Special Relativity and General Relativity Explained With A Ten Hundred Word Vocabulary

A quite lucid explanation of special relativity and general relativity with a limited vocabulary by Randall Munroe of xkcd fame has been reprinted at the New Yorker. A taste:

There once was a doctor with cool white hair. He was well known because he came up with some important ideas. He didn’t grow the cool hair until after he was done figuring that stuff out, but by the time everyone realized how good his ideas were, he had grown the hair, so that’s how everyone pictures him. He was so good at coming up with ideas that we use his name to mean “someone who’s good at thinking.”

Two of his biggest ideas were about how space and time work. This thing you’re reading right now explains those ideas using only the ten hundred words people use the most often. The doctor figured out the first idea while he was working in an office, and he figured out the second one ten years later, while he was working at a school. That second idea was a hundred years ago this year. (He also had a few other ideas that were just as important. People have spent a lot of time trying to figure out how he was so good at thinking.)

The first idea is called the special idea, because it covers only a few special parts of space and time. The other one—the big idea—covers all the stuff that is left out by the special idea. The big idea is a lot harder to understand than the special one. People who are good at numbers can use the special idea to answer questions pretty easily, but you have to know a lot about numbers to do anything with the big idea. To understand the big idea—the hard one—it helps to understand the special idea first.

Ancient DNA from Neolithic Greece and Anatolia

Investigators have managed to get right to the source of the European Neolithic Revolution with ancient DNA from Greece and Anatolia, which is described in two new papers.

Like all other Early European Farmers, genetically, they are quite similar to modern day Sardinians and lack the European and Central Asian steppe contribution that is ubiquitous in most modern European populations.

The Y-DNA in the Neolithic Greeks and Anatolians was, unsurprisingly G2a2.  The mtDNA of two Mesolithic individuals was K1c and the mtDNA of two Neolithic individuals was K1a2.

Of course, their genes look quite unlike modern Greeks and Turks.

Ancient And Modern Ideograms

The Language Log blog highlights the research of Genevieve Von Petzinger into the use of symbols that may be ideograms as a form of written proto-language in Upper Paleolithic cave art as described in a linked TED talk that she has given.

In a somewhat related point, somewhere on my blogging "to do" list is the task of figuring out how many ideograms are in common used by readers of American English, ideally accompanied by examples of the use of ideograms to convey a sound associated with the word for which the ideogram stands (in the tradition of military use of words like Victor or Charlie to spell out words in situations where radio transmission quality is poor) in languages that are predominantly ideographic.

The point, of course, would be to illustrate that the line between phonetic writing systems and ideographic writing systems is one of degree, rather than being an all out either/or alternative.

Some of the common ideograms in American English include:

@ "at"
#  "pound
$ "dollar"
% "percent"
& "and"
~ "approximately"
> "greater than"
< "less than"
= "equals"
+ "plus"
- "minus"

There are many other ideograms familiar to readers of American English that can't be produced with a single keystroke.

There are thousands of Chinese ideograms in the proto-typical ideogram based writing system (Coptic hieroglyphics being another such language).  But, I'd guess that the number of ideograms widely understood by readers of American English.

Some fields, such as mathematics, make particularly heavy use of ideograms which are typically global in reach across the lines of the languages of the people who use them.

Cosmology Based Limits On The Sum Of The Three Neutrino Masses Tighten

The Data

The sum of the three neutrino masses is less than or equal to 110 meV at a 95% confidence level, according to the latest effort to integrate multiple sources of astronomy data including the Planck satellite cosmic microwave radiation background data, the WiggleZ Dark Energy Survey, the Sloan Digital Sky Survey -Data Release 7 (SDSS-DR7) sample of Luminous Red Galaxies (LRG), and Baryon Acoustic Oscillation (BAO) data.

This is confirmed by an independent analysis of the Lyman-α power spectrum from BOSS cited in the paper, which limits the sum of the three neutrino masses to less than or equal to 120 meV at the 95% confidence level.

Background

In an inverted hierarchy of neutrino masses, the minimum sum of the three neutrino masses given current neutrino oscillation data is around 98 +/- 1 meV.

As previously noted at this blog, the state of the art measurements of the difference between the first and second neutrino mass eigenstate is roughly 8.66 +/- 0.12 meV, and the difference between the second and third neutrino mass eigenstate is roughly 49.5 +/- 0.5 meV, which implies that the sum of the three neutrino mass eigenstates cannot be less than about 65.34 meV with 95% confidence.

The hypothesis that there are more than three neutrinos that oscillate with each other has also been largely ruled out by experimental data.

Hypothesis Testing

Taken together, this data favors the normal neutrino mass hierarchy over the inverted neutrino mass hierarchy, even though the inverted neutrino mass hierarchy is not yet ruled out at a 95% confidence interval.

The body text of the paper does not expressly compare the relative likelihoods of the minimal mass normal hierarchy hypothesis to the minimal mass inverted hierarchy hypothesis, but, eyeballing the graphs with the pertinent data, it appears that the normal hierarchy is many times more likely than the inverted hierarchy.

Future Experiments

We need only about a 10% improvement in measurement precision to rule out the inverted neutrino mass hierarchy at the 95% confidence level.  We shouldn't be surprised that the neutrinos appear to have a normal mass hierarchy, as this is what we observe in the up-type quarks, the down-type quarks, and the charged leptons as well.

Knowing whether the neutrino mass eigenstates have a normal or inverted hierarchy also increases the certainty with which we can interpret neutrino oscillation data, for example, in an effort to determine the CP violating phase (if any) of neutrino oscillations.

The tight bound on the absolute neutrino masses discussed below also sets firm expectations regarding the expected amount of neutrinoless double beta decay in any particular model that has Majorana mass neutrinos.  Current experimental precision needs to improve by more than a factor of ten before it can meaningfully distinguish between Dirac and Majorana mass scenarios.

Bounds On Absolute Neutrino Masses Given What We Know

If the neutrinos do have a normal hierarchy, then the experimental bounds on the three neutrino mass eigenstates at the two sigma level based upon the latest data is:

v1: 0 meV to 12 meV              absolute precision +/- 6 meV
v2: 8.42 meV to 21.9 meV      absolute precision +/- 6.74 meV
v3: 56.92 meV to 72.4 meV    absolute precision +/- 7.74 meV

Any higher masses would violate the 110 meV upper bound on the sum of the three neutrino mass eigenstates.  So, while absolute neutrino mass has been called an "unsolved problem" we are tantalizingly close to determining it with a precision that is stunning in absolute terms and compares favorably with the precision with which we know the light quark masses in relative terms.

The bound between the minimum and maximum neutrino mass ranges in an inverted mass hierarchy is currently about 4.7 meV (i.e. +/- 2.35 meV for the lightest of the three).  If the neutrinos do indeed have an inverted mass hierarchy, the bounds upon the absolute masses are tight indeed.

An Unambitious Neutrino Mass Prediction

Given all of the data and the patterns that we see, I personally would be surprised to see anything other than a normal neutrino mass hierarchy with a lightest neutrino mass eigenstate of 2 eV or less, with a mass of 1 meV or less most favored. If that hypothesis is correct, then the neutrino masses would be:

v1: 0 meV to 2 meV          
v2: 8.42 meV to 11.9 meV    
v3: 56.92 meV to 62.4 meV

and the sum of the three neutrino masses would be not more than 76.3 meV (and not less than 65.34 meV).

Footnote On Inflation Constraints

In other news, the constraints on evidence of certain kinds of gravitational waves in the early universe which are predicted by inflation theories is also tightening considerably.  Generally speaking, this data tends to rule out many of the more elaborate inflation scenarios.

Hollywood Habits Reach Particle Physics

Usually, the abstract of a scientific journal article simply summarizes what the article says in a single paragraph (some longer, some shorter).  The main distinction among abstracts is between those that actually put their key conclusion in the lede, and those that bury the lede and tell you what the conclusion is about while forcing you to actually read the paper to get that result.

But, taking a cue from Hollywood, a researcher from the ALICE collaboration has gone one step further.  After the usual abstract telling you what the current paper says, she throws in one more sentence about coming attractions which are not actually included in the paper, stating: "Recent results obtained from these measurements will be presented and the measured cross sections will be compared to perturbative Quantum Chromodynamics calculations at next-to-leading order."

Now, admittedly, maybe she just means that they will present the results in this paper.  But, in context, it reads more to me like an announcement of an upcoming conference paper rather than a description of what is currently being presented.

New Denisovan DNA

Until now, we had one individual's Denisovan autosomal DNA and Denisovan mtDNA from two individuals.  Renanalysis of one of the teeth used the first time around and ancient DNA from a third morphologically similar tooth has given us new data.

We now have (partial) autosomal DNA from two more Denisovan individuals (the one who was the source of the mtDNA sample and a new individual) and a new set of Densiovan mtDNA (with a different haplogroup than the other two samples) from the same new individual.

This new DNA data confirm that all three teeth comes from individuals of the same Denisovan species of archaic hominin.

Denisovans appear to be a sister clade of archaic hominins to Neanderthals and all three samples come from a single cave in Siberia.  But, significant Denisovan admixture (in addition to the ordinary amount of Neanderthal mixture for East Eurasians) is present in modern humans with Australian Aboriginal ancestry or Papuan ancestry.  There may also be an independent source of Denisovan admixture in some Asian Negrito populations (e.g. in the Philippines, but not in the Andamanese) and possibly some very slight traces of Denisovan ancestry in modern humans in Southeast Asia and East Asia.  The introduction to the paper notes that:

In 2008, a finger phalanx from a child (Denisova 3) was found in Denisova Cave in the Altai Mountains in southern Siberia. The mitochondrial genome shared a common ancestor with presentday human and Neandertal mtDNAs about 1 million years ago, or about twice as long ago as the shared ancestor of present-day human and Neandertal mtDNAs. However, the nuclear genome revealed that this individual belonged to a sister group of Neandertals. This group was named Denisovans after the site where the bone was discovered. Analysis of the Denisovan genome showed that Denisovans have contributed on the order of 5% of the DNA to the genomes of present-day people in Oceania, and about 0.2% to the genomes of Native Americans and mainland Asians. 

In 2010, continued archaeological work in Denisova Cave resulted in the discovery of a toe phalanx (Denisova 5), identified on the basis of its genome sequence as Neandertal. The genome sequence allowed detailed analyses of the relationship of Denisovans and Neandertals to each other and to present-day humans. Although divergence times in terms of calendar years are unsure because of uncertainty about the human mutation rate, the bone showed that Denisovan and Neandertal populations split from each other on the order of four times further back in time than the deepest divergence among present-day human populations occurred; the ancestors of the two archaic groups split from the ancestors of present-day humans on the order of six times as long ago as present-day populations. In addition, a minimum of 0.5% of the genome of the Denisova 3 individual was derived from a Neandertal population more closely related to the Neandertal from Denisova Cave than to Neandertals from more western locations .

The abstract also notes that:

The mtDNA of Denisova 8 is more diverged and has accumulated fewer substitutions than the mtDNAs of the other two specimens, suggesting Denisovans were present in the region over an extended period. The nuclear DNA sequence diversity among the three Denisovans is comparable to that among six Neandertals, but lower than that among present-day humans. 

All of this is pretty much what we would expect from additional Denisovan DNA samples and none of them answer the big unsolved questions we have regarding the Denisovans, but it is still nice to have the additional data.

The one point I would add is that the more basal nature of the mtDNA from Denisovan 8 is used to argue that this tooth is much older and represents a prolonged occupations of the site.  This is not a necessary interpretation, or even, in my humble opinion, a likely one.

It is common for particular individuals in modern human populations living at the same time, to have both more basal and less basal mtDNA.  For example, in the same village in Nigeria, there might be one individual with mtDNA which most recently mutated 1,000 years ago, and another individual with mtDNA that most recently mutated 40,000 years ago.

This is an elementary inference from the apparent common mitochondrial origin of all hominins, and the fact that mutations happen with a low random frequency at each generation.  In any substantial sized population, the mtDNA sequence with the least recent mutation is likely to have last mutated many thousands of years earlier than the mtDNA sequence with the most recent mutation.

Given the archaeological context of the teeth, in similar layers of debris in a single cave, the likelihood that there was mtDNA diversity with both older and younger clades of mtDNA present seems more likely to me than a continuous occupation for thirty thousand or so years that managed to be deposited in such close proximity to each other.  One could estimate a predicted population size on this basis and compare it to the estimate using other methods.

The open access PNAS paper is here.  John Hawks has an analysis at his blog.

Connecting the Cultural Dots With Relics And Legends

Gruda Boljevića tumulus is one of the most important archaeological sites found recently in Europe. The reason why I believe that this tumulus is so important, is because it shows that the dolmen building, golden cross disc making culture which developed in Montenegro in the first half of the third millennium BC, has its direct cultural roots in Yamna culture of the Black Sea steppe. Why is this important?

I have already shown that the golden cross discs which appear in Ireland and Britain around 2500 BC have their predecessors in golden cross discs from Montenegro which were dated to 2700 BC (Mala Gruda) and some time between 3050 BC and 2700 BC (Gruda Boljevića). Considering that these golden cross discs first appear in Montenegro and then in Ireland and Britain and nowhere else in between suggests that this cultural trait could have been a result of a direct cultural transfer between Montenegro and Ireland and Britain. Irish archaeologists are reluctant to say whether this cultural influence was due to trade or missionary contacts, or whether it was a consequence of a migration of a group people into Ireland.

This is because Irish archaeologists don't read pseudo histories like the Irish annals. If they did they would have seen the old Irish annals tell us that right at the time when the metallurgy and the first golden cross discs appear in Ireland, a group of people, a tribe a clan lead by Partholón arrives in Ireland. Partholón and his people are credited with introducing cattle husbandry, plowing, cooking, dwellings, trade, and dividing the island in four and most importantly for this story, they are credited with bringing gold which before them was not used in Ireland. They bring the golden cross discs. But where did Partholón and his people come from? The Irish annals tell us that too. They tell us that Partholón arrived to Ireland from the Balkans via Iberia. The Lebor Gabála Érenn, an 11th-century Christian pseudo-history of Ireland, tells us more. It tells us that Partholón came to the Balkans from the Black Sea steppe, the land where at the beginning of the 3rd millennium BC we find Yamna culture...

From the Old European culture blog.

It has long been known that Iberians and remarkably similar genetically to the people of the British Isles, and that both populations are rich in Y-DNA R1b. It has also been recently discovered that the Yamna people had Y-DNA R1b, although more fine distinctions of sub-haplotypes of R1b muddy the connection between the Yamna people and Western Europeans.

It is much less well known, as observed in the comments to this post at the Eurogenes blog, the Croatians and the English, at least at a naive three ancestral component analysis level, seem to have very similar autosomal genetic makeups to each other.

Are the Irish legendary histories telling us the true tale of how the people bearing Y-DNA R1b came to arrive in Western Europe?

The Old European Culture blog, slowly and in individually intriguing and convincing installments is cumulatively making a convincing argument in that direction that can be corroborated with well dated archaeological relics. And, while this analysis doesn't name the Western European cultures involved, it does point to some very specific times and places to look for the culture that probably brought Y-DNA R1b to Europe along with a prominent role for cattle. This time and place turn out to be a pretty good fit to the Bell Beaker culture, while it is a rather poor fit to the megalithic culture that was already present when the Bell Beaker culture emerged.

The path suggested by Irish legendary history is notable, in part, because it is a match for one of several outstanding hypotheses for how Y-DNA R1b wound up in Western Europe, and also because legendary history from Ireland may be more reliable than in many other places because its position at an island isolated ocean frontier would have prevented it from being easily muddled with infusions of legendary histories from elsewhere.

This analysis also doesn't attach a definitively linguistic label to this population. Many scholars assume that the Yamna people of the steppe were Indo-Europeans, and there are some good reasons for that assumption. But, it is hardly definitive. While we have written Sumerian and Egyptian documents from this far back in history, we have no comparably old documents in any other languages.

The record is equally consistent with a hypothesis in which the Yamna people spoke a language that was in contact with Proto-Indo-European and borrowed words from it, but was itself non-Indo-European and related to one or more Caucasian languages. In this scenario, a non-Indo-European Yamna derived language arrives in Western Europe in the time frame, while Western Europe undergoes widespread language shift to Celtic or proto-Celtic languages much later, plus or minus a few centuries from Bronze Age collapse in most places. This scenario is attractive, because otherwise, the heavily Y-DNA R1b Basque people would have had to experience a language shift from an Indo-European language to Basque, which seems far less likely to be the case.

Some Musings About Nomeclature, Mesons And Forces

Almost all of the ordinary matter in the universe (as opposed to "dark matter") is made up of protons and neutrons assembled together into atomic nuclei of atoms with one or more protons and sometimes with sometimes also with some neutrons each.

The atom is completed with one electron per proton in orbit around the nucleus (strictly speaking, "orbit" is a bit misleading as a classical approximation of the actual quantum physics behavior of electrons associated with an atomic nucleus, but it is good enough for the purposes of this post).  If the correspondence between protons and electrons in an "atom" is other than one to one, it is conventional to use the term "ion" rather than "atom" to describe it.

Protons and neutrons are composite particles made up of three quarks each, which are bound together by gluons which are emitted and absorbed by the quarks in the proton or neutron respectively (the generic name that encompasses both protons and neutrons is a "nucleon" often abbreviated "N").

It turns out that protons and neutrons are actually just the two most common examples of a larger class of composite particles made up of three quarks bound together by gluons which are call "baryons".

There is a still more general class of composite particles made up of quarks (not necessarily three) that are bound together by gluons which are called "hadrons" (there is also a hypothetical class of composite particles made up solely of gluons bound together in the absence of quarks often called "glueballs", but I'm not sure if they count as hadrons or not).

Hadrons made up of two quarks (or of blended combinations of two quark pairs) are called "mesons", a term that was coined in the 1930s when the need for a force carrying particle to bind protons in atomic nuclei was hypothesized many years before the first meson was actually observed.

Mesons made up of two different kinds of quarks are usually named based upon the heaviest quark in the mesons.  When that quark is a bottom quark (formerly also known as a beauty quark), the meson is, logically, known as a B meson.  But, most of the lighter mesons were discovered and named before the quark theory of the Standard Model was worked out and the quarks were assigned names.  So, their names are quite arbitrary.

If the heaviest quark in a meson is a charm quark it is usually known as a D meson (but prior to 1986, a meson with a charm quark and a strange quark was known as an F meson). It is also curious that the physics community managed to abolish the historical irregular name for the D_s meson, but not many other of the historical irregular names of other hadrons.

If the heaviest quark in a meson is a strange quark, it is usually known as a "kaon" abbreviated "K".

If we were renaming mesons today, knowing what we do about the Standard Model, they would probably have been called S mesons, C mesons, and B mesons, respectively. But, historical accident and the immense amount of education needed to do the physics that makes knowing these names relevant has allowed the irregular historical monikers to survive.

Different naming conventions apply to "quarkonia", in which a meson and antimeson of the same flavor are both present.

I'd welcome comments from anyone who can explain how it is that Kaons, D mesons, F mesons and any of the other irregular hardon names were assigned (baryon naming, for what it is worth, has fewer irregular hadron names, perhaps because more of them were discovered after the quark model was in place).

As in other areas of language, irregular names for hadrons seem to have persisted more strongly for the most common mesons, than for the rare ones.

We still have arbitrary meson names not precisely tied to quark content for scalar and axial vector mesons, whose quark content is not well understood.

There are several kinds of mesons that contain only up and down quarks (or are at least dominantly comprised of up and down quarks).  The lightest are the pi mesons, also known as pions.  Another kind of meson containing only (or at least dominantly) up and down quarks is the rho meson.

Pions and rhos bring us from the land of history and language in physics to the land of QCD (the physics of the strong force that binds quarks with gluons called "quantum chromodynamics").

It turns out that the force hypothesized back in the 1930s that binds protons and neutrons into atomic nuclei called the "nuclear strong force" is not a fundamental force of nature.  Instead, it is basically a second order effect of the fundamental strong force which is mediated by gluons to hold hadrons together "leaking" out of hadrons to bind them to other nearby hadrons.

The nuclear strong force is mediated not by gluons, which are fundamental in the Standard Model, but by mesons, which are composite particles, although, like gluons, mesons are bosons (a class of particles that has one kind of quantum mechanical behavior) rather than fermions (a class of particles including all baryons and quarks and leptons such as electrons that has another kind of quantum mechanical behavior).

What caught my eye as I was looking into the history of the odd nomenclature of mesons was that while the nuclear strong force is mediated primarily (virtual) pions, it is also mediated in part by other kinds of mesons, especially (virtual) rhos.

This made me think about different kinds of mediator particles for different forces. Electromagnetism is mediated by photons, which are mostly identical, but can differ from each other in frequency, polariziation or helicity.  The strong force is mediated by gluons, which are also mostly identical to each other, but can come in eight different combinations of color charges.

The weak force, in contrast, is mediated by both W bosons (which come in W+ and W- varieties that are antiparticles of each other), and Z bosons which differ in mass and charge from W bosons.  In this respect, the weak force is a bit like the nuclear strong force, which has more than one kind of mediating boson, although the non-fundamental and emergent nuclear strong force, in principle at least within the Standard Model, can have more kinds of potential mediator mesons than the weak force had mediator weak force bosons.

It is interesting to consider how the Standard Model might be subtly modified to reflect the existence of additional weak force bosons that appear much less frequently the W and Z bosons in much the way that rhos and other mesons mediate the nuclear strong force much less frequently than pions do.

There are hypothetical W' and Z' particles which have been searched for experimentally (and thus far, not discovered).  But, it isn't entirely clear that those models are sufficient to account for the kinds of properties we would predict if the collection of particles that mediate the weak force are analogous to the array of mesons that can mediate the nuclear strong force.

Also, the analogy of the nuclear strong force to the weak force suggests that the W and Z bosons, unlike photons and gluons, might be composite particles, rather than being fundamental. (Electroweak unification involves a concept of blending of more fundamental particles to create the W, the Z and the photon, as opposed to a true composite concept.)  This seems like an interesting line of conjecture to extend to see how far one could take it.

And, of course, we've omitted discussion of the Higgs boson, which shows every indication of being basically a part of the electroweak unification scheme that is not closely related to QCD at all, and gravity, which just plain doesn't play well with the Standard Model, but mostly manages to stay out of the way in circumstances where gravity and the Standard Model might clash with each other.

Earliest Evidence of Marijuana Is From Jomon Japan

The earliest evidence of marijuana use by humans (for its hemp fibers) comes from Jomon Japan.

[T]he earliest traces of cannabis in Japan are seeds and woven fibers discovered in the west of the country dating back to the Jomon Period (10,000 BC – 300 BC). Archaeologists suggest that cannabis fibers were used for clothes – as well as for bow strings and fishing lines. These plants were likely cannabis sativa – prized for its strong fibers – a thesis supported by a Japanese prehistoric cave painting which appears to show a tall spindly plant with cannabis’s tell-tale leaves.

Until World War II, it was an important commercial crop in Japan.

This changed after World War II, and Japan now has some of the most strict anti-cannabis laws in the world.

The Selfish Case For Sharing Data

Some scientists horde data, on the theory that this gives them an edge that other scientists in the community lack so that they can publish on something that no one else can publish upon.  Other scientists share data, on the theory that this allows more people to engage with their work and by doing so recognize it.

In academia, the first law of career advancement is publish or perish.  More publications are good. But, academia recognizes superstars based not only upon how many articles one publishes, but how many times those articles are cited by others.

Empirically, if you are a scientist who manages to publish at all (and many people in academia publish very little once they receive tenure), the best way to advance your citation count and thrust yourself into academic superstar status, is to share your data, according to a short preprint examining the question released Sunday, at least in astrophysics, but probably in a much broader array of other disciplines as well.

Overall, making your underlying data available will increase you citation count for a paper by 20% on average.

Waiting For The Next Big Paper

There have been a number of interesting papers on historical genetics and prehistory in the past couple of weeks that I haven't covered because I've been spending lots of days litigating cases in court and in arbitration forums for my clients.

But, a fair amount of interest in the field is devoted to the next big ancient DNA paper which a number of conference announcements discussed by Bell Beaker blogger suggest is coming sometime soon this autumn (in the Northern hemisphere) that will finally shed light on the genetics of the Western European Bell Beaker phenomena.

Of course, it could turn out that the blogging community had read too much into the tea leaves.  But, if such a paper is released, it could resolve a lot of the biggest remaining questions in historical genetics and prehistory.  Western European ancient DNA has been covered much less comprehensively than Central and Eastern Europe in recent autosomal ancient DNA studies, but the archaeology of Western Europe is pretty comprehensive and the technology can now do amazing things with lower quality remains, so there is good reason to be hopeful that the rumored new paper or two will be far more than hype.

Frustratingly, some of these conferences took place in October, but the content of the presentations has nonetheless apparently escaped the Internet's grasp.  But, this does argue against any major breakthrough papers.

This information, in turn, will also shed a lot of light on the question of when, how and from where the Indo-European languages and any predecessor languages arrived in Western Europe, although since pots are not people, new data can only strengthen or weaken arguments about historical linguistics, rather than resolve them definitively.

More On Math Genius Srinivasa Ramanujan

The collected works of the mystical Indian mathematical genius Srinivasa Ramanujan are still yielding valuable mathematical insights almost a century after his death.  The latest insight's involve a class of near counter-examples to Fermat's last theorem (which was subsequently proven to be true in my lifetime, four hundred years after it was proposed).

Razib's Riff On Eurasian Origins

Razib Khan has an extended meditation on the genetic origins of the Eurasians.

Some key points:

(1) Culturally driven punctuated change has been the norm for much of the history of humanity.

(2) One factor driving this population replacement trend has been the fragility of the economic subsistence basis of the conquered people.  Often they have been so fragile and with so little excess that exacting tribute from them and exploiting them as a ruling class has been impossible and instead they were replaced.

(3) The Y-DNA R1a and R1b branches have seen the explosion of the modern sublineages since ca. 3000 BCE, which correspond with the sweeping expansions of these patrilineages into Europe and South Asia, and to a less extent, into the Middle East.

(4) The Neolithic revolution and the subsequent explosion of steppe DNA beyond the steppe has resulted in the integration of populations that were more or less isolated from each other for tens of thousands years created a new homogenized blended population genetic community that had never existed until then.

Put more bluntly, European hunter-gatherers had an extremely different phenotype from the earliest farmers of Europe.  In other words, they were of very distinct races, at least as distinct as Chinese people are from French people today.

One major blending of these two populations gave rise to Early European Farmers to produce a mix much like modern day Sardinians.

Another major blending happened when population genetics from the steppe made its way to Europe sometime in the time frame of the late Copper Age to the early Iron Age to create more or less the modern European phenotype which didn't exist until then.  These steppe people were about half Early European farmer (itself a blend of hunter-gatherers and "basal European farmers", with additional contributions of Ancestral Northern European and Eastern Hunter-Gatherer).  Admixture percentages from substrate populations varied quite a bit in a systemic fashion with more admixture where the food production package brought be the conquering people was less well suited to local conditions.

(5) Y-DNA lineages have a tendency to extend beyond the tightly knit human communities that drive their initial expansions, and also show strong tendencies towards replacement in excess of that seen in autosomal and mitochondrial DNA.

(6) Selective fitness based selection has been ongoing into the modern era.

(7) Razib feels as it most of the puzzle pieces are in place already.  In contrast, I feel as if we have lots of the puzzle pieces together and a good understanding of some regions, but still do not understand the links between the genetic shifts and the historical events that caused them, nearly so well in Western Europe as we do in Eastern Europe and some other areas.