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In any news report about the Deepwater Horizon oil spill, a lot of statistics get thrown around—mainly about the rate at which oil has been spewing out of a pipe on the floor of the Gulf of Mexico. Recent estimates put the flow up to 60,000 barrels per day, but it’s hard for most of us to comprehend exactly what that number means. Wolfram|Alpha has always been able to provide some useful comparisons for any quantity you care to input, and can easily tell you that 60,000 barrels of oil is roughly equivalent to 3.8 times the volume of an Olympic-sized swimming pool.
With the recent addition of data on production and consumption of energy resources in every country, Wolfram|Alpha can also give you a more precise socioeconomic context for numbers like this. Try “60000 barrels per day / US crude oil production”, for example, and you’ll learn that the daily output of the leak is a little less than 1.2% of total crude oil production per day for the United States.
You can also get a better sense of global production or consumption of petroleum products, as well as information on coal and natural gas.
Because each of these energy resources is measured in different units, it can be difficult to understand exactly how they compare to one another—so Wolfram|Alpha can also compute the energy equivalents of each resource, measured in quadrillions of BTUs. For example, you can compare the United States consumption of energy from coal, natural gas, and petroleum on a single scale to better visualize the relative importance of each resource. More »
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How many people are diagnosed with diabetes in a given year? Is hypertension more common in men than in women? What drugs are most commonly prescribed for anemia?
In order to address questions like these and many more, Wolfram|Alpha has now assimilated data from two different surveys conducted by the CDC: the national ambulatory medical care survey (NAMCS) and its hospital-focused counterpart, the national hospital ambulatory medical care survey (NHAMCS). Together, these surveys provide information on common reasons why people visit the doctor’s office, drug treatments that are highly correlated with a particular disease, and which diseases are most commonly diagnosed within specific races, ethnicities, and genders.
Through Wolfram|Alpha, you can investigate data on thousands of diseases and medical conditions, such as these:
Instead of looking at all the information at once, you can also try more targeted inputs, such as “fraction of US population affected by lung cancer”:
From this output, we can see that approximately .21% of all U.S. patients are diagnosed with lung cancer each year. More »
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Today (June 23, 2010) would have been Alan Turing‘s 98th birthday—if he had not died in 1954, at the age of 41.
I never met Alan Turing; he died five years before I was born. But somehow I feel I know him well—not least because many of my own intellectual interests have had an almost eerie parallel with his.
And by a strange coincidence, Mathematica‘s “birthday” (June 23, 1988) is aligned with Turing’s—so that today is also the celebration of Mathematica‘s 22nd birthday.
I think I first heard about Alan Turing when I was about eleven years old, right around the time I saw my first computer. Through a friend of my parents, I had gotten to know a rather eccentric old classics professor, who, knowing my interest in science, mentioned to me this “bright young chap named Turing” whom he had known during the Second World War.
One of the classics professor’s eccentricities was that whenever the word “ultra” came up in a Latin text, he would repeat it over and over again, and make comments about remembering it. At the time, I didn’t think much of it—though I did remember it. Only years later did I realize that “Ultra” was the codename for the British cryptanalysis effort at Bletchley Park during the war. In a very British way, the classics professor wanted to tell me something about it, without breaking any secrets. And presumably it was at Bletchley Park that he had met Alan Turing.
A few years later, I heard scattered mentions of Alan Turing in various British academic circles. I heard that he had done mysterious but important work in breaking German codes during the war. And I heard it claimed that after the war, he had been killed by British Intelligence. At the time, at least some of the British wartime cryptography effort was still secret, including Turing’s role in it. I wondered why. So I asked around, and started hearing that perhaps Turing had invented codes that were still being used.
I’m not sure where I next encountered Alan Turing. Probably it was when I decided to learn all I could about computer science—and saw all sorts of mentions of “Turing machines”. But I have a distinct memory from around 1979 of going to the library, and finding a little book about Alan Turing written by his mother, Sara Turing.
And gradually I built up quite a picture of Alan Turing and his work. And over the 30 years that have followed, I have kept on running into Alan Turing, often in unexpected places. More »
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One thing that is full of confusion is figuring out relationships. It can also be full of surprises, like the fact that Wolfram|Alpha can do it for you. If you follow this blog, you already know that Wolfram|Alpha can figure out and calculate lots of different things, including the moon and planets, and you are about to discover what it can tell you about your relationships.
Or at least relationships between your relatives. For instance, my cousin just had a son”.
We get a family tree, and it tells us that my relationship to my cousin’s son is that he is my first cousin once removed. Confusion resolved.
Like many other Wolfram|Alpha outputs, we get more than we may have expected. A few genealogical properties are related to historical laws, and a few are biological. The plots for sharing a Mendelian trait are given at the bottom after clicking More. This helps me understand how much I may have in common with my new first cousin once removed.
A dominant trait only requires one allele, while a recessive trait requires two. The other piece of information needed to say how likely it is to share a trait is how common it is in the general population. It is possible to share a trait accidentally, and for recessive traits one needs to get the other allele from the other parent. For my cousin’s son, not surprisingly, we see that the probability of sharing a genetic trait in common doesn’t seem to depend much on whether it is dominant or recessive. We are too distantly related to have much in common, and the probability of a shared trait between us depends primarily on the chance coming from the frequency in the general population.
It turns out that most traits are not simple like this, and involve more than one gene and so on, but this gives a general sense of how much we may have in common.
You probably know people who get confused about second cousins and so on, but there is also another category for relationship confusion. More »
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“It’s a quick and easy Saturday afternoon project!” We’ve all stood in the middle of our favorite home improvement store reciting that same line. Ty Pennington, Mike Holmes, Tim “The Tool Man” Taylor—they know how to make the most elaborate home improvement projects look as simple as tightening a bolt. Often the challenging part of the project is picking the perfect color of paint, or deciding between hardwood and tile flooring. But just as soon as those decisions are settled we’re faced with deciding how many feet of flooring to purchase for the kitchen or how many gallons of coral paint are needed for the north wall of the living room. But you don’t have to let a little bit of tricky math cut into your project time. Wolfram|Alpha has a number of math tools that come in handy for many common home improvement projects.
You can make quick computations and conversions from Wolfram|Alpha’s website or from the Wolfram|Alpha app for iPhone or iPad while standing in the flooring department. Wondering how many 8 x 8 square inch tiles you’ll need to cover a 12 x 14 square foot kitchen? Compute it with Wolfram|Alpha by entering “(12*14) square feet / (8*8) square inches”:
Need to know how many square feet you can cover with vinyl flooring that’s sold by the square yard? Tap into Wolfram|Alpha’s large collection of units to convert 60 square yards to square feet.
Thinking about livening up the living room with a splash of color? Query the name of your favorite hue and Wolfram|Alpha will give you a color swatch, properties, and a breakdown of related colors
Wondering how many gallons of paint you’d need per coat on a wall that’s 90 square feet? More »
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Wolfram|Alpha computes things. While the use of computations to predict the outcomes of scientific experiments, natural processes, and mathematical operations is by no means new (it has become a ubiquitous tool over the last few hundred years), the ease of use and accessibility of a large, powerful, and ever-expanding collection of such computations provided by Wolfram|Alpha is.
Virtually all known processes occur in such a way that certain functionals that describe them become extremal. Typically this happens with the action for time dependent processes and quantities such as the free energy for static configurations. The equations describing the extremality condition of a functional are frequently low-order ordinary and/or partial differential equations and their solutions. For example, for a pendulum: Frechet derivative of Integrate[x'[t]^2/2 – Cos[x[t]], {t, -inf, inf}] wrt x[tau]. Unfortunately, if one uses a sufficiently realistic physical model that incorporates all potentially relevant variables (including things like friction, temperature dependence, deformation, and so forth), the resulting equations typically become complicated—so much so that in most cases, no exact closed-form solution can be found, meaning the equations must be solved using numerical techniques. A simple example is provided by free fall from large heights:
On the other hand, some systems, such as the force of a simple spring, can be described by formulas involving simple low-order polynomial or rational relations between the relevant problem variables (in this case, Hooke’s law, F = k x):
Over the last 200+ years, mathematicians and physicists have found a large, fascinating, and insightful world of phenomena that can be described exactly using these so-called special functions (also commonly known as “the special functions of mathematical physics”), the class of functions that describe phenomena between being difficult and complicated. It includes a few hundred members, and can be viewed as an extension of the so-called elementary functions such as exp(z), log(z), the trigonometric functions, their inverses, and related functions.
Special functions turn up in diverse areas ranging from the spherical pendulum in mechanics to inequivalent representations in quantum field theory, and most of them are solutions of first- or second-order ordinary differential equations. Textbooks often contain simple formulas that correspond to a simplified version of a general physical system—sometimes even without explicitly stating the implicit simplifying assumptions! However, it is often possible to give a more precise and correct result in terms of special functions. For instance, many physics textbooks offer a simple formula for the inductance of a circular coil with a small radius:
While Wolfram|Alpha knows (and allows you to compute with) this simple formula, it also knows the correct general result. In fact, if you just ask Wolfram|Alpha for inductance circular coil, you will be simultaneously presented with two calculators: the one you know from your electromagnetics textbook (small-radius approximation) and the fully correct one. And not only can you compute the results both ways (and see that the results do differ slightly for the chosen parameters, but that the difference can get arbitrarily large), you can also click on the second “Show formula” link (near the bottom of the page on the right side) to see the exact result—which, as can be seen, contains two sorts of special functions, denoted E(m) and K(m) and known as elliptic integrals: More »
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The creation of large data repositories has been a key historical indicator of social and intellectual development—and indeed perhaps one of the defining characteristics of the whole progress of civilization.
And through our work on Wolfram|Alpha—with its insatiable appetite for systematic data—we have gained a uniquely broad view of the many great data repositories that exist in the world today.
Some of these repositories are maintained by national or international agencies, some by companies and other organizations, and some by individuals. A few of the repositories are quite new, but many date back 40 or more years, and some well over a century. But there is one thing in common across essentially every great data repository: a core of diligent and committed people who have carefully shepherded its development.
Curiously, though, few of these people have ever met their counterparts in other domains of data. And in our work on Wolfram|Alpha we are almost certainly the first group ever to have had the pleasure of getting to know such a broad range of leaders of great data repositories.
And one of the things that we have discovered is that there is much in common in both the methods used and the issues faced by these data repositories. So as part of our contribution to the worldwide data community we have decided to sponsor a data summit to bring together for the first time the leaders of today’s great data repositories.
The Wolfram Data Summit 2010 will be held in Washington, DC on September 9–10.
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Since Wolfram|Alpha launched in 2009, we’ve had numerous requests to add data on climate. As part of our one-year anniversary release, we recently added a vast set of historical climate data, drawing on studies from across the globe, which can be easily analyzed and correlated in Wolfram|Alpha.
You can now query for and compare the raw data from different climate model reconstructions and studies, as reported in peer-reviewed journals and by government agencies, many of them covering more than a thousand years of history. The full set of reconstructions was chosen from as broad a collection of sources as possible, from well-known records such as ice cores and tree rings, to corals, speleothems, and glacier lengths—and even some truly unusual ones, like grape harvest dates.
Or are you more interested in global greenhouse gas concentrations?
If you’re interested in exploring this vast area of climatology yourself, you can start by looking at a detailed summary of the most prominent models in literature: simply ask Wolfram|Alpha about “global climate”, which will bring up a selection of data sets that have figured prominently in the news over the past few years.
Wolfram|Alpha can also compute a more local analysis of recorded temperature variations. For example, you can compare the temperature variations recorded in specific parts of the globe, like the Northern Hemisphere. Or you can ask about studies conducted in specific countries, like the United Kingdom or Japan. More »
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We’re in the midst of major enhancements to military data in Wolfram|Alpha, with newly added information on army, navy, and air force personnel for over 150 countries as well as statistics on many armaments, including stockpiles of nuclear warheads.
Let’s start with the big numbers. Type “army size of all countries” and you’ll see China, India, and the Korean Peninsula topping the list. China’s army alone includes 1.4 million soldiers and dwarfs the population of many smaller countries. The size of its combined army, navy, and air force is nearly equal to the entire population of Macedonia.
There’s an abundance of data on armaments, around the world as well, including estimates on nuclear stockpiles of the nine countries known to have detonated nuclear weapons; according to the latest available estimates, Russia has the largest stockpile with 13,000 warheads. Also new in Wolfram|Alpha are figures on conventional weapons, including aircraft carriers, battle tanks, and fighter jets. Try comparing countries’ armaments, such as “tanks USA vs Russia”, or asking about the number of submarines in the NATO alliance. More »