omenti

one of the most amazing photos was taken in april of last year

Mention photography and iconic images come to mind:  a young Pakistani girl with amazing eyes, aspens in New Mexico, an assortment of shocking and brutal events.... The rarest are those that change how we see ourselves.   The full disk of the Earth against the blackness of space as seen by an astronaut on the way to the Moon is considered by some to be the most impactful environmental photo ever taken.   And then there's the  hastily captured earthrise taken on Christmas Eve in 1968 by Bill Anders of Apollo 8.  

 
I'm fascinated by imaging that is done without conventional film or sensors ...  images of Nature that eludes our limited senses.  Such imaging ..  I'll call it a branch, albeit an exotic one, of photography has been driven by science beginning around the mid 19^th century with astrophotography.  A telescope can gather much more light than a human eye and film allows long exposures making faint objects even more visible.  A bonus is you get an accurate record without having to rely on artistry.  Soon astronomers attacked prisms and began learn what stars were made of and the field of astrophysics was born.  Cameras went on microscopes.  People started using x-rays to make images.  By the 1960s computers started getting involved in particle physics experiments and now the camera on your iPhone is a computer-camera chimera .  Advanced imaging has branched out in hundreds of directions revolutionizing areas like medicine. For the time being let's stay with astronomy and look at one of the more dramatic frontiers - one that may change how we see the Universe. 

 

First you need to go out and look up on clear nights.  Around the 12th of August will be the peak of the Perseid meteor shower and it should be a doozy this year with only a new Moon lighting the sky.   If it's dark enough where you are you can enjoy the Milky Way was you wait for meteors.  Looking down towards the South you should be able to find Sagittarius -  the teapot constellation. If you're lucky enough to have a dark enough sky to see the Milky Way you'll notice it's exceptionally dense there.  You're looking straight to the center of the galaxy.   A little bit up and to the right of the spout is the galactic center.  Except there's too much dust between you and it for regular light to make the 26,000 light year journey.

 

As it happens some wavelengths of light can make it through the murk. Some infrared light makes it through to telescopes on very high and dry mountaintops and the haze is fairly transparent to one millimeter wavelength microwaves.  (about two thousand times longer than visible light).  Many radio telescopes can be tuned to watch and some rather striking things have been learned.  

 

At the galactic center is a supermassive black hole with a mass about four million times than of the Sun.   It has a name - Sagittarius A* (pronounced A-star) or Sgr A* for short.  In the past decade it's become clear that almost all galaxies have supermassive black holes  with masses ranging from a few hundred thousand to several billion Suns at their center.  Infrared observations  have revealed it's very busy around Sgr A*.    The event horizon - the boundary at which light can't escape - is too small to image, but calculations show it would just fit inside Mercury's orbit.  A region the size of our solar system has about three dozen stars orbiting it and about a million stars can be foundwithin a four light year radius (the distance from the Sun to the nearest star).

 

There are several indirect ways to deduce Sgr A* is a huge black hole.  Following the orbits of nearby stars is a one.  Here's an animation of about 15 years of observations of nearby stars.  The closest ones are moving so fast near the black hole that they provide a good test of Einstein's General Relativity (it turns out to work well:-)

 

 

It would be fantastic to take a photo of it. While you can't see the black hole itself, it will cast a shadow and bend light passeing nearby.  So how do you make an image of something so tiny so far away (an analogy is resolving a baseball on the moon).  It turns out the trick is to build a large telescope .. or more accurately synthesize a very very large telescope.

 

A group of astrophysicists have been giving it a try on a shoestring budget.  They assembled an instrument with an effective diameter roughly the same as the Earth by getting time on radio telescopes scattered around the globe.  They needed specialized receivers and atomic clocks at each telescope and there are more than a few corrections.   The main exposure took place in April of 2017.  Since then it's been a large amount of code writing, supercomputer time and trying to understand what's going on.  They posted a nice discussion of their approach.

 

 

There should be enough resolution  to see it directly and rumor has it that they're close to publication.  This has to be one of the frontiers of computational photography.

 

Computational photography has come a way in the past sixty years.  And your iPhone?  It's just getting started with sensors on it as well as those it's talking to.  Ask about communicative houseplants sometime:-)

 

Oh - and if you wanted to improve resolution on the synthetic antenna radio telescope, you could place antennas in orbit around the Sun.  Roughy in Earth's orbit would be easiest.  Then you could do some really interesting astronomy.

 

 

 

how to paint like kandinsky

My artist sister sent a link to this short video from The Tate.  It's not quite what it claims, but that turns out to be useful.  Go ahead..   I'll wait.

 

Without a bit of background in the fine arts this isn't exactly a step-by-step how-to-paint guide.   For most of us it's somewhere between art appreciation and art creation.  It reminds me of learning physics as an undergrad.  You spend a few years learning bits and snatches thinking you're learning physics.  Silly you -  in reality it's just a little background.  Slowly you begin to focus on technique - mostly math - and come to think this must be physics.  It isn't, but you're beginning to get an appreciation.  You can go to serious academic talks without getting totally lost and you start to get the sense that this is much deeper than you had imaged. A talk might give a sense of how someone did something, but rarely offers much where the creative piece came from.    A few more years and you begin to get the hang of it - at least a small corner.  Back to the video.

 

I imagine art students would see some interesting hints.  I like what Sui said about her own inspiration.  That  led me to some notes from The Tate on Kandinsky.

Painted between 1910 and 1911, Cossacks is an expression of Kandinsky’s belief in the power of art “to awaken this capacity for experiencing the spiritual in material and in abstract phenomena.” The dynamic tension between abstract form and concrete content may be read as a manifestation of the wider conflict between the forces of political oppression – Kandinsky had been deeply moved by the strikes and upheavals in Odessa a few years earlier – and the hunger for spiritual rejuvenation consequent upon the rise of soulless modernity. Like his contemporaries Piet Mondrian and Henri Matisse, Kandinsky saw painting as an extension of religion, capable, as he wrote in his Reminiscences (1913), of revealing ‘new perspectives and true truths’ in ‘moments of sudden illumination, resembling a flash of lightning.’ The echo of the Ancient Greek writer Longinus’s notion of sublime speech, which similarly strikes like a bolt of lightning, is carried over into Kandinsky’s description of the spiritual mission of the modern artist. In his 1911 essay On the Spiritual in Art, he compares the life of the spirit to ‘a large, acute-angled triangle,’ at the apex of which stands the solitary artistic genius dispensing spiritual food to the multitudes below.

Impressively deep.

 

It turns out they've done a few of these of how-tos ..  If you want to move a bit beyond art appreciation, even though you may never try painting or printing, there's more here: print like Warhol, paint watercolor like Turner and cast like Whiteread.   They're quite wonderful and I hope they keep making these. 

 

A couple of interesting issues immediately come to mind.  How to you communicate at a variety of levels and why is art so important in unexpected areas?  Since I've written quite a bit about the first, I'll skip to the second.  What is the utility of art? 

 

I find visualization critical my own thinking - particularly at the playful stage that some might call the creative piece.  You get to the point where the questions become visualizations that you manipulate.  A mathematical expression might take the form of a visualization that you play with without formally solving it.  It's part of what some call intuition.  Sometimes these are on paper or a blackboard and sometimes they're in your head and you copy them, or at least their flavor, to move the court you're playing on. 

 

I've been drawing since I was a little kid and still will sit and sketch something on a tree trunk for an hour as exercise.  I'm guessing that the ability to visually focus, something art and photography can teach you, is central to improving your ability to visualize.  It's much more powerful than anything I've seen with a computer and I suspect is very useful in many disciplines. 

 

With all this practice you'd think I'd be an ok artist, but that isn't the case.  No complaints as the practice has undoubtedly shaped my neural connections that let me, for good or not, think how I think.  I believe there are rather deep connections between our perception of beauty and Nature and this can allow us to use visualizations as a rather powerful guide.  That's conjecture, but it keeps popping up over and over.  As a physicist friend says:  If there is a God, it's almost certain she's an artist. 

 

Others have noticed the impact of the visual arts on scientific thinking and a few physics and math programs recommend students take at least a semester of a class that involves drawing.  I'd like to see that practice expanded and have been trying to encourage my undergrad school to link with a nearby art institute.  STEM is only part of an education even if you're working in one of it's fields.  Adding a visual art or music (or .. ?)  may be essential if your goal is to be creative (whatever that means).  So many stories.  It probably doesn't need to be a fine art for everyone, but the current focus on narrowness in hopes of finding employment is approximately wrong. 

 

baseball and machine learning

A few weeks ago two of us were talking about the perception of "now".  A fusion of sensory inputs, responses and thoughts takes place and a highly edited version is assigned in what we perceive as a smooth and linear flow of time.  Consider vision.  It turns out it takes us around three tenths of a second to put together a meaningful image from the time light hits the retina. First we note color, a bit later motion and finally form.  No big deal unless you have to react very quickly.  For most of us that isn't a big deal.  For athletes it is.

 

Baseball is useful as the time it takes for the ball to travel from pitcher to bat isn't much longer than the time it takes to process an image. But baseball "works."  To examine vision in baseball consider the great women's fastpitch softball player Jenny Finch.  A few years ago she broke what the best Major League Baseball hitters are capable of. 

 

Their problem is they don't know how to "read" her.  Beginning as little kids  they learned how to hit a ball getting progressively better over time.  Early on the time of flight for the ball was so slow that human vision and reflex speeds weren't the major issue.  With practice they began to learn how to read the pitcher.  Posture, arm movements and so on.  The shards of image they formed gave them information on the physics of the ball's flight path.  They were learning all of the patterns even though they thought  that they really sensed when the ball was released and when it hit their bat - after all, that's what their mind told them.  But what their mind put together wasn't accurate.  In reality they were linking reads and other early information with ball trajectories.

 

Jenny comes along with a pitch that is over ten meters per second slower than what they're used to, but the information they receive doesn't link reliably with ball trajectories.  They either try to rely on reflexes missing the ball entirely as it flies past before they can swing or they use a mistaken trajectory from their mistaken read and strike out. They could learn... give them a lot of time working with women's fastpitch experts and they'd finally build the appropriate library.  Ultimately some of them might even play the game well.

 

There's a striking similarity with machine learning.  You show a program a huge amount of data trying to be clever and you get a program that can quickly do great pattern recognition.  At least within a restricted domain.   The richness of training datasets is often poor.  Facial recognition programs might have respectable results for white people, but completely fail with people of color.    Such biases of omission are very common, but many other types of bias exist.  (again a rich and deep subject well beyond the scope of an hour). 

 

Machine learning can be useful but is only robust when the limits of where you can use it and the types of errors it makes are well-understood.  There are many areas where it's sort of good enough even though these limits aren't well established. Other areas are more critical.  We're a long way from it being generally useful in areas the tech press considers nearly solved -  self driving vehicles come to mind.

 

Back to the athlete.  Sports are played at many levels.  At an amateur level we play because it's fun.  Beyond that most of us are watching others.  In direct competition we usually prefer watching serious pros.  Beyond the beauty of watching human motion being executed so well there are those magical times where something extraordinary happens.  Athletes at the highest level develop a deep sense of the game and, in addition to being able to react faster than their vision and reflexes would suggest, are tracking and processing other channels of information.  In some games players develop a "field sense" .. they know where the other players are and how they're moving.   You see this dramatically in beach volleyball when played at the highest level and it is common in soccer and basketball.  This gives them the ability to do the impossible. These are very beautiful human moments beyond machine learning.   And it goes beyond sport ..  think of the human experts that just out of the ordinary when the time comes - like Captain Sully Sullenberger landed in the Hudson. 

 

We tend to think about athletes as having some physical gifts and a lot of training.  Certainly those are necessary, but there's an impressive mental component.  We don't say someone is good  at foreign languages because they have a dexterous tongue.

 

fitting any body by throwing away the concept of sizes

When "Distinguished" was added before my Member of the Technical Staff Bell Labs title,  I learned those of us in physics and math research were expected to spend five to ten percent of our time working on "interesting" problems of important AT&T customers.  It turned out to be a great program.  We were be exposed to problems and ways of thinking we would never have encountered.   Even when we weren't able to help,  we always learned something.  For me it was  important to realize a person with an odd skill set can sometimes offer novel thinking and insight in an area they know little about. 

 

Three of us found ourselves at the Pentagon (the military was an important AT&T customer) listening to a Colonel talk about problems with military uniforms.  At first I felt like looking for an exit, but as he went on it became clear the problem was fascinating involving math, computer vision, and manufacturing processes that hadn't been invented. 

 

It turns out it's very hard to fit clothing to people without getting sizing good enough and then following through with proper tailoring.  The Army was worrying about human performance. Clothing fit and fabric type were big issues.  They wanted to know if there was some way to quickly take about two dozen measurements that could be used to drive automated manufacturing tools. 

 

It turns out the second part - computerized manufacturing - was and is a huge problem that's beginning to see solutions now.  We focused on the measurement part and invented a laser scanner that could scan a human in about one minute producing a 3d model of their shape accurate to a few millimeters assuming they stood very still.  Several prototypes were  built at a university  and were part of the largest anthropometric study of men and women at the time..  

 

Going through the data, we learned you could  fit over 99% of male and just under 98% of female soldiers by specifying a smaller set of measurements that could be taken by an enlisted person in a few minutes.  The accuracy was better than any but the best fabrication processes of the day.  They would just let vendors bit on it and pay whatever it took.  There wasn't a need for laser scanners.

 

My sense of style is between zero and some negative or even imaginary number, but the problem of making high quality clothing without resorting high end design and tailoring continues to fascinate me.   At the time it was a hard manufacturing problem that was central to a business that was north of a trillion dollars a year worldwide.  It's more like a trillion and a half now.  Millions of people, particularly women, complain about poor fit, fabrication and materials.  I'll written about that in earlier posts in the fashion section and there is the emerging area of smart clothing that I'll skip for now. 

 

The problem returned about ten years ago when I met a friend who happens to be a very thin women who stands six foot three inches.  Getting anything that comes close was an issue and she makes regular use of a tailor.  She has a serious sense of style, but she has to work at it to the point of designing and making her own clothing.  It turned out she knew others with tall clothing issues.  Two other friends are taller yet.  When you're thinking about a problem it's often useful to start with cases where current processes are broken.

 

There are any number of custom shops, but you still pay a lot, selection is often much lower and delivery times can be weeks long with remakes and/or tailoring required.  A friend with a very long inseam spends nearly $250 for a pair of ok, but not great jeans.  That's out of her range, so she sews extensions made from old jeans legs onto the legs of regular jeans.

 

In the meantime work on automated pattern cutting and automated measurement to pattern software has made real progress.  At this point the bottleneck step that is currently hard is stitching ... it's being solved, but only works for limited types of fabrics and designs and is more expensive than skilled human labor (remember that much of the human labor is in South Asia at horrible pay levels with awful conditions).   But development is rapidly progressing and Chinese companies are sinking serious money into the technology.

 

Looking back to the Army work, one of our measurement ideas was to have people wear a bodysuit covered with fiducial marks a computer vision program could recognize.  At the time it seemed too slow and calibration would be tricky, but it was something to watch.  We tried to patent the idea, but were turned down as it was a bit out there and completely out of AT&T business interests.  Now you can do it with a smartphone.  An iPhone X with a 3d sensor could do a wonderful job, but even a regular phone might be good enough.

 

Today someone sent a piece on a stab at the problem -   Zozotown.

 

Many other important issues come to mind, but throwing away sizing and fitting a wide range of body types is part of the what's necessary.  I don't know if this company make it, but we're on the cusp of radical changes in clothing manufacture that may rival the introduction of the shipping container.  One of the largest industries on Earth may begin the process of disruption.

 

she ruled the known universe

By the late 19th century astronomy had been revolutionized by photography.  Long exposures accurately produced much more detail than the best human eyes could hope to record and spectrography lead to the creation of astrophysics.  A real revolution was underway and large sums of money were going into new telescopes.

 

There was a fly in the ointment.  A night's worth of human observations were equivalent to a few kilobytes of information.  A good photographic plate contained thousands of times more.  Astronomy was entering its first age of big data. Finding items of interest and making accurate measurements required a lot of computation.  That meant human computers.

 

To create a catalog of the location, brightness and color of every star in the observable universe Edward Pickering created of the first computer centers at the Harvard College Observatory  The first computers were Harvard students, but Pickering found the young men unreliable.  He switched to female computers .. largely educated women who were unmarriageable for one reason or another, allowing them to have a full time job.  Pay was a bit more than a female school teacher made -  twenty cents an hour.  This group became one of most remarkable computer centers of all time.

 

Henrietta Leavitt  studied music at Oberlin and went on to the Harvard Annex (now Radcliffe) to get a college degree.  She enjoyed astronomy so much that her well-to-do family supported her volunteer work at the Harvard Observatory for a few years.  Her speciality was variable stars - the oddballs that changed in brightness over relatively short amounts of time.

 

She went back to her family taking a position as an arts assistant at a local college, but continued to work on a paper based on her observations.  She became ill and became deaf making marriage and work in music unlikely.   Henrietta got in touch with Pickering.  She could come back, but he couldn't pay her.  She went back to work without a salary - after all, her family was expected to support her.  Years later he started to pay her. 

 

She set out to characterize about 1800 variable stars in the Large and Small Magellaniac  Clouds.  As she worked something started to stand out in her mind.  If she assumed these stars were a similar distance away, after all, they were in the same cluster,  she deduced the period over which their brightness changed was related to their brightness. 

 

The apparent brightness of a light changes by the inverse square of its distance.  Double the distance to a light and it appears a quarter as bright.    Henrietta had discovered if two of these variables - known as Cepheid variables - had the same period, but one was one hundred times dimmer, you could deduce it was ten times farther away than the brighter star.  

 

Measuring the distance to objects in the Universe is core to astronomy and cosmology.  Distances to nearby objects - out to about fifty light years away - could be measured using parallax.  Hold a finger in front of your face and look at it with your left eye.  Now your right.  You'll notice a shift in position.  In astronomy you note a position at one part of the Earth's orbit and measure again six months later. Knowing the diameter of the Earth's orbit and the angular difference between the two measurements allows you to calculate the distance with trigonometry.  Unfortunately the technique  only works for nearby objects as the angles become too small to measure with increasing distance. 

 

By the early teens distances to several nearby Cepheids had been measured using parallax. Leavitt's yardstick had been calibrated.  Her result was one of the most important developments in astronomy - certainly worthy of the Nobel Prize.   She was unknown outside of astronomy, but was finally nominated for the Nobel Prize in Physics.  When information was being collected by the Nobel committee it was discovered cancer had taken her a few years earlier.

 

In the mid twenties Edwin Hubble used the Hooker telescope and Leavitt's relation to measure the distance to Cepheid variables in what was then called the Andromeda nebulae. The distances he found were mind blowing - about a million light years.¹  Andromeda was much farther away than anyone had imaging and couldn't be in the Milky Way.  It was a galaxy and the Universe was made of more than just the Milky Way. 

 

The physics of the how Cepheids work took decades to work out, but her relation didn't require a detailed knowledge of the mechanism.²  It became a workhorse and is still regularly used out to distances where you can still see Cepheids.  Over time a series of other yardsticks have been created all using her notion of a knowable absolute  brightness and the inverse square law.  It's how science advances, but someone has to take that first huge leap.  Someone should make a movie about these remarkable computers, particularly the deaf one who figured out how to measure from here to the stars. 

 

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¹ The currently measured distance is something over twice as far out - well within his measurement error.  The million light year distance was mind blowing at the time.

A small detail.  Astronomers often use the parsec as a unit of length rather than light-years.  A parsec is a parallax-second - the distance one astronomical unit (the radius of the Earth's orbit) subtends an angle of one arc second..   it's about 3.26 light-years.  Everyone else seems used to light years so I use them here.

² Cepheids are bright  yellow giants - anywhere from 4 to 20 times the mass of the Sun and up to 100,000 times as luminous.  During their period they see their radius change about as much as 25 percent.   They have a lot of helium in an outer layer.  Helium changes in opacity depending on how ionized it is.  Doubly ionized helium - helium missing both electrons - is more opaque than singly ionized helium.  As helium heats up it becomes more ionized.  At the dimmest part of the star's cycle the outer layer of helium is most opaque.  It absorbs heat from the star's radiation and expands.  As it expands it cools and the helium layer becomes more transparent.  At some point it begins to contract due to gravitation getting hotter as it goes.  The transparent mostly singly ionized helium becomes doubly ionized and opaque and the cycle starts over.  It's a huge fusion powered heat engine.

 

the hike that changed pasadena and human knowledge

On a clear day there it is.  Five or six miles East-North-East of Pasadena and  a tempting climb if you were raised around mountains.  Mt Wilson's summit is a bit over 5,700 feet and the view is remarkable in more ways than one. A trail out of Chantry Flat is fine, but tends to be crowded.  It's more strenuous but I'm partial to the Mt Wilson trail.  You can also drive up ..  assuming your car can handle the nest of television, radio and microwave antennas at the summit.

 

Around 1903 George Hale, a young astrophysics professor from the University of Chicago,  took the hike to see if it was the place for his dream telescope.  Up until around the Civil War astronomy had become a nearly dead subject.  Its main purpose had drifted from science to commercial and military celestial navigation.  But something radical had taken place mostly in America.  Physicists attached prisms to telescopes and began to analyze the spectra of light from the stars.  Photographic film had advanced and was better than the human eye at recording dim images.  It was possible to learn much more about the stars and discoveries grew exponentially.

 

Astrophysics was probably the first scientific field that America took the lead in. Gathering the most light possible was essential and big light buckets were expensive.  Hale came from a well-heeled family and had been able to connect with and inspire wealthy industrialists to fund the emerging field.  At Chicago he was able to talk a streetcar magnate into funding the largest refracting telescope - the 40 inch Yerkes Observatory.  Important work was done, but it soon became clear better observing sites than semi-rural Wisconsin were necessary.

 

It was recognized Mt Wilson had potential in the late 1890s.  Harvard tried to operate a small observatory, but it failed for a number of reasons.  Hale wanted to build a much larger telescope of a radically different design..  a 60 inch reflecting telescope with a novel mount.   The trip to Mt  Wilson in the pre-light and automobile pollution days. He loved it .. the view to the ocean was fine, but the view to the stars convinced him this was the place.  He went to Andrew Carnegie and described the potential of the best instrument in the world.

 

Building and getting a 60 inch telescope up the mountain was an effort, but it was a brilliant instrument exceeding all expectations. Harlow Shapley was able to use it to discover the Sun was not the center of the Milky Way and a few other discoveries followed.   It also became clear that an even larger telescope would be useful and Hale managed to persuade  John Hooker and Andrew Carnegie into funding a 100 inch instrument - the Hooker telescope.

 

It has been argued the Hooker was the most successful telescope in history.  Edwin Hubble discovered not only that there were galaxies beyond the Milky Way, but that the universe was expanding.  Shapley was able to measure the size of our galaxy and Fritz Zwicky found the first evidence for dark matter -- back in the early 1930s!  Our perception of our place in the Universe and evidence its fundamental nature radically changed. 

 

Hale still had yet another telescope in him.  Mt Wilson was becoming victim to light and atmospheric pollution.  The 200 inch Hale telescope was installed on Mt Palomar, seeing first light in 1948.   Its observations made it clear how elements were made in stars and indirect observations of black holes were made. People had been thinking about cosmology from the beginning of recorded history and with observations made with this telescope it finally  had become a real science.

 

If you make it to the summit both of the old telescopes are still there along with a solar telescope. The location doesn't allow serious research, but amateur astronomers can rent time on them and there are small public observation nights on the 60 inch using an eyepiece.  I did it once on a very un-pristine night, OMG!

 

It turns out Hale did much more.  When he moved out to Pasadena he became a trustee of a very small and sleepy technical school - the Throop College of Technology.  It could produce engineers to help build the telescopes, but Hale saw had larger ambitions.  He brought in two very well known scientists - Arthur Noyes and Robert Millikan. The three of them conspired to build an institution that would be small - tiny even - but would hire the best and focus on work that would have a long term impact.  Probably several institutions had mission statements like that, but these people pulled it off.  They created an interesting culture of curious play, depth, rigor and collaboration.

 

Hale befriended Henry Huntington - a railroad and real estate tycoon.  Huntington is fascinating in his own right - the sprawl of Los Angeles and much of it's culture has roots in his projects. He helped with the funding of this emerging technical school and brought in cultural amenities.  By now it had been renamed the California Institute of Technology.

   

That may well have been Hale's greatest contribution to humanity.  For decades Caltech's taste in problem spaces, their cross-disciplinary nature and remarkable students have changed the world. They came a bit too late to participate in the electrification of America, but the type of fundamental and applied science that came from the place changed everything.

 

Hale would have been 150 last week.  He would have been thrilled that he created something special.  Caltech is still at the leading edge of astrophysics and cosmology .. and so much more he couldn't have dreamed.  

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¹ Without a doubt it was one of the watershed instruments - that list might include the Galileo telescope, the Hooker, Karl Jansky's radio telescope, the Hubble Space Telescope and LIGO.