By now, the intelligence of birds is well known. Alex the African gray parrot had great verbal skills. Scrub jays, which hide caches of seeds and other food, have remarkable memories. And New Caledonian crows make and use tools in ways that would put the average home plumber to shame.
Pigeons, it turns out, are no slouches either. It was known that they could count. But all sorts of animals, including bees, can count. Pigeons have now shown that they can learn abstract rules about numbers, an ability that until now had been demonstrated only in primates. In the 1990s scientists trained rhesus monkeys to look at groups of items on a screen and to rank them from the lowest number of items to the highest.
They learned to rank groups of one, two and three items in various sizes and shapes. When tested, they were able to do the task even when unfamiliar numbers of things were introduced. In other words, having learned that two was more than one and three more than two, they could also figure out that five was more than two, or eight more than six.
Damian Scarf, a postdoctoral fellow at the University of Otago, in New Zealand, tried the same experiment with pigeons, and he and two colleagues report in the current issue of the journal Science that the pigeons did just as well as the monkeys.
A 40-year-old puzzle of superstring theory solved by supercomputer
A group of three researchers from KEK, Shizuoka University and Osaka University has for the first time revealed the way our universe was born with 3 spatial dimensions from 10-dimensional superstring theory in which spacetime has 9 spatial directions and 1 temporal direction. This result was obtained by numerical simulation on a supercomputer.
“According to Big Bang cosmology, the universe originated in an explosion from an invisibly tiny point. This theory is strongly supported by observation of the cosmic microwave background and the relative abundance of elements. However, a situation in which the whole universe is a tiny point exceeds the reach of Einstein’s general theory of relativity, and for that reason it has not been possible to clarify how the universe actually originated.
In superstring theory, which is considered to be the “theory of everything”, all the elementary particles are represented as various oscillation modes of very tiny strings. Among those oscillation modes, there is one that corresponds to a particle that mediates gravity, and thus the general theory of relativity can be naturally extended to the scale of elementary particles. Therefore, it is expected that superstring theory allows the investigation of the birth of the universe. However, actual calculation has been intractable because the interaction between strings is strong, so all investigation thus far has been restricted to discussing various models or scenarios.
Superstring theory predicts a space with 9 dimensions, which poses the big puzzle of how this can be consistent with the 3-dimensional space that we live in.
A group of 3 researchers, Jun Nishimura (associate professor at KEK), Asato Tsuchiya (associate professor at Shizuoka University) and Sang-Woo Kim (project researcher at Osaka University) has succeeded in simulating the birth of the universe, using a supercomputer for calculations based on superstring theory. This showed that the universe had 9 spatial dimensions at the beginning, but only 3 of these underwent expansion at some point in time…”
Displayed are equal-loudness curves. Depending how familiar you are with isoclines, they might mean the opposite of what they look like to you. Where the curve dips down, that means that instruments playing that pitch sound louder for their deciBel level.
It’s crazy how non-monotonic these curves are. It’s like there is a general pattern that higher-pitched instruments sound louder per deciBel, but there are many pitch ranges where the pattern reverses. Strange, right?
For reference, here are some of the pitches in that 12k-20k range where some of the curviness happens.
Reminds me of the Lab colour scale — a nonlinear scale which is attuned to how we humans perceive colour, which differs from the linear scales (RGB, CMYK) along which colour “actually exists”.
This was an eye opener for me and my students. I was trying to explain in a concret manner how to add fractions with unlike denominators. I drew a rectangle on my Smartboard and cloned it so I had two rectangles exactly the same. I divided one rectangle into fifths and one in half to represent the fractions. Then with the magic of technology, I added the rectangles together by sliding one on top of the other one. This shows the common denominator in the smaller rectangles inside the whole. Then we X’d out the 2/5 in blue and the 1/2 in green so the students could see the fractions. Then I explained that each X had to have its own space in the whole, so we had to move the ones that were doubled up into their own space. This is easily done on the Smartboard and the students can actually see how this works. Then we show how many spaces have X’s in them and how many are empty. They can find the denominator and add the fractions. Many of the students in my class had some aha moments with this method. My next huge task is to translate this learning into application. Wish me luck!
Who says you can’t hoard anything in this now technological world? Here’s something for the science history buffs:
The largest collection of Isaac Newton’s papers has gone digital, committing to open-access posterity the works of one of history’s greatest scientist.
Among the works shared online by the Cambridge Digital Library are Newton’s own annotated copy of Principia Mathematica and the ‘Waste Book,’ the notebook in which a young Newton worked out the principles of calculus.
Other of his myriad accomplishments include the laws of gravity and motion, a theory of light — pictured above are notes on optics — and his construction of the first reflecting telescope.
Newton was also notoriously idiosyncratic and irascible, obsessed with the occult and vicious towards scientific rivals; a full account of his life and science can be found in James Gleick’s Isaac Newton, and a partial but entertaining fictionalization in Neal Stephenson’s Baroque Cycle. But the papers come straight from the master.
“Anyone, wherever they are, can see at the click of a mouse how Newton worked and how he went about developing his theories and experiments,” said Grant Young, the library’s digitization manager, in a press release. “Before today, anyone who wanted to see these things had to come to Cambridge. Now we’re bringing Cambridge University Library to the world.”
Approximately 4,000 pages of material are available now, and thousands more will be uploaded in coming months.
Himpunan adalah kumpulan objek-objek / benda-benda yang mempunyai sifat tertentu dan didefinisikan dengan jelas
Contoh:
Himpunan Mahasiswa statistika Undip
Himpunan Bilangan Bulat
Notasi himpunan
Himpunan biasa dinotasikan dengan huruf besar, misal : A, S atau B
Elemen/anggota himpunan biasa dinotasikan dengan huruf kecil, misal : a, b, c.
x A dibaca x anggota A dan
x A dibaca x bukan anggota A
Enumerasi : mendaftar semua anggota himpunan
Contoh :
B adalah bilangan Asli yang lebih dari 3 dan kurang atau sama dengan 15
B = { 4,5,6,7,8,9,10,11,12,13,14,15 }
Pembangun himpunan : menuliskan sifat-sifat yg harus dipenuhi oleh setiap elemen/anggota himpunan tersebut.
Contoh :
B adalah bilangan Asli yang lebih dari 3 dan kurang atau sama dengan 15
B = { x | 3
My name is Rezzy Eko Caraka,Die freundlichen Mann mit Brille. Ich bin immer bereit und immer positiv denken, egal was passiert. I'm 17th years old,called me Rezzy.
That's all enough about me,hope you'll enjoy to see my tumblr. Rezzy Eko Caraka Statistika Undip 2011
Theme based on and images from Pottermore.com by J.K. Rowling
![intothecontinuum:
Mathematica code:
Animate[ Graphics[ Table[ Circle[{0, i}, t + (16 - n) (1 + Sign[16 - n])/2], {n, 0, 100, 1}, {i, -5, 5,1}], PlotRange -> 6],{t, 0, 1, .01}]](http://25.media.tumblr.com/tumblr_lv8vd6fzsJ1qfjvexo1_500.gif)
