Archive for the 'cog' Category

Wikipedia: “squeaky clean”?

At a conference in Brazil (ISMB) this summer, an acquaintance complained how after noticing that a number of her students had the same error in their homework she tracked it down to Wikipedia. Having found the source of their confusion, she felt it incumbent upon herself to go in and edit the mistake in the Wikipedia entry. As a user of Wikipedia, I never cease to be amazed what a vast trove of information it is, vivid testimonial to our collaborative social insect behavior with over 5 million articles to date.
Wikipedia’s article count has shown rapid growth.
300px-wikipedia_growth.pngThis week, The Chronicle of Higher Education reported an assistant professor, Alexander Halavais, deliberately posted a number of errors in Wikipedia in order to see how long it would take for them to be noticed, hypothesizing they would “languish online for some time”. Remarkably, the erroneous posts were corrected within 3 hours of being posted.

I mentioned this story at dinner, and my brother protested that the entry about him in Wikipedia (!) is INCORRECT, and would I change it? They have his date of birth wrong, and made him a year older. I just tried, and I CAN’T edit the part of the entry which has the misinformation!

Post Script: I checked the entry last night (since I was at my brother’s) and low and behold– the top part got corrected! I wasn’t sure if this was because even though I was unsuccessful at editing it myself I sent some sort of message into the — or if it was a synchronous correction. However my brother noticed that the entry at the bottom was still wrong, at which point I was sufficiently enabled I was able to make the correction myself…

The big idea that won’t die

Being under attack is some kind of coming of age for string theory, according to a former skeptic turned convert in an article in the The Ottawa Citizen. Jim Cline, a string cosmologist, considers string theory to be the most likely framework to explain the world at a deeper level. String theory is based on the idea that the smallest known particles, such as electrons, are not really pointlike, but rather extended bits of “string.”In fact, present-day experiments can’t distinguish them from points. This is awkward for physicists, who judge the validity of a theory by experiment, since at the moment there is no direct evidence to say string theory is correct.

Peter Voit's Book on String Theory

Such criticisms have been brought to the public eye recently in the book Not Even Wrong by mathematician Peter Woit. According to Woit, among the bogus claims are that string theory predicts:

-supersymmetry and extra dimensions and that the LHC will test these predictions
-observable effects in the CMB (Cosmic Microwave Background) and gravitational waves

And finally that:

-string theory makes predictions testable at RHIC
-the anthropic landscape predicts the value of the cosmological constant and will make other predictions

An Immortal bites dust

Just found out Penny Smith withdrew her Immortal Smooth Solution!

Mathematicians and physicists think the breeze and turbulence can be understood via the Navier-Stokes equations governingthe flow of fluids such as water and air. Although first written in the 19th Century, we still don’t get ’em. There is no proof for the most basic questions one can ask: do solutions exist, and are they unique?
simulation

Penny Smith, a mathematician at Lehigh University, posted a paper on the arXiv that purported to solve one of the Clay Foundation Millenium problems, famous problems with a million dollar reward posted by the Clay Institute.

A few months ago, the Poincare conjecture, another one of the Clay problems appeared to have been solved by a reclusive Russian mathematician named Grigori Perelman, who refused the prize money. Now, it seems Penny Smith has withdrawn her solution.

Millennium Problems

To celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) named seven Prize Problems, with $1 million allocated to each:

Birch and Swinnerton-Dyer Conjecture
Hodge Conjecture
Navier-Stokes Equations
P vs NP
Poincaré Conjecture
Riemann Hypothesis
Yang-Mills Theory
Yang

Navier-Stokes

The Navier-Stokes equations are differential equations in four variables: pressure (p) and the three components of velocity. They describe the flow of water, air and other fluids.

Navier-Stokes Eqs

The first 3 equations, shown above, describe the time derivative of the velocity. In this notation, there is an implicit sum (Einstein convention) over indices that appear twice. The fourth equation says that the divergence of the spacial flow of the velocity is zero. This messes things up, because although the first 3 equations are local, meaning one can compute a solution at each grid point without needing to know the solution everywhere else, the fourth is not.

Computational Complexity

The theory of NP-completeness has its roots in computability theory, which originated in the work of Turing, Church, Godel, and others in the 1930’s.

turing.jpg

The class P is the class of decision problems solvable by some algorithm within a number of steps bounded by some fixed polynomial. NP stands for “nondeterministic polynomial time”, where NP is defined in terms of nondeterministic machines, machines that have more than one possible move from a given configuration.

The P versus NP problem is to determine whether every language accepted by some nondeterministic algorithm in polynomial time is also accepted by some (deterministic) algorithm in polynomial time.

Poincaré Conjecture

The Poincaré conjecture concerns a space that locally looks like ordinary three dimensional space but is finite and lacks any boundary (a closed 3-manifold). The claim is that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is really just a three-dimensional sphere. The analogous result has been known to be true in higher dimensions for some time.


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