Matt Strassler

Ongoing Chance of Northern (or Southern) Lights

As forecast, the cloud of particles from Friday’s solar flare (the “coronal mass emission”, or “CME”) arrived at our planet a few hours after my last post, early in the morning New York time. If you’d like to know how I knew that it had reached Earth, and how I know what’s going on now, scroll down to the end of this post and I’ll show you the data I was following, which is publicly available at all times.

So far the resulting auroras have stayed fairly far north, and so I haven’t seen any — though they were apparently seen last night in Washington and Wyoming, and presumably easily seen in Canada and Alaska. [Caution: sometimes when people say they’ve been “seen”, they don’t quite mean that; I often see lovely photos of aurora that were only visible to a medium-exposure camera shot, not to the naked eye.] Or rather, I should say that the auroras have stayed fairly close to the Earth’s poles; they were also seen in New Zealand.

Russia and Europe have a good opportunity this evening. As for the U.S.? The storm in the Earth’s magnetic field is still going on, so tonight is still a definite possibility for northern states. Keep an eye out! Look for what is usually a white or green-hued glow, often in swathes or in stripes pointing up from the northern horizon, or even overhead if you’re lucky. The stripes can move around quite rapidly.

Now, here’s how I knew all this. I’m no expert on auroras; that’s not my scientific field at all. But the U.S. Space Weather Prediction Center at the National Oceanic and Atmospheric Administration, which needs to monitor conditions in space in case they should threaten civilian and military satellites or even installations on the ground, provides a wonderful website with lots of relevant data.

The first image on the site provides the space weather overview; a screenshot from the present is shown below, with my annotations. The upper graph indicates a blast of x-rays (a form of light not visible to the human eye) which is generated when the solar flare, the magnetically-driven explosion on the sun, first occurs. Then the slower cloud of particles (protons, electrons, and other atomic nuclei, all of which have mass and therefore can’t travel at light’s speed) takes a couple of days to reach Earth. It’s arrival is shown by the sudden jump in the middle graph. Finally, the lower graph measures how active the Earth’s magnetic field is. The only problem with that plot is it tends to be three hours out of date, so beware of that! A “Kp index” of 5 shows significant activity; 6 means that auroras are likely to be moving away from the poles, and 7 or 8 mean that the chances in a place like the north half of the United States are pretty good. So far, 6 has been the maximum generated by the current flare, but things can fluctuate a little, so 6 or 7 might occur tonight. Keep an eye on that lower plot; if it drops back down to 4, forget it, but it it’s up at 7, take a look for sure!

Also on the site is data from the ACE satellite. This satellite sits 950 thousand miles [1.5 million kilometers] from Earth, between Earth and the Sun, which is 93 million miles [150 million kilometers] away. At that vantage point, it gives us (and our other satellites) a little early warning, of up to an hour, before the cloud of slow particles from a solar flare arrives. That provides enough lead-time to turn off critical equipment that might otherwise be damaged. And you can see, in the plot below, how at a certain time in the last twenty-four hours the readings from the satellite, which had been tepid before, suddenly started fluctuating wildly. That was the signal that the flare had struck the satellite, and would arrive shortly at our location.

It’s a wonderful feature of the information revolution that you can get all this scientific data yourself, and not wait around hoping for a reporter or blogger to process it for you. None of this was available when I was a child, and I missed many a sky show. A big thank you to NOAA, and to the U.S. taxpayers who make their work possible.

POSTED BY Matt Strassler

ON July 16, 2017

Lights in the Sky (maybe…)

The Sun is busy this summer. The upcoming eclipse on August 21 will turn day into deep twilight and transfix millions across the United States. But before we get there, we may, if we’re lucky, see darkness transformed into color and light.

On Friday July 14th, a giant sunspot in our Sun’s upper regions, easily visible if you project the Sun’s image onto a wall, generated a powerful flare. A solar flare is a sort of magnetically powered explosion; it produces powerful electromagnetic waves and often, as in this case, blows a large quantity of subatomic particles from the Sun’s corona. The latter is called a “coronal mass ejection.” It appears that the cloud of particles from Friday’s flare is large, and headed more or less straight for the Earth.

Light, visible and otherwise, is an electromagnetic wave, and so the electromagnetic waves generated in the flare — mostly ultraviolet light and X-rays — travel through space at the speed of light, arriving at the Earth in eight and a half minutes. They cause effects in the Earth’s upper atmosphere that can disrupt radio communications, or worse. That’s another story.

But the cloud of subatomic particles from the coronal mass ejection travels a few hundred times slower than light, and it takes it about two or three days to reach the Earth. The wait is on.

Bottom line: a huge number of high-energy subatomic particles may arrive in the next 24 to 48 hours. If and when they do, the electrically charged particles among them will be trapped in, and shepherded by, the Earth’s magnetic field, which will drive them spiraling into the atmosphere close to the Earth’s polar regions. And when they hit the atmosphere, they’ll strike atoms of nitrogen and oxygen, which in turn will glow. Aurora Borealis, Northern Lights.

So if you live in the upper northern hemisphere, including Europe, Canada and much of the United States, keep your eyes turned to the north (and to the south if you’re in Australia or southern South America) over the next couple of nights. Dark skies may be crucial; the glow may be very faint.

You can also keep abreast of the situation, as I will, using NOAA data, available for instance at

http://www.swpc.noaa.gov/communities/space-weather-enthusiasts

The plot on the upper left of that website, an example of which is reproduced below, shows three types of data. The top graph shows the amount of X-rays impacting the atmosphere; the big jump on the 14th is Friday’s flare. And if and when the Earth’s magnetic field goes nuts and auroras begin, the bottom plot will show the so-called “Kp Index” climbing to 5, 6, or hopefully 7 or 8. When the index gets that high, there’s a much greater chance of seeing auroras much further away from the poles than usual.

Keep an eye also on the data from the ACE satellite, lower down on the website; it’s placed to give Earth an early warning, so when its data gets busy, you’ll know the cloud of particles is not far away.

Wishing you all a great sky show!

POSTED BY Matt Strassler

ON July 15, 2017

Penny Wise, Pound Foolish

The cost to American science and healthcare of the administration’s attack on legal immigration is hard to quantify. Maybe it will prevent a terrorist attack, though that’s hard to say. What is certain is that American faculty are suddenly no longer able to hire the best researchers from the seven countries currently affected by the ban. Numerous top scientists suddenly cannot travel here to share their work with American colleagues; or if already working here, cannot now travel abroad to learn from experts elsewhere… not to mention visiting their families. Those caught outside the country cannot return, hurting the American laboratories where they are employed.

You might ask what the big deal is; it’s only seven countries, and the ban is temporary. Well (even ignoring the outsized role of Iran, whose many immigrant engineers and scientists are here because they dislike the ayatollahs and their alternative facts), the impact extends far beyond these seven.

The administration’s tactics are chilling. Scientists from certain countries now fear that one morning they will discover their country has joined the seven, so that they too cannot hope to enter or exit the United States. They will decide now to turn down invitations to work in or collaborate with American laboratories; it’s too risky. At the University of Pennsylvania, I had a Pakistani postdoc, who made important contributions to our research effort. At the University of Washington we hired a terrific Pakistani mathematical physicist. Today, how could I advise someone like that to accept a US position?

Even those not worried about being targeted may decide the US is not the open and welcoming country it used to be. Many US institutions are currently hiring people for the fall semester. A lot of bright young scientists — not just Muslims from Muslim-majority nations — will choose instead to go instead to Canada, to the UK, and elsewhere, leaving our scientific enterprise understaffed.

Well, but this is just about science, yes? Mostly elite academics presumably — it won’t affect the average person. Right?

Wrong. It will affect many of us, because it affects healthcare, and in particular, hospitals around the country. I draw your attention to an article written by an expert in that subject:

http://www.cnn.com/2017/01/29/opinions/trump-ban-impact-on-health-care-vox/index.html

and I’d like to quote from the article (highlights mine):

“Our training hospitals posted job listings for 27,860 new medical graduates last year alone, but American medical schools only put out 18,668 graduates. International physicians percolate throughout the entire medical system. To highlight just one particularly intense specialty, fully 30% of American transplant surgeons started their careers in foreign medical schools. Even with our current influx of international physicians as well as steadily growing domestic medical school spots, the Association of American Medical Colleges estimates that we’ll be short by up to 94,700 doctors by 2025.

The President’s decision is as ill-timed as it was sudden. The initial 90-day order encompasses Match Day, the already anxiety-inducing third Friday in March when medical school graduates officially commit to their clinical training programs. Unless the administration or the courts quickly fix the mess President Trump just created, many American hospitals could face staffing crises come July when new residents are slated to start working.”

If you or a family member has to go into the hospital this summer and gets sub-standard care due to a lack of trained residents and doctors, you know who to blame. Terrorism is no laughing matter, but you and your loved ones are vastly more likely to die due to a medical error than due to a terrorist. It’s hard to quantify exactly, but it is clear that over the years since 2000, the number of Americans dying of medical errors is in the millions, while the number who died from terrorism is just over three thousand during that period, almost all of whom died on 9/11 in 2001. So addressing the terrorism problem by worsening a hospital problem probably endangers Americans more than it protects them.

Such is the problem of relying on alternative facts in place of solid scientific reasoning.

POSTED BY Matt Strassler

ON January 30, 2017

Alternative Facts and Crying Wolf

My satire about “alternative facts” from yesterday took some flak for propagating the controversial photos of inaugurations that some say are real and some say aren’t. I don’t honestly care one bit about those photos. I think it is of absolutely no importance how many people went to Trump’s inauguration; it has no bearing on how he will perform as president, and frankly I don’t know why he’s making such a big deal out of it. Even if attendance was far less than he and his people claim, it could be for two very good reasons that would not reflect badly on him at all.

First, Obama’s inauguration was extraordinarily historic. For a nation with our horrific past — with most of our dark-skinned citizens brought to this continent to serve as property and suffer under slavery for generations — it was a huge step to finally elect an African-American president. I am sure many people chose to go to the 2009 inauguration because it was special to them to be able to witness it, and to be able to say that they were there. Much as many people adore Trump, it’s not so historic to have an aging rich white guy as president.

Second, look at a map of the US, with its population distribution. A huge population with a substantial number of Obama’s supporters live within driving distance or train distance of Washington DC. From South Carolina to Massachusetts there are large left-leaning populations. Trump’s support was largest in the center of the US, but people would not have been able to drive from there or take a train. The cost of travel to Washington could have reduced Trump’s inauguration numbers without reflecting on his popularity.

So as far as I’m concerned, it really doesn’t make any difference if Trump’s inauguration numbers were small, medium or large. It doesn’t count in making legislation or in trade negotiations; it doesn’t count in anything except pride.

But what does count, especially in foreign affairs, is whether people listen to what a president says, and by extension to what his or her press secretary says. What bothers me is not the political spinning of facts. All politicians do that. What bothers me is the claim of having hosted “the best-attended inauguration ever” without showing any convincing evidence, and the defense of those claims (and we heard it again today) that this is because it’s ok to disagree with facts.

If facts can be chosen at will, even in principle, then science ceases to function. Science — a word that means “evidence-based reasoning applied logically to determine how reality really works” — depends on the existence and undeniability of evidence. It’s not an accident that physics, unlike some subjects, does not have a Republican branch and a Democratic branch; it doesn’t have a Muslim, Christian, Buddhist or Jewish branch; there’s just one type. I work with people from many countries and with many religious and political beliefs; we work together just fine, and we don’t have discussions about “alternative facts.”

If instead you give up evidence-based reasoning, then soon you have politics instead of science determining your decisions on all sorts of things that matter to people because it can hurt or kill them: food safety, road safety, airplane safety, medicine, energy policy, environmental protection, and most importantly, defense. A nation that abandons evidence is abandoning applied reason and logic; and the inevitable consequence is that people will die unnecessarily. It’s not a minor matter, and it’s not outside the purview of scientists to take a stand on the issue.

Meanwhile, I find the context for this discussion almost as astonishing as the discussion itself. It’s one thing to say unbelievable things during a campaign, but it’s much worse once in power. For the press secretary on day two of a new administration to make an astonishing and striking claim, but provide unconvincing evidence, has the effect of completely undermining his function. As every scientist knows by heart, extraordinary claims require extraordinary evidence. Imagine the press office at the CERN laboratory announcing the discovery of the Higgs particle without presenting plots of its two experiments’ data; or imagine if the LIGO experimenters had claimed discovery of gravitational waves but shown no evidence. Mistakes are going to happen, but they have to be owned: imagine if OPERA’s tentative suggestion of neutrinos-faster-than-light, which was an experimental blunder, or BICEP’s loud misinterpretation of their cosmological data, had not been publicly retracted, with a clear public explanation of what happened. When an organization makes a strong statement but won’t present clear evidence in favor, and isn’t willing to retract the statement when shown evidence against it, it not only introduces immediate suspicion of the particular claim but creates a wider credibility problem that is extremely difficult to fix.

Fortunately, the Higgs boson has been observed by two different experiments, in two different data-taking runs of both experiments; the evidence is extraordinary. And LIGO’s gravitational waves data is public; you can check it yourself, and moreover there will be plenty of opportunities for further verification as Advanced VIRGO comes on-line this year. But the inauguration claim hasn’t been presented with extraordinary evidence in its favor, and there’s significant contradictory evidence (from train ridership and from local sales). When something extraordinary is actually true, it’s true from all points of view, not subject to “alternative facts”; and the person claiming it has the responsibility to find evidence, of several different types, as soon as possible. If firm evidence is lacking, the claim should only be made tentatively. (A single photo isn’t convincing, one way or the other, especially nowadays.)

As any child knows, it’s like crying wolf. If your loud claim isn’t immediately backed up, or isn’t later retracted with a public admission of error, then the next time you claim something exceptional, people will just laugh and ignore you. And nothing’s worse than suggesting that “I have my facts and you have yours;” that’s the worst possible argument, used only when firm evidence simply isn’t available.

I can’t understand why a press secretary would blow his credibility so quickly on something of so little importance. But he did it. If the new standards are this low, can one expect truth on anything that actually matters? It’s certainly not good for Russia that few outside the country believe a word that Putin says; speaking for myself, I would never invest a dollar there. Unfortunately, leaders and peoples around the world, learning that the new U.S. administration has “alternative facts” at its disposal, may already have drawn the obvious conclusion. [The extraordinary claim that “3-5 million” non-citizens (up from 2-3 million, the previous version of the claim) voted in the last election, also presented without extraordinary evidence, isn’t helping matters.] There’s now already a risk that only the president’s core supporters will believe what comes from this White House, even in a time of crisis or war.

Of course all governments lie sometimes. But it’s wise to tell the truth most of the time, so that your occasional lies will sometimes be thought to be true. Governments that lie constantly, even pointlessly, aren’t believed even when they say something true. They’ve cried wolf too often.

So what’s next? Made-up numbers for inflation, employment, the budget deficit, tax revenue? Invented statistics for the number of people who have health insurance? False information about the readiness of our armed forces and the cost of our self-defense? How far will this go? And how will we know?

POSTED BY Matt Strassler

ON January 24, 2017

What’s all this fuss about having alternatives?

I don’t know what all the fuss is about “alternative facts.” Why, we scientists use them all the time!

For example, because of my political views, I teach physics students that gravity pulls down. That’s why the students I teach, when they go on to be engineers, put wheels on the bottom corners of cars, so that the cars don’t scrape on the ground. But in some countries, the physicists teach them that gravity pulls whichever way the country’s leaders instruct it to. That’s why their engineers build flying carpets as transports for their country’s troops. It’s a much more effective way to bring an army into battle, if your politics allows it. We ought to consider it here.

Another example: in my physics class I claim that energy is “conserved” (in the physics sense) — it is never created out of nothing, nor is it ever destroyed. In our daily lives, energy is taken in with food, converted into special biochemicals for storage, and then used to keep us warm, maintain the pumping of our hearts, allow us to think, walk, breathe — everything we do. Those are my facts. But in some countries, the facts and laws are different, and energy can be created from nothing. The citizens of those countries never need to eat; it is a wonderful thing to be freed from this requirement. It’s great for their military, too, to not have to supply food for troops, or fuel for tanks and airplanes and ships. Our only protection against invasion from these countries is that if they crossed our borders they’d suddenly need fuel tanks.

Facts are what you make them; it’s entirely up to you. You need a good, well-thought-out system of facts, of course; otherwise they won’t produce the answers that you want. But just first figure out what you want to be true, and then go out and find the facts that make it true. That’s the way science has always been done, and the best scientists all insist upon this strategy. As a simple illustration, compare the photos below. Which picture has more people in it? Obviously, the answer depends on what facts you’ve chosen to use. [Picture copyright Reuters] If you can’t understand that, you’re not ready to be a serious scientist!

A third example: when I teach physics to students, I instill in them the notion that quantum mechanics controls the atomic world, and underlies the transistors in every computer and every cell phone. But the uncertainty principle that arises in quantum mechanics just isn’t acceptable in some countries, so they don’t factualize it. They don’t use seditious and immoral computer chips there; instead they use proper vacuum tubes. One curious result is that their computers are the size of buildings. The CDC advises you not to travel to these countries, and certainly not to take electronics with you. Not only might your cell phone explode when it gets there, you yourself might too, since your own molecules are held together with quantum mechanical glue. At least you should bring a good-sized bottle of our local facts with you on your travels, and take a good handful before bedtime.

Hearing all the naive cries that facts aren’t for the choosing, I became curious about what our schools are teaching young people. So I asked a friend’s son, a bright young kid in fourth grade, what he’d been learning about alternatives and science. Do you know what he answered?! I was shocked. “Alternative facts?”, he said. “You mean lies?” Sheesh. Kids these days… What are we teaching them? It’s a good thing we’ll soon have a new secretary of education.

POSTED BY Matt Strassler

ON January 23, 2017

An Interesting Result from CMS, and its Implications

UPDATE 10/26: In the original version of this post, I stupidly forgot to include an effect, causing an error of a factor of about 5 in one of my estimates below. I had originally suggested that a recent result using ALEPH data was probably more powerful than a recent CMS result. But once the error is corrected, the two experiments appear have comparable sensitivity. However, I was very conservative in my analysis of ALEPH, and my guess concerning CMS has a big uncertainty band — so it might go either way. It’s up to ALEPH experts and CMS experts to show us who really wins the day. Added reasoning and discussion marked in green below.

In Friday’s post, I highlighted the importance of looking for low-mass particles whose interactions with known particles are very weak. I referred to a recent preprint in which an experimental physicist, Dr. Arno Heister, reanalyzed ALEPH data in such a search.

A few hours later, Harvard Professor Matt Reece pointed me to a paper that appeared just two weeks ago: a very interesting CMS analysis of 2011-2012 data that did a search of this type — although it appears that CMS [one of the two general purpose detectors at the Large Hadron Collider (LHC)] didn’t think of it that way.

The title of the paper is obscure: “Search for a light pseudo–scalar Higgs boson produced in association with bottom quarks in pp collisions at 8 TeV“. Such spin-zero “pseudo-scalar” particles, which often arise in speculative models with more than one Higgs particle, usually decay to bottom quark/anti-quark pairs or tau/anti-tau pairs. But they can have a very rare decay to muon/anti-muon, which is much easier to measure. The title of the paper gives no indication that the muon/anti-muon channel is the target of the search; you have to read the abstract. Shouldn’t the words “in the dimuon channel” or “dimuon resonance” appear in the title? That would help researchers who are interested in dimuons, but not in pseudo-scalars, find the paper.

Here’s the main result of the paper:

http://cms-results.web.cern.ch/cms-results/public-results/preliminary-results/HIG-15-009/CMS-PAS-HIG-15-009_Figure_005.png

At left is shown a plot of the number of events as a function of the invariant mass of the muon/anti-muon pairs. CMS data is in black dots; estimated background is shown in the upper curve (with top quark backgrounds in the lower curve); and the peak at bottom shows what a simulated particle decaying to muon/anti-muon with a mass of 30 GeV/c² would look like. (Imagine sticking the peak on top of the upper curve to see how a signal would affect the data points). At right are the resulting limits on the rate for such a resonance to be produced and then decay to muon/anti-muon, if it is radiated off of a bottom quark. [A limit of 100 femtobarns means that at most two thousand collisions of this type could have occurred during the year 2012. But note that only about 1 in 100 of these collisions would have been observed, due to the difficulty of triggering on these collisions and some other challenges.]

[Note also the restriction of the mass of the dimuon pair to the range 25 GeV to 60 GeV. This may have done purely been for technical reasons, but if it was due to the theoretical assumptions, that restriction should be lifted.]

While this plot places moderate limits on spin-zero particles produced with a bottom quark, it’s equally interesting, at least to me, in other contexts. Specifically, it puts limits on any light spin-one particle (call it V) that mixes (either via kinetic or mass mixing) with the photon and Z and often comes along with at least one bottom quark… because for such particles the rate to decay to muons is not rare. This is very interesting for hidden valley models specifically; as I mentioned on Friday, new spin-one and spin-zero particles often are produced together, giving a muon/anti-muon pair along with one or more bottom quark/anti-quark pairs.

But CMS interpreted its measurement only in terms of radiation of a new particle off a bottom quark. Now, what if a V particle decaying sometimes to muon/anti-muon were produced in a Z particle decay (a possibility alluded to already in 2006). For a different production process, the angles and energies of the particles would be different, and since many events would be lost (due to triggering, transverse momentum cuts, and b-tagging inefficiencies at low transverse momentum) the limits would have to be fully recalculated by the experimenters. It would be great if CMS could add such an analysis before they publish this paper.

Still, we can make a rough back-of-the-envelope estimate, with big caveats. The LHC produced about 600 million Z particles at CMS in 2012. The plot at right tells us that if the V were radiated off a bottom quark, the maximum number of produced V’s decaying to muons would be about 2000 to 8000, depending on the V mass. Now if we could take those numbers directly, we’d conclude that the fraction of Z’s that could decay to muon/anti-muon plus bottom quarks in this way would be 3 to 12 per million. But sensitivity of this search to a Z decay to V is probably much less than for a V radiated off bottom quarks [because (depending on the V mass) either the bottom quarks in the Z decay would be less energetic and more difficult to tag, or the muons are less energetic on average, or both.] So I’m guessing that the limits on Z decays to V are always worse than one per hundred thousand, for any V mass. (Thanks to Wei Xue for catching an error as I was finalizing my estimate.)

If that guess/estimate is correct, then the CMS search does not rule out the possibility of a hundred or so Z decays to V particles at each of the various LEP experiments. That said, old LEP searches might rule this possibility out; if anyone knows of such a search, please comment or contact me.

As for whether Heister’s analysis of the ALEPH experiment’s data shows signs of such a signal, I think it unlikely (though some people seemed to read my post as saying the opposite.) As I pointed out in Friday’s post, not only is the excess too small for excitement on its own, it also is somewhat too wide and its angular correlations look like the background (which comes, of course, from bottom quarks that decay to charm quarks plus a muon and neutrino.) The point of Friday’s post, and of today’s, is that we should be looking.

In fact, because of Heister’s work (which, by the way, is his own, not endorsed by the ALEPH collaboration), we can draw interesting if rough conclusions. Ignore for now the bump at 30 GeV/c²; that’s more controversial. What about the absence of a bump between 35 and 50 GeV/c²? Unless there are subtleties with his analysis that I don’t understand, we learn that at ALEPH there were fewer than ten Z decays to a V particle (plus a source of bottom quarks) for V in this mass range. ~~That limits such Z decays to about 2 to 3 per million.~~ OOPS: Dumb mistake!! At this step, I forgot to include the fact that requiring bottom quarks in the ALEPH events only works about 20% of the time (thanks to Imperial College Professor Oliver Buchmuller for questioning my reasoning!) The real number is therefore about 5 times larger, more like 10 to 15 per million. If that rough estimate is correct, it would provide a ~~more powerful constraint than~~ constraint roughly comparable to the current CMS analysis.

[[BUT: In my original argument I was very conservative. When I said “fewer than 10”, I was trying to be brief; really, looking at the invariant mass plot, the allowed numbers of excess events for a V with mass above 36 GeV is typically fewer than 7 or even 5. And that doesn’t include any angular information, which for many signals would reduce the numbers to 3. Including these effects properly brings the ALEPH bound back down to something close to my initial estimate. Anyway, it’s clear that CMS is nipping at ALEPH’s heels, but I’m still betting they haven’t passed ALEPH — yet.]]

So my advice would be to set Heister’s bump aside and instead focus on the constraints that one can obtain, and the potential discoveries that one could make, with this type of analysis, either at LEP or at LHC. That’s where I think the real lesson lies.

POSTED BY Matt Strassler

ON October 25, 2016

Author: Matt Strassler

Ongoing Chance of Northern (or Southern) Lights

POSTED BY Matt Strassler

Lights in the Sky (maybe…)

POSTED BY Matt Strassler

Penny Wise, Pound Foolish

POSTED BY Matt Strassler

Alternative Facts and Crying Wolf

POSTED BY Matt Strassler

What’s all this fuss about having alternatives?

POSTED BY Matt Strassler

An Interesting Result from CMS, and its Implications

POSTED BY Matt Strassler

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Author: Matt Strassler

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POSTED BY Matt Strassler

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POSTED BY Matt Strassler

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POSTED BY Matt Strassler

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