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With a pandemic raging, I hear a lot about testing. One problem is we don't have an adequate supply of test kits to screen for Covid-19. But another problem would arise even if we had enough kits to test everyone. To explain, I'll describe an example presented in Chance in Biology: Using Probability to Explore Nature, by Mark Denny and Steven Gaines. Their analysis was based on testing for HIV, but I'll recast the story in terms of the coronavirus. Suppose we have an accurate test for Covid-19. No test is perfect, so let's assume it's correct 99.5% of the time. In other words, its error rate is 0.5% (one error for every two hundred tests). Assume this error rate is the same for false positives and false negatives. Furthermore, assume Covid-19 is not prevalent, infecting only 0.1% of the population. I doubt this is a good assumption right now, when the virus seems to be infecting everyone, but I can imagine a time not too far in the future (a few weeks maybe, a few months probably) when the fraction of people having the virus is small. In a population of a million people, 1000 would have Covid-19 and 999,000 would not. First, consider what happens when you test the thousand that are infected. The test would come back positive for Covid-19 in 99.5% of the cases, so it would produce 995 true positives. The test would be in error and give a negative result 0.5% of the time, giving 5 false negatives (the test would say you don't have the disease when in fact you do). Next, consider the results from testing the 999,000 people who are not infected. Again, the test accuracy is 99.5%, so you would get a negative result (true negatives) for 994,005 people (0.995 times 999,000). You'd make a mistake 0.5% of the time, so you get false positives in 4995 cases (the test would say you have the disease when in fact you don't). Let's summarize: True Positives 995 False Positives 4,995 True Negatives 994,005 False Negatives 5 Now, suppose Michigan Governor Gretchen Whitmer (I'm a big fan of the governor) decides that—to prevent the virus from flaring up again—everyone will be tested; anyone who tests positive for Covid-19 must be quarantined, and anyone who tests negative is free to go wherever they please (restaurants, sporting events, movies... oh how I miss them!). Out of a million people, 5990 will test positive (995 + 4995). Of those, 4995 are mistakes (false positives). In other words, 83% of the people who are forced into quarantine are false positives; they don't have the disease, but the blasted test said they do and they must suffer for it. Only 17% of the quarantined people are infected. Is this acceptable? Maybe. We might decide as a state that it's worth it; we insist on quarantines, even if five out of six people forced into isolation are actually healthy. The needs of the many outweigh the needs of the few. Or, we might decide this is too high a price to pay; people are innocent until proven guilty, so to speak. This decision is not simple. Whitmer will have people mad at her regardless of what she does. But we must decide based on the facts. If the incidence of Covid-19 is 0.1%, and the accuracy of the test is 99.5%, then five out of six quarantined people will be false positives. That's how the math works. Denny and Gaines summarize it this way: “Although individual tests have a low chance of error, most individuals who are tested are not infected with [Covid-19]. Therefore, we are multiplying a small probability of false positives by a large number of uninfected individuals. Even a minute probability of false positives for individual tests can in this circumstance produce many more false positives than true positives. As long as the disease is rare, even a very accurate test of infection will not be able to accurately identify infected individuals in a random test.” I don't know the prevalence of Covid-19 or the accuracy of Covid-19 tests. The numbers for the coronavirus may be different than what I used in this example. My point is that even an accurate test can produce many false positives for a rare disease. That's an important insight, whether or not the numbers are accurate for our current plague. Chance in Biology is full of examples like this one. It's a good book (although I like Denny's Air and Water better). It's a useful supplement to Intermediate Physics for Medicine and Biology, providing all the probability you need to understand biological physics. Originally published on April 13, 2020 at https://hobbieroth.blogspot.com/2020/04/a-problem-with-testing.html

The world is a careful orchestration of facts and logics that lay onto each other to give varied results. Choices are invariably between few options, like video simulations, that pile onto each other to result in vastly different outcomes. The law of multiplication in its grandest application. Successful is he who can decipher these truths of the world to come up with his own. As a woman of logic, it baffles me, thus, how individuals can blatantly turn an eye away from the facts that stare them in the face. Certain advocates for equality like to harp on the premise that all humans are the same, a concept that I never understood. The very aspects that make us human differentiate us. From our genetic code which dictates our physical capacities to our appearance which segregates us on a visual level to our individual psyches that transcends measurable scales, humans are literally programmed to stand out. Which is why it is ignorant to assume that all of us are cut of the same cloth and fit into the same mould. However, an admittance of dissimilarity is not a translation to advocacy for injustice. There is a difference between seeing individuality and condemning others for it. These unwritten divides that segregate us into subgroups within a larger population are not the reason for the animosity that certain individuals feel. These malicious thoughts are viruses concealed in promising packets of healthy cells which cross the barriers within our heads to infect what lies beyond, to decay our minds. These trojan horses of malevolence implant themselves into our psyche without our knowledge, they start an unalterable process of gradual decline of our thoughts and of our perspectives. They turn dissimilar people into ‘them' who are deprived of the treatment and amenities that ‘we' should receive. Early interactions with non-neurotypical individuals normalised the concept to me that certain people have quirks or habits that may not resemble my own. The brain is akin to an ocean, it is uncharted territory that is not completely understood by individuals and hides secrets that are yet to be uncovered. It is unjust to box this super-machine with infinite capability into identical, restrictive containers. The world is filled with unique individuals and while we may have come a long way in the acceptance of individuals with varied physical appearances, we have yet to accept those who different from us neurologically. A moment that sticks with me took place when I was in ninth grade. The toll of the bell had indicated that we were free to go to the cafeteria to grab something to eat. On the food counter was a boy with autism who was working the counter to gain work experience. Unlike my usual, unsocial self I decided to strike up a conversation with him. Once I returned to my unofficially designated seat, I was bombarded with questions about my interaction with him by a friend of mine. This friend expressed her disbelief at my conversation, her primary question was 'why would I want to talk to him?'. This friend was considered social and accepting of all people, she was even working with students with autism for a project, which is why it shocked me to see her react this way, to take this fellow human as an alien creature who we could share no connection with. I came to the conclusion that dissimilarity scares us- the creatures of conformity. We very easily discard those who don't conform to our idea of normalcy. These preconceived notions make people tag non-neurotypical individuals as mentally deranged r dumb. This bubbling cauldron of emotions triggered me to work towards the acceptance of non-neurotypical individuals so that some day the need to ask the question that my friend had does not arise.

In recent years, a large population of busy, working Americans have joined the wellness movement. One notable practice – meditation – has pushed to the forefront of this blossoming movement. Meditation is an ancient practice, having been practiced by Buddhist and Hindu monks since around 1500 B.C.[1], but it has only recently become accessible to a modern, secular audience as a break from the stresses and worries of day-to-day life. While meditation offers emotional perks - long-time and novice meditators alike have reported feeling relaxed, calmer, and clearer-headed after their practice - its benefits extend further into the human body, particularly the brain. SHORT-TERM BENEFITS One does not need to adapt a lifestyle change to develop resilience to stress; even short bouts of meditation prove highly beneficial to a frazzled mind. A study led by David Creswell from Carnegie Mellon University[2] examined the effects of meditation training on patients' responses to the Trier Social Stress Test (TSST), designed as a series of controlled stressful situations. Participants in the experimental group received three days of twenty-five-minute meditation trainings, during which they were instructed to pay attention to their breath, bodily sensations, and thoughts and emotions. For the same duration, participants in the control group were instructed to read and analyze a set of poems. Upon taking the TSST, the experimental group self-reported perceived lower levels of stress than did the control group. Brief meditation has also been shown to alter brain anatomy, particularly in regions associated with self-referential thinking. In a study led by Britta Hölzel from the Massachusetts General Hospital[3], participants underwent the Mindfulness-Based Stress Reduction (MBSR) program, which includes weekly group meetings and at-home exercises. Two weeks after the MBSR program concluded, MRI scans of the participants were recorded and compared to scans taken prior to the experiment. Results revealed increased gray matter concentration in four regions of the brain commonly associated with self-referential processing. Other studies[4] have identified additional brain regions positively affected by meditation. An increase in gray matter (neuronal cell bodies and connections) in these areas suggests that meditation can fortify the higher processes associated with psychological well-being and resilience against stress. Most working Americans can only practice meditation as a “moonlight” activity – a routine calming of an overworked mind – by starting or ending their day with ten minutes of mindfulness. Thankfully, even small bouts of meditation can generate psychological and neuroanatomical changes associated with overall emotional amelioration. LONG-TERM BENEFITS Those who fuse mindfulness with their everyday lives often tout the enduring benefits of prolonged, rigorous meditative practice. The portrayal of the calm, wise monk in literature and pop culture is an ever-present reminder of this common sequitur. Look no further than His Holiness the 14th Dalai Lama, who maintains his presence on the world stage with press conferences and self-penned articles urging people to practice kindness. To examine the effects of long-term meditative practice, Antonietta Manna of the G. D'Annuzio University Foundation[5] led a study comparing the functional magnetic resonance (fMRI) data of Buddhist monks and novice meditators while meditating. Novices with only ten days of practice showed fMRI activation in the posterior and anterior cingulate cortex, which was consistent with the Hölzel study conclusions. Monks also showed activation of the anterior cingulate cortex; but in addition to this area, the anterior prefrontal cortex and superior temporal gyrus were also activated above baseline. These two regions are associated with personality expression and social cognition, respectively. The increased stimulation of social cognitive regions in the brains of the monks, for whom mindfulness is a lifestyle, suggests that meditation could, in addition to bringing about peace of mind, encourage prosocial behavior. This conclusion has been verified independently by multiple other studies as well. [6,7,8] Although meditation in any dosage seems to proffer mental and emotional benefits, it remains to be seen whether the mindfulness movement alone can cultivate a prosocial environment for the working American. “Moonlight” meditators, while able to temporarily retreat into peaceful meditation, may require deeper or lengthier sessions than what currently fits in a busy schedule. Perhaps regular meditation on its own does not give rise to significant neurological or psychological benefits; but, for now, the post-Om buzz is enough to keep the movement going. See full article at: https://thetriplehelix.uchicago.edu/tth-epub-fall2016/2018/3/23/your-mind-on-meditation-by-yohyoh-wang