#101 Black Holes Collisions & Gravitational Waves, with LIGO Experts Christopher Berry & John Veitch

Episode 101 •
7th March 2024 • Learning Bayesian Statistics • Alexandre Andorra

*Proudly sponsored by **PyMC Labs**, the Bayesian Consultancy. **Book a call**, or **get in touch**!*

In this episode, we dive deep into gravitational wave astronomy, with Christopher Berry and John Veitch, two senior lecturers at the University of Glasgow and experts from the LIGO-VIRGO collaboration. They explain the significance of detecting gravitational waves, which are essential for understanding black holes and neutron stars collisions. This research not only sheds light on these distant events but also helps us grasp the fundamental workings of the universe.

Our discussion focuses on the integral role of Bayesian statistics, detailing how they use nested sampling for extracting crucial information from the subtle signals of gravitational waves. This approach is vital for parameter estimation and understanding the distribution of cosmic sources through population inferences.

Concluding the episode, Christopher and John highlight the latest advancements in black hole astrophysics and tests of general relativity, and touch upon the exciting prospects and challenges of the upcoming space-based LISA mission.

*Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at **https://bababrinkman.com/** !*

**Thank you to my Patrons for making this episode possible!**

*Yusuke Saito, Avi Bryant, Ero Carrera, Giuliano Cruz, Tim Gasser, James Wade, Tradd Salvo, William Benton, James Ahloy, Robin Taylor,, Chad Scherrer, Zwelithini Tunyiswa, Bertrand Wilden, James Thompson, Stephen Oates, Gian Luca Di Tanna, Jack Wells, Matthew Maldonado, Ian Costley, Ally Salim, Larry Gill, Ian Moran, Paul Oreto, Colin Caprani, Colin Carroll, Nathaniel Burbank, Michael Osthege, Rémi Louf, Clive Edelsten, Henri Wallen, Hugo Botha, Vinh Nguyen, Marcin Elantkowski, Adam C. Smith, Will Kurt, Andrew Moskowitz, Hector Munoz, Marco Gorelli, Simon Kessell, Bradley Rode, Patrick Kelley, Rick Anderson, Casper de Bruin, Philippe Labonde, Michael Hankin, Cameron Smith, Tomáš Frýda, Ryan Wesslen, Andreas Netti, Riley King, Yoshiyuki Hamajima, Sven De Maeyer, Michael DeCrescenzo, Fergal M, Mason Yahr, Naoya Kanai, Steven Rowland, Aubrey Clayton, Jeannine Sue, Omri Har Shemesh, Scott Anthony Robson, Robert Yolken, Or Duek, Pavel Dusek, Paul Cox, Andreas Kröpelin, Raphaël R, Nicolas Rode, Gabriel Stechschulte, Arkady, Kurt TeKolste, Gergely Juhasz, Marcus Nölke, Maggi Mackintosh, Grant Pezzolesi, Avram Aelony, Joshua Meehl, Javier Sabio, Kristian Higgins, Alex Jones, Gregorio Aguilar, Matt Rosinski, Bart Trudeau, Luis Fonseca, Dante Gates, Matt Niccolls, Maksim Kuznecov, Michael Thomas, Luke Gorrie, Cory Kiser and Julio*.

Visit https://www.patreon.com/learnbayesstats to unlock exclusive Bayesian swag ;)

**Takeaways: **

⁃ Gravitational wave analysis involves using Bayesian statistics for parameter estimation and population inference.

⁃ Nested sampling is a powerful algorithm used in gravitational wave analysis to explore parameter space and calculate the evidence for model selection.

⁃ Machine learning techniques, such as normalizing flows, can be integrated with nested sampling to improve efficiency and explore complex distributions.

⁃ The LIGO-VIRGO collaboration operates gravitational wave detectors that measure distortions in space and time caused by black hole and neutron star collisions.

⁃ Sources of noise in gravitational wave detection include laser noise, thermal noise, seismic motion, and gravitational coupling.

⁃ The LISA mission is a space-based gravitational wave detector that aims to observe lower frequency gravitational waves and unlock new astrophysical phenomena.

⁃ Space-based detectors like LISA can avoid the ground-based noise and observe a different part of the gravitational wave spectrum, providing new insights into the universe.

⁃ The data analysis challenges for space-based detectors are complex, as they require fitting multiple sources simultaneously and dealing with overlapping signals.

⁃ Gravitational wave observations have the potential to test general relativity, study the astrophysics of black holes and neutron stars, and provide insights into cosmology.

**Links from the show:**

- Christopher’s’ website: https://cplberry.com/
- John’s website: https://www.veitch.me.uk/
- Christopher on GitHub: https://github.com/cplb/
- John on GitHub: https://github.com/johnveitch
- Christopher on Linkedin: http://www.linkedin.com/in/cplberry
- John on Linkedin: https://www.linkedin.com/in/john-veitch-56772225/
- Christopher on Twitter: https://twitter.com/cplberry
- John on Twitter: https://twitter.com/johnveitch
- Christopher on Mastodon: https://mastodon.scot/@cplberry@mastodon.online
- John on Mastodon: https://mastodon.scot/@JohnVeitch
- LIGO website: https://www.ligo.org/
- LIGO Gitlab: https://git.ligo.org/users/sign_in
- Gravitational Wave Open Science Center: https://gwosc.org/
- LIGO Caltech Lab: https://www.ligo.caltech.edu/page/ligo-data
- Exoplanet, python package for probabilistic modeling of time series data in astronomy: https://docs.exoplanet.codes/en/latest/
- Dynamic Nested Sampling with dynesty: https://dynesty.readthedocs.io/en/latest/dynamic.html
- Nessai, Nested sampling with artificial intelligence: https://nessai.readthedocs.io/
- LBS #98 Fusing Statistical Physics, Machine Learning & Adaptive MCMC, with Marylou Gabrié: https://learnbayesstats.com/episode/98-fusing-statistical-physics-machine-learning-adaptive-mcmc-marylou-gabrie/
- bayeux, JAX models with state-of-the-art inference methods: https://jax-ml.github.io/bayeux/
- LBS #51 Bernoulli’s Fallacy & the Crisis of Modern Science, with Aubrey Clayton: https://learnbayesstats.com/episode/51-bernoullis-fallacy-crisis-modern-science-aubrey-clayton/
- Aubrey Clayton's Probability Theory Lectures based on E.T Jaynes book: https://www.youtube.com/playlist?list=PL9v9IXDsJkktefQzX39wC2YG07vw7DsQ_

**Transcript**

*This is an automatic transcript and may therefore contain errors. Please **get in touch** if you're willing to correct them.*

Speaker:

In this episode, we dive deep into

gravitational wave astronomy with

2

:Christopher Berry and John Vich, two

senior lecturers at the University of

3

:Glasgow and experts from the LIGO -VIRGO

collaboration.

4

:They explain the significance of detecting

gravitational waves, which are essential

5

:for understanding black holes and neutron

stars collisions.

6

:This research not only sheds light on

these distant events, but also helps us

7

:grasp

8

:fundamental workings of the universe.

9

:Our discussion focuses on the integral

role of Bayesian statistics, detailing how

10

:they use nested sampling for extracting

crucial information from the subtle

11

:signals of gravitational waves.

12

:This approach is vital for parameter

estimation and understanding the

13

:distribution of cosmic sources through

population inferences.

14

:Concluding the episode, Christopher and

John highlight the latest advancements,

15

:in black hole astrophysics and tests of

general relativity, and touch upon the

16

:exciting prospects and challenges of the

upcoming space -based LISA mission.

17

:So strap on for episode 101 of Learning

Bayesian Statistics, recorded February 14,

18

:2024.

19

:Hello my dear Bayesians!

20

:Today, I want to thank Julio

21

:joining the Good Basion tier of the show's

Patreon.

22

:Julio, your support is invaluable and

literally makes this show possible.

23

:I really hope that you will enjoy the

exclusive sticker coming your way very

24

:soon.

25

:Make sure to post a picture in the slide

channel.

26

:And now, on to the show.

27

:Christopher Barry, John Vich, welcome to

Learning Basion Statistics.

28

:Thank you very much for having us.

29

:Yes, thank you a lot for taking the time,

even more time than listeners suspect, but

30

:we're not gonna expand on that.

31

:But yeah, I'm super happy to have you on

the show and we're gonna talk about a lot

32

:of things, physics, of course

astrophysics, black holes and so on.

33

:But first,

34

:How would you both define the work you're

doing nowadays and how did you end up

35

:working on this?

36

:I can go first.

37

:I guess I'm slightly older than

Christopher.

38

:I started doing gravitational waves when I

was a physics student at Glasgow.

39

:I got involved with the LIGO, actually the

GEO experiment first of all, which is the

40

:Gravitational Weight Detector in Germany.

41

:Its bigger brother is the LIGO and the

LIGO detectors that we're going to talk

42

:about more today.

43

:And ever since then, I mean, thought the

project was fantastic.

44

:I'll you all about it.

45

:I just wanted to get involved in the

discoveries of gravitational waves and

46

:what they can tell us about black holes

and so on.

47

:I got involved back in my PhD.

48

:My PhD was largely about gravitational

waves we could maybe detect in the future

49

:with an upcoming space -based mission

d LISA, due for launch in the:

50

:I remember

51

:my advisor telling me, I hope you're OK.

52

:There's not going to be any real data.

53

:And I was like, yes, that's great.

54

:I just want to play around with the theory

stuff.

55

:And then I guess fate conspired against

me.

56

:After my PhD, I moved to the University of

Birmingham.

57

:That's where I first started working with

John.

58

:We were at University of Birmingham

together.

59

:And I got involved in LIGO, VEGO data

analysis.

60

:And we happened to make our first

detection just a couple of years after I

61

:joined in 2015.

62

:And we've been very busy since then

analyzing all the signals, figuring out

63

:the astrophysics of them.

64

:So each individual source and then putting

them together to understand the population

65

:underneath.

66

:So now we're both at the University of

Glasgow working on analyzing these

67

:gravitational wave signals and

understanding what they can teach us about

68

:the universe.

69

:Yeah.

70

:So as Liesner can already tell, I guess,

71

:Fascinating topics, lots of things to talk

about and dive into.

72

:But maybe to give us a preview of things

we're going to talk about a bit more.

73

:You guys are also using some patient stats

writing in these analysis, am I right?

74

:Yeah, so I think we look at, I guess, two

levels of Bayesian stats.

75

:So the first is what we refer to as

parameter estimation.

76

:So given a single signal trying to figure

out what are the properties of the source.

77

:So the signals we most often see are, say,

two black holes spiraling in together.

78

:So we look at the patterns of

gravitational waves that it emits.

79

:And from this, we can match templates and

then infer.

80

:These are the masses of the two black

holes.

81

:This is the orientation of binary, the

distance to the binary, and parameters

82

:like that.

83

:So we use Bayesian stats and the sampling

algorithms like nested sampling to mop out

84

:a posterior probability distribution.

85

:And then I guess the second level of this,

we do what we call a population inference,

86

:so a hierarchical inference of given an

ensemble of different detections,

87

:correcting for our selection effects that

we can detect some signals easier than

88

:others.

89

:What is the underlying astrophysical

distribution?

90

:So what is the distribution of masses of

black holes out there in the universe?

91

:Yeah.

92

:So fascinating things.

93

:And John, you want to maybe add something

to that?

94

:Just as a teaser, we're going to dive a

bit later in the episode into what you

95

:guys actually do.

96

:So as Christopher just said, nested

sampling, population inferences, but

97

:anything you want to add?

98

:teaser for Easter.

99

:I would add something about the background

of how it works within the LIGO scientific

100

:collaboration.

101

:So when I started doing my PhD, my

advisor, Graham Wohn, taught me about

102

:Bayesian statistics, Bayesian inference,

and I never learned it as an undergraduate

103

:at all.

104

:I just leave my mind, like, here we have

this mathematical theory of learning.

105

:Why are we using this everywhere?

106

:And in those days, it really wasn't being

used very much in LIGO.

107

:because a lot of the people that started

the collaboration were coming from a

108

:physical perspective and they were very

frequentists.

109

:They were counting and cutting all of

their events to try and measure the

110

:discovery that takes place on it or

whatever.

111

:So it was kind of novel in that patient's

way back then.

112

:But since then, as Christopher said, it's

been applied all over the place to all

113

:kinds of different problems.

114

:So it's been quite exciting to watch that

back over the years.

115

:I remember we had a...

116

:We had our first detection and we were

lighting up our results.

117

:And I think at that time still a lot of

the collaboration was very frequent.

118

:So we were writing in our papers, we have

a posterior probability distribution for

119

:the masses and there are people going,

hey, what's that?

120

:What's a posterior?

121

:We've never come across this before.

122

:Can you explain it to us?

123

:And now it is very much accepted.

124

:And yeah, everyone has a new detector.

125

:Where are the masses?

126

:I want to see this probability

distribution.

127

:What do you think drove that evolution and

that change?

128

:I think Bayesian statistics is very

popular in other parts of astronomy.

129

:So in a sense, it was kind of inevitable

that it would make its way over to

130

:gravitational wave astronomy as it's only

a matter of time.

131

:But I think the problems that we were

trying to solve, particularly for the

132

:parameter estimation,

133

:type analysis did lend itself to a

Bayesian analysis because you have a

134

:unique event.

135

:You you're not, we only see a very small

number of gravitational waves.

136

:We see them all the time, but it's still

measurable.

137

:The dozens, not the millions.

138

:So we have to make the most of every

single one.

139

:The second one, the ratio is rather low.

140

:So graphs from the other side.

141

:is also very important if you want to do

science.

142

:Yeah, that makes sense.

143

:And so it was mainly driven by just

patient stats entering a need in what you

144

:wanted to do basically, which is something

I often see in fields where psychology,

145

:from what I've seen in the last few years,

for instance, psychometrics, things like

146

:that, have seen a big rise in patient

statistics because they have been able to

147

:answer the questions that researchers had

and that they could not answer with the

148

:tools they had before.

149

:So basically, a very practical, oriented

view of things.

150

:And then afterwards, let's say the more

epistemological philosophical side of

151

:things enters to also justify that.

152

:But...

153

:But most of the time it's a very practical

driven mindset, which is great, right?

154

:Because in the end, why you care about

that is just, is that the right tool to

155

:answer the questions I have right now?

156

:And yeah, for what it's worth.

157

:Yeah, go ahead, John.

158

:The pragmatism is what's put in the table

at the end of the day, but during my PhD,

159

:I was trying to look...

160

:or not the kind of black hole binaries

that we'll talk about later, but from

161

:monochromatic waves.

162

:So you imagine doing a Fourier transform

of some data and you have a single spike,

163

:and it has a bit of modulation on it.

164

:But really there's no information about

that spike in any area of the prime space

165

:outside of the spike.

166

:So I learned about Bayesian statistics and

tried to do MTMC on this problem, which

167

:was kind of like the most pathological

problem that you'd be trying to do MTMC

168

:on.

169

:that basically reduces itself to doing an

exhaustive search for the ground or space.

170

:So I was kind of convinced by the

epistemology originally rather than the

171

:thesis and the only nature that we used

for the sake.

172

:Yeah, yeah.

173

:Yeah, yeah.

174

:That makes sense.

175

:And as you were saying also that patient

studies is popular in other parts of

176

:physics.

177

:That's definitely true in a sense that,

for instance, in the core developers of

178

:MC, of Stan, you have a lot of physicists,

often coming from statistical physics and

179

:historically even the algorithms that we

even use, MCMC algorithms, have been

180

:developed mainly by physicists or for

physics purposes.

181

:So there is really this integration here

almost historically.

182

:And that made me think that if listeners

are interested, there is an interesting

183

:package that's called Exoplanet.

184

:And that's basically a toolkit for

probabilistic modeling of time series data

185

:in astronomy, but with a focus on

observations of exoplanets.

186

:So that's different from what you guys do,

but that's using PIMC as a backend.

187

:So that's why I know it.

188

:And that's...

189

:mainly developed by Dan, Firm and Macky,

if I remember correctly.

190

:I'll put that in the show notes for people

who are interested because that is

191

:definitely something to check out if you

are doing that kind of models.

192

:And that made me think that I didn't even

thank our matchmaker because today is

193

:February 14th, but actually this episode

was made possible thanks to a matchmaker,

194

:Cupid, if you want, of patient statistics,

Johnny Highland.

195

:Thanks a lot for putting me in contact

with Christopher and John.

196

:Johnny is a faithful listener and I am

very grateful for that and for putting me

197

:in contact with today's guests.

198

:And so you mentioned already, Christopher,

that you two work on the LIGO -VIRGO

199

:collaboration.

200

:Maybe...

201

:Yeah, tell us a bit more about that

collaboration, what that is about, and

202

:what the goal is, so that listeners have a

clear background.

203

:And then we'll dive into the details.

204

:So yes, LIGO -VIRGO -CAGRA is a

collaboration of collaborations.

205

:So each of LIGO -VIRGO and CAGRA operate

their own gravitational wave detectors.

206

:So these are remarkable experimental

achievements.

207

:We're talking devices that can measure

208

:Distortions in space and time is what

we're looking for.

209

:So in effect, what we do is we time how

long it takes a laser to bounce up and

210

:down between some mirrors in one direction

compared to another.

211

:We're looking for a part of less than one

part in 10 to the 21.

212

:So it's equivalent to measuring the

distance between the Earth and the sun to

213

:the diameter of a hydrogen atom, or the

distance from here to Alpha Centauri to

214

:the width of a human hair.

215

:So over many decades,

216

:experimentalists have developed the

techniques to build these detectors to

217

:design them.

218

:And we're now in a very fortunate

situation that we have multiple of these

219

:detectors operating across the world.

220

:So we have two LIGO detectors in the US,

one in Livingston, Louisiana, one in

221

:Washington, in Hanford.

222

:And we've got Virgo in Italy, just outside

Pisa, Kagra underground in Japan, and

223

:coming decade another LIGO to be built in

India.

224

:And each of these observatories is looking

for gravitational wave signals.

225

:The ideal source for gravitational waves

would be a binary of two black holes or

226

:two neutron stars, very dense objects

coming together, merging very quickly,

227

:very strong gravity, very dynamical

objects.

228

:And we can detect these gravitational

waves and with those do astronomy.

229

:So instead of using a telescope to make

observations with light, we're using these

230

:gravitational wave detectors to look for

gravitational waves in undercover.

231

:the astrophysics of these sources.

232

:Yeah.

233

:Yeah.

234

:Thanks.

235

:So that's a very clear explanation.

236

:It's a bit like being able to hear the

universe itself only looking at it, right?

237

:So that's another way of getting

information about the universe that maybe

238

:allows us to also answer questions that we

had, but we were not able to answer only

239

:with a telescope data.

240

:Is that the case or is that mainly

241

:information that's parallel and similar.

242

:Yes.

243

:Go ahead.

244

:Yeah, I think that's one of the most

exciting things about this is completely

245

:set in the electron spectrum using the

structural squeezing space itself by these

246

:buckles and neutrons.

247

:The waves that we've been offering are of

an oil from the sea.

248

:So, as you said, the detectors are picking

up

249

:essentially the equivalent of sound waves,

bulk motion of the material rather than

250

:the jiggling of atoms.

251

:We're talking about the jiggling of whole

stars, movement of them in their orbits.

252

:And because you're looking at the bulk

motion rather than the surface of the

253

:object, you can see right into the heart

of what's going on in some of these very

254

:violent events.

255

:In principle, we should be able to see

also inside supernovae if there are

256

:enough...

257

:motion of material during the core

collapse.

258

:That would also give off gravitational

waves that we could see, although their

259

:thoughts would be much weaker than those

that we're looking at in the moment.

260

:I see.

261

:One thing that's particularly nice we can

do as well is really test how gravity

262

:behaves in very extreme environments.

263

:John, I don't know if you want to mention

something about looking at the ring down

264

:of black holes.

265

:Sure.

266

:I mean, as Christopher says, there's a

very detailed prediction for how two stars

267

:should approach each other in their own

spiral over time.

268

:And the equations are horrendously

complicated.

269

:talking about the full view of general

relativity.

270

:But once they've collided and they form a

larger black hole, suddenly everything

271

:becomes rather simple and acts just like a

wine glass that's been excited with a fork

272

:and then it actually decays down and

settles into its final state.

273

:Therefore a black hole that happens

extremely fast because they want to

274

:settle down as quickly as they possibly

can, if you like.

275

:So the notes that we give off are

milliseconds long rather than seconds

276

:long.

277

:But the frequencies in the damping times

of those notes are measurable with their

278

:picture waves.

279

:And by looking at them and comparing them

to each other, we can check to see that

280

:the predictions of the theory are indeed

what we would see in the world.

281

:So far, they seem to be the case.

282

:Yeah.

283

:Something I'm wondering is that these

collisions that you're talking about, they

284

:are happening millions of light -wears

away.

285

:How are we even able to study them and

also maybe tell us what we already have

286

:learned from them?

287

:They're really quite rare events, the

types of collisions that we're seeing.

288

:I mean, this is why there are millions,

hundreds of millions or even billions of

289

:light years away is because they're so

rare in the universe that we need to look

290

:out a very long way before we see one

often enough to make the detections often.

291

:So they do happen in local galaxies as

well as the reason to think it wouldn't,

292

:but it's just they're so rare.

293

:I've seen one near black source.

294

:Yeah.

295

:Yes, they are remarkably energetic.

296

:The amount of energy that is output as

gravitational waves when you've got, say,

297

:two black holes coming together is

phenomenal.

298

:For just that moment as they smash in

together, more energy, so the luminosity,

299

:the amount of energy per unit time emitted

right at that peak is higher in

300

:gravitational waves than if you were to

add up.

301

:or the visible light from all the stars

that you could see in the universe.

302

:So it's a phenomenal amount of energy just

over a very short way.

303

:So yeah, we just need to be listening to

the universe to see these, to discover

304

:these sources and find out what they're

trying to tell us.

305

:The energy flux from these black hole

collisions, despite the fact that they're

306

:hundreds of millions of light years away,

is actually comparable to the flux from

307

:the full moon.

308

:So the brightest object in the night sky,

309

:is surpassed by gravitational wave

signals, except we can't see the

310

:gravitational waves because they don't

interact very strongly with matter.

311

:And it's only by building these incredibly

sensitive detectors to pick up their

312

:effect on distances that we can still look

at.

313

:Yeah, that's just fascinating to me that

we're even able to see...

314

:like hear these waves in a way.

315

:So, yeah, just to finally point home,

there's so much energy that you're

316

:carrying away, but the effect is so tiny,

as Chris said, 10 to the minus 21, no

317

:less.

318

:Yeah.

319

:If you think about how those two things

could be true at once, it's telling you

320

:that it takes an enormous amount of energy

to produce a tiny distortion in space.

321

:So it's very, very difficult to walk

space.

322

:And that's...

323

:the consequences of general malpractice.

324

:Yeah.

325

:And then, so I think now it's a good time

for you to tell us.

326

:So maybe Christopher, you can tell us

that.

327

:How do you use patient stats to extract as

much information as possible from these

328

:tiny wave signals?

329

:How is base useful in this field?

330

:And how do you also actually do it?

331

:Are you able to use any...

332

:widespread open source packages or do you

have to write everything yourself?

333

:How does that work concretely?

334

:Yes, so for the type of sources we've been

seeing these binaries, we have predictions

335

:for what the signal should look like.

336

:So we have a template that is a function

of the parameters and we have a decent

337

:understanding of the properties of our

noise.

338

:So the data is a combination of the signal

plus some noise which you assume to be

339

:stationary over the short time scales that

we're analyzing and characterized such

340

:that the noise at individual frequencies

is uncorrelated.

341

:So if you like, you get your data,

transform it to the frequency domain,

342

:subtract out your template, you should be

just left with noise, which is Gaussian at

343

:each frequency bin.

344

:And so you have a lot of Gaussian

probabilities that you combine to get.

345

:So that gives us our likelihood.

346

:You map that out, you change your

parameters for your template.

347

:evaluate that at another point in

parameter space, map that out with your

348

:suitable prior, and you end up with your

posterior probability for a single event.

349

:The number of parameters that we're

typically dealing with is something like

350

:15 for typical binary.

351

:Maybe that goes up to 17 when we add in a

couple of extra ones, a few more if we're

352

:maybe looking at tests of general

relativity.

353

:So it's enough that exploring the

parameter space can't be just done by

354

:gridding it up and exploring it.

355

:We generally use some kind of stochastic

sampling algorithm.

356

:But it's not one of these problems, at

least yet, where we've got millions of

357

:parameters and it's a really high

parameter space.

358

:In terms of the algorithms that we use to

explore parameter space, we've got a long

359

:history of using MCMC and nested sampling

for these.

360

:And John's really the expert on this.

361

:So, John, do want to say some more about?

362

:We'll get to that, yeah.

363

:Oh, you are done?

364

:OK, perfect.

365

:So yeah, John, maybe if you can tell us.

366

:Yeah, maybe let's start with nested

sampling that you use a lot for your

367

:inferences.

368

:So can you talk about that, why that's

useful, and also why you end up using that

369

:a lot in your work?

370

:Which problem does that solve?

371

:So nested sampling is an alternative to

MCMC.

372

:I don't know if you're...

373

:listeners will all have encountered it

before.

374

:If you're a regular user of MCMC though,

it's definitely worth a look.

375

:It was invented in 2006 -2007 by John

Scaling.

376

:He was a physicist.

377

:The idea is that you're actually trying to

evaluate the evidence, the normalization

378

:constant of the posterior to allow you to

do model selection in a basic way.

379

:But as a by -product, it can generate

samples from the Bistidia as well.

380

:So this popped up around about the time

that I started a full stock position in

381

:Birmingham and thought, well, why don't we

give it a go and apply it to the problem

382

:of compact binaries.

383

:So at that point, there was no off -the

-shelf package available to do this.

384

:And so we had to create our own.

385

:That was all coded up in C for so time.

386

:It wasn't such a big thing.

387

:There was thousands of lines of code and

all that.

388

:But yeah, so the reason is that you might

prepare it for MCMC.

389

:People were trying to solve the same

problem with parallel tempered MCMC.

390

:The compact binary parameter space has a

fair amount of degeneracies, multiple

391

:data, and in amongst those modes.

392

:They make it difficult to sample the

waveforms are facilitated in a nonlinear

393

:problem.

394

:It can be quite complicated.

395

:Getting a decent exploration of the prior

was proving to be difficult for the MCMC.

396

:Hence the need for parallel tempering.

397

:And this is something that works a little

bit differently because it starts off by

398

:sampling the whole prior in the first

place.

399

:So you know, say thousands of points,

they're called live points.

400

:scatter them across the entire prior and

then compute the likelihood for every one

401

:of those.

402

:If you then eliminate the point that has

the lowest likelihood and replace it with

403

:one that has the higher likelihood of the

lowest one, then people still have a

404

:thousand points, so they will all have a

likelihood higher than the worst one.

405

:And you can see that, roughly speaking,

the volume of that remaining set of points

406

:will be about

407

:999 thousandths of the original one just

by random large numbers.

408

:And so if you repeat that process, always

replacing the point of the next iteration,

409

:you'll have 999 thousandths of 999

thousandths of the original.

410

:And so eventually you'll shrink in a

geometric fashion the volume that your

411

:points are contained within.

412

:And...

413

:In doing so, you're walking uphill, you're

moving towards the peak of the posterior.

414

:So, what I have seen to see it is

guaranteed to terminate once you have held

415

:the climb up, which was a nice feature.

416

:And it gives you the evidence for doing

multi -selection.

417

:Once you've done the entire chain, you can

resample those points from the chain and

418

:weight them according to the posterior to

produce either independent samples or

419

:weighted.

420

:posterior samples are to meet.

421

:Yeah, so it's a really effective

algorithm.

422

:I like it because it's reliable.

423

:And as I say, your run is guaranteed to

finish.

424

:It might take a long time, but it will get

there.

425

:There are of course, places where it falls

down.

426

:If you don't have an upline, you can end

up missing a mode.

427

:The challenge is really how do you explore

that constrained prior distribution.

428

:And so over the years, there have been

different approaches to doing that.

429

:The one that I started, I was coding in

Oracle Struct, was using MCMC inside the

430

:nested sampling.

431

:So just do a little MCMC chain to draw the

next sample, which works fine, especially

432

:because we already knew how to do MCMC's

for this problem quite well.

433

:But other people have invented the

ellipsoidal multiness algorithm, was one

434

:of the first very popular.

435

:off -the -shelf solutions and that was

used also for gravitational waves.

436

:These days there are more modern, I

packages that do everything you need,

437

:either with MCMC or with side sampling or

more complicated things like normalizing

438

:flows.

439

:I should mention the Bowman or most of the

gravitational wave using dynasty, which is

440

:next to sampling.

441

:myself and the students, there's no force

with it.

442

:That's the image that connects it

something with artificial intelligence

443

:that attempts to use some machine learning

to accelerate this whole process.

444

:Well, that sounds like fun.

445

:Yeah, I'm definitely going to link to

Genesty.

446

:So the package you're using right now to

do the NST sampling in the show notes and

447

:If you have anything you can share on this

new package you're working on, for sure,

448

:please add that to the channel.

449

:These listeners will be very interested.

450

:And maybe you want to add a bit more about

this project.

451

:So how would you use machine learning in

this way to help you do the nested

452

:sampling?

453

:Yeah, I can say something about that.

454

:It's a cool idea.

455

:I mean, the...

456

:Enabling technology for this is a tool

called the normalizing flow.

457

:And I don't know if you've talked about it

in podcast before, but they have a way of

458

:approximating complicated distributions

using single ones with a remapping of the

459

:coordinate system.

460

:So in that context, we were trying to make

a good fit to the jump proposal for the

461

:sample, if you like, because that has to

evolve.

462

:with the scale of the problem as the

nested sample proceeds.

463

:The mode shrinks and it can shrink by a

factor of 10 to the 20 over the course of

464

:the run.

465

:So you're going to need something adaptive

to continue to have good efficiency.

466

:So we took this normalizing flow technique

and applied it to this problem of fitting

467

:the existing samples.

468

:And then the advantage being that it

allows you to draw independent samples, a

469

:bit like the ellipsoidal.

470

:technique, but it doesn't require a fixed

shape.

471

:So it's able to make more complicated

shapes for distribution.

472

:Yeah, I'll pop the link in and people are

very welcome to give a go.

473

:Yeah, for sure.

474

:Yeah.

475

:So folks give it a go, try it.

476

:If you see issues, report them on the

GitHub, even better.

477

:If you can do a PR, I'm sure John will

appreciate it.

478

:And actually, so that could not be better

because I will refer people to episode 98

479

:of the podcast where I talked with Maridu

Gabriel, who is one of the persons

480

:developing these kinds of methods.

481

:And we talked exactly about that.

482

:Adaptive MCMC augmented with normalizing

flows.

483

:And we...

484

:talked in the episode about how it offers

a powerful approach, especially for

485

:sampling multimodal distributions, how it

also scales the algorithm to higher

486

:dimensions, how you can handle discrete

parameters, and how all these ongoing

487

:challenges in the field.

488

:So if you're interested in the nitty

gritty details of what John just

489

:mentioned, I recommend listening to

episode 98 because, well, Marilou is

490

:really a f***.

491

:One of the persons developing all that

stuff.

492

:Sounds super interesting Alex.

493

:I'm amazed at the power of some of these

new techniques.

494

:There's a revolution going on at the

moment in this area.

495

:It's a good time to be involved.

496

:Yeah, I know for sure.

497

:I will link to that.

498

:Also, Colin Carroll, who is one of the

PIMC developers, he also has a new

499

:package, well, working on a new package

called Biox.

500

:And I know that they implemented these

normalizing flow algorithm.

501

:And so now you can use that in PyMC

directly through BIOX and to use that kind

502

:of algorithm and handle your multi

-dimensional, multi -model distributions

503

:more easily.

504

:So I also link to that because it's

definitely super interesting if you have

505

:lots of weird distributions.

506

:Like that.

507

:And Christopher, to come back to you, you

also mentioned that you guys do population

508

:inferences.

509

:And that's hierarchical models where you

use a bunch of observations to infer the

510

:underlying distribution of the sources of

the signal, if I understood correctly.

511

:So what does that look like?

512

:What do you guys do here?

513

:Yeah, so we do the calculation in a couple

of stages that we always run the parameter

514

:estimation to get the events parameters

for just one signal of time first.

515

:And so the result of that is a set of

posterior samples calculated with a

516

:fiducial prior.

517

:And what we want to do is then divide out

that prior, put in a population model, see

518

:how well that fits.

519

:So calculate the, I guess, the evidence.

520

:under the assumption of a particular set

of hyperparameters.

521

:And then we have an inference one level up

where we vary the population parameters,

522

:the hyperparameters for the population

model, explore that to see what fits work.

523

:So that really is starting to get the

astrophysics.

524

:So looking at the distribution of masses,

are there more low mass black holes and

525

:high mass black holes?

526

:How does that scale?

527

:Is there a little?

528

:bumps in the distribution and things like

that.

529

:So, yeah, it's next level up.

530

:The likelihood isn't quite as expensive as

evaluating the waveforms, but we have some

531

:data handling issues of reading in order

of the posterior samples.

532

:And key to this is, as I alluded to, is

correcting for the selection effects so

533

:that we need to account for the fact that

with our gravitational wave detectors, we

534

:can preferentially see some sources over

other sources.

535

:So if you were just to look at our

536

:distribution of sources that we detect,

you'll see, hey, there are lots of 30

537

:solar mass black holes, there aren't too

many 10 solar mass black holes, and if you

538

:didn't know about our selection effects,

you can actually assume, okay, the

539

:universe is full of 30 solar mass black

holes, and 10 solar mass ones are much

540

:rarer.

541

:Whereas because our detectors are more

sensitive to the high mass signals, those

542

:are intrinsically louder, so we can see

them further away, we can see more of

543

:them.

544

:Once you correct for the selection

effects, you actually see it's the other

545

:way around, there are many more

546

:At least there should be many more 10

solar mass black holes than 30 solar mass

547

:black holes.

548

:And the fact we don't see so many 50 solar

mass black holes, 90 solar mass black

549

:holes, tells you that the distribution

does drop off quite rapidly.

550

:So this is a field that's growing quite

nicely as we get more and more detections.

551

:Your uncertainties on the population

basically go as the square root of the

552

:number of detections.

553

:what we're seeing a lot of work on is what

does one assume for the population model.

554

:So when we started off with, I guess,

following what is common in astronomy, we

555

:put a power law through for the masses,

just infer the power law index basically

556

:in the normalization for the overall rate

and see how that worked.

557

:Then we like that's a bit simplistic.

558

:Let's add in a couple more parameters.

559

:Let's have

560

:say a little peak, a Gaussian add on top

of that to get peak.

561

:Let's say have two parallels with the

break, see how those fit.

562

:Let's put in another peak.

563

:And now people are looking at semi

-parametric models.

564

:So OK, what if we add a spline on top of

that?

565

:See how we can vary that.

566

:Or what if we do something really

flexible, so allow a bunch of kernels to

567

:come together and further the population

to get out of there?

568

:So a lot of.

569

:A lot of the work at the moment is trying

to see what is a good fit for the data and

570

:then checking is this overly complex?

571

:Are we overfitting?

572

:Is there a little bump there?

573

:Is that just because of a pass on

fluctuation that we've only seen so many

574

:events?

575

:So a small number of statistics means

there's a few more here and a few fewer

576

:there.

577

:Or is there actually some feature of the

underlying population, which may be a hint

578

:to how stars are formed?

579

:I think it's quite an interesting time at

the moment from this testing out models,

580

:trying to determine do they fit the

observations quite well.

581

:And I'm very excited for getting the

results of our upcoming observing runs

582

:when we're having a much larger number of

detections and we'll really be able to

583

:constrain the models to higher accuracy

and precision.

584

:Yeah, so that's super interesting.

585

:And so here to understand what you're

doing, it's like your...

586

:hearing different sounds and you're trying

to infer not really what the sound is

587

:about, but what is emitting that sound?

588

:What is the source of that sound?

589

:And the issue is that these sounds can be

emitted by a lot of entities and a lot of

590

:these sources you don't really care about

because I know they are on earth, they are

591

:like, but what you're interested in are

the sources.

592

:outside, which are in space and which tell

you something about the universe, which

593

:here would be mainly neutron stars and

black holes colliding.

594

:How weird was that characterization?

595

:Yes, I guess maybe a nice analogy might

be, imagine you have a room full of people

596

:and you're trying to judge the composition

of the room.

597

:And some of the people there, you have a

bunch of librarians who are very quiet.

598

:And you have some heavy metal stars who

are very, very loud.

599

:And so you've made your recording of the

audio in the room, and then you need to

600

:try and reconstruct that.

601

:OK, I can only hear one librarian.

602

:But given that the librarians are very

quiet, there's probably a whole host of

603

:other librarians who I just missed because

they're being too quiet.

604

:and I can hear lots of electric guitars

going on, so I know there's some rock

605

:stars here, but I know they're very loud

and easy.

606

:I probably will have detected 100 % of

those, so correct for those bias from the

607

:detection.

608

:We're very fortunate actually in

gravitational wave detection that we can

609

:calculate our selection effects.

610

:It's quite easy for us to determine what

sources we can detect and what we can't.

611

:This is a standing problem in astronomy

that you're

612

:We only have one universe, so we need to

make sure we understand what we're seeing.

613

:And you can know what you detect, but it's

very hard to know what you're not

614

:detecting.

615

:So a lot of astronomy is trying to correct

for these.

616

:And if you have a telescope, that can be

very difficult because you've got to

617

:calculate, OK, not just what did I see,

but what could I have seen?

618

:So that would depend on where I was

pointing the telescope.

619

:It would depend on the weather on a

particular day and how cloudy it was.

620

:Whereas with our gravitational wave, it's

much simpler.

621

:What we do is we can inject the

terminology we use.

622

:We simulate signals, put those into our

data, run our detection pipelines on that,

623

:and see what fraction of the signals that

we injected would we recovered and from

624

:that work out.

625

:As a function of source parameters, what

was the probability that something was

626

:detected?

627

:And then use that in renormalizing our

likelihood to establish.

628

:Okay, how many of these sources should

have there have been given that we saw

629

:this money?

630

:Okay, it helps a lot that gravitational

waves are not blocked by anything in the

631

:universe that we know about except for

other black holes But even then other

632

:black holes tend to be very small So when

we are able to calculate exactly what the

633

:source is doing it means that we've got a

very good idea of what we will see.

634

:It doesn't really matter what's in the

entropy space.

635

:The two veins of astronomy are dust and

magnetic fields, and gravitational waves

636

:are just don't really care about any of

those two things.

637

:Yeah, okay.

638

:I see.

639

:And that's actually a good thing.

640

:Indeed, that's quite a luxury to be able

to compute your own selection bias.

641

:That's pretty amazing.

642

:Me, who've done a lot of political

science, you usually cannot do that, so

643

:I'm very jealous.

644

:And can you tell us actually where does

that noise come from?

645

:Because it seems like you're saying there

is a lot of noise in your observations.

646

:Thankfully, you are able to tame that

somewhat easily.

647

:Can you tell us a bit more about that?

648

:And John, it seems like you want to add

something about that.

649

:Most of the noise, all the noise is not of

extraterrestrial origin.

650

:It's coming from the detectors and coming

from the environment around the detectors.

651

:So in order to understand that you have to

know a little bit about how to light over

652

:a porp.

653

:So imagine a giant in all shape, four

kilometres long, in bits of light, with

654

:the letters at the ends of the arms

shining a laser into the coin, if like.

655

:It gets split into two and sent down both

arms, bounces off them into the end and

656

:then comes down.

657

:and if they aren't the same length then

the light will constructively interfere or

658

:destructively, I may have that wrongly

written.

659

:The point is if they aren't at different

lengths or if they're changing lengths

660

:then the pattern of the light that comes

out will change over time.

661

:So we are really worried about anything

that can change that output of the laser

662

:in the detector.

663

:And so that could be due to the laser

itself.

664

:All lasers have some noise in them.

665

:So the lasers that they use in these

detectors are some of the most stable

666

:lasers that you can use.

667

:have been invented from scratch basically

for this one.

668

:It could be the thermal motion of the

atoms in the matrix of the complex.

669

:It would be better in that, simply having

a wide enough laser beam approaching the

670

:whole surface of the metal, cancelling out

the mean motion to the low enough level to

671

:get it ready.

672

:But the laser also

673

:You know, there's energy and that energy

fishes on the mirrors of radiation, which

674

:causes the mirrors to move a little bit.

675

:And now, think about the algorithms, the

laser energy is carried by photons, which

676

:are ultimately quantum objects, so they

get off the radar distinctly.

677

:Kind of raindrops on the roof, if you

imagine, or if you're in a tent, you get

678

:raindrops of rain.

679

:That's kind of what it's like.

680

:The lasers are enormously hard.

681

:still they are made of individual photons.

682

:And so there's a shot noise associated

with them, just due to the statistical

683

:fluctuation in the number of photons that

are writing per second.

684

:Then we've got the environment as well,

which is especially dominant at low

685

:frequencies.

686

:So we can't sense anything below about 10

Hertz with these detectors that are above

687

:the ground.

688

:because of seismic motion.

689

:Now we do have a lot of techniques to try

and screen the mirrors out in the motion

690

:of the Earth.

691

:They're hung on suspended optics, which

act as a natural filter to prevent ground

692

:motion from propagating through to the

mirror.

693

:But even so, we need to have active

oscillation systems as well.

694

:And on top of all of that, even if you

manage to screen out all the mechanical

695

:coupling,

696

:There's unfortunately the gravitational

coupling that we can't spin out because we

697

:actually want to measure gravity in the

first place.

698

:So if you imagine a seismic wave as a

pressure wave in the rock, I mean, when

699

:pressure is high, the rock is actually

compressed slightly.

700

:And because it's compressed, it's denser

than average.

701

:And because it's denser than average, it

exerts a gravitational pull on the mirrors

702

:that tends to pull them along.

703

:with the seismic waves.

704

:So this tiny effect, I mean, you've

probably never even thought about it, but

705

:it's there as a small gravitational

coupling of seismic waves to the detector.

706

:And you can't really get around these

things tall on the earth.

707

:And so that's why one of the challenges

that we're working on at the moment is

708

:looking at sending a detector into space,

which is hopefully going to open up a

709

:whole new range of...

710

:objects for us to look at.

711

:Yeah, thanks a lot, That's definitely

clear, and I didn't have, indeed, any idea

712

:of all these sources of noise, which is

pretty incredible that we're able to

713

:filter that out, knowing that already the

signals you're looking at are already so

714

:weak.

715

:So it feels pretty incredible to still be

able to do it, even though the signals are

716

:weak.

717

:and the result of noise.

718

:It's really amazing the technology that is

required to do these experiments has been

719

:developed decades and decades for people

to develop it and almost all aspects of

720

:the detectors have to be invented for that

purpose.

721

:There's very little off -the -shelf

technology and of course the spinoffs from

722

:that then taken up in other areas but it's

the pure science that was driving the

723

:development of the law.

724

:Yeah, exactly.

725

:It's like, it's not even as if the all the

engineering of these was already available

726

:and you could just go on Amazon and buy

it, right?

727

:You have like everything has to be

developed custom for these and you don't

728

:even know if that's going to work before

you actually try it out.

729

:So that's like all these endeavors are

absolutely incredible.

730

:And so that makes me think and I think on

these Christopher, you will have stuff to

731

:add.

732

:Because, so if I understood correctly, all

these detectors that we have right now are

733

:on Earth.

734

:These gravitational waves detectors.

735

:Hopefully, we'll be able to do a video

documentary on Learned Bay stats in one of

736

:these detectors.

737

:It's just some of the backstage I'm

telling to the listeners.

738

:We'll see if that's possible.

739

:But, so these detectors are on Earth.

740

:If you go to space and were able to put

one of these detectors around the earth or

741

:I don't know, in space floating somewhere,

I'm guessing that solves these problems,

742

:even though there are other sources of

issues if you do that in space.

743

:But if I understood correctly, the LISA

mission is space -based.

744

:And so is that a way of doing that?

745

:Can you tell us a bit more about that?

746

:Christopher and...

747

:Yeah, mainly tell us what the discoveries

will be with that.

748

:Also the data analysis problems that will

engender, especially when it comes to the

749

:size of the data, I'm guessing.

750

:Yeah.

751

:So Lisa's Space Space Gravitational Wave

mission, it's led by the European Space

752

:Agency with NASA as a junior partner

there.

753

:And the idea is we...

754

:launch a constellation of satellites, so

three satellites that will orbit around

755

:the Sun lagging behind the Earth in a

triangular formation and we bounce the

756

:lasers between them to make the same sort

of measurements that we do for

757

:gravitational waves but over a much larger

scale, so really massive arms.

758

:So this is great because we can avoid the

ground -based noise that John mentioned

759

:and this

760

:is really good.

761

:So for Lisa, we're not trying to see

exactly the same sources as with our

762

:ground -based detectors, but we're trying

to look for lower frequencies.

763

:So one of the things we've learned in

astronomy over the last century or so is

764

:that each time you're observing the

universe in a new way, you discover new

765

:things.

766

:So we want to look at a different part of

the spectrum of gravitational waves.

767

:So Lisa's most sensitive is the millihertz

range, so much lower frequencies.

768

:And a much lower frequency gravitational

wave,

769

:corresponds to a bigger source.

770

:So these could be the same type of binary,

but just much further apart in that orbit,

771

:so much earlier before they come in and

merge much further apart.

772

:Or we could be looking at much more

massive objects, so massive black holes.

773

:We believe at the center of every galaxy

is a massive black hole.

774

:Our own galaxy has one about four million

solar masses, four million times the mass

775

:of our sun.

776

:And we think galaxies merge, and so the

massive black hole should merge.

777

:And so we'd be able to see these out to a

much greater distance.

778

:So Lisa's objective is to see what we can

observe in the gravitational wave sky at

779

:these much lower frequencies.

780

:And there's a whole host of different

sources.

781

:So these massive black hole mergers we

should be able to see out across the

782

:entire history of the universe.

783

:We should be able to see regular stellar

mass black holes.

784

:So black holes formed from.

785

:stars at the end of their lives spiraling

into these supermassive black holes.

786

:It's a topic I've studied quite a lot.

787

:Those signals are extremely complicated.

788

:The orbits they undergo are very

intricate, which is great if we observe

789

:one because we can measure the parameters

to tiny, tiny precision, to one part in a

790

:million, something like that.

791

:But it's a huge pain from a data analysis

point of view because you've got to find

792

:the part of parameter space where this is.

793

:And we're also going to see

794

:huge numbers of binaries in our own galaxy

of white dwarfs, maybe neutron -style

795

:white dwarfs, so the wide binaries here.

796

:And so the real data analysis problem for

LISA will be how to fit all of this

797

:information all at once, because with our

ground -based detectors, at least at the

798

:moment, we basically just see here's a

signal and then here's another signal.

799

:So you can analyze each signal in

isolation.

800

:With Lisa, you cannot you see everything

all at time.

801

:Some of these lights, they don't

supermassive black hole mergers might be

802

:quite short to compare to place a

localized in time, but they will still be

803

:overlapping these long lives.

804

:So the the in spiraling objects or the

very wide bindings will basically be there

805

:for the entire mission or a large fraction

of the mission.

806

:So to analyze the data, you need to fit

everything or this is what we call a

807

:global fit problem.

808

:And you

809

:So you potentially have hundreds of

thousands of sources, each with a dozen

810

:parameters or so, maybe less than simpler

sources.

811

:But you've got to do all of these all at

the same time.

812

:And it potentially does matter how you do

this, because things like the massive

813

:black hole binaries are extremely loud, so

signal -to -noise ratios of thousands.

814

:So if you get that wrong by just a little

percentage,

815

:residual power in your data stream would

be enough to bias your measurements of the

816

:quieter signals underneath.

817

:So this is a huge, I think possibly the

most complicated data analysis problem in

818

:astronomy and we're just starting to

figure out how we're going to tackle this.

819

:So yeah, space -based detectors I think

extremely exciting, a whole host of new

820

:sources that we can see, a new host of

astrophysics that we can unlock through

821

:these observations, but also

822

:some extremely complicated data analysis

challenges that need to be tackled and

823

:solved before the mission launches in the

:

824

:And what's the timeline on this mission?

825

:Are we close to launch?

826

:Where are things right now?

827

:So just in the last couple of months, the

mission was approved by ESA.

828

:So that's them looking at the designs and

going, OK, we think we can build this.

829

:And now the serious work on putting it

together comes.

830

:So it's due to launch in the 2030s,

exactly when that be, I'm sure.

831

:People are very confident on when it will

be, but we know space -based missions are

832

:hard.

833

:So it might, maybe, maybe it's a little

early to say exactly what date it will

834

:launch.

835

:But it will go up and then there'll be a

little period of commissioning and then it

836

:will start observing.

837

:So in the late 2030s, we should hopefully

get the observations from that.

838

:So the current timeline, 2035 for launch,

which I guess is...

839

:Good news to any of your listeners who are

inspired by the problems that we're

840

:talking about and think this is really

cool and think that maybe they'd like to

841

:tackle these problems.

842

:There's certainly enough time to go out,

get a degree, start a PhD in the field

843

:before we get the real data.

844

:Yeah, for sure.

845

:Exactly.

846

:And also, historically, these kind of huge

missions tend to take a bit of delay.

847

:So, you know, like...

848

:You can start your PhD on this.

849

:I mean, that's better to launch later than

to launch on time, but have a mission that

850

:fails, right?

851

:Yes.

852

:We're talking a billion euro cost of these

things.

853

:So you definitely don't want to explode on

the launch pad.

854

:Exactly.

855

:Way better to take a few more months and

do some double checks than just launch

856

:because we said we would launch on that

arbitrary date.

857

:Yeah, the space agencies do take these

things.

858

:It's been fascinating seeing the order,

the things that needed to be rubber

859

:stamped to get the approval for the

mission.

860

:So very good work people getting that

done.

861

:So there are also other proposed space

-based missions, some potential ones in

862

:China.

863

:There's a potential follow -up mission, I

guess, slightly in the future, maybe in

864

:Japan that's been proposed for a few

years.

865

:status of these, I guess, it's difficult

getting the funding for these things.

866

:So I think it's an exciting time in the

field.

867

:Hopefully we'll expand the range of

gravitational waves we can detect and

868

:that'll be great.

869

:Yeah, yeah, for sure.

870

:And I mean, that must be...

871

:So I don't know how directly involved you

are on these, Lounch, but I'm guessing

872

:that if you're still working on these

when...

873

:the mission launches, I'm pretty sure the

day of the launch, you will be pretty

874

:nervous and excited.

875

:Have you already lived that actually, or

would that be new to you?

876

:So I mean, the closest analogy would have

been there was a technology mission to

877

:test some of the key components of Lisa

called Lisa Pathfinder that went up a few

878

:years ago, an extremely successful

mission.

879

:And so watching that from the sidelines,

my PhD was on LISA.

880

:If this mission didn't work, then there'd

be no LISA mission.

881

:So all my PhD work would be in vain.

882

:But thankfully, it worked very well and

worked better than what was hoped for, in

883

:fact.

884

:So that was great.

885

:And I guess that's a real testament to the

experiment, as saying I was feeling

886

:worried because it was my PhD work.

887

:But there really people in the field who

have spent their entire careers working on

888

:this technology, you know, multiple

decades.

889

:So it's all.

890

:Yeah, real testament to their

determination, I guess, their vision going

891

:into a field right at the beginning before

anything worked to look at these things.

892

:It's also honestly quite remarkable that

we somehow managed to convince the funding

893

:agencies to fund these things for so long

before there would be scientific returns.

894

:So, yeah, we're extremely grateful that

they had the forethought and the patience

895

:to invest in something so long before it

would give returns.

896

:Yeah, definitely.

897

:Yeah, that must be absolutely fascinating.

898

:John, anything you want to add on that?

899

:I think Christopher is doing a great

overview of WISA, which indeed will be an

900

:enormous challenge on the ground.

901

:There are also plans to take things

forward into the:

902

:Currently, there are two major...

903

:detectors in the kind of scoping design

stage.

904

:One is led by the Europeans called the

Einstein Telescope and the other one is

905

:led by the US called Cosmic Explorer.

906

:They're taking different approaches.

907

:They're both going by detectors.

908

:The challenge there is to lower the noise

floor.

909

:So giving them a sort of order of

magnitude improvement in the range that

910

:you can see things to, which translates to

911

:thousand -fold increase in the volume that

you can see things to, more or less.

912

:At these kinds of distances, you do

actually have to worry about the size of

913

:the universe, getting in the way of these

calculations.

914

:But yeah, these new experiments will

require a new infrastructure.

915

:So they're also going to require a new

batch of experiments from national,

916

:indeed, European land.

917

:best friend.

918

:A lot of the data analysis challenges for

those are kind of similar to the ones that

919

:we're tackling with the current generation

of ground -based detectors.

920

:But the major difference is that the

signals would be much longer because the

921

:low frequency end is really the target for

improvement.

922

:I think that's the way that the binaries

chop.

923

:I mean, okay, I told you that they sort of

make this characteristic, whoop, type

924

:noise.

925

:Maybe you can find a sample.

926

:and pluck out my pale imitation.

927

:The lower in frequency you start, the

longer the signal will be.

928

:That multiplies the amount of data that

you have to analyze, which with a Bayesian

929

:problem can be a bit challenging.

930

:If you're doing many millions of light

-weighting evaluations, you don't want

931

:each light -weighting evaluation to be

expensive.

932

:And also the signal -to -noise ratio will

be huge.

933

:Least effects are 10 higher.

934

:So you will run into problems with our

uncertainties on the nature of the

935

:sources.

936

:So the models that we have are very good

theoretical models at the moment and

937

:they're good enough for the current

generation of detectors, but they will

938

:break down once observations become good

enough.

939

:They will probably show the crops in

theories, which I should say is probably

940

:not a fundamental part in the theory.

941

:I think most people probably would put

their money on general relativity being

942

:correct.

943

:The problem is that there is a translation

layer between general relativity and the

944

:types of temperament we can use it that

requires approximations and shortcuts and

945

:models to be created.

946

:So there's challenges with modeling and

balance that are quite difficult to

947

:overcome and people are searching that as

well at the moment.

948

:Yeah, fantastic.

949

:Thanks a lot, guys.

950

:That's really fantastic to have all these

overviews of the missions.

951

:And actually, I'm wondering, so with all

that work that you've been doing, all

952

:these studies that you've been talking

about since we started recording, we've

953

:been able to study actually what

954

:we want to do, right?

955

:So study the astrophysics of black holes

and also some tests of general relativity,

956

:as you were saying, Christopher.

957

:Can you tell us about that and mainly what

are the current frontiers on those fronts?

958

:What are we trying to learn with the

current missions?

959

:That's a big question.

960

:So general relativity, I guess, we really

want to find somewhere where it doesn't

961

:work.

962

:So for the point of view of understanding

gravity, there's this tension within

963

:physics that how do you reconcile general

relativity with quantum theory?

964

:And that is rather tricky and the whole

host of different theoretical frameworks

965

:to try and reconcile this.

966

:But we don't know for certain what the

answer is.

967

:And finding some hint where general

relativity breaks down would give a

968

:pointer in the right direction.

969

:Of course, finding a place where general

relativity breaks down is very difficult.

970

:The place where I think it makes sense to

look most is the most extreme environment.

971

:So where is gravity strongest?

972

:Where is the spacetime most dynamical?

973

:Where do things change the quickest?

974

:So black hole mergers, I think, are

really, and the gravitational wave

975

:signals, they admit, are the

976

:best place to look for that.

977

:So that's why we're looking there.

978

:And what we'd really love to find is some

deviation from general relativity that we

979

:could actually be certain is a deviation

from general relativity and not just a

980

:noise artifact.

981

:So I think we're pursuing a whole host of

different things to look for deviations

982

:there.

983

:On the astrophysics point of view, there's

just so much we don't know about the

984

:progenitors of these sources.

985

:So how do

986

:we end up with black holes and neutron

stars.

987

:So stars are pretty important in

astronomy.

988

:Exactly how they work is kind of

complicated.

989

:So there's a lot of uncertainties in that.

990

:And I think it's really quite remarkable

how rapidly the field has progressed.

991

:So back in 2015, before we made our first

detection, it wasn't at all certain that

992

:we would find pairs of black holes

orbiting each other and merging.

993

:We knew there would be neutron stars.

994

:But we didn't know they're black holes

because we'd never seen them.

995

:They're really hard to see other than

gravitational waves.

996

:That's kind of why we built the

gravitational wave detectors.

997

:But we hadn't seen any of them.

998

:So our first detection confirmed, yes,

they exist.

999

:And they exist in sufficient numbers that

we can actually detect them.

:

01:04:51,069 --> 01:04:53,909

And then the follow up was when we

measured the masses, they were about 30

:

01:04:53,909 --> 01:04:55,409

times the mass of our sun.

:

01:04:55,409 --> 01:04:58,329

We'd never seen black holes in that mass

range before.

:

01:04:59,249 --> 01:05:01,529

We now know, yep, there's quite a few of

them.

:

01:05:01,529 --> 01:05:04,045

But whether you can form black holes that

big,

:

01:05:04,045 --> 01:05:07,685

tells you something about the way that

stars live, how much mass they lose

:

01:05:07,685 --> 01:05:09,365

through their lifetime.

:

01:05:09,425 --> 01:05:13,905

So that's a key uncertainty that we don't

really understand about how stars evolve.

:

01:05:14,005 --> 01:05:18,805

So now, as we're building up statistics,

really teasing out the details of the mass

:

01:05:18,805 --> 01:05:21,665

distribution, what is the biggest black

hole that you can build?

:

01:05:21,805 --> 01:05:25,925

Currently, we know there are these black

holes that form from stars collapsing.

:

01:05:26,065 --> 01:05:32,065

And we know there are these massive stars,

massive black holes, millions of solar

:

01:05:32,065 --> 01:05:32,945

masses.

:

01:05:33,215 --> 01:05:36,185

lightest ones, hundreds of thousands, tens

of thousands.

:

01:05:36,185 --> 01:05:39,965

But we don't know, is there a continuous

distribution of black holes in between?

:

01:05:39,965 --> 01:05:42,725

So are there hundreds of thousands of mass

black holes?

:

01:05:42,725 --> 01:05:44,485

So that's one of the key things to figure

out.

:

01:05:44,485 --> 01:05:45,585

Is there a key thing?

:

01:05:45,585 --> 01:05:49,025

Where do these big, really big, massive

black holes come from?

:

01:05:49,725 --> 01:05:51,825

And how do stars evolve?

:

01:05:51,825 --> 01:05:55,815

The details of all the different ways that

you could end up with massive black holes

:

01:05:55,815 --> 01:05:57,085

that people theorized?

:

01:05:57,085 --> 01:05:58,305

Which ones are correct?

:

01:05:58,305 --> 01:06:00,905

In what ratio out there?

:

01:06:01,165 --> 01:06:02,733

And then I guess one...

:

01:06:02,733 --> 01:06:07,023

One additional key thing, we talked about

black holes in nature gravity.

:

01:06:07,023 --> 01:06:09,773

We've talked about how you form black

holes in neutron stars.

:

01:06:10,253 --> 01:06:13,533

But there's also what neutron stars are

really made of.

:

01:06:13,953 --> 01:06:18,613

So neutron stars, from the name you might

suggest, OK, they're made of very neutron

:

01:06:18,613 --> 01:06:19,773

-rich matter.

:

01:06:19,833 --> 01:06:23,933

But actually, what happens inside the core

of a neutron star, we get a whole host of

:

01:06:23,933 --> 01:06:28,653

different phase changes, really quite

exotic matter going on that we can't hope

:

01:06:28,653 --> 01:06:30,363

to replicate in the lab here on Earth.

:

01:06:30,363 --> 01:06:31,897

So we really don't know.

:

01:06:32,203 --> 01:06:33,083

this behaves.

:

01:06:33,083 --> 01:06:37,033

If we did, that would be really

informative for understanding the dynamics

:

01:06:37,033 --> 01:06:39,053

of the particles that make those.

:

01:06:39,053 --> 01:06:43,633

So by making measurements of the neutron

stars we observe, how much they stretch

:

01:06:43,633 --> 01:06:48,123

and squeeze, we can hopefully get some

constraints on what neutron stars are made

:

01:06:48,123 --> 01:06:52,073

of, which would be an exciting frontier

there.

:

01:06:53,533 --> 01:06:54,393

John?

:

01:06:55,353 --> 01:07:00,603

One thing that I think we can zoom out

from looking at the individual black holes

:

01:07:00,603 --> 01:07:02,275

and neutron stars and

:

01:07:03,213 --> 01:07:08,313

Still with the theme of trying to

understand gravity is on the other scale

:

01:07:08,313 --> 01:07:15,443

is cosmology, the very, very largest

scales, how is the universe evolving over

:

01:07:15,443 --> 01:07:16,453

time?

:

01:07:17,833 --> 01:07:23,393

Hopefully with the current generation and

the next generation, we'll be able to do

:

01:07:23,393 --> 01:07:28,333

cosmology in a completely different way

than what we have done up until now.

:

01:07:28,333 --> 01:07:32,013

By looking at the gravitational wave

signal, so those...

:

01:07:32,013 --> 01:07:37,193

properties of those signals, the fact that

we know exactly what they look like, their

:

01:07:37,193 --> 01:07:41,873

amplitude and how it would case with

distance means that they can be used as an

:

01:07:41,873 --> 01:07:43,613

independent co -coxmology.

:

01:07:43,613 --> 01:07:48,923

Now we've already done this with the

prying intrastar signal and with black

:

01:07:48,923 --> 01:07:53,843

holes that we've seen up to now,

relatively low numbers of sources such

:

01:07:53,843 --> 01:07:58,863

that the constraints that we're able to

cook are not yet competitive with the best

:

01:07:58,863 --> 01:08:01,753

constraints that we can get from other

techniques.

:

01:08:01,933 --> 01:08:06,313

But going forward, as the numbers improve,

as the SNRs and the applies ratio

:

01:08:06,313 --> 01:08:09,593

improves, this is going to get better and

better over time.

:

01:08:09,593 --> 01:08:14,833

And so even if we don't see anything on

the scale of the individual black holes,

:

01:08:14,833 --> 01:08:20,563

if this agrees with general relativity, it

could still help us en masse to pin down

:

01:08:20,563 --> 01:08:24,563

what's going on with cosmology, where

there are many things that we don't

:

01:08:24,563 --> 01:08:29,253

understand, including discrepancies in the

existing constraints we have.

:

01:08:31,757 --> 01:08:32,897

No one.

:

01:08:36,333 --> 01:08:44,203

And I'm curious, among all of these

burning issues, burning questions, if you

:

01:08:44,203 --> 01:08:49,493

could choose one that you're sure you're

going to get the answer to before you die,

:

01:08:49,493 --> 01:08:50,693

what would it be?

:

01:08:55,821 --> 01:09:00,421

I don't know how long I'm going to live,

but the thing that really motivates me is

:

01:09:00,421 --> 01:09:05,201

trying to understand whether the black

holes that we're seeing really are the

:

01:09:05,201 --> 01:09:08,661

things that you can write down with pencil

and paper when you're teaching people

:

01:09:08,661 --> 01:09:13,101

general relativity, or are they more

complicated than that in reality?

:

01:09:13,261 --> 01:09:17,781

I think if there was one problem I have to

choose in this field, that would be the

:

01:09:17,781 --> 01:09:19,981

one that I found the most interesting.

:

01:09:20,761 --> 01:09:24,907

I think I'd really like to know the answer

to that one as well.

:

01:09:24,941 --> 01:09:28,951

I think that might be one of the most

challenging to actually get the solution

:

01:09:28,951 --> 01:09:30,001

to.

:

01:09:30,441 --> 01:09:33,881

The best way to answer it might be to

travel into a black hole.

:

01:09:33,901 --> 01:09:38,741

But then the question of whether you

observe anything before you die becomes

:

01:09:38,741 --> 01:09:40,221

rather technical.

:

01:09:40,441 --> 01:09:41,361

Yeah.

:

01:09:41,821 --> 01:09:46,901

Certainly something not advised for your

listeners to give that a go.

:

01:09:46,901 --> 01:09:53,357

Yeah, I am not sure it would end up like

Matthew McConaughey in The

:

01:09:53,357 --> 01:09:54,237

What's the movie?

:

01:09:54,237 --> 01:09:55,437

You know that?

:

01:09:55,437 --> 01:09:56,657

Interstellar.

:

01:09:56,657 --> 01:10:01,097

So Kip Thorne is one of the founders of

LIGO.

:

01:10:01,097 --> 01:10:06,397

One of the recipients of the Nobel Prize

for Gravitational Analytics.

:

01:10:06,397 --> 01:10:08,717

He's behind Interstellar.

:

01:10:08,897 --> 01:10:10,857

So he advised on a lot of it.

:

01:10:10,857 --> 01:10:16,737

Yeah, the bit at the end is not backed up

by science.

:

01:10:18,297 --> 01:10:18,957

For sure.

:

01:10:18,957 --> 01:10:20,237

At least for now.

:

01:10:21,005 --> 01:10:26,385

They originally were going to have the

wormhole thing that opens up in

:

01:10:26,385 --> 01:10:26,605

Interstellar.

:

01:10:26,605 --> 01:10:29,505

They're going to have that detected with

gravitational waves at LIGO.

:

01:10:29,505 --> 01:10:32,165

Unfortunately, Christopher Nolan cut that

bit.

:

01:10:32,345 --> 01:10:33,075

Oh, that's a shame.

:

01:10:33,075 --> 01:10:34,625

It wasn't in the film.

:

01:10:35,185 --> 01:10:40,625

Maybe that would be for Interstellar 2.

:

01:10:40,625 --> 01:10:41,805

We don't know.

:

01:10:43,005 --> 01:10:44,415

So guys, thanks a lot.

:

01:10:44,415 --> 01:10:46,765

I've already taken a lot of your time.

:

01:10:47,085 --> 01:10:50,207

And I still have a good talk for you.

:

01:10:50,207 --> 01:10:54,817

hours because this is really really

fascinating but it's time to call it a

:

01:10:54,817 --> 01:11:00,147

show before that though as usual i'm gonna

ask you the the two questions i ask every

:

01:11:00,147 --> 01:11:05,517

guest at the end of the show first one if

you had unlimited time and resources which

:

01:11:05,517 --> 01:11:09,963

problem would you try to solve um who

wants to start

:

01:11:13,261 --> 01:11:20,981

I think if you're really serious about the

unlimited time resources, then the most

:

01:11:20,981 --> 01:11:25,791

pressing problem I think would be nothing

to do with adaptation waves, but it's more

:

01:11:25,791 --> 01:11:28,321

to do with the climate breakdown.

:

01:11:28,341 --> 01:11:34,477

So if you want an honest answer, that's my

answer, is solve climate change.

:

01:11:35,981 --> 01:11:38,401

That's a very popular answer.

:

01:11:38,941 --> 01:11:41,441

Get nuclear fusion working.

:

01:11:41,601 --> 01:11:44,381

That would be very nice.

:

01:11:45,001 --> 01:11:51,061

In our field with infinite resources, I

tackle the quantum theory of gravity and

:

01:11:51,061 --> 01:11:53,061

get the evidence for that.

:

01:11:53,061 --> 01:11:55,141

Would be nice.

:

01:11:56,461 --> 01:11:58,561

Yeah, definitely.

:

01:11:58,601 --> 01:12:02,341

That is a great answer.

:

01:12:02,341 --> 01:12:05,293

And I think also some people answered

that.

:

01:12:05,293 --> 01:12:08,433

So you're in good company, Christophe.

:

01:12:08,513 --> 01:12:13,833

And second question, if you could have

dinner with any great scientific mind

:

01:12:13,833 --> 01:12:17,509

dead, alive or fictional, who would it be?

:

01:12:20,887 --> 01:12:28,717

Maybe Chris, the only answer for, uh,

dead, I think for this podcast, and James

:

01:12:28,717 --> 01:12:29,897

would be my choice.

:

01:12:29,897 --> 01:12:32,257

You may know him if you're a Bayesian.

:

01:12:32,257 --> 01:12:32,877

Yeah.

:

01:12:32,877 --> 01:12:35,737

Um, I think he would be very good dinner

company.

:

01:12:35,957 --> 01:12:41,057

Um, his textbook was one of the formative

influences on me as a young Bayesian.

:

01:12:41,057 --> 01:12:41,977

Yeah.

:

01:12:41,997 --> 01:12:42,477

Yeah.

:

01:12:42,477 --> 01:12:43,417

Yeah, for sure.

:

01:12:43,417 --> 01:12:49,117

And, uh, there is a, there is a really

great, uh, YouTube.

:

01:12:49,117 --> 01:12:55,017

series playlist by Aubrey Clayton, who was

here on episode 51.

:

01:12:55,017 --> 01:13:00,827

So Aubrey Clayton wrote a book called

Bernoulli's Fallacy, The Crisis of Modern

:

01:13:00,827 --> 01:13:01,837

Science.

:

01:13:01,957 --> 01:13:02,957

Really interesting book.

:

01:13:02,957 --> 01:13:07,657

I'll link to the episode and also to his

YouTube series where he goes through E .T.

:

01:13:07,657 --> 01:13:11,417

Jane's book, Probability Theory, I think

it's called.

:

01:13:12,397 --> 01:13:17,807

which is a really great book, also really

well written and already goes through its

:

01:13:17,807 --> 01:13:22,987

chapters and explain the different ideas

and so on.

:

01:13:22,987 --> 01:13:27,947

So that's also a very fun YouTube playlist

if you want I'm definitely going to go and

:

01:13:27,947 --> 01:13:29,177

look that up.

:

01:13:29,177 --> 01:13:30,097

Awesome, yeah.

:

01:13:30,097 --> 01:13:31,877

I'll send that your way.

:

01:13:32,417 --> 01:13:32,957

And Christopher?

:

01:13:32,957 --> 01:13:35,217

One of my favorite books, yeah.

:

01:13:36,717 --> 01:13:42,317

I don't know, I think I might be somewhat

boring and just go for Einstein for the...

:

01:13:42,317 --> 01:13:46,037

of both gravity, I think he'd like to know

what we're up to.

:

01:13:46,037 --> 01:13:51,357

And also just to see what, you know, his

thoughts were being about being such a

:

01:13:51,357 --> 01:13:57,157

public intellectual and what it was like

being that would be being cool.

:

01:13:57,157 --> 01:14:00,557

I could invite a guest might be

interesting to get Newton along as well,

:

01:14:00,557 --> 01:14:02,097

and see what they think about gravity.

:

01:14:02,097 --> 01:14:07,837

But I think that would be quite awkward in

a conversation, I get the feeling, not the

:

01:14:07,837 --> 01:14:11,769

socially the most interactive.

:

01:14:12,525 --> 01:14:13,925

Yeah, yeah.

:

01:14:14,345 --> 01:14:20,435

Do you think Einstein would accept at that

point the, like all the advances in, like

:

01:14:20,435 --> 01:14:25,895

all the ramifications of actually general

relativity and so on and the crazy

:

01:14:25,895 --> 01:14:30,805

predictions that that was making and in

the end, most of them, like for now, at

:

01:14:30,805 --> 01:14:36,105

least were true, but at the end of his

career, he was not really accepting that.

:

01:14:36,105 --> 01:14:38,313

Do you think he would accept that now?

:

01:14:39,629 --> 01:14:43,989

I think he would accept the general

relativity and he would be delighted to

:

01:14:43,989 --> 01:14:49,049

find that we've seen some of the effects

that he never thought he observed.

:

01:14:50,669 --> 01:14:55,889

And again, he himself knew the general

relativity couldn't be the final answer to

:

01:14:55,889 --> 01:14:57,749

the correction of gravity.

:

01:14:57,929 --> 01:15:02,629

So he'd probably also be interested to

know how we've seen any signs of it

:

01:15:02,629 --> 01:15:03,319

breaking down.

:

01:15:03,319 --> 01:15:06,949

And I think the stuff that motivated him

towards the end of his career is

:

01:15:06,949 --> 01:15:07,725

probably...

:

01:15:07,725 --> 01:15:10,185

still what's motivating a lot of people.

:

01:15:15,085 --> 01:15:23,025

Well, if you are invited to such a dinner,

please let me know and I will gladly come.

:

01:15:24,585 --> 01:15:25,585

Awesome guys.

:

01:15:25,585 --> 01:15:28,135

I think it's time to call it a show.

:

01:15:28,135 --> 01:15:29,675

You've been wonderful.

:

01:15:29,675 --> 01:15:32,005

Thanks a lot for taking so much time.

:

01:15:32,005 --> 01:15:37,405

As usual, I will put resources and a link

to your websites in the show notes for

:

01:15:37,405 --> 01:15:38,861

those who want to dig deeper.

:

01:15:38,861 --> 01:15:42,801

The show notes are huge for this episode,

I can already warn listeners.

:

01:15:43,101 --> 01:15:45,781

So lots of things to look at.

:

01:15:45,781 --> 01:15:50,411

And well, thank you again, Chris and John

for taking the time and being on this

:

01:15:50,411 --> 01:15:51,059

show.

:

01:15:52,685 --> 01:15:54,085

Thank you very much.

:

01:15:54,745 --> 01:15:58,865

I may put in one thing that your listeners

might like.

:

01:15:58,865 --> 01:16:02,025

They're interested in trying gravitational

wave data analysis.

:

01:16:02,105 --> 01:16:03,225

Data are public.

:

01:16:03,225 --> 01:16:07,825

They can look up the Gravitational Wave

Open Science Center, download the data

:

01:16:07,825 --> 01:16:08,605

there.

:

01:16:08,605 --> 01:16:12,165

Also, they'll find links to tutorials.

:

01:16:12,405 --> 01:16:18,815

There are workshops held fairly regularly

that they can maybe sign up to to get some

:

01:16:18,815 --> 01:16:21,197

data analysis experience.

:

01:16:21,197 --> 01:16:24,577

And there's a whole list of open source

packages for gravitational wave data

:

01:16:24,577 --> 01:16:28,337

analysis linked from those so they can go

and have a look at themselves.

:

01:16:29,377 --> 01:16:31,477

Yeah, this is indeed a very good ad.

:

01:16:31,477 --> 01:16:32,697

Thank you very much, Christopher.

:

01:16:32,697 --> 01:16:37,717

I actually already put these links in the

show notes and forgot to mention them.

:

01:16:37,717 --> 01:16:39,637

So thank you very much.

:

01:16:39,637 --> 01:16:44,377

Because we're all very dedicated to open

source and open source here.

:

01:16:44,517 --> 01:16:49,297

So if any of the listeners are interested

in that, like how these things are done,

:

01:16:50,157 --> 01:16:57,247

You have all the packages we've mentioned

in the show notes, but also the open

:

01:16:57,247 --> 01:17:03,457

source and open science efforts from your

collaborations, Christopher and John.

:

01:17:03,457 --> 01:17:06,037

So definitely take a look at the show

notes.

:

01:17:06,037 --> 01:17:07,817

Everything is in there.

:

01:17:08,457 --> 01:17:09,657

Thank you guys.

:

01:17:09,717 --> 01:17:15,583

And well, you can come back on the podcast

any...

:

01:17:15,583 --> 01:17:25,197

Any time, hopefully around:about Lysa and the space -based mission.

:

01:17:26,765 --> 01:17:28,625

I'll put it in my calendar.