Most problems (including analytically intractible ones) can be modeled with a relatively simple monte-carlo simulation. Most simple monte-carlo simulations can be fully implemented in a spreadsheet.
Using timing coincidences in particle physics experiments is incredibly powerful. If multiple products from the same reaction can be measured at once, it's usually worth looking into.
Circular saws using wood cutting blades with carbide teeth can cut aluminum plates.
You can handle and attach atomically thin metal foils to things by floating them on water.
Use library search tools and academic databases. They are entirely superior to web search and AI.
I feel like the Monte-Carlo simulation modeling trick is one I picked up intuitively but only recently heard formalized. Do you (or anyone else) have a list of example problems that are solved in this way? Like a compendium of case studies on how to apply this trick to real world problems?
_How to Measure Anything_ by Douglas Hubbard includes a chapter on Monte Carlo simulations and comes with downloadable Excel examples: https://www.howtomeasureanything.com/3rd-edition/ (scroll down to Ch. 6)
The main example is, you're considering leasing new equipment that might save you money. What's the risk that it will actually cost more, considering various ranges of potential numbers (and distributions)?
I think it's harder to apply to software since there are more unknowns (or the unknowns are fatter-tailed) but I still liked the book just for the philosophical framing at the beginning: you want to the measure things because they help you make decisions; you don't need perfect measurements since reducing the range of uncertainty is often enough to make the decision.
> I think it's harder to apply to software since there are more unknowns (or the unknowns are fatter-tailed)
Talking purely in agile software development, there is an idea of "Flow Metrics" [1] to use for estimation, basically boiling it down to "How many stories can we finish in the next timeframe (Sprint or whatever), and what is the uncertainty associated with this number?"
I really like the idea, but haven't been able yet to test it.
Great suggestion. I'm having solar panels installed on my house partially because I ran thousands of Monte Carlo simulations on a range of variables and almost all of them pointed to a great NPV.
A simple example that highlights the strength of this method: a 137Cs point source is at the origin. A detector consisting of a right cylinder at arbitrary distance and orientation is nearby. What is the solid angle?
There may exist an analytical solution for this, but I wouldn't trust myself to derive it correctly. It would certainly be a huge mess.
If we add that the source is also a right cylinder instead of point source, and we want to add first order attenuation of emitted gammas by the source itself, the spreadsheet becomes only a bit more complex, but there will not be a pen and paper equation solution.
In this example every row of the spreadsheet would represent a hypothetical ray. One could randomly choose a location in the source, a random trajectory, and check if the photon intersects the detector. An alternative approach would be randomly choosing points in both target and detector, then doing additional math.
The results are recovered by making histograms and computing stats on the outputs of all the rows. You probably need a few thousand for most things at least. Remember roughly speaking 10k hits gets you ~1% statistics.
What annoys me with Monte Carlo methods is trying to get self-consistent statistics at multiple parameter values. E.g., in your example, what is the derivative of the solid angle as the detector is moved? Or more generally, if we have some 'net goodness' measure for a system depending on parameters, how can we efficiently maximize it, when simulations are noisy and basins are shallow?
My understanding is that these sorts of questions come up in ML, and there are ways of dealing with it, but they can't converge nearly as fast as simple iterations like Newton's method. Even if I have to take a series approximation instead of a simple formula, I'll be able to use autodiff (or at worst, symbolic differentiation) to get quick and precise answers to these questions.
Not a list, but a street fighting tactic is to apply this to finding counterexamples. Don't know whether a thing is true or false? Generate a bunch of random examples and check whether they all agree. Do this before you commit any energy to theoretical analysis. Obviously not a proof, but possibly gives a counterexample faster than you can think of one.
On the other hand, if you find yourself running 1hour+ numpy simulations for days on end you might want to consider an analytical approach.
I've used various commercial databases over the years. Some popular commercial databases relevant to HN readers include Web of Science, Scopus, and Engineering Village. When I worked at the USPTO, I used the less popular database Dialog, which I preferred. To my knowledge, none of these are available direct to consumers. I've only been able to get access from places with subscriptions. Some university libraries allow visitors where you can use these databases for free on-site.
I would call these databases complementary, not "entirely superior". There are two main advantages. One is that these databases will contain many things that you can't find on Google. The second advantage of these databases is that they are designed for advanced searchers and have more powerful query languages. Google on the other hand is dumbed down and will try to guess what you want, often doing a poor job. You can get very specific on these databases in ways that you can't with Google.
Related: I'm somewhat fascinated by more specialized bibliographic databases because they often contain things that can't be found on Google or the major commercial databases I listed above. I started keeping a list of them. https://github.com/btrettel/specialized-bibs
On a related note, if you studied and got a degree at a university, check if they have an alumni program. I pay a small yearly fee that lets me access the university's academic databases and their VPN, so I get some other perks as it looks like I'm connected through eduroam.
reminds me that my first taste of the internet was the days where you pretty much had t have a university account. I used a friend's, and was blown away by what I found on Usenet
Super helpful, thanks! Used to be up on the Databases when in school years ago, but it’s been so long. I wouldn’t actually know which ones are any good anymore did recognize scopus rest are new to me
Using timing coincidences in particle physics experiments is incredibly powerful. If multiple products from the same reaction can be measured at once, it's usually worth looking into.
Circular saws using wood cutting blades with carbide teeth can cut aluminum plates.
You can handle and attach atomically thin metal foils to things by floating them on water.
Use library search tools and academic databases. They are entirely superior to web search and AI.