Doc Madhattan: 2015

One hundred years

Creativity is the residue of time wasted

This interesting quotation by Albert Einstein linked him with Henri Poincaré not only with the contribution of French math to special relativity, but also for the utility of the creative leisure. Indeed Poincaré told that, after some fruitless attempts to sole a particularly difficult mathematical problem, he decided to go away for a geological excursion, in this way stimulating conditions to resolve the problem!
But the most important reason in order to write something about Einstein is the general relativity birthday, that was presented by Einstein on the 25th november 1915 at the Prussian Accademy of Sciences.

A brief history of neutrinos' oscillations

I just write a more detailed post about the model behind neutrino's oscillations. Here I would simply recall that the idea was proposed by Bruno Pontecorvo in 1957 and developed by Ziro Maki, Masami Nakagawa e Shoichi Sakata in 1962. Today I try to summarize the experimental way.

via nobelprize.org

Some geometrical aspects of 3- and 4-spaces

A couple of abstracts about the geomtery of space:

Historically, there have been many attempts to produce the appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's quaternions, Gibbs' vector system using the dot and cross products. We illustrate however, that Clifford's geometric algebra (GA) provides the most elegant description of physical space. Supporting this conclusion, we firstly show how geometric algebra subsumes the key elements of the competing formalisms and secondly we show how it provides an intuitive representation and manipulation of the basic concepts of points, lines, areas and volumes. We also provide two examples where GA has been found to provide an improved description of two key physical phenomena, electromagnetism and quantum theory, without using tensors or complex vector spaces. This paper also provides pedagogical tutorial-style coverage of the various basic applications of geometric algebra in physics.

James M. Chappell, Azhar Iqbal & Derek Abbott (2011). Geometric Algebra: A natural representation of three-space, arXiv: 1101.3619v3

We indicate that Heron's formula (which relates the square of the area of a triangle to a quartic function of its edge lengths) can be interpreted as a scissors congruence in 4-dimensional space. In the process of demonstrating this, we examine a number of decompositions of hypercubes, hyper-parallelograms, and other elementary 4-dimensional solids.

J. Scott Carter & David A. Mullens (2015). Some Elementary Aspects of 4-dimensional Geometry, arXiv: 1504.01727v1

There's also a minimalistic introduction to euclidean planes.

Water on Mars

"Our quest on Mars has been to 'follow the water', in our search for life in the universe, and now we have convincing science that validates what we've long suspected. This is a significant development, as it appears to confirm that water -- albeit briny -- is flowing today on the surface of Mars."

John Grunsfeld from the press release. The abstract of the paper follows:

Determining whether liquid water exists on the Martian surface is central to understanding the hydrologic cycle and potential for extant life on Mars. Recurring slope lineae, narrow streaks of low reflectance compared to the surrounding terrain, appear and grow incrementally in the downslope direction during warm seasons when temperatures reach about 250–300 K, a pattern consistent with the transient flow of a volatile species. Brine flows (or seeps) have been proposed to explain the formation of recurring slope lineae, yet no direct evidence for either liquid water or hydrated salts has been found4. Here we analyse spectral data from the Compact Reconnaissance Imaging Spectrometer for Mars instrument onboard the Mars Reconnaissance Orbiter from four different locations where recurring slope lineae are present. We find evidence for hydrated salts at all four locations in the seasons when recurring slope lineae are most extensive, which suggests that the source of hydration is recurring slope lineae activity. The hydrated salts most consistent with the spectral absorption features we detect are magnesium perchlorate, magnesium chlorate and sodium perchlorate. Our findings strongly support the hypothesis that recurring slope lineae form as a result of contemporary water activity on Mars.

Ojha, L., Wilhelm, M., Murchie, S., McEwen, A., Wray, J., Hanley, J., Massé, M., & Chojnacki, M. (2015). Spectral evidence for hydrated salts in recurring slope lineae on Mars Nature Geoscience DOI: 10.1038/ngeo2546

Freedom and truth in mathematics

The way we deal with today's numbers in schools is essentially the same manner used by our ancestors Pythagoreans, who saw the numbers as concrete objects, of course, but in a way that prevented them from conceiving the infinity. The only ancient mathematician who approached the infinity was Archimedes, but in the history of mathematics can be considered a fairly unique case of lack of development mainly due to the isolation of the mathematicians at that time and of noticeable difference in quality between the Sicilian and colleagues. In order to return to touch the wall of infinity and use them in a profitable way the Earth had to wait the arrival of Georg Cantor.
The German mathematician actually faced numbers, revolutionizing mathematics, using essentially sets and logic, two tools that enabled him not only to approach, but even manipulate the infinite thanks to the transfinite numbers. Leading his steps was probably the following conviction:

The very essence of mathematics is its freedom.

According to Daniel Bonevac, this veritable mantra, written in 1883, is emblematic of the Cantor's libertarian approach to mathematics. With this milestone, Bonevac try to write a theory of mathematical truth, in order to explain some facts more or less established:

1) that the mathematical statements are either necessarily true or necessarily false;
2) that mathematical truth is derived primarily from logical truth;
3) that the existence in mathematics involves a kind of modality, which requires only the consistency or the constructability.

Hyperbolic Pascal triangles and other stories

A new set of mathematical abstracs. We start with the hyperbolic Pascal trianlges:

Fibonacci and Pell sequences in the hyperbolic Pascal triangle

In this paper, we introduce a new generalization of Pascal's triangle. The new object is called the hyperbolic Pascal triangle since the mathematical background goes back to regular mosaics on the hyperbolic plane. We describe precisely the procedure of how to obtain a given type of hyperbolic Pascal triangle from a mosaic. Then we study certain quantitative properties such as the number, the sum, and the alternating sum of the elements of a row. Moreover, the pattern of the rows, and the appearence of some binary recurrences in a fixed hyperbolic triangle are investigated.

Hacene Belbachir, László Németh & László Szalay (2015). Hyperbolic Pascal triangles, arXiv: 1503.02569v1

Alexander Gerst's timelapse

Watch Earth roll by through the perspective of ESA astronaut Alexander Gerst in this six-minute timelapse video from space. Combining 12 500 images taken by Alexander during his six-month Blue Dot mission on the International Space Station this Ultra High Definition video shows the best our beautiful planet has to offer.
Marvel at the auroras, sunrises, clouds, stars, oceans, the Milky Way, the International Space Station, lightning, cities at night, spacecraft and the thin band of atmosphere that protects us from space.
Often while conducting scientific experiments or docking spacecraft Alexander would set cameras to automatically take pictures at regular intervals. Combining these images gives the timelapse effect seen in this video.
Watch the video in 4K resolution for the best effect and find out more about Alexander Gerst's Blue Dot mission.

Hints of physics behind standard model?

The LHCb collaboration is studying the decay of mesons $B$ in order to find some violations in standard model rules. In particular LHCb has measured a particular ratio, named $R (D^*)$, between two decay modes of $\overline{B}^0$ and they find a violation from the standard model prediction that is compatible with other similar measures:

In the SM all charged leptons, such as taus ($\tau$) or muons ($\mu$), interact in an identical fashion (or, in physicists' language, have the same "couplings"). This property is called "lepton universality". However, differences in mass between the leptons must be accounted for, and affect decays involving these particles. The $\tau$ lepton is much heavier than the $\mu$ lepton and therefore the SM prediction for the ratio $R(D^*)$ is substantially smaller than 1. This ratio is considered to be precisely calculable thanks to the cancellation of uncertainties associated with the $B$ to $D^*$ meson transition.

from press release | read also LHC signal hints at cracks in physics' standard model

But there is another hint of new physics. At the end of July Nature Physics published a new paper from the LHCb collaboration about the possible existence of a new particle:

The LHCb collaboration published in Nature Physics a paper based on run 1 data which reports the determination of the parameter $|V_{ub}|$ describing the transition of a $b$ quark to a $u$ quark. This measurement was made by studying a particular decay of the $\Lambda_b^0$ baryon. Other measurements of $|V_{ub}|$ by previous experiments had returned two sets of inconsistent results, depending on which method was used to determine the parameter. Theorists had suggested that this discrepancy could be explained by the presence a new particle contributing to the decay process, which affected the result differently, depending on the measurement method. Today's result from LHCb removes the need for this new particle, while the puzzle of why the original sets of measurements do not agree persists.

from press release | read also: From generation to generation

where $|V_{ub}|$ is connected to the Cabibbo-Kobayashi-Maskawa matrix.

Learning abstracts: from mathematics, to the neural trasnformation machines

A coulpe of abstracts about e-learning:

This paper presents a new framework for adding semantics into e-learning system. The proposed approach relies on two principles. The first principle is the automatic addition of semantic information when creating the mathematical contents. The second principle is the collaborative tagging and annotation of the e-learning contents and the use of an ontology to categorize the e-learning contents. The proposed system encodes the mathematical contents using presentation MathML with RDFa annotations. The system allows students to highlight and annotate specific parts of the e-learning contents. The objective is to add meaning into the e-learning contents, to add relationships between contents, and to create a framework to facilitate searching the contents. This semantic information can be used to answer semantic queries (e.g., SPARQL) to retrieve information request of a user. This work is implemented as an embedded code into Moodle e-learning system.

Iyad Abu Doush, Faisal Alkhateeb, Eslam Al Maghayreh, Izzat Alsmadi & Samer Samarah (2012). Annotations, Collaborative Tagging, and Searching Mathematics in E-Learning, arXiv: 1211.1780v1

As far as Learning Management System is concerned, it offers an integrated platform for educational materials, distribution and management of learning as well as accessibility by a range of users including teachers, learners and content makers especially for distance learning. Usability evaluation is considered as one approach to assess the efficiency of e-Learning systems. It is used to evaluate how well technology and tools are working for users. There are some factors contributing as major reason why LMS is not used effectively and regularly. Learning Management Systems, as major part of e-Learning systems, can benefit from usability research to evaluate the LMS ease of use and satisfaction among its handlers. Many academic institutions worldwide prefer using their own customized Learning Management Systems; this is the case with Moodle, an open source Learning Management Systems platform designed and operated by most of the universities in Sri Lanka. This paper gives an overview of Learning Management Systems used in Sri Lankan universities, and evaluates its usability using some pre-defined usability standards. In addition it measures the effectiveness of Learning Management System by testing the Learning Management Systems. The findings and result of this study as well as the testing are discussed and presented.

Selvarajah Thuseethan, Sivapalan Achchuthan & Sinnathamby Kuhanesan (2015). Usability Evaluation of Learning Management Systems in Sri Lankan Universities, Global Journal of Computer Science and Technology, 15 (1) arXiv: 1412.0197v2

And the last abstract about the learning processo in neural network:

We propose Neural Transformation Machine (NTram), a novel architecture for sequence-to-sequence learning, which performs the task through a series of nonlinear transformations from the representation of the input sequence (e.g., a Chinese sentence) to the final output sequence (e.g., translation to English). Inspired by the recent Neural Turing Machines [8], we store the intermediate representations in stacked layers of memories, and use read-write operations on the memories to realize the nonlinear transformations of those representations. Those transformations are designed in advance but the parameters are learned from data. Through layer-by-layer transformations, NTram can model complicated relations necessary for applications such as machine translation between distant languages. The architecture can be trained with normal back-propagation on parallel texts, and the learning can be easily scaled up to a large corpus. NTram is broad enough to subsume the state-of-the-art neural translation model in [2] as its special case, while significantly improves upon the model with its deeper architecture. Remarkably, NTram, being purely neural network-based, can achieve performance comparable to the traditional phrase-based machine translation system (Moses) with a small vocabulary and a modest parameter size.

Fandong Meng, Zhengdong Lu, Zhaopeng Tu, Hang Li & Qun Liu (2015). Neural Transformation Machine: A New Architecture for Sequence-to-Sequence Learning, arXiv: 1506.06442v1

The expansion entropy

In simply: the expansion entropy is a new way to calculate the entropy of a given system.

Expansion entropy uses the linearization of the dynamical system and a notion of a volume on its state space

From a mathematical point of view, we can describe the evolution of a given system $M$ using a map (a function, an application) that acts in the same system $M$: $f: M \rightarrow M$. Every maps $f$ are depending on time, that it could be discrete or continuous.
Using these maps we can construct the so called derivative matrix $Df$, that is constituted by the partial derivatives of $f$ respect the coordinates of the $n$-space $M$.
At this point with $Df$, you can calculate the function $G(Df)$, that is

a local volume growth ratio for the (typically nonlinear) $f$.

or in other words a way to measure the growth of $M$ in time.
Now $G(Df)$ will be integrated on the whole $n$-space and renormalized on the volume, and the new quantity $E(f, S)$, will be used to define the expansion entropy: \[H_0 (f, S) = \lim_{t' \rightarrow \infty} \frac{\ln E_{t', t} (f, S)}{t'-t}\] where $t'$ is the final time, $t$ is the initial time.
In this way the expansion entropy measure the disorder of the system, like the topological entropy, but using the expansion entropy we can define the chaos when $H_0 > 0$.

Hunt, B., & Ott, E. (2015). Defining chaos Chaos: An Interdisciplinary Journal of Nonlinear Science, 25 (9) DOI: 10.1063/1.4922973 (arXiv)

The cosmological un-constant

Just a couple of abstract:

A general line element and a general metric tensor are defined as functions of two parameters $\alpha$ and $\alpha'$. The related Einstein's field equations of a gravitational potential field in a vacuum, including parameter $\Lambda$, have been derived. The parameters $\alpha$ and $\alpha'$ are identified in a gravitational field by the solution of the Einstein's field equations. Parallel with this, it has been find out that the so‐called cosmological constant $\Lambda$, is not really constant, but a function of gravitational radius, $\Lambda = f(r)$. This discovery is very important, among the others, for cosmology. One of the consequences is the new form of the acceleration equation of the universe motion that can be attractive (negative) or repulsive (positive). According to the observations, the repulsive acceleration gives rise to accelerating expansion of the universe at the present time. The obtained solution of the diagonal line element can be applied in a very strong gravitational field. Besides, this solution gives the Ricci scalar equal to zero, $R=0$. This is in an agreement with the current observation that our universe is flat.

from Novakovic B.M., Novakovic D.B. & Novakovic A.B. (2004). The Cosmological Constant $\Lambda$ is not Really Constant but the Function of a Gravitational Radius, AIP Conference Proceedings, 718 133. DOI: 10.1063/1.1787318

Universe

Pluto's Panorama with the Sun far far away imagined in the documentary Universe - via @astroperinaldo

Quarks of power

Once upon a time, there was a controversy in particle physics. There were some physicists who denied the existence of structures more elementary than hadrons, and searched for a self-consistent interpretation wherein all hadron states, stable or resonant, were equally elementary. Others, appalled by the teeming democracy of hadrons, insisted on the existence of a small number of fundamental constituents and a simple underlying force law. In terms of these more fundamental things, hadron spectroscopy should be qualitatively described and essentially understood just as are atomic and nuclear physics.⁽¹¹⁾

The need of the partons

From FermiLab Today

When we descrive the collisions between particles, we calculate the cross section, the area of the distribution of the collisions' products. The mathematical object used to calculate the cross section are the structure functions, that mathematically describes the inner structure of the particle. In 1969 studying the deep inelastic scattering J. D. Bjorken^{(4, 18)}, in order to explain the experimental results, proposed a particular property for the hadronic structure function in the cross section called scaling. In the same year Richard Feynman^{(5, 18)} suggested the necessity to adopt a new description of hadrons: they had to be made by smaller components, more elementary than the hadrons themselves. These components are called partons.
The Feynman's thesys was immediatly verified by Bjorken and Paschos^{(6, 7, 18)}, in this way starting a great discussion about the parton models, described in the paper by De Rújula, Georgi and Glashow quoted at the beginning of the post⁽¹¹⁾ (an interesting review of the parton model and its story is in Greenberg⁽¹⁸⁾).
Probably the most strong motivation to adopt the parton model to describe hadrons is the great production of particles in the ring particles accelerators⁽⁵⁾. So, theoretical physicists produced a lot of model, but the most succesfull is the quarks model, developed by Murray Gell-Mann⁽¹⁾ and Georg Zweig^{(2, 3)}, that introduced a new quantum number, the flavor. The first formulation involved three type of quarks (and so three flavors): up, down and strange. To this first set of elementary particles in 1970 the quark charm was added by Glashow, Iliopulos and Maiani⁽⁸⁾ and finally in 1973 Kobayashi and Maskawa⁽⁹⁾ completed the family with the two last quark, top and bottom, named by Harari⁽¹⁰⁾ in 1975.

Three quarks for Muster Mark!
Sure he has not got much of a bark
And sure any he has it's all beside the mark.
from Finnegan's Wake by James Joyce

The telescopic view of the Moon

John Philipps Emslie (1839–1913) was a British topographical artist and folklorist.
From 1854, Emslie studied at The Working Men's College, and was a student of Dante Gabriel Rossetti. He became a topographical artist, and illustrated The Illustrated topical record of London vol. 9. in 1900. He wrote and illustrated the New Canterbury Tales (Griffith, Farran, Okeden & Welsh) ca.1887.
Emslie was an original member of The Folklore Society and was a council member for that Society. He gathered local folklore from around England, making notes and topographical drawings.

He also realized a lot of scientific illustration, something like the modern infographics. For example the map of the Moon (via core77) at the beginning of the post. The caption of the map was a quotation by William Scoresby about his observation of the Moon at the Lord Rosse's telescope between 1847-48:

It appeared like a Globe of Molten Silver, and every object of the extent of a hundred yards was quite visible. Edifices, therefore of the size of York Minster might be early perceived if they had existed. But there was no appearance of anything of that nature neither was there any in diction of the existence of water or of an atmosphere. There was a vast number of extinct volcanoes, several miles in the breadth through one of them there was a line in continuance of one about 160 miles in length, which ran in a straight direction on like a railway. The general appearance however was like one vast ruin of nature.

Lovecraft and the discovery of Pluto

The story of the Pluto's discovery started with Urban Le Verrier, a French mathematician that he was interested in celestial mechanics: performing some newtonian calculation, on on 31 August 1846, he announced the prediction of a planet beyond Uranus. This planet, Neptune, was discovered one month later by the astronomer Johann Gottfried Galle about 1° of the position predicted by Le Verrier. From further observation, astronomers supposed that there was another planet that perturbed Uranus' orbit.

Meanwhile in Providence a young boy growing with the passion of astronomy: Howard Phillips Lovecraft, in a letter to Rheinhart Kleiner on 16 November 1916, wrote:

In the summer of 1903 my mother presented me with a 2-1/2" astronomical telescope, and thenceforward my gaze was ever upward at night. The late Prof. Upton of Brown, a friend of the family, gave me the freedom of the college observatory, (Ladd Observatory) & I came & went there at will on my bicycle. Ladd Observatory tops a considerable eminence about a mile from the house. I used to walk up Doyle Avenue hill with my wheel, but when returning would have a glorious coast down it. So constant were my observations, that my neck became much affected by the strain of peering at a difficult angle. It gave me much pain, & resulted in a permanent curvature perceptible today to a close observer.⁽¹⁾

Thanks to this passion for cosmos, Lovecraft starting to write The Rhode Island Journal of Astronomy:

In January, 1903, astronomy began to engross me completely. I procured a small telescope, and surveyed the heavens constantly. Not one clear night passed without long observation on my part, and the practical, first-hand knowledge thus acquired has ever since been of the highest utility to me in my astronomical writing. In August 1903 (though I knew nothing of the press associations) I commenced to publish an amateur paper called The R.I. Journal of Astronomy, writing it by hand, and duplicating it on a hectograph. This I continued for four years, first as a weekly, later as a monthly.⁽¹⁾

he wrote in a letter to Maurice W. Moe, on 1 January 1915.
In this way he could perform a lot of observations and he also supposed the possible existence of a new planet beyond Neptune, like he wrote on a letter to the Scientific American:

Balloon, art and mathematics

A couple of week ago Ethan Siegel published a post about ballon animals, so I decide to repost an old piece that I wrote in 2011 for my italian blog: the english version is lost, but it is magically reposted here!

Two one-balloon constructions and their associated graphs

I recently discovered this interesting site, vihart. In the site there are some interesting paper and today I want to write something about Computational Balloon Twisting: The Theory of Balloon Polyhedra by Erik and Martin Demaine and Vi Hart (the paper was reported in 2010 by the Improbable Research blog).
The interest about ballon twisting was motivated by...

Balloon twisting is fun: the activity can both entertain and engage children of all ages. Thus balloon twisting can be a vehicle for teaching mathematical concepts inherent in balloons. As we will see, these topics include graph theory, graph algorithms, Euler tours, Chinese postman tours, polyhedra (both 3D and 4D), coloring, symmetry, and even NP-completeness. Even the models alone are useful for education, e.g., in illustrating molecules in chemistry.

There's also a second motivation: building architectural structures with air beams (Army blows up building, Center manages technology of inflatable composite structures).

Our approach suggests that one long, low-pressure tube enables the temporary construction of inflatable shelters, domes, and many other polyhedral structures, which can be later reconfigured into different shapes and re-used at different sites. In contrast to previous work, which designs a different inflatable shape specifically for each desired structure, we show the versatility of a single tube.

Twisting baloons

The problem of the researchers is to determine the twistable graphs. Referring to a phisical balloon like a bloon, we have the following definitions:

(...) a bloon is a (line) segment which can be twisted at arbitrary points to form vertices at which the bloon can be bent like a hinge. The endpoints of a bloon are also vertices. Two vertices can be tied to form permanent point connections. A twisted bloon is stable if every vertex is either tied to another vertex or held at a nonzero bending angle.

The three researchers also defined two models

The chirality at the beginning of the universe

Within the particles that constitute atomic nuclei, protons and neutrons, there are the quarks, the elementary particles with fractional charges, linked to each other thanks to the gluons, bosons that carry the nuclear interaction. Thanks to the gluons it is impossible to observe, at present, free quarks, but it is expected that in the very first stage of the universe, matter was in a state called quark-gluon plasma. Thanks to the observation of so-called quark jets we know, indirectly, that the interior of the accelerators RHIC and LHC, in particular in heavy ion collisions, this kind of plasmas were created and, according to the theory, in the presence of axial anomalies, dued by the presence of strong electromagnetic fields, we can create two special effects: the Chiral Magnetic Effect (CME) and the Chiral Separation Effect (CSE).

The CME is the phenomenon of electric charge separation along the axis of the applied magnetic field in the presence of fluctuating topological charge.
The Chiral Separation Effect (CSE) refers to the separation of chiral charge along the axis of external magnetic field at finite density of vector charge (e.g. at finite baryon number density)⁽⁵⁾

These two effects are generated by the topology of the system: indeed, within the theory^{(1, 2, 3)} is contemplated the existence of some numbers (called topological invariants, or winding number⁽⁴⁾) that, while not associated with an observable, still generate effects physically relevant because of their link with the fundamental symmetries of the system.

The fifth shot of a tau neutrino

From the press release:

The OPERA (Oscillation Project with Emulsion-tRacking Apparatus) international experiment at the National Institute for Nuclear Physics (INFN) Gran Sasso Laboratory (Italy) has detected the fifth occurrence of a tau neutrino. The neutrino started its flight at CERN as muon neutrino and, after traveling 730 km through the Earth, it arrived at Gran Sasso Laboratories showing up as a tau neutrino. This important result was announced yesterday during a seminar held at the Gran Sasso Laboratories. According to the Spokesperson of the international research team, Giovanni De Lellis, from Federico II University and INFN in Naples, "The detection of a fifth tau neutrino is extremely important: the direct observation of the transition from muon to tau neutrinos has now achieved for the first time the 5 sigma statistical precision, the usual particle physics threshold for a discovery. We can thus definitely report the discovery of the appearance of tau neutrinos in a muon neutrino beam." The detection of tau neutrinos from the oscillation of muon neutrinos was the motivation of the OPERA project, designed in the late nineties. "This task is extremely difficult due to two conflicting requirements: a huge, massive detector and a micrometric accuracy. The challenge is to bring to the thousands ton scale a detector based on the nuclear emulsion technology, a photographic technique unique in ensuring the required accuracy", De Lellis says.

The tau neutrino was discovered in july 2000 by DONUT collaboration (arXiv). It is produced in the tau decay, where tau is a lepton, an elementary particle with a negative electric charge and spin 1/2 and with a mass of 1776.82 ± 0.16 MeV: with a great simplification we can say that tau is an electron with a very big mass!
Now, first of all I share the paper about the fourth observation:

Math education: calculus in South Korea and the Rubik's cube

A couple of mathematical abstracts from arXiv:

N. Karjanto (2015). Calculus teaching and learning in South Korea Jurnal Matematika Integratif 9(2): 179-193, 2013 arXiv: 1504.07803v1

This article discusses an experience of teaching Calculus classes for the freshmen students enrolled at Sungkyunkwan University, one of the private universities in South Korea. The teaching and learning approach is a balance combination between the teacher-oriented traditional style of lecturing and other activities that encourage students for active learning and classroom participation. Based on the initial observation during several semesters, some anecdotal evidences show that students' learning is improved after implementing this student-oriented active learning approach, albeit a longer period of time is definitely needed to transform general students' attitude from passive learners to active ones.

From the conclusion I would emphasize the following paragraph:

From this study we have seen some anecdotal evidences that students' learning is improved when they are actively engaged with the study material, instead of only sitting passively in the classroom and listening to the lecture. More success can be achieved when the classroom activities are also fun. With a proper balance between lecturing and engaging students new concepts and activities in which students, alone or in groups, need to struggle themselves with these concepts, makes the learning time in the classroom more effective and the time spent in class becomes more enjoyable for the students. Students also show appreciation for this style of teaching. Despite classroom participation and group activities are generally more successful in classes with a small number of students, some promising and good results have been accomplished even though the class sizes were relatively large.

Sandor Kiss (2015). Educational Challenges of Rubik's Cube X Workshop on Particle Correlations and Femtoscopy arXiv: 1505.00750v1

The first 2x2x2 twisty cube was created as a demonstration tool by Erno Rubik in 1974 to help his students understand the complexity of space and the movements in 3D. He fabricated a novel 3x3x3 mechanism where the 26 cubies were turning, and twisting independently, without falling apart. The cube was dressed in sophisticated colors which made it a unique puzzle. Even without instruction is the aim of the game was self-explanatory. Its educational value in VSI (Visual-Spatial Intelligence), developing strategy, memorization and logistics, improve concentration and persistence in problem solving is high in every age group. A logical puzzle has outreach far beyond. Those aspects are briefly covered in this article.

LHC restars at 13 TeV

Today at CERN, LHC restarts after a stopping period, at the energy of 13 TeV. It's a great day because we expect signals of new physics beyond particle standard model.

42 and Douglas Adams

Alan Turing's declassified papers

Recently Ian Taylor has uploaded on arXiv a couple of declassified papers by Alan Turing about statistics, probability and cryptography:

1. The Statistics of Repetitions

In order to be able to obtain reliable estimates of the value of given repeats we need to have information about repetition in plain language. Suppose for example that we have placed two messages together and that we find repetitions consisting of a tetragramme, two bigrammes, and fifteen single letters, and that the total overlap was 105, i.e. that the maximum possible number of repetitions which could be obtained by altering letters of the messages is 105; suppose also that the lengths of the messages are 200 and 250; in such a case what is the probability of the fit being right, no other information about the day's traffic being taken into consideration, but information about the character of the enciphered text being available in considerable quantity?

2. The Applications of Probability to Cryptography

The theory of probability may be used in cryptography with most effect when the type of cipher used is already fully understood, and it only remains to find the actual keys. It is of rather less value when one is trying to diagnose the type of cipher, but if definite rival theories about the type of cipher are suggested it may be used to decide between them.

Inge Lehmann: the core of the Earth

Inge Lehmann was a Danish seismologist and geophysicist. Using seismic data, she discovered the inner solid core of the Earth with some physical properties distinct from the outer liquid core:

No rays emerged at epicentral distances between 112° and 154°. I then placed a smaller core inside the first core and let the velocity in it be larger so that a reflection would occur when the rays through the larger core met it. After a choice of velocities in the inner core was made, a time curve was obtained, part of which appeared in the interval where there had not been any rays before. The existence of a small solid core in the innermost part of the earth was seen to result in waves emerging at distances where it had not been possible to predict their presence.

Lehmann, I. (1987). Seismology in the days of old Eos, Transactions American Geophysical Union, 68 (3) DOI: 10.1029/EO068i003p00033-02 (full paper)

Read also: Bolt, B. (1994). Inge Lehmann Physics Today, 47 (1) DOI: 10.1063/1.2808386

The mathematics and geometry in John Hejduck

In the Diamond project he articulates his idea of the architect's plan as perpendicular to the observer's frontality. This makes the opposite positions between the architect and the imaginary observer equivalent, which, building on Mondrian's ideas, maximises the strength of the contrary oppositions. Hejduk's axes are no longer ordinary axes, not really comparable witb the axis of x,y and z of conventional descriptive geometry. As we turn around, the line becomes a plane. The plane becomes imagined as a wall, a wall corresponding to the bodily movement. It's the moment of passage. The outline is also a membrane, Hejduk's says, and as the relatioosbip between our present and future, the relationship between the architect and the observer, the moment of passage through the wall is a "moment of the hypotenuse", of moving from one condition to another, through an edge between two elements. The concept of the "hypotenuse" is like a cut between the equivalence, as an opening and a movement, moving across two apparently fixed conditions. Hejduk's moment of the hypotenuse, when you become physically inside, is the moment of thought appearing, memory, seeing and moving. It resembles the experience of reading a book; all of a sudden you are in it, on the inside, and it bas become a part of you. But tbere is a difference, Hejduk remarks: there is something special about the physical encounter.

from Architecture of the ineffable: on the work of John Hejduk by Einar Bjarki Malmquist

Snowden and the debate on surveillance versus privacy

In June 2013, NSA contractor Edward Snowden met with journalists Glenn Greenwald and Ewen Macaskill and film-maker Laura Poitras in Hong Kong. The whistleblower gave them documents which proved the existence of a massive scale surveillance system that allows the American NSA and other intelligence and security agencies to gather information on citizens without judicial supervision. While in the USA and in Germany the major media outlets reported extensively on the issue, in Italy there hasn't been a proper public debate on privacy and surveillance, as - except for the work of handful of journalists – the media chose not to cover the implications of such revelations. On the other hand, politics is quick to use the fight against terrorism to push for reforms that might limit people's privacy, a fundamental human right that is currently under attack all over the world. Without a proper balance between surveillance and privacy, the freedom of citizens is at risk. Without a proper public debate, it is hard to understand what is at stake. For the first time in Italy, such debate will take place including the voices of the people who made the information public: Edward Snowden, the whistleblower who revealed the scope of the NSA surveillance practices, will be joining the conversation, as well as the independent film-maker Laura Poitras. Poitras recently won an Academy Award for the documentary Citizenfour, where she shows the meetings between the whistleblower and the journalists, and a Pulitzer prize for her journalistic work on the story. The human rights implications will be explored by Ben Wizner (ACLU), Snowden's lawyer, and Andrea Menapace, who directs the newly-born Italian Coalition for Civil Rights and Freedoms. Organised in association with Italian Coalition for Civil Rights and Freedoms (CILD) and American Civil Liberties Union (ACLU) Speakers: Edward Snowden (via Skype) Laura Poitras (via Skype) Ben Wizner (ACLU) Andrea Menapace (CILD) Simon Davies (Privacy International) Introduction: Patrizio Gonnella (CILD) Moderator: Fabio Chiusi Con: Fabio Chiusi (journalist and author), Simon Davies (founder Privacy International), Patrizio Gonnella (president CILD), Andrea Menapace (director CILD), Laura Poitras (documentary film-maker (via Skype)), Edward Snowden (whistleblower (via Skype)), Ben Wizner (ACLU), Ben Wizner

Cassini ovals

via commons

A Cassini oval is a quartic plane curve defined as the set (or locus) of points in the plane such that the product of the distances to two fixed points is constant. This may be contrasted to an ellipse, for which the sum of the distances is constant, rather than the product. Cassini ovals are the special case of polynomial lemniscates when the polynomial used has degree 2.
Cassini ovals are named after the astronomer Giovanni Domenico Cassini who studied them in 1680. Other names include Cassinian ovals, Cassinian curves and ovals of Cassini.

Read also: MathWorld, McTutor

Louis Nirenberg, the geometry and the Abel Prize

Great news: John Nash and Louis Nirenberg win the Abel Prize for 2015:

The Norwegian Academy of Sciences and Letters has decided to award the Abel Prize for 2015 to the American mathematicians John F. Nash Jr. and Louis Nirenberg “for striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.” The President of the Academy, Kirsti Strøm Bull, announced the new laureates today 25 March. They will receive the Abel Prize from His Majesty King Harald at a ceremony in Oslo on 19 May.

While Nash is known for his contribution to game theory with Nash equilibria, Nirenberg is

considered one of the outstanding analysts of the twentieth century. He has made fundamental contributions to linear and nonlinear partial differential equations and their application to complex analysis and geometry.

His first result was the completion of the solution of a problem in differential geometry, starting from the 1916 work of Weyl (read On the work of Louis Nirenberg by Simon Donaldson, pdf).

The statement is very simple: an abstract Riemannian metric on the 2-sphere with positive curvature can be realised by an isometric embedding in $R^3$.

In 1994 he received the Steele Prize by the American Mathematical Society. In that occasion, the Society writes (via MacTutor) a good summary of his activity:

Nirenberg is a master of the art and science of obtaining and applying a priori estimates in all fields of analysis. A minor such gem is the useful set of Garliardo-Nirenberg inequalities. A high point is his joint research with [Shmuel] Agmon and [Avron] Douglis on a priori estimates for general linear elliptic systems, one of the most widely quoted results in analysis. Another is his fundamental paper with Fritz John on functions of bounded mean oscillation which was crucial for the later work of [Charles] Fefferman on this function space. Nirenberg has been the centre of many major developments. His theorem with his student, Newlander, on almost complex structures has become a classic. In a paper building on earlier estimates of [Alberto] Calderón and [Antoni] Zygmund, he and [Joseph] Kohn introduced the notion of a pseudo-differential operator which helped to generate an enormous amount of later work. His research with [François] Trèves was an important contribution to the solvability of general linear PDEs. Some other highlights are his research on the regularity of free boundary problems with [David] Kinderlehrer and [Joel] Spuck, existence of smooth solutions of equations of Monge-Ampère type with [Luis] Caffarelli and Spuck, and singular sets for the Navier-Stokes equations with Caffarelli and [Robert] Kohn. His study of symmetric solutions of non-linear elliptic equations using moving plane methods with [Basilis] Gidas and [Wei Ming] Ni and later with [Henri] Berestycki, is an ingenious application of the maximum principle.

I hope that you can appreciate the list of collaboration performed by Nirenberg: indeed he is one of the most collaborative mathematician in the word. In particular for this reason I'm really happy for the award to Nirenberg.

Read also: Interview with Louis Nirenberg (pdf)

Pi day: Zilienski, Wallis and the square

A good pi day to all readers! I hope that the following post, that I cannot review after the first writing, could be interesting to all!

The technique used by the ancient Greek for their geometric constructions was called "ruler and compass". In this way you can build a lot of regular polygons, for example, but there are three problems that are impossible unless you use different techniques: the angle trisection, doubling the cube, squaring the circle.
In particular for the squaring, it is easy to calculate the relation between the radius $r$ of the circke and the side $l$ of the square with the same area of the starting circle: \[L = \sqrt {\pi} r \] Now, since $\pi$ is a transcendental number, the formula above is the simplest representation of the impossibility of squaring the circle using ruler and compass: with these devices you can treat rational and irrational numbers, such as $\sqrt{2}$ (in this case simply draw a square of side 1).
So, using these two tools it is possible to obtain an approximate construction and, therefore, a corresponding approximate value for $\pi$: during the XX century there are produced a lot of approximations, for example by CD Olds (1963), Martin Gardner (1966), Benjamin Bold (1982). They are all variations of the geometric construction discovered by Srinivasa Ramanujan in 1913, that approached $\pi$ with the fraction \[\frac{355}{113} = 3.1415929203539823008 \dots\] right up to the sixth decimal place.
In 1914, Ramanujan discovered a more accurate approximation (to eight decimal places), always using ruler and compass: \[\left (9^2 + \frac{19}{22}^2 \right)^{1/4} = \sqrt[4]{\frac{2143}{22}} = 3.1415926525826461252 \dots\]

Riemann zeta function's fractal

via imgur

The quadratic Mandelbrot set has been referred to as the most complex and beautiful object in mathematics and the Riemann Zeta function takes the prize for the most complicated and enigmatic function. Here we elucidate the spectrum of Mandelbrot and Julia sets of Zeta, to unearth the geography of its chaotic and fractal diversities, combining these two extremes into one intrepid journey into the deepest abyss of complex function space.

Fractal Geography of the Riemann Zeta Function by Chris King

Rock, paper, scissors, lizard, Spock

by SciFiCat

One popular five-weapon expansion is "rock-paper-scissors-lizard-Spock", invented by Sam Kass and Karen Bryla, which adds "Spock" and "lizard" to the standard three choices. "Spock" is signified with the Star Trek Vulcan salute, while "lizard" is shown by forming the hand into a sock-puppet-like mouth. Spock smashes scissors and vaporizes rock; he is poisoned by lizard and disproven by paper. Lizard poisons Spock and eats paper; it is crushed by rock and decapitated by scissors. This variant was mentioned in a 2005 article of The Times and was later the subject of an episode of the American sitcom The Big Bang Theory in 2008.

The majority of such proposed generalizations are isomorphic to a simple game of modulo arithmetic, where half the differences are wins for player one. For instance, rock-paper-scissors-Spock-lizard (note the different order of the last two moves) may be modeled as a game in which each player picks a number from one to five. Subtract the number chosen by player two from the number chosen by player one, and then take the remainder modulo 5 of the result. Player one is the victor if the difference is one or three, and player two is the victor if the difference is two or four. If the difference is zero, the game is a tie.
Alternatively, the rankings in rock-paper-scissors-Spock-lizard may be modeled by a comparison of the parity of the two choices. If it is the same (two odd-numbered moves or two even-numbered ones) then the lower number wins, while if they are different (one odd and one even) the higher wins. Using this algorithm, additional moves can easily be added two at a time while keeping the game balanced:
Declare a move N+1 (where N is the original total of moves) that beats all existing odd-numbered moves and loses to the others (for example, the rock (#1), scissors (#3), and lizard (#5) could fall into the German well (#6), while the paper (#2) covers it and Spock (#4) manipulates it).

Declare another move N+2 with the reverse property (such as a plant (#7) that grows through the paper (#2), poisons Spock (#4), and grows through the well (#6), while being damaged by the rock (#1), scissor (#3), and lizard(#5)).

(via en.wiki)

The dark side of the moon

The first photo of the lunar far side taken by the Soviet spacecraft Luna 3 on Oct. 7, 1959 - via Universe Today

What Einstein thought about Galilei

Galileo's Dialogue Concerning the Two Chief World Systems is a mine of information for anyone interested in the cultural history of the Western world and its influence upon economic and political development.
(...) To begin with, the Dialogue gives an extremely lively and persuasive exposition of the then prevailing views on the structure of the cosmos in the large. The naïve picture of the earth as a flat disc, combined with obscure ideas about star-filled space and the motions of the celestial bodies, prevalent in the early Middle Ages, represented a deterioration of the much earlier conceptions of the Greeks, and in particular of Aristotle’s ideas and Ptolemy’s consistent spatial concept of the celestial bodies and their motions.
(...) In advocating and fighting for the Copernican theory Galileo was not only motivated by a striving to simplify the representation of the celestial motions. His aim was to substitute for a petrified and barren system of ideas the unbiased and strenuous quest for a deeper and more consistent comprehension of the physical and astronomical facts.
The form of dialogue used in his work may be partly due to Plato’s shining example; it enabled Galileo to apply his extraordinary literary talent to the sharp and vivid confrontation of opinion. To be sure, he wanted to avoid an open commitment in these controversial questions that would have delivered him to destruction by the Inquisition. Galileo had, in fact, been expressly forbidden to advocate the Copernican theory. Apart from its revolutionary factual content the Dialogue represents a down-right roguish attempt to comply with this order in appearance and yet in fact to disregard it. Unfortunately, it turned out that the Holy Inquisition was unable to appreciate adequately such subtle humor.
(...) It is difficult to us today to appreciate the imaginative power made manifest in the precise formulation of the concept of acceleration and in the recognition of its physical significance.
Once the conception of the center of the universe had, with good reason, been rejected, the idea of the immovable earth, and, generally, of an exceptional role of the earth, was deprived of its justification (...)
(...) Galileo takes great pains to demonstrate that the hypothesis of the rotation and revolution of the earth is not refuted by the fact that we do not observe any mechanical effects of these motions. Strictly speaking, such a demonstration was impossible because a complete theory of mechanics was lacking. I think it is just in the struggle with this problem that Galileo’s originality is demonstrated with particular force. Galileo is, of course, also concerned to show that the fixed stars are too remote for parallaxes produced by the yearly motion of the earth to be detectable with the measuring instruments of his time. This investigation also is ingenious, notwithstanding its primitiveness.
It was Galileo’s longing for a mechanical proof of the motion of the earth which misled him into formulating a wrong theory of the tides. The fascinating arguments in the last conversation would hardly have been accepted as proofs by Galileo, had his temperament not got the better of him. It is hard for me to resist the temptation to deal with this subject more fully.
The leitmotif which I recognize in Galileo’s work is the passionate fight against any kind of dogma based on authority. Only experience and careful reflection are accepted by him as criteria of truth. Nowadays it is hard for us to grasp how sinister and revolutionary such an attitude appeared at Galileo’s time, when merely to doubt the truth of opinions which had no basis but authority was considered a capital crime and punished accordingly. Actually we are by no means so far removed from such a situation even today as many of us would like to flatter ourselves; but in theory, at least, the principle of unbiased thought has won out, and most people are willing to pay lip service to this principle.
It has often been maintained that Galileo became the father of modern science by replacing the speculative, deductive method with the empirical, experimental method. I believe, however, that this interpretation would not stand close scrutiny. There is no empirical method without speculative concepts and systems; and there is no speculative thinking whose concepts do not reveal, on closer investigation, the empirical material from which they stem. To put into sharp contrast the empirical and the deductive attitude is misleading, and was entirely foreign to Galileo. Actually it was not until the nineteenth century that logical (mathematical) systems whose structures were completely independent of any empirical content had been cleanly extracted. Moreover, the experimental methods at Galileo’s disposal were so imperfect that only the boldest speculation could possibly bridge the gaps between the empirical data. (For example, there existed no means to measure times shorter than a second). The antithesis Empiricism vs. Rationalism does not appear as a controversial point in Galileo’s work. Galileo opposes the deductive methods of Aristotle and his adherents only when he considers their premises arbitrary or untenable, and he does not rebuke his opponents for the mere fact of using deductive methods. In the first dialogue, he emphasizes in several passages that according to Aristotle, too, even the most plausible deduction must be put aside if it is incompatible with empirical findings. And on the other hand, Galileo himself makes considerable use of logical deduction. His endeavors are not so much directed at "factual knowledge" as at "comprehension". But to comprehend is essentially to draw conclusions from an already accepted logical system.

(from the foreword to Dialogue Concerning the Two Chief World Systems: Ptolemaic and Copernican (1953), Einstein Archives 1-174 - via Open Parachute)

About the italian physicist, Galileo Galilei and the impossible biomechanics of giants is an interesting reading.

The mathematics of love

\[\left (x^2 + \frac{9}{4} y^2 + z^2 - 1 \right )^3 - x^2 z^3 - \frac{9}{200} y^2 z^3 = 0\]

via Wikipedia

Black holes and revelations: their large interiors

The 3d volume inside a spherical black hole can be defined by extending an intrinsic flat-spacetime characterization of the volume inside a 2-sphere. For a collapsed object, the volume grows with time since the collapse, reaching a simple asymptotic form, which has a compelling geometrical interpretation. Perhaps surprising, it is large. The result may have relevance for the discussion on the information paradox.

Marios Christodoulou & Carlo Rovelli (2014). How big is a black hole?, arXiv: http://arxiv.org/abs/1411.2854v2

A sphere $S$ on the event horizon bounds a spacelike hypersurface, a large portion of which coincides with an $r$ = constant hypersurface. We show this hypersurface with one dimension suppressed, and cut in the middle, omitting the long cylindrical part which gives the main contribution to its volume. We also illustrate the argument showing that most of the volume is contained in a region out of causal contact with matter that has advanced far into the black hole.

Ingemar Bengtsson & Emma Jakobsson (2015). Black holes: Their large interiors, arXiv: http://arxiv.org/abs/1502.01907v1

Black holes and revelations: the seeds of the galaxies

The centre of the Milky Way - via Nasa

In this paper we present a new scenario where massive Primordial Black Holes (PBH) are produced from the collapse of large curvature perturbations generated during a mild waterfall phase of hybrid inflation. We determine the values of the inflaton potential parameters leading to a PBH mass spectrum peaking on planetary-like masses at matter-radiation equality and producing abundances comparable to those of Dark Matter today, while the matter power spectrum on scales probed by CMB anisotropies agrees with Planck data. These PBH could have acquired large stellar masses today, via merging, and the model passes both the constraints from CMB distortions and micro-lensing. This scenario is supported by Chandra observations of numerous BH candidates in the central region of Andromeda. Moreover, the tail of the PBH mass distribution could be responsible for the seeds of supermassive black holes at the center of galaxies, as well as for ultra-luminous X-rays sources. We find that our effective hybrid potential can originate e.g. from D-term inflation with a Fayet-Iliopoulos term of the order of the Planck scale but sub-planckian values of the inflaton field. Finally, we discuss the implications of quantum diffusion at the instability point of the potential, able to generate a swiss-cheese like structure of the Universe, eventually leading to apparent accelerated cosmic expansion.

Sébastien Clesse & Juan García-Bellido (2015). Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the seeds of Galaxies, arXiv: http://arxiv.org/abs/1501.07565v1

A probabilistic approach to the prime numbers distribution

The prime numbers theorem states the asymptotic approximation for the prime-counting function. The first statement for the theorem is given by Euler in 1737 (pdf):

The sum of the series of the reciprocals of the prime numbers, \[\frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{11} + \frac{1}{13} + \cdots\] is infinitely large, but it is infinitely many times less than the sum of the harmonic series, \[1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \cdots\] Furthemore, the sum of the former series is like the logarithm of the sum of the latter series.

After Euler, the most known attempt to evaluate the prime numbers distribution is given by Bernard Riemann, and the most recent is posted on arXiv some days ago:

A magnet falling in a metal tube

Sometimes teach physics, and a couple of years ago the colleague of the educational laboratory proposed to the students a simple experiment: a magnet that descends along a metal tube⁽¹⁾ does not fall at the same speed of the same magnet that we throw from the same height, for example, inside a not metal tube. The magnet inside the metal tube will drop almost as if it remained in suspension, swinging a little to the right a little to the left, in a manner apparently inexplicable, but just let us allow to the students, exceeded the initial amazement, to think above the phenomena, even without too much knowledge, and they realize that in some way that the behavior of the magnet inside the tube is due to an interaction between the two objects that goes beyond the simple direct contact.
The secret behind the behavior of the magnet is the so-called Lenz's law:

An induced electromotive force (emf) always gives rise to a current whose magnetic field opposes the original change in magnetic flux.

Annihilator: Hollywood, the galaxy and everything

Rabbits are animals extremely prolific, almost legendary in their rate of reproduction, so that Leonardo Fibonacci, thanks to these cute rodents, discovered (or re-discovered) the series that bears his name: 1 1 2 3 5 8 13 21 and so on, and where each number is the sum of the previous two.
However, it is astonishing to note how pervasive within nature this series of numbers is: we can find it, for example, in the arrangement of seeds of sunflowers⁽¹⁾, in the structure of shells of turtles, in the spirals of seashells. Or, again, in the spiral galaxies⁽²⁾.

M51 (Whirlpool Galaxy) - source: reddit, NASA

Journey through the universe

The galactic matter, in fact, revolves around the center of every galaxy often making spiraling structures, arms of solid and gaseous matter that we can describe with the Fibonacci series as they fall toward the center, slowly swallowed up by an object apparently absurd but absolutely real: the supermassive black hole. So, within each spiral galaxy there is a black hole^{(3, 4)}, which at the same time is the reason for the existence⁽⁵⁾ and the ultimate fate of galaxies like our Milky Way, the center of which lies Sagittarius A*⁽⁶⁾.
Almost nothing escapes from the event horizon of this cosmic monster: let you imagine the matter while, piece by piece, falls within it, decomposed into its fundamental constituents, and the only trace of this meal is a simple, small radiation X⁽⁷⁾, a slight heat that escapes, evidence of a millennial digestion. It is in this border area that is brought Max Nomax, adventurer and genius, looking for "a cure for death", a way to be reunited with his beloved in life, the protagonist of a classic cosmic science fiction story written by the equally genial Ray Spass, Hollywood screenwriter in creative crisis and tormented by his manager, who presses him to get the script for a new film series, Annihilator.
With this latest work Grant Morrison, mixing the classic kirbyan superhero inspiration with real insights arrived from his Hollywood's patronage, builds a story that is a bit of an existential drama, a bit of a parody of the world of cinema, a bit of a great science fiction story. The comparison between creature and creator, here achieved simply with the description of their respective alternate adventures, brings near the two main characters, both anti-heroes, and from another point of view move them away for motivation and potential, creative or destructive according to their motivation.

The deadly irony of gunpowder

In the mid-ninth century, Chinese chemists, hard at work on an immortality potion, instead invented gunpowder. They soon found that this highly inflammable powder was far from an elixir of life -- they put it to use in bombs against Mongol invaders, and the rest was history. Eric Rosado details how gunpowder has caused devastation around the world, despite the incandescent beauty of fireworks.

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