Mathematics
Alex, The Brainy Parrot Who Knows About Zero
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Alex is a 28-year-old grey parrot who lives in a lab at Brandeis University in Waltham, Mass., and can count, identify objects, shapes, colors and materials. And now, Alex has grasped the concept of zero, according to World Science. In fact, Alex can describe the absence of a numerical quantity on a tray containing colored cubes. When a color is missing, Alex consistently identified this “zero quantity” by saying “none.” You might think that this is just a parrot trick, but this research about ‘bird intelligence’ might also help autistic and other learning-disabled children “who have trouble learning language and counting skills.” Read more…
One of the really interesting things about Alex is that it had learned in the past that “none” meant a lack of information. And without any training, when Alex was asked to say how many green or red cubes were on a tray in front of him, he spontaneously said “none” when there was no cubes with this color. In fact, he was able to connect two different concepts, a lack of information and the absence of a quantity. Pretty brilliant parrot, isn’t?
Before going further, below is a picture of Alex in front of his counting blocks (Credit: Brandeis University). And here is a link to a larger version (193 KB).
Now, let’s look at how the researchers made the discovery that Alex possessed a “zero-like concept.”
The story began when researchers started testing Alex to see whether he understood small numbers, between one and six. Zero wasn’t expected of him. The researchers would lay out an array of objects of different colors and sizes, and asked questions such as “what color four?” — meaning which color are the objects of which there are four.
Apparently, Alex was pretty good on these tests, until he got bored. So the researchers “found some more interesting toys to give as rewards.” And here came the decisive experiment.
One of these apparent lapses occurred one day when an experimenter asked Alex “what color three?” Laid out before Alex were sets of two, three and six objects, each set differently colored. Alex insisted on responding: “five.” This made no sense given that the answer was supposed to be a color.
After several tries the experimenter gave up and said: “OK, Alex, tell me: what color five?” “None,” the bird replied. This was correct, in that there was no color that graced exactly five of the objects. The researchers went on to incorporate “none” into future trials, and Alex consistently used the word correctly, they said.
A few days after this article was published, Brandeis University decided to issue a press release adding that Alex was the “first bird to comprehend numerical concept akin to zero.”
“It is doubtful that Alex’s achievement, or those of some other animals such as chimps, can be completely trained; rather, it seems likely that these skills are based on simpler cognitive abilities they need for survival, such as recognition of more versus less,” explained comparative psychologist and cognitive scientist Dr. Irene Pepperberg.
Dr. Pepperberg’s research, which uses a training method called the model-rival technique, also holds promise for teaching autistic and other learning-disabled children who have difficulty learning language, numerical concepts and even empathy.
So far, results using this learning technique with small groups of autistic children have been very promising.
The latest research work about Alex and his comprehension of zero has been published by the Journal of Comparative Psychology in its May 2005 issue (Volume 119, Issue 2) under the name “Number Comprehension by a Grey Parrot (Psittacus erithacus), Including a Zero-Like Concept.” You’ll get to the abstract from this page (scroll to number #8).
A Grey parrot (Psittacus erithacus) that was able to quantify 6 item sets (including subsets of heterogeneous groups, e.g., blue blocks within groupings of blue and green blocks and balls) using English labels was tested on comprehension of these labels, which is crucial for numerical competence . He was, without training, asked “What color/object [number]?” for collections of various simultaneously presented quantities (e.g., subsets of 4, 5, and 6 blocks of 3 different colors; subsets of 2, 4, and 6 keys, corks, and sticks). Accuracy was greater than 80% and was unaffected by array quantity, mass, or contour. His results demonstrated numerical comprehension competence comparable to that of chimpanzees and very young children. He also demonstrated knowledge of absence of quantity, using “none” to designate zero.
For more information, you can buy this article for $11.95.
Finally, if you still want to know more about Irene Pepperberg’s work with gray parrots, you can visit the Alex Foundation, where you’ll find that someday, Alex may be able to read. Amazing…
Sources: World Science, July 2, 2005; and various web sites
Related stories can be found in the following categories.
- Education
- Mathematics
- Nature
- Psychology
- Science
Eastern Ink Painting on a Computer
Traditional Oriental ink painting is more easily done with real brushes than with a computer program because you need to model how the ink is flowing into an absorbent surface such as paper. In this brief article, Technology Research News writes that “researchers from the Hong Kong University of Science and Technology have developed a brush-and-ink-style paint program, dubbed MoXi, that uses a model of pigment particles in water flowing into paper.” These virtual Chinese brushes simulate in real time the ink dispersion and could be available on your PC within two years. Read more…
Here is some general information about MoXi provided by Technology Research News.
The software models the gritty details of paper absorbing water and pigment moving through water, including the way pigment concentrates at ink boundaries as water evaporates from drying ink. The technique promises to make computer paint programs with more realistic and could also be used in computer animation packages, according to the researchers.
The simulation is based on mathematics — the lattice Boltzmann equation — that physicists use to model the complex behaviors of fluids. The model simulates more complex effects than previous work, and is also fast enough to deliver ink dispersion simulations in real-time on a reasonably large canvas, according to the researchers.
Below are two images generated with MoXi, the first one being called “Lotus leaves” and the second one “Planet” (Credit: Hong Kong University of Science & Technology)
Here are two links to larger versions of these images, the “Lotus leaves” (1.30 MB) and the “Planet” (1.47 MB).
The researchers behind the MoXi project are Chiew-Lan Tai, Associate Professor at the Department of Computer Science, and Nelson Siu-Hang Chu, her Research Assistant.
For more information about their projects, you can read these two pages about the Virtual Chinese Brush and about MoXi. On this page, you’ll have access to several videos and images. The two pictures above come from this page.
The MoXi project will be presented at SIGGRAPH 2005 under the name “MoXi: Real-Time Ink Dispersion in Absorbent Paper.” Here is a link to the paper submitted by the researchers (PDF format, 1 page, 145 KB). Here are an excerpt from the introduction.
Our paint system, MoXi, allows users to paint in the spontaneous style of Eastern ink painting, on a computer. The simulations of both brush and ink are essential for a successful extension of this traditional art into the digital domain. For real-time performance, we have implemented our ink flow model entirely on the GPU, leaving the CPU for the brush simulation.
According to the researchers, this technique “could be used practically in one or two years.” But is this possible that this technology can be sold under the name MoXi? There already is a Digeo service named Moxi which offers High Definition TV (HDTV). And Digeo claims in its press releases (check this one for example) that Moxi is one of its registered trademarks.
However, it’s not so clear. I visited the United States Patent and Trademark Office (USPTO) to know more. And for more information about this trademark, you can either click on the “Status” button in the Trademarks section, and enter the serial number 76279215 on the next screen, or go directly here. Here is the status of this trademark application as of April 25, 2005.
A non-final action has been mailed. This is a letter from the examining attorney requesting additional information and/or making an initial refusal. However, no final determination as to the registrability of the mark has been made.
If I correctly understand English, this means that Moxi IS NOT a registered trademark. But at the same time, Digeo writes it is registered. Who is right?
If one of the readers of this note is familiar with the USPTO procedures, please post an explanation below. Thanks.
Sources: Technology Research News, June 29/July 6, 2005; and various web sites
Related stories can be found in the following categories.
- Computers
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A Master Equation for All Life Processes?
In “Life on the Scales,” Science News recently wrote that some simple mathematical equations, known as quarter-power scaling laws, can explain the metabolic rates of living organisms. For example, “an animal’s metabolic rate appears to be proportional to mass to the 3/4 power.” And this “3/4-power law appears to hold sway from microbes to whales, creatures of sizes ranging over a mind-boggling 21 orders of magnitude.” The ecologists, physicists and chemists behind this research are now successfully applying this equation to plants, fish, full ecosystems and even biology and genetics, by adding a new key parameter: temperature. Please read this fascinating article for many more details and references. But save some time to read another long article, “Ecology’s Big, Hot Idea,” published by PLoS Biology, which states that “the way life uses energy is a unifying principle for ecology in the same way that genetics underpins evolutionary biology.” Read more…
The Science News article starts with a simple observation. Although a mouse has a shorter life than an elephant, both clock approximately the same number of heartbeats during their lives. Simply, their metabolisms are different. Now, let’s go back several decades ago.
Scientists have long known that most biological rates appear to bear a simple mathematical relationship to an animal’s size: They are proportional to the animal’s mass raised to a power that is a multiple of 1/4. These relationships are known as quarter-power scaling laws. For instance, an animal’s metabolic rate appears to be proportional to mass to the 3/4 power, and its heart rate is proportional to mass to the –1/4 power.
In subsequent decades, biologists have found that the 3/4-power law appears to hold sway from microbes to whales, creatures of sizes ranging over a mind-boggling 21 orders of magnitude.
But nobody had an explanation for this scaling law – until 1997.
The beginnings of an explanation came in 1997, when ecologist James Brown of the University of New Mexico in Albuquerque, physicist Geoffrey West of Los Alamos (N.M.) National Laboratory, and Brian Enquist, an ecologist at the University of Arizona in Tucson, described metabolic scaling in mammals and birds in terms of the geometry of their circulatory systems. It turns out, West says, that Rubner was on the right track in comparing surface area with volume, but that an animal’s metabolic rate is determined not by how efficiently it dissipates heat through its skin but by how efficiently it delivers fuel to its cells.
The idea, West says, is that a space-filling surface scales as if it were a volume, not an area. If you double each of the dimensions of your laundry machine, he observes, then the amount of linens you can fit into it scales up by 23, not 22. Thus, an animal’s effective surface area scales as if it were a three-dimensional, not a two-dimensional, structure.
This law also can be applied to plants, fish, or even cancer growth rates — providing you add a new parameter: temperature.
In 2001, after James Gillooly, a specialist in body temperature, joined Brown at the University of New Mexico, the researchers and their collaborators presented their master equation, which incorporates the effects of size and temperature. An organism’s metabolism, they proposed, is proportional to its mass to the 3/4 power times a function in which body temperature appears in the exponent.
When the researchers filter out the effects of body temperature, most species adhere closely to quarter-power laws for a wide range of properties, including not only life span but also population growth rates. The team is now applying its master equation to more life processes — such as cancer growth rates and the amount of time animals sleep.
Now, it’s time for two key quotes [which don't appear in bold characters in the original article.]
“We’ve found that despite the incredible diversity of life, from a tomato plant to an amoeba to a salmon, once you correct for size and temperature, many of these rates and times are remarkably similar,” says Gillooly.
“Metabolic rate is, in our view, the fundamental biological rate,” Gillooly says. There is a universal biological clock, he says, “but it ticks in units of energy, not units of time.”
Then the researchers applied their master equation to ecosystems such as forests, and even to evolutionary biology, trying to answer this question: “Why do the fossil record and genetic data often give different estimates of when certain species diverged?”
When the researchers use their master equation to correct for the effects of size and temperature, the genetic estimates of divergence times — including those of rats and mice — line up well with the fossil record, says Allen, one of the paper’s coauthors.
As I wrote in the introduction, don’t miss this other paper by John Whitfield in PLoS Biology on a similar subject, “Ecology’s Big, Hot Idea.” Here are the two first paragraphs.
Life is complicated. It comes in all sorts of shapes, sizes, places, and combinations, and has evolved a dizzying variety of solutions to the problem of carrying on living. Yet look inside a cell and life takes on, if not simplicity, then at least a certain uniformity — a genetic system based around nucleic acids, for example, and a common set of chemical reactions for turning food into fuel. And looked at in broad swathes, life shows striking generalities and patterns. Every mammal’s heart will beat about one billion times in its lifetime. Both within and between species, the density of a population declines in a regular way as the size of individuals increases. And the number of species in all environments declines as you move from the equator towards the poles.
Wouldn’t it be good if there were a simple theory that used life’s shared fundamentals to explain its large-scale regularities, via its diversity of individuals? In the past few years, a team of ecologists and physicists have come up with just such a theory. At its heart is metabolism: the way life uses energy is, they claim, a unifying principle for ecology in the same way that genetics underpins evolutionary biology. They believe that energy use, in the form of metabolic rate, can be understood from the first principles of physics, and that metabolic rate can explain growth, development, population dynamics, molecular evolution, the flux of chemicals through the environment, and patterns of species diversity — to name a few.
If you don’t have enough time today, print the two articles I mentioned and read them next weekend. I promise you will not waste your time.
Sources: Erica Klarreich, Science News, Vol. 167, No. 7, p. 106, February 12, 2005; John Whitfield, PLoS Biology, Vol. 2, Issue 12, December 14, 2004
Related stories can be found in the following categories.
- Biotechnology
- Environment
- Genetics
- Mathematics
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