Knowing Infinity

•June 6, 2016 • Leave a Comment

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If you love math as much as I do, you’re pretty much constantly starving for a juicy math movie. Pi, Good Will Hunting, A Beautiful Mind, The Imitation Game, there are only a handful. The Man Who Knew Infinity left me inspired and hungry to know more about its actual star – mathematician Srinivasa Ramanujan. With actors like Jeremy Irons and Dev Patel carrying you down the story’s path, you’ll find yourself on a fascinating journey of one man’s perseverance to prove himself to 1913 English academia – 5000 miles away from his home in Madras, India. Why prove himself? Because of his self-taught, inherent, almost mystical understanding of mathematical partitions and the establishment’s demand for verification through proofs and theorems.

Partitions is part of a mathematical number theory concept of combinatorics, where a partition is a way of writing a positive integer (n) as a sum of positive integers. For example, the seven partitions of five would look like:

  • 5
  • 4+1
  • 3+2
  • 3+1+1
  • 2+2+1
  • 2+1+1+1
  • 1+1+1+1+1

I am not sufficiently qualified to paraphrase the significance of (the real) Ramanujan’s formula, but it has been used in statistical physics and in calculating quantum partition functions of atomic nuclei.

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Ramanujan’s English mentor, Professor G.H. Hardy (portrayed by Jeremy Irons), played the role of lion tamer, forcing the young genius to dress like an Englishman and mold himself into that of his peers. But Ramanujan had nothing in common with his peers…nor anybody else.

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Ramanujan didn’t need to walk the path of scientific rigor to deduce partitions – he knew them; he understood them. Said Professor Littlewood in the film of Ramanujan, “Every positive integer is like one of (his) personal friends.” But, as Hardy demanded, in order to publish and be taken seriously, he must do more than simply provide an answer. He must demonstrate each painstaking step and identify the path. And while Hardy honed Ramanujan’s untamed genius, the young mathematician suffered through mathematical proofs to try to verify and validate his formula.

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Ramanujan’s life in Madras is a fascinating part of the story, so far removed from the stilted, structured academic fortress of Cambridge’s elite ruling class. It is here, in Madras, that the most compelling character conflict exists – between Ramanujan’s mother and his young wife, Janaki. Certain that his young, beautiful wife has forgotten him, he mourns her lack of correspondence and drowns his sorrow into deeper consumption of his endless proofs. Combined with cold, rainy English weather, lack of food befitting a vegetarian diet, and constant humiliation by his English benefactors, Ramanujan’s broken heart causes his health to deteriorate.

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The very brief, culturally unlikely and deeply meaningful collaboration between Hardy and Ramanujan resulted in Ramanujan becoming a Fellow of the Royal Society of London and what became known as The Hardy-Ramanujan Asymptotic Partition Formula, the effect of which has had a transformative impact on modern mathematics. You can read about and practice the partitions formula here.

Director Matthew Brown, in this portrayal of one of mathematics’ brightest stars, shows you Ramanujan’s inspiration, alienation, desperation, but not without validation of his work. It’s a meaningful ride into a fascinating slice of history and a tiny glimpse into the mind of a true genius.

Thanks for reading, and if you know of a good math movie that I’ve missed, please comment!

Bike Riding to Bliss

•October 16, 2015 • 1 Comment

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I love when unlikely things pull me out of my typical midweek work-eat-sleep treadmill. I called my parents today, and they couldn’t talk because they were having one of their favorite rituals – bike riding across the Cape Cod Canal and then eating hot dogs on the grass by the water. It sounds like something 7-year olds would do. My parents are in their 70’s and have been married for 50 years. Precious!!

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So does five decades of marriage together make it unlikely that they would still make time for romantic rituals like this? I guess so. But I also feel so touched to know that they still have this deep connection, and so happy that these are my primary role models in life. They have set this example for my sister and I about making things like bike riding and hot dogs a top priority. I don’t eat hot dogs, but I hope with all my heart that I get to spend 50 years with my husband and that we’re still riding bikes together by then.

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What’s cluttering up YOUR space?

•July 8, 2015 • Leave a Comment

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Find five things on your desk that are taking up space but unused.

  1. Empty water glass, been there for at least 3 weeks
  2. Note pads, various sizes, some empty, some half-used
  3. Vitamin E (unopened bottle), been there since January
  4. 3 t-shirts from a vendor presentation, folded, never worn, stuffed in bookcase
  5. Broken telephone

I’m looking at this list and remembering that “things” have and use energy, related to why we kept them in the first place, relationship associations, memories, not to mention their potential for distraction. What can you put away, file, organize, hand off or toss out? Do you want to consciously populate these spaces with new, shiny, inspiring items, or just simply enjoy the emptiness?

Some good reading on space and clutter here:

http://lifehacker.com/how-clutter-affects-your-brain-and-what-you-can-do-abo-662647035

https://www.psychologytoday.com/blog/the-good-life/201207/home-clutter-confusion-and-chaos

clean desk

Yes, Teacher

•October 19, 2014 • 1 Comment

Though I’m the farthest thing from a stereotypical history buff, I’m fascinated by ancient civilizations, especially the variety that purportedly vanished under a cloak of intrigue. Anasazi, Olmec, Minoan, Nabateans, Moche. As you read more about them, their disappearances seem more legitimate and evolutionary than conspiracy theorists care to admit. But without a time machine, we can’t really say for sure what happened thousands of years ago.

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And this line of inquiry piques my curiosity about the ultimate fate of our own fragile species on earth. Drought, meteors, earthquakes, or will it be something more home-grown and insidious, like an organism? Maybe something too microscopic for our eyes to detect, though wielding an unspeakable power over our physiology, immunity, and strength.

Like a virus.

Ebola

What is the root cause of the mishandling of the Ebola epidemic in West Africa so far? Is it an internal, organizational breakdown, a lack of education to the local population about the threat, or a perilous political funding dilemma? Can we continue to blame escalating death toll on operational logistics like containment, or is it always about money? The GOP and Tea Party will no doubt continue to oppose broad funding for institutions like the WHO and CDC. So I wonder, then, what Ebola is now revealing about how our political divisions are hindering progress and preventing us from fighting back on the same team. Look at Ebola 2014’s track record so far…how much more time do we really have to waste?

Look at things like the Black Death which, in the 1300s, claimed up to 200 million lives. The cause? A pathogen (yersenia pestis) carried by rat fleas and spread by contact with exposed animals. In 1300, we didn’t know that washing your hands with soap and water could protect our health. And cigarette smoking in the early to mid 1900’s – no one knew it was harmful back then. Now we know. And in 2014 in the absence of budgetary allocation, education and awareness are the strongest tools we have.

Black Death (Yersinia pestis)

Black Death (Yersinia pestis)

HIV

HIV

H1N1 (swine flu)

H1N1 (swine flu)

Mimivirus, the largest and possibly the oldest virus on earth

Mimivirus, the largest and possibly the oldest virus on earth

The reality: viruses such as Ebola are smart, more than smart. They learn. They can adapt, and change. A virus mutates for the same reasons any other organism mutates – to survive. Host organisms are not passive observers of this process either. The host, a human body in the case of Ebola, will constantly deploy strategies to prevent viral infection. So the next time the virus comes in contact with a host cell, it may have issues attaching itself to the cell’s surface membrane. To compensate for this temporary setback, the virus could change its surface proteins to essentially trick the host into allowing it to attach. Scary. Sort of like Star Trek shield modulations to prevent a sensor lock by an enemy species.

What this means is that Ebola could, at some point, mutate into something more easily transmittable, and with that comes unthinkable possibilities. So until we discover a cure, Ebola comes to gives us another chance to pay attention, to hear her wisdom, to learn to listen to each other, and to change.

BrainTrain

•October 5, 2014 • 1 Comment

How much brain anatomy do you remember from high school? Forebrain, midbrain, hindbrain, what do they all do again?

300px-Brain_Lobes

Lobes:

  • Frontal – Planning, organizing, problem solving, memory, impulse control, decision making
  • Parietal – Sensory information (hot, cold, pain), orientation (up, down), balance
  • Temporal – Sound, speech, language, memory, fear
  • Occipital – Shape and color perception, seeing, reading
  • Cerebellum – Balance, movement, coordination
  • Brain stem – Breathing, heart rate, blood pressure, swallowing

Peeling back a layer, we get to the center of our emotional life – the limbic system.

limbic system

  • Thalamus – The brain’s relay station, channeling impulses from most of the senses. Important in sorting the importance and significance of some information over others.  The “waiting room” where sensory information is sent before going to the cerebral cortex for processing.
  • Hypothalamus – Moods and motivation, sexual maturation, temperature regulation, hormones, hunger, thirst, using both electrical and chemical messages
  • Amygdala – Center of emotions and motivation
  • Hippocampus – Long term memory, best explained as your computer harddrive, involved in the storage of huge amounts of data
  • Basal ganglia – Cognition, movement coordination, voluntary movement, procedural learning, habits, decisions about how to act in a given situation

Up until twenty or thirty years ago, we thought the brain’s composition was fixed at birth. And now, we’re discovering that it’s more like a lump of clay that can be molded and changed – not just by what we learn and experience, but by how we want it to change. As an infant brain begins to grow, so do neurons, growing in length and numbers, and extending and making critical connections as we view, understand, and reciprocate our world.

Neuroplasticity, the notion that the brain is trainable at any age and can adapt, has become a ubiquitous household term. The concept is that you’re never too old (or young) to learn new things, deepen your connections, evolve beyond baggage,  develop new skills, and heal. And all this magic happens in the neurons.

brain

Neurons make up the communication highway in our brains, through which we process, understand, and build our world and reality. Neurons are cells within the nervous system that send information to other nerve cells, muscles, or gland cells. They have a cell body, axon, and dendrites covered with synapses, which are contact points where one neuron touches another. Mammals generally have between one million and one billion (!!!) neurons.

neurons

Check out these neurons under a microscope:

neurons under scope

As homo sapiens, we’re capable of not only higher consciousness but of growing/training/evolving our brains, and that process requires care. Think stress management. Stress adversely affects almost everything in the body and mind.  Aside from our cardiovascular health, the release of cortisosteroids (hormones) inhibits brain growth, affecting our ability to learn and retain information.  Try to incorporate a few of these each week as a recipe for Brain Health:

  • Yoga – Reduces anxiety and stress and improves cognitive performance. It lifts your mood, helps regulate blood pressure and hypertension, calms your nervous system.
  • Aerobics – The release of BDNF (a protein) enhances the growth of neural connections. Weight training increases our ability to focus and make decisions, flooding the brain with mental mojo. Think SWEAT!
  • Nutrition and supplements – Try antioxidants like E and C, B-Complex for combatting stress (B6, B12, Folic acid),  Gingko, Magnesium, CoQ10.
  • Meditation as a regular practice (even just a few minutes a day) calms the mind and body, quiets the amygdala (emotions) and activates the hippocampus.
  • Sleep – Do you get enough, and roughly the same amount each night? Sleep regulates the nervous system, boosts concentration and coordination, keeps memory sharp and gives you the agility to adapt to different stresses.
  • Rest and downtime – Different from sleep but of equal importance. Try reserving 5 minutes a day for mental resting without any kind of stimulus. No reading, no TV, no iPhone, iPad, no music. Just resting quietly, breathing, with your eyes open, alert, and calm. Can’t do 5 minutes? How about 1?
  • Caffeine management – Could you take 2 days off a month to optimize its benefits?  Caffeine and in particular coffee, now comes with a short list of advantages, including the ability to store long-term memories.
  • Brain Stretch – Push the limits of your comfort zone and try new things to keep your brain active and healthy. Drive an alternate route to work. Wear your hair a different way. Write with your non-master hand. Or take a class to develop a skill you never thought you’d be able to learn. Piano lessons? Absolutely!

piano

Explore MOROCCO: Chicken Tagine

•September 7, 2014 • 2 Comments

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What do you think of when you see the word Morocco? Desert, perhaps? For me, it’s tile.

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I can’t get enough of the eye candy color combos, intricate patterns and textile interweaving of lines and shapes. So, I thought, how about a foray into the historical realm of Moroccan cuisine? And what better way than trying my hand at Chicken Tagine? If you’ve never made this dish before, I recommend starting with a spice mix, allowing the professionals to blend them in just the right amounts and ratio. The result – you can put this dish together in about 40 minutes start to finish. Here’s the one I used: Urban Accents Moroccan Tagine, containing a sensory overload of coriander, cinnamon, cardamom, garlic, red pepper, black pepper, basil, cumin, you get the picture.

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Start with boneless, skinless chicken breasts and cut them into cubes. Brown them in a skillet with olive oil and chopped onions. Next, add the spice mix, chicken broth, and dried apricots and simmer for 30 minutes. The spice mix contains a recipe and ingredients list for reference. Serve the dish over a bed of cous cous and sprinkle with slivered almonds and fresh mint leaves. OMG!! So good.

So the word ‘tagine’ not only refers to a Moroccan tagine stew (which can be made with chicken or lamb) but also a piece of cookware historically used to slow-cook the stew.

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The terracotta earthenware tagines are made for slow cooking tagine stew over an open fire. And then some are decorative serving pieces. I cooked my dish in a stainless steel skillet and served it out of a beautiful cobalt tagine.

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Like Tony Bourdain, I like to study and reflect on the social and cultural elements that influence the food I love – in this case, Berber culture.

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There’s so much more I’m hungry to learn. But for now, I’m happy with tonight’s small mastery. Bon Apetite!

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Crazy About Pi

•September 2, 2014 • 3 Comments

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Curious about pi and jealous of your geeky math-adept friends who have the first forty decimals memorized? This is an awesome video I discovered that provides just enough detail to be interesting:

The Infinite Life of Pi by Reynaldo Lopes

But my deepest Pi passion belongs to Darren Aronofsky in his legendary 1998 masterpiece “Pi” starring Sean Gullette as the tortured, genius mathematician Max Cohen.

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From Pi the movie: “Personal note, When I was a little kid, my mother told me not to stare at the sun. So once, when I was six, I did. The doctors didn’t know if my eyes would ever heal. I was terrified, alone in that darkness. Slowly, daylight crept in through the bandages and I could see. But something else had changed inside me.”

Max is a solitary number theorist frantically searching for a numerical key that he believes will unlock all of the universe’s mysteries. This 216-digit number key, spit out by his computer just before it crashed, could just as easily decode stock market patterns as it could be the name of God. 

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Chased by paranoia, hallucinations, and social anxiety disorder, Max unravels further when he is pursued by Wall Street agents showing a more than casual interest in his work.   

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Meanwhile, Max meets Lenny Meyer at a coffee shop, a Hassidic Jew who also studies number theory in the context of the Torah. He shows Max the relationship between the Hebrew alphabet and numbers, and his theory that these numbers are messages sent to the Jewish people by God.

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Max finally realizes that he doesn’t need to search for the elusive number. He knows it, he feels it, it lives in his head. And it’s killing him.

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Aronofsky shot the film on high contrast black and white reversal film for a stark, edgy feel that leaves you asking more questions than you had to start with. For the intellectually-curious, that’s a good thing.

“One: Mathematics is the language of nature. Two: Everything around us can be represented and understood through numbers. Three: If you graph the numbers of any system, patterns emerge. Therefore, there are patterns everywhere in nature.”

If you love math, number theory, and you frequently ponder the nature of the universe, you will love this film.

Watch the trailer here

 

 

 
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