# Why Has More Than One Person Solved Einstein's Equations?

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Viktor T. Toth:

For the same reason more than one person solves most other types of equations.

Unlike simple equations such as, say, the quadratic equation you learn about in high school, most equations do not have nice, simple, general solutions. Rather, specific solutions exist for specific values, or specific sets of values, of the equations' parameters.

Einstein’s field equations are like this. Spelled out in full, they represent a set of 10 coupled second-order differential equations in 10 unknown functions. That is not something that you just whip up a solution for.

The solutions that do exist are solutions representing special cases. The most famous among these is perhaps the Schwarzschild solution. This is a solution that represents a highly symmetric scenario: a vacuum solution (with no matter present), which does not depend on time, and which is spherically symmetric, so it depends only on the radial coordinate. In the end, this turns out to be a solution of only two unknown functions, in the form of two very simple differential equations that can be readily solved.

Other solutions are not this simple. In most cases, nice, elegant, closed form solutions do not exist, so the equations need to be solved numerically. And even that is a challenge, as it is difficult to specify initial values for the unknown functions that correspond to physically meaningful, stable configurations of matter. There is an entire discipline, numerical relativity, devoted to this topic alone.

Bottom line: most equations do not have nice, simple, generic solutions, and Einstein’s field equations are no exception.

# What Do the Numbers and Letters on a Boarding Pass Mean?

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Picture this: You're about to embark on a vacation or business trip, and you have to fly to reach your destination. You get to the airport, make it through the security checkpoint, and breathe a sigh of relief. What do you do next? After putting your shoes back on, you'll probably look at your boarding pass to double-check your gate number and boarding time. You might scan the information screen for your flight number to see if your plane will arrive on schedule, and at some point before boarding, you'll also probably check your zone and seat numbers.

Aside from these key nuggets of information, the other letters and numbers on your boarding pass might seem like gobbledygook. If you find this layout confusing, you're not the only one. Designer and creative director Tyler Thompson once commented that it was almost as if "someone put on a blindfold, drank a fifth of whiskey, spun around 100 times, got kicked in the face by a mule … and then just started puking numbers and letters onto the boarding pass at random."

Of course, these seemingly secret codes aren't exactly secret, and they aren't random either. So let's break it down, starting with the six-character code you'll see somewhere on your boarding pass. This is your Passenger Name Reference (or PNR for short). On some boarding passes—like the one shown below—it may be referred to as a record locator or reservation code.

Piergiuliano Chesi, Wikimedia Commons // Public domain

You might also see a random standalone letter on your boarding pass. This references your booking class. "A" and "F," for instance, are typically used for first-class seats. The letter "Y" generally stands for economy class, while "Q" is an economy ticket purchased at a discounted rate. If you see a "B" you might be in luck—it means you could be eligible for a seat upgrade.

There might be other letters, too. "S/O," which is short for stopover, means you have a layover that lasts longer than four hours in the U.S. or more than 24 hours in another country. Likewise, "STPC" means "stopover paid by carrier," so you'll likely be put up in a hotel free of charge. Score!

One code you probably don’t want to see is "SSSS," which means your chances of getting stopped by TSA agents for a "Secondary Security Screening Selection" are high. For whatever reason, you've been identified as a higher security risk. This could be because you've booked last-minute or international one-way flights, or perhaps you've traveled to a "high-risk country." It could also be completely random.

Still confused? For a visual of what that all these codes look like on a boarding pass, check out this helpful infographic published by Lifehacker.

Have you got a Big Question you'd like us to answer? If so, send it to bigquestions@mentalfloss.com.

# Does Having Allergies Mean That You Have A Decreased Immunity?

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Tirumalai Kamala:

No, allergy isn't a sign of decreased immunity. It is a specific type of immune dysregulation. Autoimmunity, inflammatory disorders such as IBS and IBD, and even cancer are examples of other types of immune dysregulation.

Quality and target of immune responses and not their strength is the core issue in allergy. Let's see how.

—Allergens—substances known to induce allergy—are common. Some such as house dust mite and pollen are even ubiquitous.
—Everyone is exposed to allergens yet only a relative handful are clinically diagnosed with allergy.
—Thus allergens don't inherently trigger allergy. They can but only in those predisposed to allergy, not in everyone.
—Each allergic person makes pathological immune responses to not all but to only one or a few structurally related allergens while the non-allergic don't.
—Those diagnosed with allergy aren't necessarily more susceptible to other diseases.

If the immune response of each allergic person is selectively distorted when responding to specific allergens, what makes someone allergic? Obviously a mix of genetic and environmental factors.

[The] thing is allergy prevalence has spiked in recent decades, especially in developed countries, [which is] too short a time period for purely genetic mutation-based changes to be the sole cause, since that would take multiple generations to have such a population-wide effect. That tilts the balance towards environmental change, but what specifically?

Starting in the 1960s, epidemiologists began reporting a link between infections and allergy—[the] more infections in childhood, [the] less the allergy risk [this is called hygiene hypothesis]. Back then, microbiota weren't even a consideration but now we have learned better, so the hygiene hypothesis has expanded to include them.

Essentially, the idea is that the current Western style of living that rapidly developed over the 20th century fundamentally and dramatically reduced lifetime, and, crucially, early life exposure to environmental microorganisms, many of which would have normally become part of an individual's gut microbiota after they were born.

How could gut microbiota composition changes lead to selective allergies in specific individuals? Genetic predisposition should be taken as a given. However, natural history suggests that such predisposition transitioned to a full fledged clinical condition much more rarely in times past.

Let's briefly consider how that equation might have fundamentally changed in recent times. Consider indoor sanitation, piped chlorinated water, C-sections, milk formula, ultra-processed foods, lack of regular contact with farm animals (as a surrogate for nature) and profligate, ubiquitous, even excessive use of antimicrobial products such as antibiotics, to name just a few important factors.

Though some of these were beneficial in their own way, epidemiological data now suggests that such innovations in living conditions also disrupted the intimate association with the natural world that had been the norm for human societies since time immemorial. In the process such dramatic changes appear to have profoundly reduced human gut microbiota diversity among many, mostly in developed countries.

Unbeknownst to us, an epidemic of absence*, as Moises Velasquez-Manoff evocatively puts it, has thus been invisibly taking place across many human societies over the 20th century in lock-step with specific changes in living standards.

Such sudden and profound reduction in gut microbiota diversity thus emerges as the trigger that flips the normally hidden predisposition in some into clinically overt allergy. Actual mechanics of the process remain the subject of active research.

We (my colleague and I) propose a novel predictive mechanism for how disruption of regulatory T cell** function serves as the decisive and non-negotiable link between loss of specific microbiota and inflammatory disorders such as allergies. Time (and supporting data) will tell if we are right.

* An Epidemic of Absence: A New Way of Understanding Allergies and Autoimmune Diseases Reprint, Moises Velasquez-Manoff

** a small indispensable subset of CD4+ T cells.