More on Technology
James Brockbank
3 years ago
Canonical URLs for Beginners
Canonicalization and canonical URLs are essential for SEO, and improper implementation can negatively impact your site's performance.
Canonical tags were introduced in 2009 to help webmasters with duplicate or similar content on multiple URLs.
To use canonical tags properly, you must understand their purpose, operation, and implementation.
Canonical URLs and Tags
Canonical tags tell search engines that a certain URL is a page's master copy. They specify a page's canonical URL. Webmasters can avoid duplicate content by linking to the "canonical" or "preferred" version of a page.
How are canonical tags and URLs different? Can these be specified differently?
Tags
Canonical tags are found in an HTML page's head></head> section.
<link rel="canonical" href="https://www.website.com/page/" />These can be self-referencing or reference another page's URL to consolidate signals.
Canonical tags and URLs are often used interchangeably, which is incorrect.
The rel="canonical" tag is the most common way to set canonical URLs, but it's not the only way.
Canonical URLs
What's a canonical link? Canonical link is the'master' URL for duplicate pages.
In Google's own words:
A canonical URL is the page Google thinks is most representative of duplicate pages on your site.
— Google Search Console Help
You can indicate your preferred canonical URL. For various reasons, Google may choose a different page than you.
When set correctly, the canonical URL is usually your specified URL.
Canonical URLs determine which page will be shown in search results (unless a duplicate is explicitly better for a user, like a mobile version).
Canonical URLs can be on different domains.
Other ways to specify canonical URLs
Canonical tags are the most common way to specify a canonical URL.
You can also set canonicals by:
Setting the HTTP header rel=canonical.
All pages listed in a sitemap are suggested as canonicals, but Google decides which pages are duplicates.
Redirects 301.
Google recommends these methods, but they aren't all appropriate for every situation, as we'll see below. Each has its own recommended uses.
Setting canonical URLs isn't required; if you don't, Google will use other signals to determine the best page version.
To control how your site appears in search engines and to avoid duplicate content issues, you should use canonicalization effectively.
Why Duplicate Content Exists
Before we discuss why you should use canonical URLs and how to specify them in popular CMSs, we must first explain why duplicate content exists. Nobody intentionally duplicates website content.
Content management systems create multiple URLs when you launch a page, have indexable versions of your site, or use dynamic URLs.
Assume the following URLs display the same content to a user:
A search engine sees eight duplicate pages, not one.
URLs #1 and #2: the CMS saves product URLs with and without the category name.
#3, #4, and #5 result from the site being accessible via HTTP, HTTPS, www, and non-www.
#6 is a subdomain mobile-friendly URL.
URL #7 lacks URL #2's trailing slash.
URL #8 uses a capital "A" instead of a lowercase one.
Duplicate content may also exist in URLs like:
https://www.website.com
https://www.website.com/index.php
Duplicate content is easy to create.
Canonical URLs help search engines identify different page variations as a single URL on many sites.
SEO Canonical URLs
Canonical URLs help you manage duplicate content that could affect site performance.
Canonical URLs are a technical SEO focus area for many reasons.
Specify URL for search results
When you set a canonical URL, you tell Google which page version to display.
Which would you click?
https://www.domain.com/page-1/
https://www.domain.com/index.php?id=2
First, probably.
Canonicals tell search engines which URL to rank.
Consolidate link signals on similar pages
When you have duplicate or nearly identical pages on your site, the URLs may get external links.
Canonical URLs consolidate multiple pages' link signals into a single URL.
This helps your site rank because signals from multiple URLs are consolidated into one.
Syndication management
Content is often syndicated to reach new audiences.
Canonical URLs consolidate ranking signals to prevent duplicate pages from ranking and ensure the original content ranks.
Avoid Googlebot duplicate page crawling
Canonical URLs ensure that Googlebot crawls your new pages rather than duplicated versions of the same one across mobile and desktop versions, for example.
Crawl budgets aren't an issue for most sites unless they have 100,000+ pages.
How to Correctly Implement the rel=canonical Tag
Using the header tag rel="canonical" is the most common way to specify canonical URLs.
Adding tags and HTML code may seem daunting if you're not a developer, but most CMS platforms allow canonicals out-of-the-box.
These URLs each have one product.
How to Correctly Implement a rel="canonical" HTTP Header
A rel="canonical" HTTP header can replace canonical tags.
This is how to implement a canonical URL for PDFs or non-HTML documents.
You can specify a canonical URL in your site's.htaccess file using the code below.
<Files "file-to-canonicalize.pdf"> Header add Link "< http://www.website.com/canonical-page/>; rel=\"canonical\"" </Files>301 redirects for canonical URLs
Google says 301 redirects can specify canonical URLs.
Only the canonical URL will exist if you use 301 redirects. This will redirect duplicates.
This is the best way to fix duplicate content across:
HTTPS and HTTP
Non-WWW and WWW
Trailing-Slash and Non-Trailing Slash URLs
On a single page, you should use canonical tags unless you can confidently delete and redirect the page.
Sitemaps' canonical URLs
Google assumes sitemap URLs are canonical, so don't include non-canonical URLs.
This does not guarantee canonical URLs, but is a best practice for sitemaps.
Best-practice Canonical Tag
Once you understand a few simple best practices for canonical tags, spotting and cleaning up duplicate content becomes much easier.
Always include:
One canonical URL per page
If you specify multiple canonical URLs per page, they will likely be ignored.
Correct Domain Protocol
If your site uses HTTPS, use this as the canonical URL. It's easy to reference the wrong protocol, so check for it to catch it early.
Trailing slash or non-trailing slash URLs
Be sure to include trailing slashes in your canonical URL if your site uses them.
Specify URLs other than WWW
Search engines see non-WWW and WWW URLs as duplicate pages, so use the correct one.
Absolute URLs
To ensure proper interpretation, canonical tags should use absolute URLs.
So use:
<link rel="canonical" href="https://www.website.com/page-a/" />And not:
<link rel="canonical" href="/page-a/" />If not canonicalizing, use self-referential canonical URLs.
When a page isn't canonicalizing to another URL, use self-referencing canonical URLs.
Canonical tags refer to themselves here.
Common Canonical Tags Mistakes
Here are some common canonical tag mistakes.
301 Canonicalization
Set the canonical URL as the redirect target, not a redirected URL.
Incorrect Domain Canonicalization
If your site uses HTTPS, don't set canonical URLs to HTTP.
Irrelevant Canonicalization
Canonicalize URLs to duplicate or near-identical content only.
SEOs sometimes try to pass link signals via canonical tags from unrelated content to increase rank. This isn't how canonicalization should be used and should be avoided.
Multiple Canonical URLs
Only use one canonical tag or URL per page; otherwise, they may all be ignored.
When overriding defaults in some CMSs, you may accidentally include two canonical tags in your page's <head>.
Pagination vs. Canonicalization
Incorrect pagination can cause duplicate content. Canonicalizing URLs to the first page isn't always the best solution.
Canonicalize to a 'view all' page.
How to Audit Canonical Tags (and Fix Issues)
Audit your site's canonical tags to find canonicalization issues.
SEMrush Site Audit can help. You'll find canonical tag checks in your website's site audit report.
Let's examine these issues and their solutions.
No Canonical Tag on AMP
Site Audit will flag AMP pages without canonical tags.
Canonicalization between AMP and non-AMP pages is important.
Add a rel="canonical" tag to each AMP page's head>.
No HTTPS redirect or canonical from HTTP homepage
Duplicate content issues will be flagged in the Site Audit if your site is accessible via HTTPS and HTTP.
You can fix this by 301 redirecting or adding a canonical tag to HTTP pages that references HTTPS.
Broken canonical links
Broken canonical links won't be considered canonical URLs.
This error could mean your canonical links point to non-existent pages, complicating crawling and indexing.
Update broken canonical links to the correct URLs.
Multiple canonical URLs
This error occurs when a page has multiple canonical URLs.
Remove duplicate tags and leave one.
Canonicalization is a key SEO concept, and using it incorrectly can hurt your site's performance.
Once you understand how it works, what it does, and how to find and fix issues, you can use it effectively to remove duplicate content from your site.
Canonicalization SEO Myths

Liz Martin
3 years ago
A Search Engine From Apple?
Apple's search engine has long been rumored. Recent Google developments may confirm the rumor. Is Apple about to become Google's biggest rival?
Here's a video:
People noted Apple's changes in 2020. AppleBot, a web crawler that downloads and caches Internet content, was more active than in the last five years.
Apple hired search engine developers, including ex-Googlers, such as John Giannandrea, Google's former search chief.
Apple also changed the way iPhones search. With iOS 14, Apple's search results arrived before Google's.
These facts fueled rumors that Apple was developing a search engine.
Apple and Google Have a Contract
Many skeptics said Apple couldn't compete with Google. This didn't affect the company's competitiveness.
Apple is the only business with the resources and scale to be a Google rival, with 1.8 billion active devices and a $2 trillion market cap.
Still, people doubted that due to a license deal. Google pays Apple $8 to $12 billion annually to be the default iPhone and iPad search engine.
Apple can't build an independent search product under this arrangement.
Why would Apple enter search if it's being paid to stay out?
Ironically, this partnership has many people believing Apple is getting into search.
A New Default Search Engine May Be Needed
Google was sued for antitrust in 2020. It is accused of anticompetitive and exclusionary behavior. Justice wants to end Google's monopoly.
Authorities could restrict Apple and Google's licensing deal due to its likely effect on market competitiveness. Hence Apple needs a new default search engine.
Apple Already Has a Search Engine
The company already has a search engine, Spotlight.
Since 2004, Spotlight has aired. It was developed to help users find photos, documents, apps, music, and system preferences.
Apple's search engine could do more than organize files, texts, and apps.
Spotlight Search was updated in 2014 with iOS 8. Web, App Store, and iTunes searches became available. You could find nearby places, movie showtimes, and news.
This search engine has subsequently been updated and improved. Spotlight added rich search results last year.
If you search for a TV show, movie, or song, photos and carousels will appear at the top of the page.
This resembles Google's rich search results.
When Will the Apple Search Engine Be Available?
When will Apple's search launch? Robert Scoble says it's near.
Scoble tweeted a number of hints before this year's Worldwide Developer Conference.
Scoble bases his prediction on insider information and deductive reasoning. January 2023 is expected.
Will you use Apple's search engine?

Nikhil Vemu
2 years ago
7 Mac Apps That Are Exorbitantly Priced But Totally Worth It
Wish you more bang for your buck
By ‘Cost a Bomb’ I didn’t mean to exaggerate. It’s an idiom that means ‘To be very expensive’. In fact, no app on the planet costs a bomb lol.
So, to the point.
Chronicle
(Freemium. For Pro, $24.99 | Available on Setapp)
You probably have trouble keeping track of dozens of bills and subscriptions each month.
Try Chronicle.
Easy-to-use app
Add payment due dates and receive reminders,
Save payment documentation,
Analyze your spending by season, year, and month.
Observe expenditure trends and create new budgets.
Best of all, Chronicle features an integrated browser for fast payment and logging.
iOS and macOS sync.
SoundSource
($39 for lifetime)
Background Music, a free macOS program, was featured in #6 of this post last month.
It controls per-app volume, stereo balance, and audio over its max level.
Background Music is fully supported. Additionally,
Connect various speakers to various apps (Wow! ),
change the audio sample rate for each app,
To facilitate access, add a floating SoundSource window.
Use its blocks in Shortcuts app,
On the menu bar, include meters for output/input devices and running programs.
PixelSnap
($39 for lifetime | Available on Setapp)
This software is heaven for UI designers.
It aids you.
quickly calculate screen distances (in pixels) ,
Drag an area around an object to determine its borders,
Measure the distances between the additional guides,
screenshots should be pixel-perfect.
What’s more.
You can
Adapt your tolerance for items with poor contrast and shadows.
Use your Touch Bar to perform important tasks, if you have one.
Mate Translation
($3.99 a month / $29.99 a year | Available on Setapp)
Mate Translate resembles a roided-up version of BarTranslate, which I wrote about in #1 of this piece last month.
If you translate often, utilize Mate Translate on macOS and Safari.
I'm really vocal about it.
It stays on the menu bar, and is accessible with a click or ⌥+shift+T hotkey.
It lets you
Translate in 103 different languages,
To translate text, double-click or right-click on it.
Totally translate websites. Additionally, Netflix subtitles,
Listen to their pronunciation to see how close it is to human.
iPhone and Mac sync Mate-ing history.
Swish
($16 for lifetime | Available on Setapp)
Swish is awesome!
Swipe, squeeze, tap, and hold movements organize chaotic desktop windows. Swish operates with mouse and trackpad.
Some gestures:
• Pinch Once: Close an app
• Pinch Twice: Quit an app
• Swipe down once: Minimise an app
• Pinch Out: Enter fullscreen mode
• Tap, Hold, & Swipe: Arrange apps in grids
and many more...
After getting acquainted to the movements, your multitasking will improve.
Unite
($24.99 for lifetime | Available on Setapp)
It turns webapps into macOS apps. The end.
Unite's functionality is a million times better.
Provide extensive customization (incl. its icon, light and dark modes)
make menu bar applications,
Get badges for web notifications and automatically refresh websites,
Replace any dock icon in the window with it (Wow!) by selecting that portion of the window.
Use PiP (Picture-in-Picture) on video sites that support it.
Delete advertising,
Throughout macOS, use floating windows
and many more…
I feel $24.99 one-off for this tool is a great deal, considering all these features. What do you think?
CleanShot X
(Basic: $29 one-off. Pro: $8/month | Available on Setapp)
CleanShot X can achieve things the macOS screenshot tool cannot. Complete screenshot toolkit.
CleanShot X, like Pixel Snap 2 (#3), is fantastic.
Allows
Scroll to capture a long page,
screen recording,
With webcam on,
• With mic and system audio,
• Highlighting mouse clicks and hotkeys.
Maintain floating screenshots for reference
While capturing, conceal desktop icons and notifications.
Recognize text in screenshots (OCR),
You may upload and share screenshots using the built-in cloud.
These are just 6 in 50+ features, and you’re already saying Wow!
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Vivek Singh
3 years ago
A Warm Welcome to Web3 and the Future of the Internet
Let's take a look back at the internet's history and see where we're going — and why.
Tim Berners Lee had a problem. He was at CERN, the world's largest particle physics factory, at the time. The institute's stated goal was to study the simplest particles with the most sophisticated scientific instruments. The institute completed the LEP Tunnel in 1988, a 27 kilometer ring. This was Europe's largest civil engineering project (to study smaller particles — electrons).
The problem Tim Berners Lee found was information loss, not particle physics. CERN employed a thousand people in 1989. Due to team size and complexity, people often struggled to recall past project information. While these obstacles could be overcome, high turnover was nearly impossible. Berners Lee addressed the issue in a proposal titled ‘Information Management'.
When a typical stay is two years, data is constantly lost. The introduction of new people takes a lot of time from them and others before they understand what is going on. An emergency situation may require a detective investigation to recover technical details of past projects. Often, the data is recorded but cannot be found. — Information Management: A Proposal
He had an idea. Create an information management system that allowed users to access data in a decentralized manner using a new technology called ‘hypertext'.
To quote Berners Lee, his proposal was “vague but exciting...”. The paper eventually evolved into the internet we know today. Here are three popular W3C standards used by billions of people today:
(credit: CERN)
HTML (Hypertext Markup)
A web formatting language.
URI (Unique Resource Identifier)
Each web resource has its own “address”. Known as ‘a URL'.
HTTP (Hypertext Transfer Protocol)
Retrieves linked resources from across the web.
These technologies underpin all computer work. They were the seeds of our quest to reorganize information, a task as fruitful as particle physics.
Tim Berners-Lee would probably think the three decades from 1989 to 2018 were eventful. He'd be amazed by the billions, the inspiring, the novel. Unlocking innovation at CERN through ‘Information Management'.
The fictional character would probably need a drink, walk, and a few deep breaths to fully grasp the internet's impact. He'd be surprised to see a few big names in the mix.
Then he'd say, "Something's wrong here."
We should review the web's history before going there. Was it a success after Berners Lee made it public? Web1 and Web2: What is it about what we are doing now that so many believe we need a new one, web3?
Per Outlier Ventures' Jamie Burke:
Web 1.0 was read-only.
Web 2.0 was the writable
Web 3.0 is a direct-write web.
Let's explore.
Web1: The Read-Only Web
Web1 was the digital age. We put our books, research, and lives ‘online'. The web made information retrieval easier than any filing cabinet ever. Massive amounts of data were stored online. Encyclopedias, medical records, and entire libraries were put away into floppy disks and hard drives.
In 2015, the web had around 305,500,000,000 pages of content (280 million copies of Atlas Shrugged).
Initially, one didn't expect to contribute much to this database. Web1 was an online version of the real world, but not yet a new way of using the invention.
One gets the impression that the web has been underutilized by historians if all we can say about it is that it has become a giant global fax machine. — Daniel Cohen, The Web's Second Decade (2004)
That doesn't mean developers weren't building. The web was being advanced by great minds. Web2 was born as technology advanced.
Web2: Read-Write Web
Remember when you clicked something on a website and the whole page refreshed? Is it too early to call the mid-2000s ‘the good old days'?
Browsers improved gradually, then suddenly. AJAX calls augmented CGI scripts, and applications began sending data back and forth without disrupting the entire web page. One button to ‘digg' a post (see below). Web experiences blossomed.
In 2006, Digg was the most active ‘Web 2.0' site. (Photo: Ethereum Foundation Taylor Gerring)
Interaction was the focus of new applications. Posting, upvoting, hearting, pinning, tweeting, liking, commenting, and clapping became a lexicon of their own. It exploded in 2004. Easy ways to ‘write' on the internet grew, and continue to grow.
Facebook became a Web2 icon, where users created trillions of rows of data. Google and Amazon moved from Web1 to Web2 by better understanding users and building products and services that met their needs.
Business models based on Software-as-a-Service and then managing consumer data within them for a fee have exploded.
Web2 Emerging Issues
Unbelievably, an intriguing dilemma arose. When creating this read-write web, a non-trivial question skirted underneath the covers. Who owns it all?
You have no control over [Web 2] online SaaS. People didn't realize this because SaaS was so new. People have realized this is the real issue in recent years.
Even if these organizations have good intentions, their incentive is not on the users' side.
“You are not their customer, therefore you are their product,” they say. With Laura Shin, Vitalik Buterin, Unchained
A good plot line emerges. Many amazing, world-changing software products quietly lost users' data control.
For example: Facebook owns much of your social graph data. Even if you hate Facebook, you can't leave without giving up that data. There is no ‘export' or ‘exit'. The platform owns ownership.
While many companies can pull data on you, you cannot do so.
On the surface, this isn't an issue. These companies use my data better than I do! A complex group of stakeholders, each with their own goals. One is maximizing shareholder value for public companies. Tim Berners-Lee (and others) dislike the incentives created.
“Show me the incentive and I will show you the outcome.” — Berkshire Hathaway's CEO
It's easy to see what the read-write web has allowed in retrospect. We've been given the keys to create content instead of just consume it. On Facebook and Twitter, anyone with a laptop and internet can participate. But the engagement isn't ours. Platforms own themselves.
Web3: The ‘Unmediated’ Read-Write Web
Tim Berners Lee proposed a decade ago that ‘linked data' could solve the internet's data problem.
However, until recently, the same principles that allowed the Web of documents to thrive were not applied to data...
The Web of Data also allows for new domain-specific applications. Unlike Web 2.0 mashups, Linked Data applications work with an unbound global data space. As new data sources appear on the Web, they can provide more complete answers.
At around the same time as linked data research began, Satoshi Nakamoto created Bitcoin. After ten years, it appears that Berners Lee's ideas ‘link' spiritually with cryptocurrencies.
What should Web 3 do?
Here are some quick predictions for the web's future.
Users' data:
Users own information and provide it to corporations, businesses, or services that will benefit them.
Defying censorship:
No government, company, or institution should control your access to information (1, 2, 3)
Connect users and platforms:
Create symbiotic rather than competitive relationships between users and platform creators.
Open networks:
“First, the cryptonetwork-participant contract is enforced in open source code. Their voices and exits are used to keep them in check.” Dixon, Chris (4)
Global interactivity:
Transacting value, information, or assets with anyone with internet access, anywhere, at low cost
Self-determination:
Giving you the ability to own, see, and understand your entire digital identity.
Not pull, push:
‘Push' your data to trusted sources instead of ‘pulling' it from others.
Where Does This Leave Us?
Change incentives, change the world. Nick Babalola
People believe web3 can help build a better, fairer system. This is not the same as equal pay or outcomes, but more equal opportunity.
It should be noted that some of these advantages have been discussed previously. Will the changes work? Will they make a difference? These unanswered questions are technical, economic, political, and philosophical. Unintended consequences are likely.
We hope Web3 is a more democratic web. And we think incentives help the user. If there’s one thing that’s on our side, it’s that open has always beaten closed, given a long enough timescale.
We are at the start.

Vitalik
3 years ago
An approximate introduction to how zk-SNARKs are possible (part 2)
If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.
Polynomials
Polynomials are a special class of algebraic expressions of the form:
- x+5
- x^4
- x^3+3x^2+3x+1
- 628x^{271}+318x^{270}+530x^{269}+…+69x+381
i.e. they are a sum of any (finite!) number of terms of the form cx^k
There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.
Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:
- A(0)+B(0)=C(0)
- A(1)+B(1)=C(1)
- A(2)+B(2)=C(2)
- A(3)+B(3)=C(3)
And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:
- 12+1=13
- 10+8=18
- 15+8=23
- 15+13=28
You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:
- A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
- B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
- C(x)=5x+13
Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.
Comparing a polynomial to itself
You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)
As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.
Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).
Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!
Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.
see part 3

Nick Nolan
3 years ago
How to Make $1,037,100 in 4 Months with This Weird Website
One great idea might make you rich.
Imagine having a million-dollar concept in college that made a million.
2005 precisely.
Alex Tew, 21, from Wiltshire, England, created The Million Dollar Homepage in August 2005. The idea is basic but beyond the ordinary, which is why it worked.
Alex built a 1,000,000-pixel webpage.
Each website pixel would cost $1. Since pixels are hard to discern, he sold 10x10 squares for $100.
He'd make a million if all the spots sold.
He may have thought about NFTs and the Metaverse decades ago.
MillionDollarHomepage.com launched in 2005.
Businesses and individuals could buy a website spot and add their logo, website link, and tagline. You bought an ad, but nobody visited the website.
If a few thousand people visited the website, it could drive traffic to your business's site.
Alex promised buyers the website would be up for 5 years, so it was a safe bet.
Alex's friend with a music website was the first to buy real estate on the site. Within two weeks, 4,700 pixels sold, and a tracker showed how many were sold and available.
Word-of-mouth marketing got the press's attention quickly. Everyone loves reading about new ways to make money, so it was a good news story.
By September, over 250,000 pixels had been sold, according to a BBC press release.
Alex and the website gained more media and public attention, so traffic skyrocketed. Two months after the site launched, 1,400 customers bought more than 500,000 pixels.
Businesses bought online real estate. They heard thousands visited the site, so they could get attention cheaply.
Unless you bought a few squares, I'm not sure how many people would notice your ad or click your link.
A sponge website owner emailed Alex:
“We tried Million Dollar Homepage because we were impressed at the level of ingenuity and the sheer simplicity of it. If we’re honest, we didn’t expect too much from it. Now, as a direct result, we are pitching for £18,000 GBP worth of new clients and have seen our site traffic increase over a hundred-fold. We’re even going to have to upgrade our hosting facility! It’s been exceptional.”
Web.archive.org screenshots show how the website changed.
“The idea is to create something of an internet time capsule: a homepage that is unique and permanent. Everything on the internet keeps changing so fast, it will be nice to have something that stays solid and permanent for many years. You can be a part of that!” Alex Tew, 2005
The last 1,000 pixels were sold on January 1, 2006.
By then, the homepage had hundreds of thousands of monthly visitors. Alex put the last space on eBay due to high demand.
MillionDollarWeightLoss.com won the last pixels for $38,100, bringing revenue to $1,037,100 in 4 months.
Many have tried to replicate this website's success. They've all failed.
This idea only worked because no one had seen this website before.
This winner won't be repeated, but it should inspire you to try something new and creative.
Still popular, you could buy one of the linked domains. You can't buy pixels, but you can buy an expired domain.
One link I clicked costs $59,888.
You'd own a piece of internet history if you spent that much on a domain.
Someone bought stablesgallery.co.uk after the domain expired and restored it.
Many of the linked websites have expired or been redirected, but some still link to the original. I couldn't find sponge's website. Can you?
This is a great example of how a simple creative idea can go viral.
Comment on this amazing success story.
