Before spending far too much time on the first question, it’s worth it to spend a little bit of time on the second: what’s the quickest way to show that this can’t possibly work? Often this takes the form of looking for statements such as “If X worked, then Y would work too”, and then you go test Y. Just because Y holds, doesn’t mean X does… but if it doesn’t, you know X doesn’t.
It can feel like a bit of a diversion in the moment (“why am I wasting my time with Y, when I really care about X?”) but it has saved me months, possibly years of going down rabbit holes in my career. Likewise, it definitely helps with that anxiety you mention, because it means I at least have some motivation that my idea isn’t completely crazy.
Scott Aaronson has a checklist on how to quicky reject a P?=NP paper, and one of the best methods is to check whether the paper proves something weaker first.
I had a function that performed a 256-bit division. I thought there was a good chance it could be optimized, because the dividend was fixed: the function computed 2^256 / d. Surely, if the dividend was always the same (and such a nice, power-of-2 number!), there should be a way to exploit that, right?
I poked at it for a few hours before it occurred to me that I could ask someone else who knew a lot about division. So I cold-emailed Daniel Lemire. He replied with the following argument:
Suppose you had an algorithm that could compute 2^k / d much more efficiently than the typical algorithm. You could then use this algorithm to speed up any division n / d, by rewriting the expression as (n - 2^k)/d + 2^k/d. This works because both dividends will now be less than 2^k, and division algorithms get faster as the dividend gets smaller.
In other words: it's not impossible that there's an efficient algorithm for 2^k / d, but if it does exist, then all the people who have dedicated their time to optimizing integer division over the years have missed some enormous low-hanging fruit.
That was compelling enough for me, and I gave up trying to optimize my function. :)
"90% of dentists agree you should own a motorbike" is an appeal to authority fallacy.
"90% of dentists agree you should floss" is not.
An appeal to authority is any logical argument that relies significantly upon the authority of the person making that argument as support for that argument. It then becomes circular and flawed.
If you were to replace the person who is actually speaking with anyone else, and look at the same argument and its support, and it doesn't hold up, that's an appeal to authority.
It doesn't matter who the authority is. Just that there was an authority used to support a significantly unsupported argument
> An argument from authority (argumentum ab auctoritate), also called an appeal to authority, or argumentum ad verecundiam, is a form of argument in which a claim made by an authority on some topic is used as evidence to support one's own claim.
Further down:
> Historically, opinion on the appeal to authority has been divided: some hold that it can be a valid or at least defeasible.
You seem to be arguing for appeals to authority as defeasible.
Incorrectly understanding the authority you are quoting shows how problematic it is to make pure appeals to authority.
>all the people who have dedicated their time to optimizing . . . over the years have missed some enormous low-hanging fruit.
When I was a teenager one of my most worthwhile early chemical breakthroughs as an undergraduate was a typical lesson (these are dubbed "experiments") where students produced a product from raw materials and were evaluated on their final yield of acceptable recovered product, compared to the theoretical amount that could be obtained if perfection were to be achieved across all steps in the reaction and subsequent processing & handling.
This was a reaction that was known not to go very far to completion when equilibrium was reached to begin with, so most emphasis was placed on technique for subsequent separation and purification of the desired product recovered afterward. Good yield was considered 25%, poor at 10% or less, the historical high score was 27%. It was also accepted that the final product was not considered very stable, subject to degradation from exposure to things like heat, air and moisture, and there were some literature references this was based on.
Basically an overall view of the combined laboratory techniques applied across the study, compared to how the other students were doing. The product was not actually a commercially useful material but it had proven worthwhile in this regard.
The university had been doing this same challenging competition for decades, designed back then by a still-active professor, and it was considered a good comparison of how each year's students were performing on the same real-world problems over the decades. Same old same old.
I went through it one time and it came out pretty good, but before refining my technique I dived a bit deeper into the physical properties of all chemicals involved, in my case looking for a way to drive the equilibrium further to begin with.
One of the well-known ways to drive reversible reactions to completion is to remove product as you go along, not always easy but also quite essential in many industrial processes.
Seemed to me distillation would be most feasible except the product was a solid and one of the raw materials was a liquid having a known boiling point, much lower than the expected boiling point of the dissolved solid raw material product in the reaction flask, and the solvent much lower in boiling point than that.
Ended up vacuum distilling from the incompleted reaction flask where the water of reaction was removed along with the solvent, "excessive" heat actually helped complete the reaction before the remaining lower-boiling raw material was vaporized, and the desired solid product had a lower boiling point under vacuum while melted than the remaining "heavy solid" raw material, and the good stuff was recovered in over 50% yield as an oil in it's own dedicated receiver, which crystallized wonderfully by itself with no further purification needed. Earned me my first A+ and encouraged me to continue going further than average ever since.
Turns out all the original professors were wrong about heat instability, and also had never fully considered as many physical properties of the exact chemicals being worked with, only similar materials for which there was much more common knowledge and published references.
The final lesson was that sometimes the most respected elements of "common sense" amount to more or less "common lack of sense".
Also, I've said this before, when all recommended solutions have been attempted and failed to deliver, the actual solution will be something that is not recommended.
A “upper bound” approach would be to simulate some data that is perfectly clean and meets all my model assumptions, and test my basic method on it. If it doesn’t work on the clean data, it won’t work on the noisy data.
The “lower bound” approach would be to try the simplest and dumbest thing I can think of to deal with the noise in the real data. If I can pick up some amount of signal even with the dumb approach, it makes me much more confident that if I spend time making a sophisticated noise model, it will be worth it.
For physical problems. Newtons law of conservation of energy is an obvious first sanity check. Given some objects mass and the desired travel, you can get the required energy and from there the required power. Before you even start designing a prototype.
I think the bigger risk to this approach is that it can be disheartening and demotivating to see your ideas that you already got attached to and were looking forward to pursuing shut down. But it's still less demotivating than spending a year on it before watching it fail.
If X, then Y.
To test X works you first you start on Y?
If Y succeeds then you don't know if X failed or not && if Y fails then you know that X failed too?
In the case of a an X that is hard to figure out on its own, and it is easy to figure out Y, then it might be worth testing Y first, even if you will only get useful information if Y is false.
Using the same logic as the parent comment, I would be very suspicious of the general applicability of this algorithm. Because, if this algorithm was correct, P would be equal to NP based off of this algorithm, because you'd have a polynomial solution to SAT. This, in turn, would invalidate pretty much all practical cryptography, most likely turn bitcoin on its head, and cause a significant number of other disruptions.
That is this line of thinking. The formal name is Modus Tollens, but it basically says: If your assumption is right, I can propose a much more preposterous assumption that would also be right. Or I could propose something enabled or validated by your assumption which is much easier to invalidate.
I constantly use this in stupid security discussions as well. There are so many people asking about silly threat scenarios, but the specific threat scenarios generally imply that an attacker already has control of critical infrastructure anyway, and all of these nitpicky things they wonder about are just not relevant. Like, if you assume this action to be possible, they have control of the secret management solution, and then we are doomed already.
If you don't find the coat in your closet, you will don't know whether you left it at work. It could be in your car or maybe you left it on the train. But it's still worth checking your closet first because that gives you an early possible solution.
In logic, that's: If coat is at work, then closet is empty.
X = "Coat is at work".
Y = "Closet is empty".
Modus tollens tells us that "If X, then Y" implies "If not Y, then not X." So: If closet is not empty, then coat is not at work.
If it applies, have a "testing" version that runs quickly, on limited (but error-prone) data cases. Ideally, run it with the rest of your test suite.
There comes a point where explaining why we can’t have something is more painful than just fixing it.
A bug can't be reproduced? Take a video of it working fine, and show the logical path for how the bug couldn't happen.
Can't build X in 3 months? What's the minimum for X? What's the missing component that takes 2 months? We can't have a partnership with A, but why wouldn't it be possible to have a partnership with A's competitor?
Anxiety about problems often leads to rumination, which causes more anxiety. It can be a bad feedback loop. In a rumination cycle, people generally don't seek out new information, so their mind spends time analyzing and re-analyzing the same incomplete information. Lots of tricks on this thread really come down to ways to trick yourself into systematically getting more information.
But I think it's also worth taking a step back and looking at the anxiety as a "problem" in itself that can be solved. And as a psychological problem it's amenable to all sorts of treatments like exercise, therapy, etc. So don't forget to take care of your brain!
That said, one of my personal favorite strategies when I find myself ruminating is to put the problem aside and do some curiosity-driven learning that's adjacent to the problem. It both gives me more information and makes my brain feel less antagonism toward the topic. I usually find this is enough to get unstuck.
I once got in that cycle, ruminating on possible interpretations of a situation. It can really bring you down. I noticed that each of my possible interpretations produced a different (strong) emotional response and concluded that was driving a "need to know". There is a thing in psychology called "intolerance of uncertainty" and for me the emotional uncertainty was driving the rumination.
So when ruminating, ask yourself "why is this so important to me?" If you can't answer that, get some distance from it before the rumination bring you down. In my case I knew that the answer to "why is this important to me?" was itself very important to understand so I kept at it until I had my answer to that.
- Documentation: Write up the history of the problem, when it occurs, which users are affected, what previous work has been done toward solving the problem, etc.
- Reduction: Only look for limited solutions - proving a few of the "easy" cases for some difficult mathematical theorem. Patches or work-arounds that only reduce the impact of a computer program failing. Chemical synthesis of a less-tricky part of a complex organic molecule.
- Counter-example: A counter-example can be literal - the problem was to prove a mathematical theorem, and your counter-example proves that the theorem is wrong. Or, it can be a proof that the problem is impossibly difficult. The mathematical theorem you were told to prove is equivalent to the Axiom of Choice. The computer programming challenge is equivalent to P vs. NP. The physical theory/device you need to create would violate the laws of thermodynamics.
Boss: "Hey how are you getting on? You said this'll take two weeks tops, we've got so many clients asking for this thing."
It's most problematic when something looks simple and easy at first glance but then ends up with corner cases upon corner cases and the damn thing refuses to work properly while you sink into a pit of despair amidst calls to deliver already.
- you are able to organize your work. If a problem is potentially without a solution, you're likely not going to be able to hold all of that info in your brain at all times.
- when you bring someone in to help, they could get all the context they need by reading the materials - emails, documents, comments, etc, that you already created and organized. They will likely not have all the context you have, but they will have information available and digested.
- it helps keep stakeholders up to date on the progress and risks. Maybe you are able to just talk to your boss, but you don't want to repeat all of that each time you tell someone new. You don't want to setup a meeting just to update your stakeholders
- in case you are able to solve the problem, the materials you write while solving the problem will serve as a staring point for the documentation of the feature/product
a) Given a quality photograph, detect if it's of a bird.
b) For the same photograph, detect if it's taken in a national park.
The first problem may seem much easier if one does not know about EXIF geodata, assuming it's available in this scenario.
I understand that my approach frustrates managers who demand timelines. But sometimes reality interferes with those timelines, and I'm the one steeped in reality.
- “The difference between screwing around and science is writing it down.” ― Adam Savage (via Good Reads)
- "Divide and Conquer" ― Many
There is reddit post with imgur link, both from Adam Savage himself that clarifies the correct quote:
"remember kids, the only difference between screwing around and science is writing it down" - ballistics expert Alex Jason
They are both easily findable when searching the correct quote, its a good story. sources: https://www.reddit.com/r/mythbusters/comments/3wgqgv/the_ori... https://imgur.com/1h3K2TT/
- Define a very clear target. Include quantities. If the goal is "speed up the api endpoint"... measure the current performance and define a target. The goal must become tangible and measurable in an objective way. Otherwise, it's just up to someone's opinion whether the goal was reached.
- Get stakeholder buy-in on that target. Also communicate your estimate of the probability of success.
Over the past few years when I have had problems that pop up or what really happens is that I go looking for problems, the most often solution has been to literally do nothing.
And having that as an active option when I first start looking at the problem and listing solutions ends up having far more options to me for the problem than if I was like "I MUST SOLVE THIS".
It could also mean "wait" is the best possible action I can take now. And instead of being perturbed by waiting it is an active decision to wait.
E.g. mulling for weeks over optimizing some code until you realize to measure it as-is and it isn't even slow!
Or maybe there's room in the underlying design to shift the weight off the problem, thus "solving" it laterally (by solving some other, easier, problem instead).
> Il est urgent d'attendre
which loosely translates to:
> waiting is of utmost urgency
The french quote can be traced to a translation of Asimov's Foundation, but I can't seem to find the original version :/
It's actually much older than that, I read it already in 19th century books; no idea when it first came out.
As an example: I worked on a PhD in applying machine learning to certain tasks in programming and mathematics. I ended up burning-out and had to quit.
When I started in 2014, most cutting-edge ML research was on image processing like convolutional neural networks. That's a very bad fit for the sorts of tree-structures and text sequences I wanted to use. The state of the art for the latter were RNNs which are notoriously slow (hard to parallelise), suffer exploding/vanishing gradients (needing e.g. LSTM), etc.
Transformers and LLMs solve the issues I was facing; so in hindsight it would have been better to wait a few years (I believe the Attention Is All You Need paper came out in 2017?)
Look at it from different angles to understand the problem better. Understand its properties better.
Look for its underlying causes. That is, may be you need to solve different problems!
Nibble at it. That is, solve sub problems so that you are left with a smaller (but possibly harder) problem.
Work on them subconsciously. That is, when you learn something new, let it sink in by walking away and doing something else.
Conversely, focus on the problem 100% when you are working it. If necessary, block out all distractions, including mental ones.
Look at it from a potential solution point of view. That is, if there is a solution, think of what properties it must have.
Never give up! Assuming the problem is worth solving.
Conversely, try to prove it is unsolvable so that you give up on it ASAP!
Keep notes and review them often. You may find clues in something you have already noted.
Try to explain the problem, what you have learned and your attempts to an interested person who can act as your sounding board. The process of explaining will force you to organize your thoughts and the other person can ask questions that will force you to think about cases you may not have considered. Without a sounding board and without writing down your observations you may end up going in circles.
I once explained this to an audience using a riddle: "How far can you walk into a forest?" That type of riddle has no method or algorithm for solution. The answer usually "comes to you" or doesn't. But knowing that riddles depend on a play on words or different meanings of words in different contexts, I suggested that one can analyse each word at a time: e.g. "you vs. someone else?", "walk vs. some other way of moving?", "into vs. out of?", "why specifically a forest?" etc. The answer, of course, comes from "into vs. out of" -- you can only walk into a forest till the mid point. After that you're walking out. Not an ideal example, but I always remember it when I'm faced with an intractable problem.
The method also helps stay motivated because there's a sense of progress: you're racking up a count of things that are definitely not the cause of the problem.
- Determine what is the problem. Easier said than done. You most likely don't understand the problem. Finding the right abstractions to understand what is the problem is half the work. Focus on that a lot early on.
- You will not solve the problem by sitting for two hours and trying to think of a solution. Accept that. If it is a hard problem, it will take you months of thinking, writing prototypes/solutions, trying different angles. And then, at a random moment it will click, and the solution will feel obvious.
- Iterate a lot. Start with something small, solve it, and do it again and again. Accept that you will fail hundreds of times until finding the right solution. Try to make the process enjoyable. If it is a research project, break it into parts, where the solution of each small part provides value (a paper), so that you can enjoy some success that keep you working. If it is a startup, build products that provide value and are in the road to solving the big product.
- Some problems can be solved in a phd, some in a career, some in a generation. If you are targeting poverty, accept that you will spend your life on that with the hope of making small progress.
> Iterate a lot. Start with something small, solve it, and do it again and again.
> Accept that you will fail hundreds of times until finding the right solution.
The human brain is usually quite adapted to iterating on some existing thing vs summoning a novel solution from the void of unexistance. So, just find Some starting point.
Polya even talks about this in his famous book “How To Solve It”: “If you cannot solve the proposed problem”
Essentially, the advice boils down to:
1. use the defining features of the set up
2. give things/variables meaningful names
3. leverage symmetry
4. try describing one object in two different ways
5. draw a picture, flowchart to visually represent
6. ask a simpler version of the problem by removing some constraints or considering very specific cases
7. read a lot and think about problems a lot
Prompts that I use that significantly aid the process:
* Provide a concise definition of [specific topic or concept] and explain its key characteristics.
* List three advantages and three disadvantages of [specific technology, method, or approach].
* Explain the step-by-step process of [specific task or procedure] in a clear and logical manner.
* Compare and contrast [two different approaches, methods, or models] in terms of their strengths and limitations.
* Predict the potential impact of [emerging technology or trend] on [specific industry or domain].
* Describe the main challenges associated with [problem or issue] and propose possible solutions.
* Summarize the main findings and conclusions of [research paper or study] in three concise points.
* Create a comprehensive list of resources, including books, articles, and websites, related to [specific topic].
* Provide examples of real-world applications or use cases for [specific technology or methodology].
* Offer insights and recommendations for optimizing [specific process or system] based on industry best practices.GPT 4 with browsing isn't quite there yet either, usually takes at least two or three attempts to not have it fail somewhere in between. Should be pretty good once they iron it out though.
You don't need to use Edge to be able to utilize Bing Chat :)
https://github.com/sunner/ChatALL
This one let's you send to 9 models simultaneously and in parallel. Interesting the differing responses for each.
So even if the "quality" is different, the way to verify the information is the same.
There is another factor that causes problems for many people. They don't really give a <insert-obscentity-here> for what they are doing. Bad jobs, stupid ways of doing things, senseless tasks. Just say no. :-)
And finally, we often forget how physically competent we are. Humans can run and walk for hours and hours once they get use to it. Go walk 10 miles. Or better yet run. It helps.
In case of scientific research also, it depends on the situation. A PhD student's approach to a difficult problem with apparantly no solution would be and should be different from someone who does not have a deliverable. If you are a student, you need to deliver some result for a degree. So after some time it would be better to forget about a seemingly unsolvable problem and focus on a new problem which you can solve in perhaps a better way.
A senior researcher however in my opinion should persistently try to solve the harder problems. As I feel it is their job.
Coming back to different problems than scientific research, I can only think of one approach. Ask the question, how important is this problem to you and your life? If it is as important as the the well being of you, or your close ones, then you have no choice but to focus and fight to find a solution.
Minimise work on problems with an obvious solution and identify working on the ones that are more mysterious as the most valuable work there is to do. Make a habit of extracting the most from the process, even if it didn't end up in a solution. For example: writing down (and sharing with others) what was learned.
Psychologically, you need enough repeated positive reinforcement, where you work on a problem, end up not solving it, extract the most learning, get recognition from yourself and from others that it was worth the effort. After enough itterations it starts feeling better.
1. Try to solve the smallest (but similar) problem you can think of. You'll learn a lot along the way and might figure out if it is doable or not. As a reminder, just because a problem is solvable doesn't mean it's solvable at an acceptable level of cost/time/effort. Solving a similar, but smaller problem will help you estimate the feasibility of the larger problem.
2. If the problem is worth solving, it's probably affecting people who in turn have tried to solve it before and are using either approximations or imperfect solutions. Talk to them, understand what they've tried, what works and what doesn't. If the problem affects enough people It's very likely that a solution exists already, it just hasn't been generalised, productised, or automated yet.
Evaluate the severity of the problem first. This usually falls into a bell-curve with the X axis starting at "not a problem" to "armageddon." Attempt to gauge the timeliness of the problem. This tends to fall between "already happened" to "years in the future."
Comparing the severity with the timeliness will give you a good idea of the urgency of the situation, which is then compared to current priorities.
Gather the information you can given the urgency constraints that can give you the best understanding of the problem and accept that this information may necessarily be incomplete.
Recognize that many times you don't have to solve a high-urgency problem but can instead pursue a partial course of action that increases the timeliness, which reduces the urgency as well as provides you more time to gather information to reduce the unknowns.
When deciding a course of action with incomplete information you need to commit to that decision strongly, but always be looking for evidence that the decision is incorrect. Until you have such evidence, stay with your decision. If you find such evidence, re-evaluate since you have the ability to make a more informed decision now. This is generally referred to as "strong opinions, weakly held."
One thing I very much try to do when executing a plan that is based on incomplete information is to have an exit strategy. Try to make choices that give you the ability to roll back changes and restore to the previous state if things go wrong. This will give you more confidence in committing to action.
Always remember that discovering a choice you've made is incorrect is valuable because it increases your knowledge and often leads to greater understanding in an environment in which you lack sufficient information. Don't fear learning this way, it's too valuable to avoid.
Today's mantra of 'fail fast' discourages the kind of steady work required to solve some problems. If a solution can't be found in a very short time, they tell you to give up. This can be beneficial in some cases, but some problems are just not easily solved.
How you deal with this, really is dependent on what kind of person you are. If you are patient and willing to stick with something over a long time, then you could create something truly unique. If you get too anxious when a quick solution eludes you, maybe go with the fail fast method.
If I solve that problem, that normally allows me to build from there, otherwise I may have to re-frame the problem. But by just starting, I get more information and ideas on how to tackle it.
When faced with what sounds like an insurmountable,"where the heck do I even begin?" type of challenge, I like to slice it up and get the obvious bits working, just to build confidence & domain knowledge, while my brain autonomously digests the main problem.
When you see a seemingly impossible question in an interview. You know there’s a trick. You’ve been handed a riddle to be solved.
When my boss hands me a seemingly impossible problem, it might actually be impossible. At best it’s a mystery, at worst an enigma, or a paradox. It’s a very different skill set to go searching for a solution that is not obvious and not found in the literature (because nobody wrote it down or they used jargon nobody else knows).
I have a coworker who says things like, “we can do anything in software” if he says it again I’m getting him a biography of Claude Shannon, because apparently he did not learn about Information Theory in school.
One thing I would add is the perspectives and ideally the participation of other people. Absolutely essential if the challenge has any kind of social dimension.
Often you realize that some parts of the original problem statement were adding complexity with no real benefit. And the techniques you use for the simple version are likely still relevant for the big version.
If the simplified version is still hopelessly difficult, it might be a good starting point for a counterexample/lower bound to convince yourself that the full problem is hard.
* https://math.stackexchange.com/questions/899109/problems-tha...
* https://mathoverflow.net/questions/21214/particular-problem-...
The second link has the neat particular example of showing that something is nonzero by showing that it is odd, which I quite like.
Or in the words of Thomas Edison: “I have not failed. I've just found 10,000 ways that won't work.”
The attainability of a solution is the product of a well-defined problem. So focus less on the "have I solved this" and focus more on the "have I made useful progress in defining the problem".
As for strategies for finding solutions for complex/potentially unsolvable problems:
- Try to sketch it out. When thinking about complex problems, we tend to spiral and sometimes they seem too abstract when contained in our heads, putting them to paper makes them more comprehensible and less overwhelming. Even if you can't sketch out the whole problem, better understanding parts of it makes it easier to understand the whole
- Explain it to someone else. Aside from the benefit of the rubber duck approach, talking it out with people with different backgrounds and cognitive processes helps you look at it differently. Maybe you're a deep narrow thinker and someone who is a shallow wide thinker will help you se the whole picture or vice versa
- Can you break it up into smaller components? If yes, great! Even if you don't solve all the components, you'll still end up with a smaller problem then you started with. And solving some parts of it may change it all together.
- Review the context and everything surrounding the problem. My colleague recently mentioned that when they get a ticket for an issue, they often end up fixing or upgrading a completely different part of the system than the one where issue occurs, and that issue just falls into place
Learning more about the problem and the system where it happens may give a different perspective, a broader point of view, another attack angle. Or, in the worst case, realize that is not that critical, that it can be redefined, or adapt around it.
1. Set a time budget and be willing to walk away if I'm not making progress. Sometimes "yep, sucks, but is what it is" is the answer.
2. If it looks impossible, be more willing than usual to reframe it. If it's a detail problem, zoom out and see if the bigger picture offers you a way around. If it's a big picture problem, challenge the assumptions. If it's still impossible, see 1.
3. Involve other people with other points of view early in the process. There are a bunch of different teams that work in sync to get anything out the door at my company. Getting any difficult problem solved will usually involve understanding the work of at least two of them. The challenge with potentially unsolveable problems is knowing which two.
4. I cannot reiterate number 1 enough. Sometimes a problem might have a solution, but I just have to be ok with the fact that I'm not going to be the one to find it. Maybe the next problem I tackle will present me with a nicely reframed version of this problem for me to go back and take on.
By technical, I mean something like "The service keeps crashing roughly once a week and we can't figure it out."
By conceptual, something like "How do I hire the best engineers within my tiny budget?" or "How do we get SOC2 certification even though we do this or that poorly?"
In either case, I always start with building an understanding of the problem. Gather what you do know about it. Write down why it is hard. Note any contradictions. Note things you don't know, such as terminology, concepts, or data that is not available.
Next, research the things you don't know. Look up the terminology. Read up on the concepts. See what you need to do to get the data. At this point, you don't need perfect answers. Anything that improves your knowledge and understanding is a step in the right direction.
At this point you should be able to talk about the problem in clear terms. It should be clear what you know and what you don't know. Tackle the unknowns now. Take steps to make them known. Read. Talk to people. Observe.
At some point you might run into contradictions. Think long and hard if they are really contradictions, or if you are making some assumptions incorrectly which are leading to a contradiction. What if you change some assumptions? Does the contradiction go away?
If the contradictions seem firm, see if you can redefine the problem ina different way that removes the contradiction. Solving this other problem might not solve the original problem, but it might make the situation better. It might mitigate the problem.
This is not a straight path. It's applying the learning loop iteratively. Assess where you are. Decide on a next step to change something. Take those steps. Repeat.
In the case of wicked problems, lots of meetings with all the shareholders followed by lots of simulations.
The point here is just to get moving in some direction, get familiar with your data and start testing some assumptions. I learned a lot about my problem from doing this and eventually came up with some testable theory.
Forget architecture, "elegant code", time complexity, "does it scale" etc - just write things that give you answers or allow you to gain some insight and do so with the minimum of effort spent on design. If you ever find yourself onto something you can refactor then. For me the main thing is to get the learning process started.
Don't give up before at least you:
1. Prototype many solutions, and identify their "dead ends" through engagement with reality.
2. Share your progress as widely as you can - If at a company, share your progress internally once you reach a dead end / challenge you can't overcome. "Many minds make light work". Your challenge might not be the same as a colleague or leader has encountered before, but it may be similar in some way, and there may be a smaller piece of the puzzle that they have solved before. Have faith that creative solutions you could never have anticipated at first most likely will emerge, but maybe not first from your own mind. If a public project, share as widely as you can. When sharing, skip to the dead-end part quickly so you can spark the minds of your audience and engage them in the search for solutions.
3. Use true "design thinking" which is abductive reasoning and reframing. For more on what exactly that is, and how to do it, I recommend the writing of Kees Dorst in his book "Frame Innovation". "Universal Traveler" is another good resource.
https://www.amazon.com/Frame-Innovation-Create-Thinking-Desi...
https://www.amazon.com/Universal-Traveler-Soft-Systems-Creat...
Here's a good video of a talk by Kees Dorst that can help you understand what Reframing is: https://www.youtube.com/watch?v=j60jMV00kfk
Because of a sad conjecture of circumstances I ended up having a problem to resolve quickly. The more I was thinking about it, the harder it looked.
I then went to some people who were also physicists (not necessarily in my specialty) to discuss it, and see how it goes. It was confirmed that the problem was indeed hard.
So I did the only think which made sense in that context: I simplified it. And was crossing fingers to still have a more or less working model, with known limitations.
Which ended up not being that easy, but was ok-ish - and solvable.
I then want for dinner with a friend, and by main course she casually suggested a completely different approach. It flipped my depressed world around.
So to summarize the advices: see if the problem is really hard, then discuss with clever people to see if they feel the same, then simplify. Or take a few steps back and consider looking at it though a completely different perspective.
Good luck!
If the "anxiety/paralysis" is the real issue here, then it is a completely different topic that probably needs external help.
For a "problem you are not sure has a solution", if it's related to job/technology, I search for a workaround (if applicable which, most of the times, it is).
It does a very good job guiding me in areas where I'm less familiar.
That's assuming we're talking about technical problems. For non-technical problems I'd reach out to friends (or even better - a therapist). But asking on HN and/or Reddit might be a good idea too, depending on the context.
Surprisingly often this method works.
So basically, look hard at the problem, chisel it a bit and back off for a moment. If you can't solve it right away it's a substantial task that has to be treated with respect. Naturally this process is poorly suited for meeting deadlines.
But here are some non logical ways: - reframing - ignoring/delaying - accepting - praying - delegating
Or what the stoic/religion used to say
God, grant me the serenity to accept the things I cannot change, the courage to change the things I can, and the wisdom to know the difference.
P.s I ain't religious or superstition but there is some wisdom in those teachings.
Now in the context of a project if you really can't find any solution, then document and communicate your findings until the budget runs out..
Lots of good tactics here, but ultimately I think everything boils down to understand the problem better.
Your solution will only come from superior understanding of the problem, if there is one. It probably won't come from testing different solutions.
Almost all software starts with "what is the intput and what is the output" and then understanding how the input leads to the output. If you don't know the input and the output to your system, then you don't have understanding.
Even in your text, you have a "solution" based frame to your statement. Subordinating the problem to the solution rather than the solution to the problem puts so much focus on the solution that the problem itself gets defined in terms of the solution. I have seen feature developers play this out time and time and time again. When the problem gets redefined in terms of the solution, often the original problem remains resulting in increased complexity at little additional value.
So I would start by understanding that not being sure a problem has a solution means you don't understand the problem and its context enough to even be asking if it has a solution which means you should be asking "how do you better understand problems?" or "when do you stop investing in understanding problems?" or "what is a good time trade off between 'understanding problems' and 'directly handling business concerns'"?
When you understand the problem, you'll probably come to the realization that you were asking the wrong question altogether. There are so many times someone came to me with a problem with a system I understood that they did not and it was clear they were asking the wrong question. Frequently, I could tell them what question they were trying to ask because I knew things they didn't know they didn't know.
You may find Bloom's taxonomy interesting as a frame for thinking about how to achieve better understanding: https://en.wikipedia.org/wiki/Bloom%27s_taxonomy
If the challenge is something work related (i.e. I do a lot of math) then I timebox it. My journal, status report, and other docs will read upon failure: "I spent X hours reviewing Y problem. I assessed A, B, and C. Their shortcomings were Yada Yada Yada."
If the challenge is relationship related, it's dicier. More information would be needed.
One slightly more generic tip is that your task isn't to to solve the maybe unsolvable thing; it's to do a number of sub-tasks, learn more about it, communicate expectations to those who care, still schedule other important bits of your life despite a workload of unknowable magnitude, work on any essential backup plans, and so on. You have intermediate thoughts and actions between where you are and where you want to be. Focus there, and the fact that you're working on solvable problems might help.
A tangentially related idea -- math students often mistakenly assume the point of the homework is to figure out how to get it right. Rather, it's an opportunity to think through all the ways you can get it wrong and ingrain those so that in the future the right path forward is obvious. Failing to quickly solve the problem is the express point of the activity, and approaching the homework from the perspective of figuring out how to learn from it rather that how to get full marks tends to overcome a lot of mental hurdles and give you that latter benefit as a side effect. You're similarly, at least in the very near term, not actually working on getting the final solution; you're working on learning about the problem.
I have to go through this at least once a week in my support role, knowing a problem does not have an obvious solution or that it might but we have yet to find it - and not being able to necessary say that to the user in those words - 'setting expectation' and 'communicate expectations to those who care.
Often I find that this is often 'good enough' for the short to medium term, get them back up and working as best you can, show that you understand the issue even if you don't know the solution.
Based on my life experience, I have learned that small actions can lead to significant outcomes, whereas starting with grand endeavors often leads to mental stagnation and lack of progress.
For instance, let's consider the challenge of addressing climate change and global warming. This is a complex issue composed of numerous interconnected problems. It becomes challenging to determine where to start, which aspect to tackle first, and from which angle to approach it. However, if we narrow our focus to a smaller component, such as plastics recycling, we gain more clarity. We can explore existing initiatives like the cleanup of the Pacific's floating garbage patch or the utilization of otherwise unrecyclable plastics in making blacktop pavement. This narrowed focus provides us with a direction to follow.
If we want to address emissions, a core aspect of combating global warming, the best technical approach would likely involve improving batteries that don't rely on rare metals. I've heard of advancements in saline-based and bacteria-grown batteries. By restricting the scope to batteries, we can identify specific areas to investigate. By avoiding broad and vague objectives, individuals can offer recommendations, share knowledge, and contribute effectively to the cause. If we remain with a large and vague goal it's very hard to make any progress at all.
You can always come up with a list of 3-5 next steps that seem pretty reasonable, and that you can reliably execute. That's the key, because if they're unreasonable or you're not sure of being able to execute them then they'll continue to produce anxiety/paralysis. But these steps aren't solving the whole problem, they're just progress towards it.
Any single step might be to find 5 relevant papers, to read the papers, to send e-mails to 5 people who might have ideas, to make a list of all the things you know you know and all the things you know you don't know, to spend 60 minutes writing free-association brainstorming, to test out 3 different solutions, and so forth. It's all going to depend on your situation.
But the point is that you can always come up with bite-sized tasks and then execute on them. And when you can't, the task is always to start going around to other people and asking them for help.
And of course some things don't have current solutions, which you need to accept to. Always look to identify the point where, after researching and reaching out to people and gathering a reasonable amount information, whether it makes sense to continue or to move on to something else entirely.
The story from math is that of a student who fell asleep and was late going to his final. He walks in, sees three problems on the blackboard, and works frantically to solve them in the time he has left. Valiantly, he manages to solve all three, turns it in, and just hopes for a passing grade.
Later he gets a call from the professor who asks "do you know what you did?" The student's heart drops, thinking he's failed miserably. The professor continues: "You were only supposed to do the first two problems," the professor explained. "That last one was an example of an equation that mathematicians since Einstein have been trying to solve without success. I discussed it with the class before starting the test. And you just solved it!"
Note that this story is actually (approximately) true! George Dantzig, a UC Berkeley PhD candidate at the time, solved an unsolved problem in math as homework, and the plot was later used in Good Will Hunting. Dantzig was later awarded National Medal of Science by President Gerald Ford.
https://www.snopes.com/fact-check/the-unsolvable-math-proble...
> A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.
The "two problems" being referenced here are, of course, the two unsolved problems he solved as homework.
- Not all problems need to be solved.
- People can relate to your struggle and may be willing to share time with you to think about your problems (me included) if it would help
- Take a break. Go outdoors, into nature, for an extended period of time. Focus on the present, not your work.
Depending on the domain you work in, close may be perfectly ok.
Then walk away knowing you did your best.
This sounds easier than it actually is, particularly if you have an obsessive compulsive personality.
It took me years to "let go".
What worked for me:
1) Experience. I am much better at prioritizing tasks today than when I was younger and I can focus on things that matter instead of going into rabbit holes with stuff that doesn't.
2) Running every day at lunch break and avoiding big meals. I believe my mind works better when I return to my desk, I'm awake and energized. I have a small snack usually fruits but definitely no carbs or refined sugar.
3) Having a "manual" hobbie. I got into film photography and directed my obsession to it. There's something about the almost totally manual process of film photography that has a calming effect on me. I know people that described a similar effect with painting, analog music production and writing.
4) Walk away. When I'm working on an issue and get stuck I say F this and leave, then come back to it later that day or even days later. It's almost like it is a totally different problem and usually appears much easier when you see it after a break. Call it a day and go home, go for a walk or work on other stuff.
So, at least for me, there are 2 sources of this anxiety:
1. Does it even make sense to solve this? - Best thing is to try to validate the problem. Find people to talk to, get feedback. Or think about alternatives and constraints. Every now and then, I start feeling like “what I work on makes no sense, I should just abandon it”. Only to then analyse it, walk through the different options and decisions and realise I’ve done this decision making exercise previously when starting the project and I still agree with the outcome. But I guess it’s good to recheck the assumptions every now and then.
2. Can I solve the problem? - I often get discouraged when I realise things are a lot more difficult than expected and I start to doubt myself. Usually results in me procrastinating and taking a break. Things that help me are: taking a deep breath, doing some searching for similar problems, breaking the problem down into smaller tasks, finding a smaller, yet similar problem to address first. Again, talking to people and reaching out for help can be great. People are often happy and flattered when you come to them with well-formed questions and acknowledge them as someone you consider an expert in a field.
Hope this helps. In general, when working on very hard problems that might not be solvable, try and break them down, find the riskiest piece that seems solvable, and try to tackle it. If you fail, at least you fail fast and you can rinse and repeat :)
Finding what the components of $Thing will do, where else they may be useful, and being critical on if they're needed.
Sometimes you find that it's not as big as anticipated, there's existing work, or the idea just doesn't hold water.
In general, it helps to break the problem down. Trying to bite the whole thing at once is overwhelming
Sometimes I find that if I do 20% of this, it fixes a much bigger problem than what I was even looking at
If at some point some position sounds more plausible than the other, I try to put into words why is that. Either I convince myself of some position, for example that it is impossible, or the hardness of getting convinced at one position encourages me that maybe it's the other position that's true.
Either way I don't have anxiety because either I'm confident in some direction and making progress, even if it is at proving something is impossible, or the doubt from failing to prove it is impossible makes me more confident it is possible.
Even if you're making progress at the direction you didn't prefer, you should still see it as progress, and if you're confident in one direction you see it as an indication that you can make progress.
Anyways, it's not enough to just hold a general feeling that something is impossible, you need to put it into words and see if it's truly convincing. When it's just general intuitive unspoken feeling you can't change it, but when you make it concrete, you can understand what's possible.
> One specific mental image that I can communicate easily with collaborators, but not always to more general audiences, is to think of quantifiers in game theoretic terms. Do we need to show that for every epsilon there exists a delta? Then imagine that you have a bag of deltas in your hand, but you can wait until your opponent (or some malicious force of nature) produces an epsilon to bother you, at which point you can reach into your bag and find the right delta to deal with the problem. Somehow, anthropomorphising the "enemy" (as well as one's "allies") can focus one's thoughts quite well. This intuition also combines well with probabilistic methods, in which case in addition to you and the adversary, there is also a Random player who spits out mathematical quantities in a way that is neither maximally helpful nor maximally adverse to your cause, but just some randomly chosen quantity in between. The trick is then to harness this randomness to let you evade and confuse your adversary.
If I'm approaching the problem first and not the solution, I try to classify if the problem is technical or organizational. If it's technical, I try to identify each of the barriers, and search endlessly for something that looks like it would get me a little further along in getting insight into how to solve the problem. It its organizational, I look at how I would restructure how I am approaching the problem or work or communicate with others in solving the problem.
Sometimes, I need to redefine the problem, scope of the problem, or what a successful outcome looks like. For example, I wanted to find a way to verify that the reports I was entering in PDF forms were being filled out properly. I spent forever trying to find a tool or program the PDF form to be verified. After a while (several months), I realized that verifying a spreadsheet would be a lot easier, and that I could generate the same report from the spreadsheet. Once that perception changed, I was able to tackle the problem I had: not being able to ensure that a procedure was filled out properly.
- break the problem up into smaller parts which are easier to grasp, plus some framework to combine the individual parts. If this is possible, you might be able to solve all easier parts and thus the mother problem
- start with a problem that looks like the original one but which is easier. Once you have been able to solve it, you can clean up space in your head to focus on the step from the easy problem towards the final one. Also, during the process you have probably gained some experience and understanding of the mother problem
- just start with the problem without expecting to solve it. Then do something else. E.g. have a good night sleep, do some household chore etc. When you're not focusing on the problem, your brains continue to work on it so when you look at the problem again the next day, it can well be that your are able to link parts together that you were overlooking the day before
- talk about the problem with someone else. It could be of course that the other person has some hints that you didn't think about. But the main thing is that while talking and explaining the problem, you often get a better understanding of the problem yourself as well.
- Experiment as much as possible
- Keep your feedback loop as short as possible between reading and doing
- Visualize things (debug outputs, scratchpad of short lived diagrams, etc.)
- When possible, envision what the finish line looks like and go backwards from there
The last bullet is especially useful for building tools or APIs where you can start with using your tool / API as if it does exist exactly how you want it in a best case scenario and work backwards to implement the solution you want. Break down the steps along the way.
Celebrate the small wins find enjoyment in the process and motivate yourself with peptalk’s imagining how great it will be when you solve it, or how close you are. get a feel for the problem and believe that it has a solution. I just keep trying to get there, enjoy the uncertainty and the excitement of discovery.
Remember, you may be the first person to tred these paths. So don’t forget to stop to take it all in once in a while. Even if you’re not The first person to do so, you’re doing the first time you’ve been there, so still stop to take it all in because it’s important to you, and that makes it important.
"Is this work worth anything?"
"Am I wrong?"
"Does this path just lead to a giant brick wall?"
I find there are a couple of tips that will keep you sane when tackling problems like this:
- Don't try to solve the problem at first. Spend more time than you think you should characterizing it, and describing how you'd know you'd reach a solution
- you will lose motivation and start to doubt yourself if you dont achieve small, conclusive milestones. Embark on a problem, set an ambitious deadline, and if you haven't hit your mark, divide it up again, start with the most doable segment and repeat.
- don't take shortcuts. This will only feed the doubt you already have. The biggest antidote for the existential crises I describe is trusting yourself. That becomes easier when you convince yourself of your methodology before you embark on a problem. Shortcuts lead to wobbly assumptions which undermine conclusiveness and just makes all your work feel like it rests on a foundation of sand and regrets.
I try to give as much context as possible. Stating goals and risks of the project. The more info you give it, the better it does at helping you. Around 500 words for an initial prompt gets good results.
Break down the project into parts and take on the most risky/uncertain part first.
As you work through the design, continue to refine the ChatGPT conversation by giving it more info. Keeping around 200 words is good. New articles can be summarized to get it up to speed on post 2021 info. Blog posts can also be chunked out and passed through to give it more info about the problem.
When the plan seems good enough, code through the steps to create the solution. Keeping things realistic and making some slow but steady progress is better than hammering it all out in a day. Discipline over passion.
I used it for a recent project and it completely exceeded my expectations. Not trying to hook onto the current AI bandwagon, it just brought me to solutions I would have never gotten to on my own.
However, that works only when you're dealing with certain types of contexts.
Many things can only be "improved", "managed" and "satisficed". For example, for many a politician, social stability, keeping the economic system going, maintaining peace can be considered "success".
Reading the biographies of people from different professions, and understanding their thinking seems to have helped me.
Another thing viewpoint is to see everything as a process, that just keeps running and evolving. Usually there is never a final solution to things. What's considered a "solved" problem pops up again in the future in some other form. Many problems are highly contextual, dependent on time/place. When the environment changes, the so-called "solution" no longer works.
Such flexibility of thought, that of questioning the limited paradigm of problem/solution may help as well.
* There is no known solution or path to the solution
* There might be none
* There might be one
* There might be multiple
* These might be approximations
* The solution will be so complex, it will not be sustainable
I usually just try to solve it with my current knowledge, as practical as i can (implementing it). Even if i cant solve it that way, i will have learned something and i can try again another time or using another approach. Looking for similar topics and approaches helps. Mind-Map thinking can help broadening the field and see adjacent topics which help finding a solution. Very often the knowledge from other fields help me solve something i could not without the broader knowledge.
* You might be bought-in, eg emotionally, to a situation that prevents solution
Imagine the global boost in productivity and knowledge-sharing...
Failing fast at a smaller problem is a lot easier (which is what my last set of difficult problems ended up failing at) ... turns out applying a LUT to a camera stream on Android is a harder problem than expected if you want good performance.
For example, Logic Mathematical Inference and a few other areas have formal methods which you can use to identify properties which can then be used towards or against proving something.
Computation for example has System's Properties that are required (such as determinism, time invariance, and step), and certain problems are derived from that which dictate some of the fundamental limits of computation.
When you know what the limits are, you know when you start pushing up against impossible problems.
Sometimes its useful to think of impossible problems as possible, and try to build a bridge, but these often require significant background knowledge and experience to avoid circular thinking of self reference.
Also sometimes the problem that needs resolution isn't what you think at the outset, so keep an open mind. Maybe your implicit assumptions are at fault so you may need to go back several steps to identify and validate those first.
Indeed, the 'solution' may be to do nothing at all but rather to think about the world in a new way. The 'problem' to be solved might then disappear like mist.
Is it your idea, to tackle it or is someone else pushing for the problem to be fixed?
Is there anyone who knows for sure if it can be done or not?
Does it sound reasonable, within the known laws of physics/engineering that the problem is solvable?
Is that problem that unique that you can't just google it?
Make a list of all the possible attempts to solve it; ask all parties involved if they have other ideas or suggestions, and then time box each one of them.
Then start attempting each option.
If it takes you longer, document what you tried and either move on or ask someone else if it's worth it to continue that approach.
For the anxiety:
Why are you anxious about? In the worst case scenario where the problem is not solvable, what does that mean to you? Are you anxious you won't do it fast enough? Or you won't do it in the best way? Or that you're not capable to do it and someone else is capable of doing it?
So many wild goose chases come from never asking "Who actually want this, and why do they think they need it?"
- Mathematics/physics textbook problem: can you prove it has no solution? E.g. you can start by assuming it has and then find a contradiction. That also works for finding a solution.
- Programming: can it be done by a series of pen-and-paper operations? If yes, then it has solution and you must keep on trying. Can you find an equivalence between your problem and and a well known problem? This last point is true also for math/physics.
On equating your problem with a well-known one: there are not so many new things under the sun. Try to formalize the problem statement, then you might come to conclusions of the form:
- This is equivalent to solving the traveling salesman (bad for you) - This is essentially a system of linear equations (good)
When you do this you can take advantage of all existing literature, i.e. the knowledge of smarter people.
Break your problem into a set of smaller problems. Then partition this set of problems into tractable and intractable subsets. The definition of tractable and intractable can change over time, but must be precise and computable.
Start addressing the tractable problems and show progress. For intractable problems, research effort is required and the costs must justify benefits.
Let us say 60% of your customers are facing issue type A, 30% are facing issue type B, 10% are facing issue type C. Issue type B has a workaround/known solution whereas issue type A and C don't have obvious solutions. Instead of getting stuck with working on issue type A, you and your customers will be better off if you worked on and deployed the solution for issue type B. That is better than the status quo.
As the leader, you may need to shut down directions of inquiry often. Every situation where “I wish I had pulled the plug on that sooner…” wasted time and effort.
Then you have to be willing to pull the plug for good. Whether you’re an employee or an external advisor, it’s always difficult to justify time and expense with no solution, but wasted/higher time and expense is worse.
This also applies to the individual, you still have to fight your own internal desire to push something to conclusion.
First, it is important that your customer and/or team know that you are in that problem context. If you are alone there is a big issue and you should communicate this immediately. There is a saying (Knuth?) about how to differente between an exercise or research problem: if you can solve it it is an exercise, if you can't it is a research problem.
Anxiety probably comes from a mismatch between the complexity of the problem you have in front of you and the expectations others have on you.
Then I take each piece to work on and daily make a list of 3-5 tasks i feel I could complete in the day towards the overall goal. Sometimes task #1 is super simple, eg put name on top of paperwork today, or cleanup stale files, etc. But the goal is to always be able to say I completed a task towards the overall current piece of the whole project I'm building.
The stress is still there but everyday I can say ... See how far you've come, little by little it's coming together; the "process" is reassuring.
Keep reviewing the overall project plan, and biting off little pieces. It helps to manage the anxiety in this way.
If it is unsolvable, the only strategy is to learn to live with it. Or of it's "just" very hard, you need to find dignity in fighting and losing. You might even win, but it's more difficult if you're anxious.
Also consider that concern and guilt are weapons that some organizations use to involve people in their agendas. Persons that struggle to have a minimally functional life feel as if it's their responsability to save the world. Sometimes the answer is: fuck the planet and live a little.
If you're going to solve something like this, then a better way is to find the right way to do it first, but often this correct way is only discovered in the process of doing it.
Haha, it's like a paradox, if you don't do this then you can't find a solution, and as a result, this thing can't be done, and if you do it, then you will face an uncertainty.
So, you need to keep trying and trying and making mistakes, and then make adjustments, get closer to the unknown right direction, and finding the right direction is not a one-time achievement.
Break the problem up into pieces and solve the pieces.
Problems: Analyze, break down, examine from all angles and add details. Then try solving.
I spent my career trying to teach this exact concept to my engineering teams. I agree with you 100%.
The evidence is that I spend a lot of time searching for error messages of which I am apparently the first recipient in the world.
I’m working with systems that are opaque and hostile to developers. I’m using platforms in ways that are very removed from the mainstream, provided by enormous companies.
I know a solution exists but what I don’t know is if a business viable solution exists.
The way I deal with it is to focus at each stage on what I do know, what I need to find out, and whether it is worth trying.
The “worth trying” part is often subjective but metrics such as revenue can help in the decision making process.
He had gotten some new heavy machine, some 400 pound stuff, that he needed to put down in the basement.
He had no idea how he'd get it down the stairs, but he started pushing it closer, since that got the problem closer to a solution. He'd figure the stairs later, once the machine was on the edge.
It's simple, but I found it insightful.
When I'm faced with a problem and am not sure how to solve it or if it's actually solvable, I think of how a solution would look like and start making small steps in that direction, hoping to get elucidated later on :-)
Always be transparent over how confident you are in your analysis and what will be the consequences if you are wrong.
Try to always focus on the practical implications of what you are analyzing.
Always keep in mind what are you trying to prove/disprove. If you to dismiss a business idea for example, you do not need to analyze every possible aspect of you can rule out the opportunity based on napkin calculations.
I worked with pricing ML models for some time, and if a problem has a 40% irreducible error rate you shouldn’t account for uncertainties that sum up to 0.3% of it.
Try to find similar but easier problems.
Analysis is just an activity, and is not the whole job.
In a business context, there's always an itching problem or a potential value creation and you can frame it in those terms and timebox it (drop it after X time working on it and write about the results of your tests).
As much as possible, you should have a plan B that is workable even if suboptimal.
On the "problem solving itself". Just break down the problem as much as possible to ensure you're slowly removing risk and learning early if there's a problem. That helps with the paralysis since tasks should feel tryable.
If you can't even think about the problem then you clearly don't know enough about the domain and some separate theory and practice should help.
You often don't need to solve the problem to provide some business benefit.
So. Can you break it down at all? Is there some part of it that has a business benefit?
Can you do it manually, what's the trade-off of time and cost? Can you document it to make it a manual task for a lower level employee?
If not worth doing manually, often it's good to do some of it manually a few times so you get an idea of what's the same / different for different situations.
Can you automate the same parts?
Can you find a way to deal with some cases where it differs?
Can you now solve any of the remaining pieces?
This process can often be done with manual scripts, I forget the right term, where you create a script that prints out what the user should do and asks them to press enter when they've done it. You can then automate parts of it over time.
This kind of process helps have a useful output at all stages whenever a higher priority problem comes along. It's also easier to come back to it in a few months.
And if not, if you can't even do it manually it pushes it more towards unsolveable.
For problems that don't fit this kind of process, I often leave the problem to settle in my mind and talk it through while walking somewhere. Explain to imaginary people what we're doing what we can't do etc. Kind of like rubber duck debugging.
Prototypes, just trying can be good.
Most of all if you can, get an idea of the value of solving it and the value of your time. That helps put an upper bound on how long you should ever spend on it. A problem that causes a £10/mo extra aws charge a month is fundamentally not worth solving for almost any developer salary.
Finally, it's ok. It's ok if the problem can't be solved. It's ok if it's not worth it. It's ok if someone else sees the answer easily.
When you're done, see if you can think of more approaches. If you can't, you probably can't solve this problem and it's time to call it a day.
But that's ok, because there's almost certainly some higher level goal you're aiming to achieve. So think about other ways that you could achieve that without solving your original problem. Maybe there's a way to solve a similar problem that has looser constraints which is easier.
If you are not experienced then your battle is with fear and depending on the cause, a good way of getting past that is to work with others who can encourage you when you do well and help you understand when you are going awry and why.
And ultimately, don't bullshit. Be honest about what you think and how you might approach something and if the boss isn't convinced, let them give the job to someone else.
From there, the game is to take that silly solution and work it toward something that's not so silly. It's not easy, but it gives you incremental successes that are vital when struggling with anxiety/paralysis. Also, deliberately looking for bad ideas takes off the pressure to have a good idea. (You may even find that the "bad" idea you were avoiding wasn't actually all that bad in the first place!)
Cutting the Gordian Knot [1] When solving impossible problems, ask yourself:
* Is there an easier way?
* Am I solving the right problem?
* Why is this a problem?
* What makes it hard?
* Do I have to do it this way?
* Does it have to be done at all?
[0] - https://en.wikipedia.org/wiki/The_Pragmatic_Programmer
[1] - https://github.com/HugoMatilla/The-Pragmatic-Programmer#cutt...
That being said: Consider that sometimes there are problems where you yourself will be unable to judge the problem you're in, because you are in it. It can be a bit of a bootstrapping problem: If you were the person who could see the solution, you might not have ended up in the situation in the first place. So the logical solution can be to get outside help so advice by a trusted person or actual therapy.
Getting out of a hole can sometimes be done by clawing yourself out, but sometimes having someone throw you a rope is the smarter move.
The more relevant question is: At what cost?
For example, in layman terms we all consider factoring RSA2048 impossible. But, given all the computing power in the world or 10 years more on quantum research this becomes possible.
For sure you can split hairs about this all day, like adding cost constraints as part of the problem and formal mathematical proofs may be an exception here.
In the end, what really matters is, how much is it worth to solve the problem and how much is it worth to estimate this cost. Investigations to reach an accurate estimate also cost effort.
my advice is to do something without worrying that it might not be the right thing.
This may sound like a lot of woo but it usually works. One particularly hard problem took me eighteen months to solve. I should note that I'm stuck on a real bad bad problem right now though, been at it for nine months. It's not technical, more spiritual. I did get a solution but I am not sure I can follow through with it.
If instead the uncertainty comes just from the "size" of the problem, then I split it into smaller parts that are easier to face, and I look into each of them the bare minimum to be able to confirm that a solution exists. Once I am confident a solution exists for all of the smaller parts and therefore for the whole problem, then I start the actual work.
1. Choose your battles. There are important problems out there, but our time is limited. If it is important and in my domain, I will pick it up. 2. Is it developmental? Depends on what stage you are in, but a couple of years ago I picked up lots of problems without solutions. It was a risky move, I wasted a ton of time, and the payoff wasn't obvious --- I definitely did some short-term damage. I am reaping some benefits now because of the skills I developed.
Trying to work through these is like far harder than any "hard" problem I've seen on leetcode. It actually makes me feel like sick to my stomach when I spend 12 hours on it without making a lot of progress
I know that there's some hairiness around maintainer manners and the drama expected in any large enough group of people, but our ability to communicate with our peers is really advanced compared to other disciplines.
The halting problem is unsolvable, but you usually can say with certainty that a particular piece of code is not an infinite loop. The knapsack problem may take ridiculous time to solve precisely, but moat of the time you have little trouble packing your backpack or bag so that everything you need fits. Etc.
Often you only need to solve 20% of the problem to get 80% of the benefit. Make this step, and you will face further problems from a much better position.
I find that this kind of first principles approach gives me a much better understanding of the nature of the problem. I may still not know how to solve it but it usually gives me insight into how to attack it most effectively.
This is a common approach to mathematical problems, but it's helped me break down more practical situations too.
I suggested that the least important thing is How you start, and the most important thing is That you start. Starting the process, in any form, focuses you quickly on the most important things that need to get done first.
Often you at least have some intuition or assumption on sth and then you just keep doing experiments to either confirm or falsify this. When sth does not work yet, you do experiments or analysis to better understand why it is failing. And then you try out more ideas to compensate those problems.
There is really no ending here, you can push it further and further as much as you like. You will get a better understanding along the way on what is possible and what is not.
So I sometimes divide problems into "Can a human do it or not?"
(Years later I would finally have the inklings of how to get a computer to do it. It would be quite complex but I think it might actually be feasible. A lot of subconscious introspection happened.)
It does not mean there is no space for creativity - the plan will not last as new things come to light, but the plan means you move forward in a structured manner.
A memorable quote from the book:
"It’s fine to work on any problem, so long as it generates interesting mathematics along the way—even if you don’t solve it at the end of the day."
[1] https://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-...
For some inspiration, I recommend watching this talk by Bret Victor https://www.youtube.com/watch?v=oUaOucZRlmE (Media for Thinking the Unthinkable)
They often have a bizzare idea somehow leading to the right track. They solve it in a completely different way or know that the problem does not matter to begin with.
Its like rubber duck programming with a smart duck.
I once had some weird data problem and complained about it to a sales guy. He called the customer to not enter certain things,and the problem was gone.
Prove that a solution does not exist. This removes any form of doubt. It guarantees that no one else can find a solution either. Attempting to prove it may also help to more clearly understand what is required and what isn't, which may simplify the problem.
That problem has neither a theoretical nor a practical solution.
That what I was talking about in my first sentence, but my post wasn't clear, I admit. Thank you, it helped me clarify.
NP=P? There are many other famous math problems. No one found solutions yet and it is also unclear whether one is able to find a solution. And it's unclear if there is even a solution.
By narrowing the unsolvable problem it can help to communicate the issue to others (e.g customers or management) or help to find a solution. If that fails it provides some solvable problems to work on. Often solutions, workarounds, or compromises become evident over time.
From there:
1. Write down and solve/suggest for what you know on the edges of the problem
2. Extremely pinpoint what the problem is
3. Talk it out with the rubber duck/coworkers
4. Escalate the issue.
5. Design out the solution and leave question marks where you can't solve it.
6. Go out for a walk
And in some cases where you truly have no idea, it helps push your brain into a choice.
- How do analogies for this resolve? e.g. what else is an n-part dynamic?
- What is a test for a solution?
- Do I want the general solution or just a specific result and is this actually a problem I need to solve?
Same as for problems I am certain have solutions.
For me, it's all about the work, not the fruit.
But the caveat, I focus on projects that are going to bear fruit because most problems that might bear fruit probably won't and I'd rather be productive than important.
YMMV and that's aOK.
Do whatever seems to work or may work. Don't think about it. Just do it.
The midwit meme pretty much sums this entire problem up: https://www.swyx.io/simplicity-rush
It's always good to have an easier and more attractive backup problem in your back pocket to make your current problem jealous and your approach to it more playful.
Reminds me of the Edison quote: "I have not failed. I've just found 10,000 ways that won't work."
If your anxiety/paralysis is specifically tied to the problem, seek help from a mental health professional.
Put yourself into the world where the solution exists.
I tend to find that assumptions/etc that get made in that proof can be attacked and something trackable can be found this way.
James Fadiman also conducted research on microdosing aiding problem solutions.
Sometimes, when you can’t come to a solution, it’s best to let the solution come to you.
1. Prove its not impossible
2. Prove it’s possible
3. Do it
So, in that vein, both the solution *and the problem* are fair game for attack.
There is a wonderful, wonderful short essay by Michael Jackson (the other one) called "Brilliance" in his book "Software Requirements and Specifications". It is poignant, even painful, in the way that the the TV shows Silicon Valley or The Office are exquisitely painful. It is, alas, impossible to find unless you know exactly what you are looking for, but...
*Brilliance*, by Michael Jackson (from "Software Requirements and Specifications")
Some time ago I spent a week giving an in-house program design course at a manufacturing company in the mid-west of the United States. On the Friday afternoon it was all over. The DP Manager, who had arranged the course and was paying for it out of his budget, asked me into his office.
"What do you think?" he asked. He was asking me to tell him my impressions of his operation and his staff. "Pretty good," I said. "You've got some good people there." Program design courses are hard work; I was very tired; and staff evaluation consultancy is charged extra. Anyway, I knew he really wanted to tell me his own thoughts.
"What did you think of Fred?" he asked. "We all think Fred's brilliant." "He's very clever," I said. "He's not very enthusiastic about methods, but he knows a lot about programming." "Yes," said the DP Manager. He swiveled round in his chair to face a huge flowchart stuck to the wall: about five large sheets of line printer paper, maybe two hundred symbols, hundreds of connecting lines. "Fred did that. It's the build-up of gross pay for our weekly payroll. No one else except Fred understands it." His voice dropped to a reverent hush. "Fred tells me that he's not sure he understands it himself."
"Terrific," I mumbled respectfully. I go the picture clearly. Fred as Frankenstein, Fred the brilliant creator of the uncontrollable monster flowchart. That matched my own impression of Fred very well. "But what about Jane?" I said. "I thought Jane was very good. She picked up the program design ideas very fast."
"Yes," said the DP Manager. "Jane came to us with a great reputation. We thought she was going to be as brilliant as Fred. But she hasn't really proved herself yet. We've given her a few problems that we thought were going to be really tough, but when she finished it turned out they weren't really tough at all. Most of them turned out pretty simple. She hasn't really proved herself yet - if you see what I mean?"
I saw what he meant.