up (just for completeness). And now on to the calculations.

If the house were lifted with one balloon, how big would it be and what would it look like?

There is one important thing to estimate - the weight of the balloon material. I have no clue how much this would weigh. Let me just say that the balloon is a sphere with a thickness oft. If I had to off the wall guess t, I would say 1 mm. If this is latex, the density would be about ? = 950 kg/m3 (wikianswers.com). From this I can do some stuff. Here is my approach. I have the buoyancy force = weight of house plus weight of balloon plus the weight of the helium. Of course the weight of the balloon depends on the size of the balloon.

Here, r is the radius of the balloon. If I put this all together, I get:

I just need to solve this for r. Problem, this is a cubic equation. There are quite a few ways to solve a cubic equation, but I will use the plotting method. If I let f(r) be written as:

And then I can plot this to find the zeros. Here is a plot from zoho:

Looking at the graph, r = 23 meters seems close to a solution. Just as a check, I calculated the size of the balloon if the mass of the balloon were negligible (it’s in the zoho sheet). This is a much easier calculation, and I get a radius of 22 meters. Seems reasonable. Note, if I change the thickness of the balloon to 2 mm, the radius moves up to around 24 meters - but you can play with the spreadsheet yourself if you like. A couple more notes:

  • I assumed that the balloon was a sphere - clearly, it would not be.
  • I assumed that the thickness of the balloon was very small compared to the size. This way I can calculate the volume of rubber needed as surface area of sphere times thickness.

Ok, I want to draw this. I need the size of the house. The Slate article said that Pixar said the house was 1,800 square feet. Looks pretty square, so this would make it 42 feet by 42 feet or about 13 meters. Oh wait, it’s a two story house. That means the bottom floor is maybe 900 square feet. This would make the side 30 feet or about 9 meters. Now I just measure the pixel size of the house and use the same pixel per meter for the spherical balloon. Here it is.

But wait, I am not finished. The next question:

If the house were lifted by standard party balloons, what would it look like?

The thing with party balloons is that they are not packed tightly, there is space between them. This makes it look like it takes up much more space. Let me just use Slate’s calculation of 9.4 million party balloons. How big would this look? This could be tricky if I didn’t know how to cheat. How tightly packed do party balloons fit? Who knows? Pixar knows. From that Slate post, Pixar said they used 20,600 balloons in the lift off sequence. From that and the picture I used above and the same pixel size trick, the volume of balloons is about the same as a sphere of radius 14 meters. This would make a volume of 12,000 m3. The effective volume (can’t remember the technical term for this) of each balloon would be:

And then this would lead to an apparent volume of the giant cluster of 9.4 million balloons:

If this were a spherical cluster, the radius would be 110 meters. Here is what that would look like:

How long would it take this guy to blow up this many balloons?

You can see that there is no point stopping now. I have gone this far, why would I stop? That would be silly. The first thing to answer this question is, how long does it take to fill one balloon. I am no expert, I will estimate low. 10 seconds seems to be WAY too quick. But look, the guy is filling 9.4 million balloons, you might learn a few tricks to speed up the process. If that were the case, it would take 94 million seconds or 3 years. Well, you can see there is a problem because that time doesn’t include union bathroom breaks. Also, a standard helium balloon will only stay inflated for a few days.

What if it was just 20,600 balloons like Pixar used in the animation? At 10 seconds a balloon, that would be 2.3 days (and I think that is a pretty fast time for a balloon fill). Remember that MythBusters episode where they filled balloons to lift a small boy? Took a while, didn’t it?

How many tanks of helium would he need?

According this site, a large helium cylinder can fill 520 of the 11” party balloons and costs about $190. If he had to fill 9.4 million balloons, this would take (9.4 million balloons)(1 tank)/(520 balloons)= 18,000 tanks at a cost of 3.4 million dollars. You could buy an awesome plane for that much. Oh, maybe he got the helium at cost.