Month: May 2024

Space News for May 2024: 

Regular readers of this blog may have noticed that I haven’t been posting any Space News recently, not since February in fact. The reason for this is that I have been waiting for the Final Test Launch (FTL) and first manned mission of Boeing’s Starliner capsule. Well after years of delays and redesigns Starliner is still not ready and the launch, which was originally set for mid April was pushed back to May 6 only to have weather cause a delay until the 7th. That bad weather was probably a good thing however because on the 7th, even as the two crew members were in their seats waiting for ignition a valve on the Atlas 5 launch vehicle started misbehaving. So the whole mission was delayed yet again and the astronauts removed from the capsule.

Compared to the problems Boeing is having with their commercial aircraft their difficulties with Starliner are really rather small, but get a lot of publicity! (Credit: WESH)

The launch was then rescheduled for May 17th but while the engineers at the Kennedy Space Center were working on the malfunctioning valve on the Atlas 5 a helium valve on Starliner itself began to leak pushing back the launch until no earlier than the 25th of May, and I wouldn’t put any money on that Since I wrote this post it’s been further delayed into June!). So I decided to move on and talk about other happenings in the exploration of space.

It’s all up to the individual, some people simply cannot see any reason for exploring the Universe. If you’re reading these words however I think I can assume it’s important to you. (Credit: Earth and Space Exploration Center)

In manned spaceflight on the 25th of April China successfully launched three Taikonauts aboard the Shenzhou 18 spacecraft to their Tiangong space station. Arriving at the space station the Taikonauts relieved the Shenzhou 17 crew who had occupied Tiangong for six months. The Shenzhou 17 crew then returned to Earth several days later.

The launch of China’s Shenzhou 18 mission to their Tiangong space station. Shenzhou 18 is the seventh crew to occupy Tiangong giving China a long term presence in Low Earth Orbit (LOE). (Credit: Current Affairs – Adda247)

Crew transfer and cargo resupply missions to Tiangong have now become routine for China’s space agency just as they have for NASA and Roscommon, Russia’s space agency. China’s growing capability in space is becoming a concern to strategic analysts in the west. Along with their space station China has landed two probes on the Moon’s farside, something no other nation has achieved.

China’s Chang’e 5 lunar probe, mission currently underway, will be the first ever return sample mission from the Moon’s far side. (Credit: Business Standard)

With a stated goal of landing Taikonauts on the Moon by 2030 some commentators are trying to invent another ‘Space Race’ between the US and China. Unlike the USSR however, which simply gave up any plans for landing on the Moon after the Americans succeeded, China seems content to just move ahead at its own pace as opposed to the streaks and stops that NASA has endured because of politics here in the US.

Why does it seem like the US only gets serious about space when we think somebody else might be beating us? (Credit: Global Times)

However the big news to me this month isn’t in manned spaceflight. Rather it’s the success that the engineers at the Jet Propulsion Labouratory (JPL) have had in reestablishing communication with the Voyager 1 space probe, the farthest man made object from Earth. Launched back in 1977 the two Voyager space probes completed their flyby missions to the four gas giants of Jupiter, Saturn, Uranus and Neptune and have for over 45 years now continued to send back data about conditions in the outer solar system.

The Voyager 1 spaceprobe. This Illustration is from about 1975 but Voyager is still out there, observing the conditions in Interstellar Space now, the first man made object to ever leave our solar system. (Credit: NASA)

At 45 years old and a distance from Earth of 24 billion kilometers it was amazing that the Voyagers were still working at all so back in November of 2023 when Voyager 1 started sending back gibberish instead of readable data the engineers at JPL feared for the worst but hoped for the best. The engineers were hopeful that they might be able to fix the problem because the spacecraft was still radioing back something, so it was still alive.

To most of us the good data from Voyager would look like just a bunch of 1’s and 0’s but to the engineers at JPL those digits are worth more than gold. (Credit: USA Today)

At a distance of 24 billion kilometers it takes more than 22 hours for a radio signal to travel from Earth to Voyager, and an equal time for a response to get back to Earth. So there wasn’t going to be a quick fix to the problem. In fact it wasn’t until March of 2024 that the engineers were certain that the problem lay in one of Voyager’s three onboard computers, in a section referred to as Flight Data Subsystem (FDS).

Photo of a Voyager Flight Data Simulator from before the spacecraft was assembled. Notice this is serial number S/N 003 so this was probably installed on Voyager 1 and may very well be the cause of the problem! (Credit: Ars Technica)

The engineers finally discovered that the problem was caused by the malfunction of a single chip responsible for storing the FDS’s operating code. The engineers therefore came up with a plan to restore the software on several other chips that were still functioning. The team initiated their plan on the 18th of April and on the 20th they began receiving back usable data about the health of Voyager 1. There’s still more work to do relocating and adjusting other portions of the software that was stored on the malfunctioning chip but at least Voyager 1 is back to communicating properly with Earth.

So how long can the two Voyager spacecraft continue to operate? No one really knows for certain. Even if the engineers at JPL can keep fixing any problems the energy both Voyagers get from Radioactive Thermoelectric Generators or RTVs is slowing getting smaller. Their power has been decreasing over the last 45 years so how long they keep working is anybody’s guess. (Credit: Quora)

Finally, Sierra Space Corporation’s Dream Chaser mini-shuttle, see my post of 23 December 2023, has completed its environmental testing at NASA’s Neil Armstrong Test Facility and on the 20th of May was delivered to the Kennedy Space Center to begin preparations for its maiden flight. Sometime later this year the unmanned spacecraft be launched into orbit aboard a United Launch Alliance’s Vulcan rocket on a mission to deliver 3500 kilograms of cargo to the International Space Station (ISS). If the Dream Chaser’s mission is successful the unmanned, reusable mini-shuttle will join Space X’s cargo Dragon and Orbital Sciences Corporation’s Cygnus as commercial cargo spacecraft supplying both the ISS and any future orbital stations.

The Dream Chaser spacecraft (foreground) next to the iconic NASA space shuttle. (Credit: Autoevolution)

Sierra Space Corporation’s plans for Dream Chaser go beyond unmanned missions however, from the beginning Dream Chaser was intended to eventually become a manned craft. If that comes to pass then NASA and commercial space corporations will have three privately owned space systems for getting people into Low Earth Orbit (LOE).

There are a lot of plans out there right now for privately owned, commercial space stations. By 2030 there will almost certainly be several in orbit. (Credit: Space.com)

So imagine ten to fifteen years from now. There are maybe a half dozen space stations in orbit, being regularly supplied by three distinct cargo spacecraft. At the same time another three distinct space capsules are taking astronauts, many of them civilians, between Earth and those stations.

O’k maybe it’s going to a while before we get to this stage but it really is only a matter of time. (Credit: National Air and Space Museum)

Right now we are building the infrastructure of LOE, within a generation we really will be starting the colonization of nearby space.

Did You Get to See the Northern Lights this Weekend, May 10th-12th? This Time the Weather didn’t Cooperate and I missed out on everything.

Seems like just a couple of weeks ago that I was talking about the great American Eclipse of 8th April 2024 and how the weather in Greenville, Texas just cleared enough for me and my family to see a good show. (See my post of 20 April 2024) Well this past weekend the Solar System decided to stage another celestial event as a massive solar flare erupted in a Coronal Mass Ejection (CME) that passed by the Earth producing the biggest display of the Northern Lights, also known as the Aurora Borealis seen in decades.

Anyone who has ever actually seen the Aurora, not me, always says that pictures don’t do it justice, but here’s one anyway. (Credit: Space.com)

So what’s going on here? Why is the Sun so active this year that astronomers were predicting that the Corona during last month’s eclipse would be much bigger and more active than during the eclipse of 2017? Why does the Sun have so many sunspots this year, and what are sunspots anyway? And what do sunspots have to do with the Aurora anyway?

Closeup view of a sunspot on the surface of the Sun. One interesting thing about sunspots is that they come in pairs or even more complex combinations. That’s because they are caused by the Sun’s magnetic field and a magnetic field has to have both a north and a south pole. (Credit: IU Blogs – Indiana University)

Let’s take this one step at a time. First of all it was Galileo who discovered the fact that our Sun is often covered with dark spots, the ancient Greeks had believed that the Sun was a perfect, unblemished disk. While scientists quickly realized that sunspots are areas of the Sun’s surface that are slightly cooler than the regions around them they are actually quite bright, they only appear dark in comparison to the normal brightness of the Sun’s surface.

Drawings made by Galileo of spots on the Sun’s disk. It was by noticing how the spots moved that Galileo first realized that the Sun rotated on its axis just as the Earth did. (Credit: NASA Earth Observatory)

It took several hundred years for scientists to understand that sunspots are caused by the Sun’s magnetic field that, like the Earth’s is strongest near the Sun’s north and south poles. Unlike the Earth however, which is partly solid and partly liquid the Sun is a huge ball of ionized gas so that inside the Sun the magnetic field gets all twisted around itself.  Because of this the magnetic field can break onto the Sun’s surface at places other than the poles. When this happens the magnetic field causes the gasses on the surface to expand and cool down, generating a sunspot.

The plasma in a sunspot is still very hot, but because it is more than a thousand degrees cooler than the plasma outside sunspots appear dark! (Credit: Study.com)

It’s also been recognized for several hundred years that the Sun has an approximately eleven-year sunspot ‘cycle’. That is to say that in some years the Sun will have a very large number of sunspots, solar maximum, this year is going to be one of those years. Then five or six years later there will be a minimum number of sunspots, during the last solar minimum in 2019 the Sun went 281 days without a single sunspot on its surface. Then five or six years after that there will be another sunspot maximum. In 2023 and so far in 2024 there has been at least one sunspot on the Sun’s surface at all times. Why the Sun should have a sunspot cycle and why it should be eleven years is still poorly understood as are a great many things about our local star.

The Sun can appear very different between its solar maximum and solar minimum. (Credit: Space.com)
Not only does the Sun have an eleven year sunspot cycle but there also seems to be an even longer cycle of large versus small maximums. Why any of this should happen is still one of the Sun’s mysteries. (Credit: Wikipedia)

As I said sunspots happen when the twisting and turning of the Sun’s magnetic field breaks the surface and so sunspots are anything but stable objects, growing and shrinking in size, changing shape while moving closer or further apart. There are a large number of astronomers and physicists who have spent their entire careers studying the behavior of sunspots and one thing that they’ve learned is that there is an extraordinary amount of energy in those magnetic twists and turns. Then, if the magnetic field lines become too tangled they can snap releasing that energy in an explosion so powerful it makes a hydrogen bomb look like a firecracker.

A solar flare perhaps a half million kilometers in length. Notice again how the magnetic lines come out of and go back into the Sun. The explosion that produced this flare contained far more energy than the human race has generated in all of history. (Credit: Britannica)

Those explosions around sunspots are known as solar flares where matter from the Sun’s surface erupts tens of thousands of kilometers into space. Occasionally solar flares can be so powerful that matter, and we’re talking about millions of tonnes of matter, is ejected from the Sun and into space creating a ‘Coronal Mass Ejection’ or CME.

A Coronal Mass Ejection (CME) back in 2000 as seen by the European Space Agencies two Soho Satellites. The satellite’s cameras block the Sun itself, creating an artificial eclipse so that they can observe what’s going on in the Sun’s Corona. (Credit: NASA)

That’s what happened to sunspot AR3664 on the 8th of May when it produced the largest CME observed since at least 2005, measuring at X5.8 on the scale solar astronomers use. AR3664 it itself a monster, one of the largest sunspots ever seen being about as large as 17 Earths laid side by side, so large in fact that it is one of the biggest sunspots ever seen. When it erupted AR3664 wasn’t quite pointed right at the Earth but that CME was so huge that it still hit our planet in two waves on the nights of May 11th and 12th moving at a speed in excess of 600 km per second.

Close up view of sunspot AR3664, the source of the CME that struck the Earth on May 10th producing the largest aurora display in decades. (Credit: SpaceWeather.com)
Sunspot AR2664 compared in size to Carrington’s sunspot back in 1859 which is considered to be the most active sunspot ever observed caused extensive aurora displays across the world. (Credit: Daily Mail)

Now the matter in a CME, like most of the Sun’s material isn’t either a solid, liquid or a gas like the matter here on Earth, it’s far too hot for that. Instead it’s mostly just a huge cloud of Protons and Electrons that’s called a plasma. As everyone knows protons and electrons are charged particles so that when those particles come near the Earth they are deflected by the Earth’s magnetic field towards our planet’s poles before finally striking the atmosphere. So it’s the Earth’s magnetic field that normally keeps the aurora at our planet’s polar regions.

The four states of matter, solid, liquid, gas and plasma. Plasma is the most energetic with many of the atoms being stripped of one or more electrons making it an ionized form of matter. Here on Earth plasma may be rare but most of the matter in the Universe is in this state. (Credit: Ferrarini & Benelli)

As they enter the atmosphere the charged protons and electrons collide with gas molecules, which you’ll recall are mostly Nitrogen and Oxygen. The collisions break those molecules into their separate atoms, which then recombine giving off visible light in the process. It is this light that creates the dancing streaks of the Aurora. So powerful was the geomagnetic storm generated by the X5.8 flare that the aurora it created pushed out from the polar regions reaching so far south that it was even observed by people living in northern Florida.

This was the aurora forecast as put out by the Space Weather Prediction Center. It actuality people in every state, even Texas and Florida saw the display. (Credit: X.com)

Here in Philadelphia I should have had a great chance to finally see this natural phenomenon, but to quote an old song “clouds got in my way!” Both nights that the aurora was at its maximum the Delaware valley was treated to a light, continuous rainstorm but more importantly we were blanketed by a thick layer of stratus clouds making it impossible to see any part of the sky.

Clouds so thick you’d think the sky has disappeared. That’s what Philadelphia had the two nights of the aurora so I didn’t get to see anything. (Credit: Types of Clouds)

Still, solar maximum isn’t over yet and astronomers think that anything could happen in the next 4-6 months. So to those of you who managed to see the Aurora Borealis on the nights of May 11th or 12th I envy you but I haven’t given up my hope of seeing them yet.

Whether you call it Climate Change or Global Warming it’s starting to get really serious as Scientists are Astounded by just how hot this last year was.

It certainly didn’t take long for climatologists to pronounce the year 2023 as the hottest year ever recorded for our planet. On January 1st the World Meteorological Organization (WMO) immediately declared that not only had 2023 broken all previous temperature records but that it had done so by an unprecedented amount. Many scientists blamed the record shattering heat on a combination of global warming with a particularly strong El Nino in the Pacific but many others felt that there had to be additional factors at work as well.

2023 didn’t just set the record for hottest year ever recorded it smashed it, exceeding the previous record in 2016 by a huge amount. (Credit: BBC)

And so far 2024 hasn’t been any better, the global heat wave has continued with January being the hottest January ever recorded followed by February being the hottest February ever then March and so far April. Even worse, the world’s oceans are also setting records for the hottest temperatures ever measured, and remember it takes a lot more heat, more energy to heat up water than it does to warm up air.

So far 2024 looks to be even hotter with each month from January to April being the hottest of that month ever recorded. (Credit: Axios)
And it’s not just the air that’s getting hotter, the oceans are actually absorbing most of the heat caused by greenhouse gasses. 2023 was the hottest year ever recorded and 2024 is continuing the trend. (Credit: USA Today)

In fact the WMO’s annual State of the Climate Report, which was issued on the 19th of March, gave special significance to the rising temperatures in the world’s oceans claiming the measured increases were “Off the Charts”. So huge is the amount of heat now entering the oceans that it may take centuries for them to return to pre-industrial temperatures, even after the elimination of greenhouse gas emissions. In other words, even if we ended all greenhouse gas emissions today, the world’s oceans might take several hundred years to fully cool back down.

With so much extra heat being stored in the Earth’s oceans it will take centuries for them to cool back down to mid-20th century levels, and that’s only if we stopped warming them up right now! (Credit: Fox Weather)

And the long term consequences of the warming of the oceans is only now becoming understood. A new study published in the journal Frontiers in Marine Science and led by Alexey Mishonov of the University of Maryland’s Earth System Science Interdisciplinary Center (ESSIC) has complied decades of data on conditions in the Atlantic Meridional Overturning Circulation (AMOC). That’s the system of ocean circulations in the north Atlantic that includes the well known Gulf Stream.

One of the areas of the oceans that is warming the fastest is along the US east coast, right where the Gulf Stream passes. What effect this will have on the Gulf Stream is still controversial but many studies predict a considerable weakening of the Gulf Stream. (Credit: Vox)

What the researchers found was that the current flows of the system remained stable during the period from 1955 to 1995, but from 1995 onward all of the currents have weakened measurably. This weakening of the circulation is attributed to both the increased temperatures at the ocean’s surface but also to a decrease in salinity caused by the melting of the polar icecaps as well as the Greenland ice sheets. These scenarios were used as the main plotline in the 2004 movie ‘The Day after Tomorrow’ and while the timescale of that movie was several orders of magnitude too fast the consequences, and the climate damage they would cause, are quite within the realm of possibility.

Like most Si-Fi disaster movies ‘The Day After Tomorrow’ exaggerated both the scale and the speed of what could happen if the Gulf Stream collapses. (Credit: Disney Plus)

Worst still, another study has detailed the effects of sea level rise on the US east and Gulf coasts. The paper, which was published on March 6th in the journal Nature, used satellite images to show that not only are sea levels rising but that the land right along the coasts from Maine all the way around to Texas are sinking. The combination of these two factors is putting the homes and businesses of millions of Americans at risk of being swept away in the next major storm.

Large section of the US coastline are under threat from rising sea levels. And these areas just happen to be among the most densely populated portions of the country. (Credit: USGS)

According to the study there are many reasons for the subsidence of the land, most of them related to human activity. In Louisiana and eastern Texas the pumping out of oil and natural gas from the ground is the leading cause but in Charlestown South Carolina and Atlantic City New Jersey it’s the pumping out of groundwater to use as drinking and household water that is causing the land to sink. Regardless of the cause many very expensive beachfront homes must now either be protected by very expensive dykes and breakwaters, or simply abandoned to the ocean.

Everyone knows that the nation of Holland is protected from the sea by a large series of dykes. Some people claim that we could do the same to protect our coastlines from sea level rise. The dykes of Holland were constructed over centuries however, and Holland is a much smaller country than the US! (Credit: Van Oord)

Finally one more small item dealing with climate change. The ever increasing temperatures around the globe obviously includes the world’s wine growing regions as well. For centuries different parts of the globe, like Italy or Spain, grew grapes that were acclimated to the heat of the country they grew in while other regions like The Rhineland in Germany or Burgundy in France, grew grapes that liked weather that was a bit cooler.

It’s predicted that by 2050 many of the world’s best known wine producing regions will become practically deserts unable to produce much of anything. (Credit: Wine Folly)

Well thanks to global warming that’s all changing with Germany and France now getting as hot as Italy and Spain were while Italy and Spain are just getting too hot. One consequence of the increased heat might sound at first like a good thing, the grapes are producing more sugar and after fermentation that means more alcohol. Wine experts however say that the wines no longer taste the same, the increase in strength is taking away something of the complex flavour of many varieties of wine. 

Making good wine these days pretty much requires a degree in chemistry. To get the best flavour a balance of many different complex compounds is needed. Climate change is changing that balance by increasing the alcohol content at the expense of taste. (Credit: Quora)

Now what is bad for some parts of the world, Italy, Spain and southern California, could actually be good for places that are not generally thought of as wine producing areas like the UK or New England. At the same time places like Germany or France may need to change the types of wines they grow to reflect that their climate is now more like the way Italy and Spain used to be.

England and the rest of the British Isles have always been known for their beers not wine. That’s one more change that Global Warming may cause. (Credit: Brew Your Own)

Just one more way that climate change is forcing entire industries to make major changes to the way they do business. All just so the petroleum companies can continue to make their unholy profits.

Mathematicians have confirmed a long held conjecture concerning the Eigenvalues of a disk. What that means and just what are eigenvalues anyway?

When you were little did you ever jump rope, or if you were a little boy like me did you at least watch the little girls as they jumped rope? If you did then you are familiar with the shape that the rope takes as it’s being twirled around. You remember how it sort of has a hill shape when the rope is above the jumper’s head and the exact opposite valley shape when it’s coming down and she has to jump over it.

There’s a lot of Physics in this simple child’s activity. Whether up or down the shape the rope takes is one half of a sine wave. (Credit: Reddit)

Later on, in high school, you may have learned in your math class that the shape the rope takes is that of the trigonometric function known as the Sine of an angle, Sin (θ). Or more properly a jump rope is half of a sine wave, the positive half on the up stroke and the negative half on the down.

As a function of angle, here in degrees, a sine wave is generated. Here the right half is a jump rope on the up swing while the left half is a jump rope on the down swing. (Credit: R. A. Lawler)

Now that half a wave phenomenon is an important point, because if you take a jump rope and twirl it really fast you can actually get a shape that is two-half waves, one up one down which of course makes a full sine wave. Even faster and you get three halves or 1½ waves, and so on. When I taught freshman physics I would always take a jump rope to class when we started to study waves and by tying one end to a door knob and twirling the other as fast as I could I usually managed to get six half or three full waves.

With practice it is relatively easy to get a rope to produce multiple ups and downs. This guy is actually doing that with two ropes at once. (Credit: Men’s Journal)

No matter how hard you try however, you will never get 2/3 of a wave, or 1¼ waves or something like π waves. Only integer multiples of ½ of a wave are allowed, ½, 1, 1½, 2, 2½, 3 and so on. In physics these special values have been given the name Eigenvalues, which is German for characteristic values.

In pure mathematics eigenvalues are defined as the unique solutions to a set of equations whose coefficients are arranged as a matrix. The eigenvalues in this problem are the values 5 and -2. (Credit: Towards Data Science)

Eigenvalues are a fundamental attribute of every musical instrument. For example when you pluck a guitar string you get a shape very much like a jump rope, a half wave vibrating up and down and the speed of that vibration is the frequency of the sound that you hear. In a similar way the eigenvalue of an single organ pipe can be calculated so that it will sound the right note.

The eigenvalues for the sound produced by a tube closed at one end, an organ pipe. Also known in acoustics as the resonant frequencies of the tube. Musically these frequencies are the fundamental note of the organ pipe and its overtones. (Credit: Lumen Learning)

If you want to try a simple experiment take a 16oz. bottle of soda and drink about half of it. Then, holding the bottle upright so the soda doesn’t spill out, blow across the opening at the top, what you’ll hear is a fairly high pitched note. Now drink about another quarter of the soda so you still have about a quarter of it left and repeat blowing across the opening. Notice how the note is different; it’s a lower note. Finally finish your drink and repeat blowing across the opening; the note will sound even lower, deeper.

If you get several bottles with different levels of liquid in them you can even construct your own musical instrument. (Credit: Quora)

It’s the size of the air chamber in the bottle, along with its shape, that determines the frequency or the note you hear. The larger the chamber the larger the fundamental eigenvalue and therefore the lower the note.

Organ pipes come in a variety of sizes because the larger the volume of the pipe the lower the frequency, the lower the tone. (Credit: Diaqnoz.Az)

All musical instruments make use of this eigenvalue phenomenon and being able to calculate the eigenvalues of an instrument is important in being able to design one. Now the examples I’ve talked about so far, the jump rope, guitar string, organ pipe and even the soda bottle are all basically one dimensional systems. Even for the soda bottle it’s the longest dimension that primarily determines the fundamental frequency.

For stringed instruments, like this guitar, it’s the tension that the string is under, as well as its length that determines the frequency of the sound it produces, its tone. (Credit: Artist Guitars)

There are two dimensional instruments as well, the best known of which are drums, that flat sheet of animal skin stretched across the round drum base is what vibrates to create a sound. Now a two dimensional problem like the disk of a drum is quite a bit more difficult to calculate than the one dimensional one, orders of magnitude more difficult in fact. You can actually get a two dimensional disk to vibrate in different ways by striking it in different places. Striking a drum head in the center causes it to vibrate something like a jump rope, if you looked at a cross section at least. Striking the drum head off center however can cause one side to go down while the other side goes up in a fashion unlike any one dimensional wave.

At first glance a drum skin may look like a pretty simple instrument. (Credit: YouTube)
But actually the vibration eigenvalues, the variety of ways that a drum skin can vibrate are very complex, requiring some very difficult mathematics. (Credit: thairghs.com)

Back in 1954 a mathematician named George Pólya stated a conjecture where you could calculate the shape of a two dimensional surface from the frequency of the sounds it gave off. Pólya succeeded himself in proving his conjecture for a two dimensional surface that is made up of shapes that tile together, see my post of 22 April 2023 for more information on geometries that tile. Round disks, like a drum head, however do not tile and Pólya never managed to prove his idea for disks.

Mathematician George Polya was another one of the European scientists who fled to the United States during the Nazi era giving us the advantage of his brilliance. (Credit: Wikipedia)

Now an international team of mathematicians, Nikolay Filonov from Steklov Institute of Mathematics in St. Petersburg Russia, Michael Levitin of the University of Reading in the UK, Losif Polterovich from the University of Montreal in Canada and David Sher of DuPaul University in the US, have succeeded in proving Pólya’s conjecture for disks. Their proof has been published in the journal Inventiones Mathematicae and while that proof may be an abstract piece of mathematical analysis it could also lead to practical applications in many fields, not just music.

Just the first of 41 pages of complex mathematics needed to prove Polya’s conjecture. (Credit: Filonov et al)

Eigenvalues are a factor wherever waves occur, acoustics, hydrodynamics, electronics and perhaps most famously in quantum mechanics. So any advance in our understanding of eigenvalues is a step forward in our understanding of the world around us.