# Happy Higgs Day!

Today, all over America (land of science enthusiasts) fireworks will be set off in remembrance of the many particle collisions that it took to bring our observations of the decay products of the Higgs up above a five sigma confidence interval.  If you need a refresher or just haven’t followed all this very closely, you’ll definitely want to watch PhD Comics‘ animated explanation below (you’ll want to see it full screen).

The best print coverage I’ve seen so far today is, unsurprisingly, at Ars Technica.  What I kind of love best about all this is that this isn’t just a triumph of theoretical physics or engineering.  It’s also a big day for statistics.  When I worked in a genetics lab, there were biostatisticians working overtime trying to figure out how to quantify all our assumptions about high thoroughput shRNA screening and decide whether tests were more about identifying plausible candidates for further testing or trying pass fewer targets that were more likely to work.  (Remember sensitivity and specificity?).

We’re a long way from the practice stat problems you did in high school where the teacher tells you how big the standard deviations are (the ‘sigma’ in five sigma).  Ars does a beautiful job giving you a conceptual sense of how complicated it is for statisticians to come up with a rigorous way of gauging the data:

But the huge number of collisions created its own problems. At times, up to 30 collisions were taking place nearly simultaneously, and the computer systems had to reconstruct which signals came from what collisions and trigger the system to save the data if something looked interesting—all within a fraction of a second. According to the talks, the software triggers were improved, the code reconstructed events faster, and the computing grid was given more sophisticated analysis tools to identify events that could come from a Higgs decay. The net result was today’s announcement (and yesterday’s accidental pre-announcement).

Where do we now stand? There are a lot of ways to look at it. One is basically the probability of finding the Higgs at a specific mass. If we assume the Higgs is 125GeV, we see a signal that’s a specific sigma above background. But there’s no particular reason to assume 125GeV and not, say, 135GeV, and the statistics need to compensate for this (called the “look elsewhere effect”). Then there are multiple channels thanks to the different decay pathways, and two different detectors. So, for the CMS detector, the two-photon channel produces a local Higgs signal that’s 4.5 sigma, but that drops to 2.5 sigma when the look elsewhere effect is considered. It’s only by combining all its channels that CMS reaches a 4.9 sigma, and the data from both detectors had to be combined to be able to declare discovery.

So huzzah for theorists, engineers, and professional heuristic makers!  Go off and caper!  Jump up and down and celebrate as your atoms, affected by the Higgs field, pull you back to earth.  And tonight, enjoy the fireworks all the more after you watch the video below.

(The fourth of July after I read an article on fireworks chemistry in Muse magazine, I had a great time yelling out the names of the elements that produced the colors we’d just seen.  Copper!  Charcoal!  Strontium! Fun times.)

Leah Anthony Libresco graduated from Yale in 2011 and lives in Washington DC. She works as a news writer for FiveThirtyEight by day, and by night writes for Patheos about theology, philosophy, and math at www.patheos.com/blogs/unequallyyoked. She was received into the Catholic Church in November 2012."

• Karen

A Higgs Boson particle walks into a church. The Priest says “we don’t allow you in here”. The particle says “but Father, without me how can you have Mass?”

• deiseach

And of course, the old joke:

Protons have Mass? I didn’t even know they were Catholic!

• Sister MM

@ Karen – Now THAT’S hysterical!
You have to be over 50 to appreciate this one, but our sisters use to tell what they claimed to have actually happened at one of their high schools:
The chemistry and physics students shared the same lab, using it during different periods of the school day. Students each had their own drawer in which to keep their lab materials. The nun who taught chemistry was extremely neat and tidy. She kept the lab and equipment immaculately clean. The nun who taught physics… not so much! And her students followed suit. The chemistry nun would come into class, day after day, dismayed to find equations on the chalkboard, erasers not cleaned, notes left lying about, and messy drawers. It was particularly disconcerting at the end of the term, when Sister had to clean up the messes left behind by those physics students. So, as the end of the next term approached, the chemistry nun decided she had suffered enough. In big, bold letters, she wrote across the chalk board: ALL STUDENTS WHO TAKE PHYSICS MUST CLEAN THEIR DRAWERS.

• grok87

Leah,
cheers,
grok

• Solarcat

Enjoyed the Higgs Boson cartoon, though I’m way behind in the real science being explained.
Also liked the fireworks explanations, however when I go out to watch them, I’ll be saying, Oooooh, Ahhhh, Wow. I’d rather be awed by the spectacle then saying the names of what chemical(s) are making the various colors. No geek in me there.
What I do find interesting, in, I guess a somewhat scientific way, is what it takes to put on the fireworks show; what must go on behind the scenes to create the beautiful show we see in the sky. The timing of the various fireworks to create the desired effect, syncing it with the music being played, etc.. It’s a very complex operation. I had the good fortune to watch it several times on the Boston Esplanade along the Charles River with 1st Arthur Fiedler and later Keith Lockhart, conducting the Boston Pops, the howitzer cannons blasting artillery shells from the shore of the Charles during the 1812 Overture, and church bells around the city ringing, the fireworks, and the crowds of people there. Joy.
Ted

• stranger danger

And of course the searing power of science prevails again

• Thinkling

One gripe I have is the Prosecuter’s Fallacy fails ad nauseum on Twitter and in web writeups. You know, “[super high number] sigma so [super high number] probability of really discovering the Higgs!” Super high facepalm.

Re the proton joke, I guess then you can sympathize with the neutrino

Re firework colors, I did the same with my nine year old (don’t forget his favorite, magnesium for sparkle), but he had the last word: “Dad, what color would it be if they used nuclear fusion?”

• deiseach

The only possible reply to that is “Awesome, son, awesome”

• Contrarian

The neatest part (to me) is that math is lagging behind physics here. Nobody knows how to tie in quantum field theoretic formalism to existing mathematical structure — all we know is that it’s a set of formal rules that make good empirical predictions. For example, the path space over which Feynman integrals are taken has a measure in only a handful of toy models, like Chern-Weyl theory on a three-manifold (if my memory serves me correctly). Otherwise, a Feynman integral should really be in scare quotes, “Feynman integral”, because it’s a symbol without mathematical meaning.

For more, see http://www.claymath.org/millennium/Yang-Mills_Theory/yangmills.pdf Description of the Higgs field and mechanism enters with Glashow-Weinberg-Salam theory in the middle of the second page.

• Contrarian

Actually, I think it’s *Chern-Simons theory. But that’s not my area, so I could well be wrong.

• Ted Seeber

From a theological perspective (you KNOW I had to go there) statistics is “We don’t know but we are pretty sure, and there’s a heck of a lot left to learn”.

It’s the difference between absolute assurance and moral assurance.

In Catholicism, absolute assurance is a big no-no. It’s one of the biggest heresies, and it’s practiced both by certain types of atheists AND by fundamentalist Christians.

That’s why, while the Church is dogmatic, doctrine happens, and develops organically. Because we, as finite human beings, cannot be absolutely sure we’ve understood everything God gave to us in revelation, and we can’t even be sure that Apostolic Authority has been enough to protect Tradition. We’re morally certain this is so, but we’re not absolutely certain.

Switching it back to science and the topic at hand- five sigma confidence is VERY morally certain. But as the cartoon explained- the difference between Higgs existing and Higgs NOT existing is very very very small; and so even with the huge number of collisions it took us to get to this point, we’re STILL not absolutely certain that Higgs exists. Human certainty is limited by Zeno’s Paradox (if you don’t know what that is, I recommend a book off of Leah’s reading list whose title is usually reduced to the initials GEB).

• Contrarian

Human certainty is not limited by Zeno’s Paradox. The two have nothing to do with each other.

• Ted Seeber

Then why only 5 sigma confidence? Why not infinite sigma confidence? And why does the Heisenberg Uncertainty Principle exist?

You can come close to zero. You can come close to infinity. But you will NEVER get there.

• Thinkling

I am not sure what Zeno’s paradox has to do with anything either. The delta-epsilon folks exorcised this paradox but good in the last couple of centuries or so.

But I do have to admit that GEB-EGB is a fantastic book.

• Contrarian

I think it’s pretty clear that human uncertainty is limited by measurement instrument resolution (and ultimately by the uncertainty principle).

• Ted Seeber

Which goes right back to Zeno’s Paradox, which is all about errors in measurement. Achilles can’t ever catch the tortoise, because there is always a smaller unit we haven’t discovered yet. (there probably really is a limit there- and in real life Achilles jumps over the tortoise to get ahead, but the point is uncertainty).

• David Inc

I love the answer the Pope gives below. Here is the Pope in a Q&A session with the diocesan youth of Rome in 2006. A 17 year old student asked this question.

Holy Father, I am Giovanni, I am 17 years old, I am studying at “Giovanni Giorgi” technological and scientific secondary school in Rome, and I belong to Holy Mary Mother of Mercy Parish. I ask you to help us to understand better how biblical revelation and scientific theory can converge in the search for truth.
We are often led to believe that knowledge and faith are each other’s enemies; that knowledge and technology are the same thing; that it was through mathematical logic that everything was discovered; that the world is the result of an accident, and that if mathematics did not discover the theorem-God, it is because God simply does not exist. In short, especially when we are studying, it is not always easy to trace everything back to a divine plan inherent in the nature and history of human beings. Thus, faith at times vacillates or is reduced to a simple sentimental act. Holy Father, like all young people, I too am thirsting for the truth: but what can I do to harmonize knowledge and faith?

The great Galileo said that God wrote the book of nature in the form of the language of mathematics. He was convinced that God has given us two books: the book of Sacred Scripture and the book of nature. And the language of nature – this was his conviction – is mathematics, so it is a language of God, a language of the Creator.

Let us now reflect on what mathematics is: in itself, it is an abstract system, an invention of the human spirit which as such in its purity does not exist. It is always approximated, but as such is an intellectual system, a great, ingenious invention of the human spirit.

The surprising thing is that this invention of our human intellect is truly the key to understanding nature, that nature is truly structured in a mathematical way, and that our mathematics, invented by our human mind, is truly the instrument for working with nature, to put it at our service, to use it through technology.

It seems to me almost incredible that an invention of the human mind and the structure of the universe coincide. Mathematics, which we invented, really gives us access to the nature of the universe and makes it possible for us to use it.

Therefore, the intellectual structure of the human subject and the objective structure of reality coincide: the subjective reason and the objective reason of nature are identical. I think that this coincidence between what we thought up and how nature is fulfilled and behaves is a great enigma and a great challenge, for we see that, in the end, it is “one” reason that links them both.

Our reason could not discover this other reason were there not an identical antecedent reason for both.

In this sense it really seems to me that mathematics – in which as such God cannot appear – shows us the intelligent structure of the universe. Now, there are also theories of chaos, but they are limited because if chaos had the upper hand, all technology would become impossible. Only because our mathematics is reliable, is technology reliable.

Our knowledge, which is at last making it possible to work with the energies of nature, supposes the reliable and intelligent structure of matter. Thus, we see that there is a subjective rationality and an objectified rationality in matter which coincide.

Of course, no one can now prove – as is proven in an experiment, in technical laws – that they both really originated in a single intelligence, but it seems to me that this unity of intelligence, behind the two intelligences, really appears in our world. And the more we can delve into the world with our intelligence, the more clearly the plan of Creation appears.

In the end, to reach the definitive question I would say: God exists or he does not exist. There are only two options. Either one recognizes the priority of reason, of creative Reason that is at the beginning of all things and is the principle of all things – the priority of reason is also the priority of freedom -, or one holds the priority of the irrational, inasmuch as everything that functions on our earth and in our lives would be only accidental, marginal, an irrational result – reason would be a product of irrationality.

One cannot ultimately “prove” either project, but the great option of Christianity is the option for rationality and for the priority of reason. This seems to me to be an excellent option, which shows us that behind everything is a great Intelligence to which we can entrust ourselves.

However, the true problem challenging faith today seems to me to be the evil in the world: we ask ourselves how it can be compatible with the Creator’s rationality. And here we truly need God, who was made flesh and shows us that he is not only a mathematical reason but that this original Reason is also Love. If we look at the great options, the Christian option today is the one that is the most rational and the most human.

Therefore, we can confidently work out a philosophy, a vision of the world based on this priority of reason, on this trust that the creating Reason is love and that this love is God.

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