In this episode of SciTech Now, a mysterious pattern called Universality; a high tech treatment treating movement disorders; and up close and personal with wildlife.
In this episode of SciTech Now, a mysterious pattern called Universality; a high tech treatment treating movement disorders; and up close and personal with wildlife.
Coming up... Mathematicians connecting the dots.
Essentially, it's this mysterious mathematical pattern in everything from heavy atomic nuclei to distribution of prime numbers.
A tiny tech solution.
We can treat the symptoms of Parkinson's -- tremor, stiffness, slowness of movement.
Up close and personal with wildlife.
We train our birds to show off all of their natural behaviors to show people and get them up close to have these really great nose-to-beak experiences with them.
It's all ahead.
Hello. I'm Hari Sreenivasan.
Welcome to our weekly program, bringing you the latest breakthroughs in science, technology, and innovation.
Let's get started.
Scientists have discovered a mysterious pattern that somehow connects a bus system in Mexico and chicken eyes to quantum physics and number theory.
It's known as universality.
Take a look.
A hidden pattern is popping up in seemingly unrelated places -- from a bus system in Mexico, to chicken eyes, to number theory, and quantum physics.
This phenomenon, known as universality, continues to surprise mathematicians and reveal a deeper understanding of our world.
♪♪ Imagine arriving at an empty bus stop in New York City.
The last bus must have just left, but the sign says the bus comes every 10 minutes on average.
What's the probability that the next bus will arrive within five minutes?
The probability of a random event happening within some interval, like a bus coming within the next five minutes, is given by a curve called a Poisson Distribution.
But what if bus-arrival times are not independent?
In the 1970s, in Cuernavaca, Mexico, bus drivers would hire spies to sit along their route and the drivers either speed up or wait at a stop depending on how long ago their spy said the previous bus left.
This spaced out the buses and maximized their profits.
♪♪ In that case, the spacing between buses is defined by a very different probability distribution.
The Cuernavaca bus system, the Riemann zeta function related to prime numbers, chicken retinas, and atomic nuclei are all examples of complex correlated systems.
The components of these systems aren't independent.
They interact and repel one another, and this leads to a statistical distribution in between randomness and order.
The same distribution or pattern arises even though the components of these various systems are very different.
They are said to exhibit universality.
Mathematicians model these complex correlated systems using random matrices.
The numbers in random matrices are drawn randomly from probability distributions.
The matrix might be randomly filled with zeros and ones or with any set of numbers, like the integers between one and 100.
You can characterize a matrix but its eigenvalues -- a series of numbers that can be calculated by multiplying components of the matrix together in a certain way.
Eigenvalues and random matrices are always spaced along a number line in a characteristic pattern with consecutive eigenvalues never too close together or too far apart.
The same pattern of eigenvalue spacing arises no matter how you fill the matrix with random numbers.
If you plot the distance between consecutive eigenvalues on the x-axis, and the probability of getting a particular spacing on the y-axis, the familiar lopsided curve begins to appear.
Researchers are still looking for a general answer to where this universal pattern comes from, but clues continue to emerge.
The idea of random matrix universality goes back to Eugene Wigner, a Nobel Prize-winning theoretical physicist, who worked on the Manhattan Project.
Wigner was attempting to calculate the energy levels of a uranium nucleus, which has more than 200 protons and neutrons that can arrange themselves in all different configurations.
The associated energy levels of the system were far too complex to calculate.
Wigner used random matrices instead and plotted the statistical distribution of eigenvalues.
He found that the spacing of these numbers matched the spacing of energy levels of uranium and other heavy atomic nuclei.
Two decades later, the pattern was seen in gaps between consecutive numbers called zeros of the Riemann zeta function.
These zeros are thought to control how prime numbers are distributed.
Since then, the pattern has been seen in many different settings, like in human bones and social networks.
Just recently it showed up in yet another unlikely place -- the eyes of chickens.
It was the first instance of the pattern seen in biology.
While the number line exhibits a pattern of universality in one dimension, the chicken retina cells reveals it in two dimensions.
♪♪ The color-sensitive cone cells on the chicken's retina seem haphazardly distributed, but with a remarkably uniform density.
Looking closer, the cells appear to be surrounded by what's called an exclusion region -- a space where cones with different color sensitivity can be found, but cones of the same kind cannot.
♪♪ Just how these cone cells create the exclusion zones remains a mystery, but it's similar to the repulsion between consecutive random matrix eigenvalues on the number line.
Researchers say we're just at the tip of the iceberg in understanding universality in math, physics, and even biology.
Thomas Lin is the Editor in Chief of magazine and the editor of two math and science books, 'The Prime Number Conspiracy' and 'Alice and Bob Meet the Wall of Fire.'
He joins us now to discuss a unique mathematical phenomena across the world known as universality.
Universality means what?
Okay, so universality, as the name suggests, means that it's something that's found in a lot of different places and settings, and, essentially, it's this mysterious mathematical pattern that scientists have found in everything from heavy atomic nuclei to the distribution of prime numbers to models of the Internet to chicken eyes and independent bus systems, and so you wouldn't think these things have any real connection with each other, and so, you know, as scientists do, they want to understand what's at the heart of these different systems and why would this pattern emerge?
And so, in the 1950s, the Nobel Prize-winning physicist Eugene Wigner discovered this pattern in the energy spectra of the uranium nucleus...
...and he had this idea that, well, maybe this is a pattern that is universal and that emerges in lots of different complex correlated systems -- 'complex' just meaning that there are many, many elements, and 'correlated' means that they strongly interact with each other, and, subsequently, it was found in all these different places, including in this bus system in Mexico, which is just strange and fascinating.
So, give me an idea.
How do you describe this pattern?
I mean, you know, in music it winds up 'A,' 'A,' 'B,' 'A,' and we repeat that over and over again...
...or, you know, fractal theory says, okay, look at this nautilus shell and the spiral galaxy...
...but what does this pattern look like?
That's a great question, and so I think the best way to describe it is that it sits somewhere between order and randomness, and so it's neither completely regular or periodic like in order.
If you think of a barcode or something that's very periodic, that would be a very regular order structure, and random would just be all over the place, and a random pattern would have, potentially, a lot of these lines in it in a barcode closer together, and some could be really far apart and be all over the place, but this has -- this pattern, universal pattern -- essentially, because the different elements interact with each other, they sort of push off from each other, and so it's disordered, and yet it also has a certain amount of regularity because you'll never get them too close to each other or too far apart, and what mathematicians found, which is really surprising, and Eugene Wigner, as well, way back decades ago, was that these kind of systems could be modeled by a kind of math called matrices, but not just any matrices, but by random matrices.
A matrix is, essentially, a rectangular array filled with numbers or elements and somehow, just with random elements, the characteristic values or the eigenvalues of these matrices form this exact same pattern that we're seeing in uranium nuclei, in bus systems, in chicken eyes, and other places.
So, okay, if I have a rectangular box, and I fill it with random numbers, you're telling me that there is a pattern in there even though I can't see it?
I'm specifically saying I'm gonna heads-and-tails, I'm gonna keep flipping coins, I gonna write down these numbers, and there's a pattern in there?
And, so, to just make clear, it's not the random numbers themselves that are the pattern, it's the eigenvalues that come out of the matrix that form this same sort of special pattern, and the reason for that is that if you look at very simple atoms, if you look at hydrogen and helium, physicists can come up with exact matrices that describe their energy levels because they're simple enough, but when you get to heavier atoms like uranium, the nucleus is so big and complex, and there's so many interacting parts, and there's so many different energy levels that you can't do that.
You can't find the exact matrix.
And so what was surprising was that a physicist decades ago discovered that you could just use a random matrix to model it because say you're in a room full of people...
...and say there's only a few people.
That would be like a simple atom, and one person could really become -- his or her personality could just take over the conversation.
But in a room with many, many more people all talking to each other, no one person is gonna stand out or control the conversation, and it will just sort of get washed out almost like noise, and that's, essentially, what a random matrix is, and that's why this universal pattern emerges.
So, let me give you another example of the bus system in Mexico.
This is kind of a funny situation where a physicist who happened to be in a city called Cuernavaca, Mexico, 1999, happened to be waiting for a bus.
They're independent buses, so different bus drivers come and go as they please, and they want to have as much business as possible.
So they want to arrive at a stop where there are enough people so that they can have enough business to take them to the next destination, and so what this physicist saw and noticed was that the bus drivers, these independent bus drivers, were paying somebody at each stop and getting a piece of paper from them, and later, after a lot of cajoling, and I think he had to give some tequila to some of the drivers, as well, to find out what was happening -- or to the spies that they were paying.
Essentially, the drivers were paying spies to ask to sit there and see when the previous bus had left so that they could then decide, 'Well, should I slow down because the other one just left, and I don't want to go too soon because then there'll be nobody at the next stop, or should I speed up if the previous bus had left a long time ago to try to beat the other buses to the next stop and get all the passengers?'
And so because of the spies and because of that knowledge and information, that created this correlation between the bus arrivals...
...and the most surprising thing about this is when the physicists gathered all the pieces of paper and all this data, they found this exact same universal pattern that was found in the nuclei of uranium atoms.
So, how do we make these patterns work for us?
What are applications that you can take?
If this universal pattern is in so many things, is there a way that we can manipulate it to our own interests?
So, the way a lot of basic science works, first you have to understand things, right, before you can think about applications, but one thing, because of this connection to random matrices, one thing that it does help scientists do is that when they find other complex correlated systems that they want to understand, but they can't model it precisely, they can use different types of random matrices to model them very accurately, and they can learn things from that.
Let me give you another example that may be a little bit more sort of practical and connected to our daily lives.
This universal pattern has also been found in human bones, and so you take a special measurement of human bones, and a bone that has deteriorated through osteoporosis might not be correlated enough to exhibit this universality pattern, but ones that are healthy bones would have those connections and would exhibit the pattern.
So it could, potentially.
It hasn't yet, I don't think, but it could, potentially, lead to ways to detect whether your bone is healthy or not.
So, is there a school of mathematics that is chasing down more examples of where these patterns exist and where they don't?
This is a fundamental interest, I think, to both mathematicians and physicists and people studying climate, for example.
Arctic melt ponds are another example.
If, as the Arctic ice melts, and you get these pools of water, if they are separated enough, then they don't exhibit universality, but once the pools start sort of sloshing into each other and connecting and forming these interconnected melt ponds, then they start exhibiting this universal pattern, and, again, this is a way to understand these very complicated systems, which can then potentially lead to better models for things like understanding climate and a whole host of other phenomena out there.
Thomas Lin of magazine, thanks so much.
♪♪ [ Computer keys clacking ] ♪♪
A high-tech treatment that allows neurosurgeons to treat movement disorders like tremors derived from Parkinson's disease has just gotten more advanced.
Reporter Maddie Orton has the story.
Ann McCloskey was diagnosed with Parkinson's disease in 1986.
Twelve years later, she became one of the first patients in the country to receive deep brain stimulation, or DBS surgery to help treat her disease.
It's a procedure where a device implanted in the upper chest sends electrical impulses into the brain through wires called leads that are tipped with electrode contacts.
The neurostimulation calms Parkinson symptoms like tremors, but recently McCloskey's 20-year-old device stopped working.
So, two decades after her first DBS surgery, she's scheduled for another one at Mount Sinai Hospital in New York City.
Dr. Brian Kopell is McCloskey's surgeon.
The lead fractured, and, like any man-made device, these leads can break.
You know, DBS is a pacemaker for the brain, and if it breaks, the electricity can't flow, and then they lose efficacy, and so that's, essentially, what happened with Ann.
Going into her second of two lead implant surgeries, McCloskey is optimistic.
She says she knows the procedure will allow her to go back to doing activities without a tremor because her first deep brain stimulation surgery two decades ago worked wonders.
It was a miracle -- just plain and simple, a miracle.
I was shaking when I went into the operating room, and I wasn't when I came out.
Nurse practitioner Joan Miravite, who is also assisting McCloskey with this process, says it's not entirely known why neurostimulation calms Parkinson symptoms, but its use in a case like this is clear.
For someone who has so many years of Parkinson's disease, it's hard for us to cover those symptoms with just medication alone.
She does respond well to medication, but it doesn't last as long, so the deep brain stimulation helps us to manage these on/off fluctuations, and so the off times become better, and so her medication can really last through the day.
The new DBS system will be implanted in both sides of McCloskey's brain, so the surgery is done over two days.
Once the leads are in, and she's had time to heal, McCloskey will return to have the device calibrated to the level of stimulation she requires.
This whole process has become more accurate thanks to a recent advance in the field.
The product that we use today is the first of the advances in the DBS lead design since DBS was introduced in the United States in the late '90s.
The traditional DBS lead had four contacts, and each four contacts looked like a little cylinder, so when you stimulated, you created a field that was symmetric on all sides of the lead.
If the lead were slightly too close to some area that you didn't want to stimulate, you had to sort of trade off between effective stimulation and side effects.
Kopell says surgeons like him wanted a lead that provides asymmetrical stimulation, allowing doctors to stimulate in one area, but not affect an adjacent area.
These new leads provide that capability.
In the operating room, Kopell orients the lead to take advantage of the new electrode layout.
Prior to the implant surgery, Kopell does several checks through brain imaging to make sure he identifies the optimal implant location.
All right. Ann?
Do me a favor.
McCloskey is awake, but sedated.
In addition to following the map provided through brain imaging, Kopell also listens to frequencies given off by the brain's nuclei, which help him identify where the lead is stimulating within the brain.
Once the lead is in the targeted location, Kopell turns on the electrodes and asks the patient to follow commands.
He checks her reactions to see whether the stimulation causes McCloskey's normal tremor or stiffness to subside.
Open and close your hand big and wide.
How does that feel?
One month later, McCloskey visits Mount Sinai for a follow-up appointment, where her new DBS device is programmed by Nurse Practitioner Miravite.
Today is Ann McCloskey's first initial programming visit.
So we're going to be turning on her electrodes today.
She'll be off medicine, so we'll turn on the stimulation.
We'll see what the stimulation does by itself, and then we will have her take her meds so we can see what stimulation and medication does at the same time.
Five, four, three, two, one.
Just a little tremor.
Miravite uses software on a smart device that allows her to go through each electrical contact in McCloskey's brain, set the amplitude, and test what happens to her symptoms.
Typically, we can treat the symptoms of Parkinson's.
They're called motor symptoms.
We can treat tremor, stiffness, slowness of movement, and dyskinesias, which are extra movements after patients are taking meds.
So those are the symptoms that I'm going to be targeting.
McCloskey's symptoms do lessen in intensity as Miravite tests her patient's ability to do basic physical movements while receiving the deep brain stimulation.
The appointment is a relief for Ann McCloskey, who arrived in a wheelchair suffering from freezing and tremors, but leaves the appointment walking with the help of her medication and the deep brain stimulation.
[ Computer keys clacking ] ♪♪
Birds of prey are usually seen from afar, but at the Carolina Raptor Center in Huntersville, North Carolina, visitors can be up close and engaged with the birds in the natural world.
Take a look.
This is our red-legged seriema, and his name is Ya-Ya.
He's a gentle giant.
He's very curious about everything.
[ Chuckles ]
To understand the mission of the Carolina Raptor Center, you've got to meet Ya-Ya.
So, and what we've done is we've trained him to follow along with us.
So we have these sticks that have a tennis ball attached to them, and when we present them down to the ground, he knows to run up towards the target stick.
After he does that, we bridge him.
So we say, 'Good,' which is just marking the behavior that we want him to do, and then we give him a food reinforcement.
So we mix it up.
Sometimes he gets berries.
Sometimes he gets superworms -- things he would naturally eat out in the wild.
No, I can't let you do that.
And it's important to not only meet Ya-Ya, the Center hopes you have what it calls a nose-to-beak encounter with him.
You're so beautiful.
Oh, my gosh.
This is a great thing that we can do.
We can introduce him to visitors.
He's just so curious.
He's like, 'Those people look familiar.
I want to come see them again.'
I like his little...
The little crest.
So this is exactly why we have a bird like him so we can get him out really close to people 'cause a really close experience is what makes it so special.
It makes people really care about these birds.
We want to get them in front of people, so that's the whole training part -- getting them used to people, not being nervous when they're in front of a group of people, and then we would love to show something that they would do in the wild.
Ya-Ya was born at another avian park and given to the Raptor Center.
He's one of 85 birds who are permanent residents.
A lot of people just don't know that birds have their own experiences.
They have their own personality.
You don't normally think about that, and I think it's just because we see them so much from a distance, and a lot of our job here is showing that off to people.
The Center's mission includes environmental education and environmental stewardship.
It's believed that is best accomplished by getting people as close to birds as possible, whether it's on display or trained.
He is actually so far along in his training that I can voluntarily check his feet.
So I'll just give him a reward first, and then I'll just slightly pick up one of his feet...and check it.
We train our birds to show off all of their natural behaviors to show people and get them up close to have these really great nose-to-beak experiences with them so they can really learn a lot about their environment and feel empowered to go out and do something for the natural world.
But we can also use training to help us on our husbandry side of things.
So we can train them to go to a scale to get weights on them, to get health indicators.
There's a lot we can do just to overall improve their lives.
This is a typical chart of a barred owl.
So he came in 27 days ago.
A barred owl's a very common bird that we see around here, and here's an x-ray.
The mission also includes the rehabilitation of injured and orphaned raptors.
The medical center treats about 1,000 birds every year.
About 70% of those are released back into the wild.
And in this case, you can see this poor guy has two broken shin bones -- tibiotarsus.
He probably got clipped by the hood of a car, and he's actually a real trouper.
Could you imagine having two broken legs?
And here he is two weeks later with bright white steel implants in both legs.
We repaired both bones on separate days 'cause it would be pretty hard on him if we did them all at once, and he's doing quite well.
He's actually starting to stand on those legs, and if all goes well, we'll be removing those implants in about -- I don't know -- three and a half more weeks.
He'll be with us for a while to recuperate and to get back into flight shape and all that thing, but he's healing quite well.
And that brings us back to Ya-Ya.
Their habitat is grassland, so he's probably looking at that like, 'This is perfect.'
About half of the Center's resident birds are brought out for education.
Ya-Ya seems happy about his job.
So, if you hold out your stick here...
...that's the signal to come over here, right?
So he is supposed to touch his beak on the tennis ball, and then he'll get his reward.
So, if I'm standing here, that's gonna throw things off, or will that...?
I don't think so.
You can try.
He's a little interested in other things right now.
And then you reward the behavior?
So the 'Good' is our bridge.
So that lets him know that that's what we wanted.
As soon as he touched his beak to the tennis ball, I bridged and then gave him the reward, which is a superworm.
And that wraps it up for this time.
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Until then, I'm Hari Sreenivasan.
Thanks for watching.
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