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The cosmic "dark ages"

Sunday, March 22, 2009

In brief, "dark ages" refers to the period after recombination occurred, about 380,000 years after the big bang, creating the cosmic microwave background (CMB), up to and partly including the time that the first stars had formed, perhaps as early as four hundred million years later, and caused the reionization of much of the neutral hydrogen in the universe.

That's a mouthful, but it's important to understand in order to have a useful discussion of the conditions that existed when the first stars and first galaxies in the universe formed. Many important open questions in astrophysics right now have to do with the nature of these events. Since I expect to discuss some of these questions, it's necessary to say some things about the "dark ages". That's what this note is about.

Let's start with the CMB. I'm going to give just a sketch. You might want to consult other references if you need more detail.

The period of time in which the CMB emerged is also known as the period of recombination. This was not an instantaneous process, but it did proceed relatively quickly, and is often thought of as a single event.

Basically, before recombination matter (mostly hydrogen and helium) and energy (light, i. e. photons) existed in thermal equilibrium. That is, the following reaction could occur with equal probability in either direction:
H + γ ⇄ p + e-

Here, H stands for a hydrogen atom (with one electron), γ is a photon, p is a proton, and e- is an electron. (We'll ignore helium, for simplicity.) What this formula says is that a photon of sufficient energy could dislodge an electron from a hydrogen atom to form a proton and a free electron, and with equal probability protons and free electrons could combine to form a hydrogen atom and a photon.

As the universe cooled after the big bang, the average temperature of the matter-energy plasma steadily dropped. Before the period of recombination, hydrogen atoms could exist, but not for very long, because most photons had enough energy to completely dislodge an electron, so the reaction went from left to right as often as from right to left.

Over a period of time lasting a few tens of thousands of years the situation changed so that most photons no longer had enough energy to dislodge an electron. (A low energy photon could still interact or "scatter" with a hydrogen atom by raising an electron to a higher energy level, but we can gloss over that detail.) Note that the average or "typical" photon energy may be a lot lower than what's needed to dislodge an electron, as long as there are still enough higher-energy photons around. This is a statistical situation governed by the Maxwell-Boltzmann equation, but all that really matters is that eventually photons and neutral hydrogen atoms "decouple" statistically.

So at some point you have recombination, when electrons combine with protons to make neutral hydrogen, and the process (mostly) doesn't reverse. Occasionally, a photon and a hydrogen atom may still interact, but as the universe expands, it's increasingly less likely for a photon and an atom to come close enough to interact, until the probability of interaction is essentially zero. This second stage is sometimes referred to as "decoupling" of matter and photons.

Thus the period of "dark ages" began right after the relatively brief process of recombination and decoupling. For simplicity, we date this point to a single time when the process was about half complete, roughly 380,000 years after the big bang.

This period is termed "dark", even though there were plenty of photons around, because there were as yet no stars or other compact sources of illumination. (There's another reasons for calling it "dark", which we'll get to in a moment.)

CMB photons have a nearly perfect black-body distribution. There is a clear peak of maximum energy in this distribution. What we observe is that this peak occurs at about 2 mm, in the microwave part of the spectrum. But the time of decoupling, 380,000 years after the big bang, corresponds to a redshift of z≈1100, so at the time of decoupling the peak photon energy was around a wavelength of just 2.2 μm (2200 nm) in the infrared part of the electromagnetic spectrum. (If you need to refresh your memory about how redshift works, check here.) So "dark" is not exactly the right term to use, but compared to abundant light from stars, it's not unreasonable.

After the time of recombination/decoupling, most hydrogen and helium atoms were neutral and un-ionized. This went on for several hundred million years. One of the most interesting open questions is about determining more exactly how long this lasted. We can reasonably guess what probably brought the dark ages to an end: formation of the first stars in the universe. But we don't have a good idea of just when this started, or how long the process took.

In this period, matter was beginning slowly to come together in higher-density clumps under the force of gravity. Dark matter, which outweighed ordinary matter then (as now), by a ratio of about 5.5:1 speeded up this process.

It was precisely this formation of regions of higher matter density that enabled the first stars to form. But because of this same higher density of matter around newborn stars, the abundant high-energy photons produced by these stars were again likely to interact with the nearby un-ionized matter, which scattered them and reduced their energy – dimming the light of these first stars.

One of the large uncertainties concerns the characteristics of this first generation of stars. We have no direct evidence about them. What we think we know about them is based on theoretical models rather than direct observation. (We discussed formation of the first stars back here.) However, it's widely believed that these stars were unlike stars formed later, right up to the present time. The first stars were probably quite large (maybe as much as 200 solar masses), very hot, and very bright. Because they burned their fuel so rapidly, their lifetimes would be very short, perhaps less than a million years.

Some of the light from extremely hot, massive stars such as those of the first generation is well into the ultraviolet part of the spectrum, around 90 nm. Such photons have an energy above 13.6 eV (91.2 nm wavelength), enough to completely ionize hydrogen. If these stars formed, say, 400 million years after the big bang, at a redshift of z≈11, the wavelength of their light would be shifted to the area beyond 1100 nm, which is in the infrared. That's beyond the range of human eyes, or most astronomical instruments. Consequently, we would have a very hard time detecting light from the first stars, even if they weren't so far away (over 13 billion light-years) and obscured by clouds of atomic hydrogen. That time period would still seem "dark" to us – there would be very little we could "see".

However, the first stars radiated so much energy, especially at ultraviolet wavelengths, that over time they effectively reionized all of the hydrogen in their vicinity. And this is (probably) what brought about the epoch of reionization in the universe, effectively ending the "dark ages".

The first stars were probably not part of galaxies, though we don't know for sure. If that's the case, they would be even harder to observe. The first objects we will be able to detect from this period almost certainly will be galaxies or quasars (which are galaxies with a very active central black hole). So the question of when galaxies began to form is separate, but equally puzzling. There is evidence that the first galaxies in fact did form before the end of the dark ages – because we can actually observe a few that show evidence of un-ionized hydrogen.

What we can say for sure is that the first stars must have consisted only of the primordial elements hydrogen and helium, since heavier elements (except for a small trace of lithium) formed and dispersed only when the first stars exploded as supernovae. But that did happen rather quickly, since the first stars were very luminous, and consequently had very brief lives.

As noted, we aren't very sure about when this first generation of stars appeared, because we can't yet observe them directly. But we do have some evidence concerning the epoch of reionization, and hence we have some idea of when it ended.

One kind of evidence involves studying the spectra of some of the most distant objects we are currently able to observe – quasars. We have detected a number of quasars at redshifts between 6 and 7. This range represents a time period from about 780 to 950 million years after the big bang.

There are absorption lines in the spectra of these quasars, and they tell us not only about the redshift, but give other information as well. Among the most important lines are those due to hydrogen that's not fully ionized, such as lines of the Lyman series. For the most part these lines are due to hydrogen in the vicinity of the source, in which case the lines are quite sharp and distinct.

But suppose there is a substantial amount of incompletely ionized hydrogen between us and the source. If this gas is at a distance sufficiently less (in terms of redshift), the absorption lines will be fuzzy instead of sharp. This effect is called a Gunn-Peterson trough.

In 2001 a quasar was identified at z=6.28, which showed a Gunn-Peterson trough, while other quasars with z≤6 did not. This suggests that reionization was mostly complete by 950 million years after the big bang, but not by 900 million years. [1][2]

Quasars, by themselves, are a possible contributor to reionization, in addition to the earliest stars. Quasars certainly produce enough high-energy photons. However, the question is whether there were enough quasars in existence during the epoch of reionization to account for the effect. Since only the very brightest quasars can currently be observed at that distance (z≥6), it's not possible to reliably estimate how many quasars altogether were around then. Rough estimates suggest there weren't enough.

There is another source of evidence for reionization, one very different from the Gunn-Peterson trough. This involves a very detailed study of anisotropies (irregularities at small angular scales) in the CMB. The CMB has many anisotropies due to conditions existing from the earliest moments after the big bang. However, if reionization occurred, certain kinds of additional characteristic anisotropies will also be present. These result from polarization of CMB light due to Thomson scattering of photons by free electrons (if such exist in sufficient numbers). Since free electrons are a by-product of reionization, they provide a very good marker, if they can be detected.

Unfortunately, the earliest data analysis (in 2003) from the Wilkinson Microwave Anisotropy Probe suggested that reionization occurred in the range 11<z<30, which corresponds to a mere 100 million to 420 million years after the big bang. This is not compatible with the quasar evidence. It's also rather implausible at the high z end, if reionization was caused by the first stars.

Fortunately, however, later data analysis (released in 2008) restated the range for reionization to 7≤z≤11. [3] z=7 still doesn't quite mesh with the quasar data, but it's pretty close. z=11 corresponds to 420 million years after the big bang, which is quite plausible for appearance of the first stars. Note that if this range is correct, then the reionization process took a lot of time, maybe 400 to 500 million years. First generation stars almost certainly weren't around that long. Such stars have very short lifetimes, and new stars of this kind can't form, because the gas from which they could form would contain considerable amounts of elements heavier than helium, precluding the formation of more stars like those of the first generation.

A third possible source of evidence comes from surveys looking for very faint, high-redshift galaxies (not quasars). Some objects have been found up to z=7.5 – about 710 million years after the big bang. [4] What isn't clear is whether these objects were either abundant enough or had hot enough stars to contribute significantly to reionization. But when the James Webb Space Telescope goes to work, sometime after mid-2013, we should be able to find many more early galaxies. The planned upgrade to the Hubble Space Telescope this year would also help – if it occurs.

Further reading:

[1] Evidence for Reionization at z ~ 6: Detection of a Gunn-Peterson Trough in a z = 6.28 Quasar – 2001 research article on first evidence for reionization (open access)

[2] First Light: Astronomers Use Distant Quasar To Probe Cosmic "Dark Age," Universe Origins (8/8/01) – press release describing the preceding research

[3] A New Day in Precision Cosmology (3/11/08) – news article describing analysis of WMAP data, including information on reionization

[4] Largest Sample Of Very Distant Galaxies Ever Seen Provide New Insights Into Early Universe (7/24/08) – press release

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Propagandists and marketers agree: emotions may be more reliable when making choices

Wednesday, March 18, 2009

Here's yet another "study" that purports to show "gut reactions" are "better" than logical analysis in decision making. (Recent discussions of this are here, here, here.)

It's about how sales and marketing people and propagandists have learned to take advantage of your emotions for their own benefit.

Of course, that's not how it's presented....

Note the bait-and-switch technique going on in the research report: "reliability" is what the study seems to promise, but the fine print says that what you actually get is consistency.

Admittedly, "reliability" and "consistency" are nearly synonymous in terms of outcomes that marketing people want. But they may not be synonymous at all in terms of what decision-makers (i. e. you) want.

Trust Your Heart: Emotions May Be More Reliable When Making Choices (2/23/09)
"We investigated the following question: To what extent does relying on one's feelings versus deliberative thinking affect the consistency of one's preferences?" write the authors. To get at the question, the authors designed experiments where participants studied and chose among 8-10 products, sometimes relying upon their emotional reactions and sometimes calling upon cognitive skills. Their conclusion: "Emotional processing leads to greater preference consistency than cognitive processing."

Beware of marketing people who presume to advise you about, well, almost anything. But especially about either research conclusions or products they want to sell you.

Note the basic – and rather flagrantly expressed – dishonesty.

On one hand, the objective summary that the researchers offer of their study is: "Emotional processing leads to greater preference consistency than cognitive processing." In other words, the benefit attributed to reliance on emotion for decision making is consistency.

This isn't all that surprising: when people just go with their "gut feelings", the result is more likely to be the same each time the same decision is presented than if the actual specifics of the situation, which may vary from case to case, are analyzed.

This is also the outcome that marketers naturally prefer: predictable, consistent responses to marketing pitches.

But on the other hand, and this is the dishonest part, the authors also write "Indeed, our results suggest that the heart can very well serve as a more reliable compass to greater long-term happiness than pure reason."

This is a specious claim: where in their study did the researchers actually measure the happiness that experimental subjects experience as a result of their choices, as opposed to the consistency of the choices?

In other words, the unspoken idea they're pushing is actually this: you will enjoy more happiness if you allow your decisions to be determined according to how marketing has manipulated your emotions. (E. g.: Just go ask your doc for that Viagra prescription and have more fun in bed! And don't worry about whether your real problem in bed is something Viagra doesn't fix.)

If you think there may be some logic to that, just ask yourself whether letting yourself be manipulated by the greed of others is a good path to your happiness.

The sad truth of human behavior, despite illusions that humans are "rational" creatures, is that emotions are quite often much stronger motivators than reason. And they are generally a lot easier to control and manipulate than rational thinking about facts and logic.

As a result of that, people who stand to profit or otherwise benefit from the actions or beliefs they are able to persuade others to embrace have made a concerted effort, first of all, to persuade people that decisions are best made on an emotional basis.

What's their alternative, if facts and logic do not support whatever such people are advocating? They can always simply lie or engage in misdirection, and that's often done too, of course. But lies can occasionally be exposed, and in extreme cases can even be subject to prosecution (for fraud).

Think I'm making all this up? I suggest reading about one of the masters of propaganda techniques in the 20th century: Edward Bernays. He was a nephew of Sigmund Freud, and literally wrote the book: Propaganda.

Here's how that book begins:
The conscious and intelligent manipulation of the organized habits and opinions of the masses is an important element in democratic society. Those who manipulate this unseen mechanism of society constitute an invisible government which is the true ruling power of our country… We are governed, our minds molded, our tastes formed, our ideas suggested, largely by men we have never heard of. This is a logical result of the way in which our democratic society is organized…

I'll try to summarize some of the history and thinking of Bernays when time permits, but here are some things to read for now, if you're interested:

Stunt Man – book review of a biography on Bernays

Karl Rove & the Spectre of Freud’s Nephew – an essay on Bernays by Stephen Bender

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Into the Eye of the Helix

Tuesday, March 17, 2009

Into the Eye of the Helix
The Helix Nebula, NGC 7293, lies about 700 light-years away in the constellation of Aquarius (the Water Bearer). It is one of the closest and most spectacular examples of a planetary nebula. These exotic objects have nothing to do with planets, but are the final blooming of Sun-like stars before their retirement as white dwarfs. Shells of gas are blown off from a star’s surface, often in intricate and beautiful patterns, and shine under the harsh ultraviolet radiation from the faint, but very hot, central star. The main ring of the Helix Nebula is about two light-years across or half the distance between the Sun and its closest stellar neighbour.

NGC 7293 – click for 1280×1185 image

More: here

MicroRNA and cancer II

Sunday, March 15, 2009

We haven't recently discussed the role of microRNA in cancer. Last time (February 2008) is here. There have been some relatively recent research announcements, so let's have a look.

If you want a refresher on the subject, here's a good introductory overview from Cancer Research UK: Micro RNAs and cancer. Although this piece is fairly elementary, it does have many good links to actual research papers.

Now let's jump into a few summaries of recent research.

What's Feeding Cancer Cells? (2/17/09)
Cancer cells grow and multiply rapidly, so they need lots of nutrients. Much is already known about how cancer cells use blood sugar, but other nutrients are also needed. One of these is the amino acid glutamine. This research found that the transcription factor Myc is able to enhance the expression of the enzyme glutaminase (GLS) in cellular mitochondria. GLS is the first enzyme that processes glutamine to produce energy in mitochondria. (Overexpression of Myc is frequently found in cancer – see here.)

The research found that depriving cancer cells of GLS slowed their growth significantly. It was suspected that Myc could directly up-regulate the GLS gene, but it was not that simple. Instead, it appears that Myc down-regulates genes for two types of microRNA: mi-R23a and mi-R23b. Since these mircoRNAs interfere with the GLS messenger RNA, the net effect of Myc is to enhance GLS production.

Research abstract: c-Myc suppression of miR-23a/b enhances mitochondrial glutaminase expression and glutamine metabolism

A new discovered mutation can hold the key to treat a large number of different cancers (2/17/09)
Since microRNA normally inhibits production of certain proteins, if the proteins affected promote cancer, the inhibitory miRNA will counteract this. This research examined cells of twelve different cancer types.

The basic finding was that mutations of the gene TARBP2 disrupts a pathway that produces anti-oncogenic microRNAs. Mutated TARBP2 diminishes TRBP protein expression, resulting in a defect in the processing of miRNAs. Specifically, the DICER1 protein, which is necessary for miRNA production, is adversely affected.

Research abstract: A TARBP2 mutation in human cancer impairs microRNA processing and DICER1 function

Micro RNA Plays A Key Role In Melanoma Metastasis (2/15/09)
Metastasis is the main process by which cancer becomes deadly, and it is especially problematic in melanoma. In order for cancer cells to metastasize (spread to another body location) they must become able to migrate and establish themselves in the new location. This research finds that the microRNA miR-182 assists in this process.

MiR-182 is frequently up-regulated in human melanoma, usually because melanoma cellular DNA contains extra copies of the miR-182 gene. This up-regulation was shown to assist metastasis. Conversely, down-regulation impedes invasion and triggers apoptosis. Over-expressed miR-182 is shown to repress the expression of two tumor suppressors, FOXO3 and MITF, which are both transcription factors. (For more on FOXO3, see here.)

Research abstract: Aberrant miR-182 expression promotes melanoma metastasis by repressing FOXO3 and microphthalmia-associated transcription factor

New Genes Involved In Acute Lymphoblastic Leukemia Play Fundamental Role In Prognosis Of The Disease (2/6/09)
This investigation found that 13 microRNAs were epigenetically regulated in an abnormal way in many patients with acute lymphoblastic leukaemia (ALL). This means that instead of having actual gene mutations, certain parts of the DNA were methylated in an unusual way, so that the underlying genes, which coded for microRNAs, were down-regulated. More precisely, certain histones of the cell's chromatin were methylated, so that genes located on the DNA wrapped around those histones would not be expressed. The genes involved coded for microRNAs that, evidently, are important for suppressing cancer. When approriate steps were taken to reverse abnormal epigenetic regulation of the affected genes, expression levels rose, confirming that the abnormal methylation patterns were responsible for down-regulation.

65% of 352 ALL patients had one or more methylation abnormalities affecting microRNA under investigation. There was a highly significant positive correlation between patient survival at 14 years after diagnosis and absence of such abnormalities. Consequently, tests for methylation problems with the appropriate microRNA genes should be good predictors of survival prospects.

Research abstract: Epigenetic regulation of microRNAs in acute lymphoblastic leukemia

Researchers Identify Another Potential Biomarker For Lung Cancer (1/13/09)
The research showed that smoking impacts bronchial airway gene expression. Various miRNAs were found that were differently expressed in bronchial airway epithelial cells, mostly down-regulated. Messenger RNAs were also identified, whose expression was inversely correlated to the miRNA expression (so that the corresponding genes appear to be down-regulated by the miRNA.)

MiR-218 was especially noteworthy. It is known to be strongly affected by smoking. The conclusion is that miR-218 levels modulate airway epithelial gene expression response to cigarette smoke, suggesting a role for miRNAs in regulating response to environmental toxins.

Research abstract: MicroRNAs as modulators of smoking-induced gene expression changes in human airway epithelium

Molecule Linked To Muscle Maturation, Muscle Cancer (12/31/08)
The study clarified the role of MiR-29 in myogenesis (muscle cell formation) and found that its down-regulation is associated with rhabdomyosarcoma (RMS), a cancer caused by the proliferation of immature muscle cells. While miR-29 is required for maturation of myoblasts (immature muscle cells), it is also found to be mostly absent from RMS cells.

The study found, further, that the transcription factor NF-κB is responsible for down-regulating miR-29. (NF-κB is an old friend of ours. See here for a small part of the story about its role in inflammation. There's also much more to be said about the role of NF-κB in cancer, where it provides an important connection between inflammation and cancer.)

NF-κB acts to repress miR-29 through another transcription factor, YY1, and Polycomb-group proteins (which remodel chromatin to block transcription factors from DNA promoter sequences).

During myogenesis, NK-κB and YY1 are down-regulated, permitting expression of miR-29, which then further down-regulates YY1 and accelerates cell differentiation. However, in RMS the NF-κB–YY1 pathway remains active, silencing miR-29 and inhibiting differentiation. But reconstitution of miR-29 in RMS in mice inhibits tumor growth and stimulates differentiation,

Research abstract: NF-κB–YY1–miR-29 Regulatory Circuitry in Skeletal Myogenesis and Rhabdomyosarcoma

Harnessing MiRNA Natural Gene Repressors For Anticancer Therapy (12/1/08)
This research investigates the potential therapeutic use of miR-181a through its ability to repress expression of selected genes. If successful, this would provide a very clever kind of immunotherapy for cancer and possibly other diseases.

In immune system T cells miR-181a is highly expressed in developing T cells, but is markedly down-regulated in mature T cells. Mouse bone marrow cells were engineered to express desired therapeutic genes only when miR-181a is down-regulated. These cells were transplanted into mice and allowed to develop into mature T cells. The proteins repressed by miR-181a would therefore not be found in the immature cells, but would show up in the mature T cells. And so when the genes repressed by miR-181a corresponded to proteins that direct T cells to attack tumor cells expressing the protein hCD19, mice with the engineered bone marrow cells were able to reject tumors expressing hCD19.

Research article (open access): Harnessing endogenous miR-181a to segregate transgenic antigen receptor expression in developing versus post-thymic T cells in murine hematopoietic chimeras

Molecule Linked To Aggressive Cancer Growth And Spread Identified (11/13/08)
EZH2 is a polycomb group protein, which helps maintain transcriptional repression of genes over successive cell generations. It contributes to the epigenetic silencing of target genes and enables the survival and metastasis of cancer. The research indicates that miR-101 inhibits the expression and function of EZH2 in cancer cells.

The researchers found that miR-101 is significantly underexpressed in a variety of cancers, including prostate and breast cancer. In human prostate tumors miR-101 expression decreases as cancer progresses and expression of EZH2 increases. MiR-101 is coded for at two locations in cell DNA. One or both of those locations is found to be defective in 37.5% of localized prostate cancer cells and in 66.7% of metastatic cells. This suggests that that underexpression of miR-101 is responsible for overexpression of EZH2 and consequent cancer progression.

More: here (11/13/08)

Research abstract: Genomic Loss of microRNA-101 Leads to Overexpression of Histone Methyltransferase EZH2 in Cancer

Further reading:

MicroRNA—implications for cancer – excellent open access review article

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Splitting of prime ideals in quadratic extensions of ℚ, part 1

Sunday, March 8, 2009

Our discussion of algebraic number theory returns by popular demand. Way back last April we presented some generalities on factorization of prime ideals in extension fields. (For explanation of what that means, including other necessary concepts, you'll have to review earlier installments of this series, which can be found here.)

If this is all Greek to you, I apologize, but that's unavoidable at this stage of a rather technical subject. You may want to go back to the earliest parts of the series to see how the subject got its start and why it may be interesting.

The discussion in the previous installment probably seems rather dry and abstract, but when we look at simple examples, such as quadratic extensions, why it's interesting becomes clearer.

Because of how the ramification indexes and inertial degrees are related, for any prime ideal (p) of ℤ there are only three different possibilities for how the ideal factors in the ring of integers of a quadratic extension:

  1. (p)=P1⋅P2, so (p) splits completely. (e=f=1, g=2)
  2. (p)=P is a prime ideal in ℚ(√d), so p is inert. (e=g=1, f=2)
  3. (p)=P2 where P is prime, and p is ramified. (f=g=1, e=2)

It turns out that there are simple criteria for each of these cases. But figuring out what the criteria are is tricky.

Recall that in ℚ(√3) we found (13)=(4+√3)⋅(4-√3) and (-11)=(8+5√3)⋅(8-5√3), so both (11) and (13) split completely. Clearly, (3)=(√3)2, so (3) is an example of a prime ideal if ℤ that is ramified. How about an example of a prime ideal that is inert in the extension? This is a little harder for a couple of reasons. (p) will be inert just in case it neither splits nor is ramified, but we don't yet have simple criteria to rule out those cases.

So let's back up a little and look at the details. We found examples where (p) splits in the integers of ℚ(√3) by solving the equation ±p=a2-3b2, because that gave elements a±b√3 whose norm was ±p. Being able to find such elements guaranteed that the prime split. But ℚ(√d) with d=3 is a special case, since here d≡3 (mod 4). In that case, and also if d≡2 (mod 4), the integers of the extension have the form a+b√d with a,b∈ℤ.

If d≡1 (mod 4), integers can also have the form (a+b√d)/2, with a,b∈ℤ, and we might have a factorization like (p) = ((a+b√d)/2)⋅((a-b√d)/2), so we would have also to consider solvability of ±4p=a2-3b2. If we were to look at solvability of the approriate equation, according as to whether or not d≡1 (mod 4), the solvability would be a sufficient condition for (p) to split (or ramify if a=0). Notice that this sufficient condition for (p) to split holds regardless of whether or not ℚ(√d) is a PID.

Now we need to find a convenient necessary condition for (p) to split. Unfortunately, solvability of one simple equation is not a necessary condition in general. It would be, as we'll see in a minute, if the ring of integers of ℚ(√d) happens to be a PID, as is true when d=3. However, in quadratic extensions where the ring of integers isn't a PID, being unable to solve the applicable equation doesn't guarantee (p) cannot split, because there might be non-principal ideals that are factors of (p).

So let's ignore that problem for a moment and just focus on the case where the ring of integers of ℚ(√d) is a PID. Can we then find a necessary condition on p for (p) to split or ramify, i. e. for (p) to not be a prime ideal of the integers of ℚ(√d)? That is, what must be true about p if (p) splits or ramifies?

If (p) splits or ramifies, then (p)=P1⋅P2 for nontrivial ideals Pi. (The ideals are the same or distinct according as (p) ramifies or splits.) Assuming ℚ(√d) is a PID, then P1 is generated by a+b√d where both a,b∈ℤ, if d≡2 or 3 (mod 4), or else by (a+b√d)/2 with a,b∈ℤ, if d≡1 (mod 4). Likewise, the conjugate ideal P2 is generated by a-b√d or (a-b√d)/2. Since p∈P1⋅P2, by definition of a product of ideals, p is of the form p = ε(a+b√d)(a-b√d) = ε(a2-db2) or p = ε(a+b√d)(a-b√d)/4 = ε(a2-db2)/4 for some integer ε of ℚ(√d).

Recall that the norm of an element of a Galois extension field is the product of all conjugates of the element. So for an element that is also in the base field, the norm (with respect to a quadratic extension, which is always Galois) is the square of the element. Taking norms of both sides of the possible equations, then either p2 = N(&epsilon)(a2-db2)2 or 16p2 = N(&epsilon)(a2-db2)2. For simplicity, consider just the first case. Then N(ε) is a positive integer that has to be 1, p, or p2. If N(ε)≠1 then N(a±b√d) = a2-db2 must be ±1, so a±b√d must be a unit, and both Pi must be non-proper ideals (i. e. equal to the whole ring). Hence N(ε)=1. This will be true also in the other case (when d≡1 (mod 4)), so ±p=a2-db2 or ±4p=a2-db2. Consequently, solvability of the appropriate equation (depending on d mod 4), is a necessary condition for (p) to split or ramify.

So we have a necessary and sufficient condition for (p) to split or ramify in ℚ(√d), in terms of solvability of Diophantine equations, provided Oℚ(√d) is a PID. Since the only other possibility is for (p) to be inert, we also have a necessary and sufficient condition for that.

However, still assuming that Oℚ(√d) is a PID, we can find a further necessary condition for (p) to split or ramify. Take those equations we just found and reduce them modulo p. Then both equations become a2≡db2 (mod p). Since p is prime, ℤ/pℤ is a field. Assume first that b≢0 (mod p). Then b has an inverse in the finite field. So we have d≡(a/b)2 (mod p). In other words, d is a square mod p. This is the additional necessary condition we were looking for on p in order for (p) to split or ramify. Since it's a necessary condition, if d is not a square mod p, then (p) must not split or ramify, and thus p is inert. And so, for d to be a non-square mod p is a sufficient condition for p to be inert.

(What if b≡0 (mod p)? Then b=b1p. So ±p = a2 - (b1p)2d or else ±4p = a2 - (b1p)2d. Either way, p∣a, hence p2 divides the right side of either equation, and hence the left side also. But that's not possible unless p=2 – which is always a special case.)

To summarize, then, let p≠2 be prime and d square-free and not 0 or 1. Then the solvability of ±tp=a2-db2 (where t is 4 or 1 according as d≡1 (mod 4) or not), is sufficient for (p) to split or ramify. And if the integers of ℚ(√d) are a PID, then solvability of the appropriate equation provides a necessary and sufficient condition for (p) to split or ramify. Further, in that case, d being a square mod p is necessary for (p) to split or ramify.

Remarkably, d being a square mod p is a necessary and sufficient condition for (p) to split or ramify, even if the integers of ℚ(√d) aren't a PID, but that's harder to prove. Since solvability of Diophantine equations is generally not obvious by inspection, it's very convenient to have a necessary and sufficient conditions for (p) to split or ramify simply in terms of the properties of d mod p.

In the next installment, which hopefully will not be as long in coming as this one, we'll show a much cleaner way to state necessary and sufficient conditions for (p) to split, ramify, or remain inert, in the case of any quadratic extension of ℚ, whether or not the ring of integers is a PID. This will be done in terms of what has long been called a "reciprocity law".

However, that will be only the beginning. It turns out that there are far more general kinds of reciprocity laws for many other types of field extensions. That's what "class field theory" is all about, and why the whole subject is so appealing, once you get the basic ideas.


The war continues . . .

The war against science, that is. Waged by followers of certain religious and political ideologies. Aided and abetted by a populace which has little or no interest in what science is or how it works – but likes to take sides anyhow, regardless of their lack of information on the many issues.

Here's a good, brief summary of the current state of play, from Earle Holland:

The war continues . . .
Ultimately, science is an easy target. Inherent in its practice is its openness to critiques. The “facts” of science will always be corrected, changed, modified, enhanced and altered over time as our understanding improves. Opponents of science recognize this and use it to their advantage.

Researchers and research institutions need to understand this sad truth, and prepare accordingly.

If you need any more evidence about this, just read some of the comments to his post. What's amazing to me is that people who have the same uninformed, radio-talk-show-level opinions on the hot-button issues also have the time to read and comment on a blog like Earle's, but (apparently) not enough time to actually learn some of the relevant science.

Also be sure to have a look at this posting at The Scientist's community BBS, McCain twitters against science. Nonsense from a failed political candidate who has been ignorant about most issues involving science, and much else besides. Does he believe his own nonsense? Silly question. He demonstrated in his campaign failing memory of his own positions on various issues, or even regarding how many homes he owns. But he does know what his political party's base wants to hear...

Not good news for antioxidant therapies

Wednesday, March 4, 2009

Forget The Antioxidants? Researchers Cast Doubt On Role Of Free Radicals In Aging (2/17/09)
For more than 40 years, the prevailing explanation of why we get old has been tied to what is called oxidative stress. This theory postulates that when molecules like free radicals, oxygen ions and peroxides build up in cells, they overwhelm the cells' ability to repair the damage they cause, and the cells age.

An industry of "alternative" antioxidant therapies -- such as Vitamin E or CoQ10 supplements in megadose format -- has sprung up as the result of this theory. However, clinical trials have not shown that these treatments have statistically significant effects.

And now researchers at McGill University, in a study published in the February issue of the journal PLoS Genetics, are calling the entire oxidative stress theory into question. Their results show that some organisms actually live longer when their ability to clean themselves of this toxic molecule buildup is partially disabled. Collectively, these molecules are known as reactive oxygen species, or ROS for short.

Author summary of the open-access paper:

Deletion of the Mitochondrial Superoxide Dismutase sod-2 Extends Lifespan in Caenorhabditis elegans
In this paper, we examine the oxidative stress theory of aging using C. elegans as a model system. This theory proposes that aging results from the accumulation of molecular damage caused by reactive oxygen species (ROS). To test this theory, we examined the effect of deleting each of the five individual superoxide dismutase (SOD) genes on lifespan and sensitivity to oxidative stress. Since SOD acts to detoxify ROS, the oxidative stress theory predicts that deletion of sod genes should increase oxidative stress and decrease lifespan. However, in contrast to yeast, flies, and mice, where loss of either cytoplasmic or mitochondrial SOD results in decreased lifespan, we find that none of the sod deletion mutants in C. elegans exhibits a shortened lifespan despite increased sensitivity to oxidative stress. Surprisingly, we find that sod-2 mutant worms have extended lifespan and even worms with the primary cytoplasmic, mitochondrial, and extracellular sod genes deleted can live longer than wild-type worms. By examining genetic interactions with other genes known to extend lifespan and by comparing the phenotype of worms lacking sod-2 to that of known long-lived mitochondrial mutants such as clk-1 or isp-1, we provide evidence that the loss of sod-2 extends lifespan through alteration of mitochondrial function.

Moral neuropolitics and ideology

Sunday, March 1, 2009

An interesting paper was recently brought to my attention. It's all worth reading, but I want to focus on one specific passage, because I think it spotlights a very important question, and provides a springboard for discussion of a number of significant issues in political psychology.

This is the paper:

We Empathize, Therefore We Are: Toward a Moral Neuropolitics

It's by Gary Olson, who is currently Chair of the Political Science Department at Moravian College, Bethlehem, PA.

Olson begins by pointing out the important human characteristic of being able to empathize with the experienced injustice and suffering of others. Citing the empathy felt by people who viewed art depicting victims of the transatlantic slave trade, Olson connects this with recent neuroscience having to do with mirror neurons:
The abolitionist's most potent weapon was the dissemination of drawings of the slave ship Brooks. Rediker asserts that these images were "to be among the most effective propaganda any social movement has ever created" (p. 308).

Based on recent findings from neuroscience we can plausibly deduce that the mirror neurons of the viewer were engaged by these images of others suffering. The appeal was to the public's awakened sense of compassion and revulsion toward graphic depictions of the wholesale violence, barbarity, and torture routinely practiced on these Atlantic voyages. Rediker notes that the images would instantaneously "make the viewer identify and sympathize with the 'injured Africans' on the lower deck of the ship . . ." while also producing a sense of moral outrage (p. 315, Olson, 2008).

In our own day, the nonprofit Edge Foundation recently asked some of the world's most eminent scientists, "What are you optimistic about? Why?" In response, the prominent neuroscientist Marco Iacoboni cited the proliferating experimental work into the neural mechanisms that reveal how humans are "wired for empathy." This is the aforementioned discovery of the mirror neuron system or MNS. The work shows that the same affective brain circuits are automatically mobilized upon feeling one's own pain and the pain of others.

Iacoboni's optimism is grounded in his belief that with the popularization of scientific insights, these findings in neuroscience will seep into public awareness and " . . . this explicit level of understanding of our empathic nature will at some point dissolve the massive belief systems that dominate our societies and that threaten to destroy us" (Iacoboni, 2007, p. 14).

Given that background, the crucial passage in Olson's paper seems to me to be this:
That said, one of the most vexing problems that remains to be explained is why so little progress has been made in extending this empathic orientation to distant lives, to those outside certain in-group moral circles. That is, given a world rife with overt and structural violence, one is forced to explain why our deep-seated moral intuition doesn't produce a more ameliorating effect, a more peaceful world. Iacoboni suggests this disjuncture is explained by massive belief systems, including political and religious ones, operating on the reflective and deliberate level. As de Waal reminds us, evolutionarily, empathy is the original starting point out of which sprang culture and language. But over time, the culture filters and influences how empathy evolves and is expressed (de Waal, 2007, p. 50). These belief systems tend to override the automatic, pre-reflective, neurobiological traits that should bring people together.

Right off the bat, of course, we have a problem. As I've just been writing about (here, here), there may be serious scientific difficulties with the whole concept of a "mirror neuron system" in humans.

Olson says "we can plausibly deduce that the mirror neurons of the viewer were engaged by these images of others suffering." He does mention fairly recent (2007-8) studies that seemed to indicate the existence of mirror neurons in humans, but the skeptical opinions of neuroscientists like Gregory Hickok, whose very recent paper I wrote about, suggest that this whole issue is still up in the air.

But perhaps the issue of mirror neurons isn't all that important. While it can be questioned whether humans have mirror neurons, and whether such mirror neurons (if they do exist) actually account for empathy in humans, surely it would be hard to dispute the existence of empathy in humans.

Or would it? One does have to question how often empathy, even if it exists, plays a dominant role in humans affairs. Sometimes it does, as the ending of the transatlantic slave trade and the final ending of slavery in the U. S. attest. On the other hand, different forms of slavery still persist in the world, as well as all manner of other ills, such as crime, genocide, war, territorial occupations, and economic exploitation.

Nevertheless, let's leave that whole question aside. Human empathy does exist in many circumstances (even if we don't have an adequate neurobiological explanation of it), yet even so, there seem to be social and cultural forces that all too often are able to override empathy. Olson evidently agrees with Iacoboni in identifying the responsible factor as "massive belief systems, including political and religious ones, operating on the reflective and deliberate level."

Let's refer to those political and religious belief systems as "ideology".

The key question, then, is how to explain the substantial power that ideology has over human social behavior – not just behavior that is culturally conditioned, but even behavior that has evolutionary, biological roots, such as the empathy that derives (perhaps) from mirror neurons. That is, we have to explain how "belief systems tend to override the automatic, pre-reflective, neurobiological traits that should bring people together."

It seems to me that this is a rather important open question that political science ought to be addressing.

Because we are dealing with phenomena that can override neurobiological traits, I think we have to look at explanations that also refer to neurobiology. It just makes the most sense to consider the problem as a whole at that level.

How is it that ideology has such a compelling influence over people? What is it that ideology has to offer? How does it fit with underlying psychological factors?

We need some frame of reference to consider these issues. For the sake of concreteness, I'm going to proceed here using a circle of ideas championed by Jonathan Haidt as a convenient reference frame.

What Haidt has proposed is a "moral foundations theory" that claims to identify five "fundamental moral values" that are held by a large number of people, to greater or lesser extents, in a wide variety of cultures around the world (and in history). I think his list is incomplete as a comprehensive foundation for "morality" in general, and there are valid questions about whether some aspects of the "values" he describes even merit consideration as part of a fundamental set. Nevertheless, each of the "values" does have its devoted adherents, and so ipso facto plays a role in social behavior in those cultures where the "value" is recognized.

Here, according to Wikipedia, are the five "fundamental moral values":
  1. Care for others, protecting them from harm. (He also referred to this dimension as Harm.)
  2. Fairness, Justice, treating others equally.
  3. Loyalty to your group, family, nation. (He also referred to this dimension as Ingroup.)
  4. Respect for tradition and legitimate authority. (He also referred to this dimension as Authority.)
  5. Purity, avoiding disgusting things, foods, actions.

Further references (listed at the end of this article): [1], [2], [3], [4].

I'm not ready to make an overall evaluation of Haidt's ideas, but let's look at them and see where they might lead.

On the basis of cross-cultural research Haidt came up with these five distinguishable biological bases of morality. If nothing else, they should be factors that would give significant force and impact to ideologies that are leveraged from them.

The first two factors are (quoting from [1]) "(i) harm, care, and altruism (people are vulnerable and often need protection) or (ii) fairness, reciprocity, and justice (people have rights to certain resources or kinds of treatment)."

Haidt sees these as having evolutionary origins in kin selection and the mechanism of reciprocal altruism.

I think they could have other evolutionary origins as well. In addition, I find it a little difficult to distinguish these two factors. Both encode an obvious "golden rule" sort of morality. However that may be, it seems that mirror neurons, or something equivalent, might play a role in the neurobiology of these factors, which both relate to "empathy".

So another important question we can ask is: what are the evolutionary origins of mirror neurons (or equivalents)? Since other primates, and indeed other animals (e. g. dogs), seem to have something functionally like mirror neurons, and also notions of fairness and justice that resemble human notions, we probably need to look back further in time than the origins of hominids.

It seems to me that something like mirror neurons should be useful equipment for a member of any species that engages in intra-species combat, which is probably a large percentage of species. That certainly doesn't mean many species necessarily have mirror neurons. But, at least, the evolution of mirror neurons certainly could be a useful adaptation for many species. So something like mirror neurons could well be a primary evolutionary development, not a mere side effect of something else. And if empathy, altruism, etc. have roots in such a mechanism, they too are at least useful side effects of evolution, even if they were not directly adaptive in themselves. (Though there are plenty of reasons to think they are adaptive in themselves, especially if you believe in group selection.)

But perhaps the more interesting aspect of Haidt's ideas comprises the three other factors he regards as basic to many human moral codes.

Quoting again from [1], "In addition to the harm and fairness foundations, there are also widespread intuitions about ingroup-outgroup dynamics and the importance of loyalty; there are intuitions about authority and the importance of respect and obedience; and there are intuitions about bodily and spiritual purity and the importance of living in a sanctified rather than a carnal way."

Let's look at these separately. First up is group loyalty, preference for the ingroup, and fear/aversion towards the outgroup. This is pretty clearly, at least in part, a kin selection sort of thing.

There is also another clever evolutionary argument for this factor. It's spelled out by Choi and Bowles in [5]. They call the idea "parochial altruism". The authors present computer simulation evidence for their idea. It has the interesing property of being able to explain the otherwise paradoxical fact that humans are a fairly warlike species, in spite of countervailing empathetic tendencies. I wrote about it here at some length. See also [6].

There are, of course, other evolutionary arguments for group loyalty, such as basic considerations of group selection – successful groups should tend to be cohesive and behave something like kin groups, even in the absence of near kinship. And this would be especially true in time of resource scarcity (which probably was not infrequent).

Among the neurobiological bases of group loyalty would be any neural capabilities that enable the detection of cheating and disloyalty. These need not be discrete neural systems or brain modules. They might be just general capabilities that enable individuals to remember the past behavior of others and reason about it in such a way as to recognize signs of loyalty or disloyalty to the group. Capability for cheater detection might be a general learning ability, like the ability to learn language. Individuals need not be born being good cheater detectors. They just need to be able to learn how to be good at it.

I'm not aware of neurobiological research into cheater detection mechanisms, or other mechanisms that could support group loyalty. Studies of loyalty and cheater detection and conditions for extending trust to others should also connect up easily with the importance of "patriotism" and "solidarity" in various ideologies. This would seem to be a great area for future research.

The bottom line here is that there are very good reasons to expect ingroup/outgroup dynamics to have neurobiological underpinnings, and that these factors would strongly influence ideology. ("Deutschland uber alles." "Defend the fatherland." Etc.)

Turning to the next factor Haidt mentions: authority and the importance of respect and obedience. The psychological power of authority is quite well established. Including the Milgram experiment, which provides a glaring example of how social psychology can override any innate sense of empathy for others. Zimbardo's prison experiment is also relevant.

Respect for and obedience to authority pretty clearly have evolutionary roots in any social species that has a hierarchically organized social life – which is many species, even insects. (Some very recent research shows that even ants will attack other ants that don't follow the rules.)

Interestingly, though, degree of respect for authority varies a lot in humans. (But then, so to does a propensity to cheat.) Political scientists have known for a long time of Theodor Adorno's concept of an "authoritarian personality".

Again, respect for and obedience to authority are key features of many powerful ideologies – features that easily override empathy-based respect for peers.

This is another area that calls for much more neurobiological research. What characteristics of our neurobiology equip us to recognize and defer to authority? Is is just fear based on the consequences of disobedience to actors with substantial social/physical power? Are obedient personalities just a result of a kind of "Stockholm syndrome"?

Haidt's last factor is "intuitions about bodily and spiritual purity." This is, to my mind, the murkiest of the factors. Clearly, humans have evolved good instincts for avoiding contaminated or corrupt food, or other gathering places of pathogenic things. Exactly how that bootstraps into elaborate ideologies featuring supernatural beings is a whole bigger question.

I think there are quite a few additional factors that go into the social psychology of religion and its ideologies, including group loyalty and obedience to authority. And research into such factors seems to be pretty active these days, though not primarily into neurobiological factors. This is a large area of research all by itself. So I don't have clear ideas about how important "purity" is as a factor, by itself, that influences ideology.

Pascal Boyer has an interesting recent essay in Nature ([7]). He writes, "So is religion an adaptation or a by-product of our evolution? Perhaps one day we will find compelling evidence that a capacity for religious thoughts, rather than 'religion' in the modern form of socio-political institutions, contributed to fitness in ancestral times. For the time being, the data support a more modest conclusion: religious thoughts seem to be an emergent property of our standard cognitive capacities."

As an aside, this suggests that what we may find is that political behavior in general, and specific ideologies, are also emergent properties of our standard cognitive capacities. And that's a disquieting thought. Our cognitive capacities were shaped in a time when humans were far fewer in number, and had much less ability to cause large-scale problems for themselves and the rest of the world. Our inherited cognitive traits may result in less sanguine outcomes today than they did in the past. In particular, religion as a common sort of ideology, and Haidt's other moral predispositions, may be less beneficial for humans now than they may have been in the past.

One token of this may be seen in moral principles that do not seem to have deep roots in evolution and neurobiology. For example: aversion to war, faithful attention to truthfulness and honesty in dealing with others, sensitivity to and aversion towards manipulative behavior on the part of social elites, and respect and concern for the natural environment. Such principles don't even appear in Haidt's scheme.

Alternative reference frame: fear and emotions in general

All that said, Haidt's ideas are not the only way to approach the question of neurobiological bases of ideology. Another distinct approach involving neurobiology would center on the importance of the emotion of fear. There is, of course, a voluminous amount of research on the underpinnings of fear and its opposite (trust), as mediated by anatomical features like the amygdala and the limbic system in general.

I've just summarized a number of previous comments on this topic here. Since we're concerned with ideology in this note, it seems especially worth observing the similarities between beliefs about government and about religion, in particular the significant role that fear plays in both (see here).

Fear obviously plays a role in practical politics. How it interacts with organized ideologies is less clear. Certainly, fear of death or great harm is enough to motivate ideologies that feature institutions of authority that "protect" the populace. In any case, fear in some form or other is a strong motivator, another factor that can easily override an individual's healthier empathetic instincts.

Alternative reference frame: personality theory

Yet another direction of possible research involves trying to relate specific personality traits to ideological preferences. Perhaps the best supported of such findings could provide clues as to underlying mechanisms that link psychological tendencies to ideological features.

However, I'm skeptical. Personality traits, in fact, have been defined empirically by looking at the way people tend to use labels to describe other people. The most widely accepted type scheme, the "Big Five", is based on studies of language usage, in which factor analysis is employed to group certain behaviors using labels given to people who exhibit those behaviors. So it's entirely driven by data of a particular type, rather than theory.

That raises two problems. Firstly, there is little logical relationship between either the traits or the behavioral characteristics associated with them and specific ideologies. This is in contrast with Haidt's morality types that do connect reasonably well with ideologies. While empirical correlations between personality traits and ideologies have been found, they usually aren't very strong.

The second problem is that there's little apparent connection between personality traits and neurobiology. Perhaps that will change as more laboratory work is done that investigates the underpinnings of emotions and behavior, but I don't have the sense that clarity is close at hand.

The net result is that personality traits aren't an obvious way to make connections with either ideology or neurobiology.


All in all, it certainly looks like there's a huge need for research to explore how neurobiology interacts with social behavior, politics, and ideology. Understanding the potential role of something like mirror neurons is certainly important. But I think there's a whole lot more we need to understand, especially concerning the darker sides of human nature.

References and further reading:

[1] The New Synthesis in Moral Psychology – 5/18/07 Science review article by Jonathan Haidt

[2] The Roots of Morality – 5/9/08 Science News Focus article by Greg Miller

[3] Is ‘Do Unto Others’ Written Into Our Genes? – 9/18/07 New York Times article by Nicholas Wade

[4] The Moral Instinct – 1/13/08 New York Times Magazine article by Steven Pinker

[5] The Coevolution of Parochial Altruism and War – 10/26/07 research paper in Science by Jung-Kyoo Choi and Samuel Bowles

[6] The Sharp End of Altruism – 10/26/07 Perspectives article in Science by Holly Arrow

[7] Being human: Religion: Bound to believe? – 10/23/08 essay in Nature by Pascal Boyer

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Emotions and politics

We've been having a little discussion about how "gut feelings" influence decisions: here, here, here.

"Gut feelings" are obviously related to emotions, but not entirely. As mentioned here, they can also be based on "implicit memory".

Alongside of this, we've also been discussing a particular type of decision making – where the domain is politics. In that case, the emotions involved are often related to fears of death and mortality. Posts in that vein: here, here, here, here.

I have another, broader post on political psychology coming up, but as a lead-in, I just thought I'd wrap up where we've been so far with decision-making, emotions, and fear specifically.

In order to do that, let's look at one more article published last October, just before the U. S. elections. It's an interview in Scientific American with Sheldon Solomon, a psychology professor at Skidmore College. Solomon's thing is an idea called "terror management theory" (TMT), which is derived from cultural anthropology.

Here's the article, with Solomon's elevator talk on TMT:

Fear, Death and Politics: What Your Mortality Has to Do with the Upcoming Election (10/23/08)
Terror management theory (TMT) is derived from cultural anthropologist Ernest Becker’s efforts to explain the motivational underpinnings of human behavior. According to TMT, one defining characteristic of human beings is self-awareness: we’re alive and we know it. Although self-awareness gives rise to unbridled awe and joy, it can also lead to the potentially overwhelming dread engendered by the realization that death is inevitable, that it can occur for reasons that can never be anticipated or controlled, and that humans are corporeal creatures—breathing pieces of defecating meat no more significant or enduring than porcupines or peaches.

TMT posits that humans ingeniously, but quite unconsciously, solved this existential dilemma by developing cultural worldviews: humanly constructed beliefs about reality shared by individuals in a group that serve to “manage” the potentially paralyzing terror resulting from the awareness of death. All cultures provide a sense of meaning by offering an account of the origin of the universe, a blueprint for acceptable conduct on Earth, and a promise of immortality (symbolically, by creation of large monuments, great works of art or science, amassing great fortunes, having children; and literally, through the various kinds of afterlives that are a central feature of organized religions) to those who live up to culturally prescribed standards.

Thus, although cultures vary considerably, they share in common the same defensive psychological function: to provide meaning and value and in so doing bestow psychological equanimity in the face of death.

So how's that related to politics? Well, as noted in other posts on this topic, thinking about death seems to raise people's awareness of and commitment to ideals and values of the tribe they affiliate with, and reject values and worldviews of other tribes:
A large body of evidence shows that momentarily making death salient, typically by asking people to think about themselves dying, intensifies people’s strivings to protect and bolster aspects of their worldviews, and to bolster their self-esteem. The most common finding is that MS [mortality salience] increases positive reactions to those who share cherished aspects of one’s cultural worldview, and negative reactions toward those who violate cherished cultural values or are merely different.

Some of the evidence Solomon is referring to was uncovered by Solomon himself, along with colleagues Jeff Greenberg and Tom Pyszczynski. For one account, see this 2004 press release, which we referenced here. (There's also a Scientific American article about it, but that requires a few shekels to view.)

Solomon thinks that these considerations definitely influenced the 2004 U. S. presidential election:
Based on these experiments, and other research demonstrating a positive relation between government-issued terror warnings and poll data on Americans’ opinions of President Bush from 2001 to 2004, I believe the outcome of the 2004 presidential election was influenced by repeated reminders of death by President Bush’s campaign, which was carefully crafted to emphasize the war on terrorism and domestic security. ... The effort was aided by the release of a video by Osama bin Laden the weekend before the election. This finding is not to suggest that all support for President Bush was necessarily a defensive reaction to concerns about death, or that the strategic use of fear to advance political agendas, which has a long history in American politics, is confined to the Republican party.

Other accounts of the research of Solomon and colleagues: here, here.

The 2008 U. S. presidential election was a much different story. MS was a lot lower, being replaced by a quite rational dread of growing economic chaos. So, again, there was a strong emotional fear factor, though not directly related to mortality, and it quite likely influenced the election results. Sometimes fear is rational.

Perhaps political scientists could do more work to understand the variety of fear-based appeals that campaigns use, and the conditions under which they are especially effective.

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