# Watching Foundation: The Premiere

Spoiler warning, obviously.

If you followed my “Watching Loki” posts, you know what this is. Comments, thoughts and predictions as I watch the episode or maybe as I watch it again. Stuff I think is interesting. Not a review or even an essay, although I’ll give my immediate impression at the end. I’m doing these this time as I’m preparing for the Stars End Podcast but they won’t appear here until a couple of days after the newest episode is dropped. So, without further ado, here are the first two episodes.

S1E1 The Emperor’s Peace

Visually stunning. The opening reminded Joanne of the time travel scenes in ST4 but with much better graphics.

Partway through the figures, look as if they are made of sand and are eroding. That’s a nice visual indication of what is to come.

Wow, this looks good. But Star’s End isn’t at the edge of the Galaxy. Also, it doesn’t have an apostrophe.

Now, this looks like Star Wars with the land speeder.

There’s a creature called a Bishop’s Claw. As the kids approach “the Vault” I realize this is Terminus and we’re in for some non-linear storytelling.

Hmmm. “Kier.” “Gia.” “Poly.”

So, we meet Salvor Hardin before any other main character. Poly calls her “Warden.” I don’t know what that means. But the vibe here is strangely religious for Terminus and the Vault is altogether too mystical.

That is one impressive library.

“We have to remember the past and the ones who caused it all… A mathematician. A martyr. A murderer. And the most important player of all, Hari Seldon.”

There’s a sweet moment between Hari and Raych. Odd maybe, given what’s coming.

86,960,947 is prime.

86,960,957 is prime.

86,960,971 is prime.

86,960,987 is prime.

Gaal has to leave Synnax. “On Trantor, I’ll be safe.” More religion.

On the jump ship. Gaal meets Jerril who seems helpful. He mentions prayer stones.

There are odd scarred humans(?) attending to the passengers.

We see Gaal’s obvious genius when she talks about the grab generators. “I won a math contest.”

Interesting visual for preparing for the jump and the jump itself. Gaal wakes up in the middle. That’s not supposed to happen according to Jerril. Only spacers can endure that without being driven insane.

The space elevator is impressive and nicely takes the place of Gaal’s trip to the tower and hanging to see Trantor from Space. But here she seems more of a refugee than a tourist.

The projection of Brother Day has the same sand-like texture from the opening. That links the Empire to the erosion we saw earlier.

Caskets. From a “kerfuffle” between Anacreon and Thespis.

14 hours to descend and Gaal sees Trantor from space. Exposition 20:38.

We see the mural and Brother Day who is called Empire. That’s a nice device personifying the Empire so directly. Asimov did that especially well in the Mule story with both the Empire and Foundation.

And we see the empire as evil assholes quite dramatically. They’re paranoid of “Raven” Seldon and are harsh sensors. No ambiguity here. No shades of gray.

Brother Dawn learns a hunting song but it’s actually about “a boy’s first time with a woman.”

Day is again shown to execute people for tiny transgressions.

We see Demerzel. Nice visual Day, Dawn, and Dusk taking a bite in unison.

Gaal wants to see the Seer church on Trantor.

86,963,537 is prime.

86,963,549 is prime.

86,963,563 is prime.

86,963,567 is prime.

86,963,573 is prime.

It’s not praying. When Gaal’s nervous she “counts primes.”

Gaal meets Hari. The mathematics starts to bother me here. “Kalle’s Ninth Proof of folding.” Gaal solved Abraxas evidently how she won her “math contest.” That has religious overtones (see below). And no one thought to use the ninth proof in five hundred years.

Kalle writes poetically so “serious scholars don’t read her.” But “reading between the lines” she’s talking about “rings of integers in non-Archimedean local fields.” I think that kind of hangs together based on a quick Google search but it’s far from something that normal folks could glean by “reading between the lines.”

There are shades here of Hardy and Ramanujan. The show has given us two unspeakably brilliant mathematicians and it’s important that one of them is a young lady of color. And they certainly sound like mathematicians here… “there’s a non-zero chance… but it’s not a number worth discussing.”

We get a quick definition of Psychohistory true to the books. Might be word for word. But we lose the sense that mathematics is hard work.

The prime radiant is cool, but it reinforces the “math is magic” theme.

“You know math is never just numbers. In the wrong hands, it’s a weapon in the right hands, deliverance.” “Stealing is a mercy.”

The Ancreonians give Day a weapon while the Thepians give a book of ablution honoring the peace. Exposition on the disagreement.

Subtle messages in the gifts. 36:47. Day and Dusk are training Brother Dawn.

Gaal goes to the Seer church. “The heretic and I will talk.” The religion on Synnax is extreme and all-consuming. The floor is covered with water.

Gaal in water. A dream or a memory of the removal of her prayer stones. Also is it foreshadowing of the end of episode 2? The water is clearly a symbol of the Synnax religion. Gaal’s face turns out of the water as she has the prayer stones removed.

Those hoods they put on prisoners are brutal.

Courtroom scene. And Sig!

It “can only be proved to another mathematician conversant in ordinal analysis.”

Damn Harris is great! And intense!

This loses a lot of the mathematics from the book. And Seldon “thanks the gods.”

Jerril tries to bribe Gaal and gives her the Prime Radiant. The Empire threatens to kill her. There’s water surrounding them as he tempts her to disavow the mathematics.

Spectacular shot.

She was awake on the jump ship. She’s special.

The prime radiant again reinforces the idea that mathematics is magic.

Back to the trial. Encyclopedia Galactica. Saving our story.

It’s a nice moment when Gaal gets to speak truth to power.

It bothers me that one of the terrorists looks middle eastern. The other one doesn’t but still.

The orbital tower is falling snapped off the top. On earth, the geosynchronous orbit is 22,300 miles. Stretched out that’s most of the way around the planet. (C = 24,900 miles).

Nice attention to detail; the fake sky is pixelated as the tower smashes through it.

I really think they understated the amount of damage this devastation would cause. Compare it to the size of the asteroid that killed the dinosaurs. This should be an extinction-level event.

“The tether wrapped around the planet like a Garrote.” Yup.

86,963,777 is prime.

86,963,791 is prime.

100 million deaths. Has Raych lost faith?

Lee Pace has a surprising amount of gravitas. More than as Ronan which was overdone. It’s a lot subtler here. I would not have expected this watching Please Don’t Eat The Daisies.

Gaal bluffs Day. If you kill him the fall accelerates.

Seldon: “I see the value in difference, in the new.”

There’s something called a slow ship. A fundamental difference from the world in the stories.

“You lied.” “I hypothesized.” that’s pure Wrath of Khan stuff right there.

The seas on Synnax were rising. So Gaal Dorrnik here is a cross between Greta Thunberg and Srinivasa Ramanujan; a mathematical prodigy who wants to save her planet from destruction. The water doesn’t merely represent her home planet’s religion; there’s a lot of levels here. On Synnax the rising water signals , one presumes, the growing threat of global warming AND the rampant anti-intellectualism that’s hastening the crisis.

Episode:

Rating: 4.5 out of 5.

S1E02: “Preparing to Live”

On a dwarf planet: a brutal take down of a biohacking facility. And some torture to extract information.

Day (wanting to blame the Foundation): “Say they did it every hour on the hour until it becomes the air that we breathe.” These guys are the Bush administration.

800 odd days? Or 54 months?

Gail and Raych are like crazed weasels.

Then we have the Kobayashi Maru in a simulated cave. We get to see a bishop’s claw looks like first hand.

There were robot wars.

These assholes really are the Bush administration. More brutality. There is circumstantial evidence against the Anacreonian and Thepians. But that about it.

Brother Dusk is declining.

Gaal deposits an embryo, then talks to an engineer who refuses.

Dusk visits the Synnax priest. Wants to know if Gaal is a seer who can predict the future. Demerzel is injured on the way out. So not slow playing the Robot thing.

“The most advanced Math is like a sixth sense.” No, not necessarily.

Seldon seems to be using Tony Stark’s computer system.

Lots of aphorisms “Shame grows in darkness.”

Seldon never thought he’d be on the ship and he’s uncomfortable with the growing familiarity amongst the colonists.

Gaal says the mathematics is not complete. Rayce is upset.

Encyclopedia Meeting. Gaal is asking questions. This base 10 thing is a bunch of nonsense. It’s not the same thing as a different language. I get the point that they’re trying to make but damn it, that’s different. The writers must have scanned “The Crest of the Peacock” and didn’t understand it.

They’re shoehorning in as much math as they can. They either need to get a better consultant or to listen to the good consultant they already have.

Demerzel repairs herself. We see she’s a robot.

Demerzel: “The rest of my kind didn’t die. They were destroyed by your kind.”

Dusk criticizes Cleon I (who has been stuffed) for arrogance. Not sure what the point of Taxidermy Cleon is, it’s odd.

“The Empire going to kill you,” says Dusk to the Anacreonian and Thepian ambassadors. But there’s plenty of reason to think Seldon is behind the Terrorist Attack

The Laundry. Yawn. Hari gets to make a speech.

“A theorem so abstract it might as well have been a prayer.” Damn it. Mathematics isn’t magic.

This handshaking thing is kind of trite.

Raych is out of sorts. Hari is trying to be gregarious and showing Raych to be a thief angers him.

Raych cries talking to Gaal in the holodeck.

Who’s really behind the star bridge? They don’t know. “The best face we can project outward now is one of strength.”

More brutality. Really over the top and disturbing and directed at people who aren’t responsible. These guys really are the Bush Administration.

Still, the little kid shows some humanity. Unfortunately, Demerzel tells him he’ll grow out of it.

A composite number means what? Raych “kills” Hari and takes something from behind Hari’s ear. Gaal is left in space counting primes (in water yet again) and the episode ends? What the hell?

———-

Some thoughts from after we recorded the podcast. I think most people felt confused after this episode. In retrospect, I’m liking this episode more because it’s been so much fun to ponder what was going on in a Total Recall kind of way.

So, here’s a narrative that I think makes sense.

The key moment is when Gaal realizes that the math is incomplete. But here’s the thing: the math didn’t “have holes in it” because Hari didn’t finish. It was incomplete because he and Gaal are in the colony. We know from the books that predictions about the Foundation won’t work correctly if there are Psychohistorians on Terminus. They have to go.

So Hari realizes that he has to be murdered (or fake his death… something). He makes plans with Raych to do it. Then his personality shift, the wandering around the ship, reminiscing about his “son,” missing his favorite shirt, and awkwardly saying goodbye to people including the laundry workers all make sense as the actions of a condemned man or a man who’s planning suicide.

Raych’s behavior now makes sense too. Gaal gets the wet pneumatic tube treatment but she’ll still be gone. It explains his weepiness on the Holodeck during the sunset; he knows they’re not going to have those kids together. This also explains why Raych is suddenly so peevish with Hari.

The psychohistorians are now gone and the Foundation can develop as intended. This may not be right but it holds together, explains all the stuff that feels weird, and is consistent with the books. Where do we see Gaal again? I bet she’ll be central to founding the Second Foundation. Maybe Hari too. Eventually we’ll learn that this was the ultimate plan all along.

Rating: 3.5 out of 5.

Some Stuff From Wikipedia:

Abraxas (Biblical Greek: ἀβραξάς, romanized: abraxas, variant form ἀβρασάξ romanized: Abrasax) is a word of mystic meaning in the system of the Gnostic Basilides, being there applied to the “Great Archon” (megas archōn), the princeps of the 365 spheres (ouranoi).[1] The word is found in Gnostic texts such as the Holy Book of the Great Invisible Spirit, and also appears in the Greek Magical Papyri. It was engraved on certain antique gemstones, called on that account Abraxas stones, which were used as amulets or charms.[2] As the initial spelling on stones was Abrasax (Αβρασαξ), the spelling of Abraxas seen today probably originates in the confusion made between the Greek letters sigma (Σ) and xi (Ξ) in the Latin transliteration.

Gnosticism (from Ancient Greek: γνωστικός, romanized: gnōstikós, Koine Greek: [ɣnostiˈkos], ‘having knowledge’) is a collection of religious ideas and systems which originated in the late 1st century AD among Jewish and early Christian sects.[1] These various groups emphasized personal spiritual knowledge (gnosis) above the orthodox teachings, traditions, and authority of traditional religious institutions. Viewing material existence as flawed or evil, Gnostic cosmogony generally presents a distinction between a supreme, hidden God and a malevolent lesser divinity (sometimes associated with the Yahweh of the Old Testament)[2] who is responsible for creating the material universe.[3] Gnostics considered the principal element of salvation to be direct knowledge of the supreme divinity in the form of mystical or esoteric insight. Many Gnostic texts deal not in concepts of sin and repentance, but with illusion and enlightenment.[3]

Anacreon (/əˈnækriən/; Greek: Ἀνακρέων ὁ Τήϊος; c. 582 – c. 485 BC)[1] was a Greeklyric poet, notable for his drinking songs and erotic poems. Later Greeks included him in the canonical list of Nine Lyric Poets. Anacreon wrote all of his poetry in the ancient Ionicdialect. Like all early lyric poetry, it was composed to be sung or recited to the accompaniment of music, usually the lyre. Anacreon’s poetry touched on universal themes of love, infatuation, disappointment, revelry, parties, festivals and the observations of everyday people and life.

All Images from Foundation on Apple TV+

# The Grouping Number Method

This is an excerpt from a previous post, but if I want to introduce someone to the grouping number method, they don’t need all of the commentary about the AC method.

Are you looking for a nice and intuitive method for factoring quadratics when the leading coefficient isn’t one? Most people were probably taught to break these these things down by trial and error. That isn’t awful once you’ve developed some intuition, but if you haven’t, trial and error quickly becomes tedious. What should we start with instead? The grouping number method works well, especially if you’re just starting out.

To set up the Grouping Number Method, let’s think about what happens in the following polynomial multiplication.

$(4x-1)(2x-3)$

$=2x(4x-1)-3(4x-1)$

$=8x^2 -2x -12x +3$

$=8x^2 -14x +3$

Normally, you’d just skip the second step, but it’s important to realize that what you’re really doing is using the distributive property twice. Additionally, let’s think about the -12 and the -2. It’s clear that they add up to the final coefficient of x, but it’s also true that their product (-12)(-2) = 24 is the same as the product of the leading coefficient and the constant term, (8)(3). Notice this has to be true. In either case, it’s the product of 4, -1, 2 and -3, merely in a different order.

So, how do we go in the other direction? That is, how do we factor instead of multiply? We’ll demonstrate the grouping number method on the polynomial $8x^2 - 14x + 3$.

The grouping number of a quadratic polynomial is the leading coefficient multiplied by the constant term.

So, in this case, it would be $8 times 3 = 24$.

Next, you want to look for two factors of your grouping number that add up to the coefficient of $x$. In this case, $(-12)(-2) = 24$ and $(-12)+(-2) = -14$. We use these two numbers to rewrite the middle term to get the following.

$8x^2 - 14x + 3 = 8x^2 - 2x - 12x + 3$.

In other words, to rewrite the polynomial in this way, you find two factors of your grouping number that add up to the coefficient of $x$ and use those to break down the middle term.

Why rewrite the polynomial in this way? Because it sets us up perfectly to factor by grouping.

Factoring by grouping is a technique for factoring a polynomial with four terms. In a nutshell, to factor by grouping, you remove the greatest common factor from the first two terms, then remove the greatest common factor from the last two terms. If the resulting binomial factors are the same you can factor this out to get the product of two binomials. Notice, that’s using the distributive property twice, just in the opposite direction as before.

Therefore, to finish factoring the polynomial we can factor by grouping.

$8x^2 - 14x + 3$

$= 8x^2 - 2x - 12x + 3$

$= 2x(4x - 1) - 3(4x - 1)$

$= (4x - 1)(2x - 3)$

Notice this exactly reverses the steps of the multiplication with which we started.

In short, as long as you have no common factors, the quadratic polynomials where the grouping number can be factored into two numbers that add up to the middle coefficient are exactly the ones that can be factored by grouping. All the others are prime.