### The day of mathematical poetry

Bridges: Mathematical Connections in Art, Music, and Science (discovered via Mr Honner) is an annual conference where mathematicians, scientists and artists explore the mathematical connections between these subjects. In particular today is the poetry day, and I decide to publish an interesting scientific poetry, that was submitted and published on Nature!
Frederick Soddy, who winned the Nobel Prize in Chemistry in 1921, composed The Kiss Precise, in which he rediscovered the Descartes' Circle Theorem
originally proved by Rene Descartes, which involves the radii of four mutually tangent circles
He wrote his result in verses:
For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.
Four circles to the kissing come.
The smaller are the benter.
The bend is just the inverse of
The distance from the center.
Though their intrigue left Euclid dumb
There's now no need for rule of thumb.
Since zero bend's a dead straight line
And concave bends have minus sign,
The sum of the squares of all four bends
Is half the square of their sum.(1, 2)
The most interesting thing is the generalization of the result, that was submitted also(7) in poem by Thorold Gosset:
And let us not confine our cares
To simple circles, planes and spheres,
But rise to hyper flats and bends
Where kissing multiple appears,
In n-ic space the kissing pairs
Are hyperspheres, and Truth declares,
As n + 2 such osculate
Each with an n + 1 fold mate
The square of the sum of all the bends
Is n times the sum of their squares.(3, 4)
It's interesting to observe that Soddy's poetry is the oldest poem submitted to a scientific journal, being older than The Detection of Shocked Co/ Emission from G333.6-0.2 by J. W. V. Storey, published in 1984 on the Proceedings of the Astronomical Society of Australia and discovered by Maria Popova.

### What is 5 sigma?

Before the announce of the discover of a new boson in LHC by the two experiments ATLAS and CMS, I try to explain the concepts of sigma, $\sigma$. Today I would propose you a video from Fermilab about the statistics used in physics and in particular in the high energy field:
In alternative you can read 5 Sigma - What's that? by Evelyn Lamb.

### PoincarĂ©, Einstein and Picasso: children of time

A great thanks to Marco Fulvio Barozzi: his post(1) about Miller's book is the main inspiration of my post.

Yesterday, on the Guardian, Arthur I. Miller, the author of the book Einstein, Picasso: Space, Time and the Beauty that Causes Havoc, wrote a briefly article in which he resumed his thesis about the connections between PoincarĂ© and Einstein, between PoincarĂ© and Picasso and, for translation, between Einstein and Picasso.
Henri PoincarĂ© was one of the most important mathematician of the early XX century: his most important contributions, that have a great impact also in physics, are in group theory and representation theory. His work was indeed important for the birth of the ray representations (the theory was developed in particular by Valentine Bargmann starting from Weyl and Wigner's works) and basic for special relativity and in particular for general relativity. PoincarĂ© was the first to propose the symmetrical form of the Lorentz transformations, and his work was important for the creation of the PoincarĂ© group, the symmetry group of the general relativity. In particular about the relativity, PoincarĂ© written on his book Science and Hypothesis (1902)
Our Euclidean geometry is itself a sort of linguistic convention; we may state the facts of mechanics in relation to a non-Euclidean space, but this would be a less convenient reference, although legitimate like our ordinary space.(1)
He also defined the principle of relative motion like
the physical impossibility of observing absolute motion.(1)
Two years later he named it Principle of Relativity.
At the other hand, Einstein did not cite PoincarĂ©'s works in his paper published in 1905 by Annalen der Physik and only in a conference in 1921 Einstein confirmed his debt to the french mathematician, but only about general relativity and non-euclidean geometry. And this is the only documented connection between Einstein and PoincarĂ©: we must suppose that the two scientists worked indipendetly and also after his first paper Einstein used PoincarĂ©'s discoveries in order to develop the mathematical formalism of the general relativity.
Some years later the first Einstein's paper, the cubism was born in France:
A circle of poets and critics, and followers of the philosopher Bergson, stood up for cubism in the visual arts. This group became known as the Cubists. The poet and publicist G. Apollinaire became the undisputed leader of this movement.(2)
It seems that relativity played a relevant role in the phylosophy of the artistic movement
Like the scientists, the artists has come to recognize thatclassic conceptions of space and volume are limited and one-sided. (...) The presentation of objects from several point of view introduces a principle which is intimately bound up with modern life - simultaenity. It is a temporal coincidence that Einstein should havebegan his famous work (...) with a careful definition of simultaneity.(5)
In this quotation by Sigfried Giedion, the connection was simply casual, only a temporal coincidence, but a lot of art historians think that the connection is not so casual. One of this is Paul M. Laporte, who published two paper about cubism and relativity, and submitted them to Albert Einstein. The great physicist reply with a long letter, in which he concludes:
This new artistic "language" has nothing in common with the Theory of Relativity.(5)
And probably it is so. Indeed in 1903 the Introduction to Metaphysics by Henri Bergson was published. In the book Bergson argued that
human consciousness experiences space and time as ever-changing and heterogeneous. With the passage of time, an observer accumulates in his memory a store of perceptual information about a given object in the external visible world, and this accumulated experience becomes the basis for the observer’s conceptual knowledge of that object. By contrast, the intellect or reasoning faculty always represents time and space as homogenous. Bergson argued that intellectual perception led to a fundamentally false representation of the nature of things, that in nature nothing is ever absolutely still. Instead the universe is in a constant state of change or flux. An observer views an object and its surrounding environment as a continuum, fusing into one another. The task of metaphysics, according to Bergson, is to find ways to capture this flux, especially as it is expressed in consciousness. To represent this flux of reality, Picasso began to make references to the fourth dimension by "sticking together" several three-dimensional spaces in a row.(4)

### Les Cernettes

Les Horribles Cernettes is a rock-swing group that started its activity with the... birth of the web!
Indeed the first photo uploaded on web by Tim Berners-Lee was a promotional photoshop by the fab four girl from LHC!
The group is, today, formed by three girls Michele de Gennaro, Anne MacNabb, Colette Marx-Nielsen, and this is the original story from the official web site:
Once upon a summer there was a girl. She was a CERN secretary tired of waiting day and night for her permanently-on-shift physicist boyfriend, and so she decided to attract his attention by stepping on stage during the CERN Hardronic Festival to sing about her lonely nights in front of the entire CERN population. She asked Silvano [de Gennaro, an IT developer who worked with Tim Berners-Lee] to write a song about her life and a couple of girlfriends to back her up on stage. A few weeks later the Cernettes were on stage for the first time, for the delight of thousands of happy Physicists, singing Collider, the song that since that day became the National Anthem of the High Energy Kingdom.
Their first success was Liquid Nitrogen, but today I would share a live version of Mr. Higgs:

### The mysterious Mr. Higgs

From The God Particle: If the Universe Is the Answer, What is the Question? by Leon Lederman (via ellegio)

### Linux at CERN

On reddit (via Ubuntu Vibes) an anonimous researcher from CERN published the following message:
I don't see any CERN related things here, so I want to mention how Linux (specifically, Scientific Linux and Ubuntu) had a vital role in the discovery of the new boson at CERN. We use it every day in our analyses, together with hosts of open software, such as ROOT, and it plays a major role in the running of our networks of computers (in the grid etc.) used for the intensive work in our calculations.
Yesterday's extremely important discovery has given us new information about how reality works at a very fundamental level and this is one physicist throwing Linux some love.
If you want, you can download the distributions used at CERN at the page Linux @ CERN. The CERN distribution is a Scientific Linux (a distribution used also at Fermilab) rebuilded with the Red Hat. In general the Linux distributions are the most used in the scientific world, in particular in physics and mathematics, and the reasons are the same that the anonimous research writes in another comment:
In terms of data analysis, Windows could be used in principle. We could also use some type of device that manipulates symbols on a strip of tape according to a simple table of rules. Linux is used because it is most appropriate for the job. Linux is ubiquitous in HPC and we use a lot of computing power in LHC physics, so the arguments for the use of Linux in HPC are very similar to the arguments for the use of Linux in LHC physics analyses. Naturally, it's important to have an operating system that is free, open source and reliable (Scientific Linux is basically Red Hat Linux), but here's a quotation from the Scientific Linux website that should give some idea of why Scientific Linux is needed:
"Our main goal for the base distribution is to have everything compatible with Enterprise, with only a few minor additions or changes. Examples of items that were added are Alpine, and OpenAFS.
Our secondary goal is to allow easy customization for a site, without disturbing the Scientific Linux base. The various labs are able to add their own modifications to their own site areas. By the magic of scripts, and the anaconda installer, each site is to be able to create their own distributions with minimal effort. Or, if a user wishes, they can simply install the base SL release."
I work primarily in physics, not in computing, so I doubt that I am able to argue very competently for Linux over something such as BSD. The fact is that Linux was the operating system used in the overwhelming majority of the analyses contributing to the discovery, so, in that sense I think I am justified in claiming that Linux played a vital role in the discovery.
And he also writes about Apple and Comic Sans:
In many ways, some Apple fans are similar to religious people in their devotion to something; that is, their support is not really derived from a critical appraisal of the technical standard of Apple products. I don't identify with this kind of motivation, but I am much happier seeing people religiously attached to new technological gadgetry than to invisible sky daddies.
Similarly, Comic Sans is grotesque, but if it contributes to directing attention to the recent discovery, then it could be argued that it is a good thing.
In direct answer to your question, I think that you can thank Microsoft Bob for the existence of Comic Sans.
And finally he explain (one of many) that, with the data collected since june 2012, we can say that the new particle is a new boson, but we are not certain that it is a Higgs boson:
The properties of the discovered boson have yet to be scrutinised thoroughly before one can reliably claim it to be a Higgs boson (note that I do not claim the discovered boson to be the Higgs particle in the post). This is a phase of analysis we are now moving into.
And don't forget to read the post about the discover of the new boson!

### Discovering a boson

I'm partially wrong! Yesterday I write that no Higgs could be announced, but today ATLAS and CMS presented the observation of a new boson, that it's to soon to identify with certainty like the Higgs boson, but it is certainly a new boson to add to the picture of the universe. The next quest is to find its properties and to confront with the theoretical properties of the Higgs boson. It could be that the new boson presented today could be different for a bit of properties from the Higgs, but this is not so incredible: like I write, with a Higgs boson with a mass around 125 GeV, we need other ingredients to complete a picture of our stable universe.

Candidate Higgs decay to four electrons recorded by ATLAS in 2012 (source ATLAS)
But... what did it happen today?
The two experiments, CMS, represented by Joe Incandela, and ATLAS, represented by Fabiola Gianotti, showed the results of their last data elaboration about Higgs research. The results come from the combination of the complete data set from 2011 (see, for example, the ATLAS' preprint) with the first part of data from 2012. The conclusions are: CMS sees an excess with $m_H = 125.3 \pm 0.6 GeV$ with a significance of $4.9 \sigma$; ATLAS sees an excess with $m_H = 126.5 GeV$ with a significance of $5.0 \sigma$, that it means discover!

CMS' final result

ATLAS' final result

### Are we close to discovering the Higgs Boson?

Today ATLAS and CMS will present, during two scientific conferences, their results with the complete set of data from 2011. ATLAS has also released a preprint, submitted to the Physical Review D, in which the experiment propose a measure for the Higgs mass: $m_H = 126GeV$ with a significance of $2.9 \sigma$ (like I wrote yesterday). There are not the numbers for a discover, but we are really close to the Higgs boson, like John Ellis explains in the following video:
You can follow the conference in webcast, on internet thanks to the live blogging from Sean Carroll, or following the hashtags on twitter: #Higgs #ICHEP2012 #CERN #LHC #LargeAdronCollider.

### Higgs? Probably not tomorrow

I try to explain because I think that tomorrow it will not be the announce of the Higgs boson discover. First of all the official statements of Sergio Bertolucci, CERN Director for Research and Computing (CERN press release):
We now have more than double the data we had last year that should be enough to see whether the trends we were seeing in the 2011 data are still there, or whether they've gone away. It's a very exciting time.
and of James Gillies, CERN spokesman (Not Even Wrong):
Combining the data from two experiments is a complex task, which is why it takes time, and why no combination will be presented on Wednesday.
And today, a preprint is published by ATLAS: Combined search for the Standard Model Higgs boson in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector
A combined search for the Standard Model Higgs boson with the ATLAS detector at the LHC is presented. The datasets used correspond to integrated luminosities from 4.6 $fb^-1$ to 4.9 $fb^-1$ of proton-proton collisions collected at sqrt(s) = 7 TeV in 2011. The Higgs boson mass ranges of 111.4 GeV to 116.6 GeV, 119.4 GeV to 122.1 GeV, and 129.2 GeV to 541 GeV are excluded at the 95% confidence level, while the range 120 GeV to 560 GeV is expected to be excluded in the absence of a signal. An excess of events is observed at Higgs boson mass hypotheses around 126 GeV with a local significance of 2.9 standard deviations (sigma). The global probability for the background to produce an excess at least as significant anywhere in the entire explored Higgs boson mass range of 110-600 GeV is estimated to be ~15%, corresponding to a significance of approximately one sigma.
I must rember you that, to declare a discover of a new particle, the result must be released with 5 sigma, and ATLAS data is given with 2.9 sigma(1).
We are really near to the Higgs boson, but we don't have the certainty, so I think that tomorrow nobody say We have discovered the Higgs boson (but I could be wrong).

### Higgs at the Tevatron

This is the week of the Higgs. Indeed, wednesday, at CERN, ATLAS and CMS announced the results of the elaboration of the data collected in the first part of 2012... and a lot of journalists write about the probable discover of the Higgs boson. Indeed the two collaborations are disegned in order to discover the boson related to the mechanism that provides the mass to the other particles. Waiting for the conference, today CDF and DZero, the two collaborations of Tevatron, publicize in two conferences the first elaboration of the complete set of data about Higgs research. Their result was summarize by the following plot:
In the image there is the combination of the final results from the two collaborations. The two experiments combined detecte an excess in signals around 125 GeV with a 2.5 sigma. It is not the discover of the Higgs boson, but it could be a good clue for the existence of the boson. So I don't know if ATLAS and CMS will confirm or update this result in their next conferences, but in every case I must remmber to the readers that with a mass of 125 GeV we have need of physics beyond Standard Model, because the only SM is not sufficient to explain our universe. In order to explain better, I reprint here some considerations that I just published for the previous Higgs day:

### Rethinking Mathematics, 2nd Edition

It seems interesting for all mathematics teachers (via Tiny Teaching)
Rethinking Mathematics (RM) is ready for its second edition and needs contributors! We are excited to put forward this call and are calling on authors to submit manuscripts for consideration to Rethinking Schools as soon as possible. Our deadline for submissions for next edition of the book is September 1.
We are looking for submissions in four principal areas:
• manuscripts describing teaching and learning mathematics for social justice (e.g., see RM chapters 1, 5, 9, or 12);
• manuscripts describing salient issues in T/L mathematics for social justice (e.g., RM chapters 2, 3, 4, 7, or 14);
• one- to three- page "mini-lessons" or "activity boxes" that teachers can use and adapt to their contexts (see RM pp. 16-18; p. 23; 29-30; or 64-67);
• resources for teaching math for social justice (see RM, "Resources" section and RM itself) including cartoons, graphics, graphs, pictures, and other creative and lively ideas.
Of these, the first is our priority. And for these, we are especially looking for chapters written by (or with) classroom teachers who have actually taught the social justice lessons, and those manuscripts that emphasize student voice, real classrooms, and all the challenges of doing this work (including how teachers themselves learn and grow in the process). If you are not familiar with the Rethinking Schools magazine, please read the chapters in RM and articles in the magazine to get a sense of what Rethinking Schools publishes, and see the Rethinking Schools contributor guidelines.
Several areas that we want to emphasize are articles for younger grades (K-5), international perspectives (and authors from the Global South), issues of mathematics and bi/multilingual contexts, contributions focusing on culture and cultural relevance, and submissions by authors of color.
Our view is that Rethinking Mathematics is really an ongoing project for Rethinking Schools and the wider teaching and learning mathematics for social justice "community". That is, we will always be open to considering articles for the magazine and for future editions of the book in case we are not able to accept your submission for this edition. Of course, Rethinking Schools can never guarantee publication, but the Rethinking Schools editors are committed to working with potential authors in shaping your submissions for the book or magazine.