A wire network that learns, wave-like dark matter, Mars's core & more science news from this week.

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  • čas přidán 17. 05. 2024
  • Try out my quantum mechanics course (and many others on math and science) on Brilliant using the link brilliant.org/sabine. You can get started for free, and the first 200 will get 20% off the annual premium subscription.
    Today we talk about wave-like dark matter, wires that learn, the core of planet mars, why quasars ignite, a superconducting highway, fabric that changes shape and colour, chemistry on a quantum computer, the Brazil nut effect, and of course, the telephone will ring.
    💌 Support us on Donatebox ➜ donorbox.org/swtg
    👉 Transcript and References on Patreon ➜ / sabine
    📩 Sign up for my weekly science newsletter. It's free! ➜ sabinehossenfelder.com/newsle...
    🔗 Join this channel to get access to perks ➜
    / @sabinehossenfelder
    🖼️ On instagram / sciencewtg
    00:00 Intro
    00:26 Wavelike Dark Matter
    04:11 Wires That Learn
    05:42 Mars Has a Liquid Core
    07:38 How Quasars Ignite
    09:28 A Superconducting Highway
    11:35 Fabric That Changes Shape and Color
    13:52 Chemistry on a Quantum Computer
    14:55 The Brazil Nut Effect Without Shaking
    16:37 Learn Science With Brilliant
    #science #sciencenews
  • Věda a technologie

Komentáře • 848

  • @unmoored7414
    @unmoored7414 Před rokem +340

    Finally, The News.

    • @seriousmaran9414
      @seriousmaran9414 Před rokem +6

      And the telephone rang, nearly everyone happy 😊

    • @ASBOmarc
      @ASBOmarc Před rokem +5

      You are not wrong, not only is it the news but it makes me happy not depressed

    • @InTrancedState
      @InTrancedState Před rokem +2

      The newsest news

    • @Ajibolaa
      @Ajibolaa Před rokem +1

      Only news I care about

    • @gppg1799
      @gppg1799 Před rokem +5

      This lady is the most unlikely youtuber, and it makes my day evertime I see her 😂❤❤😂

  • @sehichanders7020
    @sehichanders7020 Před rokem +365

    So... Dark Matter isn't just invisible, it also has random properties that change according to whatever effect you want to explain. I think this is an amazing discovery with an unlimited amount of applications. For example: next time I'm late for an appointment I can perfectly explain this with Dark Matter having a bad day.

    • @anarchisttechsupport6644
      @anarchisttechsupport6644 Před rokem +14

      I keep hearing rumors about Dark Matter being based on Newtonian physics applied at a Relativistic scale (measuring the mass of galaxies/the universe) where some Brazilian paper made it almost entirely disappear by using a Relativistic model.

    • @mitch_the_-itch
      @mitch_the_-itch Před rokem +1

      Invisible things can still interact with matter. How does Dark Matter interact with our Universe?

    • @KaiHenningsen
      @KaiHenningsen Před rokem +9

      @@anarchisttechsupport6644 I dunno, that description makes pretty close to zero sense to me. The way to measure mass distribution in a galaxy cluster is to figure out a model that replicates the effect of gravitational lensing through that cluster. That model is based on general relativity (gravitational lenses come from general relativity). I don't see where you'd use Newtonian physics there, nor what you'd want with relativistic effects.
      Maybe you mean the galaxy rotation thing? But again, it's unclear to me how relativistic effects would help in that context. General relativity is our current theory of gravity, and until you're looking at gravity strong enough to create frame dragging, I don't know of any gravity effects you could reasonably call relativistic.
      Maybe there's something I don't know, but I thought I understood at least the basics reasonably well.
      Now if you're talking about theories that try to explain this stuff with "modified gravity", all bets are off, because you're essentially inventing your own formulas at that stage, with - as far as I can tell - the only idea that it has to reproduce the galaxy rotation thing. I haven't heard if anyone managed to explain lensing effects through a cluster that way. Or maybe the idea is modified gravity for galaxies and dark matter for more irregular effects like those lensing effects? Sounds a bit arbitrary to me.

    • @daarom3472
      @daarom3472 Před rokem +2

      Aa the Architect said about Dark Matter:
      "Your life is the sum of a remainder of an unbalanced equation inherent to the programming of physics."

    • @scribebat
      @scribebat Před rokem +11

      @@mitch_the_-itch 'Dark Matter' is supposed to interact gravitationally with the universe but, as deGrasse Tyson pointed out, 'Dark Matter' should be called 'Dark Gravity', since a discrepancy in observed apparent gravitational force from what is predicted by present physics is thus far the only measurable evidence we have for the existence of any such thing as 'Dark Matter'. 'Dark Matter' got proposed as an explanation for that discrepancy. The data never lies but between the data and the interpretation falls the shadow.

  • @Moon_Metty
    @Moon_Metty Před rokem +5

    Gobbledygook must be a wave-like crinkle too, the Mexican wave is a good example.

  • @Ratamahata7
    @Ratamahata7 Před rokem +13

    I loved that quote "the future may be brighter than you think"

  • @28reinvent
    @28reinvent Před rokem +162

    "The future may be brighter than you thought." Sabine, you could have a second career as a standup comic. Only you can make physics that funny. Also love your skeptical nature and sensitive bullshit meter. You are definitely my favorite physicist of all time.

  • @KeithCooper-Albuquerque
    @KeithCooper-Albuquerque Před rokem +83

    Thanks Sabine for another funny and interesting look at science!

  • @bodotrenaud7441
    @bodotrenaud7441 Před rokem +15

    This is what the world needs, knowledge and humor.
    Thank you for your work❤

  • @LooseGripHandle
    @LooseGripHandle Před rokem +1

    Im a simple guy that barley understands much or retains much.
    But listening and watching all the information possible, relative to my interests. You my dear, have caught my attention enough to add you to my regular information binge
    Your comedic and thorough attitude towards the future is inspiring. 🤘👍

  • @jimbob1103
    @jimbob1103 Před rokem +6

    That highway sounds as legitimate as the old "solar freakin roadways".

    • @MetalheadAndNerd
      @MetalheadAndNerd Před rokem +1

      Or the hyperloop. That's why she immediately asked Elon.

  • @sarahenson9659
    @sarahenson9659 Před rokem +1

    Before watching the video, I mention to my mathematics and quantum mechanics loving 17 that a new paper suggests that dark matter acts like waves. His response? “Oh really? I’ve read a lot of papers on dark matter and they’ve all been wrong.” I roll my eyes and then watch Sabine. Guess he was right again.

  • @andrewpaulhart
    @andrewpaulhart Před rokem +3

    Superconducting highways needs to be nominated for the ignobel awards

  • @macemoneta
    @macemoneta Před rokem +1

    Back when my dad was still alive, I tried to explain what I did in Computer Science. He thought about it for a bit, and came up with: "computers are just a bunch of tiny wires". I wish he were alive to see this video.

  • @fredg.sanford634
    @fredg.sanford634 Před rokem +6

    I am so glad to have found your channel, Sabine. It has been a year of learning and laughter. Thank you for your excellence!

  • @roygalaasen
    @roygalaasen Před rokem +30

    The brazil nut effect - isn’t that the same effect that forces you clear the potato field for rocks, year after year? No matter how many rocks you clear, new ones pop up next year?

    • @andyf4292
      @andyf4292 Před rokem +1

      nah, thats the Elves, obviously

  • @Stadtpark90
    @Stadtpark90 Před rokem +3

    1:52 Dark Matter with Ketchup

  • @tostupidforname
    @tostupidforname Před rokem +20

    Ok so in my memory this is a pretty small 50k science channel. So when did you get to almost a million??? Congrats you deserve it but i genuinely did not notice this channel explode!

    • @baileescott401
      @baileescott401 Před rokem +3

      She reached 500K a year ago.

    • @tostupidforname
      @tostupidforname Před rokem +3

      @@baileescott401 yeah i think i subscribed in like 2021 or something and idk just didnt notice ig

    • @SabineHossenfelder
      @SabineHossenfelder  Před rokem +16

      yes I'm not sure what happened there

    • @Thomas-gk42
      @Thomas-gk42 Před rokem +9

      @@SabineHossenfelder perhaps a brand new music video for the millionth?

    • @DirkThys
      @DirkThys Před rokem +7

      @@SabineHossenfelder I know what happened: you're good, and you kept up your high standards and finally people started to notice

  • @nkdibai
    @nkdibai Před rokem +5

    11:30 "maybe Elon will be interested" *looks profoundly at the phone* had me LAUGHING 😂😂😂

    • @Thomas-gk42
      @Thomas-gk42 Před rokem +2

      Maybe he was just working on a sponsor contract with Sabine

  • @galaxy_brain
    @galaxy_brain Před rokem +8

    Starting to love these weekly updates as much as deep dives - on topic, educational, and sabiney (adj., being similar or related to Sabine)

  • @Treyast
    @Treyast Před rokem +3

    The superconductor highway is absolutely vacuous. You might as well replace the entire network with high speed rail at that point; I don't understand why they think making each car a mini maglev and retrofitting the entire highway system is more efficient than just expanding and upgrading the rail system. Completely bonkers.

  • @AlexanderPearson
    @AlexanderPearson Před rokem +3

    I continue enjoying your new format of science news weekly, please keep up the good work.

  • @HisCarlnessI
    @HisCarlnessI Před rokem +11

    The Brazil Nut effect, for me, was observed and understood as a child... in my Lego bin lol.

  • @MaryAnnNytowl
    @MaryAnnNytowl Před rokem +3

    I do so enjoy what you do, Sabine - thank you for your time!
    ❤❤

  • @MrWildbill
    @MrWildbill Před rokem +1

    That is brilliant how you just slide into the commercial at the end :)

  • @dactylntrochee
    @dactylntrochee Před rokem +1

    "The future may be brighter than you thought". Great one.

  • @kingjamez80
    @kingjamez80 Před rokem +1

    Wow. You do such a great job explaining esoteric papers. Shows a true knowledge of the science you talk about. Super valuable. Thank you.

  • @ricardochong6834
    @ricardochong6834 Před rokem +2

    The glass nano wire network and how they are using it reminds me exactly of the wizards' computer at the Unseen University at Ankh Morpork in Terry Pratchett's Disc World series. I'll lay odds that the scientists at play here can tell you where the counter-weight continent is, too.

  • @tooearly4616
    @tooearly4616 Před rokem +2

    Maglev highways will be the new fly paper for forest creatures

  • @sststr
    @sststr Před rokem +3

    I love that you don't just categorically accept that dark matter must exist. It may, it may not, we're still unsure, and you communicate that uncertainty where no other science communicator will. Such a relief that at least one person is allowing for the possibility that the theory could be wrong.

  • @wesleyschouw
    @wesleyschouw Před rokem +6

    Density driven gravity by Wesley Schouw

  • @TheRealStructurer
    @TheRealStructurer Před rokem +2

    Wow those metal wire 'neutrons' are fantastic. Thanks for sharing 👍🏼

  • @nonsuch9301
    @nonsuch9301 Před rokem +2

    I have to hope that superconducting highway paper was published on the 1st April.

  • @jeffgriffith9692
    @jeffgriffith9692 Před rokem +7

    I am ready for this weeks Science News!!

  • @dennistucker1153
    @dennistucker1153 Před rokem +24

    Love the humor and content. Thank you Sabine.

  • @ParameterGrenze
    @ParameterGrenze Před rokem +1

    I loved the chancellor call bit. You could do a “isn’t chancellor the bad guy from Star Wars” bit…

  • @raymitchell9736
    @raymitchell9736 Před rokem +1

    "Spacetime crinkles" sound like a breakfast cereal for astrophysicists, you just need a big enough bowl and pour just a portion of the milky-way. But the French fries with catsup joke was better than mine.

  • @MCsCreations
    @MCsCreations Před rokem +2

    Oh... Super fast cars that the drivers can't steer? Brilliant!
    Thanks, Sabine! 😊
    Stay safe there with your family! 🖖😊

  • @kevinsayes
    @kevinsayes Před rokem +21

    Re: the nanowire network, I think it’s fascinating how complex systems naturally (so it seems) form this type of structure, such as the brain’s neural network, galaxy filaments, tree root systems, and so on. It’s a seemingly efficient structure to pass on information and resources (plant nutrients, hydrogen, etc.) Very cool!

    • @valdisandersons129
      @valdisandersons129 Před rokem +3

      Do tree roots form a network though? To me it looks more like an upside down tree structure that doesn’t have links between parallel nodes.

    • @inthefade
      @inthefade Před rokem

      The shortest distances between points.

    • @fandomguy8025
      @fandomguy8025 Před rokem

      Creating connections between things is simply how things work when you boil everything down.

  • @mina_en_suiza
    @mina_en_suiza Před rokem +1

    Jetzt habe ich gelernt, wie "Memory" auf Englisch heißt. Das wird mir garantiert auf ewig im Gedächtnis bleiben.

  • @tehklevster
    @tehklevster Před rokem

    Entertaining and informative as always Sabine!

  • @ronaldjorgensen6839
    @ronaldjorgensen6839 Před rokem

    thank you for your time and persistence

  • @mariodegroote6756
    @mariodegroote6756 Před rokem +2

    that was the best transition to brilliant you put down here:D funny as always, and sharp as a samoerai sword, respect sabine!

  • @hymenpierce
    @hymenpierce Před rokem +7

    This is the best news channel in existence, full of facts, no culture wars..... perfect. Thank you Sabine.

  • @alexandrascherer5463
    @alexandrascherer5463 Před rokem +1

    They did a simple quantum chemical calulation on both a quantum and a convential computer and received lots of funding - congrats!

  • @alexandra2014
    @alexandra2014 Před rokem

    Ma'am. Thank. You.
    You're way of breaking down the terms so it's easier to understand for those who only had high school level sciences? -chefs kiss- I greatly appreciate it. Adding in your lovely humor, sarcasm and accent, I LOVE spotting a weekly news update ❤
    It's also a fun way for me to keep up with new topics and scientific findings. No idea that maglev cars would have potentially been possible, but contemplating it... the idea of freezing to the road brings to mind more wildlife issues.... And what happens if a car "falls off" the road? Would need fully automated cars to attempt adjustments at that speed.
    🤘🖖🖒🖒🖒

  • @jubjubfriend64
    @jubjubfriend64 Před rokem +1

    So good, I'm loving these

  • @bobtarmac1828
    @bobtarmac1828 Před rokem +1

    It’s the tune that haunts you all week! 👍

  • @NewMediaServicesDe
    @NewMediaServicesDe Před rokem

    Love it when you get sarcastic. I really do.

  • @gokuldas027
    @gokuldas027 Před rokem +2

    Thanks, that's a much needed, scientifically solid hope about a bright future.

  • @wesleypires3141
    @wesleypires3141 Před rokem

    Finally, Brazil mentioned🎉🎉🎉

  • @therealzilch
    @therealzilch Před rokem

    Sabine, du bist nach wie vor meine Go-To Quelle für diesbezügliches. Cheers from cloudy Vienna, Scott

  • @kanwaljitsingh3248
    @kanwaljitsingh3248 Před rokem +4

    Wow, Happy to see you

  • @eonasjohn
    @eonasjohn Před rokem +1

    Thank you for the news.

  • @lindsayforbes7370
    @lindsayforbes7370 Před rokem +2

    Another interesting video 👍.
    Not sure about the transitions though

  • @nova_supreme8390
    @nova_supreme8390 Před rokem +1

    Surely we all agree that brave little quantum computer still deserves a participation trophy although its contribution to the task was pretty much obsolete.

  • @charlesspringer4709
    @charlesspringer4709 Před rokem

    The "Computer Chronicles" 1980's intro music always gets my attention :-)

  • @mfbe73
    @mfbe73 Před rokem +2

    Your intro to the Brilliant ad was inspired. But I thought you were introducing your new GPT-4/Wolfram physics course! ❤

  • @curiousuranus810
    @curiousuranus810 Před rokem +1

    Cracking stuff, Sabina.

  • @Alexus00712
    @Alexus00712 Před rokem +2

    Me, a swedish person: We have a quantum computer??

  • @galvestonbragg9718
    @galvestonbragg9718 Před rokem +1

    Great show & content! Will be watching all your past & future vids. Entertaining & informative, keep it up Sabine.

  • @Kevin_Street
    @Kevin_Street Před rokem

    Thank you for another fascinating video!

  • @RobFomenko
    @RobFomenko Před rokem

    Sabine, I find your sense of humor refreshing.
    I'm just a regular human with some interest in science, yet I find dark energy and dark matter to be constructs by humans that are unable to understand our true nature of the universe. We are learning so much over the years yet we seem not to understand the most basic and fundamental aspects of our universe. Over our lifetime we have gone from the Atom being the smallest thing and it being a smaller model of the solar system, to quantum fields and particles popping in and out of existence from where?
    I doubt very much that we will ever find out in my lifetime what the true nature of our existence is.
    Right now I'm in the great state of Utah looking at a large reservoir of water being blown by the wind. The sun is reflecting off of the surface of the water and Waves. There are some white caps on the top from the wind. It reminds me of a video I recently saw about quantum fields. Is there such a thing? And is it a particle or wave? What's real? And what really is real? And then there's time.... Used to be time was just something that passed or like the flow of water down a river.. now it's tied into gravity and space and particles and Fields and, truthfully it can make my head hurt. I appreciate you making the pain a little less with your knowledge and the way you present it. Thanks!

  • @theephemeralglade1935

    The Brazil Nut experiment was actually pretty interesting.

  • @danielbergstrom3526
    @danielbergstrom3526 Před rokem +2

    First time watching...LOVE IT! 🎉

  • @Nola_Travel
    @Nola_Travel Před rokem +3

    Love the hot air joke. Never gets old :)

  • @markhuebner7580
    @markhuebner7580 Před rokem +6

    Who knew physics could provide so many insights into the puzzling problems of the day! Thanks Sabine!

  • @bacca71
    @bacca71 Před rokem +2

    Thanks for this! Best dead-pan comedy of matters of science ever. A few cold buckets of realism thrown provide perspective.

  • @davidpetersonharvey
    @davidpetersonharvey Před rokem

    "The future may be brighter than you thought." LOL! GOOD ONE!

  • @ruffrider2626
    @ruffrider2626 Před rokem

    You crack me up. Thanks Sabine.

  • @ThoughtsAreReal
    @ThoughtsAreReal Před 8 měsíci

    Love you Sabine! 🥰

  • @johnniefujita
    @johnniefujita Před rokem

    Iliked the superconductor idea

  • @Piotrmiko
    @Piotrmiko Před rokem +17

    Amazing content as always, Sabine. Would you consider doing a video on mycorrhizal networks? There seem to be some controversy about the topic currently, as the original study was published in a questionably scientific way, and it even became the basis for the highest grossing movie ever. It'd be interesting to know the reality behind the "talking trees" theory.

    • @Robert-er5wq
      @Robert-er5wq Před rokem +4

      Also it has an effect on the phosphate retention (as I have learnt from a TED talk). Quite important considering the discussion around 'peak phosphorus'

    • @ExecutiveChefLance
      @ExecutiveChefLance Před rokem

      Its no Theory its Fact. But talking trees? ahh what? 80% of all Plant Life HAS to have Fungal counterpart or else it will die. As most plants cannot Fix Nitrogen. Fungi just naturally form "networks" its what they do. The networks are the Fungus Body essentially. We call these Hyphae. This strand filament looking things that are quite similar looking to a Brain. Now do they respond to pressures and react spreading out Nutrients and other stuff? Yes. Talking? Meh.
      You get a Cut. Swelling Occurs. Your body singled other areas to bring in stuff to help. That is what is happening. Weird Analogy but this Evolution Strategy, using each Piece or "End" or your body to relay information well to the whole. Instead of relying on the Whole's Features for that information. Is exactly like how Napoleon won so many battles. He created smaller Cores and gave them more leverage to act on information. Which is far more efficient.
      We also do that to a smaller extent. You foot tells your brain it hurts.

  • @fred_2021
    @fred_2021 Před rokem +3

    Our galaxy could become a quasar, so...”the future may be brighter than we thought”. That’s a Sabine-ism, lol

  • @donholmstrom6482
    @donholmstrom6482 Před rokem

    She was excellent in this video. The knowledge transfer was great and the humor was top of line.

  • @geekehUK
    @geekehUK Před rokem +2

    My bracelet is turning blue, oho I must be running a 60°C fever

  • @saschaliebig6499
    @saschaliebig6499 Před rokem

    Danke für die News!

  • @rileychadwell5635
    @rileychadwell5635 Před rokem

    Theia did it!!
    It brought us our moon, our ocean, rotational spin rate, plate tectonics, the core dynamo, and resulting magnetosphere.
    Theia was like Ceres, in that it had water ice. Smashing into Earth the way it did created a lot.

  • @Frobard
    @Frobard Před rokem

    Interesting and mind boggling as always.

  • @lesaber251
    @lesaber251 Před rokem +1

    Sabine, you might be a good match for Dr. Sheldon Cooper. Seriously, I love your work here. You teach us things in a way that is understandable to the common man. Thank you.

  • @matthewrberning
    @matthewrberning Před rokem

    Hilarious episode this week, thank you! 🤣

  • @seanharbinger
    @seanharbinger Před rokem +2

    Everything I want to know about, brilliantly communicated! Thank you Sabine!

  • @oisinryan150
    @oisinryan150 Před rokem +1

    All my homies love Sabine ❤

  • @ddavidebor
    @ddavidebor Před rokem

    The maglev-hydrogen transport is super old ! people were talking about hydrogen+superconducting wires for energy transport 10+ years ago

  • @nickasbury
    @nickasbury Před rokem

    Thx Sabine!

  • @Zift_Ylrhavic_Resfear

    Thanks for the video :)

  • @LeandroSilva08
    @LeandroSilva08 Před rokem +3

    Thanks for the video Dr. Much appreciated.
    Your sense of humour is also greatly appreciated. 😂

    • @_John_Sean_Walker
      @_John_Sean_Walker Před rokem +1

      I've heard someone call her Hossenpfeffer, but Dr. Much is new to me.

    • @LeandroSilva08
      @LeandroSilva08 Před rokem +1

      @@_John_Sean_Walker 🤣
      I was here thinking: "wth is he talking about?" It took me some seconds to realize 🤣

    • @_John_Sean_Walker
      @_John_Sean_Walker Před rokem

      @@LeandroSilva08 😂

  • @DreckbobBratpfanne
    @DreckbobBratpfanne Před rokem

    Does the Brazilian nut phenomenon allow for seperation of charges this way as well? Wouldn't this then be practically free energy (probably not, for physics reasons) if they just return to the ordered state just like that what then would allow to extract the potential energy again?

  • @ScotHarkins
    @ScotHarkins Před rokem

    Great. The Brazil Nut Theory will be used to explain why dinosaur bones turn up above tiny ocean creatures "after the Great Flood". Forrest Valkai will have fun with those.

  • @bertloreto9507
    @bertloreto9507 Před rokem +1

    OMG i nearly died laughing about your comment on the old box of cables soon good to enrol in college 😂😂 Love it

  • @paulbloemen7256
    @paulbloemen7256 Před rokem +1

    I’m so glad we have a bright future, maybe.

  • @ReynaSingh
    @ReynaSingh Před rokem +21

    Another great video. Keep it up

  • @quantumspark343
    @quantumspark343 Před rokem +1

    the wire thing is cool asf, wild

  • @Chad_Thundercock
    @Chad_Thundercock Před rokem

    Wow, hearing Sabine drop one of the "naughty words" really took me off guard.

  • @nacnud_
    @nacnud_ Před rokem +1

    I really dig your humour @sabine. Im off to start saving for a college fund for my box of wires.

  • @itowmyhome797
    @itowmyhome797 Před rokem +1

    Thank you

  • @teekanne15
    @teekanne15 Před rokem

    The Brazil-nut effect is called gravitational sorting in sedimentology and known for decades.

  • @MrKawaltd750
    @MrKawaltd750 Před rokem +1

    Your deadpan jokes get me every time !😂

  • @Socrates3001
    @Socrates3001 Před rokem

    Using liquid H2 as a superconducter for highways gives me the image of icy roads in the middle of a sweltering August ;-)

  • @Chris.Davies
    @Chris.Davies Před rokem

    When dealing with spheres, using radius often confuses people greatly due to the Pi*r-cubed ratio. Adding the volume is more helpful.
    A core with 1800km radius has a volume of 2.44×10^10 cubic km.
    A core with 3600km radius has a volume of 1.95×10^11cubic km!
    So, while the radius is double for Earth, the volume is 8 times larger.

  • @paultraynorbsc627
    @paultraynorbsc627 Před rokem

    Thanks Sabine

  • @marcusdirk
    @marcusdirk Před rokem

    Great content, as usual, but were you wiping the video up and down more than usual? It's a nice transition effect between sections, but overusing it within a section can make some of your audience feel queasy. I'd love to know more about how they manage the connections in the wire networks, and laughed out loud at your summary of the quantum computer paper 🙂