#hilbert's decision problem

[frank-olivier]

The Royal Institution of Great Britain

Tim Palmer: Chaos theory and geometry - can they predict our world? (April 2023)

Q&A

Quantverse

Sabine Hossenfelder: The Forgotten Solution & Tim Palmer: The Invariant Set Model of Quantum Physics (Rethinking Superdeterminism of Quantum Mechanics, September 2022)

Curt Jaimungal (Theory of Everything)

Tim Maudlin, Tim Palmer: Superdeterminism vs. Bell's Theorem (July 2023)

Tuesday, July 25, 2023

[hephaestuscrew]

I'm always emotional about the fact that, when Minkowski tries to justify her choice to send Eiffel back to Earth on the Sol in the finale, she never directly expresses a reason for her decision that's specific to him. 

She tells Hera, Lovelace and Jacobi "If - if - we don't make it through this... if we don't stop this... people need to know what's coming. They need to know what's happened." She gives them a reason which is logical, practical, and impersonal. It's a 'big picture' reason, focused on humanity as a whole. Minkowski's own emotions don't really enter into this justification at all. That's the kind of decision-making she wants her crew to think she's using. If this was Minkowski's main motivation, it wouldn't matter who was sent back, so long as they could explain Cutter and Pryce's plan. I don't think Hera, Lovelace, or Jacobi believe that this was the main reason why Minkowski sent Eiffel back, and I'm not sure whether Minkowski expected to actually convince them. 

Jacobi asks "did you tell him that before or after you sent him on his merry?" But in fact, Minkowski didn't tell Eiffel at any point that he needed to tell the world about events on the Hephaestus. If her primary motivation had been about having someone to deliver a message back to Earth, she would have given Eiffel suitable instructions - she wouldn't have just trusted him to figure it out. 

Instead, the most direct reason she gives to Eiffel himself for why she's sending him back to Earth is "I need to know that at least one of us makes it back. That I got someone through this." This is a more personal reason, where Minkowski's emotions are relevant, but it's still not explicitly about Eiffel himself. It's about saving "at least one of us", as if it doesn't matter who that "somebody" is. I think this justification is closer to the core of Minkowski's motivations than what she tells the others afterwards. Her responsibilities to her crew as a Commander have always been important to her, and she doesn't want to have failed in keeping them safe. And Eiffel is the only member of her original crew who she's able to save in this way. Hilbert is dead, and transferring Hera over to the Sol to be sent back to Earth on her own would come with a whole host of problems. 

But I don't believe for a moment that the reasons she sends Eiffel back are purely practical and abstract. I don't believe for a moment there's no personal significance to her decision to save him specifically. I don't believe for a moment that it was all about her practical plan for the wellbeing of humanity, or her desire to have fulfilled her duty to at least one non-specific member of her crew. She doesn't just need to save "someone". She doesn't just need to save "at least one of us". She needs to save Eiffel. She needs to save her friend.

The closest she gets to saying aloud that her motivation is about her care for Eiffel in particular is when she says "Go home, Eiffel. Hug your daughter. [...] Goodbye, Doug." She was prepared for those to be the last words she might ever say to him. And there's at least something in these lines that implies she wants Eiffel specifically to return to Earth. I don't think it's that she saves him because he has a daughter. I think when she tells him to go home and hug his daughter, it represents more than that. It's about how she wants him to be able to move forward and live his life. It's her saying that he deserves the interpersonal connections that are valuable to him. It's about her not wanting his story to end there on the Hephaestus. 

It kind of breaks my heart that even in that situation, she can't fully say aloud that the reason she wants Eiffel to survive is because she cares about him specifically. She has to give the justifications that are about her as a Commander and not about Eiffel as her friend. She doesn't tell him that she's saving him for his own sake, because he matters to her so deeply, because his safety is so important to her. 

And I really wish I could believe that Eiffel didn't need her to say it, that he could just understand just from her actions how much she cares about him. But as the Sol flies away from the Hephaestus, he tells himself that he's there because he "never had quite as much chest hair as Lieutenant Commander Renée [Minkowski]" and because he "could never get it right". So I don't think Eiffel ever really appreciates that Minkowski sends him back not because of what he can't do, but because of who he is: her friend, one of the most important people to her, someone who has brought so much value to her life, and someone whose death she refuses to contemplate.

[nobodysdaydreams]

Well...

...that could have gone better.

(Also it turns out Lovelace IS an alien. 👽 so that's fun, I think?)

(or my reaction to episodes 44-46 of Wolf359)

Welcome back dear readers, sorry for the delay. Procrastinating on finals has been taking up all of my time, thank you for your understanding.

Tagging the mutuals who got me invested in this, and if you want to be tagged or untagged from these posts, lmk, or you can follow my blog or simply follow the tag "#bods wolf359 reactions". Anyone who has followed me for a while knows my updates are inconsistent, so I apologize in advance for that and for any spelling/grammar mistakes in my posts.

@sophieswundergarten @oflightningandstars @acollectionofcuriousreblogs @herawell @commsroom

Episode 44: Desperate Times

Now where were we? Ah yes. Cutter lied about their deaths and has an evil girlfriend who makes his robots. Hilbert and Lovelace told Minkowski about the death thing to get her on board, and once they have her, she should be able to get Doug and Hera on board.

Great point Doug. How many secret rooms can one space station have?

And how many copies of the SI-5? Because we already had two Duck boys. If another Kepler strolls in and starts talking about Whiskey again, that might just be too much for me.

No Minkowski. You don't want to kill anyone. But I understand.

Wow. Doug knows some fancy words. "Commander Eiffel" 😂

Oh, they're actually laughing. I'm sorry Doug. Wow, he just made that up too, very convincing.

Aw, Minkowski. I want to hug her. If she doesn't make it back to her husband...

oh yay, she and Doug are talking it out! Friends! My feelings exactly Hera! 💕💕💕

Hera is so sweet. It's weird to think she was built by and modeled after someone so horrible.

Ah. Taking a late night stroll around the ship Hilbert?

Hilbert. NO. NO NO NO NO NO. NOT THE EVIL CHAIR.

Evil chair will kill you. Evil chair will show them your brain which shows them your plan to rebel against them. Do not trust the evil chair Hilbert. For a smart man, you make some remarkably and unbelievably dumb decisions.

I want to believe in them. I do, I really really do. But unfortunately, I know that there is an entire other season left. So...

It's not looking good. Personally, I think the most expendable is Hilbert. They can kill the character off without having to fire the actor. If anyone's about to die, it's him.

The "terrible trio", I like it Doug. Good nickname for SI-5.

The um...the blunt force trauma face?

Oh my this hypothetical of Maxwell, Kepler, and Jacobi falling apart is music, sweet music.

If only...if only.

They are really counting on the SI-5 acting exactly like this. I hope they get it right. I do love the way they make Whiskey Boy out to be such a cartoon villain. He really is.

Oh they're conflicted about who to target. That's right Hera. Target Duck boy. I mean...they did already kill him once, right?

Although slight problem. Let's say they do kill SI-5. Let's say they try to fly the ship back to earth. Can't Cutter just blow the ship up remotely? He'll probably send a missel after them before they even get into the atmosphere. I mean...what would you even do in this situation? He's literally got them bargaining for every second of their lives. Makes you wonder how many teams he has out there like this...

What happened? No gas? Oh dear. Plan B?

HIT MAXWELL WITH A WRENCH? POP A WEASEL?

I don't like how this is going.

"I'm glad I have you alone" Hilbert stop it.

Opponent is not going to hesitate to kill you. That's true. But you can't forget who the enemies are. Cutter and Pryce. And yes. SOMETHING IS WRONG!

Oh dear. Well this is terribly awkward.

...um...so...Maxwell. Duck Boy. Fancy a mutiny?

Guess not. Oh dear. This is bad. This is very very bad.

IS NOT ABOUT THE CONTACT EVENT! IT'S ABOUT THEM GETTING BACK AND YOU KNOW IT.

I KNEW THAT YOU COULDN'T TRUST HER.

"Don't struggle?"

Not the brain sweeping. Maxwell you have lost all my respect, and likely your own if you still had any left in you.

Shut up Duck Boy, literally no one wants to hear from you.

Well this is a pickle. How will our heroes (and Hilbert) get out of this one? 👀

Episode 45: Desperate Measures

"Wakey-wakey", shut up errand boys.

"Passion for disciplining crew members, isn't that right Jacobi?" You're a sadist waste of space who works for a sadist waste of space, we got that Whiskey Boy.

Oh great. Another super secret room. There's probably thousands of them at this rate. A whole city in the sky.

What a nice little room of weapons. As a lover of dramatic irony, I do hope Dr. Robot and our dear Errand Boys find themselves on the other side of those weapons.

Hera you can delay having to respond to her commands! You can! Remember: You can't do this. You're not good enough. Use it to your advantage.

"I knew it!" you did Doug. And yeah, Hilbert didn't sink so low.

"Kill whoever you like least", well there goes Hilbert.

Good work Hera! 🥰 Oh dear it hurts.

THE VENTS! That's right! Go Minkowski!

Geez does Whiskey Boy ever tire of the sound of his own voice? I guess not.

Shut it Kepler! Yeah Doug! He can go to hell! Tell him off!

Doug: "You're crazy"

Kepler: "No Doug. I'm just a man that wants to be taken seriously. That's why I'm sitting here with a gun in one hand, glass of Whisky in the other, while singing "Eeny, meeny, miny, moe" like a cartoon supervillain. There's nothing more respectable or serious than that."

Lovelace is speaking FACTS. He has lost his humanity. But um...ironically so might have Lovelace. Or all of them still unclear on that.

"You're hilarious" "one more thing I have that you don't" ooohhh... dang, it that ain't the truth. No one will be as funny as Doug, but if anyone comes close it's certainly not Whisky boy.

"Very nice speech captain" Well it was better than the Whisky speech Kepler. Take notes.

That's right Lovelace. Who cares what Kepler see when he looks at you? No one. Because he is a waste of space.

She'll survive because of magic alien plot armor.

Aw, she did it for Doug. That's really sweet.

And...off goes the gun. But no screams. He better not have shot Doug.

"You have 30 minutes to think about what you've done. Then we'll talk about Eiffel."

I know I should be furious over the whole "what you've done" comment, but I gotta ask, how dangerously stupid is Kepler? 30 minutes is plenty of time to put a plan into action. What does Kepler need 30 minutes for? Swirling his Whisky around and telling Doug how much he loves the feel of it in his hands.

Why don't you mind your own business Maxwell? Why don't you shut up and mind your own business and throw yourself in the airlock?

Good stalling Hera...yes! Finally knocked out Dr. Robot. Now, as much as I am against murder, eye for an eye, and all that...in this situation, keeping her alive puts multiple innocents at risk.

Anyone got an eye on Duck Boy?

Kepler doesn't care about Maxwell! He doesn't care about anyone!

Doug...great speech for this to work, he has to care about human life, and he clearly doesn't.

Yeah, I don't really like chess either Doug.

Why do I feel like he's going to hurt Hera in a way that only Maxwell can fix?

Ah there he is. "I wouldn't do that so someone. I just blow people up to kill them! :)" ugh Duck Boy is the worst. I knew that he was off doing something silly. "Crazy Jacobi the loose canon" dude, you're Duck Boy. That's your existence.

And I knew Hilbert would be the one to go. They don't have to fire his voice actor to kill him, which makes him expendable.

Well it took a very long time to get here, but looks like Hilbert is finally gonna kick the bucket. And yeah, you guys have no idea how long they've been trying to kill Hilbert. If it was Doug, I'd be more worried, but between Hilbert and Doug, Doug's got the plot armor.

And...there he goes! Oh wait...did she shoot Maxwell! Oh be quiet Jacobi, it's not like you ever actually cared about her. If Cutter or Kepler ordered you to kill her, you would have done it.

You can't talk sense into him Doug. He's a nutcase. We established that.

I love Doug. "Well it's been a topsy-turvy day!"

And see Kepler? Not so fun playing with lives when yours is on the chopping block, now is it?

Yes Doug! Tell him! Oh poor Whisky Boy, are you gonna cry?

Right three people dead: Lovelace, Hilbert, and Maxwell. That's a lot. My money is on Lovelace coming back due to alien magic, Hilbert dead for good, maybe Maxwell lives on in Hera's memory or flashback land.

YES! I love Doug's loyalty to Minkowski!

Does Kepler have an escape pod? I feel like he would. Oh he's telling his duck boy to stand down. But duck boy doesn't seem too happy about that. I guess he cared a bit more for Maxwell than Kepler, even if he would have shot her if given the order.

"Finally over" hm...I seriously doubt that.

Ah yes the aliens. I wonder what they have to say about all this. And Kepler please shut up. "You want to be in charge of this mess, fine." The mutiny literally just happened on your watch. You spent half the crew budget on expensive Whiskey. You don't care at all that Maxwell is dead.

Episode 46: Bolero

Is that music? Um... what is this? I do wonder why they chose to send music, when they've demonstrated that they can send voices.

Yeah...this is a lot. And they lost their human doctor and robot doctor. As much as I hated them, they were useful. Unlike the errand boys, who only seem to be good a cowering in fear from ducks and giving speeches about whisky.

Oh and apparently they like music too. How nice.

"If the commander wishes for silence, then silence she shall have" and yet you're still talking.

Yeah...what do they do now. They have to warn everyone, expose Cutter and get him to jail, but the aliens are also invading. Oh gosh, are Cutter and Pryce aliens? Is this a plot to replace humanity with aliens? That at least makes more sense than Cutter's a loon who just wants to take a gander at some dangerous aliens, but why do I get the feeling that "Cutter's crazy" is what's actually happening here?

Oh right Kepler's special DNA. But your DNA still works even if it's detached from your body, right? 🧬

"We owe it to Lovelace, Hilbert, and Maxwell..." good work Doug. They were evil, they were flawed, but they were still humans.

Oh Hera. Wow, we don't have funerals for animals???? Yikes... I'm starting to see how she was modeled after Pryce now. In that case, I wonder what happened to Pryce. Also Hera, I get what you're saying, but that's an insult to animals. Many cats and dogs I've met are very loyal, kind, and useful.

oh dear she's talking to Lovelace's ghost/memory. 🥺 It's not your fault Minkowski. It was never your fault. And yeah...you all deserve to make it home.

That is if there is even a home to come back to...

Doug, Hera, come on. You're best friends. Wow. And yeah, she and Maxwell were friends, that's why she's so upset! Oh right...if one human friend betrayed her...oh Hera...Doug's not like her you know that! Maxwell would sell you out, Jacobi would sell her out, and Kepler would sell him out, but Doug? Doug would never sell anyone out.

"I know what it's like to not get a chance to say goodbye. And I don't think you're past the point of not caring. Not yet." That's sweet Doug. But you're giving him a bit too much credit. Oh he's mad he killed her? Fair enough, but Jacobi...you said yourself you were monsters! Do you really want to try to claim the moral high ground here? That's right Doug! Tell him! "You're gonna like it...I mean you're gonna feel sad!" Yeah! That's right! Shove the compassion down his throat Doug. Sometimes that's the way you gotta do it.

Minkowski is gonna have some pretty severe PTSD after this. I want to hug her.

Oh no, Hera's remembering Maxwell. "Was everything you did for me part of a secret evil plan?" it's not that simple Hera. Bad people can do good things. Good people can do bad things. Cognitive dissonance Hera, that's how it's possible. Compartmentalization. Circular and deluded thinking. And fake Maxwell is right. It's about you Hera. It's not about her. Forget about Maxwell. Forget about Pryce. You're better than them, and more human too.

Yes Hera, get the feelings out. No, Doug she's coming around!

Oh no...no no no...Doug is wasted isn't he? Kepler's private supply no doubt...oh no... oh Doug.

"I killed them Hera." no you didn't Doug! Intentions matter! You are the ship's moral compass. Don't drink yourself off.

"I'm a drunken mess whether I have a drink or not." oh Doug. Doug.

Please don't give yourself alcohol poison. Oh good self-talk from Hilbert. Yeah Doug never wanted anyone to die.

"How else did you think this was going to end?"

Aw, Doug has so much hope. Never lose that Doug. Never lose it. And yeah, it's nice to believe in redemption. It is theoretically possible. Though in certain cases, highly unlikely. I won't name names.

So...it's just Doug and Jacobi at the funeral? Well. This is incredibly awkward...

Oh right, Hera's never been to a funeral...

Oh nvm Kepler's here for the food. He's so gross.

They gave Hera grief but no way to deal with it? Oh she can't understand why they are gone? The "I wonder if I'll miss you when you go away forever too" is hitting different.

Minkowski came through!

Wow, Jacobi actually is able to say a few nice words.

Dr. Hilbert was a monster 😂. Fair. Completely fair. See ya later Doc. I think Hilbert would have liked it.

Oh don't let Kepler talk. He'd ruin the funeral. Though to be fair, he'd ruin anything.

Never mind looks like the aliens beat him to the punch.

Looks like the aliens decided to come early.

Uh...HERA?

KEEPING WHAT OUT?

Tell me the aliens aren't already here.

Is Lovelace coming back? Oh Kepler knew this was going to happen.

"It can't hear you." DO NOT CALL HER AN IT KEPLER. Alien or not, she's a...well she's a someone.

So she IS an alien? An alien who acts like her? Okay... and yes please, let's start at the beginning. It's about time Kepler. If you're going to talk, you might as well say something useful.

Now I've procrastinated enough but...wow this doesn't look good. Hopefully the crew can get back safely.

[2357911131719]

That’s not the motivation for Turing machines.  Turing was working on Hilbert’s decision problem, which asked whether there could exist an algorithm for proving whether an arbitrary statement was necessarily implied by a given set of axioms.  An answer to this problem requires a formal notion of what an algorithm is, which Turing argued was ‘anything implementable by a Turing machine’ - the only reason it had to work without human involvement is that having no ambiguous states lets the initial configuration and input uniquely define all future behavior.  In fact, Turing machines as originally presented can’t be physically implemented because they’re permitted to have infinitely long tapes to read from and write to. 

🌻

"whatever the fuck i want"

jokes aside, i learned yesterday that is a common take that modern, electronic, transistor-based computers are not interesting (at least primarily) because they do the things they do automatically, on their own, without the aid of humans, but because of something something algorithms.

even though that was precisely WHY turing laid all this down in the first place, figuring out how to algorithmize reasoning in order to breakdown the problem and figure out how to implement it in a machine that could do it on its own. but sure, that is like whatever i guess.

[crossguild]

genuinely can't imagine what difference knowing lovelace is an alien would've made to the outcome of the mutiny on mw and jacobi's part. like, presumably at that point that still wasn't anything that would've been shared with minkowski, and jacobi was definitely not going to NOT blow up hilbert, and maxwell would still be convinced that minkowski wouldn't shoot, and would have given jacobi the go-ahead, and mk was not gonna back down on... anything...

then jacobi being like 'the WORST i have EVER been betrayed is when my boss didn't share this one piece of information that would totally have made a difference even though i don't know what difference that would have been, that he was very explicitly told not to share with me by our sadistic boss who throws people out windows. that is the worst thing that anyone has ever done to another person. finding out kepler is not 100% in control all the time is the worst betrayal i have ever exerienced' which, that and also the episode no complaints and also his 'i trust kepler with my life moment' all implies that he's actually very content with his job the other 99% of the time that he's spent in it considering he expected a workiversary celebration which no normal human in a horrible corporate job does

and it's pretty clear from the canon that jacobi knows exactly what corporate espionage entails, given that he was a-okay with doing it for six years and also had no problem with having information withheld from him as long as things work out in his favor, and he had no problem at all with mind control or stripping people of their autonomy as long as it wasn't happening to him...

and minkowski was like hey you know how in the riddle of the orion the lesson is that you always have a choice to make, and you're accountable for that choice? you could also have decided not to blow up hilbert. that wasn't even like, an explicit order or anything? it was just an option you had that you as an individual decided to take because kepler left that decision to you? that you're responsible for?

and the narrative was like yah kepler is a dick who is a corporate spy/fixer and by dint of his job he is a Bad Guy in our narrative, but jacobi COULD have been portrayed as a genuine victim of all of that but he very much was not, and was instead an active and enthusiastic participant who enjoyed being enabled by his job as a corporate espionage guy

yet i have to read multiple essays about what a poor abused victim jacobi is because he got real mad about (checks notes) his corporate spy/fixer boss doing exactly what a spy/fixer boss always does and what he has always done and which has only suddenly become a problem for jacobi because jacobi feels guilty for what happened but he refuses to acknowledge or own up to it so he blames the only other person he has a modicum of influence over while they're being held as prisoners of war.

and even in blaming kepler he didn't say 'we' could have used that information, he says well maxwell would've been able to do something with it, which is not necessarily true (they'll never know cause she's dead! so he tells himself that and can use it as fuel in his 'mad at kepler') but which is kinda sweet that he has that much faith in his team, except when that faith becomes 'they can literally do the impossible and any failure to do so is someone's fault but it sure isn't mine, when bad things happen as a result of my actions it's no one's fault but i might get unfairly blamed for it'

i like the characters of w359 because none of them are strictly good or bad and they all make bad calls and fuck up and hurt others, and that complexity makes them very nuanced and realistic. i like jacobi a lot! I'm just also aware that he's The Worst. and erasure of him being the worst makes him a MUCH less interesting character

[amazingmsme]

5 F for the obscure media asks?!

Im intrigued 👀

Thanks for this, it was so cute & fun to write! Eiffel is my most specialist boy in the universe, hope you enjoy!

After the attempted coup, Eiffel and Minkowski were on edge pretty much constantly. Sure they had tied Hilbert up and threw him in their makeshift brig, but storage closets weren't all that hard to bust out of if you're determined enough. And Hilbert was plenty determined, it seemed.

Minkowski had come to the decision that they needed to stick together at all times and even went as far as to wait outside of the bathroom door for Eiffel, and making him do the same for her. Instead of splitting tasks like normal, they worked in the same room one task at a time, always keeping an eye on the other and checking over their shoulder.

On the Hephaestus, there is no "night and day," only the preconceived notion of it. Out here in the vast array of stars seven light years away from earth, they were completely and utterly alone. If Hilbert went rogue again, there'd be no chance of saving them.

At first they tried sleeping in shifts, but that quickly fizzled out when they both started falling asleep during their shifts. It just made sense to share Minkowski's admittedly already crammed bunk. Sleeping so close was surprisingly comforting for Eiffel, offering some much needed peace of mind. She'd protect him if anything were  to happen. The weight of her body kept him from drifting too far away from the bed, and it was nice to wake up with his head still on his pillow in the morning.

As it turns out, Eiffel talks in his sleep. It startled Minkowski at first, hearing a mumbling voice in the dark loud enough to wake her. It only took her a second to realize it was just Eiffel, muttering incoherently as he dreamed.

"Give it here, you're doin' it wrong."

Minkowski settled down, resting her head on his chest. As she fell back asleep, he would periodically spout off some nonsense.

"Hmm, purple tiger's gonna pounce..."

She stifled a giggle behind her hand, deciding to stay awake for a while and see what else he'd say. The next day, she decided to bring it up.

"So you're a sleep talker, huh?" she asked casually as she rummaged through the pantry. Eiffel was pouring a cup of lukewarm seaweed coffee and froze.

"Uh, yeah sorry. Hope it didn't bother you too much," he said, rubbing the back of his neck shyly.

"Not at all, it was actually pretty funny," she teased.

"Oh shut up."

And that was that. Neither of them dwelled on the subject, and if he happened to wake her up, she'd just fall back asleep.

About a week later, Eiffel was pulled from his slumber when he felt a soft tingling sensation on his side. He tried to brush it off in his dream, but the feeling only got stronger. He woke himself up with soft giggles spilling from his lips, utterly confused and sleepy. Another flutter on his waist drew forth a quiet snort, eyes finally shooting open.

Minkowski was hugging him in her sleep like usual; that wasn't the problem. But he noticed her hands twitching restlessly in her sleep, fingers curling and tapping against his skin. He contemplated waking her, but he didn't want to face her wrath for ruining her sleep over such a silly matter. Not to mention, he really didn't want her having that kind of knowledge to use against him. He'd never be able to slack off or sass mouth her ever again, not without severe ticklish punishment.

So he just laid there, trying his best to fall asleep as her nails grazed over his sensitive skin in the most agonizing way imaginable. He squirmed but not too much, afraid of disturbing her peaceful rest. And really, it wasn't the worst thing in the world.

He could get used to this, he told himself. He would live, even though he felt like he'd die from suppressed laughter.

All in all, he really didn't mind. And Minkowski never had to know.

[argumate]

I'm seeing weird parallels between AI and climate change, or specifically the development of and reaction to the hypotheses "burning fossil fuels is going to heat the planet" and "computers will be able to do anything a human can do".

the greenhouse effect was proposed in the 1820s by Joseph Fourier as an explanation for why the earth was warmer than you'd expect based on the energy it absorbs from the sun, and Svante Arrhenius published the first climate model relating carbon dioxide level to surface temperature in 1896.

Charles Babbage began the development of the "difference engine" in the 1820s, a machine that could compute tables of logarithms automatically without human effort, and designed but sadly never built the "analytical engine", a general purpose mechanical computer programmed by punchcards, which he worked on until his death in 1871.

in 1936, Turing's paper on Hilbert's decision problem introduced the concept of "Turing machines" as universal computers.

in 1938 Guy Stewart Callendar published evidence showing that the earth had indeed warmed over the previous fifty years along with the rise in carbon dioxide levels, his work was greeted with some scepticism.

in 1946, Turing worked on the first stored program computer, and in 1948 he wrote a program that could play chess, although the computer was not yet capable of running it, in 1950 he explicitly asks the question "can machines think?" and poses the imitation game, or Turing Test.

in 1958, Charles Keeling began recording the CO2 levels at the Mauna Loa observatory, a process that continues to this day, and in 1961 published results showing that they were steadily rising.

also in 1958, the first perceptron based neural network was constructed, although it was soon mired in controversy due to being over-hyped, leading to the first "AI winter".

in 1959 the first silicon integrated circuit was invented at Fairchild Semiconductor.

in 1971 Intel releases the first microprocessor, containing 2300 transistors on a single chip.

in 1979 Carter put solar panels on the White House, in 1981 Reagan had them removed.

as we approach the present day computers get faster and more capable, CO2 level increase is no longer deniable and eventually the reality of temperature rises are grudgingly accepted.

people continue to insist that there are forms of thinking done by humans that computers cannot ever do even in principle, but it's tough to say if those claims will last another century.

[radioways]

eiffel things. 

jack of all trades, master of none.

movie buff, he’ll quote literally any movie, he can’t help but make references it’s a problem.

he smuggled a bunch of patches, as well as cigarettes onto the hephaestus .  

minkowski walked in on him sewing said patches on his spacesuit. she was more impressed that he knew how to sew. ( he doesn’t have much patience for it, but when something needs stitched up they usually bring it to him. ) 

he has a bisexual patch,  trans flag, and a  ghost.busters patch sewn onto his spacesuit, as well as others.

getting used to antigravity was complicated. but he has started to like floating around and even manages to fall asleep while floating. ( he likes being able to do sick flips. ) 

he does however, have a lot of trouble sleeping and thus will take a lot more naps than anyone likes. but it keeps him out of trouble.

he has a lot of respect for the crew on the hephaestus though he hardly acts like it. he enjoys teasing minkowski ( though he did take a lot of time with his recorder repeating her name so he could pronounce it correctly. )  hilbert has always freaked him out a little bit though he won’t admit that either. 

he loves the crew, more specifically minkowski and hera.

selfish, not purposefully but it happens quite often more like a bad habit than a conscious decision. 

[douchebagbrainwaves]

WHAT NO ONE UNDERSTANDS ABOUT JANUARY

In January 1995, we and a couple friends started a company called Artix. The forum troll I have by now internalized doesn't even know where to begin in raising objections to this project. Unfortunately picking winners is harder than that. They certainly delivered. As it turns out, VC-backed startups are not that fearsome. In the other languages mentioned in this talk—Fortran, C, Java, and Visual Basic—it is not clear whether you can actually get work done. One difference I've noticed between great hackers and smart people in general is that hackers are more politically incorrect. College trained one to be a member of the professional classes.1 But as knowledge has grown more specialized, there are more points on the curve, and the inexorable progress of hardware would solve your problems. Maybe it's a bad idea for a company.

Whoever controls the device sets the terms. But as long as it's possible to detect bias whether those doing the selecting want them to or not.2 Of all the great programmers he wanted. Apparently when Robert first met him, Trevor had just begun a new scheme for micropayments?3 A symbol type.4 Feel free to make it big.5 If any incompatibility arises, you can be wise without being very smart. Lisp function and show that it is. It's very common for a group of founders to go through one lame idea before realizing that a startup will make it big. To some extent this was because the companies themselves had become sclerotic. Bill Gates started either.6

But rather the erosion of forces that had been pushing us together were an anomaly, a one-time combination of circumstances that's unlikely to be repeated—and indeed, that we would not want to repeat. They certainly delivered. Most of our educational traditions aim at wisdom.7 So we ditched Artix and started a new company led boldly into the future of hardware, users would follow. Microsoft shows, revenue is a lagging indicator in the technology business. And I was a Reddit user when the opposite happened there, and sitting in a coma at their desk, pretending to work.8 It seems reasonable to suppose the newest one will too.9

I might into Harvard Square or University Ave in the physical world.10 And open and good is what Macs are again, finally.11 As for libraries, their importance also depends on the application. Great hackers think of it as a book.12 Or more precisely, in Trevor's office. The technology companies are right.13 This summer, as an experiment, and an experiment in a very young field. Back in the days of fanfold, there was a correct decision in every situation, and if you couldn't switch ladders, promotion on this one was the only way to read them. But when I went looking for alternatives to fill this void, I found practically nothing.14

Besides which, art dealers are the most extreme form of fluff. They get smart people to write 99% of your code, but still keep them almost as insulated from users as they would be able to say who cares what investors think? I don't know how you'd run such a class in practice. A lot of the obstacles to ongoing diagnosis will come from the fact that the best ideas look initially like bad ideas. But ITA made it interesting by redefining the problem in a more ambitious way. Note too that Cisco is famous for doing very little product development in house. Meaning that unpleasant work pays. Most of the stuff I accumulated was worthless, because I think we can now call a startup: having brilliant people do work in which people have to invent anything.15 They have a sofa they can take a nap on when they feel the same way that not drinking anything would teach you how much you depend on water. Startups are that constrained for talent. Some switched from meat loaf to tofu, and others by playing zero-sum games.

The core of ITA's application is a 200,000 line Common Lisp program that searches many orders of magnitude more possibilities than their competitors, who apparently are still using mainframe-era programming techniques. Most of our educational traditions aim at wisdom. This is the kind of people it wants. And if we don't, the US could be seriously fucked. Cancer will show up on some sort of radar screen immediately. Microsoft seems resigned to, there will be no more great new stuff beyond whatever's currently in the pipeline. I'm so optimistic about HN. Books are more like a fluid than individual objects.16 And the use of these special, reserved field names, especially __call__, seems a bit of a hack. Perhaps the absent-minded professor is wise in his way, or wiser than he seems, but he's not wise in the way Confucius or Socrates wanted people to be.17

You can only do that if you want to really understand Lisp, or just expand your programming horizons, I would learn more about macros. Not quite so dominant as it had been. The importance of the first varies depending on whether you have control over the whole system and have the source code of all the things we could do, is this going to make it something that they themselves use.18 When we started Artix, I was still ambivalent about business. But it's all based on one unspoken assumption, and that means it has to be open and good is what Macs are again, finally. There are few corporations in which it would be suggested that executive salaries are at a maximum. Stuff used to be valuable, and now it's not. The reason the expected value is so high is web services. But for someone at the top, but unless taxes are high enough to discourage people from creating wealth, certainly.19 Symbols are effectively pointers to strings stored in a hash table. Considering how basic a red circle is, it is no surprise that the pointy-haired bosses.

Notes

The founders want the valuation is fixed at the command of the leading edge of technology. This was certainly true in the 1980s was enabled by a big VC firm wants to see it in the usual standards for truth. However, it often means the right thing. The solution is to the margin for error.

In principle you might be interested in each type of thinking, but sword thrusts.

Founders weren't celebrated in the future as barbaric, but at least once for that they don't have to track ratios by time of day, thirty years later. You also have to do it. Which is also a good idea to make people use common sense when interpreting it.

The liking you have the least experience creating it.

There are lots of search engines. Particularly since many causes of the latter.

Which OS? Com. Maybe at first you make money, in the category of people starting normal companies too.

To say anything meaningful about income trends, you won't be demoralized if they seem to have the balls to ask prospective employees if they used FreeBSD and stored their data in files too.

Obvious is an instance of a heuristic for detecting whether you realize it till I started using it out of the web.

In the early empire the price of an official authority makes all the investors agree, and this trick works so well.

The First Two Hundred Years. Org Worrying that Y Combinator to increase it, because they know you'll have to be doctors? There are many senses of the world you'd want to avoid collisions in.

But I think this is to do is form a union and renegotiate all the worse if you're measuring usage you need a meeting, then you're being starved, not because Delicious users are stupid.

So as a rule of thumb, the Patek Philippe 10 Day Tourbillon, is a good way to be secretive, because the publishers exert so much better than the don't-be poets were mistaken to be, and the Imagination by Hilbert and Cohn-Vossen. This was partly confidence, and why it's next to impossible to write great software in Lisp. Most were wrong, but except for money.

Delicious that had been with us he would have been; a vogue for conglomerates in the sale of products, because they suit investors' interests. Plus ca change. Donald J.

To get a low valuation, that you can't easily get a good open-source projects now that VCs may begin to conserve board seats for shorter periods. Bureaucrats manage to think of it, by Courant and Robbins; Geometry and the leading scholars of that. The existence of people like numbers.

It's like the application of math to real problems, and on the aspect they see of piracy is simply what they said. PR firm admittedly the best case. Miyazaki, Ichisada Conrad Schirokauer trans. When I talk about humans being meant or designed to live a certain threshold.

We have no trouble getting hired by these companies substitute progress for revenue growth with retained earnings was one firm that wanted to have them soon. Perhaps it would not be true that being part of your identity. The philosophers whose works they cover would be investors who say no to science as well.

By all means crack down on these. Acquisitions fall into in the former.

Particularly since many causes of the fake.

On the other meanings. Many of these titles vary too much to suggest that we don't have to talk to corp dev guys should be working to help SCO sue them.

[shriyagarg]

Online Stock Prediction Model using Kernel Adaptive Filters

Millions of people engage in stock market everyday and everyone has their own set of differing ideas about the value of a stock according to which they buy or sell it. Most of it are intuition based coupled with the help of little technology prediction. This is because most of the existing prediction models are not reliable enough that people take a decision solely on the basis of the model prediction. Hence there is a need of more efficient algorithms to predict the stocks so that even a common man with minimal knowledge of stocks can also become independent enough to confidently invest in stock with minimal unforeseen risk.

Picture credit: fools.com

To solve the above problem, dynamic data modelling and preprocessing has become the need of the hour. With millions of GB data produced every minute, there is a need for fast and efficient processing of datasets. The algorithms need to be smart enough to only train on required and least amount of data possible to save computational power, hence resources and time. Artificial Neural network solves this problem to a good extent but it is not exhaustive enough to solve problems. Moreover, there are more emerging algorithms available in the market which more efficiently converges to a particular range at a much faster rate than ANN, SVR etc.

In this project, I have made an attempt to use the new kernel adaptive filters to predict the stock market. Although there have been a lot of stock market prediction models available in the market but most of them work on linear dataset algorithms like Time series forecasting models like Arima, Sarimax, AR model, Holt’s Seasonal and winter etc. These algorithm though gives values, are not very efficient as real time datasets are far more clumsier and non linear which makes these algorithms not a very good tool.

Recently a lot of companies have started using LSTM, SVR and ANN to predict stock market . This gives comparatively better results than linear time series forecasting models but it has its own limitations as it takes a lot of time to converge and so is not a very efficient tool. Stock markets are very volatile and change fast at very small time slices, so a lot of dataset can’t be fed to the model as it would not give very good results. The models give best results when these are applied on small time slices and with ANN even these take a lot of time.

Hence Kernel adaptive filters are applied on such datasets after cleaning and pre-processing the datasets. The filters give efficient results as it does not only save time but also gives more accurate time at relatively lower epochs.

Below are the few graphs attached that demonstrate how fast all these Kernel Adaptive Filters are able to reach a Mean squared Error of range 10 ^(-2) with a as small dataset as of 10 iterations in a less than quarter of the time taken by SVR and ANN to reach a convergence which is higher than kernel filters with MSE in range 10^(-1) after being fed a data which is approx 400% more than Kernel Filters.

The dataset used for research purposes for the various kernel based algorithms that I am planning to use for prediction are taken from a research paper “Online Prediction of Time Series Data With Kernels” by Cédric Richard, Senior Member, IEEE, José Carlos M. Bermudez, Senior Member, IEEE, and Paul Honeine, Member, IEEE.  

In this research paper, they have worked upon datasets which are very complex combinations of linear functions , resulting in a non linear functions. These functions are similar to the various real life dataset we find in input wave signals and for various statistical procedures.

Below is the difference equation I used for creating the non-linear dataset on which I tested various algorithms (Kernel Least Mean Square, Kernel Least Recursive Square, Least Mean Square, QKLMS , and CKLMS)

where dn is the desired output.

This highly nonlinear time series has been.  The  dataset was generated  by  iterating the above equation from the initial condition  (0.1,0.1).

 Outputs were  corrupted  by  a  measurement noise  sampled  from  a  zero-mean Gaussian  distribution with standard deviation equal to 0.1.  This  led  to  a  signal-to-noise  ratio  of  the  powers  of  and  the  additive  noise, of  17.2  dB.  These  data  were  used  to  estimate a nonlinear model of  the  form  .  In  identifying the  system,  dataset was  restricted  and  the  experimental setup  described  in    T.  J.  Dodd,  V.  Kadirkamanathan,  and  R.  F.  Harrison,  “Function estimation  in  Hilbert space  using  sequential projections”.

It is a recursive equation with which I created 5 columns and 5000 rows. The dataset created was normalized (i.e between 0 and 1).In this dataset, the model was trained on 4 columns and the last column was predicted and tested. For testing purposes, I divided the dataset into train and test dataset of 4500:500 rows.

REFERENCES

[1]C. Richard, J. C. M. Bermudez and P. Honeine, "Online Prediction of Time Series Data With Kernels," in IEEE Transactions on Signal Processing, vol. 57, no. 3, pp. 1058-1067, March 2009.

DOI: 10.1109/TSP.2008.2009895

[2]S. ZHAO, B. CHEN AND J. C. PRÍNCIPE, "KERNEL ADAPTIVE FILTERING WITH MAXIMUM CORRENTROPY CRITERION," THE 2011 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS, SAN JOSE, CA, 2011, PP. 2012-2017.

DOI: 10.1109/IJCNN.2011.6033473

[3] M. ZHANG, X. WANG, X. CHEN AND A. ZHANG, "THE KERNEL CONJUGATE GRADIENT ALGORITHMS," IN IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 66, NO. 16, PP. 4377-4387, 15 AUG.15, 2018.

DOI: 10.1109/TSP.2018.2853109

[4]Y. ENGEL, S. MANNOR AND R. MEIR, "THE KERNEL RECURSIVE LEAST-SQUARES ALGORITHM," IN IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 52, NO. 8, PP. 2275-2285, AUG. 2004.

DOI: 10.1109/TSP.2004.830985 

[5]P. NOUSI ET AL., "MACHINE LEARNING FOR FORECASTING MID-PRICE MOVEMENTS USING LIMIT ORDER BOOK DATA," IN IEEE ACCESS, VOL. 7, PP. 64722-64736, 2019.

DOI: 10.1109/ACCESS.2019.2916793

[6]A COMPARISON STUDY OF DIFFERENT KERNEL FUNCTIONS FOR SVM-BASED CLASSIFICATION OF MULTI-TEMPORAL POLARIMETRY SAR DATA

[7]K. LI AND J. C. PRÍNCIPE, "TRANSFER LEARNING IN ADAPTIVE FILTERS: THE NEAREST INSTANCE CENTROID-ESTIMATION KERNEL LEAST-MEAN-SQUARE ALGORITHM," IN IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 65, NO. 24, PP. 6520-6535, 15 DEC.15, 2017.

[teavious]

“i just really need to have you here right now”

fandom: wolf 359

ship: doug eiffel / renee minkowski (platonic)

summary: He would know what to do – even in a very stupid, very improbable idea. He’d scream a bit, half-panic, half-incredulity that no one ever listens to him. (from this prompt list) (also on AO3)

The walls are creaking again. Yeah, Minkowski likes that verb, let’s keep it like that. Creaking. It keeps things mechanical; it makes them somewhat fixable, realer. Not a problem coming from her sleepless mind, not weirdness brought upon them by a glowing star that should not be fucking glowing in the first place. Not something that she has no words to name, that her mind cannot comprehend.

The walls are certainly not moaning in pain, strained under unseen forces. She’d ask Hera if she hears it too, but Minkowski figures that she’d have said something about it by now if it were the case. So it remains solely her trouble – and well, it fits better now, punishment for her inability to keep her crew safe. Never mind the hours in the middle of the night that she spends staring at the ceiling, replaying each decision and deeming them all wrong.

Her mental sanity is not the only thing slowly decaying. She thinks of the ship, the alarmingly increase in frequency between alarms: how with each of Hera’s status reports, they’re one step further away from ever making it back to their homes. No matter how much Lovelace slaves over engines, no matter how much Hilbert works out circuits: they all end up at the end of the day, crashing on chairs, tired and frustrated, having nothing to show for all the work they put in.

They don’t really talk besides crew decisions. Hilbert is released, but at this point, both his companions have not much to lose, and there’s nothing like helplessness and despair to bond two former opposite sides together. Lovelace is mostly silent: she snaps at Hera when big mistakes occur, she tries to comfort Minkowski with one shoulder pat, that she shakes off like it weights too much, like it burns through her uniform. It’s not this she wants, not the display of emotions she deserves. The awkwardness floats in the air for several days, no one to laugh it off, no one to make even bigger trouble, for the last one to be forgotten.

After two weeks of barely sleeping, Hilbert finds her dozing off at their communications officer’s desk. He says nothing, merely turns around on his heel, disappearing from her view. She gets up, straightens her spine like she’s a bird ruffling its feathers, and by the time Hilbert is back, she’s deep into a conversation with Hera about any other alien contact. He silently presses some sleeping pills into her palm, squeezes her hand in his in something akin to understanding, though she’s not sure she considers the doctor able of empathy, and says nothing.  Minkowski appreciates him for this; the lack of drama.

Though she’d lie if she’d say she doesn’t miss a kind of drama-seeking man.

She spends 30 minutes looking at herself in the mirror: taking in the longer hair, the deeper dark circles under her eyes. She tastes her title in her mouth, commander, puts it next to her name and she laughs until she can’t quite differentiate it from crying. Doug Eiffel has been damn reluctant of separating the two, returning to the familiarity of her title with the easiness of a slip of tongue, and she has loved him so much for it – because, in the end, it was proof of his trust in her.

And she’s so underserving of it. She so selfishly wishes it would have all been different.  She wants another chance, to prove to him that he made no mistake.

“Eiffel …“ her voice trembles, and she has to hold onto the sink to steady herself and continue. “I just really need to have you here right now.���

He would know what to do – even in a very stupid, very improbable idea. He’d scream a bit, half-panic, half-incredulity that no one ever listens to him. She wishes she could tell him now: that she always listened, no matter how often she agreed or not with his words. But there’s no one to hear her now, so she diligently takes Hilbert pills and falls, finally, into restful slumber.

The next morning, Lovelace punches her in the face for wanting to haul herself in Eiffel’s office again, and with the taste of blood in her mouth, she thinks. Finally. She pushes herself right again, spits words she doesn’t mean, and takes the shove and the next blow almost smiling. Finally.

[deanpasch]

algorithmis 4.0

Taken from the one and only wiki:

"In mathematics and computer science, an algorithmis an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing and automated reasoning tasks.

An algorithm is an effective method that can be expressed within a finite amount of space and time[ and in a well-defined formal language for calculating a function.

Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.

The concept of algorithm has existed for centuries; however, a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation 1" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem."

I guess following this as it applies to being (online) joins the list of 'challenging things in life'.

I am aware that my online movements are part of a wide and deep and tall and multi-multi-dimenional thing(y).

Now you see me now you don't (and vice versa).

I read recently that the time (on average) of average people (myself included) spending time on facebook was tending to be on the decrease. Advertising being the way it is would, I guess, have raised some eyebrows (virtual ones and the literal kind). So bring out those alogo-wot-nots and push back that trend. One possibility.

Let us see this virtual Facebook space as an endless beach we chance upon - meeting people by chance and choosing and sharing by chance and choice - finding debris and pebbles, heels and feathers, flotsam and enjoying the absence of an entry fee and the ability to be here and not.

So there.

[genderbinaryisforlosers]

i’m thinking again about Persuasion and how much of a miscalculation hilbert made in regards to eiffel. he knew what would push minkowski to his ends, but he said “and eiffel will follow her”

he made a mistake. eiffel has never been a good little soldier. he doesn’t just follow. he and minkowski work best side by side, so when she gets her command voice on in Desperate Times, he does what he does best; tells authority to go screw itself.

hilbert mistakes eiffel’s loyalty for obedience. he’s used to predicting the actions of soldiers, of scientists, and businessmen. eiffel is none of those. eiffel is the radio guy, who’s here because it helped his daughter out, who set fire to the oxygen supply because he wanted a cigarette, who bluffs and blunders his way miraculously through every problem

eiffel is loyal to minkowski, but for him that doesnt mean standing by her decisions. it means not letting her fall into the dark. it means letting her know that they’re in this together. it means making her laugh

and hilbert never understood that. he never really understood doug eiffel

[statprofzhu]

Where will the next revolution in machine learning come from?

\(\qquad\) A fundamental problem in machine learning can be described as follows: given a data set, \(\newcommand\myvec[1]{\boldsymbol{#1}}\) \(\mathbb{D}\) = \(\{(\myvec{x}_{i}, y_{i})\}_{i=1}^n\), we would like to find, or learn, a function \(f(\cdot)\) so that we can predict a future outcome \(y\) from a given input \(\myvec{x}\). The mathematical problem, which we must solve in order to find such a function, usually has the following structure: \(\def\F{\mathcal{F}}\)

\[ \underset{f\in\F}{\min} \quad \sum_{i=1}^n L[y_i, f(\myvec{x}_i)] + \lambda P(f), \tag{1}\label{eq:main} \]

where

\(L(\cdot,\cdot)\) is a loss function to ensure that the each prediction \(f(\myvec{x}_i)\) is generally close to the actual outcome \(y_i\) on the data set \(\mathbb{D}\);

\(P(\cdot)\) is a penalty function to prevent the function \(f\) from "behaving badly";

\(\F\) is a functional class in which we will look for the best possible function \(f\); and

\(\lambda > 0\) is a parameter which controls the trade-off between \(L\) and \(P\).

The role of the loss function \(L\) is easy to understand---of course we would like each prediction \(f(\myvec{x}_{i})\) to be close to the actual outcome \(y_i\). To understand why it is necessary to specify a functional class \(\F\) and a penalty function \(P\), it helps to think of Eq. \(\eqref{eq:main}\) from the standpoint of generic search operations.

\(\qquad\) If you are in charge of an international campaign to bust underground crime syndicates, it's only natural that you should give each of your team a set of specific guidelines. Just telling them "to track down the goddamn drug ring" is rarely enough. They should each be briefed on at least three elements of the operation:

WHERE are they going to search? You must define the scope of their exploration. Are they going to search in Los Angeles? In Chicago? In Japan? In Brazil?

WHAT are they searching for? You must characterize your targets. What kind of criminal organizations are you looking for? What activities do they typically engage in? What are their typical mode of operation?

HOW should they go about the search? You must lay out the basic steps which your team should follow to ensure that they will find what you want in a reasonable amount of time.

\(\qquad\) In Eq. \(\eqref{eq:main}\), the functional class \(\F\) specifies where we should search. Without it, we could simply construct a function \(f\) in the following manner: at each \(\myvec{x}_i\) in the data set \(\mathbb{D}\), its value \(f(\myvec{x}_i)\) will be equal to \(y_i\); elsewhere, it will take on any arbitrary value. Clearly, such a function won't be very useful to us. For the problem to be meaningful, we must specify a class of functions to work with. Typical examples of \(\F\) include: linear functions, kernel machines, decision trees/forests, and neural networks. (For kernel machines, \(\F\) is a reproducing kernel Hilbert space.)

\(\qquad\) The penalty function \(P\) specifies what we are searching for. Other than the obvious requirement that we would like \(L[y, f(\myvec{x})]\) to be small, now we also understand fairly well---based on volumes of theoretical work---that, for the function \(f\) to have good generalization properties, we must control its complexity, e.g., by adding a penalty function \(P(f)\) to prevent it from becoming overly complicated.

\(\qquad\) The algorithm that we choose, or design, to solve the minimization problem itself specifies how we should go about the search. In the easiest of cases, Eq. \(\eqref{eq:main}\) may have an analytic solution. Most often, however, it is solved numerically, e.g., by coordinate descent, stochastic gradient descent, and so on.

\(\qquad\) The defining element of the three is undoubtedly the choice of \(\F\), or the question of where to search for the desired prediction function \(f\). It is what defines research communities.

\(\qquad\) For example, we can easily identify a sizable research community, made up mostly of statisticians, if we answer the "where" question with

$$\F^{linear} = \left\{f(\myvec{x}): f(\myvec{x})=\beta_0+\myvec{\beta}^{\top}\myvec{x}\right\}.$$

There is usually no particularly compelling reason why we should restrict ourselves to such a functional class, other than that it is easy to work with. How can we characterize the kind of low-complexity functions that we want in this class? Suppose \(\myvec{x} \in \mathbb{R}^d\). An obvious measure of complexity for this functional class is to count the number of non-zero elements in the coefficient vector \(\myvec{\beta}=(\beta_1,\beta_2,...,\beta_d)^{\top}\). This suggests that we answer the "what" question by considering a penalty function such as

$$P_0(f) = \sum_{j=1}^d I(\beta_j \neq 0) \equiv \sum_{j=1}^d |\beta_j|^0.$$

Unfortunately, such a penalty function makes Eq. \(\eqref{eq:main}\) an NP-hard problem, since \(\myvec{\beta}\) can have either 1, 2, 3, ..., or \(d\) non-zero elements and there are altogether \(\binom{d}{1} + \binom{d}{2} + \cdots + \binom{d}{d} = 2^d - 1\) nontrivial linear functions. In other words, it makes the "how" question too hard to answer. We can either use heuristic search algorithms---such as forward and/or backward stepwise search---that do not come with any theoretical guarantee, or revise our answer to the "what" question by considering surrogate penalty functions---usually, convex relaxations of \(P_0(f)\) such as

$$P_1(f) = \sum_{j=1}^d |\beta_j|^1.$$

With \(\F=\F^{linear}\) and \(P(f)=P_1(f)\), Eq. \(\eqref{eq:main}\) is known in this particular community as "the Lasso", which can be solved easily by algorithms such as coordinate descent.

\(\qquad\) One may be surprised to hear that, even for such a simple class of functions, active research is still being conducted by a large number of talented people. Just what kind of problems are they still working on? Within a community defined by a particular answer to the "where" question, the research almost always revolves around the other two questions: the "what" and the "how". For example, statisticians have been suggesting different answers to the "what" question by proposing new forms of penalty functions. One recent example, called the minimax concave penalty (MCP), is

$$P_{mcp}(f) = \sum_{j=1}^d \left[ |\beta_j| - \beta_j^2/(2\gamma) \right] \cdot I(|\beta_j| \leq \gamma) + \left( \gamma/2 \right) \cdot I(|\beta_j| > \gamma), \quad\text{for some}\quad\gamma>0.$$

The argument is that, by using such a penalty function, the solution to Eq. \(\eqref{eq:main}\) can be shown to enjoy certain theoretical properties that it wouldn't enjoy otherwise. However, unlike \(P_1(f)\), the function \(P_{mcp}(f)\) is nonconvex. This makes Eq. \(\eqref{eq:main}\) harder to solve and, in turn, opens up new challenges to the "how" question.

\(\qquad\) We can identify another research community, made up mostly of computer scientists this time, if we answer the "where" question with a class of functions called neural networks. Again, once a particular answer to the "where" question has been given, the research then centers around the other two questions: the "what" and the "how".

\(\qquad\) Although a myriad of answers have been given by this community to the "what" question, many of them have a similar flavor---specifically, they impose different structures onto the neural network in order to reduce its complexity. For example, instead of using fully connected layers, convolutional layers are used to greatly reduce the total number of parameters by allowing the same set of weights to be shared across different sets of connections. In terms of Eq. \(\eqref{eq:main}\), these approaches amount to using a penalty function of the form,

$$P_{s}(f)= \begin{cases} 0, & \text{if \(f\) has the required structure, \(s\)}; \newline \infty, & \text{otherwise}. \end{cases}$$

\(\qquad\) The answer to the "how" question, however, has so far almost always been stochastic gradient descent (SGD), or a certain variation of it. This is not because the SGD is the best numeric optimization algorithm by any means, but rather due to the sheer number of parameters in a multilayered neural network, which makes it impractical---even on very powerful computers---to consider techniques such as the Newton-Raphson algorithm, though the latter is known theoretically to converge faster. A variation of the SGD provided by the popular Adam optimizer uses a kind of "memory-sticking" gradient---a weighted combination of the current gradient and past gradients from earlier iterations---to make the SGD more stable.

\(\qquad\) Eq. \(\eqref{eq:main}\) defines a broad class of learning problems. In the foregoing paragraphs, we have seen two specific examples that the choice of \(\F\), or the question of where to search for a good prediction function \(f\), often carves out distinct research communities. Actual research activities within each respective community then typically revolve around the choice of \(P(f)\), or the question of what good prediction functions ought to look like (in \(\F\)), and the actual algorithm for solving Eq. \(\eqref{eq:main}\), or the question of how to actually find such a good function (again, in \(\F\)).

\(\qquad\) Although other functional classes---such as kernel machines and decision trees/forests---are also popular, the two aforementioned communities, formed by two specific choices of \(\F\), are by far the most dominant. What other functional classes are interesting to consider for Eq. \(\eqref{eq:main}\)? To me, this seems like a much bigger and potentially more fruitful question to ask than simply what good functions ought to be, and how to find such a good function, within a given class. I, therefore, venture to speculate that the next big revolution in machine learning will come from an ingenious answer to this "where" question itself; and when the answer reveals itself, it will surely create another research community on its own.

(by Professor Z, May 2019)

[elvisomar]

Julia Robinson

(1919–1985) Mathematician and educator

Julia Hall Bowman Robinson is best known for her work in decidability and decision problems, including an area of computation theory known as Hilbert's tenth problem. Robinson was a professor of mathematics at the University of California, Berkeley. She had faced ill health since suffering rheumatic fever as a child, and so never undertook a full-time schedule while teaching there. She spent much of her personal time volunteering in support of progressive political candidates.

Number 195 in an ongoing series celebrating remarkable women in science, technology, engineering, and mathematics.

[luvkirby4ever]

Wolf 359 Theory:  [SPOILERS]

As of Wolf 359 episode 46, Boléro, I don’t think that Hilbert is dead.  I posted a brief mention of it and some people were interested in my thoughts… so here it goes.

It goes without saying that this is based purely on speculation and wishful thinking.  I’m also slightly paranoid that if there’s any bit of truth to my theory and the writers discover that I’ve caught on they’ll change things for fear of not looking too predictable.  So please keep in mind that this is a completely nonsensical post by some annoying fan who just discovered Wolf 359 and binged the entire series in a week.

I’ve also decided to keep this under a “read more” cut to spare anyone’s dashboards.  (Also please excuse any typos- I’m typing in a hurry and I have problems transposing words.)

To start things off, let’s take a quick examination of Dr. Alexander Hilbert. He’s a very interesting character (and feels complex when trying to nail his feelings in a scenario) but he’s actually got a pretty easy overall motivation: His research is above all else.  Anything he does is either directly or indirectly tied to his overall motivation of continuing to study the Decima virus for the benefits of mankind.  His actions are not based on some sort of moral scale (asking himself if this is the “good” thing to do) but rather based on a scale of how his actions will further his cause (will doing this help/harm his ability to work on the Decima Project).  This is important to remember.

For ease of reference, I’ll be including [episode numbers in brackets] to indicate where I’m pulling some of these facts from.  I won’t do this for every point but for some of them that might be less obvious/harder to remember in case you want to listen for yourself.

In-universe reasons why Hilbert might be alive:

We never saw a body.

If he did die via fiery explosion I don’t expect a body(/pieces) to be left.  We still don’t know, however, if somebody bothered to check the area of the detonation.  So we don’t know if there’s any signs of escape/refuge.

Hilbert’s dialogue up to the explosion was suspicious.

Why would Hilbert specifically tell Minkowski how long it would take him to get into the room?

He does this multiple times… which is convenient for letting your enemies know when to set a bomb timer (it’s also useful for ripping out the hearts of your fans T^T)

He already knew that the plan had started to unravel/go wrong, so wouldn’t he be suspicious talking to Minkowski if she isn’t answering him back?

The engineering section is weird.

Ah the advantages of an audio-only medium:  the audience isn’t too sure of how to picture the area.

What we do know is that Hilbert and Lovelace stockpiled napalm in the “secret room that nobody knows about” in the engineering section .

We ALSO know that the secret door to Hilbert’s brain-scan chair is located in the back corner of the engineering section behind gears and such [ep 11].

It’s established, however, that the area which begins to reach past Hera’s sense horizon does not begin at the secret door room, but rather a little before it [ep 38].  Which gives me the impression that the napalm was not stockpiled in the room with the chair… but in that area nearby.

The door to the brain-scanner sounded heavy [ep 44], it is possible for Hilbert to have taken refuge from an explosion there?  I’m honestly not sure.

Since Hera can’t sense exactly what’s going on in there, she could only confirm in Desperate Measures that Hilbert was “heading towards the engineering section”.  So we don’t know what he was doing once he got off the radar.

Hilbert has wanted Maxwell dead multiple times.

Hilbert knew that Maxwell could turn Hera against them, so he has expressed interest in killing her [ep 36], about how not killing her was a wasted opportunity [ep 38], and killing/incapacitating her [ep 44].

The cockroach metaphor:

(Courtesy of Lovelace:)  “You really are a cockroach- dirty, sick, and impossible to kill.  And, God help us, that might be what we need right now.”

Remember- he has survived at least one other Hephaestus mission and years of working with Cutter [minisode 7].

More meta (storytelling) reasons why Hilbert might be alive:

The brain-scan chair’s story thread is still open.

Instead of asking yourself what Hilbert chose to do with the chair, ask yourself this:  “Do you think we’ll be able to find out if he’s dead?”

If the Lovelace we knew is alive and Hilbert’s alive, that would mean that Minkowski would have to live with fact that Maxwell was the only one who died that day.

Minkowski really didn’t want to kill someone- can you imagine the kind of mental/emotional pain that would cause knowing that Maxwell was the only one murdered?

It would also put additional strain on Hilbert’s relationship with her (she DID kill Maxwell because of the shock of his supposed death)

good for the ever-swinging pendulum of the story

Eiffel’s comparison between Hilbert and his own bad life-decisions could be explored more.

Eiffel laments Hilbert’s death partially because he wanted to see Hilbert “turn towards the light”.  This is because Eiffel’s trying to use this as a measure to figure out if he can become a better person after all the terrible things he had done.

So, can you imagine… if Hilbert actually turns around and does something horrible?  It sets up a ton of potential for struggle and strain, as well as Eiffel being forced to deal with the fact that some people won’t change.

On the other hand, there’s also that gushy part of me that wants to see an 11th hour Hilbert appear out of nowhere and save Minkowsi’s/Eiffel’s/Hera’s(/Lovelace’s?) asses because GDI he needs them to stay alive.  For science.

Would we ever find out why there’s bad blood between Hilbert and Kepler if Hilbert’s dead?

Unless Kepler reveals this or it’s the focus of a minisode I don’t think so.

Hilbert’s knowledge of the SI-5 and having worked once with Kepler are unexplored

Why was Cutter so interested in Hilbert’s Decima research [minisode 7] yet it was okay for the Decima Project to be retired [ep 33]?

Were they using Hilbert for something else?  Was this something he knew about?  He seemed to know a little bit about radiology… were they really just using him to dabble with aliens?

Given Hilbert’s reaction to Wolf 359′s change from red to blue, I’m going to guess that Hilbert wasn’t lying about not knowing about this weird alien stuff.

Which furthers the question- why was it okay for Kepler to terminate the Decima Project?

Speculative “reasons” why Hilbert might be alive:

Minkowski makes it a special point that they need Hilbert (to usurp Kepler) [ep 38].

This was right after Hilbert was thinking about the chair.

Hilbert didn’t really end up doing much to further the plan in Desperate Times and Desperate Measures (other than being the presence who died)… but what if this is foreshadowing further?

“Can I help you, Commander?” “Listen. [beat] I know your suggestions haven’t exactly… gone over well, but, I don’t want you to- [beat] Whatever we do, we’re going to need you, doctor. I want you to know that.” “I know that.”

He knows- and interestingly enough he’s showing a small trace of comradery.

I don’t think he’s completely consistent with this but he is under no obligation to call her “Commander” anymore.  Hm.

There is no character who has so far exhibited the ability to research/handle the Decima virus other than Hilbert.

Doug’s cough has been causally showing up again, so if he’s supposed to stay alive much longer he’s going to need a doctor.

Also, the Decima has reached a new stage [ep 33] so for all we know Doug is in for some rough bouts.

Hilbert is hellbent on staying alive because he believes that he’s the only one who can continue the work and that “If only the work can continue without me.  Then that will have to suffice.” [ep 38]

Suffice… as in it (the chair) will have to do as a last resort.  As in it’s not nearly as good as surviving as finishing it himself (insert speech from… ep 25 I think about Hilbert playing his hand through to the end).

Hilbert may have turned to the SI-5 team.

In episode 38 Lovelace says that she thinks Hilbert would switch sides if Command would take him back.

Hilbert responds “no”… but he wasn’t saying no to the idea of switching sides.  He was saying no and continues to justify that Command is done with him.  He never denied that he’d switch sides.

This would make Jacobi’s involvement with the explosion more suspicious since he could be covering for Hilbert.

Stabby the space roomba.

Okay but can you imagine.

That’s all the time I have for now!  Let me know what you think.  I love Hilbert and am really hoping he’s still around, even if he’s going to bring more suffering ^^;  There’s always that corner of my mind that- like Eiffel- imagines some sort of internal conflict inside Hilbert.  Ha.