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Katherine Kornei

Katherine Kornei

3 years ago

The InSight lander from NASA has recorded the greatest tremor ever felt on Mars.

The magnitude 5 earthquake was responsible for the discharge of energy that was 10 times greater than the previous record holder.

Any Martians who happen to be reading this should quickly learn how to duck and cover.

NASA's Jet Propulsion Laboratory in Pasadena, California, reported that on May 4, the planet Mars was shaken by an earthquake of around magnitude 5, making it the greatest Marsquake ever detected to this point. The shaking persisted for more than six hours and unleashed more than ten times as much energy as the earthquake that had previously held the record for strongest.

The event was captured on record by the InSight lander, which is operated by the United States Space Agency and has been researching the innards of Mars ever since it touched down on the planet in 2018 (SN: 11/26/18). The epicenter of the earthquake was probably located in the vicinity of Cerberus Fossae, which is located more than 1,000 kilometers away from the lander.

The surface of Cerberus Fossae is notorious for being broken up and experiencing periodic rockfalls. According to geophysicist Philippe Lognonné, who is the lead investigator of the Seismic Experiment for Interior Structure, the seismometer that is onboard the InSight lander, it is reasonable to assume that the ground is moving in that area. "This is an old crater from a volcanic eruption."

Marsquakes, which are similar to earthquakes in that they give information about the interior structure of our planet, can be utilized to investigate what lies beneath the surface of Mars (SN: 7/22/21). And according to Lognonné, who works at the Institut de Physique du Globe in Paris, there is a great deal that can be gleaned from analyzing this massive earthquake. Because the quality of the signal is so high, we will be able to focus on the specifics.

More on Science

Bob Service

Bob Service

3 years ago

Did volcanic 'glasses' play a role in igniting early life?

Quenched lava may have aided in the formation of long RNA strands required by primitive life.

It took a long time for life to emerge. Microbes were present 3.7 billion years ago, just a few hundred million years after the 4.5-billion-year-old Earth had cooled enough to sustain biochemistry, according to fossils, and many scientists believe RNA was the genetic material for these first species. RNA, while not as complicated as DNA, would be difficult to forge into the lengthy strands required to transmit genetic information, raising the question of how it may have originated spontaneously.

Researchers may now have a solution. They demonstrate how basaltic glasses assist individual RNA letters, also known as nucleoside triphosphates, join into strands up to 200 letters long in lab studies. The glasses are formed when lava is quenched in air or water, or when melted rock generated by asteroid strikes cools rapidly, and they would have been plentiful in the early Earth's fire and brimstone.

The outcome has caused a schism among top origin-of-life scholars. "This appears to be a great story that finally explains how nucleoside triphosphates react with each other to create RNA strands," says Thomas Carell, a scientist at Munich's Ludwig Maximilians University. However, Harvard University's Jack Szostak, an RNA expert, says he won't believe the results until the study team thoroughly describes the RNA strands.

Researchers interested in the origins of life like the idea of a primordial "RNA universe" since the molecule can perform two different functions that are essential for life. It's made up of four chemical letters, just like DNA, and can carry genetic information. RNA, like proteins, can catalyze chemical reactions that are necessary for life.

However, RNA can cause headaches. No one has yet discovered a set of plausible primordial conditions that would cause hundreds of RNA letters—each of which is a complicated molecule—to join together into strands long enough to support the intricate chemistry required to kick-start evolution.

Basaltic glasses may have played a role, according to Stephen Mojzsis, a geologist at the University of Colorado, Boulder. They're high in metals like magnesium and iron, which help to trigger a variety of chemical reactions. "Basaltic glass was omnipresent on Earth at the time," he adds.

He provided the Foundation for Applied Molecular Evolution samples of five different basalt glasses. Each sample was ground into a fine powder, sanitized, and combined with a solution of nucleoside triphosphates by molecular biologist Elisa Biondi and her colleagues. The RNA letters were unable to link up without the presence of glass powder. However, when the molecules were mixed with the glass particles, they formed long strands of hundreds of letters, according to the researchers, who published their findings in Astrobiology this week. There was no need for heat or light. Biondi explains, "All we had to do was wait." After only a day, little RNA strands produced, yet the strands continued to grow for months. Jan Paek, a molecular biologist at Firebird Biomolecular Sciences, says, "The beauty of this approach is its simplicity." "Mix the components together, wait a few days, and look for RNA."

Nonetheless, the findings pose a slew of problems. One of the questions is how nucleoside triphosphates came to be in the first place. Recent study by Biondi's colleague Steven Benner suggests that the same basaltic glasses may have aided in the creation and stabilization of individual RNA letters.

The form of the lengthy RNA strands, according to Szostak, is a significant challenge. Enzymes in modern cells ensure that most RNAs form long linear chains. RNA letters, on the other hand, can bind in complicated branching sequences. Szostak wants the researchers to reveal what kind of RNA was produced by the basaltic glasses. "It irritates me that the authors made an intriguing initial finding but then chose to follow the hype rather than the research," Szostak says.

Biondi acknowledges that her team's experiment almost probably results in some RNA branching. She does acknowledge, however, that some branched RNAs are seen in species today, and that analogous structures may have existed before the origin of life. Other studies carried out by the study also confirmed the presence of lengthy strands with connections, indicating that they are most likely linear. "It's a healthy argument," says Dieter Braun, a Ludwig Maximilian University origin-of-life chemist. "It will set off the next series of tests."

Michael Hunter, MD

Michael Hunter, MD

3 years ago

5 Drugs That May Increase Your Risk of Dementia

Photo by danilo.alvesd on Unsplash

While our genes can't be changed easily, you can avoid some dementia risk factors. Today we discuss dementia and five drugs that may increase risk.

Memory loss appears to come with age, but we're not talking about forgetfulness. Sometimes losing your car keys isn't an indication of dementia. Dementia impairs the capacity to think, remember, or make judgments. Dementia hinders daily tasks.

Alzheimers is the most common dementia. Dementia is not normal aging, unlike forgetfulness. Aging increases the risk of Alzheimer's and other dementias. A family history of the illness increases your risk, according to the Mayo Clinic (USA).

Given that our genes are difficult to change (I won't get into epigenetics), what are some avoidable dementia risk factors? Certain drugs may cause cognitive deterioration.

Today we look at four drugs that may cause cognitive decline.

Dementia and benzodiazepines

Benzodiazepine sedatives increase brain GABA levels. Example benzodiazepines:

  • Diazepam (Valium) (Valium)

  • Alprazolam (Xanax) (Xanax)

  • Clonazepam (Klonopin) (Klonopin)

Addiction and overdose are benzodiazepine risks. Yes! These medications don't raise dementia risk.

USC study: Benzodiazepines don't increase dementia risk in older adults.

Benzodiazepines can produce short- and long-term amnesia. This memory loss hinders memory formation. Extreme cases can permanently impair learning and memory. Anterograde amnesia is uncommon.

2. Statins and dementia

Statins reduce cholesterol. They prevent a cholesterol-making chemical. Examples:

  • Atorvastatin (Lipitor) (Lipitor)

  • Fluvastatin (Lescol XL) (Lescol XL)

  • Lovastatin (Altoprev) (Altoprev)

  • Pitavastatin (Livalo, Zypitamag) (Livalo, Zypitamag)

  • Pravastatin (Pravachol) (Pravachol)

  • Rosuvastatin (Crestor, Ezallor) (Crestor, Ezallor)

  • Simvastatin (Zocor) (Zocor)

Photo by Towfiqu barbhuiya on Unsplash

This finding is contentious. Harvard's Brigham and Womens Hospital's Dr. Joann Manson says:

“I think that the relationship between statins and cognitive function remains controversial. There’s still not a clear conclusion whether they help to prevent dementia or Alzheimer’s disease, have neutral effects, or increase risk.”

This one's off the dementia list.

3. Dementia and anticholinergic drugs

Anticholinergic drugs treat many conditions, including urine incontinence. Drugs inhibit acetylcholine (a brain chemical that helps send messages between cells). Acetylcholine blockers cause drowsiness, disorientation, and memory loss.

First-generation antihistamines, tricyclic antidepressants, and overactive bladder antimuscarinics are common anticholinergics among the elderly.

Anticholinergic drugs may cause dementia. One study found that taking anticholinergics for three years or more increased the risk of dementia by 1.54 times compared to three months or less. After stopping the medicine, the danger may continue.

4. Drugs for Parkinson's disease and dementia

Cleveland Clinic (USA) on Parkinson's:

Parkinson's disease causes age-related brain degeneration. It causes delayed movements, tremors, and balance issues. Some are inherited, but most are unknown. There are various treatment options, but no cure.

Parkinson's medications can cause memory loss, confusion, delusions, and obsessive behaviors. The drug's effects on dopamine cause these issues.

A 2019 JAMA Internal Medicine study found powerful anticholinergic medications enhance dementia risk.

Those who took anticholinergics had a 1.5 times higher chance of dementia. Individuals taking antidepressants, antipsychotic drugs, anti-Parkinson’s drugs, overactive bladder drugs, and anti-epileptic drugs had the greatest risk of dementia.

Anticholinergic medicines can lessen Parkinson's-related tremors, but they slow cognitive ability. Anticholinergics can cause disorientation and hallucinations in those over 70.

Photo by Wengang Zhai on Unsplash

5. Antiepileptic drugs and dementia

The risk of dementia from anti-seizure drugs varies with drugs. Levetiracetam (Keppra) improves Alzheimer's cognition.

One study linked different anti-seizure medications to dementia. Anti-epileptic medicines increased the risk of Alzheimer's disease by 1.15 times in the Finnish sample and 1.3 times in the German population. Depakote, Topamax are drugs.

Adam Frank

Adam Frank

3 years ago

Humanity is not even a Type 1 civilization. What might a Type 3 be capable of?

The Kardashev scale grades civilizations from Type 1 to Type 3 based on energy harvesting.

How do technologically proficient civilizations emerge across timescales measuring in the tens of thousands or even millions of years? This is a question that worries me as a researcher in the search for “technosignatures” from other civilizations on other worlds. Since it is already established that longer-lived civilizations are the ones we are most likely to detect, knowing something about their prospective evolutionary trajectories could be translated into improved search tactics. But even more than knowing what to seek for, what I really want to know is what happens to a society after so long time. What are they capable of? What do they become?

This was the question Russian SETI pioneer Nikolai Kardashev asked himself back in 1964. His answer was the now-famous “Kardashev Scale.” Kardashev was the first, although not the last, scientist to try and define the processes (or stages) of the evolution of civilizations. Today, I want to launch a series on this question. It is crucial to technosignature studies (of which our NASA team is hard at work), and it is also important for comprehending what might lay ahead for mankind if we manage to get through the bottlenecks we have now.

The Kardashev scale

Kardashev’s question can be expressed another way. What milestones in a civilization’s advancement up the ladder of technical complexity will be universal? The main notion here is that all (or at least most) civilizations will pass through some kind of definable stages as they progress, and some of these steps might be mirrored in how we could identify them. But, while Kardashev’s major focus was identifying signals from exo-civilizations, his scale gave us a clear way to think about their evolution.

The classification scheme Kardashev employed was not based on social systems of ethics because they are something that we can probably never predict about alien cultures. Instead, it was built on energy, which is something near and dear to the heart of everybody trained in physics. Energy use might offer the basis for universal stages of civilisation progression because you cannot do the work of establishing a civilization without consuming energy. So, Kardashev looked at what energy sources were accessible to civilizations as they evolved technologically and used those to build his scale.

From Kardashev’s perspective, there are three primary levels or “types” of advancement in terms of harvesting energy through which a civilization should progress.

Type 1: Civilizations that can capture all the energy resources of their native planet constitute the first stage. This would imply capturing all the light energy that falls on a world from its host star. This makes it reasonable, given solar energy will be the largest source available on most planets where life could form. For example, Earth absorbs hundreds of atomic bombs’ worth of energy from the Sun every second. That is a rather formidable energy source, and a Type 1 race would have all this power at their disposal for civilization construction.

Type 2: These civilizations can extract the whole energy resources of their home star. Nobel Prize-winning scientist Freeman Dyson famously anticipated Kardashev’s thinking on this when he imagined an advanced civilization erecting a large sphere around its star. This “Dyson Sphere” would be a machine the size of the complete solar system for gathering stellar photons and their energy.

Type 3: These super-civilizations could use all the energy produced by all the stars in their home galaxy. A normal galaxy has a few hundred billion stars, so that is a whole lot of energy. One way this may be done is if the civilization covered every star in their galaxy with Dyson spheres, but there could also be more inventive approaches.

Implications of the Kardashev scale

Climbing from Type 1 upward, we travel from the imaginable to the god-like. For example, it is not hard to envisage utilizing lots of big satellites in space to gather solar energy and then beaming that energy down to Earth via microwaves. That would get us to a Type 1 civilization. But creating a Dyson sphere would require chewing up whole planets. How long until we obtain that level of power? How would we have to change to get there? And once we get to Type 3 civilizations, we are virtually thinking about gods with the potential to engineer the entire cosmos.

For me, this is part of the point of the Kardashev scale. Its application for thinking about identifying technosignatures is crucial, but even more strong is its capacity to help us shape our imaginations. The mind might become blank staring across hundreds or thousands of millennia, and so we need tools and guides to focus our attention. That may be the only way to see what life might become — what we might become — once it arises to start out beyond the boundaries of space and time and potential.


This is a summary. Read the full article here.

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Vitalik

Vitalik

4 years ago

An approximate introduction to how zk-SNARKs are possible (part 1)

You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has 2 very powerful applications: Perhaps the most powerful cryptographic technology to come out of the last decade is general-purpose succinct zero knowledge proofs, usually called zk-SNARKs ("zero knowledge succinct arguments of knowledge"). A zk-SNARK allows you to generate a proof that some computation has some particular output, in such a way that the proof can be verified extremely quickly even if the underlying computation takes a very long time to run. The "ZK" part adds an additional feature: the proof can keep some of the inputs to the computation hidden.

You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has two very powerful applications:

  1. Scalability: if a block takes a long time to verify, one person can verify it and generate a proof, and everyone else can just quickly verify the proof instead
  2. Privacy: you can prove that you have the right to transfer some asset (you received it, and you didn't already transfer it) without revealing the link to which asset you received. This ensures security without unduly leaking information about who is transacting with whom to the public.

But zk-SNARKs are quite complex; indeed, as recently as in 2014-17 they were still frequently called "moon math". The good news is that since then, the protocols have become simpler and our understanding of them has become much better. This post will try to explain how ZK-SNARKs work, in a way that should be understandable to someone with a medium level of understanding of mathematics.

Why ZK-SNARKs "should" be hard

Let us take the example that we started with: we have a number (we can encode "cow" followed by the secret input as an integer), we take the SHA256 hash of that number, then we do that again another 99,999,999 times, we get the output, and we check what its starting digits are. This is a huge computation.

A "succinct" proof is one where both the size of the proof and the time required to verify it grow much more slowly than the computation to be verified. If we want a "succinct" proof, we cannot require the verifier to do some work per round of hashing (because then the verification time would be proportional to the computation). Instead, the verifier must somehow check the whole computation without peeking into each individual piece of the computation.

One natural technique is random sampling: how about we just have the verifier peek into the computation in 500 different places, check that those parts are correct, and if all 500 checks pass then assume that the rest of the computation must with high probability be fine, too?

Such a procedure could even be turned into a non-interactive proof using the Fiat-Shamir heuristic: the prover computes a Merkle root of the computation, uses the Merkle root to pseudorandomly choose 500 indices, and provides the 500 corresponding Merkle branches of the data. The key idea is that the prover does not know which branches they will need to reveal until they have already "committed to" the data. If a malicious prover tries to fudge the data after learning which indices are going to be checked, that would change the Merkle root, which would result in a new set of random indices, which would require fudging the data again... trapping the malicious prover in an endless cycle.

But unfortunately there is a fatal flaw in naively applying random sampling to spot-check a computation in this way: computation is inherently fragile. If a malicious prover flips one bit somewhere in the middle of a computation, they can make it give a completely different result, and a random sampling verifier would almost never find out.


It only takes one deliberately inserted error, that a random check would almost never catch, to make a computation give a completely incorrect result.

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? There is a clever solution.

see part 2

Tim Denning

Tim Denning

3 years ago

I Posted Six Times a Day for 210 Days on Twitter. Here's What Happened.

I'd spend hours composing articles only to find out they were useless. Twitter solved the problem.

Photo by Humphrey Muleba on Unsplash

Twitter is wrinkled, say critics.

Nope. Writing is different. It won't make sense until you write there.

Twitter is resurgent. People are reading again. 15-second TikToks overloaded our senses.

After nuking my 20,000-follower Twitter account and starting again, I wrote every day for 210 days.

I'll explain.

I came across the strange world of microblogging.

Traditional web writing is filler-heavy.

On Twitter, you must be brief. I played Wordle.

Twitter Threads are the most popular writing format. Like a blog post. It reminds me of the famous broetry posts on LinkedIn a few years ago.

Image Credit: Josh Fetcher via LinkedIn

Threads combine tweets into an article.

  • Sharp, concise sentences

  • No regard for grammar

  • As important as the information is how the text looks.

Twitter Threads are like Michael Angelo's David monument. He chipped away at an enormous piece of marble until a man with a big willy appeared.

That's Twitter Threads.

I tried to remove unnecessary layers from several of my Wordpress blog posts. Then I realized something.

Tweeting from scratch is easier and more entertaining. It's quicker and makes you think more concisely.

Superpower: saying much with little words. My long-form writing has improved. My article sentences resemble tweets.

You never know what will happen.

Twitter's subcultures are odd. Best-performing tweets are strange.

Unusual trend: working alone and without telling anyone. It's a rebellion against Instagram influencers who share their every moment.

Early on, random thoughts worked:

My friend’s wife is Ukrainian. Her family are trapped in the warzone. He is devastated. And here I was complaining about my broken garage door. War puts everything in perspective. Today is a day to be grateful for peace.

Documenting what's happening triggers writing. It's not about viral tweets. Helping others matters.

There are numerous anonymous users.

Twitter uses pseudonyms.

You don't matter. On sites like LinkedIn, you must use your real name. Welcome to the Cyberpunk metaverse of Twitter :)

One daily piece of writing is a powerful habit.

Habits build creator careers. Read that again.

Twitter is an easy habit to pick up. If you can't tweet in one sentence, something's wrong. Easy-peasy-japanese.

Not what I tweeted, but my constancy, made the difference.

Daily writing is challenging, especially if your supervisor is on your back. Twitter encourages writing.

Tweets evolved as the foundation of all other material.

During my experiment, I enjoyed Twitter's speed.

Tweets get immediate responses, comments, and feedback. My popular tweets become newspaper headlines. I've also written essays from tweet discussions.

Sometimes the tweet and article were clear. Twitter sometimes helped me overcome writer's block.

I used to spend hours composing big things that had little real-world use.

Twitter helped me. No guessing. Data guides my coverage and validates concepts.

Test ideas on Twitter.

It took some time for my email list to grow.

Subscribers are a writer's lifeblood.

Without them, you're broke and homeless when Mark Zuckerberg tweaks the algorithms for ad dollars. Twitter has three ways to obtain email subscribers:

1. Add a link to your bio.

Twitter allows bio links (LinkedIn now does too). My eBook's landing page is linked. I collect emails there.

2. Start an online newsletter.

Twitter bought newsletter app Revue. They promote what they own.

I just established up a Revue email newsletter. I imported them weekly into my ConvertKit email list.

3. Create Twitter threads and include a link to your email list in the final tweet.

Write Twitter Threads and link the last tweet to your email list (example below).

Initial email subscribers were modest.

Numbers are growing. Twitter provides 25% of my new email subscribers. Some days, 50 people join.

Without them, my writing career is over. I'd be back at a 9-5 job begging for time off to spend with my newborn daughter. Nope.

Collect email addresses or die trying.

As insurance against unsubscribes and Zucks, use a second email list or Discord community.

What I still need to do

Twitter's fun. I'm wiser. I need to enable auto-replies and auto-DMs (direct messages).

This adds another way to attract subscribers. I schedule tweets with Tweet Hunter.

It’s best to go slow. People assume you're an internet marketer if you spam them with click requests.

A human internet marketer is preferable to a robot. My opinion.

210 days on Twitter taught me that. I plan to use the platform until I'm a grandfather unless Elon ruins it.

Ari Joury, PhD

Ari Joury, PhD

3 years ago

7 ways to turn into a major problem-solver

Frustration is normal when faced with unsolvable problems. Image by author

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.