Terence Tao on how we measure the cosmos | Distance ladder part 1

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From: 3Blue1Brown
Duration: 28:33
Views: 1,520,723

The Cosmic Distance Ladder, how we learned distances in the heavens.
Email list: https://3b1b.co/mail
Patreon supporters see early views of new videos: https://www.patreon.com/3blue1brown

Artwork by Kurt Bruns
Thanks to Paul Dancstep for several animations, such as the powers of 10 zoom out and the simulations of shadows on the moon.

Moon composite shot by Reddit user _wanderloots: https://www.reddit.com/r/astrophotography/comments/yil0tu/partial_lunar_eclipse_composite/
https://youtube.com/@Wanderloots

Thanks to Tanya Klowden for helpful conversations about the history of the distance ladder.

Argument for why if every shadow of a convex shape is a circle, it must be a sphere: https://mathoverflow.net/questions/39127/is-the-sphere-the-only-surface-with-circular-projections-or-can-we-deduce-a-sp

Timestamps:
0:00 - About Terence Tao and the Distance Ladder
2:02 - Earth
8:07 - Moon
11:15 - Sun
15:45 - Heliocentrism in Antiquity
18:27 - Kepler’s genius
27:16 - Where this leaves us

SEV #5: https://youtu.be/uq83hprtpGE

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These animations are largely made using a custom Python library, manim. See the FAQ comments here:
https://3b1b.co/faq#manim
https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/

All code for specific videos is visible here:
https://github.com/3b1b/videos/

The music is by Vincent Rubinetti.
https://www.vincentrubinetti.com
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.

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jlvanderzwan
1 day ago
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Surface-Stable Fractal Dither on Playdate

1 Comment and 2 Shares
Rune Skovbo Johansen has a really sweet Surface-Stable Fractal Dithering technique, where the dither dots “stick” to 3D surfaces, yet the dot density adapts to the view distance and zoom level. Some people have asked whether this would be a good technique for Playdate, given that the screen is one-bit color. And so I had to try it out! Here’s a video: And here’s the code: github.com/aras-p/playdate-dither3d. This is a long-arse post, so here’s the sections: Is it practical?
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jlvanderzwan
4 days ago
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BTW, while not as cool as SSFD, there *are* modern alternatives to the classic Bayer or Floyd-Steynberg dithers that are still really cheap to compute.

If you want stable dithering but not Bayer, try interleaved gradient noise. The 8-bit version is ultra-cheap too so even software rendering would be fast:

// c = 8-bit channel,
// x and y are pixel position
(c, x, y) => c > ((142 * x + 79 * y) & 255) ? 255 : 0;

As for error diffusion, there's Ostromoukhov dithering, which comes closer to blue-noise spectra by varying the kernel depending on the local pixel value, and Zhou-Fang, which builds on Ostromoukhov by adding random modulation to the threshold to break up regular structures that would appear for certain input levels in Ostromoukhov's version, reducing aliasing problems. Online demo here:

https://observablehq.com/@jobleonard/variable-coefficient-dithering?collection=%40jobleonard%2Fimage-dithering-experiments
ttencate
4 days ago
That formula looks cheap enough, but why is it called "interleaved" or "gradient"? Looks more like a very cheap hash function to me. Zhou-Fang looks good! No idea if it'd fly on Playdate. I think most people just use thresholds to compare to a precomputed noise image.
jlvanderzwan
3 days ago
Yes, it's two multiplicative hashes. But if viewed separately as a grayscale map you get two sawtooth gradients at different angles, so adding them together is "like" interleaving gradients, I guess?
jlvanderzwan
3 days ago
The main attraction of ILG is that it's both a stable threshold map and a low-discrepency one, which makes it really good for when you want both temporal stability and minimal aliasing: https://blog.demofox.org/2022/01/01/interleaved-gradient-noise-a-different-kind-of-low-discrepancy-sequence/
jlvanderzwan
3 days ago
Anyway, even if you use a precomputed treshold map, being able to generate one cheaply on the fly with just that formula would still result in smaller binaries :)
ttencate
3 days ago
Ahh, I see. "Gradient noise" usually means something else though (e.g. Perlin and simplex noise are both types of gradient noise).
ttencate
11 days ago
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Netherlands
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Saturday Morning Breakfast Cereal - Hey

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Click here to go see the bonus panel!

Hovertext:
I posted a draft of this on bluesky and was surprised by the number of men asking where they could find such an institution.


Today's News:
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jlvanderzwan
4 days ago
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Did Andrew Tate do anything worse than usual lately to provoke being implicitly mocked by ZW? Not that there can ever be enough mockeries of Andrew Tate.
fallinghawks
4 days ago
I'm mystified as to how that chinless fool has any appeal to women whatsoever.
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Nancy by Olivia Jaimes for Fri, 14 Feb 2025

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Nancy by Olivia Jaimes on Fri, 14 Feb 2025

Source - Patreon

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jlvanderzwan
7 days ago
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Hey look, my two-year old made a guest appearance on Nancy!
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‘Shipwreck’ cartoon. Available now at tomgauld.com/shop

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A Comic strip.   Panel 1: On the horizon a large passenger ship sinks into the sea. A woman sits on a raft, "if only there was space for us both!" she says as she leans back on a large, well-stocked bookcase. Her lover, clinging to the raft replies "Maybe if we lose the bookcase...?"   Panel 2. "My poor darling!" says the woman "Oh, how I wish there was something I could do to help you". The lover, now sunk further into the water continues "... or even just empty one of the shelves?"   Panel 3. The lover is now neck-deep in the water and the raft has been carried away on the tide. "Fate can be so cruel" muses the woman, without looking up from the book that she is now reading "Farewell my love. I'll never forget you."ALT

‘Shipwreck’ cartoon. Available now at tomgauld.com/shop

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jlvanderzwan
9 days ago
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Did everyone selectively forget that in the actual scene they tried to both climb onto the door and that it didn't have enough buoyancy to carry them both?
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Pluralistic: Musk steals a billion dollars from low-income Americans and sends it to Intuit (11 Feb 2025)

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Today's links



A halftoned 2025 IRS 1040 form. To the left is a bloated billionaire figure in top hat, white gloves and tux, with the pouting face of Elon Musk. With one hand, he is yanking on a lever made out of a gilded dollar-sign. With the other hand, he contemptuously dangles a street urchin. The podium to which the lever is attached bears the Turbotax logo, a white checkmark in a red circle. To the left is a cascade of gold coins, falling out of an upended sack.

Musk steals a billion dollars from low-income Americans and sends it to Intuit (permalink)

Let me tell you about the most wasteful US federal government spending I know about. It's a humdinger. You and everyone you know are mired in it for weeks, or perhaps months, every year. It will cost you, personally, thousands of dollars over your lifetime. I'm talking about filing your taxes.

Not paying your taxes. Paying your taxes is fine. It keeps the country running, though not because the government needs our "tax dollars" to pay for things. The government annihilates the money it taxes away from us, and creates new money to pay for programs. The USA needs US citizens' dollars to build highways the same way Starbucks needs its Starbucks gift cards to make lattes – that is, not at all:

https://theglobepost.com/2019/03/28/stephanie-kelton-mmt/

I'm talking about filing your taxes. In nearly every case, a tax return contains a bunch of things the IRS already knows: how much interest your bank paid you, how much your employer paid you, how many kids you have, etc etc. Nearly everyone who pays a tax-prep place or website to file their tax return is just sending data to the IRS that the IRS already has. This is insanely wasteful.

In most other "advanced" countries (and in plenty of poorer countries, too), the tax authority fills in your tax return for you and mails it to you at tax-time. If it looks good to you, you just sign the bottom and send it back. If there are mistakes, you can correct them. You can also just drop it in the shredder and hire an accountant to do your taxes for you, if, for example, you run a small business, or are self-employed, or have other complex tax needs. A tiny minority of tax filers fall into that bucket, and they keep the tax-prep industry in other countries alive, albeit in a much smaller form than in the USA.

In the US, we have a duopoly of two gigantic tax-prep outfits: H&R Block, and Intuit, owners of Turbotax. These companies make billions from low-income, working Americans every year, charging them to format a bunch of information the IRS already has, and then sending it to the IRS on their behalf. These companies lobbied like crazy for the right to tax you when you pay your taxes.

In 2003, it looked like the IRS would start sending Americans pre-completed returns, so H&R Block and Turbotax went into lobbying overdrive, whipping up a "public private partnership" called the "Free File Alliance," that promised to do free tax prep for most Americans. But once the threat of IRS free filing was killed, they turned Free File into a sick joke. Americans who tried to use Free File were fraudulently channeled into filing products that cost money – sometimes hundreds of dollars – to use, a fact that was only revealed after the taxpayer had spent hours keying in their information. Free File sites were also used to peddle unrelated financial products to tax filers, with deceptive language that implied that buying these services was needed to file your return:

https://www.propublica.org/article/inside-turbotax-20-year-fight-to-stop-americans-from-filing-their-taxes-for-free

The big winner from the Free File scam was Intuit, which bought Turbotax in 1993. They made about one billion dollars per year ripping off Americans they'd promised to file free tax returns for. After outstanding work by Propublica, lawmakers and the IRS were finally pressured to create an IRS-based free filing service that would cut Intuit out of the loop. Intuit went on a lobbying blitz without parallel, giving out $3.5m in bribes in 2022 in a bid to kill the Treasury Department's study of a free filing service:

https://pluralistic.net/2023/02/20/turbotaxed/#counter-intuit

In 2022, nearly every US state attorney general settled their lawsuits against Intuit for the Turbotax ripoff, bringing in $141m:

https://www.agturbotaxsettlement.com/Home/portalid/0

In 2023, the FTC won a case against Intuit over the scam:

https://www.ftc.gov/business-guidance/blog/2023/09/nine-takeaways-initial-decision-intuit-turbotax-action

But Intut was undeterred. They came back in 2023 with a campaign to say that ripping off American tax-filers was antiracist and anyone who wanted the IRS to make filing free was, therefore, a racist:

https://pluralistic.net/2023/09/27/predatory-inclusion/#equal-opportunity-scammers

Strangely, no one bought that one. By May, 2023 the IRS had announced its own, in-house free file program:

https://pluralistic.net/2023/05/17/free-as-in-freefile/#tell-me-something-i-dont-know

Now, no one is forcing you to use this program. Do you have a family accountant that your grandparents started using in the Eisenhower administration? Just keep going to them. Do you like using Turbotax? Keep using it! Wanna do your own taxes? Here's the forms:

https://www.irs.gov/pub/irs-pdf/f1040s.pdf

But if you want to file your taxes for free, and you earn $84,000/year or less, here's the IRS's service:

https://www.irs.gov/filing/irs-free-file-do-your-taxes-for-free

Better use it quick, though. Elon Musk has just announced that he's killing it. Yeah, I know, no one elected him. That doesn't seem to matter to anyone, least of all Democrats on the Hill, who are still showing up for work every day and trying to engender a "spirit of comity" rather than screaming and throwing eggs:

https://apnews.com/article/irs-direct-file-musk-18f-6a4dc35a92f9f29c310721af53f58b16

Musk called IRS free file a "far left" program and announced that he had "deleted it." By the way, the median Trump voter's income is about $72k, meaning more than half of Trump voters qualified for free file:

https://fivethirtyeight.com/features/the-mythology-of-trumps-working-class-support/

(Image: Wcamp9, CC BY 4.0, modified)


Hey look at this (permalink)



A Wayback Machine banner.

Object permanence (permalink)

#20yrsago US government: Your fingerprints have expired! https://web.archive.org/web/20050213034201/https://fictioneer.blogspot.com/2005/02/government-to-immigrant-your.html

#15yrsago International Amateur Scanning League will rescue our video treasures! https://web.archive.org/web/20100213170425/http://radar.oreilly.com/2010/02/international-amateur-scanning.html

#15yrsago Interview with a Nigerian 419 scammer https://web.archive.org/web/20100130161655/http://www.scam-detectives.co.uk/blog/2010/01/22/interview-with-a-scammer-part-one/

#10yrsago Nathan Barley: old comedy turned out to be a documentary about our future https://www.theguardian.com/tv-and-radio/2015/feb/10/nathan-barley-charlie-brooker-east-london-comedy

#10yrsago Court has to a law’s diagram tortured sentence structure in order to rule https://www.loweringthebar.net/2015/02/tenth-circuit-forced-to-diagram-congressional-sentence.html">


Upcoming appearances (permalink)

A photo of me onstage, giving a speech, holding a mic.



A screenshot of me at my desk, doing a livecast.

Recent appearances (permalink)



A grid of my books with Will Stahle covers..

Latest books (permalink)



A cardboard book box with the Macmillan logo.

Upcoming books (permalink)

  • Enshittification: Why Everything Suddenly Got Worse and What to Do About It, Farrar, Straus, Giroux, October 2025
    https://us.macmillan.com/books/9780374619329/enshittification/

  • Unauthorized Bread: a middle-grades graphic novel adapted from my novella about refugees, toasters and DRM, FirstSecond, 2026

  • Enshittification, Why Everything Suddenly Got Worse and What to Do About It (the graphic novel), Firstsecond, 2026

  • The Memex Method, Farrar, Straus, Giroux, 2026



Colophon (permalink)

Today's top sources:

Currently writing:

  • Enshittification: a nonfiction book about platform decay for Farrar, Straus, Giroux. Status: second pass edit underway (readaloud)

  • A Little Brother short story about DIY insulin PLANNING

  • Picks and Shovels, a Martin Hench noir thriller about the heroic era of the PC. FORTHCOMING TOR BOOKS FEB 2025

Latest podcast: MLMs are the mirror-world version of community organizing https://craphound.com/overclocked/2025/02/09/mlms-are-the-mirror-world-version-of-community-organizing/


This work – excluding any serialized fiction – is licensed under a Creative Commons Attribution 4.0 license. That means you can use it any way you like, including commercially, provided that you attribute it to me, Cory Doctorow, and include a link to pluralistic.net.

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Quotations and images are not included in this license; they are included either under a limitation or exception to copyright, or on the basis of a separate license. Please exercise caution.


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"When life gives you SARS, you make sarsaparilla" -Joey "Accordion Guy" DeVilla

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jlvanderzwan
11 days ago
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Whenever I read anything about the way US files taxes it comes across like a typical "bad remake that's set in the US" version Terry Gilliam's Brazil, except the bureaucracy feels a little too absurd.

Someone should make a documentary (for Americans) about what it's like to pay taxes in countries that are not the US and why the US is different. I bet it would make some serious waves if it was well done and distributed widely.
ttencate
10 days ago
As soon as it gets some attention, Elon and the Felon will shout something outrageous and all the media will latch onto that instead 😭
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