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A group of researchers was studying how different people solve problems. They gathered a physicist, a mathematician, and an engineer and gave them each a problem: find the volume of a red sphere. The mathematician solves it first. Asked how, he explains that he used a simple formula. The physicist solves it next. Asked how, he explains that he submerged the sphere in water and measured the rise in water level. Hours later, they find the engineer buried in paperwork. Asked about his progress, he says “I can only find a table of values for the volume of blue spheres.”
On further inspection, it was found that the mathematician had assumed an ideal sphere of constant radius, while the real object was in fact oblate. The mathematician had neglected to take any measurements, leading to an incorrect value. The physicist’s answer was correct, but only at sea level at nominal temperature.
The engineer is currently using calipers to measure the diameter of the object at many different angles in order to build a CAD model. He said we could expect results next year.
The physicist’s answer would be correct anywhere, no matter the temperature or density of the fluid.
Supposing that the measurements with and without the sphere are taken under identical circumstances. But you deserve the upvote either way.
Interestingly, the physicist’s answer would always be correct, but not always consistent.
If the sphere is compressible, then air pressure will slightly affect its volume. And unless the thermal expansion rate of the sphere is zero, the amount of fluid displaced will also vary with temperature.
However, even if the physicist gets different answers in different environments, it’s always still a correct answer, because they correctly measured the volume of the sphere at that time.
Assuming the time between submersion and observation is greater than zero, increasing temperatures above boiling would give increasing error.
Conversely the physicist may get other error at/near freezing.
And yet another option is the fluid being above the Ball’s melting and/or boiling point, assuming changes in density with phase change.
They just said the ball was red, they didn’t say why…
Responded to inline comment saying any temp would be fine
All of which the physicist can trivially account for, control and variable test around, should the requested question be updated to require it.
The requested question did not include “In all possible scenarios”, thus determining the volume of the sphere via physics calculation at the most average of conditions, is the most correct valid solution, absent further requirement parameters.
You’re right in terms of grading a student’s homework or whatever.
In research/publication/career these assumptions must be stated unless given.
But I was responding to:
The physicist’s answer would be correct anywhere, no matter the temperature or density of the fluid.
Which includes non-standard conditions.
But I was responding to: The physicist’s answer would be correct anywhere, no matter the temperature or density of the fluid. Which includes non-standard conditions.
This is like saying “the physicist’s answer would have errors because they measured the ball and then stuck it in an oven. The volume of the ball in the oven is different than what they measured.”
No it’s more like the physicist tried to use boiling water to measure it
Using boiling water is still fine, the measurement will work, your comment literally only is a problem if they don’t measure in time. So yes, it’s exactly like sticking it in an oven and not measuring at the same time
Fair, if you do account for the change in water volume over time then you could maintain accuracy, but also good luck reading the meniscus.
Anywhere with gravity sufficient to overcome the surface tension of the water from forming around the object or clinging to the container.
They later added an Anthropologist, who understood that more questions needed to be asked. His first question was “do you want fries with that?”
Sorry for the stupid question, but doesn’t the rise in water level show the density of an object? Can you measure volume too? What if the sphere floated?
Edit: thanks everyone for helping me understand. I was totally misremembering the story about Archimedes and the crown.
If you fully submerge an object, you displace its VOLUME of water. It will always be the same amount (imagine a bowling ball and a soccer ball). You might need to push it.
When you relate that to its weight, you get the density.
Imagine you have two 1kg lumps of steel. Out of one you make a bowl with thin walls the out of the other a metal ball. Afterwards they still have (about) the same weight, volume and density - as it’s still steel.
But put the bowl onto the basin and with a little luck it will float like a boat *, put in the steel ball it will sink.
But when you put in the bowl sideways without splashing it will displace about the same amount of water than the ball. And it will still weigh 1kg.
*= The thing with floating people remember from school: The floating bowl will displace as much water as it weighs - that’s the thing Archimedes found out. So our 1kg bowl will displace 1kg of water - which is incidentally about 1 liter, because the density of water is about 1kg/l (it was intentionally defined that way, some guys in the French revolution used water to define mass by volume)
It shows volume, not density.
The amount of displaced water is the same for a lead sphere and a balloon of the same size.
You can the also calculate the density if you measure how mich of the object is submerged
Submerging the sphere gives you the volume. You’re thinking of the legend of Archimedes who measured volume this way and measured mass with an ordinary scale and deduced the density from those two values.
attach something to the bottom, pull, fix position
Edit: I am late. kudos for everyone who was faster :)
This entire post is a deep catharsis, and this comment is the pinnacle.
Ha. I had a convo with a programmer in the 90s. He was explaining a complex problem and the steps to solve in the code, to adjust things based on user choices and parameters.
And I said why wouldn’t you presolve all of them and then provide a lookup to go get the solution from a list. And he just looked stunned and walked away.
Reminds me of the first time I saw Sin and Cos lookup tables being used in early 3D gaming. The computers could calculate those just fine, especially with a math co-processor. But for 3D gaming it would be too slow to get a good framerate. So lookup tables were used to greatly improve the speed.
Back on those days all sort of neat tricks like that would be used. Often done as little demo programs that were very impressive. Before the internet it was hard to look up something like that and the latest and greatest tricks weren’t written in books yet. So often little code snippets and demo programs would be shared amongst programmers using the sneakernet, so we could all learn and get better.
Humans can invent lies. Machines can repeat lies faster.
On 8 bit CPUs we just “refactor” the circle to have 256 degrees so you can easily use 8 bit math.
Yeah, but we didn’t have an is_odd npm package, imagine the horror.
Aren’t commonly used math results fix in hardware anyways?
Ah my prior manager suggested something similar… Dynamic views that would adjust based on user set parameters… We set up canned views and called it a day.
He was let go, but always pushed for the art of the possible (even if it would take a few extra sprints to wrap)
It’s possible that the dynamic generation might be more maintainable than a lookup list, though.
With a lookup list, you may need to recalculate the whole thing every time you make a small change. And a significant change, like giving the user a new choice/parameter to adjust, may not only require recalculating the lookup table, but also exponentially increasing the size of the lookup table.
Whereas with a dynamically generated result, small adjustments to the values likely wouldn’t require any modification of the actual code at all, and adding a new choice/parameter would be fairly straightforward – it just needs to be plugged into the formula, maybe add an extra step or two in the algorithm.
It was finite, and early 90s. Calculation time is something you wanted to avoid. To put it to an analogy: you could calculate if a 3d X can be manipulated through a hole, or you can just prr evaluate and say Yes or no based on size, rather than running permutations on 6 axis of movement
why is this upvoted
Because there are plenty of scenarios where this would work.
Because he hadn’t thought of what I suggested and it was much easier than what he was trying to program. I wasn’t suggesting he write the program, solve it and table it; it was more like empirical knowledge/common sense stuff to narrow options, then fill the rest in based on what made sense. Then its just a horizontal or vertical intersection to find the outputs required instead of a complex calculation every time
I would say Computer Scientist in place of software engineer.
Yeah, software engineers are the sanitation engineers of programming. Source: am one
Scientists research. Engineers do. We are the more practical of the two.
Also, any CompSci grad I’ve worked with couldn’t write code for shit unless they learned how outside of their schooling, and yet so many go the CompSci -> programmer route instead of doing like SW Eng or something like that.
All these job titles don’t really have a formal definition. Software engineer = programmer = software developer. Computer scientist sure does sound fancy though. There’s no committee that will say “actually you’re doing too much math to be a developer sorry.” We all do the code-y thing. Businesses seem to pick one at random based on seniority. I just call myself whatever my most recent job title was.
Your industry will affect your specialisation and skills much more than anything else.
- Software Engineer (Maths)
I don’t even go that’s far. I “work in IT”. Enough for 99% of social interactions / official forms.
You’re taking my comment a little too seriously. I just know that what I do is essentially playing with other people’s legos, to make a CRUD app, to show my industry’s equivalent of cat pictures. I leave the heavy math and theory to the real computer scientists.
I couldn’t tell how serious you were being, sorry. Some people get weird about this specific topic and gatekeep the labels lol
Red thinks you’re making up words
They’re all real words, but not in an order that makes sense. And I’m not sure what algorithms there are by a Ross or Maxwell.
I think it means when the method is barely better O(Exp), even on ordered sets
B.S.
Dijkstra would have loved the lookup table solution.
He HATED complexity.
Everyone interviewing candidates believes they’re Dijkstra.
If you hand out a problem and only accept one solution out of multiple valid ones, you’re part of the problem.
It really depends on what you’re building. In an embedded shop, lookup tables are first class solutions to most problems. Computer scientists though, 100%!
Depends on the available memory and size of the tables. I’ve worked on cases where time to compute didn’t matter as much as shaving off three more bytes did. Large lookup tables would have absolutely killed us compared to running some math.
Good point! Good point.
I’ve seen bubble sort implemented because we had data that said it was faster and was slightly smaller for the exact type data we were sorting and its expected distribution.
I fondly remember the time I hired a QT expert onto an embedded app team and on his first project he imported a sort algorithm from std. He found the system got weird and glitchy, and often crashed.
Yeahhh turns out the algorithm he chose needed to make a copy in memory and the thread he was working in only had 2048 bytes of stack, so larger inputs would corrupt the stack allocated to the next thread. I had to explain to him that we had a full second to complete the math before we had to give back our semaphore, so saving a couple milliseconds on the sort was not a priority. Fun times.
not doubting you because the customer can be funny but wha?
if time to compute doesnt matter there are likely more minimal hardware options to optimize for look up tables and memory cost/space
There are so many situations where you can’t just swap hardware. Robots on an assembly line? Yeah you’ve gotta use hardware that’s gone through safety testing. They’re not going to just swap hardware to make things easier. You want to ship an update, you do it in software and under strict testing regiment. Some of that hardware is 20 or 30 years old. Medical. Aeronautics. Aerospace. All of them and more are using older hardware that’s often memory limited but can often just sit and process their next step, and they often don’t have built in complex hardware features because those add potential failure points.
the hang up for me is more the not caring about time to compute
aeroish is my experience, and for me those have all cared about time to compute
generally that’s one of the biggest constraints to the point of being super strict
like major money being spent on modeled approximations and processing speed costs eclipsing pretty much everything on the design side
tables for weather, angles, altitude, position this would be tiny compared to some we’re using
30 year old equipment is even more taxed given the likely feature creep in my experience
I’m guessing you were doing in flight aero stuff? I’ve been more in the medical and manufacturing space but the aero I did we were doing post-flight processing for reports. We had almost no memory to operate on, probably because of all the tables you’re referencing that others were using.
IIRC, Elite used lookup tables for trigonometric functions on certain target platforms (maybe the NES) because memory wasn’t as much of a constraint as computing performance. It’s a barrel of game compressed into a pint of code.
disappointing. no such algorithm.
yeah I looked it up
Good news, you can invent it!
Bijecting to an exponential curve was also a hint. Anything that bijects to an exponential would just biject to the positive reals, since that’s how logarithms work.
Your MOM is marginally optimal, nerd!
Hah, gottem.
It’s either “gotcha” or “got 'im”.
Nope. You’re wrong.
There is no such word as “gottem”. This is a recent bowel movement from ignorant people. “Gotcha” has been around for generations, and the use of the apostrophe is quite simple.
Gottem.
holy shit.
you might be the biggest fucking nerd ever for being so thoroughly “em” who just got “gott”
hahaha gottem
(no but seriously dictionaries are descriptive not prescriptive; they add new words as the language evolves. if you were correct about new implementation of the language being “bowel movements from ignorant people” then you should be speaking Shakespearean English as that is Proper English™. the language wasn’t finished changing when you stopped going to school, pal. I’d recommend you research linguistics as it seems you have a weak grasp on the concept and it’s bringing your nerd card into question.)
Wrong. It’s gotham
Talk to a linguist about how languages evolve.
Okay. So it’s not a word. That’s fine. The popular expression in this context is indeed “gottem” and it doesn’t matter if you think that’s a word or not, that’s just objective reality. Suck it, nerd.
When I was a kid and my mother was teaching me to read SQL, she really drove home that Elegance is in the eye of the beholder. While a C++ dev finds beauty in reducing a signal processing step to O(n) by recursing through five lines of bitwise ingenuity, a SQL dev finds radiance in completing the task without using any loops at all.
Alright to anyone who would question this statement. I am a mom, and have had extremely similar conversations with my kid regarding programming and perspectives.
Seriously it’s important for problem solving to not get caught up in perfect solutions or solutions you think are the right path be cause of your own bias’.
Sometimes to solve a problem you are stuck on, or is proving too challenging the best course of action is to figure out why you are trying to solve it that way, and what other solutions there might be.
When I was a kid and my mother was teaching me to read SQL
Why would a mother do this, I’m horrified
In the case of my mother, she’s pretty autistic and a very well known data scientist. This was her way of teaching me how she relates to the world - I’m quite grateful to her for it; it has given me a love of programming and allowed me get a great deal closer with her.
My mom taught me ORM. I’d rather have had the SQL mom.
It’s Bobby Tables.
I am disappointed when someone comes into my career (systems analysis) without the ability to do even a simple SQL statement and it’s become common since my employer realised they had too few analysts and hired 20 in my area for three of us to train
More mothers should teach their kids to query
Meh, Mongo and Elastic are the future, SQL is for… moms!
I sent her this thread and she’s asked me to tell you that she likes this so much she’s getting a “SQL is for Moms!” T-shirt printed.
I’m glad she liked my dumb joke. Have a good one!
I expected the bottom to say something like “instead of cloud-native scalable microservices using AI models that cost an average US household salary per day to run”, but maybe I’ve been in corporate for too long.
Depends on the scale of the project. Some apps you would get a promotion if you could get them to (reliably) run on just 50k a day.
Yeah. OP gets bonus points for the OG
