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Novel artificial neurons learn independently and are more strongly modeled on their biological counterparts. A team of researchers has programmed these infomorphic neurons and constructed artificial neural networks from them. The special feature is that the individual artificial neurons learn in a self-organized way and draw the necessary information from their immediate environment in the network.

Novel artificial neurons learn independently and are more strongly modeled on their biological counterparts. A team of researchers has programmed these infomorphic neurons and constructed artificial neural networks from them. The special feature is that the individual artificial neurons learn in a self-organized way and draw the necessary information from their immediate environment in the network.

The US has confirmed more than 480 measles cases across 19 states, the highest total since an outbreak in 2019 sickened more than 1200 people

No matter where on Earth you stand, if you have a view of the night sky, and if it is dark enough, you can see the Milky Way. The Milky Way is our home, and its faint clouds of light and shadow have inspired human cultures across the globe. And yet, our view of the Milky Way is limited by our perspective. In many ways, we have learned more from other galaxies than from our own. But when the Gaia spacecraft launched in 2013, all of that changed.

Is it more of a disadvantage to be born poor or Black? Is it worse to be brought up by rich parents in a poor neighborhood, or by poor parents in a rich neighborhood? The answers to these questions lie at the very core of what constitutes a fair society. So how do we know if it is better to have wealthy parents or to grow up in a wealthy neighborhood when “good” things often go together (i.e., kids with rich parents grow up in rich neighborhoods)? When poverty, being Black, and living in a neighborhood with poor schools all predict worse outcomes, how can we disentangle them? Statisticians call this problem multicollinearity, and a number of straightforward methods using some of the largest databases on social mobility ever assembled provide surprisingly clear answers to these questions—the biggest obstacle children face in America is having the bad luck of being born into a poor family.

The immense impact of parental income on the future earnings of children has been established by a tremendous body of research. Raj Chetty and colleagues, in one of the largest studies of social mobility ever conducted,1 linked census data to federal tax returns to show that your parent’s income when you were a child was by far the best predictor of your own income when you became an adult. The authors write, “On average, a 10 percentile increase in parent income is associated with a 3.4 percentile increase in a child’s income.” This is a huge effect; children will earn an average of 34 percent more if their parents are in the highest income decile as compared to the lowest. This effect is true across all races, and Black children born in the top income quintile are more than twice as likely to remain there than White children born in the bottom quintile are to rise to the top. In short, the chances of occupying the top rungs of the economic ladder for children of any race are lowest for those who grow up poor and highest for those who grow up rich. These earnings differences have a broad impact on wellbeing and are strongly correlated with both health and life expectancy.2 Wealthy men live 15 years longer than the poorest, and wealthy women are expected to live 10 years longer than poor women—five times the effect of cancer!

Why is having wealthy parents so important? David Grusky at Stanford, in a paper on the commodification of opportunity, writes:

Although parents cannot directly buy a middleclass outcome for their children, they can buy opportunity indirectly through advantaged access to the schools, neighborhoods, and information that create merit and raise the probability of a middle-class outcome.3

In other words, opportunity is for sale to those who can afford it. This simple point is so obvious that it is surprising that so many people seem to miss it. Indeed, it is increasingly common for respected news outlets to cite statistics about racial differences without bothering to control for class. This is like conducting a study showing that taller children score higher on math tests without controlling for age. Just as age is the best predictor of a child’s mathematical ability, a child’s parent’s income is the best predictor of their future adult income.

Photo by Kostiantyn Li / Unsplash

Although there is no substitute for being born rich, outcomes for children from families with the same income differ in predictable and sometimes surprising ways. After controlling for household income, the largest racial earnings gap is between Asians and Whites, with Whites who grew up poor earning approximately 11 percent less than their Asian peers at age 40, followed by a two percent reduction if you are poor and Hispanic and an additional 11 percent on top of that if you are born poor and Black. Some of these differences, however, result from how we measure income. Using “household income,” in particular, conceals crucial differences between homes with one or two parents and this alone explains much of the residual differences between racial groups. Indeed, the marriage rates between races uncannily recapitulate these exact same earnings gaps—Asian children have a 65 percent chance of growing up in households with two parents, followed by a 54 percent chance for Whites, 41 percent for Hispanics and 17 percent for Blacks4 and the Black-White income gap shrinks from 13 percent to 5 percent5 after we control for income differences between single and two-parent households.

Just as focusing on household income obscures differences in marriage rates between races, focusing on all children conceals important sex differences, and boys who grow up poor are far more likely to remain that way than their sisters.6 This is especially true for Black boys who earn 9.7 percent less than their White peers, while Black women actually earn about one percent more than White women born into families with the same income. Chetty writes:

Conditional on parent income, the black-white income gap is driven entirely by large differences in wages and employment rates between black and white men; there are no such differences between black and white women.7

So, what drives these differences? If it is racism, as many contend, it is a peculiar type. It seems to benefit Asians, hurts Black men, and has no detectable effect on Black women. A closer examination of the data reveals their source. Almost all of the remaining differences between Black men and men of other races lie in neighborhoods. These disadvantages could be caused either by what is called an “individual-level race effect” whereby Black children do worse no matter where they grow up, or by a “place-level race effect” whereby children of all races do worse in areas with large Black populations. Results show unequivocal support for a place-level effect. Chetty writes:

The main lesson of this analysis is that both blacks and whites living in areas with large African-American populations have lower rates of upward income mobility.8

Multiple studies have confirmed this basic finding, revealing that children who grow up in families with similar incomes and comparable neighborhoods have the same chances of success. In other words, poor White kids and poor Black kids who grow up in the same neighborhood in Los Angeles are equally likely to become poor adults. Disentangling the effects of income, race, family structure, and neighborhood on social mobility is a classic case of multicollinearity (i.e., correlated predictors), with race effectively masking the real causes of reduced social mobility—parent’s income. The residual effects are explained by family structure and neighborhood. Black men have the worst outcomes because they grow up in the poorest families and worst neighborhoods with the highest prevalence of single mothers. Asians, meanwhile, have the best outcomes because they have the richest parents, with the lowest rates of divorce, and grow up in the best neighborhoods.

We are all born into an economic caste system in which privilege is imposed on us by the class into which we are helplessly born.

The impact that family structure has on the likelihood of success first came to national attention in 1965, when the Moynihan Report9 concluded that the breakdown of the nuclear family was the primary cause of racial differences in achievement. Daniel Patrick Moynihan, an American sociologist serving as Assistant Secretary of Labor (who later served as Senator from New York) argued that high out-of-wedlock birth rates and the large number of Black children raised by single mothers created a matriarchal society that undermined the role of Black men. In 1965, he wrote:

In a word, a national effort towards the problems of Negro Americans must be directed towards the question of family structure. The object should be to strengthen the Negro family so as to enable it to raise and support its members as do other families.10

A closer look at these data, however, reveals that the disadvantage does not come from being raised by a single mom but rather results from growing up in neighborhoods without many active fathers. In other words, it is not really about whether your own parents are married. Children who grow up in two-parent households in these neighborhoods have similarly low rates of social mobility. Rather, it seems to depend on growing up in neighborhoods with a lot of single parents. Chetty in a nearly perfect replication of Moynihan’s findings writes:

black father presence at the neighborhood level strongly predicts black boys’ outcomes irrespective of whether their own father is present or not, suggesting that what matters is not parental marital status itself but rather community-level factors.11

Although viewing the diminished authority of men as a primary cause of social dysfunction might seem antiquated today, evidence supporting Moynihan’s thesis continues to mount. The controversial report, which was derided by many at the time as paternalistic and racist, has been vindicated12 in large part because the breakdown of the family13 is being seen among poor White families in rural communities today14 with similar results. Family structure, like race, often conceals underlying class differences too. Across all races, the chances of living with both parents fall from 85 percent if you are born in an upper-middle-class family to 30 percent if you are in the lower-middle class.15 The take-home message from these studies is that fathers are a social resource and that boys are particularly sensitive to their absence.16 Although growing up rich seems to immunize children against many of these effects, when poverty is combined with absent fathers, the negative impacts are compounded.17

Children who grow up in families with similar incomes and comparable neighborhoods have the same chances of success. In other words, poor White kids and poor Black kids who grow up in the same neighborhood in Los Angeles are equally likely to become poor adults.

The fact that these outcomes are driven by family structure and the characteristics of communities that impact all races similarly poses a serious challenge to the bias narrative18—the belief that anti-Black bias or structural racism underlies all racial differences19 in outcomes—and suggests that the underlying reasons behind the racial gaps lie further up the causal chain. Why then do we so frequently use race as a proxy for the underlying causes when we can simply use the causes themselves? Consider by analogy the fact that Whites commit suicide at three times the rate of Blacks and Hispanics.20 Does this mean that being White is a risk factor for suicide? Indeed, the link between the income of parents and their children may seem so obvious that it can hardly seem worth mentioning. What would it even mean to study social mobility without controlling for parental income? It is the elephant in the room that needs to be removed before we can move on to analyze more subtle advantages. It is obvious, yet elusive; hidden in plain sight.

If these results are so clear, why is there so much confusion around this issue? In a disconcertingly ignorant tweet, New York Times writer Nikole Hanna-Jones, citing the Chetty study, wrote:

Please don’t ever come in my timeline again bringing up Appalachia when I am discussing the particular perils and injustice that black children face. And please don’t ever come with that tired “It’s class, not race” mess again.21

Is this a deliberate attempt to serve a particular ideology or just statistical illiteracy?22 And why are those who define themselves as “progressive” often the quickest to disregard the effects of class? University of Pennsylvania political science professor Adolph Reed put what he called “the sensibilities of the ruling class” this way:

the model is that the society could be one in which one percent of the population controls 95 percent of the resources, and it would be just, so long as 12 percent of the one percent were black and 14 percent were Hispanic, or half women.23

Perhaps this view and the conviction shared by many elites that economic redistribution is a non-starter accounts for this laser focus on racism, while ignoring material conditions. Racial discrimination can be fixed by simply piling on more sensitivity training or enforcing racial quotas. Class inequities, meanwhile, require real sacrifices by the wealthy, such as more progressive tax codes, wider distribution of property taxes used to fund public schools, or the elimination of legacy admissions at elite private schools.24 The fact that corporations and an educated upper class of professionals,25 which Thomas Piketty has called “the Brahmin left,”26 have enthusiastically embraced this type of race-based identity politics is another tell. Now, America’s rising inequality,27 where the top 0.1 percent have the same wealth as the bottom 90 percent, can be fixed under the guidance of Diversity, Equity and Inclusion (DEI) policies and enforced by Human Resources departments. These solutions pose no threat to corporations or the comfortable lives of the elites who run them. We are obsessed with race because being honest about class would be too painful.

Attending a four-year college is unrivaled in its ability to level the playing field for the most disadvantaged kids from any race and is the most effective path out of poverty.

There are, however, also a number of aspects of human psychology that make the powerful impact of the class into which we are born difficult to see. First, our preference for binary thinking,28 which is less cognitively demanding, makes it easier to conjure up easily divisible, discrete, and visible racial categories (e.g., Black, White, Asian), rather than the continuous and often less visible metric of income. We run into problems when we think about continuous variables such as income, which are hard to categorize and can change across our lifetimes. For example, what is the cutoff between rich and poor? Is $29,000 dollars a year poor but $30,000 middle class? This may also help to explain why we are so reluctant to discuss other highly heritable traits that impact our likelihood of success, like attractiveness and intelligence. Indeed, a classic longitudinal study by Blau and Duncan in 196729 which studied children across the course of their development suggests that IQ might be an even better predictor of adult income than their parent’s income. More recently Daniel Belsky found that an individual’s education-linked genetics consistently predicted a change in their social mobility, even after accounting for social origins.30 Any discussion of IQ or innate differences in cognitive abilities has now become much more controversial, however, and any research into possible cognitive differences between populations is practically taboo today. This broad denial of the role of genetic factors in social mobility is puzzling, as it perpetuates the myth that those who have succeeded have done so primarily due to their own hard work and effort, and not because they happened to be beneficiaries of both environmental and genetic luck. We have no more control over our genetic inheritance than we do over the income of our parents, their marital status, or the neighborhoods in which we spend our childhoods. Nevertheless, if cognitive differences or attractiveness were reducible to clear and discrete categories, (e.g., “dumb” vs. “smart” or “ugly” vs. “attractive”) we might be more likely to notice them and recognize their profound effects. Economic status is also harder to discern simply because it is not stamped on our skin while we tend to think of race as an immutable category that is fixed at birth. Race is therefore less likely to be seen as the fault of the hapless victim. Wealth, however, which is viewed as changeable, is more easily attributed to some fault of the individual, who therefore bears some of the responsibility for being (or even growing up) poor.

We are obsessed with race because being honest about class would be too painful.

We may also fail to recognize the effects of social class because of the availability bias31 whereby our ability to recall information depends on our familiarity with it. Although racial segregation has been falling32 since the 1970s, economic segregation has been rising.33 Although Americans are interacting more with people from different races, they are increasingly living in socioeconomic bubbles. This can make things such as poverty and evictions less visible to middle-class professionals who don’t live in these neighborhoods and make problems with which they may have more experience, such as “problematic” speech, seem more pressing.

Still, even when these studies are published, and the results find their way into the media, they are often misinterpreted. This is because race can mask the root causes of more impactful disadvantages, such as poverty, and understanding their inter-relations requires a basic understanding of statistics, including the ability to grasp concepts such as multicollinearity.

Tragically, the path most certain to help poor kids climb out of poverty is closed to those who are most likely to benefit.

Of course, none of this is to say that historical processes have not played a crucial role in producing the large racial gaps we see today. These causes, however, all too easily become a distraction that provides little useful information about how to solve these problems. Perhaps reparations for some people, or certain groups, are in order, but for most people, it simply doesn’t matter whether your grandparents were impoverished tenant farmers or aristocrats who squandered it all before you were born. Although we are each born with our own struggles and advantages, the conditions into which we are born, not those of our ancestors, are what matter, and any historical injustices that continue to harm those currently alive will almost always materialize in economic disparities. An obsession with historical oppression which fails to improve conditions on the ground is a luxury34 that we cannot afford. While talking about tax policy may be less emotionally satisfying than talking about the enduring legacy of slavery, redistributing wealth in some manner to the poor is critical to solving these problems. These are hard problems, and solutions will require acknowledging their complexity. We will need to move away from a culture that locks people into an unalterable hierarchy of suffering, pitting groups that we were born into against one another, but rather towards a healthier identity politics that emphasizes economic interests and our common humanity.

Photo by Towfiqu barbhuiya / Unsplash

Most disturbing, perhaps, is the fact that the institutions that are most likely to promote the bias narrative and preach about structural racism are those best positioned to help poor children. Attending a four-year college is unrivaled in its ability to level the playing field for the most disadvantaged kids from any race and is the most effective path out of poverty,35 nearly eliminating any other disadvantage that children experience. Indeed, the poorest students who are lucky enough to attend elite four-year colleges end up earning only 5 percent less than their richest classmates.36 Unfortunately, while schools such as Harvard University tout their anti-racist admissions policies,37 admitting Black students in exact proportion to their representation in the U.S. population (14 percent), Ivy League universities are 75 times more likely38 to admit children born in the top 0.1 percent of the income distribution as they are to admit children born in the bottom 20 percent. If Harvard was as concerned with economic diversity as racial diversity, it would accept five times as many students from poor families as it currently does. Tragically, the path most certain to help poor kids climb out of poverty is closed to those who are most likely to benefit.

The biggest obstacle children face in America is having the bad luck of being born into a poor family.

Decades of social mobility research has come to the same conclusion. The income of your parents is by far the best predictor of your own income as an adult. By using some of the largest datasets ever assembled and isolating the effects of different environments on social mobility, research reveals again and again how race effectively masks parental income, neighborhood, and family structure. These studies describe the material conditions of tens of millions of Americans. We are all accidents of birth and imprisoned by circumstances over which we had no control. We are all born into an economic caste system in which privilege is imposed on us by the class into which we are helplessly born. The message from this research is that race is not a determinant of economic mobility on an individual level.39 Even though a number of factors other than parental income also affect social mobility, they operate on the level of the community.40 And although upward mobility is lower for individuals raised in areas with large Black populations, this affects everyone who grows up in those areas, including Whites and Asians. Growing up in an area with a high proportion of single parents also significantly reduces rates of upward mobility, but once again this effect operates on the level of the community and children with single parents do just as well as long as they live in communities with a high percentage of married couples.

One thing these data do reveal—again, and again, and again—however, is that privilege is real. It’s just based on class, not race.

In this age of exoplanet discovery, the flaring of red dwarf stars (M-dwarfs) has taken on new importance. M-dwarfs are known to host many terrestrial planets in their putative habitable zones. The problem is the flaring could make their habitable zones uninhabitable.

Between reading science stuff that I’m going to write about elsewhere, and my pleasure reading of a mammoth book (not one about the woolly mammoth!), I don’t have many books to report on. In fact, I’m about to be at a loss for books to read, and thus will tell you what I’ve read as a way of extracting suggestions from readers.

For a while I was on a Holocaust kick, and (as I think I mentioned earlier) I read The End of the Holocaust, by Alvin Rosenfeld, which you can get from Amazon by clicking below. His thesis is that the true horror of the Holocaust has been lessened by everyone using the word to mean “any bad thing that happened to a lot of people.” The book is especially concerned with Anne Frank, who, he says, was just one of a number of young victims who wrote about their situation, and somehow the attention devoted to her alone lessens the experience of other victims. Well, you can argue about that, but I think the book is worth reading now that words like “genocide,” “concentration camp,” and “Holocaust” are being thrown around willy nilly in a way that distorts their original meaning.

After that I read another short but very famous book about the Holocaust, Night, by Elie Wiesel. Click below to see the Amazon link:

Wiesel, a Romanian-born Jew, was taken to the camps with his family when he was young, and managed to survive two of them, writing several books about his experiences (this one, like the others, is either partly fictional or completely fictional but Night is mostly true). Wiesel was separated from his mother and sisters at Auschwitz-Birkenau, and they did not survive (they were probably gassed). Throughout the book he tries to stay with his father and keep him alive, but the father finally expires on a forced, foodless march through the snow as the prisoners are marched to another camp by the Germans as the Russians approach. Wiesel survived, but just barely.

After the war, Wiesel dedicated himself to writing and lecturing about the Holocaust, and won the Nobel Peace Prize in 1986.  Night is one of the best books about the Holocaust, at least in conveying its horrors, and was recommended by Rosenfeld in the book above. I too recommend it highly, and, at 120 pages, it’s a short read.

Here’s a photo of Buchenwald five days after its liberation by the Red Army, showing the arrangement of bunks and the skeletal nature of those still alive. Wiesel is in the photo; I’ve circled him next to one bed post. What better proof can you have that you really did experience what you wrote about?

Buchenwald concentration camp, photo taken April 16, 1945, five days after liberation of the camp. Wiesel is in the second row from the bottom, seventh from the left, next to the bunk post. From Wikimedia Commons

And below is the behemoth I just finished, Wolf Hall by Hilary Mantel, which won both the Booker Prize and the National Book Circle Award in 2009. Click the cover to go to the Amazon site.

Several people recommended this book highly, and while I think the 730-page monster was very good, I didn’t find it a world classic. It recounts the life of Thomas Cromwell, who started life as the son of a blacksmith but worked his way up to being the head minister of Henry VIII. It deals largely with the intrigues and relationships of Henry’s court, which reminds me of Trump’s America.  Henry was sometimes amiable, but would ruthlessly order the death of those who crossed him, including Anne Boleyn, who met her end simply because she couldn’t provide Henry with a son that could be his heir.  Sir Thomas More is a prominent character, and he too meets his end for refusing to affirm that Anne Boleyn was the lawful queen. Everyone tiptoes around in constant fear of the KIng.

The book is quite involved, and has a big list of characters which are listed on the first page and to which one must constantly refer. It is the convoluted plot and surfeit of characters that made the book hard for me to read. Perhaps I’m getting old and my concentration is waning.  But the dialogue is fascinating, and parts of the book are quite lyrical, with the prose style changing quickly from conversational to rhapsodic. Here’s what Wikipedia says about Mantel’s writing of the book, and the effort shows.

Mantel said she spent five years researching and writing the book, trying to match her fiction to the historical record. To avoid contradicting history she created a card catalogue, organised alphabetically by character, with each card containing notes indicating where a particular historical figure was on relevant dates. “You really need to know, where is the Duke of Suffolk at the moment? You can’t have him in London if he’s supposed to be somewhere else,” she explained.

In an interview with The Guardian, Mantel stated her aim to place the reader in “that time and that place, putting you into Henry’s entourage. The essence of the thing is not to judge with hindsight, not to pass judgment from the lofty perch of the 21st century when we know what happened. It’s to be there with them in that hunting party at Wolf Hall, moving forward with imperfect information and perhaps wrong expectations, but in any case, moving forward into a future that is not pre-determined but where chance and hazard will play a terrific role.”

The book (part of a trilogy) was made into a mini-series for t.v., and here’s the trailer. It feature Cromwell, Cardinal Wolsey, Anne Boleyn, and Henry VIII. Has anyone seen it?

So that’s my reading. Now I ask readers to recommend books for me—and other readers. They can be fiction or nonfiction, so long as they’re absorbing.  I’m not sure I’m yet ready now for another 700-page novel (Amazon’s version says only 600-odd pages, but I have an older edition).  Please put your recommendations, as well as the subject of the book, in the comments.

Clothes that can mimic the feeling of being touched, touch displays that provide haptic feedback to users, or even ultralight loudspeakers. These are just some of the devices made possible using thin silicone films that can be precisely controlled so that they vibrate, flex, press or pull exactly as desired. And all done simply by applying an electrical voltage.

Clothes that can mimic the feeling of being touched, touch displays that provide haptic feedback to users, or even ultralight loudspeakers. These are just some of the devices made possible using thin silicone films that can be precisely controlled so that they vibrate, flex, press or pull exactly as desired. And all done simply by applying an electrical voltage.

Leveraging the power of AI and machine learning technologies, researchers developed a more effective model for predicting how patients with muscle-invasive bladder cancer will respond to chemotherapy. The model harnesses whole-slide tumor imaging data and gene expression analyses in a way that outperforms previous models using a single data type.

Researchers have uncovered a more efficient way to turn carbon dioxide into methanol, a type of alcohol that can serve as a cleaner alternative fuel.

Astronomers have used the James Webb Space Telescope to observe asteroid 2024 YR4, which earlier this year seemed to be at risk of hitting Earth in 2032. Earth is now safe, but astronomers are cheering on a possible collision with the moon

There are a number of ways that exoplanets have been discovered over recent years but a team of astronomers have been exploring other ways. One particular exciting method is to hunt for them by finding their magnetospheres! Earth and Jupiter are a great example of planets that are surrounded by strong magnetospheres that interact with solar activity and when they do, they release radio emissions. The team of researchers have been demonstrating just how they could detect Jupiter’s radio emissions using simulated data. Not only would they be able to detect it, but they could also measure its rotation and even detect interactions with its moons!

The quantum double-slit experiment, in which objects are sent toward and through a pair of slits in a wall,and are recorded on a screen behind the slits, clearly shows an interference pattern. It’s natural to ask, “where does the interference occur?”

The problem is that there is a hidden assumption in this way of framing the question — a very natural assumption, based on our experience with waves in water or in sound. In those cases, we can explicitly see (Fig. 1) how interference builds up between the slits and the screen.

Figure 1: How water waves or sound waves interfere after passing through two slits.

But when we dig deep into quantum physics, this way of thinking runs into trouble. Asking “where” is not as straightforward as it seems. In the next post we’ll see why. Today we’ll lay the groundwork.

Independence and Interference

From my long list of examples with and without interference (we saw last time what distinguishes the two classes), let’s pick a superposition whose pre-quantum version is shown in Fig. 2.

Figure 2: A pre-quantum view of a superposition in which particle 1 is moving left OR right, and particle 2 is stationary at x=3.

Here we have

• particle 1 going from left to right, with particle 2 stationary at x=+3, OR
• particle 1 going from right to left, with particle 2 again stationary at x=+3.

In Fig. 3 is what the wave function Ψ(x1,x2) [where x1 is the position of particle 1 and x2 is the position of particle 2] looks like when its absolute-value squared is graphed on the space of possibilities. Both peaks have x2=+3, representing the fact that particle 2 is stationary. They move in opposite directions and pass through each other horizontally as particle 1 moves to the right OR to the left.

Figure 3: The graph of the absolute-value-squared of the wave function for the quantum version of the system in Fig. 2.

This looks remarkably similar to what we would have if particle 2 weren’t there at all! The interference fringes run parallel to the x2 axis, meaning the locations of the interference peaks and valleys depend on x1 but not on x2. In fact, if we measure particle 1, ignoring particle 2, we’ll see the same interference pattern that we see when a single particle is in the superposition of Fig. 1 with particle 2 removed (Fig. 4):

Figure 4a: The square of the absolute value of the wave function for a particle in a superposition of the form shown in Fig. 2 but with the second particle removed. Figure 4b: A closeup of the interference pattern that occurs at the moment when the two peaks in Fig. 4a perfectly overlap. The real and imaginary parts of the wave function are shown in red and blue, while its square is drawn in black.

We can confirm this in a simple way. If we measure the position of particle 1, ignoring particle 2, the probability of finding that particle at a specific position x1 is given by projecting the wave function, shown above as a function of x1 and x2, onto the x1 axis. [More mathematically, this is done by integrating over x2 to leave a function of x1 only.] Sometimes (not always!) this is essentially equivalent to viewing the graph of the wave function from one side, as in Figs. 5-6.

Figure 5: Projecting the wave function of Fig. 3, at the moment of maximum interference, onto the x1 axis. Compare with the black curve in Fig. 4b.

Because the interference ridges in Fig. 3 are parallel to the x2 axis and thus independent of particle 2’s exact position, we do indeed find, when we project onto the x1 axis as in Fig. 5, that the familiar interference pattern of Fig. 4b reappears.

Meanwhile, if at that same moment we measure particle 2’s position, we will find results centered around x2=+3, with no interference, as seen in Fig. 6 where we project the wave function of Fig. 3 onto the x2 axis.

Figure 6: Projecting the wave function of Fig. 3, at the moment of maximum interference, onto the x2 axis. The position of particle 2 is thus close to x2=3, with no interference pattern.

Why is this case so simple, with the one-particle case in Fig. 4 and the two-particle case in Figs. 3 and 5 so closely resembling each other?

The Cause

It has nothing specifically to do with the fact that particle 2 is stationary. Another example I gave had particle 2 stationary in both parts of the superposition, but located in two different places. In Figs. 7a and 7b, the pre-quantum version of that system is shown both in physical space and in the space of possibilities [where I have, for the first time, put stars for the two possibilities onto the same graph.]

Figure 7a: A similar system to that of Fig. 2, drawn in its pre-quantum version in physical space. Figure 7b: Same as Fig. 7a, but drawn in the space of possibilities.

You can see that the two stars’ paths will not intersect, since one remains at x2=+3 and the other remains at x2=-3. Thus there should be no interference — and indeed, none is seen in Fig. 8, where the time evolution of the full quantum wave function is shown. The two peaks miss each other, and so no interference occurs.

Figure 8: The absolute-value-squared of the wave function corresponding to Figs. 7a-7b.

If we project the wave function of Fig. 8 onto the x1 axis at the moment when the two peaks are at x1=0, we see (Fig. 9) a single peak (because the two peaks, with different values of x2, are projected onto each other). No interference fringes are seen.

Figure 9: At the moment when the first particle is near x1=0, the probability of finding particle 1 as a function of x1 shows a featureless peak, with no interference effects.

Instead the resemblance between Figs. 3-5 has to do with the fact that particle 2 is doing exactly the same thing in each part of the superposition. For instance, as in Fig. 10, suppose particle 2 is moving to the left in both possibilities.

Figure 10: A system similar to that of Fig. 2, but with particle 2 (orange) moving to the left in both parts of the superposition.

(In the top possibility, particles 1 and 2 will encounter one another; but we have been assuming for simplicity that they don’t interact, so they can safely pass right through each other.)

The resulting wave function is shown in Fig. 11:

Figure 11: The absolute-value-squared of the wave function corresponding to Fig.10.

The two peaks cross paths when x1=0 and x2=2. The wave function again shows interference at that location, with fringes that are independent of x2. If we project the wave function onto the x1=0 axis, we’ll get exactly the same thing we saw in Fig. 5, even though the behavior of the wave function in x2 is different.

This makes the pattern clear: if, in each part of the superposition, particle 2 behaves identically, then particle 1 will be subject to the same pattern of interference as if particle 2 were absent. Said another way, if the behavior of particle 1 is independent of particle 2 (and vice versa), then any interference effects involving one particle will be as though the other particle wasn’t even there.

Said yet another way, the two particles in Figs. 2 and 10 are uncorrelated, meaning that we can understand what either particle is doing without having to know what the other is doing.

Importantly, the examples studied in the previous post did not have this feature. That’s crucial in understanding why the interference seen at the end of that post wasn’t so simple.

Independence and Factoring

What we are seeing in Figs. 2 and 10 has an analogy in algebra. If we have an algebraic expression such as

• (a c + b c),

in which c is common to both terms, then we can factor it into

• (a+b)c.

The same is true of the kinds of physical processes we’ve been looking at. In Fig. 10 the two particles’ behavior is uncorrelated, so we can “factor” the pre-quantum system as follows.

Figure 12: The “factored” form of the superposition in Fig. 10.

What we see here is that factoring involves an AND, while superposition is an OR: the figure above says that (particle 1 is moving from left to right OR from right to left) AND (particle 2 is moving from right to left, no matter what particle 1 is doing.)

And in the quantum context, if (and only if) two particles’ behaviors are completely uncorrelated, we can literally factor the wave function into a product of two functions, one for each particle:

• Ψ(x1,x2)=Ψ1(x1)Ψ2(x2)

In this specific case of Fig. 12, where the first particle is in a superposition whose parts I’ve labeled A and B, we can write Ψ1(x1) as a sum of two terms:

• Ψ1(x1)=ΨA(x1) + ΨB(x1)

Specifically, ΨA(x1) describes particle 1 moving left to right — giving one peak in Fig. 11 — and ΨB(x1) describes particle 2 moving right to left, giving the other peak.

But this kind of factoring is rare, and not possible in general. None of the examples in the previous post (or of this post, excepting that of its Fig. 5) can be factored. That’s because in these examples, the particles are correlated: the behavior of one depends on the behavior of the other.

Superposition AND Superposition

If the particles are truly uncorrelated, we should be able to put both particles into superpositions of two possibilities. As a pre-quantum system, that would give us (particle 1 in state A OR state B) AND (particle 2 in state C OR state D) in Fig. 13.

Figure 13: The two particles are uncorrelated, and so their behavior can be factored. The first particle is in a superposition of states A and B, the second in a superposition of states C and D.

The corresponding factored wave function, in which (particle 1 moves left to right OR right to left) AND (particle 2 moves left to right OR right to left), can be written as a product of two superpositions:

• Ψ(x1,x2)=Ψ1(x1)Ψ2(x2) = [ΨA(x1)+ΨB(x1)] [ΨC(x2)+ΨD(x2)]

In algebra, we can expand a similar product

• (a+b)(c+d)=ac+ad+bc+bd

giving us four terms. In the same way we can expand the above wave function into four terms

• Ψ(x1,x2)=ΨA(x1)ΨC(x2)+ΨB(x1)ΨC(x2)+ΨA(x1)ΨD(x2)+ΨB(x1)ΨD(x2)

whose pre-quantum version gives us the four possibilities shown in Fig. 14.

Figure 14: The product in Fig. 13 is expanded into its four distinct possibilities.

The wave function therefore has four peaks, one for each term. The wave function behaves as shown in Fig. 15.

Figure 15: The wave function for the system in Fig. 14 shows interference of two pairs of possibilities, first for particle 1 and later for particle 2.

The four peaks interfere in pairs. The top two and the bottom two interfere when particle 1 reaches x1=0, creating fringes that run parallel to the x2 axis and thus are independent of x2. Notice that even though there are two sets of interference fringes when particle 1 reaches x1=0 in all the superpositions, we do not observe this if we only measure particle 1. When we project the wave function onto the x1 axis, the two sets of interference fringes line up, and we see the same single-particle interference pattern that we’ve seen so many times (Figs. 3-5). That’s all because particles 1 and 2 are uncorrelated.

Figure 16: The first instance of interference, seen in two peaks in Fig. 15 is reduced, when projected on to the x1 axis, to the same interference pattern as seen in Figs. 3-5; the measurement of particle 1’s position will show the same interference pattern in each case, because particles 1 and 2 are uncorrelated.

If at the same moment we measure particle 2 ignoring particle 1, we find (Fig. 17) that particle 2 has equal probability of being near x=2.5 or x=-0.5, with no interference effects.

Figure 17: The first instance of interference, seen in two peaks in Fig. 15, shows two peaks with no interference when projected on to the x2 axis. Thus measurements of particle 2’s position show no interference at this moment.

Meanwhile, the left two and the right two peaks in Fig. 15 subsequently interfere when particle 2 reaches x2=1, creating fringes that run parallel to the x1 axis, and thus are independent of x1; these will show up near x=1 in measurements of particle 2’s position. This is shown (Fig. 18) by projecting the wave function at that moment onto the x2 axis.

Figure 18: During the second instance of interference in Fig. 15, the projection of the wave function onto the x2 axis. Locating the Interference?

So far, in all these examples, it seems that we can say where the interference occurs in physical space. For instance, in this last example, it appears that particle 1 shows interference around x=0, and slightly later particle 2 shows interference around x=1.

But if we look back at the end of the last post, we can see that something is off. In the examples considered there, the particles are correlated and the wave function cannot be factored. And in the last example in Fig. 12 of that post, we saw interference patterns whose ridges are parallel neither to the x1 axis nor to the x2 axis. . .an effect that a factored wave function cannot produce. [Fun exercise: prove this last statement.]

As a result, projecting the wave function of that example onto the x1 axis hides the interference pattern, as shown in Fig. 19. The same is true when projecting onto the x2 axis.

Figure 19: Alhough Fig. 12 of the previous post shows an interference pattern, it is hidden when the wave function is projected onto the x1 axis, leaving only a boring bump. The observable consequences are shown in Fig. 13 of that same post.

Consequently, neither measurements of particle 1’s position nor measurements of particle 2’s position can reveal the interference effect. (This is shown, for particle 1, in the previous post’s Fig. 13.) This leaves it unclear where the interference is, or even how to measure it.

But in fact it can be measured, and next time we’ll see how. We’ll also see that in a general superposition, where the two particles are correlated, interference effects often cannot be said to have a location in physical space. And that will lead us to a first glimpse of one of the most shocking lessons of quantum physics.

One More Uncorrelated Example, Just for Fun

To close, I’ll leave you with one more uncorrelated example, merely because it looks cool. In pre-quantum language, the setup is shown in Fig. 20.

Figure 20: Another uncorrelated superposition with four possibilities.

Now all four peaks interfere simultaneously, near (x1,x2)=(1,-1).

Figure 21: The four peaks simultaneously interfere, generating a grid pattern.

The grid pattern in the interference assures that the usual interference effects can be seen for both particles at the same time, with the interference for particle 1 near x1=1 and that for particle 2 near x2=-1. Here are the projections onto the two axes at the moment of maximal interference.

Figure 22a: At the moment of maximum interference, the projection of the wave function onto the x1 axis shows interference near x1=1. Figure 22b: At the moment of maximum interference, the projection of the wave function onto the x2 axis shows interference near x2=-1.

Reader James Blilie has returned with some recent photos of California. James’s captions are indented, and you can enlarge the pictures by clicking on them. The road he traveled down is my favorite one in the U.S., and, I think, the most scenic. I used to travel it when I went from Davis, CA. to Death Valley to collect flies.

Here is a set from our trip to the southern California desert in January 2025.

We again traveled down US 395 through eastern California to the Palm Desert area for some warmth and sunlight to break up the Pacific Northwest winter.  We returned up I-5 through California to Weed, California where we turned off onto US Hwy 97 through eastern Oregon.

These are mostly landscape photos, which is my thing.  As you can tell from the photos, we were lucky with the weather.

Descending to Mono Lake from Conway Summit:

Moonrise over the White Mountains from the Owens River valley, near Bishop, California:

Mount Whitney range from near Lone Pine, California (also in the Owens Valley):

A shot from hiking in the Andreas Canyon, near Palm Springs, California.  The canyons in the San Jacinto range above Palm Springs have flowing rivers and are full of life:

Next are two shots from a hike in Joshua Tree National Park.  Mojave Yucca (Yucca schidigera) and Teddy Bear Cholla (Cylindropuntia bigelovii).  Both of them shouting at you:  “don’t touch!”:

Next are two shots from the Thousand Palms Oasis.  An overview of the site, which has thousands of California Fan Palms (Washingtonia filifera) and then a show of the palm foliage:

Then a few shots from our homeward journey.

At a rest area on northbound I-5 in the Central Valley of California, we found olive trees growing with lots of fallen fruit underneath them.  (Olea europaea):

Mount McLoughlin and Upper Klamath Lake at dawn (Oregon):

Equipment:

Olympus OM-D E-M5 (micro 4/3 camera, crop factor = 2.0)
LUMIX G X Vario, 12-35mm, f/2.8 ASPH.  (24mm-70mm equivalent)
LUMIX 35-100mm  f/2.8 G Vario  (70-200mm equivalent)
LUMIX G VARIO 7-14mm f/4.0 ASPH

The long-standing question of how animals came to have an anus may have been solved by studies of which genes are active during development in various animals

When the James Webb Space Telescope was launched in December 2021, one of its primary purposes was to see the first galaxies in the Universe forming just a few million years after the Big Bang. In true JWST style though, it has surpassed all expectations and now, a team of astronomers think they have gone even further back, seeing one galaxy clearing the early fog that obscured the Universe! The image represents a point in time 330 million years after the Big Bang and reveals a bright hydrogen emission from the fog surrounding a galaxy. It was somewhat unexpected though as current models predict it would have been blown away long ago!

The fashion retailer, H&M, has announced that they will start using AI generated digital twins of models in some of their advertising. This has sparked another round of discussion about the use of AI to replace artists of various kinds.

Regarding the H&M announcement specifically, they said they will use digital twins of models that have already modeled for them, and only with their explicit permission, while the models retain full ownership of their image and brand. They will also be compensated for their use. On social media platforms the use of AI-generated imagery will carry a watermark (often required) indicating that the images are AI-generated.

It seems clear that H&M is dipping their toe into this pool, doing everything they can to address any possible criticism. They will get explicit permission, compensate models, and watermark their ads. But of course, this has not shielded them from criticism. According to the BBC:

American influencer Morgan Riddle called H&M’s move “shameful” in a post on her Instagram stories.

“RIP to all the other jobs on shoot sets that this will take away,” she posted.

This is an interesting topic for discussion, so here’s my two-cents. I am generally not compelled by arguments about losing existing jobs. I know this can come off as callous, as it’s not my job on the line, but there is a bigger issue here. Technological advancement generally leads to “creative destruction” in the marketplace. Obsolete jobs are lost, and new jobs are created. We should not hold back progress in order to preserve obsolete jobs.

Machines have been displacing human laborers for decades, and all along the way we have heard warnings about losing jobs. And yet, each step of the way more jobs were created than lost, productivity increased, and everybody benefited. With AI we are just seeing this phenomenon spread to new industries. Should models and photographers be protected when line workers and laborers were not?

But I get the fact that the pace of creative destruction appears to be accelerating. It’s disruptive – in good and bad ways. I think it’s a legitimate role of government to try to mitigate the downsides of disruption in the marketplace. We saw what happens when industries are hollowed out because of market forces (such as globalization). This can create a great deal of societal ill, and we all ultimately pay the price for this. So it makes sense to try to manage the transition. This can mean providing support for worker retraining, protecting workers from unfair exploitation, protecting the right for collective bargaining, and strategically investing in new industries to replace the old ones. One factory is shutting down, so tax incentives can be used to lure in a replacement.

Regardless of the details – the point is to thoughtfully manage the creative destruction of the marketplace, not to inhibit innovation or slow down progress. Of course, industry titans will endlessly echo that sentiment. But they appear to be interested mostly in protecting their unfettered ability to make more billions. They want to “move fast and break things”, whether that’s the environment, human lives, social networks, or democracy. We need some balance so that the economy works for everyone. History consistently shows that if you don’t do this, the ultimate outcome is always even more disruptive.

Another angle here is if these large language model AIs were unfairly trained on the intellectual property of others. This mostly applies to artists – train an AI on the work of an artist and then displace that artist with AI versions of their own work. In reality it’s more complicated than that, but this is a legitimate concern. You can theoretically train an LLM only on work that is in the public domain, or give artists the option to opt out of having their work used in training. Otherwise the resulting work cannot be used commercially. We are currently wrestling with this issue. But I think ultimately this issue will become obsolete.

Eventually we will have high quality AI production applications that have been scrubbed of any ethically compromised content but still are able to displace the work of many content creators – models, photographers, writers, artists, vocal talent, news casters, actors, etc. We also won’t have to use digital twins, but just images of virtual people who never existed in real life. The production of sound, images, and video will be completely disconnected (if desired) from the physical world. What then?

This is going to happen, whether we want it to or not. The AI genie is out of the bottle. I don’t think we can predict exactly what will happen. There are too many moving parts, and people will react in unpredictable ways. But it will be increasingly disruptive. Partly we will need to wait and see how it plays out. But we cannot just sit on the sideline and wait for it to happen. Along the way we need to consider if there is a role for thoughtful regulation to limit the breaking of things. My real concern is that we don’t have a sufficiently functional and expert political class to adequately deal with this.

The post H&M Will Use Digital Twins first appeared on NeuroLogica Blog.

The outer planets remain somewhat of a mystery and Neptune is no exception. Voyager 2 has been the only probe that has visited the outermost planet but thankfully the James Webb Space Telescope is powerful enough to reveal it in all its glory. With its cameras regularly fixed on Neptune it has even picked up auroral activity in some of its latest images. The data was gathered back in 2023 using Webb’s Near-Infrared spectrograph which detected the tell tale sign of auroral activity, an emission line of trihydrogen cation. The element appears on other giant planets too when aurora are present.

Some researchers propose that countries should start to rack up a carbon debt once they exceed their carbon budget, obliging them to do more to draw down carbon dioxide, but the idea is unlikely to form part of international climate agreements