Mathematics

Language is Not Mathematics

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123 or ABC

2+2=4 in every language, in every culture. Even among people with no written language, a girl having two sheep who gets two more sheep always ends up having four sheep. There is no room for ambiguity or nuance. The numbers don’t lie; they don’t hide the truth.

Language, however, cannot claim to be so straightforward. There are always two participants in language, the speaker/writer and the hearer/reader. Language always has nuance.

One could say, “He went to the store.” -Seems simple and straightforward, but the understanding is affected by the emphasis of the speaker. HE went to the store. He WENT to the store. He went TO the store. He went to the STORE. These all have different nuance of meaning.

More than speaking, writing adds another level of complexity. While the hearer has audio emphasis as well as possible facial expression and body gestures to aid understanding, the reader must gather by context which emphasis the writer means.

Language is always a conversation. Even a soliloquy must have a hearer. The hearer must always intuit the speakers meaning to some degree.

We come to the problem with translations.

The translator studies the context, and deciphers as mathematically as possible, but he can never translate without the bias of his own understanding, his own intuition.

I am not a language expert, but in my limited experience it seems that some languages are more mathematical than others. For instance, Latin is very mathematical in form and order while English leaves much freedom of order and even of form to the speaker/writer. Still, Latin is not as clearly unambiguous as mathematics.

A few years ago a series of tornadoes blew destruction across the southeastern US. Some of my neighbors discovered windblown mail from other states dropped by the swirling clouds into their backyards. Some letters were actually returned. Had I discovered a letter out of the blue and had read it, no doubt I would have found nuances that I could not intuit because I do not know the writer.

Here is my point. In order to fully understand a speaker, a hearer must know the speaker. Also, understanding is more apt to be accurate when the hearer is actually in the presence of the speaker, face to face, so to speak. Again, this is a problem for translators.

I can fully affirm my belief that the Bible is the “only infallible rule of faith and of practice.” Yet, I do not find a translation that I can fully trust to be infallible due to nuances intuited or not intuited by the translators. I study the text using several translations, paraphrases and lexicons, but none of them will ever yield a mathematically accurate understanding. I have resigned myself that I must know the speaker.

My father was a gentle, empathetic and kind man. If someone brought me a letter written in my father’s handwriting that could be interpreted as harsh, vindictive or unkind, I would reject that interpretation. Those characteristics were not in his nature. I would look into the context and the history to find clues about his meaning.

We have such clues to be used in Bible interpretation. The greatest clue as to the character of God is Jesus himself. In his own words, “If you have seen me, you have seen my Father also.” God is a spirit. It is hard for us to see Him. Jesus was “the image of the invisible God”. The best interpretation of any passage will be found by seeing God through the character of Jesus Christ. It reminds me of  the old saying, “What would Jesus do?”

 No man hath seen God at any time; the only begotten Son, which is in the bosom of the Father, he hath declared him.
John 1:18

Mathematics, More than Theology, Helps Us Know God.

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Classical theology begins with the premise that God is infinite, but how can humans possibly have knowledge of God when infinity is by definition beyond the bounds of human imagination?

First Things columnist Stephen Webb takes up the issue of an infinite God, comparing the deity to a mathematical expression called Graham’s number, a massively large number that approaches infinity (as much as one can), but still describes a real-world phenomenon (the number of dimensions inside a geometric shape known as a hypercube).

Webb argues that if God is infinite, as theologians insist, then mathematics may aid our understanding more than theology. That’s a sentiment echoed by theoretical physicist Michio Kaku, who explained during a Big Think interview that physics may be the literal mind of God:

“The goal of physics, we believe, is to find an equation perhaps no more than one inch long which will allow us to unify all the forces of nature and allow us to read the mind of God. And what is the key to that one-inch equation? Super symmetry, a symmetry that comes out of physics, not mathematics, and has shocked the world of mathematics. But you see, all this is pure mathematics and so the final resolution could be that God is a mathematician.”

 

The very idea of infinity, however, is open to question. Aristotle, for one, disliked the notion. For something to exist, it must be definable, and it must therefore have boundaries. But infinity is something without limitation so we cannot define it, meaning we cannot discuss it or even entertain the concept in our minds. And if we are unable to even think of infinity, it becomes a meaningless term.

Aristotle did, however, accept potential infinities: something that continues with no logical end. Thus our thoughts concerning God have potential understanding — a potential which is infinite — though we may still never arrive at understanding what theologians mean by God.

 

NASA’s ‘impossible’ EM Drive works: German researcher confirms and it can take us to the moon in just 4 HOURS

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Over the past whole year, there’s been a lot of excitement about the electromagnetic propulsion drive, also known as EM Drive – a logically impossible engine that’s challenged almost everyone’s prospects by continuing to stand up to experimental study. The EM drive is so thrilling because it yields enormous amounts of propulsion that could hypothetically blast us to Mars in only 70 days, without the need for dense and costly rocket fuel. Instead, it’s actually propelled forward by microwaves bouncing back and forth inside a sealed off chamber, and this is what makes the EM drive so powerful, and at the same time so debatable.

As effective as this kind of propulsion may sound, it challenges one of the essential concepts of physics – the conservation of momentum, which states that for anything to be propelled forward, some kind of propellant must be pushed out in the opposite direction. For that reason, the drive was generally laughed at and overlooked when it was designed by English scientist Roger Shawyer in the early 2000s. But a few years later, a group of Chinese researchers decided to construct their own version, and to everyone’s amazement, it really worked. Then an American inventor did the something just like that, and convinced NASA’s Eagleworks Laboratories, supervised by Harold ‘Sonny’ White, to give it a try. And they admitted that it actually works. Now Martin Tajmar, a well-known professor and chairman for Space Systems at Dresden University of Technology in Germany, has worked with his own EM Drive, and has once again revealed that it produces thrust – although for reasons he can’t clarify yet.

Tajmar offered his outcomes at the 2015 American Institute for Aeronautics and Astronautics’ Propulsion and Energy Forum and Exposition in Florida on 27th of July, and you can read his entire paper here. He has a long history of experimentally testing (and exposing) revolutionary propulsion systems, so his outcomes are a big deal for those looking for outside confirmation of the EM Drive.

Most importantly, his system produced a parallel amount of thrust as was initially forecast by Shawyer, which is more than a few thousand times greater than a typical photon rocket.

So where does all of this leave us with the EM Drive? While it’s fun to speculate about just how revolutionary it could be for humanity, what we really need now are results published in a peer-reviewed journal – which is something that Shawyer claims he is just a few months away from doing, as David Hambling reports for Wired.

So it might turn out that we need to modify some of our laws of physics in order to clarify how the drive actually works. But if that opens up the opportunity of human travel throughout the entire Solar System – and, more significantly, beyond – then it’s a sacrifice we’re certainly willing to make.

The Next World and the Next

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Award-winning sci-fi writer Alice Sola Kim imagines a beautiful and dark future world.

Lena Dunham on Alice Sola Kim’s Story and Women Innovators

Sugar-Sweet Lennys,

My father is a sci-fi nerd of the highest order. Before the Internet, that meant a closet full of dusty 25-cent paperbacks, their covers crawling with cyborgs and barren lunar landscapes and microwaves that could commence time travel. Every Saturday we would walk across then-barren Soho to the now-defunct Science Fiction Bookstore, where, desperate to be every inch his daughter, I would search for my own reading material. But even at age seven I already knew what I liked: stories about girls. And it soon became apparent I wasn’t going to find any of those here. The young-adult series, like My Teacher Is an Alien and Johnny Swift, had scrappy male protagonists traveling through space on glorified skateboards. As for the adult books, the only women I found were nude blue aliens with jaunty antennae, ready to sexually satisfy lonely space captains. I didn’t yet know about Ursula K. Le Guin or the other grand dames of sci-fi, but then again, it didn’t occur to anyone to tell me.

Science fiction is notable as a genre not just because of its escapism, but because of the way it grapples with our current reality: what are science, technology, and innovation doing to the human mind and spirit, and when they reach their inevitable full-on collision, where will that leave us humans? These are the big questions that were being contemplated in my father’s 25-cent paperbacks. But never by women. Not as writers nor as heroes.

Science, technology, engineering, and mathematics (fun and easy acronym: STEM!) are not worlds we associate with women, yet they are full of female pioneers whose stories demand to be told. GE and Lenny have partnered on a program that doesn’t just tell you that women should be at the forefront of science and technology, but shows that they already are.

So it seems only natural that GE would also share our goal of supporting an emerging female sci-fi author as she herself wrestles with questions of science and human consciousness and whether the twain shall meet. Alice Sola Kim is a writer of uncommon philosophical depth and also great imagination. Her story envisions a world in which sick people don’t die — they enter a state of cryogenic stasis instead — but the question remains: what’s in their heads when they’ve been placed on pause? In a series of vignettes, our (gal!) protagonist slowly realizes she may not be among the living anymore, but, because of the advancements in medicine and technology, she is also not dead.

We’ve been excited about our partnership with GE from the jump — we have the chance to profile industry leaders like Beth Comstock and an all-female robotics team, and to show our Lennys just how hard women in science and tech are showing up to play. But I’m especially thrilled that my child self now has some sci-fi she can get behind. No horny three-boobed alien princesses here, just an often hilarious and sometimes painful look at a future where technology enriches our lives and yet we still can’t quite escape being human.

The Next World and the Next

By Alice Sola Kim

Franny went to college, graduated with honors. After that, she got her masters and a Ph.D, and then another Ph.D, for which she completed a thesis on the hermeneutics of online bodybuilding forums. She got tired of the humanities and went back to undergrad so she could do med school. It took a lot of time, but she had the time. She made the time.

After med school, Franny decided to get an MFA. She wrote a story about catching squid with her dad, applied, got in — it all seemed to happen so fast! Franny sat in a small conference room, waiting for the other students to arrive. She hoped at least one or five of them would be cute. A cute girl walked in and sat down across the table from Franny. Franny smiled at her, the girl smiled back, and time passed in a weird way. Franny looked at the clock, which she couldn’t see very well. Her eyes were probably blurry from all the studying. “Where’s everyone else?” she said.

The girl smiled. All she had done, this whole time, was smile. It was getting a little old. “I ate them,” she said, and opened her mouth teasingly. A drop of blood trickled out, then a spurt, then more and more and faster until the blood was gushing from her mouth. The girl was still composed, now laughing, as blood covered the floor. Franny thought, I should have never gotten an MFA, then all thought left her as she paddled frantically, the blood rising to her chest, her chin, her nose, filling her eyes—

Maria had come here through a portal in her hallway closet, and now she was on the road. She was journeying toward a mountain filled with lava in order to destroy a dangerous magical ring. There were many who would attempt to stop her, but she was stalwart, and she was with friends. There was a hot short guy, another hot short guy, a hot tall guy, a hot sociopathic detective and his hot doctor friend, and these two brothers who killed demons together (also hot), who had traveled here from the future.

One day, she awoke to find them all slain. “Run,” someone screamed into her ear, and before she could think, there was a tugging at her belt and she was run-run-running, she was running and being run so fast her feet left the ground and she fluttered like a pennant in the wind—

Jim was a good boy! He couldn’t see red or green, but what he could smell was better than any color. Pebbles, soccer balls, cats, Italian hoagies, car seats, pennies, perms. Jim had no future and was happy all the time. He lived with some friends who were tall and had very long wiggly legs with flat faces balanced on top.

One day, a friend was walking Jim through his neighborhood when, suddenly, the leash went slack. Jim looked up. His friend had disappeared. In his friend’s place was a large, dark, buzzing cloud collecting itself directly above him, thickening by the second. Jim whined.

Everyone is dreaming very busily

When Aya visited her sister, she didn’t try to talk to her.

Other visitors did talk to their stacies, leaning close to the cryocases, resting their hands on top until the cold became unbearable. As you passed, you could hear their murmurs over the unending exhalation of the machines. But there was no point in Aya talking to her sister when her sister couldn’t even talk back. It would feel very bad. It would feel like every worst fight they’d ever had, her sister so nonchalantly sullen that it didn’t even seem like she was angry — more like, Aya had just suddenly never been born, so of course her sister wouldn’t think to speak to her or acknowledge her existence. Which was when Aya would freak out and apologize, saying absolutely anything her sister wanted to hear, because she couldn’t stand glimpsing that dark, lonely universe where her sister would nothear and understand every thought Aya wanted to share with her.

Which were honestly a lot of them.

Aya’s sister was wide and long and flat like Gumby, or an Olympic swimmer. Her shoulders filled the cryocase like she could rip it out of its mooring if she turned over even once during stasis. She had the most sweetly soft look on her face, as if she was about to wake up and ask a question.

But Aya knew better. She was a materials scientist, and so were her best friends. It wasn’t like that TV show with the group of best friends where one was a chef and one was a fashion designer and one was the president and one was a ghost that lived on the Internet. Aya and her closest friends had met and banded together at school, at work, at work-related conferences. Her friend Min worked in cryostasis. She had helped to develop the plasma complex that replaced the stacies’ blood. Min told Aya that what looked like a window on the cryocase was actually a screen. “Stacies aren’t cute,” she said. “Dead is dead.” Min was not unaware of people’s feelings and sensitivities; rather, she considered them and then decided it was best to be blunt anyway, which Aya usually appreciated.

It had bothered people that they couldn’t look at the faces of their loved ones in stasis. It felt abstract and chilly and stupid to visit, like, a giant silver pill. Anything could be in there. Bad for morale, bad for funding, but it would all be even worse if the visitors saw how the stacies really looked, so instead the cryocenter had screens put into the cryocases, displaying cute, cleaned-up, highest-fidelity 3-D images of the stacies resting within.

Aya thought that it was hard to know so much.

Unlike the other stacies, Aya’s sister had a private room at the cryocenter. Aya had paid for it, and for a higher quality of care. She had a lot of money, but she spent all her time hanging out with her dead-not-dead sister and working. She loved work, but she could definitely be having more fun. Going to Belize, watching the coral rebuild. Partying in a Manhattan watermanse. She had the invitations and everything; her work had helped make it all possible.

Her sister’s room was not a nice room. There was a cot in case Aya wanted a nap alongside her sister, no window, and, despite her complaints, there were always persistent dust flurries caught around the bottom of her sister’s cryocase, the same way dust and hair collected around every crevice of Aya’s free weights. But she knew that everything was as expensive as it didn’t look. It cost a lot of money to thwart death. It was hard work to keep a body ready to be alive when all it wanted was the other thing. You had to make the body so cold that entropy would ignore it, tricked into thinking that it was out of the game and thus beyond entropy’s notice. But also, this frozen body had to be a place where life could possibly return in the future, where shoots might come up and blood would rush in.

The last time Aya spoke to her sister was right before she went into stasis. The more Aya thought about it, which was a lot, the more firmly she decided that maybe this was one of those opportunities that no one should have. Her sister had been inconsolable about the prospect of dreaming for so long. During stasis, you were meant to have a kind of brain activity that was sort of like dreaming, but more consistent. The first generation of stacies had been lost because no one had known that they needed a bunch of interesting, distracting stuff going on in their brains; like, stasis was supposed to be stasis, so who knew? But what happened to the first generation was creepy and undeniable, even though everything else had gone as it should.

“What if it’s a bad dream,” her sister sobbed. “I don’t want a bad dream. I don’t want to have anything.”

“It’s not,” Aya had said. “It won’t be. It’s not.” She said it over and over again as if quantity could compensate for quality, for actual factual information, because who even did know? There was no second generation yet.

She was so tired. She had come to visit her sister from work, where the current project was a new kind of membrane for a third round of desalination machines, through which seawater sieved and came out fresh. The old ones worked OK, but they weren’t as energy-efficient as they could be, and California was still thirsty. People were moving back in droves — she really should visit. Aya knew she been born to a dirty world. A tired world. Her mother and father had waded through it, and Aya had been born miraculously, seemingly fine despite all that, but not her sister.

And it was seeing this little sister of hers in pain, in trouble after trouble after trouble, that made Aya vow to not worship a god that was a man or a deity but instead become her own god, to study and learn so that she could grow up to remake and unmake Earth how she thought best — and it was working, wasn’t it? Aya and the women she knew were creating a better world, whether they were harvesting giant beds of genetically engineered kelp or staying the hand of death.

She loved work and she loved her sister and she could not tell which of these things was making her feel tired. It should have been neither, right? Aya lay on the cot, leaving a foot on the floor like she was drunk, and dozed off for a moment.

She heard people talking. Their voices loomed over her, pleasantly stretchy and smooth. She was still sleeping and couldn’t move.

“I’m worried about her.”

“What’s to worry about?”

“This readout.”

“It’s within normal. These variations happen. It’s a long time. Just chill. Haha, get it?”

“Ugh, please stop. I guess you’re right.”

“Look, it’s not like she’s the only one—”

Their voices kept going but now they were quieting, dwindling, as if they were getting sucked out into space. But suddenly there was a new voice.

“Do you think we should eat her?” it said, right by her ear.

Aya awoke, freezing cold. She had just had a dream, possibly the most boring dream ever, about a conversation she had had a few days ago with Min about her sister. Except in the dream, she wasn’t herself, she was her sister, unable to see or move or do anything. She could hear, even though stacies couldn’t hear anything. The dream had ended weirdly — Aya couldn’t remember how, but she felt terrible. That was the thing about dreams: They could make you feel so mad or sexy or scared even when you couldn’t remember a thing about the dream. All that remained was the animal part of your brain that was convinced something had happened.

She left her sister’s room and walked down the hallway. Sometimes people worked late at the cryolab, but tonight everyone had gone home. In the bathroom, it was so dark for a moment that the darkness had heft and texture, a goopiness, but then the lights flickered on. Aya would have preferred for the lights to have been on already. Motion-sensor lights, but ones that could predict the future and would turn on right before they detected your motion so you’d never have to be scared of the dark! She yawned so hugely her mouth threatened to eat her face.

She peed, washed her hands, tried to be kind and generous about the droopy, unpromising image reflected back at her. As she left, Aya heard a sound and turned. In the stall closest to the door, she saw a pair of bare feet drop down daintily and pivot to face her. The lights flickered off. This time the dark was definitely a thing with intention (bad) and movement (swift, in her direction).

Aya dashed toward her sister’s room and slammed the door behind her. She looked out of the little window inset in the door. There was nothing in the hallway. However, there was something in the room with her. Two women and a dog were huddled in the corner. One woman was covered in blood, one woman in dirt. The dog seemed normal, happy, even. They all looked familiar.

The dirty woman stood. “Halt,” she said, “Do not go out there. You are in grave danger.”

The three of them had been fighting for days, they said. The bloody woman, whose name was Franny, had been attacked first. She had kicked a window out and spilled into the dirty woman’s world. The dirty woman, whose name was Maria, had fought off the creature with Franny’s help, and they had been moving from world to world together, but were too late or weak to save the others from being devoured. They had just rescued the dog, whose nametag read “Jim.”

Franny and Maria did not agree on what the thing was, if it was an alien or if it was bad people or if it was a manifestation of their own minds. They just called it a thought-creature. What was clear was that at some point, they would need to fight it. But not here, not yet, not when they were cornered.

Maria said, “What you must do is find the weak point into the next world.”

“Hold on,” said Aya. There was a knock at the door.

“It’s the demon,” said Maria.

“It’s the serial killer!” said Franny.

Jim barked.

Franny said, “Open that thing.”

“No!” said Aya.

Franny glared at her and kicked the cryocase. When Aya went to stop her, she saw that the cryocase had changed. Instead of her sister, it was Aya who was lying inside, sleeping, looking like she was about to wake up and ask the question. Oh. She wondered what the question might be.

The knocking grew louder, booming against the door.

Aya was nothing if not pragmatic. She was adaptable, not a dumb person or a pushover, but someone who was fully aware of all the beautiful and dark possibilities of the world. She knew she had a very short time to mourn everything. “Wait,” Aya said. “What was it like, where you came from?”

“Adventures available to brave men and women alike. Friends banding together against evil. Many hotties,” said Maria. “I want to go back.”

“Time enough for everything,” said Franny. “Me too.”

“And yours?” they asked.

Aya told them about jets the size of mansions. Mansions floating on water in Manhattan, coral reefs corseted and bolstered back to life, skyscrapers in earthquake zones that jiggled instead of cracked. “Sure,” they said. “OK.”

She told them that the world had become harder to live in. But that it was their fault, they knew that, and they were fixing it. They were learning from their mistakes. She told them about Cassandra, her friend who loved flesh so much she could think of ways to create and shape it that had never been seen before. Cassandra had developed a comfortable polymer that protected and supported the skin. It didn’t feel like you were wearing anything, and it even flattened your eye bags. She was the most beautiful woman Aya had ever known in person, and she had a different face tattoo every week. Vain Cassandra with her sumptuous kindness, who had been burned on over half her body as a child and would have no one know what it felt like to be in such suffering.

Franny and Maria looked at each other and shrugged.

“Truly, a world of miracles,” said Maria.

“I wish I could stay,” said Aya.

“For our sakes, I hope that some of this world is real,” said Franny. “It sounds like a beautiful place. I’d take a piece of it. But we really do have to go right now.”

“I love my world,” said Aya. “I will fight for it.”

“We’ll all fight for it,” Maria said.

The door began to crack. They opened the cryocase onto a narrow gray void and each jumped in, Aya last, giving one final lingering look at her world, a world made and fixed by her and her friends and people she would never meet now, her gorgeous world which she was either dreaming up or dreaming in.

What Mathematics Reveals About the Secret of Lasting Relationships and the Myth of Compromise | Brain Pickings

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Why 37% is the magic number, what alien civilizations have to do with your soul mate, and how to master the “negativity threshold” ideal for Happily Ever After.

In his sublime definition of love, playwright Tom Stoppard painted the grand achievement of our emotional lives as “knowledge of each other, not of the flesh but through the flesh, knowledge of self, the real him, the real her, in extremis, the mask slipped from the face.” But only in fairy tales and Hollywood movies does the mask slip off to reveal a perfect other. So how do we learn to discern between a love that is imperfect, as all meaningful real relationships are, and one that is insufficient, the price of which is repeated disappointment and inevitable heartbreak? Making this distinction is one of the greatest and most difficult arts of the human experience — and, it turns out, it can be greatly enhanced with a little bit of science.

That’s what mathematician Hannah Fry suggests in The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation (public library) — a slim but potent volume from TED Books, featuring gorgeous illustrations by German artist Christine Rösch. From the odds of finding your soul mate to how game theory reveals the best strategy for picking up a stranger in a bar to the equation that explains the conversation patterns of lasting relationships, Fry combines a humanist’s sensitivity to this universal longing with a scientist’s rigor to shed light, with neither sap nor cynicism, on the complex dynamics of romance and the besotting beauty of math itself.

She writes in the introduction:

Mathematics is ultimately the study of patterns — predicting phenomena from the weather to the growth of cities, revealing everything from the laws of the universe to the behavior of subatomic particles… Love — [like] most of life — is full of patterns: from the number of sexual partners we have in our lifetime to how we choose who to message on an internet dating website. These patterns twist and turn and warp and evolve just as love does, and are all patterns which mathematics is uniquely placed to describe.

[…]

Mathematics is the language of nature. It is the foundation stone upon which every major scientific and technological achievement of the modern era has been built. It is alive, and it is thriving.

In the first chapter, Fry explores the mathematical odds of finding your ideal mate — with far more heartening results than more jaundiced estimations have yielded. She points to a famous 2010 paper by mathematician and longtime singleton Peter Backus, who calculated that there are more intelligent extraterrestrial civilizations than eligible women for him on earth. Backus enlisted a formula known as the Drake equation — named after its creator, Frank Drake — which breaks down the question of how many possible alien civilizations there are into sub-estimates based on components like the average rate of star formation in our galaxy, the number of those stars with orbiting planets, the fraction of those planets capable of supporting life, and so forth. Fry explains:

Drake exploited a trick well known to scientists of breaking down the estimation by making lots of little educated guesses rather than one big one. The result of this trick is an estimate likely to be surprisingly close to the true answer, because the errors in each calculation tend to balance each other out along the way.

Scientists’ current estimate is that our galaxy contains around 10,000 intelligent alien civilizations — something we owe in large part to astronomer Jill Tarter’s decades-long dedication. Returning to Backus’s calculation, which yielded 26 eligible women on all of Earth, Fry notes that “being able to estimate quantities that you have no hope of verifying is an important skill for any scientist” — a technique known as a Fermi estimation, which is used in everything from job interviews to quantum mechanics — but suggests that his criteria might have been unreasonably stringent. (Backus based his formula, for instance, on the assumption that he’d find only 10% of the women he meets agreeable and only 5% attractive.)

In fact, this “price of admission” problem is also at the heart of a chapter probing the question of how you know your partner is “The One.” Fry writes:

As any mathematically minded person will tell you, it’s a fine balance between having the patience to wait for the right person and the foresight to cash in before all the good ones are taken.

Indeed, some such mathematically minded people have applied an area of mathematics known as “optimal stopping theory” to derive an actual equation that tells you precisely how many potential mates to reject before finding the perfect partner and helps you discern when it’s time to actually stop your looking and settle down with that person (P):

Fry explains:

It tells you that if you are destined to date ten people in your lifetime, you have the highest probability of finding The One when you reject your first four lovers (where you’d find them 39.87 percent of the time). If you are destined to date twenty people, you should reject the first eight (where Mister or Miz Right would be waiting for you 38.42 percent of the time). And, if you are destined to date an infinite number of partners, you should reject the first 37 percent, giving you just over a one in three chance of success.

[…]

Say you start dating when you are fifteen years old and would ideally like to settle down by the time you’re forty. In the first 37 percent of your dating window (until just after your twenty-fourth birthday), you should reject everyone; use this time to get a feel for the market and a realistic expectation of what you can expect in a life partner. Once this rejection phase has passed, pick the next person who comes along who is better than everyone who you have met before. Following this strategy will definitely give you the best possible chance of finding the number one partner on your imaginary list.

This formula, it turns out, is a cross-purpose antidote to FOMO, applicable to various situations when you need to know when to stop looking for a better option:

Have three months to find somewhere to live? Reject everything in the first month and then pick the next house that comes along that is your favorite so far. Hiring an assistant? Reject the first 37 percent of candidates and then give the job to the next one who you prefer above all others. In fact, the search for an assistant is the most famous formulation of this theory, and the method is often known as the “secretary problem.”

But the most interesting and pause-giving chapter is the final one, which brings modern lucidity to the fairy-tale myth that “happily ever after” ensues unabated after you’ve identified “The One,” stopped your search, and settled down him or her. Most of us don’t need a scientist to tell us that “happily ever after” is not a destination or a final outcome but a journey and an active process in any healthy relationship. Fry, however, offers some enormously heartening and assuring empirical findings, based on a fascinating collaboration between mathematicians and psychologists, confirming this life-tested and often hard-earned intuitive understanding.

Fry examines what psychologists studying longtime couples have found about the key to successful relationships:

Every relationship will have conflict, but most psychologists now agree that the way couples argue can differ substantially, and can work as a useful predictor of longer-term happiness within a couple.

In relationships where both partners consider themselves as happy, bad behavior is dismissed as unusual: “He’s under a lot of stress at the moment,” or “No wonder she’s grumpy, she hasn’t had a lot of sleep lately.” Couples in this enviable state will have a deep-seated positive view of their partner, which is only reinforced by any positive behavior: “These flowers are lovely. He’s always so nice to me,” or “She’s just such a nice person, no wonder she did that.”

In negative relationships, however, the situation is reversed. Bad behavior is considered the norm: “He’s always like that,” or “Yet again. She’s just showing how selfish she is.” Instead, it’s the positive behavior that is considered unusual: “He’s only showing off because he got a pay raise at work. It won’t last,” or “Typical. She’s doing this because she wants something.

She cites the work of psychologist John Gottman, who studies why marriages succeed or fail. He spent decades observing how couples interact, coding and measuring everything from their skin conductivity to their facial expressions, and eventually developed the Specific Affect Coding System — a method of scoring how positive or negative the exchanges are. But it wasn’t until Gottman met mathematician James Murray and integrated his mathematical models into the system that he began to crack the code of why these toxic negativity spirals develop. (Curiously, these equations have also been used to understand what happens between two countries during war — a fact on which Fry remarks that “an arguing couple spiraling into negativity and teetering on the brink of divorce is actually mathematically equivalent to the beginning of a nuclear war.”)

Fry presents the elegant formulae the researchers developed for explaining these patterns of human behavior. (Although the symbols stand for “wife” and “husband,” Fry notes that Murray’s models don’t factor in any stereotypes and are thus equally applicable to relationships across all orientations and gender identities.)

She breaks down the equations:

The left-hand side of the equation is simply how positive or negative the wife will be in the next thing that she says. Her reaction will depend on her mood in general (w), her mood when she’s with her husband (rwWt), and, crucially, the influence that her husband’s actions will have on her (IHM). The Ht in parentheses at the end of the equation is mathematical shorthand for saying that this influence depends on what the husband has just done.

The equations for the husband follow the same pattern: h,rHHt, and IHM are his mood when he’s on his own, his mood when he’s with his wife, and the influence his wife has on his next reaction, respectively.

The researchers then plotted the effects the two partners have on each other — empirical evidence for Leo Buscaglia’s timelessly beautiful notion that love is a “dynamic interaction”:

In this version of the graph, the dotted line indicates that the husband is having a positive impact on his wife. If it dips below zero, the wife is more likely to be negative in her next turn in the conversation.

What all of this translates into is actually strikingly similar to Lewis Carroll’s advice on resolving conflict in correspondence. “If your friend makes a severe remark, either leave it unnoticed, or make your reply distinctly less severe,” Carroll counseled, adding “and if he makes a friendly remark, tending towards ‘making up’ the little difference that has arisen between you, let your reply be distinctly more friendly.” Carroll was a man of great psychological prescience in many ways, and this particular insight is paralleled by Gottman and Murray’s findings, which Fry summarizes elegantly:

Imagine that the husband does something that is a little bit positive: He could agree with her last point, or inject a little humor into their conversation. This action will have a small positive impact on the wife and make her more likely to respond with something positive, too… [But] if the husband is a little bit negative — like interrupting her while she is speaking — he will have a fixed and negative impact on his partner. It’s worth noting that the magnitude of this negative influence is bigger than the equivalent positive jump if he’s just a tiny bit positive. Gottman and his team deliberately built in this asymmetry after observing it in couples in their study.

And here is the crucial finding — T- is the point known as a negativity threshold,at which the husband’s negative effect becomes so great that it renders the wife unwilling to diffuse the situation with positivity and she instead responds with more negativity. This is how the negativity spirals are set off. But the most revelatory part is what this suggests about the myth of compromise.

As Fry points out, it makes sense to suppose that the best strategy is to aim for a high negativity threshold — “a relationship where you give your partner room to be themselves and only bring up an issue if it becomes a really big deal.” And yet the researchers found the opposite was true:

The most successful relationships are the ones with a really low negativity threshold. In those relationships, couples allow each other to complain, and work together to constantly repair the tiny issues between them. In such a case, couples don’t bottle up their feelings, and little things don’t end up being blown completely out of proportion.

She adds the important caveat that a healthy relationship isn’t merely one in which both partners are comfortable complaining but also one in which the language of those complaints doesn’t cast the complainer as a victim of the other person’s behavior.

In the remainder of The Mathematics of Love, Fry goes on to explore everything from the falsehoods behind the standard ideals of beauty to the science of why continually risking rejection is a sounder strategy for success in love (as in life) than waiting for a guaranteed outcome before trying, illustrating how math’s power to abstract reality invites greater understanding of our most concrete human complexities and our deepest yearnings.

 

New Mathematics Could Neutralize Pathogens That Resist Antibiotics .

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Bacteria that make us sick are bad enough, but many of them also continually evolve in ways that help them develop resistance to common antibiotic drugs, making our medications less effective or even moot. Doctors try to reduce the evolution by cycling through various drugs over time, hoping that as resistance develops to one, the increased use of a new drug or the widespread reuse of an old drug will catch some of the bugs off guard.

Blue glowing picture of E. coli

The plans for cycling drugs are not that scientific, however, and don’t always work efficiently, allowing bacteria to continue to develop resistance. Now a new algorithm that deciphers how bacteria genes create resistance in the first place could greatly improve such a plan. The “time machine” software, developed by biologists and mathematicians, could help reverse resistant mutations and render the bacteria vulnerable to drugs again.

Miriam Barlow, a biologist from the University of California, Merced, first hit on the idea while trying to predict how antibiotic resistance would evolve several years ago. But she lacked the experimental data or the mathematics to quantify it. “We were pushing evolution forward, trying to predict how antibiotic resistance would evolve, and we saw a lot of trade-offs,” Barlow says. Introducing an antibiotic might lead to bacteria developing resistance but it might also lead to them losing resistance to some other medication. So Barlow partnered with mathematicians, including Kristina Crona from American University in Washington, D.C., and tried to figure out a series of steps to make those losses of resistance as likely as possible. Their work was published in PLoS ONE May 6.

Network of mutations with arrows leading from one to the other, labeled by drug that causes the transition

The researchers took as a starting point TEM-1, a protein stemming from an extremely common gene that confers resistance to penicillin. They considered four possible independent mutations that can occur in the gene, all of which confer resistance to new antibiotics, and they selected a range of 15 commonly used and studied antibiotics. They then measured the growth rates of Escherichia coli bacteria, as each mutation was exposed to each of the antibiotics, which let them work out the probability that the overall population of E. coli would gain or lose a mutation to adapt.

In this way the researchers could directly model possible changes to drug-resistant genes. “At every single place in the genome we can say either the mutation happened here or it did not,” Crona says. The researchers were able to sketch a network of different mutation combinations and figure out the probabilities of moving from one to the other, given certain antibiotics. They called the software for finding the path back to TEM-1, created by their collaborator, mathematician Bernd Sturmfels of the University of California, Berkeley, the “Time Machine.” Although in the real world a bacterium would not revert to its exact, prior genetic form once it had evolved, this mathematical goal revealed the best genetic targets for slowing resistance.

Network of mutations with arrows leading from one to the other, labeled by drug that causes the transition

In models of genes, researchers charted which antibiotics would encourage which of four genetic mutations in E.coli bacteria and the likelihood of each. Each mutation is represented by a “1,” so each combination is a four-digit number. Using a particular sequence of antibiotics can lead back to the wild type, 0000. Credit: Kristina Crona

The researchers were surprised to find that most mutations didn’t need a long chain of antibiotics to revert to TEM-1. They also found they could revert most mutations with about a 60 percent probability, which is more efficient than current antibiotic cycling schemes. And they found that they could reach a high level of reliability with just a few antibiotics in the cycle.

Direct network modeling like this is becoming more common in biology as researchers learn how to distill problems into the correct mathematical formats. But mathematicians are still learning the best ways to navigate and optimize networks of connections that can grow in complexity. And as with any model system, real-world work must be done. “It’s an interesting mathematical analysis based on laboratory-measured growth rates across multiple antimicrobial drugs, which is all novel,” says Joshua Plotkin, who investigates mathematical biology at the University of Pennsylvania and was not involved with this project. But he adds that researchers still need to pinpoint how long the cycles should last and the necessary dosages as well as looking into how the system adapts to more antibiotics and more complex mutations. The bacterial populations’ interactions in a clinic filled with people will be far more complex than one mutation per test tube.

To that end, Barlow’s group is currently setting up an experiment that will simulate the cross-pollination of different bacterial populations, which happens in places such as hospitals where multiple patients are exposed to one another. The same mathematical process they used can also incorporate new mutations and antibiotics found in hospitals—mutations that can apply to many different bacteria, not just E. coli. “We need more mathematicians working on this,” says Jonathan Iredell, an infectious disease physician from University of Sydney in Australia. “It indicates a way forward as we are desperate to find some positive remedies to what is basically an evolutionary and ecological problem.”

Robert Beardmore, a mathematical bioscientist at University of Exeter who, along with Iredell, did not take part in the study, describes this work as trying to find the signal in the noise of bacterial resistance development. Future lab work will reveal whether the interactions the team found are strong enough to define what happens in more complex scenarios. “At the heart of what everybody wants to know is how predictable is evolution—and if it’s predictable, can we reverse it?” he says. “It’s really hard, but you’ve got to try something.”

“We’re talking about managing evolution, trying to steer evolution,” Crona adds. “And that’s very new.”

Physically Fit Boys and Girls Score Higher on Reading and Math.

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If there were a way to make your child a better reader, or improve their performance in math – and it was free, natural and absolutely safe – would you do it?

Of course you would!

Virtually every parent hopes their child will excel academically, and for kids the boost to reading and math skills can be a tremendous lift to their self-esteem.

Fortunately, yet another study has found that getting physically fit has the wonderful “side effect” of boosting your child’s cognitive abilities – no tutor required!

Healthy Heart and Lungs Boost Math and Reading Scores

According to a study done at the University of North Texas, having a healthy heart and lungs may be one of the most important factors for middle school students to excel in math and reading.1

Cardiorespiratory fitness was the only factor that was found to consistently impact grades on reading and math tests, which the researchers said should be a wake-up call to schools that have limited physical education classes. Of course, you needn’t rely on gym class to get your child active, and in fact should strive to make physical fitness a regular part of your family’s life outside of school hours as well.

The More Active Your Child, The Better They’ll Do at School

This was the finding from a review of 14 studies involving children ages 6-18.2 According to the authors:

“There are several hypothesized mechanisms for why exercise is beneficial for cognition, including:

  • Increased blood and oxygen flow to the brain
  • Increased levels of norepinephrine and endorphins resulting in a reduction of stress and an improvement of mood
  • Increased growth factors that help to create new nerve cells and support synaptic plasticity”

To put this into perspective, Naperville Central High School in Illinois implemented a special program where students could take part in a dynamic gym class at the beginning of the day and had access to exercise bikes and balls throughout the day in their classrooms. The results were astounding. Those who participated nearly doubled their reading scores, and math scores increased 20-fold!3

As many of you reading this have likely experienced, if your mind is feeling cluttered or you’re having a mid-afternoon slump, a brisk walk or a quick workout can give you a renewed sense of clarity and focus. This is certainly true for kids too. The research is pouring in that regular exercise can improve test scores, IQ levels and task efficiency for kids and adults alike. Some of the research highlights include:4

  • Among elementary school students, 40 minutes of daily exercise increased IQ by an average of nearly 4 points
  • Among 6th graders, the fittest students scored 30 percent higher than average students, and the less fit students scored 20 percent lower
  • Among older students, those who play vigorous sports have a 20 percent improvement in Math, Science, English and Social Studies
  • Fit 18-year-olds are more likely to go on to higher education and get full-time jobs
  • Students who exercise before class improved test scores 17 percent, and those who worked out for 40 minutes improved an entire letter grade

Too Much Screen Time May Negate Some Exercise Benefits

It’s a common misconception that if your child spends some time in gym class or rides his bike after school, then watching TV, playing video games or surfing the Web later won’t matter. In reality, this “screen time” – more than two hours a day in particular – is associated with increased emotional and behavioral difficulties, regardless of the time spent exercising. According to one study, researchers found that:5

  • Children who spent more than two hours a day watching TV or using a computer were 61 and 59 percent more likely to experience high levels of psychological difficulties, respectively
  • Children who spent more than two hours a day watching TV, and also failed to meet physical activity guidelines, were 70 percent more likely to experience high levels of psychological difficulties
  • This risk increased to 81 percent for children who used a computer for more than two hours a day while also failing to meet recommended exercise guidelines

I think there’s no doubt that it is imperative to limit your child’s TV, computer, and video game time, in addition to encouraging your child to spend more time doing various forms of physical activity.

What Type of Exercise is Best for Kids?

The same type that’s best for adults, which is short bursts of intense activity with periods of rest in between— this is actually the way your body was designed to move! And kids will typically fall into this behavior quite spontaneously, as long as they’re outdoors with friends, and not cooped up in front of a TV or computer screen … Like adults, kids also need variety in their exercise routines to reap the greatest rewards, so be sure your child is getting:

  • Interval training
  • Strength training
  • Stretching
  • Core-building activities

This may sound daunting, but if your child participates in a gymnastics class, sprints around the backyard after the dog often and rides his bike after school, he or she’s covered.

Also remember that acting as a role model by staying active yourself is one of the best ways to motivate and inspire your kids. If your child sees you embracing exercise as a positive and important part of your lifestyle, they will naturally follow suit. Plus, it’s easy to plan active activities that involve the whole family and double up as fun ways to spend time together, like hiking, bike riding, canoeing, swimming and sports.

Source: Dr. Mercola

 

Physical Fitness in Childhood Linked to Higher Reading and Math Scores .

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If your child is struggling in school, you may want to evaluate his level of physical activity and fitness.

Researchers have repeatedly found connections between fitness and brain health, which naturally impacts all areas of brain function, such as cognitive thinking skills and memory.

According to a study from the University of North Texas, which was recently presented at the American Psychological Association’s annual convention, having a healthy heart and lungs may actually be one of the most important factors for middle school students to make good grades in math and reading.1

According to co-author Trent A. Petrie, PhD:

“Cardiorespiratory fitness was the only factor that we consistently found to have an impact on both boys’ and girls’ grades on reading and math tests… This provides more evidence that schools need to re-examine any policies that have limited students’ involvement in physical education classes.”

Indeed, there’s plenty of evidence attesting to the fact that if you value your brainpower, and that of your children, you’ll want to make certain that exercise is a regular part of your and your family’s life. Previous research has also discovered links between physical fitness and mental acuity in seniors, so it’s equally important for all age groups.

Physical Activity Could Equate to Higher Grades

A test program not too far from our Chicago-area office at Naperville Central High School in Illinois illustrated the power of exercise to boost school performance in a powerful way two years ago. Students participated in a dynamic morning exercise program at the beginning of the day, and had access to exercise bikes and balls throughout the day in their classrooms. The results were astounding. Those who participated nearly doubled their reading scores!2 Research has also shown that after 30 minutes on the treadmill, students solve problems up to 10 percent more effectively.

Another more recent review of 14 studies,3 ranging in size from as few as 50 participants to as many as 12,000, also demonstrated that the more physically active schoolchildren are, the better they do academically. According to the authors:

“Physical activity and sports are generally promoted for their positive effect on children’s physical health; regular participation in physical activity in childhood is associated with a decreased cardiovascular risk in youth and adulthood. There is also a growing body of literature suggesting that physical activity has beneficial effects on several mental health outcomes, including health-related quality of life and better mood states.

In addition… there is a strong belief that regular participation in physical activity is linked to enhancement of brain function and cognition, thereby positively influencing academic performance.”

Clearly, the importance of encouraging your child to stay active after school and on weekends in order to reap the wonderful brain-boosting benefits that exercise has to offer cannot be overstated. Even better, be a positive role model and stay active together as a family.

Ideally, you’ll want to incorporate a variety of activities, as each type of exercise may offer unique benefits for your brain health and may even help your brain to grow as you get older, rather than shrink, which is the norm. A review of more than 100 studies, published in the Journal of Applied Physiology,4 revealed that both aerobic and resistance training are equally important for maintaining brain and cognitive health.

For instance, aerobic exercise has been found to improve your ability to coordinate multiple tasks – a skill needed for most people in today’s fast-paced world. It can also improve your ability to stay on task for extended periods. Resistance training, on the other hand, appears to improve your ability to focus amid distractions. Overall, exercise tends to improve the ability of different parts of your brain to work together. Effects such as these are thought to be due to changes in the prefrontal and temporal lobes, caused by exercise.

Your Brain “on Exercise”

Exercise encourages your brain to work at optimum capacity by causing nerve cells to multiply, strengthening their interconnections and protecting them from damage. Animal tests have illustrated that during exercise, their nerve cells release proteins known as neurotrophic factors. One in particular, called brain-derived neurotrophic factor (BDNF), triggers numerous other chemicals that promote neural health, and has a direct benefit on brain functions, including learning. Further, exercise provides protective effects to your brain through:

·         Greater blood and oxygen flow to your brain

·         The production of nerve-protecting compounds and growth factors that help create new nerve cells and support synaptic plasticity

·         Improved development and survival of neurons

Increased levels of norepinephrine and endorphins resulting in a reduction of stress and an improvement of mood

A 2010 study5 on primates published in the journal Neuroscience also revealed that regular exercise not only improved blood flow to the brain, but also helped the monkeys learn new tasks twice as quickly as non-exercising monkeys – a benefit the researchers believe would hold true for people as well.

Kids Benefit From Exercise in Many Ways

There’s absolutely no doubt that kids need exercise, and that most aren’t getting enough. Less than one-third of children aged 6 to 17 get at least 20 minutes of daily exercise in one form or another. This is tragic, considering the multitude of short- and long-term health benefits your child can gain from a regular exercise regimen, including:

Reduced risk of diabetes and pre-diabetes

Improved sleep

Stronger bones

Reduced restlessness or hyperactivity; helps decrease symptoms of ADHD

Improved immune system function

Improved mood

Weight loss

Increased energy levels

How to Get Your Kids Moving

First, it’s imperative to limit the amount of time your child spends watching TV, or playing computer and video games, and to replace some of these sedentary activities with exercise. There are plenty of physical activities to choose from, from sports and dance classes to gymnastics, bike riding and playing tag with friends. Allow your child to choose activities that appeal to them, and which are age appropriate.

Remember that the trick to getting kids interested in exercise at a young age is to keep it fun. Also keep in mind that short, spontaneous bouts of exercise throughout the day is actually the ideal way of doing it.

This is the way your body was designed to operate, and it’s what you’re mimicking when doing high-intensity interval training – i.e. short bursts of activity with periods of rest in between. Kids will typically fall into this behavior quite spontaneously, as long as they’re outdoors, and not cooped up in front of a TV or computer screen. Like adults, kids also need variety in their exercise routines to reap the greatest rewards, so be sure your child is getting:

·         Interval training

·         Strength training

·         Stretching

·         Core-building activities

This may sound daunting, but if your child participates in a gymnastics class, sprints around the backyard after the dog often and rides his bike after school, he’s covered. Also remember that acting as a role model by staying active yourself is one of the best ways to motivate and inspire your kids. If your child sees you embracing exercise as a positive and important part of your lifestyle, they will naturally follow suit. Plus, it’s easy to plan active activities that involve the whole family and double up as fun ways to spend time together. Hiking, bike riding, canoeing, swimming and sports are all great options.

Peak Fitness for Kids

As I mentioned earlier, intermittent bouts of exercise is actually the ideal form of exercise and is a key component of my comprehensive Peak Fitness program. While it may appear to be extreme to some, this type of short burst-type exercise is perhaps the most natural of all exercises for children!

Humans were simply not designed to run at a steady pace for extended periods of time, and you almost never see that type of behavior in the wild either. The research is so clear about the superior benefits of this type of exercise – which mimics natural behavior – that the American Heart Association and the American College of Sports Medicine have now changed their exercise cardio guidelines from slow but steady aerobic cardio to high-intensity interval training.

Benefits of high-intensity interval training include:

Significantly improving your insulin sensitivity, especially if you’re on a low-processed-food, low-sugar or low-grain diet

Optimizing your cholesterol ratios, when combined with a proper diet

Boosting fat metabolism and optimizing your body fat percentage (as a result of improved conservation of sugar and glycogen in your muscles)

Virtually eliminating type 2 diabetes and high blood pressure

Naturally boosting your levels of human growth hormone (HGH)

Increasing your aerobic capacity

Peak Fitness Instructions

A key component is to raise your heart rate up to your anaerobic threshold (220 minus your age) for 20 to 30 seconds, followed by a 90-second recovery period. Depending on your child’s current level of fitness, he may need to work his way up to eight cycles. I recommend starting with two to four cycles, and gradually increasing to eight. There are no rules for the specific manner in which this is achieved – your child could do this running in the backyard, or using a treadmill, elliptical machine, or recumbent bike (provided your child is old enough to use such machines safely, of course), or they could do it bicycling outdoors.

For a demonstration of the core principles, and important safety tips, please see the following video. It also includes a demonstration of proper warm-up. While this video is primarily directed to adults, as opposed to children engaged in spontaneous high-intensity play, it can still give you some helpful pointers to keep in mind when you’re coaching your kids.

Here are the core principles:

  • Warm up for three minutes
  • Then, go all out, as hard as you can for 30 seconds
  • Recover at a moderate pace for 90 seconds
  • Repeat 7 more times, for a total of 8 repetitions
  • Cool down for a few minutes afterwards by cutting down your intensity by 50-80 percent

Source: Dr. Mercola