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Thoughts on Immensity

The Hubble Deep Field images of 1995 and 1998 gave us an unprecedented look at a small patch of sky with few nearby bright objects, a region about one-tenth the diameter of the full Moon in the constellation Fornax. The ensuing Hubble Ultra Deep Field, released in 2004, contains as many as 10,000 individual galaxies. Hubble’s Advanced Camera for Surveys (ACS) was deployed for this, as well as its Near Infrared Camera and Multi-object Spectrometer (NICMOS), producing a stunning harvest of elliptical and spiral galaxies, as well as oddly shaped collections of stars from the chaotic early days of the universe.

Image: The original NASA release image of the Hubble Ultra Deep Field, containing galaxies of various ages, sizes, shapes, and colors. The smallest, reddest galaxies, of which there are approximately 10,000, are some of the most distant galaxies to have been imaged by an optical telescope, probably existing shortly after the Big Bang. Credit: NASA/ESA.

I immediately thought of a Brian Aldiss title when I first saw the HUDF: Galaxies Like Grains of Sand came out in 1960, a collection of previously published stories later linked into a kind of future history. The grains of sand analogy always captures the imagination — most of us have walked on beaches. But here all sense of scale seems to drop away.

Sara Seager commented in her powerful The Smallest Lights in the Universe (2020) that with the original Hubble Deep Field, Robert Williams, then director of the Space Telescope Science Institute, had “…revealed three thousand previously unseen points of light. Not three thousand new stars. Three thousand new galaxies. Bob Williams almost single-handedly discovered millions of billions of possible worlds.”

How many planets are there around stars in the visible universe? How many galaxies? Astronomers and mathematicians work routinely with the kind of numbers involved here, but for us civilians, I don’t think it’s possible to emotionally comprehend such immensity. The Hubble Deep UV (HDUV) Legacy Survey image, released in 2015, ups the catch to 15,000 galaxies.

Tiny lights in the sky dwarf us whether they are stars or galaxies. It was imagery from TESS, our Transiting Exoplanet Survey Satellite, that brought on these reflections. Have a look at the starfield below. TESS has discovered 74 planets at this point, with another 1200 awaiting confirmation in an ongoing mission to examine nearby stars. The field of view is 400 times larger than what Kepler could cover in its tight stare in the direction of Cygnus and Lyra, but both missions rely on the transit method, detecting the presence of a planet crossing in front of its star in the stellar lightcurve. We’re going to get a lot of planets out of TESS, but among the targeted, nearby stars, probably around 1200 to 1500.

Stars like grains of sand. Here we’re looking toward Cygnus, back in Kepler country, and the sky is a glory of objects even if TESS will have a gap in coverage in the northern hemisphere, given an attempt by the science team to minimize the effects of scattered light from the Earth and the Moon. A mosaic of the southern coverage takes in more sky.

Image: This detail of the TESS northern panorama features a region in the constellation Cygnus. At center, the sprawling dark nebula Le Gentil 3, a vast cloud of interstellar dust, obscures the light of more distant stars. A prominent tendril extending to the lower left points toward the bright North America Nebula, glowing gas so named for its resemblance to the continent. Credit: NASA/MIT/TESS and Ethan Kruse (USRA).

The TESS numbers are already robust, with each of 13 northern hemisphere sectors imaged for nearly a month with four cameras, each of the latter with 16 charge-coupled devices (CCD). That adds up to 38,000 full science images for each of the CCDs, a total of 40 terabytes of data. It’s exhilarating to realize that these numbers are about to jump as TESS goes into its extended mission, revisiting the southern sky for another year, while relying upon improvements in data collection and processing that will return full-sector images every 10 minutes, as opposed to the earlier 30. TESS measures tens of thousands of stars, says NASA, every two minutes.

“These changes promise to make TESS’s extended mission even more fruitful,” said Padi Boyd, the mission’s project scientist at NASA’s Goddard Space Flight Center in Greenbelt, Maryland. “Making high-precision measurements of stellar brightness at these frequencies makes TESS an extraordinary new resource for studying flaring and pulsating stars and other transient phenomena, as well as for exploring the science of transiting exoplanets.”

Image: This mosaic of the northern sky incorporates 208 images taken by NASA’s Transiting Exoplanet Survey Satellite (TESS) during its second year of science operations, completed in July 2020. The mission split the northern sky into 13 sectors, each of which was imaged for nearly a month by the spacecraft’s four cameras. Among the many notable celestial objects visible: the glowing arc and obscuring dust clouds of the Milky Way (left), our home galaxy seen edgewise; the Andromeda galaxy (oval, center left), our nearest large galactic neighbor located 2.5 million light-years away; and the North America Nebula (lower left), part of a stellar factory complex 1,700 light-years away. The prominent dark lines are gaps between the detectors in TESS’s camera system. Credit: NASA/MIT/TESS and Ethan Kruse (USRA).

Does anyone ever get jaded with the sheer numbers we talk about as we delve into the cosmos? I suppose a kind of workaday numbness may occasionally settle in, and I suppose it would happen as well to geologists, for example, when trying to wrap their heads around the deep time suggested by the varied strata that first gave scientists a glimpse of how old the Earth really was. I just finished reading Hugh Raffles’ extraordinary The Book of Unconformities, a startling look not only into deep time but the landscape of loss as Raffles confronts twin deaths in his family that came seemingly out of nowhere. All of this against the background of stone considered at geologically significant sites. A taste of this:

At Siccar Point on the east coast of Scotland, a path leads precipitously down the cliff to Hutton’s Unconformity, the line of contact between the two rocks that James Hutton showed the mathematician John Playfair and the experimental geologist Sir James Hall on that memorable June day in 1788. It’s the physical proof of a gap in time, in this case the gap between the Silurian graywackes that formed 440 million years ago on the seafloor at the margins of the Iapetus Ocean (ancient ocean of the Southern Hemisphere) and were forced upward as the vast water body closed, and the Devonian Old Red Sandstone that was laid down on their eroded surface sixty-five million years later by rivers flowing into what was then most likely a tropical floodplain.

Thus modern geology was born. Hutton found in Siccar Point layered sandstone pierced by gray metamorphic rock that would confirm his belief that the Earth was far older than European natural scientists had ever expected. Playfair would later write: “The mind seemed to grow giddy by looking so far back into the abyss of time; and whilst we listened with earnestness and admiration to the philosopher who was now unfolding to us the order and series of these wonderful events.”

There should be a word that signifies the mind all but buckling with the wild surmise of the scale of things. In the late 18th Century, a notion of the ‘sublime’ began to re-emerge in European thought, one suggested by the grandeur of jagged alpine landscapes, for example, but today’s usage of the word doesn’t take in the aspect of dislocation, even disorientation, that such landscapes were freighted with back then, mingling with profundity. Go back to that earlier usage, though, and I’ll maybe opt for ‘sublime’ as the right word to suggest my own response to such imagery.

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{ 39 comments… add one }
  • charlie October 8, 2020, 15:50

    Small thought here – these most distant galaxies are supposed to be something like 13.4 billion ly away. Is that simply because that’s the furthest we can see or is there some kind of physical law which when you run it through the computer says that’s how far stars could have been blown out from the Big Bang? Because the space is actually infinite and probably the number stars is actually infinite.

    • Ronald October 9, 2020, 12:33

      IMHO, the former: 13.7 billion * the expansion factor (just over 3) gives about 46 billion ly as the distance from where the light has been able to reach us since the BB.
      Somewhat like the light circle around us in a dark forest at night, when we shine a torch light around us. We can see trees around us everywhere we look, up to the edge of the circle, but not beyond. The entire forest may be vastly bigger…

      • charlie October 9, 2020, 16:32

        wonder if BB >> 46 billion yr ??

        • Ron S. October 9, 2020, 21:46

          No. Perhaps this cosmology calculator will help you (there are others with different features). However you may need to learn more about the meaning of “distance” in a universe with spacetime curvature to understand it properly.

          http://astro.ucla.edu/~wright/ACC.html

          • megis October 17, 2020, 14:18

            The link comes up as “Forbidden” ie. access denied.

            • Ron S. October 18, 2020, 9:25

              That’s odd. I have no idea what happened to it since I wrote my comment. Ned Wright’s web site has long been a valuable resource. Hopefully this is a temporary problem. But there are other cosmology calculators scattered around the internet.

  • Jens Fridthjof Knudsen October 8, 2020, 17:09

    Wow.

  • Robin Datta October 8, 2020, 18:10

    A listing and discussion of Large Numbers.
    From the Cool Worlds series: A Journey to the End of the Universe
    Liwing human memory can extend back about a hundred years.

    • Paul Gilster October 8, 2020, 19:27

      Hadn’t seen that one, Robin. Thanks. I love David Kipping’s stuff.

  • Wojciech Jacyk October 8, 2020, 19:43

    “Does anyone ever get jaded with the sheer numbers we talk about as we delve into the cosmos?”
    Jaded? Never. Awestruck? Always.

  • Wojciech Jacyk October 8, 2020, 19:51

    By the way, I stumbled on this video recently, which I recommend for a cold and dark autumn evening. A visual and musical feast about possibilities of alien life:
    LIFE BEYOND II: The Museum of Alien Life (4K)
    https://www.youtube.com/watch?v=ThDYazipjSI

  • Henry Cordova October 8, 2020, 20:27

    It works both ways. Using even a child’s microscope, look into a spoonfull of soil, or a drop of pond water. Consider Leeuwenhoek’s animalcules, those single celled specks of protoplasm, each a tiny biochemical factory more complex than our most mighty oil refinery.

    Remember the old radium dial alarm clocks? We inherited one from grandma, and the numbers used to glow with an unearthly green light, quite beautiful, but quite deadly. The clocks were banned not because they were dangerous to the consumer, but because they were poisoning the people who manufactured them. The radium was mixed up with a phosphorescent paint, and the workers (usually women) who painted the numbers on the dials would often soften the tips of their brushes by moistening them in their mouths. The result was horrible mouth and jaw cancers caused by the cumulative effect of radiation from the radium paint . Today, phosphorus appliances (like my Vion “Hocky Puck” hand bearing compass) glow by energizing the phosphor by briefly shining a flashlight on it. One flash is good for an hour or two of dim illumination of the compass card.

    But there was a time when radium phosphor dials were ubiquitous. Every family had one. Ionizing radiation from the radium (which is invisible) penetrated into the phosphorus of the paint it was mixed with and excited the latter, causing electrons in the outer shells of the phosphorus atoms to jump in and out of their orbits and emit a tiny flash of beautiful green light. The nuclear energy locked in the radium nuclei is enormous, even the light from a single atom could be seen by the human eye, if the eye was dark-adapted and if a strong magnifying glass was used. The flashes of millions of atoms, each corresponding to one disintegrating radium nucleus, combined to make the bright green glow that made it easy to see the numbers and hands on the clock face.

    Radium has a half-life of 1600 years. This means that the radium nucleus is inherently unstable, and has a tendency to blow itself apart, scattering radiation (high energy particles and waves) into its environment. We can’t tell ahead of time which atom will disintegrate or when, but we know that if we have a pile of radium atoms (size of the pile doesn’t matter) exactly half of them will disintegrate in 1600 years. Since these clocks were manufactured during the twentieth century, we know they will continue to glow beautifully for a long, long time. After centuries, the paint will still glow, only slightly diminished in brightness. And it will glow even if the clock is in a box in your attic, buried in some landfill, or lying deep at the bottom of the sea. The phosphorus doesn’t get used up in this reaction; the excited electron pops back into its orbit, emitting the energy it absorbed from the radiation as a single photon, and it is ready to be excited again. And atoms are very, very small. Each brush stroke of paint on each glowing number on the clock dial contains billions and billions of them.

    Do you have any idea how small an atom is? Or how many of them can be gathered up into a tiny speck barely visible to the human eye? Its like the distances and times and sizes we study in astronomy. We can write down the numbers, long strings of zeroes, but we can’t really grasp the
    enormity (or minuteness!) of it all. But I can. I have stared into the eye of the beast myself.

    I knew about this phenomenon, and I took my grandma’s clock into a dark closet and waited about 20 minutes until my eyes were fully dark-adapted. I brought a jeweler’s loupe with me, a small lens used to work with gem stones (about 10X magnification). Its hard to focus properly in complete darkness, but after a few moments of studying the green glow, my eye and lens right up to it, I saw it. Floating in the darkness in front of me I could see it, and if I focussed intently on it I could see it was made up of millions upon millions of continuous tiny flashes of light. It was a lot like listening to a rain storm on a tin roof–you hear a continuous roar, but you can still tell it is made up of a multitude of individual drops. The light I saw was a quivering mass of tiny overlapping flashes, each barely visible, each one blinking momentarily like a strobe, but they were millions. And I understood they went on and on, never stopping, whether I was there to watch them or not. And every single flash I could see in that roiling beehive of tiny detonations was one radium atomic nucleus shattering, imparting its locked up energy to the phosphorus atoms surrounding it. I was looking into the very heart of physical reality, the central core of matter. I was perceiving the universe one atom at a time, from the inside.

    I’ve only had that feeling, that total and complete understanding of how I fit into the universe three times in my life. In grandma’s closet, on a small boat in a gale at sea, and standing under a clear dark starry sky.

    • Robin Datta October 8, 2020, 21:38

      Way back in microbiology lab (1967) while doing Gram’s stains, I stained a speck of plaque scraped from a tooth and looked at it under the microscope. What a menagerie! (Actually not a menagerie, as they are in their natural environment, not in captivity.)

  • Michelangelo Pantaleoni October 8, 2020, 21:00

    1) We certainly don’t know if the universe is infinite. It might perfectly be finite in size and still all current observational data would fit well un that model.

    2) Even if the universe were infinite in terms of space, It is not like that for time. We have a lot of evidence that shows the universe (and time) started some billions of years ago. There’s a boundary in time. There might be more galaxies farther away, but we can’t see them, because time is not as old as to allow their light to reach us yet. We don’t see further in space because time has a lower bound.

    3) The most distant galaxies we see are not 13 billion ly away. That is a common missconception. Since the universe has expanded a lot during those billions of years the light from those galaxies has been traveling, the galaxies we see are now in fact much more farther away. Probably more than 45 billion light years away.

    • Mike Serfas October 9, 2020, 7:50

      Remember that “now” is a very tricky thing in relativity. For objects so far apart, what is simultaneous can change by many years with just a slight change in the velocity of the person counting the years – because if you had stood between the two objects and waited for the light to reach you when you had that other velocity, you would have waited a very long time and ended up in a very different place.

      From the point of view of the light that travels to us from those galaxies, no time at all has passed from when it was emitted until when it was absorbed – nor, of course, did it move.

      • Robin Datta October 10, 2020, 3:43

        How about this for a thought experiment. An observer exactly midway between two persons several light-minutes apart with light sources that they flash at each other (past the observer), upon a bi-directional signal from the observer. To each light source their flash is simultaneous with the observer’s signal, and well before the opposite party’s flash. To the observer, both flashes are simultaneous, and well after the signal.

  • Joe H. October 8, 2020, 21:46
  • DCM October 9, 2020, 4:51

    Don’t let it discourage you or become apathetic.

  • Alex Tolley October 9, 2020, 12:21

    Does anyone ever get jaded with the sheer numbers we talk about as we delve into the cosmos?

    Perhaps it is more like: the sight of a few galaxies is awesome, billions are a statistic.

    Even the famous “Powers of Ten” movie doesn’t convey the real sense of scale that we sense when traveling through a landscape. I recall watching an IMAX journey into space that starts at Earth, passes through the stars until the viewpoint exits our galaxy, and then continues onwards as our galaxy is lost to view. It wasn’t until the moment that the view of our galaxy was lost that I had a visceral sense of being lost, unable to ever find a way back to Earth. I suppose that this indicates how naively comfortable I feel when it seems possible that Earth can still be located as long as our Milky Way galaxy is locatable, but after that, the map to return is broken.

    • Michael October 9, 2020, 16:06

      We are in fact cosmic microbes with a strange misplaced sense of importance.

      • Henry Cordova October 9, 2020, 22:22

        And yet, we “cosmic microbes” (or perhaps other microbes not too dissimilar to us) may very well be the most complex and significant structures/events in this entire universe. Beyond time and space exists a third domain, that of complexity. And as far as we know, we (or perhaps some other species) are the highest level of complexity known to exist in the entire cosmos, throughout both all space and time.

        A subset of the 100-odd elements of the periodic table can combine, in aqueous solution under moderate temperature conditions, to form structures of phenomenal complexity, which can in turn grow, and evolve into webs of relationships of even more complexity. And all this occurs at a point midway in the temporal and spatial extremes. We are bigger than atoms but smaller than galaxies, and we evolve at spbut much more complex than either.

        • Henry Cordova October 10, 2020, 10:51

          …apologies…my remarks above were uploaded before they were completed. Here is the rest…

          We are midway in size, and in the speed at which we function and evolve, so in both time and space we are about midway in the range of possibilities. Granted, we are still very ignorant about the universe we inhabit, but as far as we know, we are the most complex entities in the universe, a distinction we may share with, at best, only a handful of other species.

          So we may indeed be special, unique, fundamentally different than either the quantum foam or the realm of the nebulae. Lets not be too humbled by either Deep Time or Infinite Space. In one domain at least, the universe of complexity, he dimension of possibilities, we may still matter.

          I say this not from a position of pride or arrogance or human chauvinism; but with the realization that with this distinction must also come a great responsibility.

          • Mike Serfas October 10, 2020, 16:49

            Indeed, according to the strong anthropic principle, this entire universe exists the way it does – perhaps selected out from countless other universes with different rules of physics – solely so that *we* would be there to perceive it. It is our consciousness that has made the rules and indeed all those galaxies what they are.

            A similar principle may follow in the classic Copenhagen interpretation of quantum physics. Before some”observer” was present to say where those galaxies were, did they (and indeed the Milky Way) exist in a seemingly featureless superposition of states, countless possibilities all piled on top of each other? Did we emerge from this like the one correct solution from a quantum computer?

            • Hamilton1 October 12, 2020, 17:14

              Yes, and John Barrow died recently. I was hoping Paul might have an article to mark that event, and to discuss the anthropic principle generally. Whatever we think about Mr Barrow’s theory, he was a very, very eloquent man.

              • Paul Gilster October 12, 2020, 20:34

                I do plan to write about Barrow in the not distant future.

                • Hamilton1 October 13, 2020, 18:48

                  Thank you Paul.

          • Jer October 17, 2020, 13:30

            I like these ideas, but I struggle to use ‘complexity’ as a further axis (domain) of the universe as it seems too much to mean ‘density x variety’ within a discrete entity (tightly packed and filled with every possible thing), without addressing coherence or ability/action. For example, a grandfather clock may be smashed into its many, many component parts and put into a smaller bag than its original volume; which could be argued would be of a greater complexity – but now it would no longer function. The original clock would have had a greater coherence of parts (they would provide a use greater than the sum of its parts) and that would provide a use or action. So, the entity would need to work as something and provide a large range of abilities. I would hasten to add that I doubt that a biological entity is or could be the most complex-coherent-able entity in the universe, as it is so restricted to where it could function and in how it can interact with and/or affect the universe. I envision the most advanced complex-coherent-able entity to be a dense mechatronic-energy mechanism able to sense its surroundings in a huge number of ways (near and far); ponder, analyze, and adapt to the readings; travel in time/space near physical limits; and affect large areas in profound ways — say something like an Iain Bank’s Culture Ship with the ability to make a wormhole or such. The point is: that along with Universe’s spatial immensity (and temporal span of its existence) could be an increased potential/ opportunity to spawn such a complex-coherent-able system. Would the resources needed to create such a thing or a fleet or supercluster of them then lead us along a path of increased/ accelerated entropy; closer to Universe Cold Death? Which of course brings the topic of immensity back to discussions of boundaries and terminations and limits.

      • DCM October 10, 2020, 11:40

        Verging on self-hate and apathy.
        Who, in fact, constantly needs reminding we aren’t gods?
        The horizon is forever retreating, from the patch of jungle hominids wandered, to the village 10 miles away, to the next valley or island…
        Anyone feel better if we struck a physical wall somewhere?

        • Michael October 11, 2020, 9:25

          I agree we are the next best thing since the Universe erupted into all that there is.

          • DCM October 12, 2020, 3:58

            Just realize we can’t know everything.
            We’re not physically capable of it and neither are any such inventions as AI.
            Then, keep on with what we’re doing…..

  • Michael October 9, 2020, 14:18

    In the immortal words of Douglas Adams,

    Space is big. Really big. You just won’t believe how vastly hugely mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist, but that’s just peanuts to space.

    Douglas Adams

    In the immense span of time to unfold before us these words may be equaled BUT never surpassed !

  • safely anonymous October 9, 2020, 21:44

    A pretty interesting thought someone told me on reddit the other day was that given the scale of the universe and that we haven’t begun to view very far-away regions in much detail, if you were spending a certain amount of cash on SETI then there’s a strong case for viewing star systems and looking for signals outside our galaxy or even at cosmological distances. You might notice a Dyson sphere in this galaxy but get far enough away and who knows?

  • Michael Spencer October 10, 2020, 10:09

    Wouldn’t some sort of sensor overlap eliminate the image’s dark radials in Paul’s image above? No doubt they are tolerated for an important reason, but what would that be?

    • Ron S. October 11, 2020, 11:26

      Certainly overlap would eliminate those gaps but you have to consider why they made that choice in the instrument design and the observation pattern. Although I don’t know their reasoning it is easy enough to make a good guess.

      The purpose of the instrument is not to produce pretty pictures for publication. There are constraints of the image size and shape due to the mission objectives and the available technology that may be compatible with a perfectly fitting set of images because the sky is spherical and each image is a fixed geometric shape.

      Overlap would reduce the area being studied. So they design for best coverage of the study area under a set of necessary constraints. It’s a tiling problem where the optimum solution is not perfect alignment of the tile boundaries.

  • Michael Fidler October 11, 2020, 5:06

    OCTOBER 8, 2020
    Carbon creation finding set to rock astrophysics
    by Australian National University.

    To measure the first transition, Kibédi and his team at ANU’s Heavy Ion Accelerator Facility (HIAF) fired a proton beam at an extremely thin sheet of carbon to form Hoyle state nuclei. A tiny fraction of the excited nuclei transition back to stable carbon by emitting an electron-positron pair, which the team detected with the HIAF’s SUPER-E pair spectrometer.

    At the same time, Kibédi and his team worked with researchers at the University of Oslo’s Cyclotron Laboratory to measure the second transition, in which the Hoyle state emits a photon. They observed six billion Hoyle state reactions, of which just 200 decayed via the photon decay.

    Combining the ANU and Oslo results, the team calculated the carbon production rate, its first major update in 40 years. They found it was more than a third larger than previously thought, an enormous change for such a critical astrophysical quantity.

    “It was really unexpected,” said Kibédi. “Nobody had looked at this particular measurement since 1976. Everyone assumed it was well known.”

    According to Dr. Meridith Joyce from ANU’s Research School of Astronomy and Astrophysics, such a large shift would be a major event for stellar astrophysicists.

    “An increase in the carbon production rate like this would have a big impact on a lot of our models,” Joyce said.

    “It would affect our understanding of how stars change over time, how they produce elements heavier than carbon, how we measure the age of stars and how long they will last, how often we expect to see supernova explosions, even whether they leave behind neutron stars or black holes.”

    https://phys.org/news/2020-10-carbon-creation-astrophysics.html

    We still have a lot to learn…

    • Mike Serfas October 13, 2020, 11:53

      Do we know for sure the measurement was done wrong in 1976? What if the rate actually can change? I doubt we can link it with solar flares, but it’s funny to contemplate. :)

  • ljk October 20, 2020, 12:43

    THESE MATHEMATICIANS THINK THE UNIVERSE MAY BE CONSCIOUS

    APRIL 29TH 2020

    DAN ROBITZSKI__FILED UNDER: HARD SCIENCE

    Theory Of Everything

    Scientists are doubling down on a peculiar model that attempts to quantify and measure consciousness.

    The model, known as Integrated Information Theory (IIT), has long been controversial because it comes with an unusual quirk. When applied to non-living things like machines, subatomic particles, and even the universe, it claims that they too experience consciousness, New Scientist reports.

    “This could be the beginning of a scientific revolution,” Munich Centre for Mathematical Philosophy mathematician Johannes Kleiner told the magazine.

    Full article here:

    https://futurism.com/the-byte/mathematicians-think-universe-conscious

    The paper on IIT is here:

    https://arxiv.org/pdf/2002.07655.pdf

    To quote:

    “I think mathematics can help us understand the neural basis of consciousness in the brain, and perhaps even machine consciousness, but it will inevitably leave something out: the felt inner quality of experience,” University of Connecticut philosopher and cognitive scientist Susan Schneider told New Scientist.

    The key is multidisciplinary cooperation in confronting our understanding of the Cosmos.

  • ljk October 20, 2020, 12:58

    An Infinite Universe of Number Systems

    The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.

    https://www.quantamagazine.org/how-the-towering-p-adic-numbers-work-20201019/

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