On May 22, 2010, Martin Gardner died, unexpectedly, at age 95. The previous sentence contains a paradox* explained within his book The Unexpected Hanging and Other Mathematical Diversions, one of 15 books known collectively as “the Canon,” comprising hundreds of the Mathematical Games columns Martin wrote for Scientific American between 1956 to 1981.
My fifth-grade science class had old copies of Scientific American available, and I read a few of those columns. From him I learned that math can be fascinating, perhaps one of the great lessons I’ve learned in life. I found out that the library had more issues, and whole books by Martin. I tracked down more of his columns on microfiche.
After reading all those columns, school-level math was easy. Years later, I tried to follow in Martin’s footsteps by putting recreational mathematics online. For example, I contributed a diagram of pentagon tiling to a very early version of MathWorld. “Tiling with Convex Polygons” was one of Martin’s columns, in his book Time Travel and Other Mathematical Bewilderments; today, you can explore these objects in Wolfram|Alpha.
Martin’s works influenced generations of mathematicians, and many of the topics he discussed can be found here at Wolfram|Alpha. For a Lewis Carroll expert like Martin, a snark was “something hard to find”, as in Carroll’s “The Hunting of the Snark” (for which Martin compiled a companion volume, The Annotated Snark). So he used the word “snark” to describe a graph with three edges attached to each node, but which could not be 3-colored without any clashes at a node. More »
Wolfram|Alpha’s coverage of the universe continues to grow. We have now added a large collection of observed supernovae in the universe to our ever-expanding compendium of astronomical knowledge.
What exactly is a supernova? It’s a catastrophic event in the life of a star.
The full details are very complex, but basically supernovae are the visible signs of the deaths of stars more massive than the Sun. As with all other stars, massive stars spend most of their lives fusing hydrogen gas into helium in their cores. This results in a buildup of “ash” (end product of fusion reactions) in the core that eventually chokes off the hydrogen fuel from the hottest area of the core. With no new fuel, there is less energy being produced to counter the gravity trying to squeeze the star’s huge mass more tightly together. The result is that the star’s core begins to collapse as gravity overtakes the outward pressure. This results in heating the core—eventually enough that the ash can begin fusing into heavier molecules, initially carbon and oxygen. The cycle repeats, each time beginning and ending with different products and creating the next fuel source. Eventually, the core contains iron. Iron cannot liberate energy from fusion, so at this point, energy generation in the core suddenly stops, and the full mass of the star comes crashing down and a shock wave rips the star apart. This explosion is called a Type II supernova and results in the formation of a neutron star (or more rarely a black hole). More »
We recently added data on health indicators for more than 200 countries and territories. We now have World Health Organization data on health care workers, immunizations, water and sanitation, preventive care, tobacco use, weight, and more.
Data is also now available on specific types of health care personnel, such as physicians, nurses, and dentists, and Wolfram|Alpha can also compute per capita figures for each type of health professional. Check out the figures on midwives in South Africa or dentists in Iceland—or for a particularly interesting view, try asking about doctors per capita in all countries.
Some data, such as for infant immunizations (including DTP, MCV, hepatitis B, and Hib), spans several years—which allows you to see dramatic increases in immunizations in many developing countries, as well as surprising declines in some first-world nations. More »
Sitting in your office watching and cursing the rainy outdoors, have you ever wondered what the weather beyond our protective atmosphere is like?
Yes, there is weather even in the empty space above Earth’s atmosphere. Space weather typically refers to phenomena resulting from solar activity. It’s also one of the latest content additions to Wolfram|Alpha. Space weather includes things like sunspots, solar X-rays, and solar wind, as well as their effects on the Earth itself (e.g. aurorae, radio communication blackouts, and in extreme cases power outages).
The Sun has an 11-year cycle. Every 11 years, the number of sunspots rises to a peak and then falls to a minimum. Sunspots result from areas of strong magnetic fields on the Sun that cool the surrounding gas and makes the gas appear darker. When these tangled magnetic fields reconnect, the plasma carried along with it can be flung with huge amounts of energy away from the Sun. If it is directed toward Earth, we may observe a number of effects. Depending on how the magnetic field is oriented, it may bounce off the Earth’s magnetic field with no effect. If oriented the other way, the plasma funnels down the Earth’s magnetic field lines until it encounters the atmosphere, causing it to glow. This glowing is known as the aurora borealis in the northern hemisphere and the aurora australis in the southern hemisphere.
The sunspot cycle likely plays a role in Earth’s global climate. The exact nature of its effect is still a hot area of active research. More sunspots mean more energy is likely to be absorbed by the Earth from the Sun. Fewer sunspots mean less energy and potentially a cooler climate. Between 1645 and 1715, sunspots on the Sun nearly vanished. During the same period, called the Maunder minimum, Europe experienced colder-than-average temperatures, contributing to what some have called “the little ice age”. Data for sunspots goes back much further than most other space weather data. Most other phenomena could not be measured until the advent of artificial satellites, and many much more recently than that.
In 1859, the first and most powerful solar flare ever observed occurred, known as the Carrington event. Within a couple of days of the flare, the Earth’s magnetic field oscillated wildly from the magnetized plasma thrown toward us. The magnetic field lines of the Earth bounced back and forth across telegraph wires, causing massive failures and even melted wires from the induced currents. An event of that strength today would cause untold havoc, as we are far more dependent on telecommunications via both satellites and land-based wires. More »
Years ago I wondered if it would ever be possible to systematically make human knowledge computable. And today, one year after the official launch of Wolfram|Alpha, I think I can say for sure: it is possible.
It takes a stack of technology and ideas that I’ve been assembling for nearly 30 years. And in many ways it’s a profoundly difficult project. But this year has shown that it is possible.
Wolfram|Alpha is of course a very long-term undertaking. But much has been built, the direction is set, and things are moving with accelerating speed.
Over the past year, we’ve roughly doubled the amount that Wolfram|Alpha knows. We’ve doubled the number of domains it handles, and the number of algorithms it can use. And we’ve actually much more than doubled the amount of raw data in it.
Things seem to be scaling better and better. The more we put into Wolfram|Alpha, the easier it becomes to add still more. We’ve honed both our automated and human processes, progressively building on what Wolfram|Alpha already does.
When we launched Wolfram|Alpha a year ago, about 2/3 of all queries generated a response. Now over 90% do.
So, what are some of the things we’ve learned over the past year? More »
CNN recently ran the story “Can We Compute an Answer to Every Question?” highlighting Stephen Wolfram’s TED2010 talk. The story also featured an excerpt from Stephen’s “The Story of the Making of Wolfram|Alpha” presentation from the 50 Years of Public Computing at the University of Illinois conference, which was streamed lived here on the blog. As we move closer to Wolfram|Alpha’s first birthday, we thought you might enjoy hear the story of the making of Wolfram|Alpha from its creator, Stephen Wolfram.
Near the end of his talk, Stephen mentions that he’ll be attending the evening reception via an Anybots telepresence robot. Here is a snapshot of Stephen greeting guests at the reception.
Hello, fellow readers of the Wolfram|Alpha Blog—my name’s Justin. In just a few short weeks, I’ll be graduating from the University of Illinois at Urbana-Champaign. Over the years I’ve found my own way of getting things done in regards to homework and studying routines. But this semester I realized there were tools available that would make studying and completing assignments easier and help me understand better. One tool that has become increasingly valuable in my routine and those of other students on my campus is Wolfram|Alpha. Recently, I was invited to share how Wolfram|Alpha is being used by students like myself.
Being a marketing major, I had to take some finance and accounting courses, but I was a bit rusty with the required formulas and the overall understanding of the cash flow concepts, such as future cash flows and the net present values of a future investment. A friend recommended I check out Wolfram|Alpha’s finance tools, and they’ve became indispensable in my group’s casework for the semester. Each proposed future investment we were met with, we would go directly to Wolfram|Alpha to compute the cash flows. We even went as far to show screenshots, such as the one below, of inputs and outputs in our final case presentation last week.
I’ve met other students on my campus who have found Wolfram|Alpha to be helpful in their courses. A few months ago while studying in the library, I walked by a table of freshman students all using Wolfram|Alpha on their laptops. I decided to stop and chat with them because I knew one of the girls. They explained how they were using Wolfram|Alpha to model functions and check portions of their math homework. All three girls are enrolled in Calculus III, and not exactly overjoyed about the fact of future— and most likely harder—math classes. More »
If you’re a regular reader of Boing Boing you might have seen this beautiful homemade Turing machine that tinkerer Mike Davey put together (it’s definitely worth watching the video). For those who don’t know, Turing machines are theoretical idealizations of computers. While not intended to be practical, they do allow mathematicians to construct rigorous proofs about what can be computed and what cannot. And now, you can experiment with them directly on Wolfram|Alpha!
To begin with, let’s ask Wolfram|Alpha to simulate the program that Mike Davey used in his video, a binary counter. Using Stephen Wolfram‘s notation, this one is 2-state 3-color machine number 1317953. It “counts” in binary, and marks each successive integer when the machine’s head returns to the initial position. We can more easily see how it computes the sequence 1,2,3,4,5… by only showing the steps when it returns to the center column.
Next we can try a Turing machine at random from the infinite “universe” of possible machines. Let’s say we find this particular Turing machine, and want to see how it behaves on different input tapes. We can try a tape filled with random colors, or a finite tape that wraps around, or a tape with an infinite pattern on it, or even a combination of the above. We can also try a random Turing machine that operates with many colors, such as “random 7-color Turing machine”. More »
As we all know by now, Wolfram|Alpha is a computational knowledge engine. That means not only should it be able to do computations on a wide variety of topics, but also that it needs detailed knowledge of the names and salient properties of a wide variety of entities that are commonly encountered in human inquiry and discourse.
This is obvious in the case of classes of objects that fit neatly into curated data collections, such as mathematical surfaces (e.g., Möbius strip), countries of the world (e.g., New Zealand), chemicals (e.g., caffeine), and so forth.
What is perhaps slightly less obvious is just how much knowledge needs to be encoded to have a reasonable “understanding” of almost any named result in math and the sciences. For example, most people (including non-mathematicians) have heard of Fermat’s last theorem and therefore would rightly expect Wolfram|Alpha to be able to say something sensible about it. And as one of my other hats involves writing the online encyclopedia of math known as MathWorld, which is hosted and sponsored by Wolfram Research, putting this information into Wolfram|Alpha naturally fell to me. So, for the past several months, I have been attempting to gradually build up Wolfram|Alpha’s knowledge base on named results in math and physics.
The screenshot below shows what Wolfram|Alpha now returns for Fermat’s last theorem:
As you can see, Wolfram|Alpha begins by giving you the standard name for the result in question, followed by a clearly worded (or at least as clearly worded as could be managed in the marginal space available 😉 ) plain English statement of the result. Next, at least in cases where it is possible to do so, a mathematically precise “formal statement” of the result is given. This is followed by any common alternate names the result might have, a listing of historical information, and finally an enumeration of prizes associated with it (where relevant). More »