Sean Carroll
Sean Carroll
  • 479
  • 20 791 563
Mindscape 274 | Gizem Gumuskaya on Building Robots from Human Cells
Patreon: www.patreon.com/seanmcarroll
Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/04/29/274-gizem-gumuskaya-on-building-robots-from-human-cells/
Modern biology is advancing by leaps and bounds, not only in understanding how organisms work, but in learning how to modify them in interesting ways. One exciting frontier is the study of tiny "robots" created from living molecules and cells, rather than metal and plastic. Gizem Gumuskaya, who works with previous guest Michael Levin, has created anthrobots, a new kind of structure made from living human cells. We talk about how that works, what they can do, and what future developments might bring.
Gimez Gumuskaya received her Ph.D. from Tufts University and the Harvard Wyss Institute for Biologically-Inspired Engineering. She is currently a postdoctoral researcher at Tufts University. She previously received a dual master's degree in Architecture and Synthetic Biology from MIT.
Mindscape Podcast playlist: ua-cam.com/play/PLrxfgDEc2NxY_fRExpDXr87tzRbPCaA5x.html
Sean Carroll channel: ua-cam.com/users/seancarroll
#podcast #ideas #science #philosophy #culture
Переглядів: 5 573

Відео

Mindscape 273 | Stefanos Geroulanos on the Invention of Prehistory
Переглядів 11 тис.День тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/04/22/273-stefanos-geroulanos-on-the-invention-of-prehistory/ Humanity itself might be the hardest thing for scientists to study fairly and accurately. Not only do we come to the subject with certain inevitable preconceptions, but it's hard to resist the tempt...
Mindscape 272 | Leslie Valiant on Learning and Educability in Computers and People
Переглядів 6 тис.14 днів тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/04/15/272-leslie-valiant-on-learning-and-educability-in-computers-and-people/ Science is enabled by the fact that the natural world exhibits predictability and regularity, at least to some extent. Scientists collect data about what happens in the world, then t...
Mindscape Ask Me Anything, Sean Carroll | April 2024
Переглядів 34 тис.21 день тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/04/08/ama-april-2024/ Welcome to the April 2024 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Patreons, whittle them down to a more manag...
Mindscape 271 | Claudia de Rham on Modifying General Relativity
Переглядів 21 тис.Місяць тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/04/01/271-claudia-de-rham-on-modifying-general-relativity/ Einstein's theory of general relativity has been our best understanding of gravity for over a century, withstanding a variety of experimental challenges of ever-increasing precision. But we have to be ...
Mindscape 270 | Solo: The Coming Transition in How Humanity Lives
Переглядів 26 тис.Місяць тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/03/25/270-solo-the-coming-transition-in-how-humanity-lives/ Technology is changing the world, in good and bad ways. Artificial intelligence, internet connectivity, biological engineering, and climate change are dramatically altering the parameters of human lif...
Mindscape 269 | Sahar Heydari Fard on Complexity, Justice, and Social Dynamics
Переглядів 6 тис.Місяць тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/03/18/269-sahar-heydari-fard-on-complexity-justice-and-social-dynamics/ When it comes to social change, two questions immediately present themselves: What kind of change do we want to see happen? And, how do we bring it about? These questions are distinct but ...
Mindscape Ask Me Anything, Sean Carroll | March 2024
Переглядів 54 тис.Місяць тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: Welcome to the March 2024 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Patreons, whittle them down to a more manageable number based primarily on whether I have anything interest...
Mindscape 268 | Matt Strassler on Relativity, Fields, and the Language of Reality
Переглядів 27 тис.2 місяці тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/03/04/267-matt-strassler-on-relativity-fields-and-the-language-of-reality/ In the 1860s, James Clerk Maxwell argued that light was a wave of electric and magnetic fields. But it took over four decades for physicists to put together the theory of special relati...
Mindscape 267 | Benjamin Breen on Margaret Mead, Psychedelics, and Utopia
Переглядів 7 тис.2 місяці тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: The twentieth century was something, wasn't it? Margaret Mead, as well as her onetime-husband Gregory Bateson, managed to play roles in several of its key developments: social anthropology and its impact on sex & gender mores, psychedelic drugs and their potential use for therapeutic purposes, and the...
Mindscape 266 | Christoph Adami on How Information Makes Sense of Biology
Переглядів 12 тис.2 місяці тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/02/19/266-christoph-adami-on-how-information-makes-sense-of-biology/ Evolution is sometimes described not precisely, but with some justification as being about the "survival of the fittest." But that idea doesn't work unless there is some way for one generatio...
Mindscape Ask Me Anything, Sean Carroll | February 2024
Переглядів 63 тис.2 місяці тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/02/12/ama-february-2024/ Welcome to the February 2024 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Patreons, whittle them down to a more...
Mindscape 265 | John Skrentny on How the Economy Mistreats STEM Workers
Переглядів 7 тис.2 місяці тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/02/05/265-john-skrentny-on-how-the-economy-mistreats-stem-workers/ Universities and their students are constantly being encouraged to produce more graduates majoring in STEM fields science, technology, engineering, and mathematics. That's the kind of training ...
Mindscape 264 | Sabine Stanley on What's Inside Planets
Переглядів 12 тис.3 місяці тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/01/29/264-sabine-stanley-on-whats-inside-planets/ The radius of the Earth is over 6,000 kilometers, but the deepest we've ever dug below the surface is only about 12 km. Yet we have a quite reliable idea of the structure of the Earth's interior inner core, out...
Mindscape 263 | Chris Quigg on Symmetry and the Birth of the Standard Model
Переглядів 18 тис.3 місяці тому
Patreon: www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/podcast/2024/01/22/263-chris-quigg-on-symmetry-and-the-birth-of-the-standard-model/ Einstein's theory of general relativity is distinguished by its singular simplicity and beauty. The Standard Model of Particle Physics, by contrast, is a bit of a mess. So many particles an...
Mindscape 262 | Eric Schwitzgebel on the Weirdness of the World
Переглядів 15 тис.3 місяці тому
Mindscape 262 | Eric Schwitzgebel on the Weirdness of the World
Mindscape 261 | Sanjana Curtis on the Origins of the Elements
Переглядів 16 тис.3 місяці тому
Mindscape 261 | Sanjana Curtis on the Origins of the Elements
Mindscape 260 | Ricard Solé on the Space of Cognitions
Переглядів 12 тис.4 місяці тому
Mindscape 260 | Ricard Solé on the Space of Cognitions
Mindscape Holiday Message 2023 | Reflections on Immortality
Переглядів 13 тис.4 місяці тому
Mindscape Holiday Message 2023 | Reflections on Immortality
Mindscape 259 | Adam Frank on What Aliens Might Be Like
Переглядів 24 тис.4 місяці тому
Mindscape 259 | Adam Frank on What Aliens Might Be Like
Mindscape Ask Me Anything, Sean Carroll | December 2023
Переглядів 60 тис.5 місяців тому
Mindscape Ask Me Anything, Sean Carroll | December 2023
Mindscape 258 | Solo: AI Thinks Different
Переглядів 51 тис.5 місяців тому
Mindscape 258 | Solo: AI Thinks Different
Mindscape 257 | Derek Guy on the Theory and Practice of Dressing Well
Переглядів 9 тис.5 місяців тому
Mindscape 257 | Derek Guy on the Theory and Practice of Dressing Well
Mindscape 256 | Kelly & Zach Weinersmith on Building Cities on the Moon and Mars
Переглядів 9 тис.5 місяців тому
Mindscape 256 | Kelly & Zach Weinersmith on Building Cities on the Moon and Mars
Mindscape Ask Me Anything, Sean Carroll | November 2023
Переглядів 33 тис.5 місяців тому
Mindscape Ask Me Anything, Sean Carroll | November 2023
Mindscape 255 | Michael Muthukrishna on Developing a Theory of Everyone
Переглядів 9 тис.6 місяців тому
Mindscape 255 | Michael Muthukrishna on Developing a Theory of Everyone
Mindscape 254 | William Egginton on Kant, Heisenberg, and Borges
Переглядів 13 тис.6 місяців тому
Mindscape 254 | William Egginton on Kant, Heisenberg, and Borges
Mindscape 253 | David Deutsch on Science, Complexity, and Explanation
Переглядів 48 тис.6 місяців тому
Mindscape 253 | David Deutsch on Science, Complexity, and Explanation
Mindscape Ask Me Anything, Sean Carroll | October 2023
Переглядів 44 тис.6 місяців тому
Mindscape Ask Me Anything, Sean Carroll | October 2023
Mindscape 252 | Hannah Ritchie on Keeping Hope for the Planet Alive
Переглядів 7 тис.7 місяців тому
Mindscape 252 | Hannah Ritchie on Keeping Hope for the Planet Alive

КОМЕНТАРІ

  • @user-vadimsirbu
    @user-vadimsirbu 7 хвилин тому

    ..!. Senators bounce your balls in here ...

  • @RamblinJer
    @RamblinJer Годину тому

    That's quite a bit of information on dark energy considering we don't know if it exists. We should be addressing the many problems and contradictions within Big Bang Cosmology and resolving those before speculating.

  • @newrev9er
    @newrev9er 5 годин тому

    This is incredible! Dr. Gumuskaya is wonderfully articulate.

  • @johnbruss5190
    @johnbruss5190 12 годин тому

    Your historic media exposure was often very provocative and singularly (deliberately?) opinionated and now you are taking more of a "host" role in your podcast. So for me, it was/is hard to transition from the "old you" to this "new you". I liken this to political primaries where the candidates go way left or way right (trying to gain attention and a core group of supporters, no doubt) but in the final election, many of the candidates rush to the center and are far less controversial (alarmist) since they want to be seen as "more understanding and uniting" regarding everyone's preferences/priorities. So I sensed this too, about the old Sean and this new Sean. 🤔

  • @sirmrdresqmd9200
    @sirmrdresqmd9200 16 годин тому

    Damn man like every other episode you're pushing your atheist agenda. I love the science but you seriously need to back off the whole religious talk.

  • @ddeibler1826
    @ddeibler1826 День тому

    This is beautiful. Im but a lowly wannabe scientist. My hero was Thomas Edison. I checked out books from my school library about him and others. Thats all I wanted to be. Now I watch this and follow your podcast and i am amazed. You became the scientist I always wanted to be, Thank you so much for sharing this with we mere mortals!!!!

  • @NalitaQubit
    @NalitaQubit День тому

    Dr. Carrol, thank you for a great lecture. Cat and Physics, my 2 highlights of the day.

  • @Ersin_Dogan
    @Ersin_Dogan День тому

    Wow, that was intense. If it were shown in a movie, I wouldn't watch it, because I would think it is completely unrealistic. But now I fear everything is possible. Puh 😮.

  • @GRUMIAM
    @GRUMIAM День тому

    Sean the greatest

  • @1badjesus401
    @1badjesus401 2 дні тому

    Is there a list of questions asked you can post Sean?

  • @user-gj7vp6wk3e
    @user-gj7vp6wk3e 2 дні тому

    SHAME ON KATIE MACK; SHE MIGHT BE A THEIST. BUT, ANYWAY, I HOPE THE COVID DOES NOT GET ME, JASON, OR YOU, SEAN.✌🏼✌🏼 THEISM IS NOT WELL DIFINED, AND GOD AND IMMORTALITY IS NOT A GOOD THEORY. BUT, ANYWAY, THANK YOU FOR TEACHING EVERYONE ASTRONOMY AND PARTICLE PHYSICS AND CLASSICAL PHYSICS. THANK YOU, PROFFESSOR SEAN CAROL.

  • @posthocprior
    @posthocprior 2 дні тому

    I work in the field, robotics. This was close to impossible for me to understand. This researcher is unable to use terms that most would understand (from outside of the field) and there are many run on sentences in which there were so many cell robotic words I’ve never heard ( can provide a long list, if anyone asks), I got lost in the complexity. Finally, she’s so verbose, it took her a long time to answer even a simple question.

    • @trevorcrowley5748
      @trevorcrowley5748 4 години тому

      I think this is intentional. Human cells coaxed into directed behaviour that can cross the blood-brain barrier --- what could possibly go wrong? Excellent funding prospects if things go right...

  • @filippoalemagna1528
    @filippoalemagna1528 2 дні тому

    I didn't get what's the function of the biological circuits as these spheroids aren't programmed to do anything, so what's the role of these circuits?

  • @codecatscuddlescreativity
    @codecatscuddlescreativity 2 дні тому

    Is it just me, or is the audio of this solo episode of lower quality than previous ones? With more echo? And a different mic? Or is it just me.

  • @tlog181
    @tlog181 2 дні тому

    The Bob Ross of science

  • @ARNFL13
    @ARNFL13 3 дні тому

    Still waiting for that episode with Lady Gaga

  • @user-tf1cn9ve5n
    @user-tf1cn9ve5n 3 дні тому

    Imagine house build of cells. Wow.

  • @person0542
    @person0542 3 дні тому

    the fact that there are negative implications to not believing in free will is not a good reason to believe in free will

  • @michaelerdmann4447
    @michaelerdmann4447 3 дні тому

    Natural Harmonies and Hierarchies self-construction and regeneration ...AnoBioNanoXeno....Bots (not robot not organism) ...sensing, sending, healing, curing.... valued synthetic morphogenesis _________ UniPhotoElectroChemistry and BioCytoNeuroPsychiatry _______ Artificially Engineered Intellects

  • @michaelerdmann4447
    @michaelerdmann4447 3 дні тому

    native messengerRNA and modifiedRNA vaccines

  • @Hecarim420
    @Hecarim420 3 дні тому

    Sane Sean Carroll 👀ツ

  • @gtziavelis
    @gtziavelis 3 дні тому

    I'm all in favor of improving quality of life and/or healing diseases with biotech, but inevitably tech falls into the wrong hands with nefarious intent. It's a package deal like that. You can have both, or you can have neither. We already have evolution, and I think that's the name of the game; it is the one natural intelligence. When we play god in our self-accelerated world, we can expect only bad results, like for example "organic" humans will driven to extinction, everyone remaining will be engineered by their contemporaries instead of by evolution, and the self-engineered will say "who cares? we're better!" and nature will say "certainly not I. goodbye!" Fermi paradox largely explained by that; other civilizations gleefully offed themselves before they could really reach out to the stars, and it seems we are poised to do the same. "Sculpted" and "nudged" with trusted tech tools, toward our own oblivion, and because this is probably on the order of centuries, a humanoid living ~80 years may not even notice that anything went wrong, especially as they become more A.I.-integrated. So, I'm noticing it now, while I can. Just copypasta me into the word salad remixing algorithm, that way there are two write-ups to choose from, instead of just one, and then we can have a "healthy debate" as to which is better, but as tantalizing as it is, of course it's a trick, because a stream of ones and zeroes cannot have a healthy debate with a co-evolved human with roots billions of years deep, so again it seems that successfully time traveling will be easier than successfully redesigning ourselves with tech such as in this podcast.

  • @ludviglidstrom6924
    @ludviglidstrom6924 4 дні тому

    Fantastic!

  • @BrianFedirko
    @BrianFedirko 4 дні тому

    Gravity waves are infinitely minute, so why can't we ascertain that the energy they fluctuate at the quantum level is what feeds the vibrations of the constituents of atoms? They travel through spacetime from every direction of the universe, so they must be transmitting energy. Energy at the tiniest levels we see actions of quarks etc. The electron may stay in oscillation around the atom being fed by gravitational waves. Gr8! Peace ☮💜Love

  • @mrich2164
    @mrich2164 4 дні тому

    when is Stephen Wolfram back on, best episode ever?

  • @twonumber22
    @twonumber22 4 дні тому

    enjoyed

  • @desgreene2243
    @desgreene2243 4 дні тому

    Yes I agree that biology will be very exciting for the near future especially with the added impetus of AI. Good times ahead!

  • @_7club_
    @_7club_ 4 дні тому

    Why does the UA-cam algorithm play this channel next after every flat earth video?

  • @zorro5651
    @zorro5651 5 днів тому

    A physicist who wants the government to play Robin Hood. First, large corporations are owned by middle class people who own shares. If you let politicians rob them, they will simply give the money to whomever is donating to their election campaigns and instead of leaving the $ with the efficient productive corporations, transfer it instead to losers. Just look at the war on poverty by lbj. More people are on welfare than ever before and the country can't create much of anything on its own. And there simply are not enough billionaires to bail us out - do the math. Second, the problem is crony capitalism, not free market capitalism. The biggest problems with science today are that government decides who gets the grants. I worked at NASA for 31 years and before I retired, we were told to make up anything about climate change to add to our proposals so we could get more $. And of course, you don't get the money unless you agree with their agenda, whatever that might be. And finally, look at the state of America today. In less than 1/2 a century we went from the most productive society in the world to the biggest dead beat debtor of all times. Then only thing we produce today is war and inflation. You can thank Robin Hood for the demise.

  • @JimmSlimm1
    @JimmSlimm1 5 днів тому

    Conways' game of life, but remastered and in 3D :)

  • @longlostkryptonian5797
    @longlostkryptonian5797 5 днів тому

    It’s astounding how much we know AND don’t know about these processes. A really captivating subject. Thanks so much for providing this type of content. It’s really appreciated!

  • @billybaab73
    @billybaab73 5 днів тому

    Brilliant!

  • @Confuseddave
    @Confuseddave 5 днів тому

    That last line about listening to Mindscape "in the hood" made me chuckle - I'm assuming she meant the tissue culture hood, rather than her proverbial neighbourhood

  • @HarryNicNicholas
    @HarryNicNicholas 5 днів тому

    all i can say is, crikey.

  • @Gws525
    @Gws525 5 днів тому

    Crazy that I can listen to this, enjoy it, and yet understand literally nothing in it.

  • @user-wl7zi6pc3j
    @user-wl7zi6pc3j 5 днів тому

    As bayraklari ! 🇹🇷

  • @Life_42
    @Life_42 5 днів тому

    Congratulations on 200k UA-cam subscribers!

    • @stephencolbertcheese7354
      @stephencolbertcheese7354 5 днів тому

      @ least there r 200,000 smart people left

    • @SG-kj2uy
      @SG-kj2uy 5 днів тому

      Congrats! If he gives lectures again, its very easy for him to reach 1 million🤔

  • @milkshakeplease4696
    @milkshakeplease4696 5 днів тому

    emergentism is circular and all theories in a materialistic worldview guided by blind laws are non-sequiturs as they all assume purpose and none of that follows from purposeless material and blind laws. atheism is a disease of the mind and heart. determinism destroys the possibility of justified true belief.

  • @sbassett5572
    @sbassett5572 6 днів тому

    I've spent 20 years in disaster zones.. 100% my mental clock speeds up in an emergency situation, but its not because I'm "falling" or my physical movement. Its the same if you're walking and spot a snake 1m ahead and you're stood still. You just "switch on". I'd say it's more a response to danger and an awareness we need full processing power than a physical reaction to a fall or similar though. We call it part of RPD, recognition primed decision making and it takes time in those extreme environments to develop (10 years typically) but then you can "think" "see" "analyse" etc everything much better and several times faster. Hope there's more done on this, its fascinating. Also there seems to have been an assumption that heart rate increases in these situations to get blood pumping and to extremities which would make sense but it appears (more weirdly) its actually to increase the likelihood our heart beats at the same moment as others, because this (weirdly) makes us much more cooperative, and this is the real key to surviving a sudden threat above how your muscles react.. Will my friends jump to my aid. It was taught to us for the job so I don't know enough but alot of interesting points in this area.

  • @ludviglidstrom6924
    @ludviglidstrom6924 6 днів тому

    Just to point out one thing about the Indo-European languages: their common ancestor Proto-Indo-European was spoken maybe 6000 years ago, so it’s very far removed from any hypothetical first language. There is no reason at all to believe that PIE is closer to the first language than any random language spoken today. The study of Indo-European languages is very much a real science, so it’s unfortunate that it has become so ideologically charged for historical reasons.

  • @ludviglidstrom6924
    @ludviglidstrom6924 6 днів тому

    This might be the reason why I often don’t really like to watch science documentaries about the origin of humanity: they seem to have too much of an agenda. That’s why I tend to prefer documentaries about physics or cosmology and so on; they seem to be more objective.

  • @CharlesPayet
    @CharlesPayet 6 днів тому

    7:08 sounds a little like psychohistory. 😀

  • @cloudysunset2102
    @cloudysunset2102 6 днів тому

    I understood exactly 6 and 1/2 words of this but I loved hearing it and imagining the concepts and processes that led to the discoveries. Ain't us humans grand?

  • @Ph0_Q
    @Ph0_Q 7 днів тому

    "Its gonna be May" - Justin Timberlake

  • @Animatthias
    @Animatthias 7 днів тому

    Dear Sean, if the curvature of spacetime is affected by large masses and masses are determined by the interaction of particles with the Higgs field, wouldn't it make sense to assume that dark matter is a distortion in the Higgs field. I've heard that it's supposed to be isotrope, but maybe we are wrong about that? It would be great, if you could help me understand more about that! Thank you for your great content!

  • @sd-ti4yv
    @sd-ti4yv 7 днів тому

    Why do they say that the causality is not to be found in physics? The 2nd Newton law says p(t+dt) = p(t) + F(t) dt, which means the values of p and F at time t predict/cause the value of p at time t+dt. It seems all physics is based on causality.

  • @andywilliams8540
    @andywilliams8540 7 днів тому

    this guy is boring

    • @trevorcrowley5748
      @trevorcrowley5748 6 днів тому

      Well I was intrigued by the topic... and your comment. According to Prof Geroulanos' bio, he is "particularly interested in the ways that the concept of the human has been transformed in course of the last hundred years." Believe this means he would be interested in you as well. Take care.

  • @filipgren6091
    @filipgren6091 7 днів тому

    Whole new respect for You, good Sir. Listening to You was a great pleasure.

  • @sbassett5572
    @sbassett5572 8 днів тому

    I'm 4 years late for the Q&A.. Is it possible to do a Q&A video just for my questions to each video? I'll respond to those videos by email, we go back and forth, I still don't understand, you do another video, I post a question, you do a Q&A, I respond by email, we go back and forth, I still don't understand, you do another video........

  • @mrervinnemeth
    @mrervinnemeth 8 днів тому

    27:55 In plain linear algebra this is true, but geometric algebra (Clifford algebra) extends the idea of vectors with n-vectors. A bivector for example has an orientation and an area, just like a vector has orientation and length. And in 2 dimensions you get a basis bivector I = e₁⋀e₂, and this acts exactly like the imaginary i. It rotates vectors with π/2 in a geometric product. The algebra you get this way is homomorphic with complex numbers. And the beauty is that all these 2 dimensional bivectors are in fact antisymmetric grade-2 tensors.