Microsoft co-founder Bill Gates assesses digital assets while the bull is caged.

Bill Gates is well-respected.

Reasonably. He co-founded and led Microsoft during its 1980s and 1990s revolution.

After leaving Microsoft, Bill Gates pursued other interests. He and his wife founded one of the world's largest philanthropic organizations, Bill & Melinda Gates Foundation. He also supports immunizations, population control, and other global health programs.

When Gates criticized Bitcoin, cryptocurrencies, and NFTs, it made news.

Bill Gates said at the 58th Munich Security Conference...

“You have an asset class that’s 100% based on some sort of greater fool theory that somebody’s going to pay more for it than I do.”

Gates means digital assets. Like many bitcoin critics, he says digital coins and tokens are speculative.

And he's not alone. Financial experts have dubbed Bitcoin and other digital assets a "bubble" for a decade.

Gates also made fun of Bored Ape Yacht Club and NFTs, saying, "Obviously pricey digital photographs of monkeys will help the world."

Why does Bill Gates dislike digital assets?

According to Gates' latest comments, Bitcoin, cryptos, and NFTs aren't good ways to hold value.

Bill Gates is a better investor than Elon Musk.

“I’m used to asset classes, like a farm where they have output, or like a company where they make products,” Gates said.

The Guardian claimed in April 2021 that Bill and Melinda Gates owned the most U.S. farms. Over 242,000 acres of farmland.

The Gates couple has enough farmland to cover Hong Kong.

Bill Gates is a classic investor. He wants companies with an excellent track record, strong fundamentals, and good management. Or tangible assets like land and property.

Gates prefers the "old economy" over the "new economy"

Gates' criticism of Bitcoin and cryptocurrency ventures isn't surprising. These digital assets lack all of Gates's investing criteria.

Volatile digital assets include Bitcoin. Their costs might change dramatically in a day. Volatility scares risk-averse investors like Gates.

Gates has a stake in the old financial system. As Microsoft's co-founder, Gates helped develop a dominant tech company.

Because of his business, he's one of the world's richest men.

Bill Gates is invested in protecting the current paradigm.

He won't invest in anything that could destroy the global economy.

When Gates criticizes Bitcoin, cryptocurrencies, and NFTs, he's suggesting they're a hoax. These soapbox speeches are one way he protects his interests.

Digital assets aren't a bad investment, though. Many think they're the future.

Changpeng Zhao and Brian Armstrong are two digital asset billionaires. Two crypto exchange CEOs. Binance/Coinbase.

Digital asset revolution won't end soon.

If you disagree with Bill Gates and plan to invest in Bitcoin, cryptocurrencies, or NFTs, do your own research and understand the risks.

But don’t take Bill Gates’ word for it.

He’s just an old rich guy with a lot of farmland.

He has a lot to lose if Bitcoin and other digital assets gain global popularity.

This post is a summary. Read the full article here.

Zero-Knowledge Proofs for Beginners

Published here originally.

Introduction

I Spy—did you play as a kid? One person chose a room object, and the other had to guess it by answering yes or no questions. I Spy was entertaining, but did you know it could teach you cryptography?

Zero Knowledge Proofs let you show your pal you know what they picked without exposing how. Math replaces electronics in this secret spy mission. Zero-knowledge proofs (ZKPs) are sophisticated cryptographic tools that allow one party to prove they have particular knowledge without revealing it. This proves identification and ownership, secures financial transactions, and more. This article explains zero-knowledge proofs and provides examples to help you comprehend this powerful technology.

What is a Proof of Zero Knowledge?

Zero-knowledge proofs prove a proposition is true without revealing any other information. This lets the prover show the verifier that they know a fact without revealing it. So, a zero-knowledge proof is like a magician's trick: the prover proves they know something without revealing how or what. Complex mathematical procedures create a proof the verifier can verify.

Want to find an easy way to test it out? Try out with tis awesome example! ZK Crush

Describe it as if I'm 5

Alex and Jack found a cave with a center entrance that only opens when someone knows the secret. Alex knows how to open the cave door and wants to show Jack without telling him.

Alex and Jack name both pathways (let’s call them paths A and B).

1. In the first phase, Alex is already inside the cave and is free to select either path, in this case A or B.

2. As Alex made his decision, Jack entered the cave and asked him to exit from the B path.

3. Jack can confirm that Alex really does know the key to open the door because he came out for the B path and used it.

To conclude, Alex and Jack repeat:

1. Alex walks into the cave.

2. Alex follows a random route.

3. Jack walks into the cave.

4. Alex is asked to follow a random route by Jack.

5. Alex follows Jack's advice and heads back that way.

What is a Zero Knowledge Proof?

At a high level, the aim is to construct a secure and confidential conversation between the prover and the verifier, where the prover convinces the verifier that they have the requisite information without disclosing it. The prover and verifier exchange messages and calculate in each round of the dialogue.

The prover uses their knowledge to prove they have the information the verifier wants during these rounds. The verifier can verify the prover's truthfulness without learning more by checking the proof's mathematical statement or computation.

Zero knowledge proofs use advanced mathematical procedures and cryptography methods to secure communication. These methods ensure the evidence is authentic while preventing the prover from creating a phony proof or the verifier from extracting unnecessary information.

ZK proofs require examples to grasp. Before the examples, there are some preconditions.

Criteria for Proofs of Zero Knowledge

1. Completeness: If the proposition being proved is true, then an honest prover will persuade an honest verifier that it is true.

2. Soundness: If the proposition being proved is untrue, no dishonest prover can persuade a sincere verifier that it is true.

3. Zero-knowledge: The verifier only realizes that the proposition being proved is true. In other words, the proof only establishes the veracity of the proposition being supported and nothing more.

The zero-knowledge condition is crucial. Zero-knowledge proofs show only the secret's veracity. The verifier shouldn't know the secret's value or other details.

Example after example after example

To illustrate, take a zero-knowledge proof with several examples:

Initial Password Verification Example

You want to confirm you know a password or secret phrase without revealing it.

Use a zero-knowledge proof:

1. You and the verifier settle on a mathematical conundrum or issue, such as figuring out a big number's components.

2. The puzzle or problem is then solved using the hidden knowledge that you have learned. You may, for instance, utilize your understanding of the password to determine the components of a particular number.

3. You provide your answer to the verifier, who can assess its accuracy without knowing anything about your private data.

4. You go through this process several times with various riddles or issues to persuade the verifier that you actually are aware of the secret knowledge.

You solved the mathematical puzzles or problems, proving to the verifier that you know the hidden information. The proof is zero-knowledge since the verifier only sees puzzle solutions, not the secret information.

In this scenario, the mathematical challenge or problem represents the secret, and solving it proves you know it. The evidence does not expose the secret, and the verifier just learns that you know it.

My simple example meets the zero-knowledge proof conditions:

1. Completeness: If you actually know the hidden information, you will be able to solve the mathematical puzzles or problems, hence the proof is conclusive.

2. Soundness: The proof is sound because the verifier can use a publicly known algorithm to confirm that your answer to the mathematical conundrum or difficulty is accurate.

3. Zero-knowledge: The proof is zero-knowledge because all the verifier learns is that you are aware of the confidential information. Beyond the fact that you are aware of it, the verifier does not learn anything about the secret information itself, such as the password or the factors of the number. As a result, the proof does not provide any new insights into the secret.

Explanation #2: Toss a coin.

One coin is biased to come up heads more often than tails, while the other is fair (i.e., comes up heads and tails with equal probability). You know which coin is which, but you want to show a friend you can tell them apart without telling them.

Use a zero-knowledge proof:

1. One of the two coins is chosen at random, and you secretly flip it more than once.

2. You show your pal the following series of coin flips without revealing which coin you actually flipped.

3. Next, as one of the two coins is flipped in front of you, your friend asks you to tell which one it is.

4. Then, without revealing which coin is which, you can use your understanding of the secret order of coin flips to determine which coin your friend flipped.

5. To persuade your friend that you can actually differentiate between the coins, you repeat this process multiple times using various secret coin-flipping sequences.

In this example, the series of coin flips represents the knowledge of biased and fair coins. You can prove you know which coin is which without revealing which is biased or fair by employing a different secret sequence of coin flips for each round.

The evidence is zero-knowledge since your friend does not learn anything about which coin is biased and which is fair other than that you can tell them differently. The proof does not indicate which coin you flipped or how many times you flipped it.

The coin-flipping example meets zero-knowledge proof requirements:

1. Completeness: If you actually know which coin is biased and which is fair, you should be able to distinguish between them based on the order of coin flips, and your friend should be persuaded that you can.

2. Soundness: Your friend may confirm that you are correctly recognizing the coins by flipping one of them in front of you and validating your answer, thus the proof is sound in that regard. Because of this, your acquaintance can be sure that you are not just speculating or picking a coin at random.

3. Zero-knowledge: The argument is that your friend has no idea which coin is biased and which is fair beyond your ability to distinguish between them. Your friend is not made aware of the coin you used to make your decision or the order in which you flipped the coins. Consequently, except from letting you know which coin is biased and which is fair, the proof does not give any additional information about the coins themselves.

Figure out the prime number in Example #3.

You want to prove to a friend that you know their product n=pq without revealing p and q. Zero-knowledge proof?

Use a variant of the RSA algorithm. Method:

1. You determine a new number s = r2 mod n by computing a random number r.

2. You email your friend s and a declaration that you are aware of the values of p and q necessary for n to equal pq.

3. A random number (either 0 or 1) is selected by your friend and sent to you.

4. You send your friend r as evidence that you are aware of the values of p and q if e=0. You calculate and communicate your friend's s/r if e=1.

5. Without knowing the values of p and q, your friend can confirm that you know p and q (in the case where e=0) or that s/r is a legitimate square root of s mod n (in the situation where e=1).

This is a zero-knowledge proof since your friend learns nothing about p and q other than their product is n and your ability to verify it without exposing any other information. You can prove that you know p and q by sending r or by computing s/r and sending that instead (if e=1), and your friend can verify that you know p and q or that s/r is a valid square root of s mod n without learning anything else about their values. This meets the conditions of completeness, soundness, and zero-knowledge.

Zero-knowledge proofs satisfy the following:

1. Completeness: The prover can demonstrate this to the verifier by computing q = n/p and sending both p and q to the verifier. The prover also knows a prime number p and a factorization of n as p*q.

2. Soundness: Since it is impossible to identify any pair of numbers that correctly factorize n without being aware of its prime factors, the prover is unable to demonstrate knowledge of any p and q that do not do so.

3. Zero knowledge: The prover only admits that they are aware of a prime number p and its associated factor q, which is already known to the verifier. This is the extent of their knowledge of the prime factors of n. As a result, the prover does not provide any new details regarding n's prime factors.

Types of Proofs of Zero Knowledge

Each zero-knowledge proof has pros and cons. Most zero-knowledge proofs are:

1. Interactive Zero Knowledge Proofs: The prover and the verifier work together to establish the proof in this sort of zero-knowledge proof. The verifier disputes the prover's assertions after receiving a sequence of messages from the prover. When the evidence has been established, the prover will employ these new problems to generate additional responses.

2. Non-Interactive Zero Knowledge Proofs: For this kind of zero-knowledge proof, the prover and verifier just need to exchange a single message. Without further interaction between the two parties, the proof is established.

3. A statistical zero-knowledge proof is one in which the conclusion is reached with a high degree of probability but not with certainty. This indicates that there is a remote possibility that the proof is false, but that this possibility is so remote as to be unimportant.

4. Succinct Non-Interactive Argument of Knowledge (SNARKs): SNARKs are an extremely effective and scalable form of zero-knowledge proof. They are utilized in many different applications, such as machine learning, blockchain technology, and more. Similar to other zero-knowledge proof techniques, SNARKs enable one party—the prover—to demonstrate to another—the verifier—that they are aware of a specific piece of information without disclosing any more information about that information.

5. The main characteristic of SNARKs is their succinctness, which refers to the fact that the size of the proof is substantially smaller than the amount of the original data being proved. Because to its high efficiency and scalability, SNARKs can be used in a wide range of applications, such as machine learning, blockchain technology, and more.

Uses for Zero Knowledge Proofs

ZKP applications include:

1. Verifying Identity ZKPs can be used to verify your identity without disclosing any personal information. This has uses in access control, digital signatures, and online authentication.

2. Proof of Ownership ZKPs can be used to demonstrate ownership of a certain asset without divulging any details about the asset itself. This has uses for protecting intellectual property, managing supply chains, and owning digital assets.

3. Financial Exchanges Without disclosing any details about the transaction itself, ZKPs can be used to validate financial transactions. Cryptocurrency, internet payments, and other digital financial transactions can all use this.

4. By enabling parties to make calculations on the data without disclosing the data itself, Data Privacy ZKPs can be used to preserve the privacy of sensitive data. Applications for this can be found in the financial, healthcare, and other sectors that handle sensitive data.

5. By enabling voters to confirm that their vote was counted without disclosing how they voted, elections ZKPs can be used to ensure the integrity of elections. This is applicable to electronic voting, including internet voting.

6. Cryptography Modern cryptography's ZKPs are a potent instrument that enable secure communication and authentication. This can be used for encrypted messaging and other purposes in the business sector as well as for military and intelligence operations.

Proofs of Zero Knowledge and Compliance

Kubernetes and regulatory compliance use ZKPs in many ways. Examples:

1. Security for Kubernetes ZKPs offer a mechanism to authenticate nodes without disclosing any sensitive information, enhancing the security of Kubernetes clusters. ZKPs, for instance, can be used to verify, without disclosing the specifics of the program, that the nodes in a Kubernetes cluster are running permitted software.

2. Compliance Inspection Without disclosing any sensitive information, ZKPs can be used to demonstrate compliance with rules like the GDPR, HIPAA, and PCI DSS. ZKPs, for instance, can be used to demonstrate that data has been encrypted and stored securely without divulging the specifics of the mechanism employed for either encryption or storage.

3. Access Management Without disclosing any private data, ZKPs can be used to offer safe access control to Kubernetes resources. ZKPs can be used, for instance, to demonstrate that a user has the necessary permissions to access a particular Kubernetes resource without disclosing the details of those permissions.

4. Safe Data Exchange Without disclosing any sensitive information, ZKPs can be used to securely transmit data between Kubernetes clusters or between several businesses. ZKPs, for instance, can be used to demonstrate the sharing of a specific piece of data between two parties without disclosing the details of the data itself.

5. Kubernetes deployments audited Without disclosing the specifics of the deployment or the data being processed, ZKPs can be used to demonstrate that Kubernetes deployments are working as planned. This can be helpful for auditing purposes and for ensuring that Kubernetes deployments are operating as planned.

ZKPs preserve data and maintain regulatory compliance by letting parties prove things without revealing sensitive information. ZKPs will be used more in Kubernetes as it grows.

Successful workers don't talk this way.

"I know it's unprofessional, but I can't stop." — Author Sandy Hall

Do you realize your unprofessionalism? Do you care? Self-awareness?

Everyone can improve their unprofessionalism. Some workplace phrases and words shouldn't be said.

People often say out loud what they're thinking. They show insecurity, incompetence, and disrespect.

"Think before you speak," goes the saying.

Some of these phrases are "okay" in certain situations, but you'll lose colleagues' respect if you use them often.

Your word choice. Your tone. Your intentions. They matter.

Choose your words carefully to build work relationships and earn peer respect. You should build positive relationships with coworkers and clients.

These 10 phrases are unprofessional. 

1. That Meeting Really Sucked

Wow! Were you there? You should be responsible if you attended. You can influence every conversation.

Alternatives

Improve the meeting instead of complaining afterward. Make it more meaningful and productive.

2. Not Sure if You Saw My Last Email

Referencing a previous email irritates people. Email follow-up can be difficult. Most people get tons of emails a day, so it may have been buried, forgotten, or low priority.

Alternatives

It's okay to follow up, but be direct, short, and let the recipient "save face"

3. Any Phrase About Sex, Politics, and Religion

Discussing sex, politics, and religion at work is foolish. If you discuss these topics, you could face harassment lawsuits.

Alternatives

Keep quiet about these contentious issues. Don't touch them.

4. I Know What I’m Talking About

Adding this won't persuade others. Research, facts, and topic mastery are key to persuasion. If you're knowledgeable, you don't need to say this.

Alternatives

Please don’t say it at all. Justify your knowledge.

5. Per Our Conversation

This phrase sounds like legal language. You seem to be documenting something legally. Cold, stern, and distant. "As discussed" sounds inauthentic.

Alternatives

It was great talking with you earlier; here's what I said.

6. Curse-Word Phrases

Swearing at work is unprofessional. You never know who's listening, so be careful. A child may be at work or on a Zoom or Teams call. Workplace cursing is unacceptable.

Alternatives

Avoid adult-only words.

7. I Hope This Email Finds You Well

This is a unique way to wish someone well. This phrase isn't as sincere as the traditional one. When you talk about the email, you're impersonal.

Alternatives

Genuinely care for others.

8. I Am Really Stressed

Happy, strong, stress-managing coworkers are valued. Manage your own stress. Exercise, sleep, and eat better.

Alternatives

Everyone has stress, so manage it. Don't talk about your stress.

9. I Have Too Much to Do

You seem incompetent. People think you can't say "no" or have poor time management. If you use this phrase, you're telling others you may need to change careers.

Alternatives

Don't complain about your workload; just manage it.

10. Bad Closing Salutations

"Warmly," "best," "regards," and "warm wishes" are common email closings. This conclusion sounds impersonal. Why use "warmly" for finance's payment status?

Alternatives

Personalize the closing greeting to the message and recipient. Use "see you tomorrow" or "talk soon" as closings.

Bringing It All Together

These 10 phrases are unprofessional at work. That meeting sucked, not sure if you saw my last email, and sex, politics, and religion phrases.

Also, "I know what I'm talking about" and any curse words. Also, avoid phrases like I hope this email finds you well, I'm stressed, and I have too much to do.

Successful workers communicate positively and foster professionalism. Don't waste chances to build strong work relationships by being unprofessional.

“Unprofessionalism damages the business reputation and tarnishes the trust of society.” — Pearl Zhu, an American author

This post is a summary. Read full article here

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:

1. https://www.website.com/category/product-a/

2. https://www.website.com/product-a/

3. https://website.com/product-a/

4. http://www.website.com/product-a/

5. http://website.com/product-a/

6. https://m.website.com/product-a/

7. https://www.website.com/product-a

8. https://www.website.com/product-A/

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

For some people, the glass is half empty. For others, it’s half full. And for some, the question is, How do I get this glass totally full again?

Problem-solvers are the last group. They're neutral. Pragmatists.

Problems surround them. They fix things instead of judging them. Problem-solvers improve the world wherever they go.

Some fail. Sometimes their good intentions have terrible results. Like when they try to help a grandma cross the road because she can't do it alone but discover she never wanted to.

Most programmers, software engineers, and data scientists solve problems. They use computer code to fix problems they see.

Coding is best done by understanding and solving the problem.

Despite your best intentions, building the wrong solution may have negative consequences. Helping an unwilling grandma cross the road.

How can you improve problem-solving?

1. Examine your presumptions.

Don’t think There’s a grandma, and she’s unable to cross the road. Therefore I must help her over the road. Instead think This grandma looks unable to cross the road. Let’s ask her whether she needs my help to cross it.

Maybe the grandma can’t cross the road alone, but maybe she can. You can’t tell for sure just by looking at her. It’s better to ask.

Maybe the grandma wants to cross the road. But maybe she doesn’t. It’s better to ask!

Building software is similar. Do only I find this website ugly? Who can I consult?

We all have biases, mental shortcuts, and worldviews. They simplify life.

Problem-solving requires questioning all assumptions. They might be wrong!

Think less. Ask more.

Secondly, fully comprehend the issue.

Grandma wants to cross the road? Does she want flowers from the shop across the street?

Understanding the problem advances us two steps. Instead of just watching people and their challenges, try to read their intentions.

Don't ask, How can I help grandma cross the road? Why would this grandma cross the road? What's her goal?

Understand what people want before proposing solutions.

3. Request more information. This is not a scam!

People think great problem solvers solve problems immediately. False!

Problem-solvers study problems. Understanding the problem makes solving it easy.

When you see a grandma struggling to cross the road, you want to grab her elbow and pull her over. However, a good problem solver would ask grandma what she wants. So:

Problem solver: Excuse me, ma’am? Do you wish to get over the road? Grandma: Yes indeed, young man! Thanks for asking. Problem solver: What do you want to do on the other side? Grandma: I want to buy a bouquet of flowers for my dear husband. He loves flowers! I wish the shop wasn’t across this busy road… Problem solver: Which flowers does your husband like best? Grandma: He loves red dahlia. I usually buy about 20 of them. They look so pretty in his vase at the window! Problem solver: I can get those dahlia for you quickly. Go sit on the bench over here while you’re waiting; I’ll be back in five minutes. Grandma: You would do that for me? What a generous young man you are!

A mediocre problem solver would have helped the grandma cross the road, but he might have forgotten that she needs to cross again. She must watch out for cars and protect her flowers on the way back.

A good problem solver realizes that grandma's husband wants 20 red dahlias and completes the task.

4- Rapid and intense brainstorming

Understanding a problem makes solutions easy. However, you may not have all the information needed to solve the problem.

Additionally, retrieving crucial information can be difficult.

You could start a blog. You don't know your readers' interests. You can't ask readers because you don't know who they are.

Brainstorming works here. Set a stopwatch (most smartphones have one) to ring after five minutes. In the remaining time, write down as many topics as possible.

No answer is wrong. Note everything.

Sort these topics later. Programming or data science? What might readers scroll past—are these your socks this morning?

Rank your ideas intuitively and logically. Write Medium stories using the top 35 ideas.

5 - Google it.

Doctor Google may answer this seemingly insignificant question. If you understand your problem, try googling or binging.

Someone has probably had your problem before. The problem-solver may have posted their solution online.

Use others' experiences. If you're social, ask a friend or coworker for help.

6 - Consider it later

Rest your brain.

Reread. Your brain needs rest to function.

Hustle culture encourages working 24/7. It doesn't take a neuroscientist to see that this is mental torture.

Leave an unsolvable problem. Visit friends, take a hot shower, or do whatever you enjoy outside of problem-solving.

Nap.

I get my best ideas in the morning after working on a problem. I couldn't have had these ideas last night.

Sleeping subconsciously. Leave it alone and you may be surprised by the genius it produces.

7 - Learn to live with frustration

There are problems that you’ll never solve.

Mathematicians are world-class problem-solvers. The brightest minds in history have failed to solve many mathematical problems.

A Gordian knot problem can frustrate you. You're smart!

Frustration-haters don't solve problems well. They choose simple problems to avoid frustration.

No. Great problem solvers want to solve a problem but know when to give up.

Frustration initially hurts. You adapt.

Famous last words

If you read this article, you probably solve problems. We've covered many ways to improve, so here's a summary:

1. Test your presumptions. Is the issue the same for everyone else when you see one? Or are your prejudices and self-judgments misguiding you?

2. Recognize the issue completely. On the surface, a problem may seem straightforward, but what's really going on? Try to see what the current situation might be building up to by thinking two steps ahead of the current situation.

3. Request more information. You are no longer a high school student. A two-sentence problem statement is not sufficient to provide a solution. Ask away if you need more details!

4. Think quickly and thoroughly. In a constrained amount of time, try to write down all your thoughts. All concepts are worthwhile! Later, you can order them.

5. Google it. There is a purpose for the internet. Use it.

6. Consider it later at night. A rested mind is more creative. It might seem counterintuitive to leave a problem unresolved. But while you're sleeping, your subconscious will handle the laborious tasks.

7. Accept annoyance as a normal part of life. Don't give up if you're feeling frustrated. It's a step in the procedure. It's also perfectly acceptable to give up on a problem because there are other, more pressing issues that need to be addressed.

You might feel stupid sometimes, but that just shows that you’re human. You care about the world and you want to make it better.

At the end of the day, that’s all there is to problem solving — making the world a little bit better.