Mindscape 214 | Antonio Padilla on Large Numbers and the Scope of the Universe

Patreon: / seanmcarroll
Blog post with audio player, show notes, and transcript: www.preposterousuniverse.com/...
It’s a big universe we live in, so it comes as no surprise that big numbers are needed to describe it. There are roughly 1022 stars in the observable universe, and about 1088 particles altogether. But these numbers are nothing compared to some of the truly ginormous quantities that mathematicians have found to talk about, with inscrutable names like Graham’s Number and TREE(3). Could such immense numbers have any meaningful relationship with the physical world? In his recent book Fantastic Numbers and Where to Find Them, theoretical physicist Antonio Padilla explores both our actual universe and the abstract world of immense numbers, and finds surprising connections between them.
Antonio (Tony) Padilla received his Ph.D. in physics from the University of Durham. He is currently a Royal Society Research Fellow in the School of Physics and Astronomy at the University of Nottingham. He is a frequent contributor to the KZbin series Sixty Symbols and Numberphile.
Mindscape Podcast playlist: • Mindscape Podcast
Sean Carroll channel: / seancarroll
#podcast #ideas #science #philosophy #culture

[@Xen2288]

A fantastic episode. Please consider having Ed Copeland on

[@JeroenBaxexm]

+ 1 on Ed!

[@Pow3llMorgan]

That would be so great! I love professor Copeland!

[@CivilWarcraft]

Came for Numberphile, stayed for Sean Carroll

[@MrCheeze]

here for a series that definitely isn't the same thing as -1/12

[@GetawayFilms]

You came to Sean Carroll's channel for numberphile, then stayed because Sean Carroll was here!? Interesting...

[@smlanka4u]

The Interpretation of the growth of space called vacuum energy is simply a misleading interpretation, and it is just the extra space that comes faster uniformly into the observable universe. Likely, there were a lot of extra space outside the observable universe.

[@josephhall2748]

@@smlanka4u what the fuck is your comment a reply to here? Dumb shit

[@smlanka4u]

@@josephhall2748, Energy is not something that exist. Energy is an output. The name vacuum energy is an irrelevent answer because it only mentions the output, ignoring the growth of space (virtual particles). The space (virtual particles) inside galaxies show that space doesn't make extra space from nothing.

[@rickcygnusx1]

So cool to see Tony on Mindscape!!! Thanks Sean!!

[@yogran1]

First :D Glad to see two of my favourite scientists talking about one of my favourite topics to think about :)

[@Billy-xl4sv]

Crossover of the decade

[@famistudio]

That was such a fun episode. Tony is the best!

[@spaceinyourface]

Great choice of guest for me,,I like watching Tony whenever he's on 60 symbols podcast 👍 😀 👌 👏

[@fs5775]

Man, I don't know who this guy is but he has such a kind, open, genuine face!

[@TheManInRoomFive]

Look up Numberphile here on KZbin, he is a regular there.

[@SocietyIsCollapsing]

Tony's quality. Does a lot of good Numberphile topics. The Tree(3) one referenced is great.

[@PronatorTendon]

What a great guest to have on

[@DavidSchilter]

Antonio is great! This is one of my fave Mindscape episodes :)

[@TheMemesofDestruction]

“Fantastic Numbers and Where to Find Them,” totally dig the Harry Potter reference. ^.^

[@bentationfunkiloglio]

Loved podcast. Mathematical topics are almost always fun and interesting.

[@ZokRs]

That was the best introduction to a guest I've heard.

[@hmp01]

Wow, this was so incredible to listen to, had a smile on my face throughout, thank you so much, Sean and Antonio!

[@shinjirigged]

What a great conversation, thanks for letting us listen!

[@ianmackenzie8831]

I like feeling cozy!

[@peterz53]

Very interesting discussion. Antonio's book has been in my "to read" stack for a few weeks. looking forward.

[@gkelly34]

My home google home is going bonkers in the background listening on this 🤣

[@archielundy3131]

The Holographic Principle always reminds me of a line from The Simpsons: "There’s no trick to it, it’s just a simple trick."

[@gcewing]

We used to think a black hole was the result of a collapsing star, but it turns out it's just someone who tried to think about Graham's number.

[@linkingwithnaz1295]

I'm surprised that Antonio Padilla stated that we believe that the universe is finite.

[@yaserthe1]

OMG, this is like when Spiderman crosses paths with the X-Men, 🤯🤯🤯

[@Life_42]

One of my favorite mathematicians!

[@PronatorTendon]

There's about 8.798479339500144*10¹³⁰ cubic Planck lengths in the observable universe

[@ilikenicethings]

Might as well round that number to 8.8*10^130… Unless there’s meaning in the details…

[@PronatorTendon]

@@ilikenicethings I would have done all the digits if my calculator didn't stop at 100

[@TheUArabej]

Unfortunately, it doesn't even touch g(0)

[@Al-ji4gd]

@@TheUArabej It doesn't even touch a googolplex.

[@vikingforties]

Name drop, I met Tony after a Parkrun. We came to the conclusion his Numberphile appearances were way better than Zoella stuff.

[@heepajunk]

Awesome guest.

[@sibbsmat2926]

Thoroughly enjoyed it! Though I still don't understand what tree(3) means...

[@Life_42]

Antonio made a video about it on Numberphile KZbin channel

[@robinbrowne5419]

Bedtime in Tralfamadore Ok you kids. Time for bed. Awww Dad... Can we just finish our game of Tree(3) first.

[@sjhayes93]

Haha definitely wasn't expecting a scouser on this one. Great episode

[@gcewing]

Maybe the universe isn't finite or infinite. Maybe we're in a Minecraft universe -- potentially infinite, but it gets created on demand as we explore it.

[@DrewTrox]

On the topic of the cosmological crisis of the vacuum energy discrepancy, my armchair theoretical physics idea is; instead of solving the equations for a 4d Spacetime, what if we use an infinitely dimensioned Spacetime. Maybe at that string theory scale it really is an infinite sea of possible dimensions.

[@gavrielcohen5095]

Is it just me or did this guy not know who he was talking to trying to describe Sean's own research to him? I think he's right about finite universe though

[@WildMessages]

Hmmm So our brains are too slow to think of the largest numbers before the Universe would end ... I guess I'll stop now then :0

[@KaliFissure]

I have video on large numbers hypothesis and the geometric understanding it can give. which in the end links to the universal process itself. Neutron decay cosmology. The path of least action, physical process solution to black hole paradoxes, dark energy, dark matter and critical density maintenance. Neutrons/matter which eventually contacts event horizons (because limits) becomes the vacuum energy for one single Planck second then re-emerges from the lowest energy density point of space where it is most permeable, with lowest quantum basement. There is deep voids, the Neutrons decay, into a proton, an electron and an antineutrino. Amorphous atomic hydrogen. This decay, from near point particle to one cubic meter of gas is a volume increase of 10⁴⁵. This is the necessary expansion to compensate for the compression of gravity over lifetime of the particle. The decay product, amorphous atomic hydrogen, doesn't have a stable orbital electron so can't emit or absorb photons. Dark matter. In time the hydrogen stabilizes, scintillates, and we can see it. It then follows usual evolution pathway from gas to filament to proto star to star until in the far distant future it is again about to contact an event horizon. The universe is steady state. A continuous flow down the gravity hill. Event horizons act as energy pressure release valves venting from highest energy pressure conditions to lowest energy density points of space. From aggregated singularity to dispersed distributed diffuse. And then gravity gathered it back up again. Neutron decay cosmology.

[@smlanka4u]

Time continues mathematically, increasing and maintaining emptiness, and making the entire universe.

[@bjpafa2293]

@52" holographic principle, there we go into entropic principle... Great open ideas. Get the rest later. It looks like an 🥚 egg, difficult to compute? Congrats to both speed talkers. 🥚👍

[@marcomattano3705]

The number of possible numeric comninations arranged in a human lenght strand of DNA would certainly be bigger than the 10 at 80 universe particle count number, although I searched for it and couldn't find a reputed scientific answer. Am I wrong?

[@bryandraughn9830]

I wonder how many Planck units are in the observable universe?

[@MrXperx]

World collide. Sixty Symbols and Sean Carroll.

[@HarryNicNicholas]

this idea of doppelganger is really interesting, much easier to picture than dimensions and universes. surely a really, REALLY big number could be just as good as an infinity, when it comes to the "extent of the universe" REALLY big could mean we can never find a boundary even if there is one, and if REALLY big, is a really big enough number, is it possible that the universe doesn't have a shape that has a boundary? my gut tells me maybe the universe, the cosmos is BOTH, finite but infinite in some geometric way. anyway, fascinating episode.

[@kapsi]

Hey it's the math man

[@qunningStunts]

This wasn't long enonugh!!

[@bjpafa2293]

Ok. Couldn't turn it off. 😉 Now One hour...crazy in the best sense ✨AntideSitter etc, vacuum energy...finite debate, more derivations...

[@bjpafa2293]

Be Proud.

[@kapsi]

So the part about vacuum energy being 10^60 times, or whatever, smaller in observations than in theory - is there any research towards explaining that? Seems like a big failure of the theory.

[@DjomlaMitrovic]

It's probably just a rounding error...

[@leegale1993]

How did my school mates meet up with my uni mates without me.

[@wilfredoaldarondo5649]

Tony, your name and last name are Latino or common Spanish speaking names, are yours parents from Spain or America?

[@RC-wi6xm]

Cantor and Conway

[@ZoloftSmoothie]

Too bad it is a silly coincidence, because chess is a pretty good analogy for the multiverse chess pieces, board, annotation = particles + spacetime rules of chess = laws of physics any individual game = any given timeline in the multiverse chess variants = universes with different laws

[@teapot_]

Yep got to agree, for me infinity is not an answer just an error code. Sean I admire that you do not enter click bait and woo fields to generate viewing figures, sticking to the scientific method and just saying sometimes I do not know. However as our understanding improves, as it has done todate, we can move forward with better understanding.

[@antifajesus]

I got it now so super duper is just slightly less than infinity

[@johnnycharisma162]

Has a very similar accent to Brian Cox.

[@desgreene2243]

Maybe number is not the way to describe our world…

[@emilylowrance7930]

have you ever done a show on chess?

[@aprylvanryn5898]

I've watched all his shows and I don't recall him ever doing one on chess

[@wallstreetoneil]

This was incredible - thank you - I've watched both your online content for years. I agree with Tony - it has to be finite - we simply invented Limits & Calculus to make our world easier to pontificate about. Gravity & the Plank length reveal that while our infinite mathematical tools are nice to use, they don't imply reality. Maybe Pi doesn't have infinite digits because it would collapse into a Blackhole?

[@joshua3171]

fluctuations of the muonic field,

[@joshua3171]

fractals Mandelbrot and the weak field

[@joshua3171]

light is cool and all but has limited applications,

[@tatotato85]

[@rv706]

I think you guys are really misrepresenting mathematicians! No serious mathematician would complain for the typographical aspect of your proof. What we care about is logic: things have to _work_ from the logical point of view. Also, we are pedantic when we _need_ to be, not randomly. Even mathematicians skip parts of proofs and logical arguments in their papers, _but_ , if the article is well-written, every expert should be able to reconstruct the skipped arguments at least in principle. A relevant point is that something that might appear easy superficially might in fact be the hard part of a proof. We don't count theorems as easy or difficult depending on how easy or difficult they _superficially_ _seem_ to be. I had an eye-opening experience about this aspect during my second uni year. We were being presented a proof of the change of variable formula for integration in several variables. The proof consisted of a series of steps of reduction that culminated in proving this: a square with sides parallel to the Cartesian axes has the same area of a slightly rotated square (This is not a tautology if area is defined via the Cartesian product of Lebesgue measures of two copies of the real line). Well, believe it or not, the hard step in the proof was proving this stupidly easy-looking statement! This opened my eyes to the fact that spotting the _actual_ obstacle to a proof might be nontrivial.

[@ingoos]

Fast forward The answers to our key questions are also found within the problem-the data succinctly referred to as, the initial conditions-more precisely, its finely-tuned values-culminating to the Big Bang or, more correctly, the Beginning. TLDR: since it is highly unlikely (actually, "absurdly" so, to put it mildly, even flattering) to be from random processes then, logically, it is not and, therefore, by design-deliberate & intelligently intentional design. Furthermore, postulating multiverses is even more highly & absurdly so unlikely, since the unlikelihood is exponentially compounded to way beyond comprehension! Just do the math! Interestingly, prior to science being formalized, the Bible begins with, "in the beginning." Coincidence?-The fine-tuning suggests intelligent design and, so, intentionally!

[@orthoplex64]

Discussing large numbers without mentioning busy beaver numbers is like talking about the earth's largest bodies of water without mentioning its oceans.