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Hubble Telescope Discovers a Light-Bending 'Einstein Ring' In Space (space.com)

Space.com reports of the Hubble Space Telescope's discovery of a light-bending "Einstein Ring" in space: The perfect circle surrounding a galaxy cluster in a new Hubble Space Telescope image is a visual indicator of the huge masses that are bending time and space in that region. The galaxy cluster, called SDSS J0146-0929, features hundreds of individual galaxies all bound together by gravity. There's so much mass in this region that the cluster is distorting light from objects behind it. This phenomenon is called an Einstein ring. The ring is created as the light that comes from distant objects, like galaxies, passes by "an extremely large mass, like this galaxy cluster," NASA said in a statement. "In this image, the light from a background galaxy is diverted and distorted around the massive intervening cluster and forced to travel along many different light paths toward Earth, making it seem as though the galaxy is in several places at once." The ring is named after Albert Einstein, who wrote his theory of general relativity in the early 1900s. In it, he suggested that a massive object would warp space and time. This process is known today as a gravitational lens. When the most massive galaxies and galaxy clusters get in line with a more distant object, they produce an Einstein ring -- a type of gravitational lens.

71 comments

  1. The ring is not the lens by Anonymous Coward · · Score: 0

    It's an image of a distant object. The image is produced by the lens, in a particular arrangement of lens, object and observer.

  2. The Einstein Ring is really amazing by 93+Escort+Wagon · · Score: 3, Interesting

    But, whenever I see these Hubble deep space images, I am still blown away just looking at all the galaxies in the photo.

    Douglas Adams nailed it.

    --
    #DeleteChrome
    1. Re:The Einstein Ring is really amazing by Anonymous Coward · · Score: 1

      Douglas Adams nailed it.

      Though, our local pharmacy closed down, so for us, it's not peanuts for us anymore...

  3. That's why I love astronomy! by plumwhite23091 · · Score: 1

    "making it seem as though the galaxy is in several places at once." sounds cool. Just like in sci-fi movies.

    --
    WilliamReview.com
  4. How is this news? by Edis+Krad · · Score: 4, Insightful

    Not to flame or anything - I'm honestly asking - but haven't we discovered already hundreds of gravitational lensed galaxies already? What's different about this one?

    1. Re:How is this news? by Anonymous Coward · · Score: 0

      Not so much... I was surprised that this wasn't a medium.com article....

    2. Re:How is this news? by The+Evil+Atheist · · Score: 4, Insightful

      It's just a newly discovered one. Not everything in the news has to always be about "first of its kind".

      --
      Those who do not learn from commit history are doomed to regress it.
    3. Re:How is this news? by Anonymous Coward · · Score: 0

      nothing different -- but in general, these are probably not gravitational but optical by way of the stellar matter acting like a lens.

    4. Re:How is this news? by Anonymous Coward · · Score: 0

      Uhm no, it is not an optical lens.

    5. Re:How is this news? by heson · · Score: 4, Funny

      I brushed my teeth this morning.

    6. Re:How is this news? by Anonymous Coward · · Score: 0

      This one is the shiniest of them all

    7. Re:How is this news? by The+Evil+Atheist · · Score: 3, Interesting

      There are billions of people on this planet and hundreds of millions who do the same this morning.

      There are quintillions of galaxies in the observable universe, and only "hundreds" of gravitationally lensed galaxies, all of which are the result of (literally) astronomical coincidence.

      --
      Those who do not learn from commit history are doomed to regress it.
    8. Re:How is this news? by eepok · · Score: 1

      First time or repeat?

    9. Re:How is this news? by AlwinBarni · · Score: 2

      Shouldn't the title be more appropriate then, e.g. "Yet another Einstein ring discovered ..."?

    10. Re:How is this news? by war4peace · · Score: 1

      So are his teeth.

      --
      ...gis sdrawkcab (usually not responding to ACs; don't bother posting as AC)
    11. Re:How is this news? by Anonymous Coward · · Score: 0

      > but haven't we discovered already hundreds of gravitational lensed galaxies already? What's different about this one?

      We haven't discovered many Einstein rings.

    12. Re:How is this news? by Anonymous Coward · · Score: 0

      It's just a newly discovered one. Not everything in the news has to always be about "first of its kind".

      These phenomena also open the possibility that we are seeing more objects out there than there really are.

      If light can be bent over, then it is also possible that light from a galaxy can be caught in the gravitational field of a cluster, orbit it, and be sent back to same galaxy.

      In other words, we may as well be seeing our own Milky way gravitational reflection among the other objects we see in the night. Along with thousands, millions, of other reflections.

    13. Re:How is this news? by RoloDMonkey · · Score: 2
      1. The gravitational lensing is caused by a galaxy cluster, not a single galaxy.
      2. This one is a much larger and more complete ring than I have seen in other examples. Also, there are other smaller arcs in the picture. This allows for a lot more extrapolation about what is going on in that cluster, including dark matter
      3. It's a cool picture, Brent
      --
      Long live the Speaker Bracelet
      Rolo D. Monkey
    14. Re:How is this news? by Anonymous Coward · · Score: 0

      This is more like a gravitational "fly eye toy" than the traditional gravitational "lens".

      The refractive properties of the gravity well make it look like there are a bunch of identical galaxies when it's actually just a repeated image of one galaxy.

    15. Re:How is this news? by meglon · · Score: 1

      There's lot of lensed galaxies, but few that show on both sides of the object as a ring; most are a single image lense. Abel 1689 is a great view of a lot of single sided ones (just because i absolutely love this pic) https://en.wikipedia.org/wiki/...

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      Fascism: An authoritarian and nationalistic right-wing system of government and social organization. See also: NAZI's
    16. Re:How is this news? by Anonymous Coward · · Score: 0

      Did brushing your teeth cost as much as the equipment used in this new observation? Neoliberalism alone dictates that this story is more interesting than your teeth, because it involves more money.

    17. Re:How is this news? by ShamblerBishop · · Score: 1

      And just think about how many intelligent life forms are out there in all those galaxies, brushing their teeth right now!

  5. Are they sure? by shayd2 · · Score: 0
    The image looks a LOT like the start of a REALLY BIG Dyson sphere.

    Maybe there are lots of those already built. It would explain "dark matter"

  6. My Precious! by Anonymous Coward · · Score: 0

    My Precious!

  7. Not a perfect circle by Anonymous Coward · · Score: 1

    It is not a perfect circle - not even close. To make a perfectly circular Einstein ring would require the large mass to be at a singularity, with no other mass nearby, and no mass between the ring and the observer, to further perturb the bending light (from the observer's frame of reference).

    Problem is, the mass that is creating the ring is not a singularity, so light is not bent uniformly around it, and the "circle" is not perfect.

    1. Re:Not a perfect circle by scottrocket · · Score: 2

      "...and the circle is not perfect."

      No such thing as a perfect circle anywhere, except maybe in just the math itself - and pi goes on & on...

    2. Re:Not a perfect circle by Ol+Olsoc · · Score: 1

      "...and the circle is not perfect."

      No such thing as a perfect circle anywhere, except maybe in just the math itself - and pi goes on & on...

      I've been called a perfect asshole from time to tie. Does that count?

      --
      The shepherds did so well protecting the flock that the sheep no longer believed that wolves existed.
    3. Re:Not a perfect circle by scottrocket · · Score: 1

      Hey leave my asshole outa this! : ) I was just carrying the torch of pedantry forward-there are limits to the precision of our measurements. Personally, I read "perfect circle" as visually "close enough" to a circle, to count as perfect. 0..o..O...there we go!

    4. Re:Not a perfect circle by DamnRogue · · Score: 1

      No such thing as a perfect circle anywhere, except maybe in just the math itself - and pi goes on & on...

      Profile of a neutron star?

    5. Re:Not a perfect circle by EETech1 · · Score: 1

      Isn't that more like a *
      Only one asshole I know of looks like a O

    6. Re:Not a perfect circle by meglon · · Score: 1

      Interestingly.... https://www.nasa.gov/content/g...

      Maybe not perfect all the time.

      --
      Fascism: An authoritarian and nationalistic right-wing system of government and social organization. See also: NAZI's
    7. Re:Not a perfect circle by Anonymous Coward · · Score: 0

      NASA didn't describe the Einstein Ring as a perfect circle. It was Elizabeth Howell @ Space.com (or her editor) that developed that entirely baseless claim.

  8. Why this one? by sTERNKERN · · Score: 2

    I have seen this article pop up on every major site, but it still makes me wonder.. why are we so keen on this particular ring? We have seen this phenomenon quite many times.

  9. reminder by Anonymous Coward · · Score: 1

    reminder for me to don't take shit too seriously as it relates to the cosmos, it really is small potatoes.
    happy Friday!

    1. Re:reminder by Anonymous Coward · · Score: 0

      Happy Friday man!

  10. Re:And... ? by Anonymous Coward · · Score: 0

    A time will come when we will need to leave our solar system to survive. Anyway, what are you doing wasting time on /.?

  11. Pebble in water? by Okian+Warrior · · Score: 1

    "...and the circle is not perfect."

    No such thing as a perfect circle anywhere, except maybe in just the math itself - and pi goes on & on...

    Drop a pebble into a calm pool of water?

    (I commented to my physics professor once that primitive humans see lines everywhere, but never circles. This is what he responded with.)

    1. Re:Pebble in water? by xxxJonBoyxxx · · Score: 2

      >> I commented to my physics professor once that primitive humans see lines everywhere, but never circles

      If you had grown up outside of Seattle, you might have also thought about "the sun" and "the moon" as examples of circular things primitives could experience.

    2. Re:Pebble in water? by Anonymous Coward · · Score: 1

      >> I commented to my physics professor once that primitive humans see lines everywhere, but never circles

      If you had grown up outside of Seattle, you might have also thought about "the sun" and "the moon" as examples of circular things primitives could experience.

      Oblate spheroids [like the Sun] can only be circles from certain points of vantage.

    3. Re:Pebble in water? by meglon · · Score: 1

      And from a human point of vantage on planet dirt, it's anywhere... at least until your eyes burn out. Advisor tip #47a: stick with looking at the moon.

      --
      Fascism: An authoritarian and nationalistic right-wing system of government and social organization. See also: NAZI's
    4. Re:Pebble in water? by Quirkz · · Score: 1

      The human pupil is pretty circular, isn't it?

  12. A ring? by Walter+White · · Score: 1

    Was there any sign of the protomolecule? :o

  13. Uh, no. by Kludge · · Score: 2

    Sorry. As cool as your teeth are, gravitationally lensed galaxies are SO MUCH MORE AWESOME.

  14. Obligatory... by Anonymous Coward · · Score: 0

    It's seeing light being sucked around by the black hole formed by Zuck's massive ego.

  15. Like the rest of them by nospam007 · · Score: 1

    "The galaxy cluster, called SDSS J0146-0929, features hundreds of individual galaxies all bound together by gravity."

    Not to be picky, but all the other trillions of galaxies are also bound together by gravity, it's sort of a 'thing' that all galaxies have.

    1. Re:Like the rest of them by Anonymous Coward · · Score: 0

      Bound to each other by gravity.

  16. Galactic Lens Flare by flygeek · · Score: 2

    I dunno - are they sure JJ Abrams was not involved in taking the photograph?

    1. Re:Galactic Lens Flare by meglon · · Score: 1

      Yeh, that's not enough lens flare to be one of his.

      --
      Fascism: An authoritarian and nationalistic right-wing system of government and social organization. See also: NAZI's
  17. Not necessarily gravitational by paradigmsareconstruc · · Score: 2

    It is getting ahead of the observations to label the observation as gravitational. If we were looking down the barrel of a plasma filament, Weâ(TM)d probably see something similar.

    1. Re:Not necessarily gravitational by meglon · · Score: 1

      Electric Universe crap is bullshit. It explains nothing, and requires Einstein to be wrong.... he wasn't, and the electric universe cult of morons can't even come up with math to show their own bullshit might be right, let alone any observational data that does. Give up your religious Eu bullshit and quit being stupid.

      --
      Fascism: An authoritarian and nationalistic right-wing system of government and social organization. See also: NAZI's
    2. Re:Not necessarily gravitational by Anonymous Coward · · Score: 0

      Einstein requires Newton to be wrong. You are clearly so heavily invested in flawed-by-definition current models that you must emotionally condemn any new idea. The smug outrage your post drips with recalls the #metoo movement. Are you sure you're not defending an arbitrary social consensus, the very thing Feynman warned about in Cargo Cult Science?

    3. Re:Not necessarily gravitational by meglon · · Score: 1

      Every time relativity has been put to the test, it's been shown to be correct. As for Newton, most everyone knew there were problems with his gravitational theory in the 1890's... try to keep up. http://theory.uwinnipeg.ca/use... Newton gravity doesn't even account for the time differences from the ground to a GPS satellite. Newton didn't have satellites to contend with, so he never saw that particular problem... so he never knew it was a problem to fix. But, that's what science does... as technology progresses, we have to revisit earlier ideas to account for new observations. Hence, yes, Relativity replaced Newton's gravity.

      Gravitational lensing has been a mathematical thing longer than General Relativity has been published. http://www.einstein-online.inf... In 1979 the first one was found, just as had been predicted. We understand them fairly well (the mechanism). So, just like EVERY OTHER prediction Relativity makes that has undergone experimental testing, Relativity was shown to be correct.

      Electric universe bullshit, on the other hand, has no math behind it, has no observational data, and can't even find what few things it predicted we'd find. It's complete and utter bullshit trying to legitimize itself as science via really stupid people continuing to bring it up every chance they get. Additionally, Relativity has to be wrong for the electric universe cult of stupidity to be right. Yet experiments keep showing Relativity is correct.

      Electric universe wise, even Alfvén can't find his radio transmissions that are REQUIRED. EU is complete and utter bullshit. It's not a new idea, it's an older idea that was disproven a couple decades ago.... it's just really stupid people keep bringing it up. It's not science, it's a quasi-religious pseudoscience cult of stupidity driven by their need to con people out of money for their t-shirts.

      If you put forth a scientific hypothesis, and the only predictions it makes are shown to be wrong, your hypothesis is wrong. In the case of electric universe, that doesn't dissuade the fucking idiots from trying to make a buck off it conning people... or posting anon to try to defend complete rubbish. EU is the very definition of your cargo cult science, while people suggesting relativity, which has been verified EVERY SINGLE TIME it's been tested for 99 years now is... those people are complete fucking idiots.

      --
      Fascism: An authoritarian and nationalistic right-wing system of government and social organization. See also: NAZI's
    4. Re:Not necessarily gravitational by paradigmsareconstruc · · Score: 2

      You're completely whitewashing the history of gravitational lensing. I've reviewed the actual history of lensing claims in former Slashdot posts. For example, here is a quote by one of the astronomers who discovered the first lens:

      "All that can be said in rebuttal is that it would be even more remarkable if the 4 images, all with the same redshift, existed for some other reason, in a configuration which can be so well modelled by the lensing hypothesis"

      Notice the obvious implication: No alternative inferences were considered.

      You might consider your process for evaluating science, and contrast it with mine. What I am doing is seeking out the best critique I can find. In this case, that involves reading books by Halton Arp, the world's most vocal and knowledgeable critic of the lensing hypothesis. He presents a critical perspective of the origin of this idea in his many books.

      Now look at what you're doing: You've gone online to defend the gravitational lensing hypothesis without ever seeking out strong critiques. You learn about these critiques as you are "debunking" those who have taken the time to understand both sides of the debate.

      The EU's math is extensive, and has also been posted into Slashdot comments. At this point, you're now creating a serious problem for your own community, because you are creating an unfounded bias against electricity in space in the tech community. I mean, it's really hard to put into words just how wrong these behaviors are. You are posting ideas which are literally centuries old and conceived at a time when space was assumed to be an empty vacuum, and shouting down ideas which were conceived as a reaction to unexpected Space Age discoveries that actually there are charged particles and enough ionization wherever we look that most of what we are actually seeing is matter in the plasma state (99%+). Your approach is also directing your community towards a dead-end: the dark matter problem. The EU offers a simple physical solution to this problem which you repeatedly ignore at your own peril.

      The Slashdot community needs to distance itself from people who get emotional each time that the idea of electricity in space is brought up. The crux of the issue has already basically been settled, and the astrophysical community has already acknowledged that electricity in space happens. The debate at this point now centers around whether or not there are consequences. This is not something that a person can judge without putting any effort at all into learning about the debate. The only way to judge the debate is to track it over many years. It foremost takes listening and reading, then some thinking, and perhaps interactions with the theorists involved with the claims. You've done none of these things which would qualify you to have an opinion on the issue. You've decided that you can judge the debate without actually immersing yourself into both sides, and in terms of process, it's a horrible approach which will have a very predictable outcome for yourself.

    5. Re:Not necessarily gravitational by meglon · · Score: 1

      Electric universe is bullshit, regardless of whether you post using your name or as an anon coward. The "bias" against EU is because it is pure shit, explains nothing, and requires us to throw away the last 100 years of progress. Only a fucking idiot would suggest that.

      Tell yah what, my new theory is the universe came into being when my pet 6 foot tall invisible rabbit shit it out. Guess what... that has as much "science" behind it as the electric universe shit. Actually, as electric universe made some predictions that proved WRONG, and i haven't done that with my rabbit... my rabbit is better scientifically than the electric universe bullshit.

      You're not doing science... you're doing religion trying to masquerade as science, and you're either incredibly stupid and have no understanding of the scientific method, or you're a fucking con artist trying to make a buck.

      The predicted outcome: no one takes electric universe seriously because it is bullshit pseudo-science... yet we'll keep having out planes, ships, cars, and hikers navigate fine because RELATIVITY WORKS. The "crux" is, you're either lying, or have fallen for a lie. Your choice, and i don't really care, because you can't talk to someone who doesn't even acknowledge reality.... Relativity works, and electric universe hasn't done shit (and requires relativity to not work). You are nothing more than a religious zealot, too stupid to understand reality.

      --
      Fascism: An authoritarian and nationalistic right-wing system of government and social organization. See also: NAZI's
    6. Re:Not necessarily gravitational by meglon · · Score: 1
      https://motherboard.vice.com/e...

      "At best, the 'electric universe' is a solution in search of a problem; it seeks to explain things we already understand very well through gravity, plasma and nuclear physics, and the like," said astronomer Phil Plait, who runs the blog Bad Astronomy at Slate. "At worst it's sheer crackpottery like homeopathy and astrology, making claims clearly contradicted by the evidence."

      And here's part of the con....

      One hundred seventy-five people donate $1,905 per month to the Thunderbolts Project Patreon campaign for video production.

      "We know stars generate energy through nuclear fusion, not plasma discharge; we know craters are formed from asteroid and comet impacts, not huge electric arcs; we absolutely know that special and general relativity work, despite some EU proponents' claims," said Plait, who has tangled with EU commenters a time or two. "From what I've seen, most EU claims are on the cranky end of [the] scale. That's why most astronomers ignore it: No evidence for it, tons of evidence against it, and no support mathematically or physically."

      http://dealingwithcreationismi...

      Electric universe is a con. Are you a conman, or just a stupid rube?

      --
      Fascism: An authoritarian and nationalistic right-wing system of government and social organization. See also: NAZI's
    7. Re:Not necessarily gravitational by paradigmsareconstruc · · Score: 2

      Re: "... and requires us to throw away the last 100 years of progress ..."

      This is really the crux of the debate: You view cosmology, the planetary sciences and astrophysics as functioning domains of science devoid of any persistent mysteries even as the scientists themselves admit the problems ...

      "Astronomy: Planets in chaos

      The discovery of thousands of star systems wildly different from our own has demolished ideas about how planets form. Astronomers are searching for a whole new theory.

      Over the past 15 years, for example, experiments designed to detect individual particles of dark matter have become a million times more sensitive, and yet no signs of these elusive particles have appeared. And although the Large Hadron Collider has by all technical standards performed beautifully, with the exception of the Higgs boson, no new particles or other phenomena have been discovered.

      The stubborn elusiveness of dark matter has left many scientists both surprised and confused. We had what seemed like very good reasons to expect particles of dark matter to be discovered by now. And yet the hunt continues, and the mystery deepens.

      In many ways, we have only more open questions now than we did a decade or two ago. And at times, it can seem that the more precisely we measure our universe, the less we understand it. Throughout the second half of the 20th century, theoretical particle physicists were often very successful at predicting the kinds of particles that would be discovered as accelerators became increasingly powerful. It was a truly impressive run.

      But our prescience seems to have come to an end -- the long-predicted particles associated with our favorite and most well-motivated theories have stubbornly refused to appear. Perhaps the discoveries of such particles are right around the corner, and our confidence will soon be restored. But right now, there seems to be little support for such optimism.

      In response, droves of physicists are going back to their chalkboards, revisiting and revising their assumptions. With bruised egos and a bit more humility, we are desperately attempting to find a new way to make sense of our world."

      Based on theoretical studies of how magnetism is generated in stars, it’s thought that the fully convective interiors of ultracool dwarfs can’t support large-scale magnetic field formation. This should prevent these stars from exhibiting activity cycles like the Sun. But recent radio observations of dwarf stars have led scientist Matthew Route (ITaP Research Computing, Purdue University) to question these models ...

      Inspired by this possibility, Route conducted an investigation of the long-term magnetic behavior of all known radio-flaring ultracool dwarfs, a list of 14 stars. Using polarized radio emission measurements, he found that many of his targets exhibited similar polarity flips, which he argues is evidence that these dwarfs are undergoing magnetic field reversals on roughly decade-long timescales, analogous to those reversals that occur in the Sun.

      If this is indeed true, then we need to examine our models of how magnetic fields are generated in stars ...

      Planetary scientists have admitted that they have no idea how to construct the vast majority of the exoplanetary systems which have been observed using existing theory. Cosmologists have admitted that they cannot -- using your cherished approach -- explain basic observations for how galaxies rotate.

      Solar scientists cannot even explain how it is that the solar wind fails to appreciably decelerate even as it passes the Earth's orbit (in the lab, we accelerate such particles w/ electric fiel

    8. Re:Not necessarily gravitational by paradigmsareconstruc · · Score: 2

      The Electric Universe apparently sins for trying to address the unresolved problems of mainstream science. If your preferred set of ideas is so great, then why are theorists struggling to apply these models to explain so many basic observations? The mainstream offers us ever more complex, less empirical, more hypothetical ideas as answers, while positioning the application of laboratory observations of the only other candidate force as somehow out-of-bounds. This is the definition of an anti-science approach. You've been convinced that the answers are not to be found in laboratory study, and you point to ideas rooted in a creation event -- as if you are talking about science just because equations were used. Get a grip, and take a look at the big picture of what you are pitching.

    9. Re:Not necessarily gravitational by meglon · · Score: 1

      That's the point... electric universe doesn't try to address unresolved problems, it tries to tell us that problems we've solved over the past 100 years were solved wrong, even though there's technology built and used EVERY SINGLE DAY based on those solutions. The sin is some lying little conman trying to make money off the pseudo-science electric universe crap when it is WRONG. You're either too stupid to understand that, or you are the lying conman.

      I get it, physics is hard... and stupid people who can't learn it wish it was easier. It ain't. Deal with it.

      --
      Fascism: An authoritarian and nationalistic right-wing system of government and social organization. See also: NAZI's
    10. Re:Not necessarily gravitational by paradigmsareconstruc · · Score: 2

      So, what you're saying -- repeatedly -- is that since the math of Relativity works, then there can be no other explanation. I mean, just stunning.

      The irony is that Herbert Dingle, history's most outspoken critic of Relativity, eloquently argued against just this claim back in 1972 in his famous Science at the Crossroads. The following quote comes from pages 15 - 18:

      "It was particularly Galileo who realised that mathematics provided the most effective terms in which to express physical observations, and it was he who contributed most to the introduction of those terms into science. The book of nature, he wrote, 'is written in the mathematical language'. But there are two things that should be said about this oft-quoted aphorism. The first is that 'nature', or 'the universe', as Galileo conceived it was a much more restricted concept than that which we hold and that with which modern science is concerned. It comprised only what we study in mechanics; all other phenomena — sights, sounds, smells, etc. — belonged in his view not to the external world but to the observing subject, and it was not at all his idea that mathematics played the all-comprehensive role in science that it is nowadays often assumed to do. Secondly, a language is a medium for expressing ideas, and it is just as capable of expressing false ideas as true ones. The fact, therefore, that something can be expressed with rigorous mathematical exactitude tells you nothing at all about its truth, i.e. about its relation to nature, or to what we can experience.

      The most dangerous intellectual error of modern science ... lies in the fact that this has been overlooked. Mathematics is an immensely more powerful tool than the Aristotelian syllogism, and its use as a language in which to express the facts of experience has been so successful that the idea has crept unperceived into the minds of physicists that whatever it says must be true. This is openly expressed in the statement already quoted, that everything that is not mathematically forbidden is necessarily observable. Accordingly the habit has developed of assuming that a physical theory is necessarily sound if its mathematics is impeccable: the question whether there is anything in nature corresponding to that impeccable mathematics is not regarded as a question; it is taken for granted.

      The fact is, however, that mathematical truths are far more general than physical truths: that is to say, the symbols that compose a mathematical expression may, with equal mathematical correctness, correspond both to that which is observable and that which is purely imaginary or even unimaginable. If, therefore, we start with a mathematical expression, and infer that there must be something in nature corresponding to it, we do in principle just what the pre-scientific philosophers did when they assumed that nature must obey their axioms, but its immensely greater power for both good and evil makes the consequences of its misapplication immensely more serious.

      There are so many instances, even in the most elementary uses of mathematics, in which its indications are obviously false, that it may seem strange that this fact is almost automatically overlooked in the more advanced uses of the tool. But there is a universal tendency, not only in science but in everyday life as well, to pay exaggerated attention to predictions that are realised and to ignore those that are not ...

      Suppose we want to find the number of men required for a certain job under certain conditions. Every schoolboy knows such problems, and he knows that he must begin by saying: 'Let x = the number of men required.' But that substitution introduces a whole range of possibilities that the nature of the original problem excludes. The mathematical symbol, x, can be positive, negative, integral, fractional, irrational, imagina

  18. Not just very large masses bend light! by Nivag064 · · Score: 1

    All mass, without any exceptions bend light, not just very large masses.

    However, we don't normally notice these effects unless the mass is very large.

    At very tiny scales, like single protons, quantum and other effects dominate -- but the tiny mass does effect light.

    I suspect that masses greater than that of Jupiter are required, before we can easily notice a mass bending light. Here I'd love to be wrong!