I always found it difficult to think abstract. It was not until physics class at college, that I started to understand physics formulas, because our professor gave practical examples from real life, i.e. he made me understand why the sky was blue. Mathematics was all right as long as we stayed in two dimensions, but stereometry was already one dimension too much. Molecules, chemical bonds and atomic structure were also vague especially when wave-particle duality came into play. It was even hard to imagine what DNA really looks like. At one stage I even tried to make a DNA structure at home from matches and colored clay. But the model was so fragile, that it crashed before the first minor groove was finished.
Nowadays, students are so lucky: a computer, the internet, beautiful graphs, videos, 3D-animations.
Below a mixture of recent and some old animations and 3D representations, that highlight our understanding of numbers and dimensions, the infinite small and the infinite large.
First 3D image of an individual molecule and its bonds!
A real breakthrough was the visualization of the atomic backbone of an individual molecule (pentacene) and its atomic bonds. As reported in the August 28 issue of Science magazine, IBM Research Zurich scientists (in collaboration with Peter Liljeroth of Utrecht University), accomplished this by using an atomic force microsope (ATM) operated in an ultrahigh vacuum and at very low temperatures ( 268oC or 451oF). According to the researchers this is reminiscent of X-rays that pass through soft tissue to enable clear images of bones.
Below you see:
- the chemical structure of pentacene with 22 carbon atoms (Wikipedia).
- the force map image of pentacene (IBM).
- a video-interview with the researchers explaining their research (IBM-Labs).
Hattip: @jensmccabe (twitter) and Greg Laden (twitter and blog)
More info: www.physorg.com and gizmodo.com
The Galaxy mapped
Now quite the opposite infinity: the universe: “what 100,000 nearby large (i.e., Milky Way sized and larger) galaxies, look like reduced each reduced to a point” (translation by @dreamingspires) or “will give you an idea how totally insignificant we are” (@scanman). These tweople referred to Etann Siegel’s blog “It starts with a bang”.
One of the original researchers (Dominique Proust) has also posted a short description of the study and an image on the internet which shows the clustering pattern of about 100,000 nearby galaxies, revealed by the 6dF Galaxy Survey (see here) : “Each galaxy is shown as a dot. The galaxy we live in is at the centre of the pattern” (an enlargement of the image is here).
The astronomers came from all over the world (Australia, the UK, USA, South Africa, France and Japan). Their survey “will reveal not only where the galaxies are but also where they’re heading, how fast, and why. “It’s like taking a snapshot of wildebeest on the African plain. We can tell which waterholes they’re heading to, and how fast they’re travelling,” said D. Heath Jones of the Anglo-Australian Observatory (AAO), lead scientist for the Six-Degree Field Galaxy Survey (6dFGS)”
1, 2, 3 ….no here are 10 dimensions explained
but the 4th dimensions will do for me
Powers of 10
A classical video: the powers of ten. It dates from 1977. I have seen it during college and it made a lasting impression.
Powers of Ten explores the relative size of things from the microscopic to the cosmic. The 1977 film travels from an aerial view of a man in a Chicago park to the outer limits of the universe directly above him and back down into the microscopic world contained in the man’s hand.
There is even a website “powers of ten”. At the right you can click on a power of ten. Like 10 ¹³ and 10 -¹³
Measuring in meters, this power of ten is equal to 10 billion kilometers. We see the outer planets as they circulate counterclockwise, all in nearly the same plane.
Measuring in seconds, this power of ten equals
- Space 10 billion kilometers
- 317, 097 years.
- Unmanned Space Probes
- Johannes Keppler
- Space First Images Of Jupiter through Time
Measuring in meters, this power of ten is equal to .1 picometer or 100 fermis. We see the kernel of a carbon atom, bound by six neutrons and six protons. This nucleus is dubbed carbon-12.
Measuring in seconds, this power of ten equals 100 femtoseconds.
- 100 fermis
- 100 femtoseconds
- Niels Bohr
Also the Wikipedia explains large numbers and astronomically large numbers. The Dutch Wikipedia gives more examples from daily life:
Do you still need some help in mathematics? Here is a tip from a Dutch educator @trendmatcher: your free online 24/7 math help, meant to help high school students with their homework. (There is also non-free material)
Modern steps through time (via @scanman and @drves) : kalman.blogs.nytimes.com
And a Twitter visualization tool that shows about 11,000 “good morning” tweets over a 24 hour period, between August 20th and 21st. All tweets are color-coded: green blocks are early tweets, orange ones are around 9am, and red tweets are later in the morning. Black blocks are ‘out of time’ tweets which said “good morning” (or a non-english equivalent) at a strange time in the day. Seen at the blog of @zbdigitaal (Edwin)
The original post and the video can be found here
Leo Gross, Fabian Mohn, Nikolaj Moll, Peter Liljeroth, and Gerhard Meyer. “The Chemical Structure of a Molecule Resolved by Atomic Force Microscopy.” Science, 28 August 2009: Vol. 325. no. 5944, pp. 1110 – 1114. DOI: 10.1126/science.1176210
The 6dF Galaxy Survey: Final Data Release (DR3) and Southern Large Scale Structures
Jones D Heath., Read Mike A., Saunders Will., Colless Matthew., Jarrett Tom., Parker Quentin., Fairall Anthony., Mauch Thomas., Sadler Elaine., Watson Fred., Burton Donna., Campbell Lachlan., Cass Paul., Croom Scott., Dawe John., Fiegert Kristin., Frankcombe Leela., Hartley Malcolm., Huchra John., James Dionne., Kirby Emma., Lahav Ofer., Lucey John., Mamon Gary., Moore Lesa., Peterson Bruce., Prior Sayuri., Proust Dominique., Russell Ken., Safouris Vicky., Wakamatsu Ken-ichi., Westra Eduard., Williams Mary: 2009,
submitted to Monthly Notices of the Royal Astronomical Society