Ask HN: How can I “work-out” critical thinking skills as I age?
54 comments
From the description, it sounds like what you're asking about is more along the lines of mental acuity rather than critical thinking per se (the latter is more about analysis in order to form judgments -- recognizing fallacies, rhetoric, and using deductive/inductive logic to form arguments).
If you're asking about mental acuity so you can think faster and solve brain teasers at interviews, many of the other comments in this thread offer great suggestions. Achieving familiarity with the problem space and pure practice are keys.
If you're asking about actual "critical thinking" (though I suspect that is not the case from your description, but it's an interesting topic that you might want to pursue anyway), the classic methods are the Socratic method, disputation and critical discussion of ideas with other people. If you don't have that luxury, you can train yourself by arguing with authors in the margins when you read books. Writing is key -- it helps crystallize thoughts and reveal weaknesses in thinking. Courses in philosophy also help provide a foundation on different approaches to reasoning.
If you're asking about mental acuity so you can think faster and solve brain teasers at interviews, many of the other comments in this thread offer great suggestions. Achieving familiarity with the problem space and pure practice are keys.
If you're asking about actual "critical thinking" (though I suspect that is not the case from your description, but it's an interesting topic that you might want to pursue anyway), the classic methods are the Socratic method, disputation and critical discussion of ideas with other people. If you don't have that luxury, you can train yourself by arguing with authors in the margins when you read books. Writing is key -- it helps crystallize thoughts and reveal weaknesses in thinking. Courses in philosophy also help provide a foundation on different approaches to reasoning.
Any books about this ? Thanks
I’m surprised no one has mentioned, but cardiovascular exercise is the number one know method to improve the health and function of your brain. Other suggestions are great as well if used in conjunction. I’ll come back and edit this with sources when I get the time.
I upvoted this but want to add that a good a diet is also a strong component. Exercise will not make much of an impact if one is eating tons of transfats, excessively drinking, abusing many drugs, etc. Mental and emotional health make a difference too. Prolonged periods of depression change the physiological and anatomical aspects of the brain.
Oh that’s a great point. Maybe it would be even better to have a somewhat blanket idea of taking care of yourself physically.
I may get downvoted for this but do check your Vitamin D3 and Vitamin B12 levels.
Is this in some way controversial? Seems like good advice.
Play chess, and do physical exercise.
Both will develop your mental stamina, and chess especially will hone your adversarial thinking.
You may even find that your chess fitness is directly comparable to your programming fitness and vice-versa. When you're programming fit through working on some incredibly hard problems in the week (think distributed systems or file systems or algorithms), then your chess will show an improvement. And when you're playing several hours of chess a day against a good opponent, then your programming will likewise benefit and your bug count drop as you naturally start thinking further ahead.
Both will develop your mental stamina, and chess especially will hone your adversarial thinking.
You may even find that your chess fitness is directly comparable to your programming fitness and vice-versa. When you're programming fit through working on some incredibly hard problems in the week (think distributed systems or file systems or algorithms), then your chess will show an improvement. And when you're playing several hours of chess a day against a good opponent, then your programming will likewise benefit and your bug count drop as you naturally start thinking further ahead.
I recommend go instead of chess, for the same reasons.
I played chess for years, learned go, and haven’t looked back. I personally prefer it.
YMMV
I played chess for years, learned go, and haven’t looked back. I personally prefer it.
YMMV
Pardon me for a stupid question, but you're not referring to go-language, are you?
Nope! The game! Though I think learning other programming languages through toy projects is useful, that’s a separate opinion
Do you have a favoured online site?
I play mostly on the Asian servers (Tygem and Fox Weiqi) because it is very fast to get games. For beginners and players ranked up to about 10kyu I recommend online-go.com! The Asian servers mentioned are also good for beginners, just not as easy to get into
I second physical exercise and add eating right. Diet and exercise can improve health, including cognitive health.
++ fasting
It will be a combination of things. Make sure you are getting enough sleep and exercise.
Pretty mind boggling that they are still asking brain teasers in interviews. If that is the type of question they are asking you can practice brain teaser and consulting type questions before an interview to.
Have a good grasp of the fundamentals of any subject matter before an interview. Practice is key.
Outside of that apply the concept of katas daily (http://codekata.com)
Outside of that apply the concept of katas daily (http://codekata.com)
For Data Science brain teasers, solving math problems that require clever use of the fundamentals. That means calculus, linear algebra, and basic stats.
A ninja is not defined by his sword. Reading books gives you new weapons, but you must learn to use them proficiently. Solving problems is therefore critical.
Some good sources of problems:
Sanjoy Mahajan (2010) "Street Fighting Mathematics"
Xingfeng Zhou (2008) "A Practical Guide to Quantitative Finance Interviews"
Timothy Crack (2019) "Heard on The Street: Quantitative Questions from Wall Street Job Interviews"
A ninja is not defined by his sword. Reading books gives you new weapons, but you must learn to use them proficiently. Solving problems is therefore critical.
Some good sources of problems:
Sanjoy Mahajan (2010) "Street Fighting Mathematics"
Xingfeng Zhou (2008) "A Practical Guide to Quantitative Finance Interviews"
Timothy Crack (2019) "Heard on The Street: Quantitative Questions from Wall Street Job Interviews"
What do you recommend for data structure and algo interviews to keep the brain sharp?
Others would know more about classic CS interviews.
I suppose that solving the problems in CLRS "Introduction to Algorithms" couldn't do any harm.
I suppose that solving the problems in CLRS "Introduction to Algorithms" couldn't do any harm.
Competitive Programming
https://cpbook.net/#CP4content
Kattis online judge you can use many languages https://open.kattis.com/help
Kattis online judge you can use many languages https://open.kattis.com/help
I stumbled onto brilliant.org recently and while it’s a bit narrow (Math skills), it seems better suited to cognitive training than most other attempts I’ve seen
Reading definitely helps a lot. Pick up different types of books, such as entomology, city planning, history, marathon training. Even beginner level is good enough. You just want to see how people solve problems.
Problem solving: https://en.wikipedia.org/wiki/Problem_solving
Critical thinking: https://en.wikipedia.org/wiki/Critical_thinking
Computational Thinking: https://en.wikipedia.org/wiki/Computational_thinking
> 1. Problem formulation (abstraction);
> 2. Solution expression (automation);
> 3. Solution execution and evaluation (analyses).
Interviewers may be more interested in demonstrating problem solving methods and f thinking aloud than an actual solution in an anxiety-producing scenario.
https://en.wikipedia.org/wiki/Brilliant_(website) ;
> Brilliant offers guided problem-solving based courses in math, science, and engineering, based on National Science Foundation research supporting active learning.[14]
Coding Interview University: https://github.com/jwasham/coding-interview-university
Programmer Competency Matrix: https://github.com/hltbra/programmer-competency-checklist
Inference > See also: https://en.wikipedia.org/wiki/Inference
- Deductive reasoning: https://en.wikipedia.org/wiki/Deductive_reasoning
- Inductive reasoning: https://en.wikipedia.org/wiki/Inductive_reasoning
> This is the [open] textbook for the Foundations of Data Science class at UC Berkeley: "Computational and Inferential Thinking: The Foundations of Data Science" http://inferentialthinking.com/
Critical thinking: https://en.wikipedia.org/wiki/Critical_thinking
Computational Thinking: https://en.wikipedia.org/wiki/Computational_thinking
> 1. Problem formulation (abstraction);
> 2. Solution expression (automation);
> 3. Solution execution and evaluation (analyses).
Interviewers may be more interested in demonstrating problem solving methods and f thinking aloud than an actual solution in an anxiety-producing scenario.
https://en.wikipedia.org/wiki/Brilliant_(website) ;
> Brilliant offers guided problem-solving based courses in math, science, and engineering, based on National Science Foundation research supporting active learning.[14]
Coding Interview University: https://github.com/jwasham/coding-interview-university
Programmer Competency Matrix: https://github.com/hltbra/programmer-competency-checklist
Inference > See also: https://en.wikipedia.org/wiki/Inference
- Deductive reasoning: https://en.wikipedia.org/wiki/Deductive_reasoning
- Inductive reasoning: https://en.wikipedia.org/wiki/Inductive_reasoning
> This is the [open] textbook for the Foundations of Data Science class at UC Berkeley: "Computational and Inferential Thinking: The Foundations of Data Science" http://inferentialthinking.com/
I'm not sure you can if the definition of "critical thinking" is forming snap solutions to novel problems in a few minutes. Experience is expressed by coming to quick solutions to familiarish problems and considered solutions to unfamiliar problems. And with experience comes intuition about what is and isn't so important. There is just no way to move braing-teasers to the important side of an experienced intuition when the problem domain resembles that in which a mature individual is experienced.
When I was actively providing advice on the Architectural Registration Examination, I used to see this all the time with the Site Design test. The test gave the test candidate ninety minutes to organize several components on an unfamiliar site against a set of competing requirements and constraints. A common rant in the discussion forum was "I failed even though I've been laying out sites professionally for {N} years," where {N} might be from three to ten.
The first ninety minutes of real world site design consists of opening the civil engineer's email, creating a directory to for the project, saving the attached CAD file, cleaning it up enough to be usable for architectural design purposes, printing the regulatory requirements for the project file, talking with the principal-in-charge about the client requirements, and then going to lunch because it's been four hours and maybe starting on the design in the afternoon or later in the week because that's the way the world works and the client requirements will probably change anyway.
Which is how experience made it easy to fail the test because of the ways the test did not reflect the real world. The real world has depth and a lot it-depends and experience pays off precisely because it handles the depths and makes informed choices about all the it-depends.
Or to put it another way, Fizz-Buzz in TensorFlow, https://joelgrus.com/2016/05/23/fizz-buzz-in-tensorflow/
When I was actively providing advice on the Architectural Registration Examination, I used to see this all the time with the Site Design test. The test gave the test candidate ninety minutes to organize several components on an unfamiliar site against a set of competing requirements and constraints. A common rant in the discussion forum was "I failed even though I've been laying out sites professionally for {N} years," where {N} might be from three to ten.
The first ninety minutes of real world site design consists of opening the civil engineer's email, creating a directory to for the project, saving the attached CAD file, cleaning it up enough to be usable for architectural design purposes, printing the regulatory requirements for the project file, talking with the principal-in-charge about the client requirements, and then going to lunch because it's been four hours and maybe starting on the design in the afternoon or later in the week because that's the way the world works and the client requirements will probably change anyway.
Which is how experience made it easy to fail the test because of the ways the test did not reflect the real world. The real world has depth and a lot it-depends and experience pays off precisely because it handles the depths and makes informed choices about all the it-depends.
Or to put it another way, Fizz-Buzz in TensorFlow, https://joelgrus.com/2016/05/23/fizz-buzz-in-tensorflow/
I can't believe no one has mentioned writing - try thinking about something you strongly believe in (but others disagree with, like a political/philosophical view), then write out your argument for why it is true. Then write out what you think your opponent believes and think about how they would pick apart your argument. Then rewrite your side again. Have someone else read both sides and critique each.
Also try explaining how to do some task. Give it to someone else and, based only on your instructions, have them try and do the thing you laid out. We're they able to do it effectively? What questions did they have and where did they get confused? These will help you improve your explanation and argument skills.
Also try explaining how to do some task. Give it to someone else and, based only on your instructions, have them try and do the thing you laid out. We're they able to do it effectively? What questions did they have and where did they get confused? These will help you improve your explanation and argument skills.
Brain teasers are really useful for job interviews where the role involves solving brain teasers. Other than that they can get in the sea.
This.
I am about that age (that I guess the OP is) where, luckily for me, I have created a curriculum and experience that will be wasted solving brain teasers.
Haven't interviewed in a good while (at least not from the interviewed side), but if the interview consists of 'how much orange juice is consumed in the US per day' kind of questions, I'd probably excuse myself, thank everyone for their time and look for greener pastures elsewhere.
I am about that age (that I guess the OP is) where, luckily for me, I have created a curriculum and experience that will be wasted solving brain teasers.
Haven't interviewed in a good while (at least not from the interviewed side), but if the interview consists of 'how much orange juice is consumed in the US per day' kind of questions, I'd probably excuse myself, thank everyone for their time and look for greener pastures elsewhere.
Fish oil is a good one. It's supposed to prevent Alzheimer's if you take one gram a day, and it may improve your eyesight and heart at that dose.
You can take five a day. You can take 10. People with heavy brain damage (many minutes without oxygen) take 15 a day for six months to learn to walk and talk again, and they get recover.
You can take five a day. You can take 10. People with heavy brain damage (many minutes without oxygen) take 15 a day for six months to learn to walk and talk again, and they get recover.
Joe Rogan recently had Dr Andrew Huberman on his show [0]. Dr Huberman had a lot of fantastic information about changes in mental plasticity and how to triggering learning in adults.
[0] https://m.youtube.com/watch?v=gLJowTOkZVo
[0] https://m.youtube.com/watch?v=gLJowTOkZVo
Joe Rogan spam is an invasive species.
Friend, I just finished listening to the podcast after seeing this comment. It is genuinely relevant. The episode is full of useful information related to brain plasticity that OP would benefit from. Don't dismiss all of a creator's content as spam.
I think both math and (analytic) philosophy can help. When I say math, there's two different things I have in mind. One is just solving problems. Get any old text book at your level and start doing homework problems. Same works for physics. The other thing I have in mind is theorem proving. Look at Paul Halmos' book on Naive Set Theory for example or pick something more at your level.
As for philosophy, trying to pin down subtle distinctions and following the extremely abstract arguments could help. You could start there with text books, or reading in the history of philosophy like Aristotle, Plato, Descartes or maybe by looking up concepts and problems you're already familiar with in SEP.
Good luck and have fun.
[1] hhtp://plato.stanford.edu/
As for philosophy, trying to pin down subtle distinctions and following the extremely abstract arguments could help. You could start there with text books, or reading in the history of philosophy like Aristotle, Plato, Descartes or maybe by looking up concepts and problems you're already familiar with in SEP.
Good luck and have fun.
[1] hhtp://plato.stanford.edu/
Meditation can help maintain neuroplasticity and help you in many other parts of your life as well. I recommend the waking up app for a good intro
https://www.wakingup.com/
https://www.wakingup.com/
If you haven't already, check out https://projecteuler.net/. It's a huge collection of logic problems of varying difficulty that require a mix of math and programming to solve. There are 723 problems at the time of this writing, and a new one is added each week. After solving a problem (you need an account to submit solutions, but can view all problems anonymously), you get access to a discussion thread where you can gawk at the often mind-blowing solutions that other solvers have hacked up in all kinds of languages.
I hope you can afford my answer. It’s time to live your life for you, not “them.”
Yeah.. Ideally you can find a job that plays to your strength. If you don't like and aren't good with this type of work, it's probably a sign that you should focus on something you find easy and like. It's easy to be good when you really enjoy something
I agree, don’t get me wrong. I’m all for that mentality and generally draw the boundaries between work and life. However, in this precarious time, I need to find another job.
1) Think hard about things that you have to work at in order to understand
2) Engage in exercise that regularly includes anaerobic intensity
3) Sleep well and deeply
Learning is brain growth that occurs as a result of thinking, largely during rest and sleep following the activity. Exercise will increase the amount of growth that occurs (mentally and physically), and good cardiovascular health is effectively the same thing as good brain health
And, maybe obviously, practice the brain teasers and interview questions. They are a skill that is not the same thing as being mentally sharp
Learning is brain growth that occurs as a result of thinking, largely during rest and sleep following the activity. Exercise will increase the amount of growth that occurs (mentally and physically), and good cardiovascular health is effectively the same thing as good brain health
And, maybe obviously, practice the brain teasers and interview questions. They are a skill that is not the same thing as being mentally sharp
I notice the same issues as I approach 50.
Here's what seems to work for me:
1. Plenty of cardiovascular exercise.
2. Eat well, including plenty of green plants.
3. Get plenty of sleep.
4. Limit online consumption and other unimportant inputs (TV, gaming, podcasts, etc).
5. Practice being bored^W^Wmindfulness. This could be meditating, or just sitting outside contemplatively, or not consuming content while performing #1.
6. Keep spot checking yourself for where you're coming up short with the above 5 items. It's all too easy to fix the issue, feel great, and then fall out of the above habits. But you can't. You've got to stick to the plan.
Here's what seems to work for me:
1. Plenty of cardiovascular exercise.
2. Eat well, including plenty of green plants.
3. Get plenty of sleep.
4. Limit online consumption and other unimportant inputs (TV, gaming, podcasts, etc).
5. Practice being bored^W^Wmindfulness. This could be meditating, or just sitting outside contemplatively, or not consuming content while performing #1.
6. Keep spot checking yourself for where you're coming up short with the above 5 items. It's all too easy to fix the issue, feel great, and then fall out of the above habits. But you can't. You've got to stick to the plan.
One thing I haven't seen mentioned is that you could use Lions Mane mushroom, or it's extract. There was a double blind study from Japan that shows this is a nootropics.
Also, brain teasers are a BS way to interview. One of the best interviews I had was a mock architecture session (I didn't get the job). They gave me an overview of a project, told me to use AWS tech, and let me ask questions as I worked through a rough architecture.
Also, brain teasers are a BS way to interview. One of the best interviews I had was a mock architecture session (I didn't get the job). They gave me an overview of a project, told me to use AWS tech, and let me ask questions as I worked through a rough architecture.
Develop Shamatha, which is a calm abiding mind, meditative equipoise, single pointed concentration.
Then engage in analytical meditation, typically known as Vipassanā in the Buddhist tradition, but essentially it involves analytically decomposing whatever you're meditating on.
I realized that before I ever dove into Tibetan philosophy that I was developing these two as I designed and constructed software (as I'm sure a lot of us do).
Then engage in analytical meditation, typically known as Vipassanā in the Buddhist tradition, but essentially it involves analytically decomposing whatever you're meditating on.
I realized that before I ever dove into Tibetan philosophy that I was developing these two as I designed and constructed software (as I'm sure a lot of us do).
Always be skeptical, objective, and learn to deeply appreciate originality.
I wrote this yesterday after confronting somebody saying something short-sighted: https://github.com/prettydiff/wisdom/blob/master/faulty_prem...
I wrote this yesterday after confronting somebody saying something short-sighted: https://github.com/prettydiff/wisdom/blob/master/faulty_prem...
Not a bad read. In the opening paragraph you conflate argument validity with argument soundness, though. Thanks for the link.
Grey matter is where knowledge is stored. White matter is where the connections are. Enhance those connections. For that, I recommend learning to juggle. https://www.sciencedaily.com/releases/2009/10/091016114055.h...
This is a gross overextension of the results of that study. From the article you linked, emphasis mine:
> ‘This exciting new result raises a lot of questions,’ says Dr Johansen-Berg, ‘MRI is an indirect way to measure brain structure and so we cannot be sure exactly what is changing when these people learn. Future work should test whether these results reflect changes in the shape or number of nerve fibres, or growth of the insulating myelin sheath surrounding the fibres.’
> ‘Of course, this doesn’t mean that everyone should go out and start juggling to improve their brains. We chose juggling purely as a complex new skill for people to learn.
If OP takes your advice, they'd end up being decent at juggling, but at the huge opportunity cost of not practicing actual critical-thinking skills directly, or reading articles and books relevant to their target domain of expertise, or some other approach to prepare for interviews and a career in data science that's more effective than juggling, of all things.
Besides, OP already said they've been juggling two kids!
> ‘This exciting new result raises a lot of questions,’ says Dr Johansen-Berg, ‘MRI is an indirect way to measure brain structure and so we cannot be sure exactly what is changing when these people learn. Future work should test whether these results reflect changes in the shape or number of nerve fibres, or growth of the insulating myelin sheath surrounding the fibres.’
> ‘Of course, this doesn’t mean that everyone should go out and start juggling to improve their brains. We chose juggling purely as a complex new skill for people to learn.
If OP takes your advice, they'd end up being decent at juggling, but at the huge opportunity cost of not practicing actual critical-thinking skills directly, or reading articles and books relevant to their target domain of expertise, or some other approach to prepare for interviews and a career in data science that's more effective than juggling, of all things.
Besides, OP already said they've been juggling two kids!
Although not directly related to critical thinking, product questions or brain teasers but what works for me is reading and reading whatever floats my boat. I consider it weight lifting for the brain.
It just takes practice. I had to do the same. I started solving Sudoku, George summers puzzles.
In the process, I could develop a general process to solve problems.
Using systems thinking helped a lot.
In the process, I could develop a general process to solve problems.
Using systems thinking helped a lot.
[deleted]
Thinking in general is greatly affected by two things:
1. Physical exercise. Some blend of cardio and strength training is preferable, but at least cardio is pretty much a requirement.
2. Sleep quality. Not just duration, but quality as well. If you have sleep apnea especially (many people do and don't even know it), you need to address that.
Also, if you're getting _interviewed_ in such detail as a consultant, you're playing the consulting game wrong. People should just hire you based on your track record as exemplified by direct recommendations from previous customers and people within your network.
One of the benefits of a consultant from a customer standpoint is that if they determine they've made a mistake, they can just terminate your contract. So an elaborate interview is a waste of time for both sides.
1. Physical exercise. Some blend of cardio and strength training is preferable, but at least cardio is pretty much a requirement.
2. Sleep quality. Not just duration, but quality as well. If you have sleep apnea especially (many people do and don't even know it), you need to address that.
Also, if you're getting _interviewed_ in such detail as a consultant, you're playing the consulting game wrong. People should just hire you based on your track record as exemplified by direct recommendations from previous customers and people within your network.
One of the benefits of a consultant from a customer standpoint is that if they determine they've made a mistake, they can just terminate your contract. So an elaborate interview is a waste of time for both sides.
If you just care about brain teasers, caffeine is quite effective at inducing small temporary increases in cognitive ability and is totally safe. Try having a big 'ol cup of joe before interviews.
If you want to learn how to think more critically, you need to force yourself to continuously engage new ideas and learn to recognize an author's motivations and biases while still evaluating their arguments objectively, putting aside your own past conclusions temporarily in order to understand their argument. Then do the same for ideas you have previously agreed with, and see which ideas hold up to scrutiny. Only then can you truly call conclusions your own.
If you want to learn how to think more critically, you need to force yourself to continuously engage new ideas and learn to recognize an author's motivations and biases while still evaluating their arguments objectively, putting aside your own past conclusions temporarily in order to understand their argument. Then do the same for ideas you have previously agreed with, and see which ideas hold up to scrutiny. Only then can you truly call conclusions your own.
Listening to Beethoven before a test is also known to induce a small cognitive gain for 15 minutes after listening.
Any help or resources will be tremendously appreciated.