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RIP Professor Maryam Mirzakhani. The first woman awarded the Fields Medal prize died of breast cancer on 15 July 2017. Read this informative tribute by +John Baez.
Maryam Mirzakhani, 1977 - 2017

She died yesterday, a mathematician who had not yet reached the height of her powers: the first Fields medalist from Iran, and also the first woman to win that honor. Here's what I wrote when she won:

As a child in Tehran, she didn't intend to become a mathematician - she just wanted to read every book she could find! She also watched television biographies of famous women like Marie Curie and Helen Keller. She started wanting to do something great... maybe become a writer.

She finished elementary school while the Iran-Iraq war was ending, and took a test that got her into a special middle school for girls. She did poorly in math her first year, and it undermined her confidence. “I lost my interest in math," she said.

But the next year she had a better teacher, and she fell in love with the subject. She and a friend became the first women on Iranian math Olympiad team. She won a gold medal the first year, and got a perfect score the next year.

After getting finishing her undergraduate work at Sharif University in Tehran in 1999, she went on to grad school at Harvard. There she met Curtis McMullen, a Fields medalist who works on hyperbolic geometry and related topics.

Hyperbolic geometry is about curved surfaces where the angles of a triangle add up to less than 180 degrees, like the surface of a saddle. It's more interesting than Euclidean geometry, or the geometry of a sphere. One reason is that if you have a doughnut-shaped thing with 2 or more holes, there are many ways to give it a hyperbolic geometry where its curvature is the same at each point. These shapes stand at the meeting-point of many roads in math. They are simple enough that we can understand them in amazing detail - yet complicated enough to provoke endless study.

Maryam Mirzakhani took a course from McMullen and started asking him lots of questions. “She had a sort of daring imagination,” he later said. “She would formulate in her mind an imaginary picture of what must be going on, then come to my office and describe it. At the end, she would turn to me and say, ‘Is it right?’ I was always very flattered that she thought I would know.”

Here's a question nobody knew the answer to. If an ant walks on a flat Euclidean plane never turning right or left, it'll move along a straight line and never get back where it started. If it does this on a sphere, it will get back where it started: it will go around a circle. If it does this on a hyperbolic surface, it may or may not get back where it started. If it gets back to where it started, facing the same direction, the curve it moves along is called a closed geodesic.

The ant can go around a closed geodesic over and over. But say we let it go around just once: then we call its path a simple closed geodesic. We can measure the length of this curve. And we can ask: how many simple closed geodesics are there with length less than some number L?

There are always only finitely many - unlike on the sphere, where the ant can march off in any direction and get back where it started after a certain distance. But how many?

In her Ph.D. thesis, Mirzakhani figured out a formula for how many. It's not an exact formula, just an 'asymptotic' one, an approximation that becomes good when L becomes large. She showed the number of simple closed geodesics of length less than L is asymptotic to some number times L to the power 6g-6, where g is the number of holes in your doughnut.

She boiled her proof down to a 29-page argument, which was published in one of the most prestigious math journals:

• Maryam Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces, Annals of Mathematics 168 (2008), 97–125,

This is a classic piece of math: simple yet deep. The statement is simple, but the proof uses many branches of math that meet at this crossroads.

What matters is not just knowing that the statement is true: it's the new view of reality you gain by understanding why it's true. I don't understand why this particular result is true, but I know that's how it works. For example, her ideas also gave here a new proof of a conjecture by the physicist Edward Witten, which came up in his work on string theory!

This is just one of the first things Mirzakhani did. She's now a professor at Stanford.

"I don't have any particular recipe," she said. "It is the reason why doing research is challenging as well as attractive. It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out."

She has a lot left to think about. There are problems she has been thinking about for more than a decade. "And still there’s not much I can do about them," she said.

"I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers."

I got some of my quotes from here:

and some from here:

They're both good to read. For a mathematically informed obituary, see this by Terry Tao:

The animated gif is a clip from this video:

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+John Baez on the science of red sprites: Sprites are quite different from lightning. They're not electric discharges moving through hot plasma. They involve cold plasma - more like a fluorescent light.
Red sprites

Far above a thunderstorm in the English Channel, red sprites are dancing in the upper atmosphere.

You can't usually see them from the ground - they happen 50 to 90 kilometers up. People usually photograph them from satellites or high-flying planes. But this particular bunch was videotaped from a distant mountain range in France by Stephane Vetter, on May 28th.

Sprites are quite different from lightning. They're not electric discharges moving through hot plasma. They involve cold plasma - more like a fluorescent light.

They're quite mysterious. People with high speed cameras have found that a sprite consists of balls of cold plasma, 10 to 100 meters across, shooting downward at speeds up to 10% the speed of light... followed a few milliseconds later by a separate set of upward moving balls!

Sprites usually happen shortly after a lightning bolt. And about 1 millisecond before a sprite, people often see a sprite halo: a faint pancake-shaped burst of light approximately 50 kilometres across 10 kilometres thick.

Don't mix up sprites and ELVES - those are something else, for another day:

You also shouldn't confuse sprites with terrestrial gamma-ray flashes. Those are also associated to thunderstorms, but they actually involve antimatter:

A lot of weird stuff is happening up there!

The photo is from here:


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Hidden Secrets of Parasitic Plants
Dr +Tommy Leung has written about a common but mysterious parasite, buried deep in the roots of other trees and plants in Brazil (and also found in other parts of Central and South America). Unlike other plant parasites, the Langsdorffia hypogaea is is wholly dependant on its host. Unless you know what to look for, this parasite will easily escape your gaze; however, once you recognise its red, mushroom-like flowers, you'll find they are widespread. The flowers only appear during the dry seasons and it is the only external signs of this parasitic plant. Dr Leung writes:

Parasitic plants are important parts of many ecosystems due to the wide range of organisms they interact with. While they can be detrimental to the host plant's growth and reproduction, they are also a food source for many animals. For most parasitic plants very little is known about their basic natural history, let alone the impact they have on the surrounding environment.

Find out about how this parasitic plant pollinates and its secrets yet to be uncovered by science.
Red Flowers And Parasitic Tubers
I've written a new Parasite of the Day post! This one is about a type of parasitic plant from Central and South America that lives as a parasitic tuber attached to the roots of its host plant, and sprouts red flowers that pokes out the ground like mushrooms. To read more about this parasitic plant, follow the link below.

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Tribute to Astrophysicist Vera Rubin, the "Mother" of Dark Matter
Astrophysicist Professor Vera Rubin, National Medal of Science awardee who confirmed the existence of dark matter, died on 25 December 2016.

Dark matter is "the invisible material that makes up more than 90% of the mass of the universe." Rubin's pioneering work progressed from 1965 to the late 1970s. Her webpage describes the beginning of this discovery:

"By the late 1970s, after Rubin and her colleagues had observed dozens of spirals, it was clear that something other than the visible mass was responsible for the stars’ motions. Analysis showed that each spiral galaxy is embedded in a spheroidal distribution of dark matter — a “halo.” The matter is not luminous, it extends beyond the optical galaxy, and it contains 5 to 10 times as much mass as the luminous galaxy. The stars' response to the gravitational attraction of the matter produces the high velocities. As a result of Rubin's groundbreaking work, it has become apparent that more than 90% of the universe is composed of dark matter."

Rubin's research remained prolific until the early 2000s, as she continued to study various models for the composition of the dark halos. Among her most recent publications was an examination of the rotation curves of spiral galaxies.

Until her retirement, Rubin worked at the Carnegie Institution for Science Department of Terrestrial Magnetism in Washington, D.C. She was awarded the National Medal of Science in 1993. She was also a member of the National Academy of Sciences and in 1996, she received the Royal Astronomical Society’s Gold Medal, the first woman to do so 168 years after Caroline Hershel (1828).

Neta Bahcall of Princeton University describes Rubin's scientific significance: “A pioneering astronomer, the ‘mother' of flat rotation curves and dark-matter, a champion of women in science, a mentor and role model to generations of astronomers.”

Carnegie Science describes Rubin's scientific impact extends far beyond her pioneering research: "She was an ardent feminist, advocating for women observers at the Palomar Observatory, women at the Cosmos Club, Princeton, and she even advised the Pope to have more women on his committee."

See +Yonatan Zunger's tribute to Professor Rubin in the linked post.

Learn more
Read some background on Rubin from Carnegie Science:

See Rubin's biography and publications: #stemwomen #astrophysics #astronomy
And in the continuing march of the Angel of Death, I am sad to report that Vera Rubin died today at the age of 88. Rubin was most famous as the discoverer of dark matter: the invisible and still-mysterious substance which makes up 85% of the mass of the universe.

Dark matter had been hypothesized back in the 1930's, but it wasn't until the 1970's that it was finally observed. Rubin was studying distant galaxies when she noticed that the rotation speed of their outer edges didn't jibe with the speed they should have based on the amount of visible matter.

You can tell how fast something is moving relative to you using the Doppler effect: the same thing that makes a siren sound higher-pitched as it moves towards you and lower-pitched as it moves away. It works because sound looks like a sine wave of rising and dropping pressure, and pitch corresponds to the time between successive peaks. When the source is moving towards you, the first peak emitted by the siren is already moving towards you at the speed of sound, but the second peak will get there sooner than expected, because it had the benefit of moving towards you at the siren's speed for one more period and then being sent off at the speed of sound. This means that if you know the original pitch of the siren, you can even figure out how fast it's moving based on the pitch you hear.

The same trick works with light, only now instead of pitch, it's color that depends on the time between peaks; things appear bluer when they approach, and redder when they recede. Since starlight contains a lot of easily measured standard lights in it - colors like those that Hydrogen and Helium emit when heated, and which have a very distinct pattern when viewed through a prism - we can measure the speed of distant stars and galaxies. And by comparing the speed of the left and right edges of a galaxy, you can tell how fast it's spinning.

But we've known how to calculate the orbits of stars since Kepler, and from the amount of light a galaxy emits, we can make a pretty good guess at how heavy it is. From that, you would conclude that the stars at the outside of a galaxy should be moving more slowly than the ones at its center, in a nicely predictable way.

But that's not what Rubin saw! Instead, she discovered that the stars at the outside were moving at the same speed as the ones at the center - something only possible if there was some extra, invisible mass pulling them.

What Rubin discovered was that there is an invisible halo of "dark matter" surrounding each galaxy, nearly ten times as massive as the galaxy itself. It's "dark" in the plainly literal sense: unlike stars, it's not actively on fire and glowing.

In the decades since, dark matter has become a core area of study in astrophysics. Using the same techniques and ever-more-sophisticated telescopes, including dedicated satellite observatories, we've mapped the presence and motion of dark matter in greater detail, and discovered that it's far more mysterious than we first suspected. For example, we know it's not made up of ordinary atomic or molecular stuff, because its dynamics is all wrong; neither is it made up of massive neutrinos or any other kind of matter we understand.

(There's also dark energy, an even more widespread and invisible field, discovered a few decades later. Unlike dark matter, which attracts things by gravity, dark energy seems to provide a universe-spanning, diffuse, but very distinctly measurable repulsive force. It's even less understood than dark matter; most scientists suspect that if we understood these things well, we'd know a lot more about the nature of the universe)

Rubin therefore sits in the pantheon of the great astronomers of the 20th century. Alas, her death means she will not get the Nobel Prize that many have been arguing she deserves for a very long time: the prize cannot (by the terms of its founding grant) be awarded posthumously. But she remains one of the most important researchers in the field, and her work will continue to have a profound impact on our understanding of Nature for generations to come.

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Elixir or Bunk: Do alkaline foods protect against cancer?
Alkaline Water
Elixir or Bunk?

When people say:
"You must alkalinize your body."

You can respond with:
"What are you talking about? A healthy body drastically ranges in pH depending on the organ system and its function."

(They weren't told this at their MLM meeting where magic water cures every known disease.)

Note: pH refers to acid/alkaline level. The lower the number the more acid. When the stomach is functioning optimally the normal pH is around 1.2 (very acid!!). This is why drinking apple cider vinegar (which is acidic) actually improves digestion.

Blood pH
The pH balance of your blood stays within a very narrow range. If it changes too much you would go into a coma then die. For this reason it is ridiculous to think that any change in your diet will significantly affect your blood pH. If this was the case, we would never have survived as a species (that first pizza would've killed us off for sure).

Btw, checking your urinary and oral pH has nothing to do with blood pH. These numbers can change per meal making the conclusions people draw from them sometimes silly.

Buffer Systems
There are a handful of buffer systems that constantly adjust the climate of the body. The kidneys, for example, have two very crucial roles in maintaining the pH balance: to reabsorb and regenerate bicarbonate from urine, and to excrete hydrogen ions and fixed acids (anions of acids) into urine. 

Your body adjusts its pH so that you don't have to.

How Food Can Actually Affect pH
If you eat foods that damage your body, and subsequently damage your buffer systems, then you're in trouble. For example, eating a diet high in carbohydrates (especially processed) is associated with diabetes and related kidney dysfunction. If the kidneys are not functioning properly then the acid balance function will be compromised resulting in acidosis (bad). But this is not because the carbohydrate foods are directly changing your pH!

Notice on the chart that fruit is very alkaline but is actually not good for a diabetic because it's high in sugar.

Drinking Alkaline Water
Many of the claims are bogus and founded on false notions. With that said, these people are often experiencing improvements in their health. This could be for many reasons. If they joined a belief system then it could be psychogenic. Positive beliefs are powerful. In practice I come across many bizarre and unfounded ideas but if it helps the patient emotionally, and is not harmful, then I leave it alone. Joining MLMs can be very motivating. A person might start taking better care of themselves, exercise more, eat better, and of course drink more water all of which will significantly improve health.

It is possible that introducing large amounts of alkaline water into the stomach (which is normally acid) creates a compensatory response of the stomach to produce more acid thus improving its function. Digestion would improve short term but because the stomach is stressed it will be followed by a worsening of digestive function over time.

Claim: Cancer Grows in Acid
This is major oversimplification. Cancer is an opportunist and takes root in a compromised system. There are many aspects of that system to consider with each person being unique. Anyone pointing to the one and only factor is likely selling something. 

What to Eat?
The pH of many foods completely changes after digestion as the components hit the blood stream making this charts like this hard less useful. I see great foods above and below the neutral line. I suggest eating a whole foods diet low in processed foods and to see a doctor trained in clinical nutrition if needed.

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PSA on Discerning #JunkScience
How to Read a Medical Research Paper

Biomedical research is a field that touches all our lives at some point or another. Through it, we have identified new ways to prevent, diagnose, or treat most of the diseases that affect us. As such it is unsurprising to come across people who have various opinions about the accuracy of these discoveries. By confusing large-scale data with personal anecdotes, by mistaking peer-reviewed research with pseudoscience, the waters are made muddy until even undecided fence-sitters become needlessly skeptical thanks to the "well we must teach the controversy!" stories.

All this has led to an unprecedented epidemic of anti-science rhetoric, where overwhelming scientific consensus is regarded with suspicion. Vaccines, genetically modified food, diet, nutrition, chemotherapy, vitamins, supplements, acupuncture, 'cupping' (thanks Michael Phelps)...the list is endless. Matters aren't helped when newspapers overhype findings to increase circulation or clicks - CANCER CURE FOUND or DIABETES VACCINE SORTED or TRUMP MANIA CURED (I wish) or whatever.

So how do you decide for yourself, without being misled by snake-oil salesmen trying to sell their latest elixir or inexperienced journalists trying to get more clicks? Unfortunately academic jargon means reading the original research paper isn't easy unless you have a science background. Assuming the paper isn't behind a paywall and you actually get your hands on a copy, how do you begin to make sense of it? How do you know whether it's legit, so to speak?

It's all the more heartbreaking when patients, who have so much at stake, can end up endangering their health because of false promises. Open access research means more people can access research papers, but that doesn't necessarily mean the research itself is accessible.

Today I stumbled across an awesome, interactive, free to use website that guides people through the process of reading a scientific paper. It teaches you the things you should look out for, such as;

Is the paper peer-reviewed?
Who carried out the research?
Who funded it?
Was it reviewed by an ethics committee?

If it's paid for by a tobacco company and it says smoking doesn't cause lung cancer then you should rightly be very suspicious!

It also teaches you the difference between a review or meta analysis vs an individual study, and whether it's good for basing decisions on. It even goes on to explain clinical studies, and how you should evaluate them before deciding actually no, organic kale juice can't cure cancer...

Check it out -

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Nobel Laureates' Letter Supporting Precision Agriculture (GMOs)
Genetically modified foods are one the most misunderstood scientific processes of our day. The world's leading research organisations have shown that there is no scientific basis for the moral panic over GMOs. Billions of people eat foods that have been enhanced or otherwise modified every day - without problems or objections, mostly because people are unaware of what GMOs are and how the science works. From the humble carrot to new developments like Golden Rice, designed to address vitamin and food shortages, GMOs have long been a part of our food supply.

A new letter signed by over 100 Nobel Laureates addresses a Greenpeace campaign against Golden Rice, a food source that the United Nations and international scientists have endorsed as an important way to address vitamin A deficiency in developing nations.

"Greenpeace has spearheaded opposition to Golden Rice, which has the potential to reduce or eliminate much of the death and disease caused by a vitamin A deficiency (VAD), which has the greatest impact on the poorest people in Africa and Southeast Asia.

"The World Health Organisation estimates that 250 million people, suffer from VAD, including 40 percent of the children under five in the developing world. Based on UNICEF statistics, a total of one to two million preventable deaths occur annually as a result of VAD, because it compromises the immune system, putting babies and children at great risk. VAD itself is the leading cause of childhood blindness globally affecting 250,000 - 500,000 children each year. Half die within 12 months of losing their eyesight."

Background on Golden Rice
Much of the opposition to GMOs, and Golden Rice specifically is due to poor scientific literacy. A study by the Pew Research Centre finds that 88% of scientists from the American Association for the Advancement of Science understand that GMOs are safe, compared with only 37% of the public, who have a limited understanding of the science.

Professor Ingo Potrykus addresses the science and emotional backlash over Golden Rice. Note he has given away the patent.

"Golden rice fulfils all the wishes the GMO opposition had earlier expressed in their criticism of the use of the technology, and it thus nullifies all the arguments against genetic engineering with plants in this specific example. Golden rice has not been developed by or for industry. It fulfils an urgent need by complementing traditional interventions. It presents a sustainable, cost-free solution, not requiring other resources. It avoids the unfortunate negative side effects of the Green Revolution. Industry does not benefit from it. Those who benefit are the poor and disadvantaged. It is given free of charge and restrictions to subsistence farmers."

From an earlier Community discussion, via our moderator Professor +Rajini Rao: "Golden Rice technology is based on the simple principle that rice plants possess the whole machinery to synthesise β-carotene, and while this machinery is fully active in leaves, parts of it are turned off in the grain. By adding only two genes, a plant phytoene synthase (psy) and a bacterial phytoene desaturase (crt I), the pathway is turned back on and β-carotene consequently accumulates in the grain." More:

Beta carotene is the more "natural", safer, bioavailable precursor to Vit A. The same compound in carrots. 

The World Health Organisation, the European Commission, the National Academy of Sciences, the American Medical Association, the American Association for the Advancement of Science, seven of the world's science academies, and various other science organisations have endorsed the technology and found no safety issues.

Further References
The letter:

Image, from the Genetic Literacy Project, with more resources on GMOs and Golden Rice:

A reminder that we are a science community and that we support the science of GMOs:

WHO publications on GMOs:

Richard Green on the scientific consensus of GMOs:

The science and safety of GMOs:

Misinformation about GMOs dispelled by an analytical chemist:

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Don't try this at home
+Corina Marinescu digests this interesting development in origami robots.
Ingestible origami robot
In experiments involving a simulation of the human esophagus and stomach, researchers at MIT, the University of Sheffield, and the Tokyo Institute of Technology have demonstrated a tiny origami robot that can unfold itself from a swallowed capsule and, steered by external magnetic fields, crawl across the stomach wall to remove a swallowed button battery or patch a wound.

Say you accidentally swallow a battery (it's not uncommon, about 3,500 button batteries are swallowed each year in the US alone). Rather than undergo surgery to have it removed, you can swallow a robot! ;)

Here's how it works:
The origami robot, made of dried pig intestine, is folded into an ice capsule that travels down the esophagus and into the stomach.

The ice then melts, allowing the robot to unfold. Currently, the robot is controlled by an external magnetic field, but researchers hope that in the future it will be able to control itself.

Once in the stomach, the robot is controlled to perform its specific task, so in the event that you swallow a battery, the robot will attach to it and then eliminate it through the digestive tract. This is a less invasive alternative to the current solution: surgery.

The little battery warrior hasn't been tested on humans yet, but it was successful in its mission to remove a battery from a synthetic stomach.

Anyways, no AAAs please!


Source & further reading:

#robos   #scitech   #robomed   #medicine   #innovation  
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Crystallizing thoughts on oxalates
If you like the post below from +annarita ruberto about calcium oxalate, check out these other posts.

Rhubarb poisoning not from a rube via +Chad Haney

Living Stones via +Carissa Braun

Jackstone calculi via +Corina Marinescu

Did Popeye the Sailor get his strength by eating spinach? via +Siromi Samarasinghe
Rounded Earthstar (Geastrum saccatum)

Geastrum saccatum, commonly known as the rounded earthstar, is a species of mushroom belonging to the Geastrum genus. It has a worldwide distribution and is found growing on rotting wood.
It is a small but beautiful mushroom that features a round spore case sitting atop a star with 4-9 arms.

It is considered inedible by mushroomers because of its bitter taste. It is a common mushroom, but collections are at their peak during late summer. The opening of the outer layer of the fruiting body in the characteristic star shape is thought to be due to a buildup of calcium oxalate crystals immediately prior to dehiscence.

G. saccatum is distinguished from other earthstars by the distinct circular ridge or depression surrounding the central pore. In Brazil, its common name translates to "star of the land".

A β-glucan–protein complex extracted from Geastrum saccatum was isolated and analysed and shown to have antiinflammatory, antioxidant, and cytotoxic activities. It is suggested that the mechanism for the antiinflammatory activity is due to inhibition of the enzymes nitric oxide synthase and cyclooxygenase. See in the "further reading* section below.

► Image source of a Specimen from Tasmania, Australia>>


Further reading

► Antiinflammatory, antioxidant and cytotoxic actions of β-glucan-rich extract from Geastrum saccatum mushroom>>

► Calcium Oxalate Crystals and Basidiocarp Dehiscence in Geastrum saccatum (Gasteromycetes)>>

#biodiversity, #mushrooms , #Geastrum_saccatum  , #Fungi  

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"The Fundamental Questions of the Future Will be Profound"
+Daniel Estrada shares a post by Prof Frank Wilczek, the Herman Feshbach Professor of Physics at MIT. It is inspiration for +Physics Today's Essay Contest: Physics in 2116:

"Physics Today would like you to join Frank Wilczek in thinking about what the next 100 years will bring to physics. We invite you to imagine yourself in 2116... Your essay should report on an exciting discovery, an advance in physics, or a new technology." What might you write about?
> A recurring theme in natural philosophy is the tension between the God’s-eye view of reality comprehended as a whole and the ant’s-eye view of human consciousness, which senses a succession of events in time. Since the days of Isaac Newton, the ant’s-eye view has dominated fundamental physics. We divide our description of the world into dynamical laws that, paradoxically, exist outside of time, and initial conditions on which those laws act. The dynamical laws do not determine which initial conditions describe reality. That division has been enormously useful and successful pragmatically, but it leaves us far short of a full scientific account of the world as we know it. The account it gives—things are what they are because they were what they were—raises the question, Why were things that way and not any other?

The God’s-eye view seems, in the light of relativity theory, to be far more natural. Relativity teaches us to consider spacetime as an organic whole whose different aspects are related by symmetries that are awkward to express if we insist on carving experience into time slices.

// This whole essay is wonderful, but the paragraph below makes me want to cheer out loud.

> The work of designing algorithms can be considered as a special form of teaching, aimed at extremely clever but literal-minded and inexperienced students—that is, computers—who cannot deal with vagueness. At present those students are poorly motivated and incurious, but those faults are curable. Within 100 years they will become the colleagues and ultimately the successors of their human teachers, with a distinctive style of thought adapted to their talents.

via +Jon Lawhead
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