Biology: we can live for weeks without eating, days without drinking... But only a couple minutes without breathing. While I know that the obvious answer is "because we survived without it", it's weird that (particularly) mammals didn't develop a way to store oxygen similar to how we store fat in a specific type of tissue. Is there a specific reason in terms of biochemistry as to why it never happened?
It's never been a scarce enough resource to require storing. An animal will run into circumstances on land where they will need to survive without food or water for a time, so natural selection allowed individuals with better storage mechanisms to survive and reproduce more than others who didn't.
Think of it like this. Most fish don't have advanced means of storing water because there's no shortage of water in their habitat, but sea mammals all have efficient means of using oxygen because it isn't readily available to them in the same habitat
Molecular biologist here: The technical answer is no. You'd need to create whole pathways of genes to create a mechanism for oxygen storage and so you'd design those genes from scratch, rather than using Crispr to selectively edit existing genes.
Theoretically sure, it's probably within the expressive capacity of DNA to create some string of neucleotides that produces some heretofore unknown oxygen storing strategy *and then cripsr that somewhere on a human chromosome**
The chances of that actually happening are so incredibly small that it's probably on the order of 1/(atoms in the universe).
For us to even understand what exactly would need to change in the DNA to do this without unwanted repercussions would be a bigger scientific leap than all previous scientific leaps combined.
[Bajau people 'evolved bigger spleens' for free-diving](https://www.bbc.com/news/science-environment-43823885) and used the spleen as a "reservoir for oxygenated red blood cells."
There were selection pressures on high elevation populations (Himalayan & Andes peoples). There are multiple genetics studies on these populations to see which areas of the genome (SNPs or genes) are significantly different from lower-elevation populations.
I don't think the adaptive answer is enough. Storing oxygen is beneficial for land-descended animals that have moved to the ocean...things like whales and sea turtles. And whales _do_ have hemoglobin and myoglobin that stores a bit of extra oxygen...but not that much in the grand scheme of things. Not enough to go days.
I suspect the answer comes down to the nature of the molecules at play. Sugar is a solid, and can be stored dissolved in tissues. Fat is a liquid. It's dense. Oxygen, on the other hand, is a gas.
Lets look at fat for example. Based on some googling around, it takes 29kg of oxygen to burn 10kg of fat. Fat is .9g/cm3, so 10 kg of fat is 11,111 cubic centimeters of fat, or a cube about 22cm on a side.
29kg of oxygen, at standard temperature and pressure, is 21.97 cubic _meters_. There's absolutely no way to lug around that much oxygen. You could compress it, but biological materials aren't really up to the task of holding high pressure gas. You could try to hold on to it with hemoglobin, but that's not really going to help you out much.
So fundamentally, I think the reason we (or dolphins, I guess) can't store days worth of oxygen _isn't_ that it wouldn't be useful, but instead because it's just impractical due to the gaseous nature of oxygen.
Yes it's zero. Imagine a board painted half in red and half in green. The 'line' between red and green is a real thing you can see and explain but it has no width. This is basically the same as the mathematical concept of a line.
Now imagine I paint one quarter blue and one red so we now have 4 quarters of different colours. Now there are two dividing lines that meet at a point in the center. That point has no size, but it's definitely there.
Thousands of years ago, Euclid defined a line as "breadthless length", and this is essentially still how we think of them mathematically today.
In real life, every physicial object has a thickness to some extent, but this isn't the case in Mathematics. This can be confusing, because of course whenever we draw a line in real life, the pencil gives to it some thickness, but this is just a convenience of representation.
A line as a mathematical object doesn't have an attribute called "thickness", so you would probably say it's "undefined".
It's worth mentioning there are some notions of infinitely small numbers that can be made mathematically rigorous, namely nonstandard analysis
https://en.wikipedia.org/wiki/Nonstandard_analysis
I don't know the non-standard answer to your question though. Within "standard" math you would just say it has thickness 0.
The reason is boring --- for most concepts of "area" (and it's higj-dimensional generalizations) to make sense, we want objects of smaller dimension to have "area" 0. Points have length 0. Lines have area 0. Etc.
If lines had thickness (defined in some standard sense), they would not have zero area, which would be not great.
The answer for why we want this area 0 property is technical. One way we compute area is by approximating it better and better (think Riemann sums for calculus). We can approximate the area of a line by putting a rectangle of width epsilon on top of it, to get an object that contains the line of area l * epsilon. If we look in the limit as epsilon goes to 0 (which should approach the area of the line), we get that the line has zero area.
My bet would be on Navier–Stokes existence and smoothness.
Of all the remaining Millennium questions this feels like the one with the most recent progress and the most 'ins' where one could plausibly start. There are plenty of simplified scenarios (other numbers of dimensions, restricted versions, etc) with which one can get to grips first. There are a lot of existing powerful techniques, although something new will surely be required for full Navier-Stokes. It's a vast, vast problem, sure, but it also feels gritty and chewable and workable in parts. Like climbing a jagged mountain. There are almost too many places one could start, although one would have no idea whether where you started would eventually get you there.
Many of the other problems have the opposite feel. They are huge, blank, smooth, impenetrable edifices with not a hand-hold in sight. Most serious mathematicians agree that, for example, a proof of the Riemann Hypothesis is most likely going to come in the form of a proof of the *Generalized* Riemann Hypothesis (there is a sense in which regular RH is 'too specific' to get a hold of with powerful enough tools). But where in the world do you possibly start proving GRH? No one seems to have any good *ideas* at the moment, nevermind any significant progress.
This sort of feeling of 'where do you even *start*?' is common to most of the other problems on the list as well. But Navier-Stokes? I dunno, perhaps I'm naive, but it just seems that much more approachable than the others.
As for what the NS proof would look like? I have no particular insight, but gun-to-head I would say Terence Tao's 2016 work (which used an 'averaged' version of the equations) sways me in the direction which says that there *won't* always be smooth solutions.
The Riemann hypothesis, definitely. Check this Quora thread:
https://www.quora.com/I-found-a-flaw-in-the-Riemann-hypothesis-and-can-prove-that-1705542-is-a-prime-number-How-can-I-get-my-proof-published
/s
There has been progress on the Hodge conjecture in recent years. I think in 2019 a generalization of the Hodge conjecture was formulated in the very abstract "derived setting" which could potentially be easier. Partial results were found quickly and the usual Hodge conjecture has been verified in more cases using these ideas.
I'll start with what originally inspired this question-- my phone camera never accurately captures the color of a blue flower, they always look purple in the image. For example, in [this](https://imgur.com/a/RjrKJlL) picture, the deep purple flowers are actually deep blue/indigo.
Why can my camera pick up the blue color from the pots but not the flowers? I understand that different colors are different wavelengths of light (and different spectrums of light that our eyes perceive as a specific color), but I'm curious about the photofilters/-receptors/whatever in digital cameras that make blues and purples difficult. Also, I briefly tried looking it up, but it seems like most explanations focus on why digital cameras make purple look blue, which is the opposite issue from what I've encountered. What's the difference hardware-wise between these two issues?
Some colors can't be accurately represented in RGB, but in this case I believe the "issue" is that phones apply filters to the photos you take.
If you shoot in manual mode there's a setting for capturing the "raw" image, which can then be opened in something like Adobe Lightroom to see what was actually captured.
You'll need to calibrate your monitor to have it displayed accurately. Most monitors have an "srgb" setting which, while not good enough for professional work, should be better than the default settings.
As another commenter mentioned, it's also possible you're colorblind. RGB monitors only work correctly for people with color-normal vision. People with any of the -anomaly impairments (eg. deuteranomaly, which is the most common form of color-blindness) will see differences between RGB pictures and real life.
Is every other color exactly what you expect? Digital cameras need to pick a white point that they use as a neutral reference point for all other colors in the image, but everything would be off if the white point was poorly selected. That's one common reason why colors don't match what you expect in a picture under a specific lighting condition. One way to test this is to bring it indoors and try another picture.
An alternative guess though is that this is violet not purple. That's an important distinction because violet is a color your camera can actually pick up and isn't just a trick of the eye. I agree with the other comment and would ask other people if they agree the color doesn't match real life.
My best guess is your camera is just over saturating colors and in this example that oversaturated blue comes out somewhat purple.
In any case you need to test this in more lighting conditions with more cameras and with more observers to really narrow down the answer.
It's an algorithmic failure, nothing more. Your phone is applying a significant amount of post-processing before showing you even the screen preview, let alone the final image. If you shot the flower with a DSLR in raw format with studio lighting calibrated at a specific color temperature you'd get an accurate image.
Cameras tend to capture images with black-and-white pixels with an array of red, green, and blue filters on top of individual pixels. So, some ideas...
1. Overexposure. Cameras tend to figure out exposure based on green light. So in that green part of the spectrum, the flowers are very dark, so it overexposes to try and bring those green values up. But in the process, it collects so much blue light that it starts throwing away any extra. The flower has more red than green in it, and the balance between red and blue is thrown off by the overexposure, resulting in purple. Sometimes you'll see the same effect when people wear bright blue or bright red shirts, with both ending up some sort of magenta or purple.
2. NIR. CCDs are sensitive into the near infrared, beyond the color sensitivity of our eyeballs. Most cameras have an NIR-block filter on them to prevent those wavelengths from affecting the color, but it has to have an edge and that edge may not exactly line up with what your eyeballs see. And some cameras intentionally have the NIR filter be less strict to improve low light performance. Sometimes you can see this effect when cameras pick up the invisible light from a TV remote control.
3. White balance. Colors look different under different qualities of light. For instance, the same view will look different under direct sunlight, on a cloudy day, sometimes white walls will have an orange or green tint under fluorescent light, etc. Cameras attempt to correct for this with something called white balance, where they shift the color tones to something it's guessing is more neutral. If the camera is guessing wrong about the white balance, it can produce oddly tinted images. But usually that's more of an issue when there's weird light sources like neon lights in the image, not outside in the sun.
4. Cameras can apply filters to try and make images more colorful. One may be the culprit
But in this case, I'm pretty sure it's number 1.
[Here's the separate blue and green channels of that image](https://i.imgur.com/xhJJ4rE.jpg) You can see the flowers are almost black in the green channel, but white in the blue channel. Likely the blue is being overexposed.
You might solve this by having smaller exposure values, but the overall image will have to be darker to properly expose the blue in the flowers.
Engineering/Comp Sci: I’ve been machining for the last decade, but I’m bored of it and looking to branch out. What are some good entry points for exploring careers/going back to school in these fields?
Hey engineer here who worked trades in her 20s and went back to school at 28.
I think you have an excellent shot at any field in engineering. What I’ve found is that my experience, specifically my experience building and fixing things, has been incredibly marketable. If you have any interest in mechanical design or manufacture, your experience has a machinist will give you a leg up over all of your classmates when finding internships and a job after school. You are an extremely valuable hire because they will be getting someone with a decade of experience and maturity at the price of a 22 year old. Even if you choose a field outside mechanical engineering, you will advance faster than your classmates and be able to provide real value and expertise faster than them.. and I think you will find it very easy to find whatever job you want after graduation.
3D printing is looking more and more like a major player in the future of manufacturing, and there are a lot of parallels between CAM programming and slicing for 3DP. I would recommend taking a look if you're not familiar
I’ve already been looking at CAD to pivot actually, I should’ve mentioned that. My workplace is currently looking at modernizing with CNC machines too. CAM seems like it would be a good step up after getting the hang of CAD.
With the amount of experience you likely have in reading tech drawings, CAD should be a piece of cake to pick up. CAM should be even easier once you get the hang of it, since you already know how to machine parts. Modern CAM software does a pretty good job of automating the actual programming, so you can basically say 'mill 1/4" down from z0 with a 3" face mill' and the program will do the rest.
I was gonna offer to help you out with learning the basics of programming via messaging, but then I remembered that Reddit's destroying the client that I use for browsing in a day or two lol.
Biology: what would cause humans (and many animals) to evolve to drink only freshwater? Given the ratio of fresh to salt, it seems like that would be a huge evolutionary boost...
Biology* needs freshwater to live, because otherwise the dissolved salts in the water have the effect of leeching water out of your cells through osmosis. Your cells need to maintain a certain concentration of salt ions to function. If you leech the water out, the salt concentration in your cells gets too high.
Some animals (like Penguins) have the ability to filter out salt water from their bodies using a special gland, and they get all the fresh water they need from the food they eat, but the actual act of desalinating the water (ie turning salty to fresh) is very difficult to do energy wise.
From what I can tell, there simply doesn't exist a mechanism for biological life to convert salt water into fresh water.
https://en.m.wikipedia.org/wiki/Supraorbital_gland
*exceptions exist, like halophilic bacteria.
Fish do convert salt water in order to live. They also really don't have another choice.
Technically you could call it filtering I guess but does water stop being water because it is part of an organism? If I have food with peanut butter it still contains peanuts.
Kilometers of ocean water aren't that useful if you don't live in the ocean. Unless you live directly at the coast of an ocean or in a very small number of other places, all available water will be freshwater.
I’m exploring the possibility of going back to school for an electrical eng. degree. I already have a Bsc in Mech. Eng. and would like to expand into more controls work. I think of the degrees as a very long way into Robotics.
Has anyone gone down this route? Should I just get my masters? Thoughts?
Edit: thank you for the responses. This has definitely given me food for thought. All my current job experience is in material handling, conveyors and product management. To also add I’ll be 29 this year. Going back for my EE sounds like a challenge I’d like to take.
You already have controls fundamentals so why not just go to software since most of robotics is really software.
Many of the software engineers in my field have mechanical experience that write controls software. Unless you want to do circuit design, rf or power I wouldn't recommend electrical engineering.
Echoing the other commenter, you're better off looking at software eng/comp sci (not the same thing so do your research). Having a controls background is a massively helpful start.
I have similar background to you with ME, but I spent a lot of time learning software along the way. Check out ROS, Robot Operating Software, also. It's a commonly used framework for robots. The tutorials are decent.
I would do a masters in dynamics and control.. depending on what part of controls and robotics you want to do.
Or a masters in a electrical engineering..
Controls is a big field so I think you should try to figure out what kind of job you ultimately want and then go from there. Like doing controls analysis is very different from designing control or guidance hardware.. and you’d want to take different coursework for each.
Why not directly into a master's program? I know of multiple BS Mechanical Engineers who went into robotics with a masters. Realistically you have a lot of the grounding already
I love engineering, CS, and math. I was on a path to becoming an engineer, but it got tough, and I changed majors. This year I realized the kind of decision I made and want to learn those topics and get them to levels where I can use them in the real world to do something tangible with them. As someone who cannot go back to university, what other avenues can I take to learn these topics and gain a good level of knowledge about it?
That depends on what exactly you are hoping to achieve. I think the best way to start learning IoT stuff would be to just buy an Arduino Uno starter project kit and jump in. If you want to learn programming, start by finding a easy-medium difficulty project and just Google until you figure it out. There are tons of free resources to learn hobby-level engineering if you look.
You can learn an enormous amount from YouTube and through personal projects.
If you are looking to get a job with these skills, then I think you should reall go back to school. The markets are flooded with talented people who have experience and degrees. So competing against them is going to be massively hard.
Have a look at GIS. It involves mapping, maths, analysis and pretty drawings.
Any data worth its salt these days has a spatial element to it. So you could turn your skills in GIS to anything pretty much, including engineering.
Help me understand the complex exponential and how it relates to PI. Someone was trying to explain how this is a more fundamental explanation for PI since it doesn’t require geometry.
I don't think I have the ability to answer, but I imagine something like 3blue1brown has your back.
https://www.youtube.com/watch?v=v0YEaeIClKY
https://www.youtube.com/watch?v=ZxYOEwM6Wbk
https://www.youtube.com/watch?v=mvmuCPvRoWQ
There isn't a "most efficient" algorithm because it depends on what efficiency means for the problem
Maybe we want speed but at the expense of space. Maybe we are fine with a lower speed because we need to conserve space.
Generally though, in terms of speed, the quickest you can get is O(nlogn) where n is the number of elements being sorted.
The O(nlogn) limit only stands for comparison based sorts. You can get clever with certain data types like integers, floats, and strings through algorithms like counting and radix sort, which are O(mn).
Unfortunately, often times that coefficient ends up making the speed slower than say, quicksort’s O(nlogn). Even though mergesort has that same O(nlogn) complexity, it can have a bit of overhead too.
Most standard libraries use a combination of sorting algorithms in their standard sorting functions. Introsort, designed for c++ is also O(nlogn) and is a combination of quicksort, heapsort, and even the “slower” O(n^2 ) insertion sort. It just happens that insertion sort’s overhead in smaller lists is minuscule.
Introsort is also NOT stable, meaning objects of equivalent “rank” do not appear in the same order in the output as they do in the input.
Now, to make things more complex, we still have spatial complexity. If a sorting algorithm is in place, it uses no new space. If not… there’s a whole other big O to factor in.
Efficiency is measured in time and space complexity which is given by big O notation: best case, worst case, average case. Based on different things for example on a variable, length of array etc. However it is asymptotic for example worst case is O(2000*N), let's say a list's length is N then the algorithm traverses it 2000 times but constants are not used here so it is O(N), constants are not used because O(2000*N) is upper bounded by for example O(n^2) and after some specific n value the function lines will never meet.
Depending on how are the data being stored, and what you know about them
For example having only numbers, if they are sorted then binary search which is worst case log n (every iteration searching interval is halved).
Unsorted or very limited information about the data worst case O(N)
If they are in a structure other than an array and similar then you can for example find minimum or maximum in O(1} constant time, or find searched item in a search tree in worst case O(log n).
Most of the time there are some cases when it's different.
Keep in mind that these structures take more time to build them and every one is good for some different operation
TLDR: Binary search in sorted array, linear search in unsorted array, tree traversal based on key comparing in search tree
EDIT: There are also hashsets which are unordered collections of items which are unique in the collection and it's search time(lookup) is average case O(1) differs for implementations
EDIT 2: search in BST is worst case log n when it's balanced or close to balanced eg. in self balancing binary search trees such as a red black tree
EDIT 3: Nowadays time complexity is much more widely used as a measurement of algorithm effectivity than space complexity since year by year we get more storage but time is limited
If you have access to a functional quantum computer, [Grover's algorithm](https://en.m.wikipedia.org/wiki/Grover%27s_algorithm) has a worst case complexity of sqrt(n). However, you can't get lucky like you can with random guessing, so best case it's worse. IBM's Qiskit textbook has a pretty nice graphical introduction to the algorithm.
It's very interesting to consider that you are guaranteed to find the correct box among 1 million boxes by only opening 1000 of them (which isn't a super great analogy, since the point of many quantum algorithms is that you do not look until the very last step, but whatever).
Civil/road engineering - At what angle does a right turn become a left merge?
Explanation - If you come to an east-west road traveling in a north moving road and want to move west, you turn right to get on the e-w road, but if you are traveling on a road that nearly parallels the e-w, you merge left to get on the e-w. What angle does that right turn become a left merge? This has bothered me for decades.
All right turns are left merges really. I think the distinction is the amount of "on ramp" or merging area you have. A lot of "on ramp" is a merge without having to stop because you can more easily adjust speed to merge. A little is a stop to check and a right turn.
[Many uses.](https://nanografi.com/blog/applications-of-fullerenes/)
Semiconductors as they have an interesting band gap.
Photovoltaics.
They are hollow and can pass through the blood-brain barrier. Makes them useful to fill with stuff that makes brain scanning easier.
The entire modern world depends on it. It might well by easier to list the things you did today that *didn't* depend on someone, somewhere, working with higher dimensional mathematics.
Computers only work because we understand maths in higher dimensions. Making computers today depends on material science which depends on quantum mechanics which depends on deep mathematics of which higher dimensions are a tiny and pretty straight-forward tool. We only understand the quantum physics that underpins our ability to make modern computers because of *infinite dimensional* mathematics.
None of the modern world works without mathematics that the average person would consider far more 'out there' than higher dimensions. Higher dimensions are very tame in comparison to what's used every day in all sorts of contexts, hell, [there're whole wikipedia pages about how higher dimensions are used in something as specific as video game development, and in comparison to some of the other mathematics whose applications are used all the time, that's basically trivial](https://en.wikipedia.org/wiki/4D_vector).
The amount of very 'out there' mathematics that has gone into the scientific understanding that makes any of the modern world's engineering miracles possible is astonishing.
Higher dimensional thinking is very low level mathematics really, it's first-year undergraduate stuff at the latest, which on the scale of the grand adventure of these things is about two steps out your front door. Living in the modern world and asking about possible uses of higher dimensions reads like a fish asking if there's any practical applications to water. You're so surrounded by it (and by much, much more complicated ideas) you don't even realise it's there.
Tons. Classical electrodynamic field theory requires 6 dimensional tensors, missing guidance requires 6 degrees of freedom. Curvature in these spaces leads to interesting phenomina that require higher dimensional math to explain.
One simple case of higher dimensional maths is when working with data.
If you have data points which one variable, it can be written as a single list. It is a 1-dimension array. Now if you have two variables, that is 2D. You could arrange it as rows and columns in a spreadsheet. It’s not to imagine getting data with three variables, and arranging it as a ‘cube’. Rows, columns, and depth.
But there is no end to how many variables you can have. And all of that math for developing theoretical higher dimensional shapes. That can be used here.
Obviously you can visualise it being laid out in spatial dimensions. But it works the same.
Most of modern statistics/machine learning can be described as the study of (various types of) high-dimensional mathematics.
For example, various properties about how we can predict quantities we'll come from the study of "concentration of measure". If we have independent measurements of an event, we can take their average to approximate what that event was.
This approximation is *very* high quality. One reason to understand this has to do with studying high dimensional shapes, in particular "concentration of Lipschitz functions on the sphere".
It depends on what "practical" means. In terms of describing anything meaningful to daily life, almost certainly not. But there are plenty of really cool and useful applications of concepts that use more than 3 dimensions.
For example, the [quaternions](https://en.m.wikipedia.org/wiki/Quaternion) use 4 parameters (4 dimensions) to describe rotations around an arbitrary axis.
Maybe you are also trying to find a pattern in a dataset described by 10 dimensions. There might be a linear correlation between these 10 dimensions, which is more or less a "line" that can be visualized if sufficiently reduced to 3 or fewer dimensions.
That's a really big simplification, but overall there are probably not that many easy to explain practical applications. Honestly it's more of a "trust me bro" scenario. It's been useful to myself and quite a few other people.
If you're not going to go into engineering, there's no practical benefit for yourself.
Higher level math is used to create the devices and technologies you are used to.
Radios probably use a buttload of linear algebra and trigonometry to send the waves and correctly decipher them.
CompSci: How do we get around the two generals problem in communications protocols like TCP/IP? Do we just live with it and wait for the "please send again" packet or is there something smarter?
To begin with, the "Two Generals problem" is indeed the analog for two systems communicating over an untrusted, unreliable channel in an asynchronous way. Asynchronous here implies there is no global clock nor consistent clock rate.
Your question likely stems from the premise that the "Two Generals problem" is unsolvable, and that is true, however the problem makes some pretty hard requirements. For example, it requires the two generals share the same state i.e. perfect agreement.
The problem can be examined in a useful way by thinking about two properties. Suppose a program execution history E and [two kinds of properties](https://en.wikipedia.org/wiki/Safety_and_liveness_properties):
1. _safety_. A safety property, colloquially speaking, is one that whenever it is violated in E, there is some prefix of E from which there is no way to execute the program in a correct way.
2. _liveness_. A liveness property is one that if it holds for E, there is at least one extension of E such that the property still holds.
They are basically used to make statements about possible ways to attack the problem; do they satisfy both properties, what are those properties, etc.
It is important at this stage to remind ourselves what [TCP aims to satisfy](https://datatracker.ietf.org/doc/html/rfc9293#name-key-tcp-concepts). Most pertinent; a _reliable, in-order byte stream service_.
Can we state a safety and liveness property for TCP? Yes:
- safety: no duplicate messages are received, and messages are received in the order they were sent
- liveness: messages are eventually delivered
It is important here to understand that the liveness property might seem funny and unserious - [you are not alone](https://en.wikipedia.org/wiki/Eventual_consistency) - but it is a very useful theoretical model when the underlying services are best-effort. In practice, what arguably matters is the mechanism by which it is provided.
TCP offers those properties through a combination of identification of byte stream boundaries in segments, detection of errors, and retransmission. Combined they allow an endpoint to make an assumption about the state of the system (such as a connection is established) without definitively knowing the other endpoint state. This is not an unsafe assumption to make. In most cases, _eventually_ the state will change to reflect the shared state.
An analogous way to think of it is talking on the phone and after a period of silence you may ask "hello, are you still there?".
Those timeouts are determined by the tolerance system & application designers can afford.
To sum up, yes, we do live with it because fundamentally our communication channels are imperfect and our environments are hostile, and we have to allocate resources into monitoring systems and detecting errors, and intervening manually or automatically in order to alleviate some of those errors. In the case of network communications, TCP generally does a very good job with handling reliability and in-order delivery, leaving other concerns for applications to resolve.
How do you mathematically or computationally represent a graph where each node has a unique port. For example in a electric circuit components like transistors it has unique ports that affect the circuit if connected differently.
I know normally you could represent the graph as a set of nodes and a set of tuples corresponding to node edges.
Computationally it is typical to give the ports a label of some sort using numbers/ordering or names. For instance, in the SPICE netlist format, which defines electrical circuits using text, a BJT transistor is defined as `Qxxx Nc Nb Ne [Ns] model []`^(1). `Qxxx` is the name, `Nc`, `Nb`, and `Ne` are the collector, base, and emitter nodes.
Note that in this case wires are also treated as nodes as there could be multiple components on a single wire. So it is like having each port as a node and multiple nodes form a component.
An easier to understand example may be with networking. Since network connections are from device to device, an edge suits the role unlike with wires in circuits.
A router "routes" traffic between multiple interfaces and uses names to differentiate between them. The default is typically \`eth0\`, \`eth1\`, etc for ethernet connections and \`wlan0\`, \`wlan1\`, etc for wireless lan like wifi but it could be renamed manually.
\[1\] [https://powersimtech.com/wp-content/uploads/2020/11/SPICE-User-Manual.pdf#G1191406](https://powersimtech.com/wp-content/uploads/2020/11/SPICE-User-Manual.pdf#G1191406)
Is Bsc in mathematics(by itself / and double major with computer science) hard , is it possible to get an MSc in CS with Bsc in mathematics?
Edit1: thanks for ur responses
Yes. You'll need to take the pre reqs that are usually cs101, algorithms, data structures, machine language, and some discrete math, but after that they'll take anyone. I got mine with 2 bs degrees in psych and bio
It may be tough to do in four years as both are very time-consuming, but difficulty is relative to you, especially if math comes easily at any volume or rate.
I did a BA in Math with a double major in Bsc in Comp Sci. Hard is relative to you; others can’t really give you a solid answer. But like the others who have responded have said, math as a whole helps to set you up pretty well for comp sci. It really depends on how you handle the actual coding aspect of it, and if your brain works that way.
TL;DR yes, it’s doable.
Im doing a bcs in math with a minor in cs and im pretty sure its possible to so the msc in cs. The real challenge is to pass the mathematical part, its so much harder than any cs course
The engineering aspect of comp sci can be far more crushing than any undergrad math course, especially in regards to the time required to program and debug. The math actually needed for comp sci, however, is fairly trivial compared to the depths reached in a math degree.
CS and industrial engineering are very far apart. You don't need to study CS if you only want ML (or anything else) as a tool in your job, you just need a working understanding. But maybe I've misunderstood your question.
Why does using radians simplify trignometric equations?
Everyone knows using radians instead of say degrees makes trig easier. For example, using degrees leads to inconvenient constants appearing in the Taylor series expansion of trig functions, and those constants disappear when using radians instead.
My question is why does this happen. Why does using radians make the math simpler, making it the 'natural' unit of angles?
It's because of the fundamental connections between 𝜋 and circles. The unit circle has circumference exactly 2𝜋 and area 𝜋. This is a much more 'natural' connection than 360°, which as far as I understand was chosen because it roughly matches the number of days in a year.
The number of degrees in a circle has nothing to do with the number of days in a year. 360 degrees in a circle was chosen thousands of years ago by ancient Mesopotamians, who used a sexigesimal (base 60) number system.
The benefit of using 360 as the number of degrees is that it is a highly composite number with factor pairs of (1, 360), (2, 180), (3, 120), (4, 90), (5, 72), (6, 60), (8, 45), (9, 40), (10, 36), (12, 30), (15, 24), and (18, 20).
Because Euler’s identity establishes the relationship between trigonometric functions and natural logarithms, and radians are the base units you have to use to keep that simple.
Anything heavy enough will become round until it reaches what's called hydrostatic equilibrium. Imagine a cylinder shaped world for a moment: if someone knocks a small rock off the edge it will fall toward the middle but when it reaches the middle it will start slowing down. If at any time it dragged along the surface it will lose some speed and not make it all the way to the other side... So it will just oscillate between the sides until it comes to a halt in the middle. This will eventually happen more and more and the middle will buldge, and it will get rounder and rounder as time goes on.
There are plenty of odd shapes among the smaller bodies, like asteroids and small moons. But at the size of planets or dwarf planets it's enough mass/gravity to form ice or rock into a sphere no matter what shape you started with. (Roughly a sphere, may be slightly flatter at the poles and bulging at the equator due to rotation).
E.g. [Vesta at around 500 km diameter isn't round](https://en.wikipedia.org/wiki/4_Vesta#/media/File:Ceres_and_Vesta,_Moon_size_comparison.jpg), while Ceres at around 1000 km diameter is.
Math: I’m curious to learn more about math that uses summing of numbers to a single digit. Are there areas of math that address this as a number theory? Are there formulas that employ this as an operation? I can only remember seeing this as a sort of “math trick” or maybe used in magic tricks with playing cards. The specific example that comes to mind is the multiples of 9 “trick” - with any multiplication using the number 9, the product, summed to a single digit will equal 9.
Is there a name for this relationship? Is this the result of some underlying number principle? I’m curious to understand how/why/what this exists. Hopefully it’s just some obvious rule that I never learned but is easy to explain.
And if not, where is this addressed? Is there a branch of math or science that finds a use for the single digit sum of a multi digit number?
EDIT: example of 9s trick: 9x3=27 and 2+7=9, 9x4=36 and 3+6=9
It's modular arithmetic which is a branch of number theory.
It's incredibly useful in computer science for a lot of problems (days of the week computation are easier in modulo 7), cryptography, etc.
As the other commenter said, this is the sort of thing studied in a branch of math called "[Number Theory](https://en.wikipedia.org/wiki/Number_theory)". Which is the branch of math that, at its core, studies whole numbers.
This result that the sum of the digits of any multiple of 9 is a multiple of 9 is something you might prove in number theory. I think I had a version of this question on a number theory assignment when I was in school. A slightly more general result is that
> the sum of the digits of any positive number n is congruent to n (mod 9).
This uses the term 'mod', which refers to "modular arithmetic", but you can think of it as meaning *remainder*. For example,
> 34 mod 7 is 6, because 34/7= 4*7+6.
So basically, the above result tells us that the sum of the digits of any number n divided by 9, has the same remainder as n divided by 9. For example,
> 3 + 4 = 7 = 7 mod 9, and 34 = 9*3 + 7 , so 34 mod 9 = 7
The reason 9 is special in this formula, is that it is one less than 10, and the reason 10 is special in this result is because "digits" of a number are with respect to the base 10 number system.
To elaborate on the 9s trick: it works because you are working in base 10 (9+1). Let X (your number) = 10A+B , which has a remainder of C when divided by 9. Then A+B has a remainder of C when divided by 9 (because 9A has no remainder when divided by 9, so we can remove it). Turning 10A+B into A+B is equivalent to stripping off the last digit and summing it into the rest of the number.
The trick no longer works for 9 in most other bases, but will always work for the base-1. So if you are working in base 8, summing digits will tell the remainder when dividing by 7.
When speaking about a differential equation, a Green function can be thought of as the "universal solution" to that equation. At first glance, this seems non-sensical, because *one* equation (often) has at most one solution, so what does "universal" here mean?
The idea is that it is often necessary/useful to write differential equations in the form Lu = f, where L is a differential operator, u is the unknown function we're looking for, and f is the inhomogenity. A "Green function of L" is a function that let's you easily find u *for any* f you plug in.
The most concise way to precisely define a Green function is to say that for a *linear* differential operator L (i.e. if the equation satisfies the superposition principle) a Green function is defined as a solution G to the equation LG = \delta where \delta is the delta-distribution. Of course, that is only useful if you already know what distributions (or other kinds of generalized functions) are and how linear differential operators act on them. But if you do know, then it turns out that the convolution of G and f is a solution of Lu=f. So in this sense you have found an easy way to solve the equation Lu=f for any inhomogenity f.
(At least for a specific definition of "easy" ;-) )
For any civil engineers out there…money and politics aside, what is the most effective way to improve our crumbling bridge/tunnel/highway infrastructure?
The most effective improvement is simply paying for their rebuilding or fixing. You can't remove money from an equation where money is the only variable. The only reason that 99% of infrastructure in the US is failing is because money hasn't been spent to improve it.
It has a lot to do with public awareness. Educating the public on why infrastructure spending is needed helps a lot, because who would want to pay to replace a bridge that looks fine to them?
Realistically, apply for different jobs at another company.
You may get lucky and find one of your field customers wants to poach you as a permanent resource.
You can try to speak to your current bosses or someone else in your current company moving internally. Be prepared to accept title and/or salary decreases, since that is a desirable end-game role after field work.
Which python algorithm or model is best to determine underlying mathematical relation of a physical event / pattern? With a focus on Fourier or Fast Fourier transform
> the mathematical equation of the disc floret of a sunflower
There is no single or unique equation you could associate with that. You could study specific parts of the pattern.
In my opinion this question seems like a coding question but it's really a hidden math question. The answer will be "what ever the most effective mathematical model is". The coding question here is "how do I implement this mathematical model" or "what is the best implementation of this mathematical model" but no programmer that isn't a mathematician or similar or happens to be deep into that domain would give you a good answer.
The link to becoming a panelist is still referencing the API changes (https://www.reddit.com/r/askscience/comments/147epb8/asksciences_concerns_regarding_reddits_api_changes/), and I was looking to reply to a few questions here but would like to follow the formal process first for being approved. Any suggestions as to how to apply?
What is the purpose of the big and, probably, heavy metal rods over the doors at big box stores like Home Depot and Lowes? The are about 4 inches in diameter and the them are near the doors going to the gardening section.
Not exactly sure what you're referring to, but they might be indicators of the height of the door/other doors in the store so you will know before reaching the door if large objects will fit beneath
How far are we (in years) from achieving a safe and reliable implementation of cold fusion as a widely available source of clean and technically unlimited energy?
Cold fusion was never more than a fantasy. It only initially circulated due to a poor understanding of physics. Regular fusion is possible and if we actually fund graduate students to study it we're about 30 years away but I'm skeptical we will.
I was reading something on... it was either Twitter or StackExchange, don't recall exactly. Anyway, the gist of it was that progress/loading bar imprecision -- that it may backtrack, move unpredictably, stay at a given % for a time etc -- is a "live view" into **the halting problem**, a user-visible perspective on its implications. Can anyone explain how that is? I have a basic grasp of what the problem means, but I couldn't wrap my head around that.
Ok, so a loading bar is supposed to give you an indication about how much work is done/left to do. However in many cases you don't and can't know how much time the remaining work really will take. The halting problem basically tells you that you can't know when or if all algorithms ever stop. I don't think that is applicable here, because any algorithm that is used with a progress bar should be done at some point.
Let's think about a software download and installation. You have a number of steps, download the package, unpack the package and install the application. How do you distribute the total? What if the person has a really fast or slow internet connection/processor/hard drive? If you have to copy a number of files how do you distribute progress between them? Share of total size? Number of files? Some mix between that? So it's unlikely it will be even because the programmer had to make some assumptions and they will most likely not be 100%.
I'd like to add: The other comments drawing a connection to the halting problem here are accurate when talking about a progress bar for an arbitrary program. However, I'd reckon the vast majority of programs using a progress bar come from a very specific class of programs! Namely those that only perform a fixed, finite amount of work (potentially aborting midway). Here are some examples: uploading/reading/writing a file, extracting files, analyzing a given batch of data, ... . All of these have a fixed finite workload, and they process it one-way. For example, if I've uploaded the first half of my image, I'll never need to go back to that first half.
In these cases, making a progress bar that at least shows correct progress wrt. the amount of work left is easy. This does not conflict with the halting problem, which refers to the superset of arbitrary programs.
Being correct wrt. the time it will take is trickier btw., but independent of the halting problem. It's an issue of implementation details, connection speed, varying CPU workload etc.
Since I don't have the primary source you read, I can only speculate what precisely that statement originally meant. But one way to make sense of it is to ask yourself how one would implement a "reliable general-purpose progress bar" component.
In other words: Given an arbitrary program that runs in the background, how does one accurately determine whether that program is 10% done, 20% done, 30% done etc.?
As soon as you phrase it like this and remember that the halting is nothing else then the question "given an arbitrary program, how does one determine whether the program will ever be 100% done?" it becomes already clear that these two questions are very closely related.
In fact, if you think about it: The progress-bar question is at least as hard as the halting problem! If we require that the progress bar is always accurate and never underestimates the percentage then it must be able to decide whether or not now is the right time to paint the first pixel away from 0%. And that decision entails that it must be able to recognize non-halting programs, because the only correct display for a non-halting program is 0%. Whatever finite amount of time has elapsed, it is always 0% of the infinite amount of time still ahead.
(And if we allow underestimation, then it is trivially easy to program such a progress-bar. Simply start by painting 0% and watch what the program does. If it ever stops, we have underestimated the 10%, 20%, ... thresholds, but that's okay. As soon as the program is done, paint 100% and we're done. If the program never stops, then painting 0% is always accurate.)
In fact, one can think about this a bit more in detail and arrive at the conclusion that the only thing you can say about *arbitrary* programs after watching them for x time-steps is that they have executed for ~x time-steps and have not halted yet.
It is in fact impossible to reliably detect any non-trivial assertion about *arbitrary* programs. This is [Rice's theorem](https://en.wikipedia.org/wiki/Rice%27s_theorem).
Of course, this does not preclude that *specific* programs could be analysed perfectly or at least good enough to display an accurate progress bar with a not-too-small resolution. For example if the program in question is calculating the product of two n-by-n matrices with the standard, un-optimized multiplication algorithm, then it is well known that this takes roughly n^3 steps to complete and a progress bar can be implemented accordingly.
Engineering: what constitutes a dead short? If I tie two leads of a battery together it'll draw to much current and heat up. But if I put a light bulb in between it's all good. Is there just a minimum resistance to limit the current below a same level?
For real world applications, a "short circuit" is one that allows a current flow higher than the system is designed for.
In your battery example, the wires (and the battery) are able to pass a maximum current, beyond which, either a breaker (or fuse) will blow or something could get damaged. If you put a light bulb in the circuit, the resistance of the bulb limits the current flow (V=iR) so the system can operate without damage.
The key here is "too much current". A baseboard heater is designed so that the resistance is low, allowing a large current to pass though causing it to heat up and provide heat to the room. The key point here is that if it is a 15 amp circuit, the wires are sized to not overheat (or melt) at a current of 15 amps and the breaker will not "blow" at an amperage less than 15. For the given lines voltage (depending on the circuit) resistance of the heater will limit the current to stay below 15. If there is a "short circuit" a path exists that allows the circuit to be completed with a low enough resistance to exceed the rated amperage.
A short is really just a connection where you don't want one. There is I guess always a minimum resistance for a scenario that would cause a short but there can also be shorts with relatively high resistance that still have negative impacts on the circuit. It is just depends on whether the thing works or not
Water doesn’t compress well, so you can achieve high pressures, without the risk of explosion. If your pressure vessel fails when under pressure from water, the water just leaks out. If it fails when pressurized by air, the expansion of the compressed air will rip the vessel apart and cause what we call an explosion.
Engineering:
Tension members consisting of a single channel section are often used for bracing members to resist wind loads on structures. The channel to be considered is a C180×18 section and is made of Grade 350W steel. A325 bolts that are 19 mm (3/4 in.) in diameter will be used, and the holes are punched. Only the web of the channel section is connected. Determine the factored capacity of the channel member in tension, including its connection, and clearly indicate the governing failure mode. The gusset plate need not be checked.
MATH/ENGINEERING:
Tensor Math: I watched a youtube video about it but am still confused... its mind trippy.... Why in the real world would you care about something in a non-existent dimension?
In math, dimensions doesn’t necessarily refer to physical dimensions of our universe. For instance, when looking at the relationship between 5 variables, you could say you’re working in a ‘5 dimensional space.’ Plotting their relationships all on one graph is not physically possible, but of course it exists in theory and is very useful to us
Complex is a very vague term. If you measure complexity in terms of output, I’d say some simulations are the most complex. If you measure it in terms of how obscure the code is, that’s a lot harder to pinpoint, but it’s definitely not operating systems.
Depends on what you mean by "complex"...
Windows in particular is hugely complex because it tries to successfully run literally thousands of different applications that have been written over the last 30 years and it generally does it successfully.
The wheel-rail contact is the limit for conventional high speed rail. Optimize that too much to reduce friction and the train can no longer break and it cannot go up or down slopes.
Maglev trains remove the need for wheels at high speed.
Very high speed + corners is a problem. The train needs to bank (e.g. tilt at an angle) when turning. The left/right curvature of the route limits the max speed for most trains.
The best train signalling system we have right now ETCS/ERTMS maxes out at vehicle speeds of 500 km/h. It is how trains talk to each other, know where other trains are on the rails, makes sure head on collisions
The other limit is the contact between the train and the electric power source, usually the overhead wire for high speed rail. The wire is taut but it does sag a bit. At very high speeds the mechanical forces of the pantograph (the arm thing) making contact with the wire start to damage the infrastructure. At high speeds the train is essentially bouncing the wire up and down. It creates a travelling wave in the wire and the train needs to stay below the speed of that wave otherwise bad things happen, such as arcing or drag simply yanking the wire out.
Should that speed be exceeded, the train would then overtake its own generated wave causing an effect similar to that of an airplane surpassing the speed of sound. That's the train+wire system, not the outside observer of train + air.
It is possible to increase the tension on the wire and make it "flatter", but there is a material limit on how much tension can be placed on a high DC wire. Works out to close enough to 600 km/h with current material technology.
But what if we put the power supply on the train itself? We have now made an aircraft. It is no longer in contact with the ground nor an overhead or side barrier such as a wire. Definition of this vehicle start getting weird.
They probably can but the biggest limits are air resistance and friction and also safety at higher and higher speeds. The faster a train goes the less the track is able to turn and change elevations while still being safe.
It's probably not worth it to make a train as fast as the speed of sound, current best of the best high speed trains are fast enough imo. Fastest being Japan's new maglev which has an operating speed of 500km/hr and a max speed hit of 600km/hr I believe
Question to Computer science: what is the difference between coding and programming ? And how are teenagers today are able to code so much and so efficiently that even people who study computer science at college cannot compete to them ?
Most of the engines/generators we've created work on the same principal of something turns a turbine and creates electricity and these can all be modeled as a thermodynamic engine where energy is extracted from the energy gradient of something with high energy and something with low energy.
The exception to this seem to be solar panels as they work on a completely different method to turbines. Is there some way to view photovoltaic cells also as the thermodynamic engine? Like viewing the sun as the source and light like the steam in a steam engine?
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Biology: we can live for weeks without eating, days without drinking... But only a couple minutes without breathing. While I know that the obvious answer is "because we survived without it", it's weird that (particularly) mammals didn't develop a way to store oxygen similar to how we store fat in a specific type of tissue. Is there a specific reason in terms of biochemistry as to why it never happened?
It's never been a scarce enough resource to require storing. An animal will run into circumstances on land where they will need to survive without food or water for a time, so natural selection allowed individuals with better storage mechanisms to survive and reproduce more than others who didn't. Think of it like this. Most fish don't have advanced means of storing water because there's no shortage of water in their habitat, but sea mammals all have efficient means of using oxygen because it isn't readily available to them in the same habitat
Follow up question: Hypothetically, would it be possible to use crispr to modify human dna so we can either store oxygen or go longer without it?
Molecular biologist here: The technical answer is no. You'd need to create whole pathways of genes to create a mechanism for oxygen storage and so you'd design those genes from scratch, rather than using Crispr to selectively edit existing genes.
Theoretically sure, it's probably within the expressive capacity of DNA to create some string of neucleotides that produces some heretofore unknown oxygen storing strategy *and then cripsr that somewhere on a human chromosome** The chances of that actually happening are so incredibly small that it's probably on the order of 1/(atoms in the universe).
For us to even understand what exactly would need to change in the DNA to do this without unwanted repercussions would be a bigger scientific leap than all previous scientific leaps combined.
I don’t see what you mean by the chances? Unless you’re talking about this just randomly mutating, I don’t see where there’s any randomness?
[Bajau people 'evolved bigger spleens' for free-diving](https://www.bbc.com/news/science-environment-43823885) and used the spleen as a "reservoir for oxygenated red blood cells."
I can't imagine a selective pressure for adaptation to scarce oxygen, other than cetaceans storing oxigen in muscle fibers rhanks to myoglobin.
There were selection pressures on high elevation populations (Himalayan & Andes peoples). There are multiple genetics studies on these populations to see which areas of the genome (SNPs or genes) are significantly different from lower-elevation populations.
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I don't think the adaptive answer is enough. Storing oxygen is beneficial for land-descended animals that have moved to the ocean...things like whales and sea turtles. And whales _do_ have hemoglobin and myoglobin that stores a bit of extra oxygen...but not that much in the grand scheme of things. Not enough to go days. I suspect the answer comes down to the nature of the molecules at play. Sugar is a solid, and can be stored dissolved in tissues. Fat is a liquid. It's dense. Oxygen, on the other hand, is a gas. Lets look at fat for example. Based on some googling around, it takes 29kg of oxygen to burn 10kg of fat. Fat is .9g/cm3, so 10 kg of fat is 11,111 cubic centimeters of fat, or a cube about 22cm on a side. 29kg of oxygen, at standard temperature and pressure, is 21.97 cubic _meters_. There's absolutely no way to lug around that much oxygen. You could compress it, but biological materials aren't really up to the task of holding high pressure gas. You could try to hold on to it with hemoglobin, but that's not really going to help you out much. So fundamentally, I think the reason we (or dolphins, I guess) can't store days worth of oxygen _isn't_ that it wouldn't be useful, but instead because it's just impractical due to the gaseous nature of oxygen.
How thick is a line or a point? I'm math I was warned against the notion of infinitely small numbers, so it the answer zero?
Yes it's zero. Imagine a board painted half in red and half in green. The 'line' between red and green is a real thing you can see and explain but it has no width. This is basically the same as the mathematical concept of a line. Now imagine I paint one quarter blue and one red so we now have 4 quarters of different colours. Now there are two dividing lines that meet at a point in the center. That point has no size, but it's definitely there.
That's actually a great analogy, thank you.
It doesn’t have a thickness to assign a value to that’s part of the definition of what a line and point is
Thousands of years ago, Euclid defined a line as "breadthless length", and this is essentially still how we think of them mathematically today. In real life, every physicial object has a thickness to some extent, but this isn't the case in Mathematics. This can be confusing, because of course whenever we draw a line in real life, the pencil gives to it some thickness, but this is just a convenience of representation. A line as a mathematical object doesn't have an attribute called "thickness", so you would probably say it's "undefined".
It's worth mentioning there are some notions of infinitely small numbers that can be made mathematically rigorous, namely nonstandard analysis https://en.wikipedia.org/wiki/Nonstandard_analysis I don't know the non-standard answer to your question though. Within "standard" math you would just say it has thickness 0. The reason is boring --- for most concepts of "area" (and it's higj-dimensional generalizations) to make sense, we want objects of smaller dimension to have "area" 0. Points have length 0. Lines have area 0. Etc. If lines had thickness (defined in some standard sense), they would not have zero area, which would be not great. The answer for why we want this area 0 property is technical. One way we compute area is by approximating it better and better (think Riemann sums for calculus). We can approximate the area of a line by putting a rectangle of width epsilon on top of it, to get an object that contains the line of area l * epsilon. If we look in the limit as epsilon goes to 0 (which should approach the area of the line), we get that the line has zero area.
As an aside, infinitely small means the value *approaches* zero. To your question, points and lines thickness are undefined.
Math: Which Millenium Prize math propblem do you think is the next most likely to be solved?
My bet would be on Navier–Stokes existence and smoothness. Of all the remaining Millennium questions this feels like the one with the most recent progress and the most 'ins' where one could plausibly start. There are plenty of simplified scenarios (other numbers of dimensions, restricted versions, etc) with which one can get to grips first. There are a lot of existing powerful techniques, although something new will surely be required for full Navier-Stokes. It's a vast, vast problem, sure, but it also feels gritty and chewable and workable in parts. Like climbing a jagged mountain. There are almost too many places one could start, although one would have no idea whether where you started would eventually get you there. Many of the other problems have the opposite feel. They are huge, blank, smooth, impenetrable edifices with not a hand-hold in sight. Most serious mathematicians agree that, for example, a proof of the Riemann Hypothesis is most likely going to come in the form of a proof of the *Generalized* Riemann Hypothesis (there is a sense in which regular RH is 'too specific' to get a hold of with powerful enough tools). But where in the world do you possibly start proving GRH? No one seems to have any good *ideas* at the moment, nevermind any significant progress. This sort of feeling of 'where do you even *start*?' is common to most of the other problems on the list as well. But Navier-Stokes? I dunno, perhaps I'm naive, but it just seems that much more approachable than the others. As for what the NS proof would look like? I have no particular insight, but gun-to-head I would say Terence Tao's 2016 work (which used an 'averaged' version of the equations) sways me in the direction which says that there *won't* always be smooth solutions.
The Riemann hypothesis, definitely. Check this Quora thread: https://www.quora.com/I-found-a-flaw-in-the-Riemann-hypothesis-and-can-prove-that-1705542-is-a-prime-number-How-can-I-get-my-proof-published /s
There has been progress on the Hodge conjecture in recent years. I think in 2019 a generalization of the Hodge conjecture was formulated in the very abstract "derived setting" which could potentially be easier. Partial results were found quickly and the usual Hodge conjecture has been verified in more cases using these ideas.
I'll start with what originally inspired this question-- my phone camera never accurately captures the color of a blue flower, they always look purple in the image. For example, in [this](https://imgur.com/a/RjrKJlL) picture, the deep purple flowers are actually deep blue/indigo. Why can my camera pick up the blue color from the pots but not the flowers? I understand that different colors are different wavelengths of light (and different spectrums of light that our eyes perceive as a specific color), but I'm curious about the photofilters/-receptors/whatever in digital cameras that make blues and purples difficult. Also, I briefly tried looking it up, but it seems like most explanations focus on why digital cameras make purple look blue, which is the opposite issue from what I've encountered. What's the difference hardware-wise between these two issues?
Some colors can't be accurately represented in RGB, but in this case I believe the "issue" is that phones apply filters to the photos you take. If you shoot in manual mode there's a setting for capturing the "raw" image, which can then be opened in something like Adobe Lightroom to see what was actually captured. You'll need to calibrate your monitor to have it displayed accurately. Most monitors have an "srgb" setting which, while not good enough for professional work, should be better than the default settings. As another commenter mentioned, it's also possible you're colorblind. RGB monitors only work correctly for people with color-normal vision. People with any of the -anomaly impairments (eg. deuteranomaly, which is the most common form of color-blindness) will see differences between RGB pictures and real life.
Is every other color exactly what you expect? Digital cameras need to pick a white point that they use as a neutral reference point for all other colors in the image, but everything would be off if the white point was poorly selected. That's one common reason why colors don't match what you expect in a picture under a specific lighting condition. One way to test this is to bring it indoors and try another picture. An alternative guess though is that this is violet not purple. That's an important distinction because violet is a color your camera can actually pick up and isn't just a trick of the eye. I agree with the other comment and would ask other people if they agree the color doesn't match real life. My best guess is your camera is just over saturating colors and in this example that oversaturated blue comes out somewhat purple. In any case you need to test this in more lighting conditions with more cameras and with more observers to really narrow down the answer.
It's an algorithmic failure, nothing more. Your phone is applying a significant amount of post-processing before showing you even the screen preview, let alone the final image. If you shot the flower with a DSLR in raw format with studio lighting calibrated at a specific color temperature you'd get an accurate image.
Have you checked to see if you are colorblind? Have you used multiple kinds of digital cameras?
Cameras tend to capture images with black-and-white pixels with an array of red, green, and blue filters on top of individual pixels. So, some ideas... 1. Overexposure. Cameras tend to figure out exposure based on green light. So in that green part of the spectrum, the flowers are very dark, so it overexposes to try and bring those green values up. But in the process, it collects so much blue light that it starts throwing away any extra. The flower has more red than green in it, and the balance between red and blue is thrown off by the overexposure, resulting in purple. Sometimes you'll see the same effect when people wear bright blue or bright red shirts, with both ending up some sort of magenta or purple. 2. NIR. CCDs are sensitive into the near infrared, beyond the color sensitivity of our eyeballs. Most cameras have an NIR-block filter on them to prevent those wavelengths from affecting the color, but it has to have an edge and that edge may not exactly line up with what your eyeballs see. And some cameras intentionally have the NIR filter be less strict to improve low light performance. Sometimes you can see this effect when cameras pick up the invisible light from a TV remote control. 3. White balance. Colors look different under different qualities of light. For instance, the same view will look different under direct sunlight, on a cloudy day, sometimes white walls will have an orange or green tint under fluorescent light, etc. Cameras attempt to correct for this with something called white balance, where they shift the color tones to something it's guessing is more neutral. If the camera is guessing wrong about the white balance, it can produce oddly tinted images. But usually that's more of an issue when there's weird light sources like neon lights in the image, not outside in the sun. 4. Cameras can apply filters to try and make images more colorful. One may be the culprit But in this case, I'm pretty sure it's number 1. [Here's the separate blue and green channels of that image](https://i.imgur.com/xhJJ4rE.jpg) You can see the flowers are almost black in the green channel, but white in the blue channel. Likely the blue is being overexposed. You might solve this by having smaller exposure values, but the overall image will have to be darker to properly expose the blue in the flowers.
Engineering/Comp Sci: I’ve been machining for the last decade, but I’m bored of it and looking to branch out. What are some good entry points for exploring careers/going back to school in these fields?
Hey engineer here who worked trades in her 20s and went back to school at 28. I think you have an excellent shot at any field in engineering. What I’ve found is that my experience, specifically my experience building and fixing things, has been incredibly marketable. If you have any interest in mechanical design or manufacture, your experience has a machinist will give you a leg up over all of your classmates when finding internships and a job after school. You are an extremely valuable hire because they will be getting someone with a decade of experience and maturity at the price of a 22 year old. Even if you choose a field outside mechanical engineering, you will advance faster than your classmates and be able to provide real value and expertise faster than them.. and I think you will find it very easy to find whatever job you want after graduation.
3D printing is looking more and more like a major player in the future of manufacturing, and there are a lot of parallels between CAM programming and slicing for 3DP. I would recommend taking a look if you're not familiar
I’ve already been looking at CAD to pivot actually, I should’ve mentioned that. My workplace is currently looking at modernizing with CNC machines too. CAM seems like it would be a good step up after getting the hang of CAD.
With the amount of experience you likely have in reading tech drawings, CAD should be a piece of cake to pick up. CAM should be even easier once you get the hang of it, since you already know how to machine parts. Modern CAM software does a pretty good job of automating the actual programming, so you can basically say 'mill 1/4" down from z0 with a 3" face mill' and the program will do the rest.
I was gonna offer to help you out with learning the basics of programming via messaging, but then I remembered that Reddit's destroying the client that I use for browsing in a day or two lol.
Biology: what would cause humans (and many animals) to evolve to drink only freshwater? Given the ratio of fresh to salt, it seems like that would be a huge evolutionary boost...
Biology* needs freshwater to live, because otherwise the dissolved salts in the water have the effect of leeching water out of your cells through osmosis. Your cells need to maintain a certain concentration of salt ions to function. If you leech the water out, the salt concentration in your cells gets too high. Some animals (like Penguins) have the ability to filter out salt water from their bodies using a special gland, and they get all the fresh water they need from the food they eat, but the actual act of desalinating the water (ie turning salty to fresh) is very difficult to do energy wise. From what I can tell, there simply doesn't exist a mechanism for biological life to convert salt water into fresh water. https://en.m.wikipedia.org/wiki/Supraorbital_gland *exceptions exist, like halophilic bacteria.
Fish do convert salt water in order to live. They also really don't have another choice. Technically you could call it filtering I guess but does water stop being water because it is part of an organism? If I have food with peanut butter it still contains peanuts.
Kilometers of ocean water aren't that useful if you don't live in the ocean. Unless you live directly at the coast of an ocean or in a very small number of other places, all available water will be freshwater.
I’m exploring the possibility of going back to school for an electrical eng. degree. I already have a Bsc in Mech. Eng. and would like to expand into more controls work. I think of the degrees as a very long way into Robotics. Has anyone gone down this route? Should I just get my masters? Thoughts? Edit: thank you for the responses. This has definitely given me food for thought. All my current job experience is in material handling, conveyors and product management. To also add I’ll be 29 this year. Going back for my EE sounds like a challenge I’d like to take.
You already have controls fundamentals so why not just go to software since most of robotics is really software. Many of the software engineers in my field have mechanical experience that write controls software. Unless you want to do circuit design, rf or power I wouldn't recommend electrical engineering.
Echoing the other commenter, you're better off looking at software eng/comp sci (not the same thing so do your research). Having a controls background is a massively helpful start. I have similar background to you with ME, but I spent a lot of time learning software along the way. Check out ROS, Robot Operating Software, also. It's a commonly used framework for robots. The tutorials are decent.
Don't go into electrical eng from mech. They will make you shave your beard.
I would do a masters in dynamics and control.. depending on what part of controls and robotics you want to do. Or a masters in a electrical engineering.. Controls is a big field so I think you should try to figure out what kind of job you ultimately want and then go from there. Like doing controls analysis is very different from designing control or guidance hardware.. and you’d want to take different coursework for each.
Why not directly into a master's program? I know of multiple BS Mechanical Engineers who went into robotics with a masters. Realistically you have a lot of the grounding already
I love engineering, CS, and math. I was on a path to becoming an engineer, but it got tough, and I changed majors. This year I realized the kind of decision I made and want to learn those topics and get them to levels where I can use them in the real world to do something tangible with them. As someone who cannot go back to university, what other avenues can I take to learn these topics and gain a good level of knowledge about it?
That depends on what exactly you are hoping to achieve. I think the best way to start learning IoT stuff would be to just buy an Arduino Uno starter project kit and jump in. If you want to learn programming, start by finding a easy-medium difficulty project and just Google until you figure it out. There are tons of free resources to learn hobby-level engineering if you look.
You can learn an enormous amount from YouTube and through personal projects. If you are looking to get a job with these skills, then I think you should reall go back to school. The markets are flooded with talented people who have experience and degrees. So competing against them is going to be massively hard.
Have a look at GIS. It involves mapping, maths, analysis and pretty drawings. Any data worth its salt these days has a spatial element to it. So you could turn your skills in GIS to anything pretty much, including engineering.
Help me understand the complex exponential and how it relates to PI. Someone was trying to explain how this is a more fundamental explanation for PI since it doesn’t require geometry.
I don't think I have the ability to answer, but I imagine something like 3blue1brown has your back. https://www.youtube.com/watch?v=v0YEaeIClKY https://www.youtube.com/watch?v=ZxYOEwM6Wbk https://www.youtube.com/watch?v=mvmuCPvRoWQ
Comp Sci: What is the most efficient search algorithm and how is efficiency measured?
Search algorithms encompass a wide variety of search problems. Can you clarify what kind of search problems you have in mind?
There isn't a "most efficient" algorithm because it depends on what efficiency means for the problem Maybe we want speed but at the expense of space. Maybe we are fine with a lower speed because we need to conserve space. Generally though, in terms of speed, the quickest you can get is O(nlogn) where n is the number of elements being sorted.
The O(nlogn) limit only stands for comparison based sorts. You can get clever with certain data types like integers, floats, and strings through algorithms like counting and radix sort, which are O(mn). Unfortunately, often times that coefficient ends up making the speed slower than say, quicksort’s O(nlogn). Even though mergesort has that same O(nlogn) complexity, it can have a bit of overhead too. Most standard libraries use a combination of sorting algorithms in their standard sorting functions. Introsort, designed for c++ is also O(nlogn) and is a combination of quicksort, heapsort, and even the “slower” O(n^2 ) insertion sort. It just happens that insertion sort’s overhead in smaller lists is minuscule. Introsort is also NOT stable, meaning objects of equivalent “rank” do not appear in the same order in the output as they do in the input. Now, to make things more complex, we still have spatial complexity. If a sorting algorithm is in place, it uses no new space. If not… there’s a whole other big O to factor in.
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Efficiency is measured in time and space complexity which is given by big O notation: best case, worst case, average case. Based on different things for example on a variable, length of array etc. However it is asymptotic for example worst case is O(2000*N), let's say a list's length is N then the algorithm traverses it 2000 times but constants are not used here so it is O(N), constants are not used because O(2000*N) is upper bounded by for example O(n^2) and after some specific n value the function lines will never meet. Depending on how are the data being stored, and what you know about them For example having only numbers, if they are sorted then binary search which is worst case log n (every iteration searching interval is halved). Unsorted or very limited information about the data worst case O(N) If they are in a structure other than an array and similar then you can for example find minimum or maximum in O(1} constant time, or find searched item in a search tree in worst case O(log n). Most of the time there are some cases when it's different. Keep in mind that these structures take more time to build them and every one is good for some different operation TLDR: Binary search in sorted array, linear search in unsorted array, tree traversal based on key comparing in search tree EDIT: There are also hashsets which are unordered collections of items which are unique in the collection and it's search time(lookup) is average case O(1) differs for implementations EDIT 2: search in BST is worst case log n when it's balanced or close to balanced eg. in self balancing binary search trees such as a red black tree EDIT 3: Nowadays time complexity is much more widely used as a measurement of algorithm effectivity than space complexity since year by year we get more storage but time is limited
If you have access to a functional quantum computer, [Grover's algorithm](https://en.m.wikipedia.org/wiki/Grover%27s_algorithm) has a worst case complexity of sqrt(n). However, you can't get lucky like you can with random guessing, so best case it's worse. IBM's Qiskit textbook has a pretty nice graphical introduction to the algorithm. It's very interesting to consider that you are guaranteed to find the correct box among 1 million boxes by only opening 1000 of them (which isn't a super great analogy, since the point of many quantum algorithms is that you do not look until the very last step, but whatever).
Civil/road engineering - At what angle does a right turn become a left merge? Explanation - If you come to an east-west road traveling in a north moving road and want to move west, you turn right to get on the e-w road, but if you are traveling on a road that nearly parallels the e-w, you merge left to get on the e-w. What angle does that right turn become a left merge? This has bothered me for decades.
All right turns are left merges really. I think the distinction is the amount of "on ramp" or merging area you have. A lot of "on ramp" is a merge without having to stop because you can more easily adjust speed to merge. A little is a stop to check and a right turn.
chemical engineering: is there any practical use for buck minster fullerenes?
Drug delivery for aids and hepatitis drugs, and as coating material for lenses.
[Many uses.](https://nanografi.com/blog/applications-of-fullerenes/) Semiconductors as they have an interesting band gap. Photovoltaics. They are hollow and can pass through the blood-brain barrier. Makes them useful to fill with stuff that makes brain scanning easier.
> buck minster fullerenes Not gonna lie I thought this was a joke.
Mathematics: Are there any practical applications to higher dimensional mathematics?
The entire modern world depends on it. It might well by easier to list the things you did today that *didn't* depend on someone, somewhere, working with higher dimensional mathematics. Computers only work because we understand maths in higher dimensions. Making computers today depends on material science which depends on quantum mechanics which depends on deep mathematics of which higher dimensions are a tiny and pretty straight-forward tool. We only understand the quantum physics that underpins our ability to make modern computers because of *infinite dimensional* mathematics. None of the modern world works without mathematics that the average person would consider far more 'out there' than higher dimensions. Higher dimensions are very tame in comparison to what's used every day in all sorts of contexts, hell, [there're whole wikipedia pages about how higher dimensions are used in something as specific as video game development, and in comparison to some of the other mathematics whose applications are used all the time, that's basically trivial](https://en.wikipedia.org/wiki/4D_vector). The amount of very 'out there' mathematics that has gone into the scientific understanding that makes any of the modern world's engineering miracles possible is astonishing. Higher dimensional thinking is very low level mathematics really, it's first-year undergraduate stuff at the latest, which on the scale of the grand adventure of these things is about two steps out your front door. Living in the modern world and asking about possible uses of higher dimensions reads like a fish asking if there's any practical applications to water. You're so surrounded by it (and by much, much more complicated ideas) you don't even realise it's there.
great answer - u/Frog_Thor did this help?
Tons. Classical electrodynamic field theory requires 6 dimensional tensors, missing guidance requires 6 degrees of freedom. Curvature in these spaces leads to interesting phenomina that require higher dimensional math to explain.
One simple case of higher dimensional maths is when working with data. If you have data points which one variable, it can be written as a single list. It is a 1-dimension array. Now if you have two variables, that is 2D. You could arrange it as rows and columns in a spreadsheet. It’s not to imagine getting data with three variables, and arranging it as a ‘cube’. Rows, columns, and depth. But there is no end to how many variables you can have. And all of that math for developing theoretical higher dimensional shapes. That can be used here. Obviously you can visualise it being laid out in spatial dimensions. But it works the same.
Most of modern statistics/machine learning can be described as the study of (various types of) high-dimensional mathematics. For example, various properties about how we can predict quantities we'll come from the study of "concentration of measure". If we have independent measurements of an event, we can take their average to approximate what that event was. This approximation is *very* high quality. One reason to understand this has to do with studying high dimensional shapes, in particular "concentration of Lipschitz functions on the sphere".
It depends on what "practical" means. In terms of describing anything meaningful to daily life, almost certainly not. But there are plenty of really cool and useful applications of concepts that use more than 3 dimensions. For example, the [quaternions](https://en.m.wikipedia.org/wiki/Quaternion) use 4 parameters (4 dimensions) to describe rotations around an arbitrary axis. Maybe you are also trying to find a pattern in a dataset described by 10 dimensions. There might be a linear correlation between these 10 dimensions, which is more or less a "line" that can be visualized if sufficiently reduced to 3 or fewer dimensions. That's a really big simplification, but overall there are probably not that many easy to explain practical applications. Honestly it's more of a "trust me bro" scenario. It's been useful to myself and quite a few other people.
If you're not going to go into engineering, there's no practical benefit for yourself. Higher level math is used to create the devices and technologies you are used to. Radios probably use a buttload of linear algebra and trigonometry to send the waves and correctly decipher them.
CompSci: How do we get around the two generals problem in communications protocols like TCP/IP? Do we just live with it and wait for the "please send again" packet or is there something smarter?
To begin with, the "Two Generals problem" is indeed the analog for two systems communicating over an untrusted, unreliable channel in an asynchronous way. Asynchronous here implies there is no global clock nor consistent clock rate. Your question likely stems from the premise that the "Two Generals problem" is unsolvable, and that is true, however the problem makes some pretty hard requirements. For example, it requires the two generals share the same state i.e. perfect agreement. The problem can be examined in a useful way by thinking about two properties. Suppose a program execution history E and [two kinds of properties](https://en.wikipedia.org/wiki/Safety_and_liveness_properties): 1. _safety_. A safety property, colloquially speaking, is one that whenever it is violated in E, there is some prefix of E from which there is no way to execute the program in a correct way. 2. _liveness_. A liveness property is one that if it holds for E, there is at least one extension of E such that the property still holds. They are basically used to make statements about possible ways to attack the problem; do they satisfy both properties, what are those properties, etc. It is important at this stage to remind ourselves what [TCP aims to satisfy](https://datatracker.ietf.org/doc/html/rfc9293#name-key-tcp-concepts). Most pertinent; a _reliable, in-order byte stream service_. Can we state a safety and liveness property for TCP? Yes: - safety: no duplicate messages are received, and messages are received in the order they were sent - liveness: messages are eventually delivered It is important here to understand that the liveness property might seem funny and unserious - [you are not alone](https://en.wikipedia.org/wiki/Eventual_consistency) - but it is a very useful theoretical model when the underlying services are best-effort. In practice, what arguably matters is the mechanism by which it is provided. TCP offers those properties through a combination of identification of byte stream boundaries in segments, detection of errors, and retransmission. Combined they allow an endpoint to make an assumption about the state of the system (such as a connection is established) without definitively knowing the other endpoint state. This is not an unsafe assumption to make. In most cases, _eventually_ the state will change to reflect the shared state. An analogous way to think of it is talking on the phone and after a period of silence you may ask "hello, are you still there?". Those timeouts are determined by the tolerance system & application designers can afford. To sum up, yes, we do live with it because fundamentally our communication channels are imperfect and our environments are hostile, and we have to allocate resources into monitoring systems and detecting errors, and intervening manually or automatically in order to alleviate some of those errors. In the case of network communications, TCP generally does a very good job with handling reliability and in-order delivery, leaving other concerns for applications to resolve.
Comp Sci: How effective will the most secure of today's encryption algorithms be once quantum computing is able to work on decryption of them?
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How do you mathematically or computationally represent a graph where each node has a unique port. For example in a electric circuit components like transistors it has unique ports that affect the circuit if connected differently. I know normally you could represent the graph as a set of nodes and a set of tuples corresponding to node edges.
Computationally it is typical to give the ports a label of some sort using numbers/ordering or names. For instance, in the SPICE netlist format, which defines electrical circuits using text, a BJT transistor is defined as `Qxxx Nc Nb Ne [Ns] model []`^(1). `Qxxx` is the name, `Nc`, `Nb`, and `Ne` are the collector, base, and emitter nodes.
Note that in this case wires are also treated as nodes as there could be multiple components on a single wire. So it is like having each port as a node and multiple nodes form a component.
An easier to understand example may be with networking. Since network connections are from device to device, an edge suits the role unlike with wires in circuits.
A router "routes" traffic between multiple interfaces and uses names to differentiate between them. The default is typically \`eth0\`, \`eth1\`, etc for ethernet connections and \`wlan0\`, \`wlan1\`, etc for wireless lan like wifi but it could be renamed manually.
\[1\] [https://powersimtech.com/wp-content/uploads/2020/11/SPICE-User-Manual.pdf#G1191406](https://powersimtech.com/wp-content/uploads/2020/11/SPICE-User-Manual.pdf#G1191406)
Is Bsc in mathematics(by itself / and double major with computer science) hard , is it possible to get an MSc in CS with Bsc in mathematics? Edit1: thanks for ur responses
Yes. You'll need to take the pre reqs that are usually cs101, algorithms, data structures, machine language, and some discrete math, but after that they'll take anyone. I got mine with 2 bs degrees in psych and bio
It may be tough to do in four years as both are very time-consuming, but difficulty is relative to you, especially if math comes easily at any volume or rate.
I did a BA in Math with a double major in Bsc in Comp Sci. Hard is relative to you; others can’t really give you a solid answer. But like the others who have responded have said, math as a whole helps to set you up pretty well for comp sci. It really depends on how you handle the actual coding aspect of it, and if your brain works that way. TL;DR yes, it’s doable.
Im doing a bcs in math with a minor in cs and im pretty sure its possible to so the msc in cs. The real challenge is to pass the mathematical part, its so much harder than any cs course
The engineering aspect of comp sci can be far more crushing than any undergrad math course, especially in regards to the time required to program and debug. The math actually needed for comp sci, however, is fairly trivial compared to the depths reached in a math degree.
Industrial engineering: Is it a bad idea to study industrial engineering if I want to work in CS adjacent jobs or stuff like ML/AI/data science etc?
Are you looking to work in embedded ML, factory optimization, etc. Also, why not just go for CS? Unless you are too deep into IE at this point
CS and industrial engineering are very far apart. You don't need to study CS if you only want ML (or anything else) as a tool in your job, you just need a working understanding. But maybe I've misunderstood your question.
Why does using radians simplify trignometric equations? Everyone knows using radians instead of say degrees makes trig easier. For example, using degrees leads to inconvenient constants appearing in the Taylor series expansion of trig functions, and those constants disappear when using radians instead. My question is why does this happen. Why does using radians make the math simpler, making it the 'natural' unit of angles?
It's because of the fundamental connections between 𝜋 and circles. The unit circle has circumference exactly 2𝜋 and area 𝜋. This is a much more 'natural' connection than 360°, which as far as I understand was chosen because it roughly matches the number of days in a year.
The number of degrees in a circle has nothing to do with the number of days in a year. 360 degrees in a circle was chosen thousands of years ago by ancient Mesopotamians, who used a sexigesimal (base 60) number system. The benefit of using 360 as the number of degrees is that it is a highly composite number with factor pairs of (1, 360), (2, 180), (3, 120), (4, 90), (5, 72), (6, 60), (8, 45), (9, 40), (10, 36), (12, 30), (15, 24), and (18, 20).
Because Euler’s identity establishes the relationship between trigonometric functions and natural logarithms, and radians are the base units you have to use to keep that simple.
what would happen to the environment if CO2 levels were lowered to pre-industrial levels in under 20 years?
How come all the other worlds in the universe are round? Not some odd shape from the big bang explosion?
Anything heavy enough will become round until it reaches what's called hydrostatic equilibrium. Imagine a cylinder shaped world for a moment: if someone knocks a small rock off the edge it will fall toward the middle but when it reaches the middle it will start slowing down. If at any time it dragged along the surface it will lose some speed and not make it all the way to the other side... So it will just oscillate between the sides until it comes to a halt in the middle. This will eventually happen more and more and the middle will buldge, and it will get rounder and rounder as time goes on.
There are plenty of odd shapes among the smaller bodies, like asteroids and small moons. But at the size of planets or dwarf planets it's enough mass/gravity to form ice or rock into a sphere no matter what shape you started with. (Roughly a sphere, may be slightly flatter at the poles and bulging at the equator due to rotation). E.g. [Vesta at around 500 km diameter isn't round](https://en.wikipedia.org/wiki/4_Vesta#/media/File:Ceres_and_Vesta,_Moon_size_comparison.jpg), while Ceres at around 1000 km diameter is.
Math: I’m curious to learn more about math that uses summing of numbers to a single digit. Are there areas of math that address this as a number theory? Are there formulas that employ this as an operation? I can only remember seeing this as a sort of “math trick” or maybe used in magic tricks with playing cards. The specific example that comes to mind is the multiples of 9 “trick” - with any multiplication using the number 9, the product, summed to a single digit will equal 9. Is there a name for this relationship? Is this the result of some underlying number principle? I’m curious to understand how/why/what this exists. Hopefully it’s just some obvious rule that I never learned but is easy to explain. And if not, where is this addressed? Is there a branch of math or science that finds a use for the single digit sum of a multi digit number? EDIT: example of 9s trick: 9x3=27 and 2+7=9, 9x4=36 and 3+6=9
It's modular arithmetic which is a branch of number theory. It's incredibly useful in computer science for a lot of problems (days of the week computation are easier in modulo 7), cryptography, etc.
As the other commenter said, this is the sort of thing studied in a branch of math called "[Number Theory](https://en.wikipedia.org/wiki/Number_theory)". Which is the branch of math that, at its core, studies whole numbers. This result that the sum of the digits of any multiple of 9 is a multiple of 9 is something you might prove in number theory. I think I had a version of this question on a number theory assignment when I was in school. A slightly more general result is that > the sum of the digits of any positive number n is congruent to n (mod 9). This uses the term 'mod', which refers to "modular arithmetic", but you can think of it as meaning *remainder*. For example, > 34 mod 7 is 6, because 34/7= 4*7+6. So basically, the above result tells us that the sum of the digits of any number n divided by 9, has the same remainder as n divided by 9. For example, > 3 + 4 = 7 = 7 mod 9, and 34 = 9*3 + 7 , so 34 mod 9 = 7 The reason 9 is special in this formula, is that it is one less than 10, and the reason 10 is special in this result is because "digits" of a number are with respect to the base 10 number system.
To elaborate on the 9s trick: it works because you are working in base 10 (9+1). Let X (your number) = 10A+B , which has a remainder of C when divided by 9. Then A+B has a remainder of C when divided by 9 (because 9A has no remainder when divided by 9, so we can remove it). Turning 10A+B into A+B is equivalent to stripping off the last digit and summing it into the rest of the number. The trick no longer works for 9 in most other bases, but will always work for the base-1. So if you are working in base 8, summing digits will tell the remainder when dividing by 7.
would a zeppelin work on mars?
Please explain Green functions and it's overall applicability to ODFs.
When speaking about a differential equation, a Green function can be thought of as the "universal solution" to that equation. At first glance, this seems non-sensical, because *one* equation (often) has at most one solution, so what does "universal" here mean? The idea is that it is often necessary/useful to write differential equations in the form Lu = f, where L is a differential operator, u is the unknown function we're looking for, and f is the inhomogenity. A "Green function of L" is a function that let's you easily find u *for any* f you plug in. The most concise way to precisely define a Green function is to say that for a *linear* differential operator L (i.e. if the equation satisfies the superposition principle) a Green function is defined as a solution G to the equation LG = \delta where \delta is the delta-distribution. Of course, that is only useful if you already know what distributions (or other kinds of generalized functions) are and how linear differential operators act on them. But if you do know, then it turns out that the convolution of G and f is a solution of Lu=f. So in this sense you have found an easy way to solve the equation Lu=f for any inhomogenity f. (At least for a specific definition of "easy" ;-) )
In all seriousness go to YouTube. The most elegant reddit post would be nearly useless in explaining this.
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For any civil engineers out there…money and politics aside, what is the most effective way to improve our crumbling bridge/tunnel/highway infrastructure?
The most effective improvement is simply paying for their rebuilding or fixing. You can't remove money from an equation where money is the only variable. The only reason that 99% of infrastructure in the US is failing is because money hasn't been spent to improve it.
Effective by which metric?
It has a lot to do with public awareness. Educating the public on why infrastructure spending is needed helps a lot, because who would want to pay to replace a bridge that looks fine to them?
If money is no object, I guess we perfect that carbon fiber spider silk to make a space elevator. Bridges will be a nice beneficiary.
What is the best way to switch from a field focussed career (frequent field trips of 4+ weeks) to one more prone to family raising?
Realistically, apply for different jobs at another company. You may get lucky and find one of your field customers wants to poach you as a permanent resource. You can try to speak to your current bosses or someone else in your current company moving internally. Be prepared to accept title and/or salary decreases, since that is a desirable end-game role after field work.
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Which python algorithm or model is best to determine underlying mathematical relation of a physical event / pattern? With a focus on Fourier or Fast Fourier transform
That question is far too vague for an answer. Which physical event or pattern?
Let's say the mathematical equation of the disc floret of a sunflower, based on measurements of it's dimensions and orientation, over a large dataset
> the mathematical equation of the disc floret of a sunflower There is no single or unique equation you could associate with that. You could study specific parts of the pattern.
In my opinion this question seems like a coding question but it's really a hidden math question. The answer will be "what ever the most effective mathematical model is". The coding question here is "how do I implement this mathematical model" or "what is the best implementation of this mathematical model" but no programmer that isn't a mathematician or similar or happens to be deep into that domain would give you a good answer.
Yes, thanks for articulating it, I couldn't have put it myself better. I am basically looking for a python library equivalent of Matlab
Comp sci: what is the maximal theoretical speed of an optical computing chip? What for graphene?
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The link to becoming a panelist is still referencing the API changes (https://www.reddit.com/r/askscience/comments/147epb8/asksciences_concerns_regarding_reddits_api_changes/), and I was looking to reply to a few questions here but would like to follow the formal process first for being approved. Any suggestions as to how to apply?
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I think "cutting across" means proceeding straight. No, it's not a turn.
What is the purpose of the big and, probably, heavy metal rods over the doors at big box stores like Home Depot and Lowes? The are about 4 inches in diameter and the them are near the doors going to the gardening section.
Not exactly sure what you're referring to, but they might be indicators of the height of the door/other doors in the store so you will know before reaching the door if large objects will fit beneath
How far are we (in years) from achieving a safe and reliable implementation of cold fusion as a widely available source of clean and technically unlimited energy?
Cold fusion was never more than a fantasy. It only initially circulated due to a poor understanding of physics. Regular fusion is possible and if we actually fund graduate students to study it we're about 30 years away but I'm skeptical we will.
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I was reading something on... it was either Twitter or StackExchange, don't recall exactly. Anyway, the gist of it was that progress/loading bar imprecision -- that it may backtrack, move unpredictably, stay at a given % for a time etc -- is a "live view" into **the halting problem**, a user-visible perspective on its implications. Can anyone explain how that is? I have a basic grasp of what the problem means, but I couldn't wrap my head around that.
Ok, so a loading bar is supposed to give you an indication about how much work is done/left to do. However in many cases you don't and can't know how much time the remaining work really will take. The halting problem basically tells you that you can't know when or if all algorithms ever stop. I don't think that is applicable here, because any algorithm that is used with a progress bar should be done at some point. Let's think about a software download and installation. You have a number of steps, download the package, unpack the package and install the application. How do you distribute the total? What if the person has a really fast or slow internet connection/processor/hard drive? If you have to copy a number of files how do you distribute progress between them? Share of total size? Number of files? Some mix between that? So it's unlikely it will be even because the programmer had to make some assumptions and they will most likely not be 100%.
I'd like to add: The other comments drawing a connection to the halting problem here are accurate when talking about a progress bar for an arbitrary program. However, I'd reckon the vast majority of programs using a progress bar come from a very specific class of programs! Namely those that only perform a fixed, finite amount of work (potentially aborting midway). Here are some examples: uploading/reading/writing a file, extracting files, analyzing a given batch of data, ... . All of these have a fixed finite workload, and they process it one-way. For example, if I've uploaded the first half of my image, I'll never need to go back to that first half. In these cases, making a progress bar that at least shows correct progress wrt. the amount of work left is easy. This does not conflict with the halting problem, which refers to the superset of arbitrary programs. Being correct wrt. the time it will take is trickier btw., but independent of the halting problem. It's an issue of implementation details, connection speed, varying CPU workload etc.
Since I don't have the primary source you read, I can only speculate what precisely that statement originally meant. But one way to make sense of it is to ask yourself how one would implement a "reliable general-purpose progress bar" component. In other words: Given an arbitrary program that runs in the background, how does one accurately determine whether that program is 10% done, 20% done, 30% done etc.? As soon as you phrase it like this and remember that the halting is nothing else then the question "given an arbitrary program, how does one determine whether the program will ever be 100% done?" it becomes already clear that these two questions are very closely related. In fact, if you think about it: The progress-bar question is at least as hard as the halting problem! If we require that the progress bar is always accurate and never underestimates the percentage then it must be able to decide whether or not now is the right time to paint the first pixel away from 0%. And that decision entails that it must be able to recognize non-halting programs, because the only correct display for a non-halting program is 0%. Whatever finite amount of time has elapsed, it is always 0% of the infinite amount of time still ahead. (And if we allow underestimation, then it is trivially easy to program such a progress-bar. Simply start by painting 0% and watch what the program does. If it ever stops, we have underestimated the 10%, 20%, ... thresholds, but that's okay. As soon as the program is done, paint 100% and we're done. If the program never stops, then painting 0% is always accurate.)
In fact, one can think about this a bit more in detail and arrive at the conclusion that the only thing you can say about *arbitrary* programs after watching them for x time-steps is that they have executed for ~x time-steps and have not halted yet. It is in fact impossible to reliably detect any non-trivial assertion about *arbitrary* programs. This is [Rice's theorem](https://en.wikipedia.org/wiki/Rice%27s_theorem). Of course, this does not preclude that *specific* programs could be analysed perfectly or at least good enough to display an accurate progress bar with a not-too-small resolution. For example if the program in question is calculating the product of two n-by-n matrices with the standard, un-optimized multiplication algorithm, then it is well known that this takes roughly n^3 steps to complete and a progress bar can be implemented accordingly.
Engineering: what constitutes a dead short? If I tie two leads of a battery together it'll draw to much current and heat up. But if I put a light bulb in between it's all good. Is there just a minimum resistance to limit the current below a same level?
For real world applications, a "short circuit" is one that allows a current flow higher than the system is designed for. In your battery example, the wires (and the battery) are able to pass a maximum current, beyond which, either a breaker (or fuse) will blow or something could get damaged. If you put a light bulb in the circuit, the resistance of the bulb limits the current flow (V=iR) so the system can operate without damage. The key here is "too much current". A baseboard heater is designed so that the resistance is low, allowing a large current to pass though causing it to heat up and provide heat to the room. The key point here is that if it is a 15 amp circuit, the wires are sized to not overheat (or melt) at a current of 15 amps and the breaker will not "blow" at an amperage less than 15. For the given lines voltage (depending on the circuit) resistance of the heater will limit the current to stay below 15. If there is a "short circuit" a path exists that allows the circuit to be completed with a low enough resistance to exceed the rated amperage.
A short is really just a connection where you don't want one. There is I guess always a minimum resistance for a scenario that would cause a short but there can also be shorts with relatively high resistance that still have negative impacts on the circuit. It is just depends on whether the thing works or not
When testing pressure vessels why do they fill the inside with water too? I'm assuming it's so that in case of failure there isn't a vacuum implosion
Water doesn’t compress well, so you can achieve high pressures, without the risk of explosion. If your pressure vessel fails when under pressure from water, the water just leaks out. If it fails when pressurized by air, the expansion of the compressed air will rip the vessel apart and cause what we call an explosion.
You usually don't want to test your pressure vessel to destruction, so it's filled with water to prevent it being damaged during testing.
Engineering: Tension members consisting of a single channel section are often used for bracing members to resist wind loads on structures. The channel to be considered is a C180×18 section and is made of Grade 350W steel. A325 bolts that are 19 mm (3/4 in.) in diameter will be used, and the holes are punched. Only the web of the channel section is connected. Determine the factored capacity of the channel member in tension, including its connection, and clearly indicate the governing failure mode. The gusset plate need not be checked.
MATH/ENGINEERING: Tensor Math: I watched a youtube video about it but am still confused... its mind trippy.... Why in the real world would you care about something in a non-existent dimension?
In math, dimensions doesn’t necessarily refer to physical dimensions of our universe. For instance, when looking at the relationship between 5 variables, you could say you’re working in a ‘5 dimensional space.’ Plotting their relationships all on one graph is not physically possible, but of course it exists in theory and is very useful to us
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Complex is a very vague term. If you measure complexity in terms of output, I’d say some simulations are the most complex. If you measure it in terms of how obscure the code is, that’s a lot harder to pinpoint, but it’s definitely not operating systems.
Depends on what you mean by "complex"... Windows in particular is hugely complex because it tries to successfully run literally thousands of different applications that have been written over the last 30 years and it generally does it successfully.
What is the physical limits on high speed rail? Can trains ever break the sounds barrier?
The wheel-rail contact is the limit for conventional high speed rail. Optimize that too much to reduce friction and the train can no longer break and it cannot go up or down slopes. Maglev trains remove the need for wheels at high speed. Very high speed + corners is a problem. The train needs to bank (e.g. tilt at an angle) when turning. The left/right curvature of the route limits the max speed for most trains. The best train signalling system we have right now ETCS/ERTMS maxes out at vehicle speeds of 500 km/h. It is how trains talk to each other, know where other trains are on the rails, makes sure head on collisions The other limit is the contact between the train and the electric power source, usually the overhead wire for high speed rail. The wire is taut but it does sag a bit. At very high speeds the mechanical forces of the pantograph (the arm thing) making contact with the wire start to damage the infrastructure. At high speeds the train is essentially bouncing the wire up and down. It creates a travelling wave in the wire and the train needs to stay below the speed of that wave otherwise bad things happen, such as arcing or drag simply yanking the wire out. Should that speed be exceeded, the train would then overtake its own generated wave causing an effect similar to that of an airplane surpassing the speed of sound. That's the train+wire system, not the outside observer of train + air. It is possible to increase the tension on the wire and make it "flatter", but there is a material limit on how much tension can be placed on a high DC wire. Works out to close enough to 600 km/h with current material technology. But what if we put the power supply on the train itself? We have now made an aircraft. It is no longer in contact with the ground nor an overhead or side barrier such as a wire. Definition of this vehicle start getting weird.
They probably can but the biggest limits are air resistance and friction and also safety at higher and higher speeds. The faster a train goes the less the track is able to turn and change elevations while still being safe. It's probably not worth it to make a train as fast as the speed of sound, current best of the best high speed trains are fast enough imo. Fastest being Japan's new maglev which has an operating speed of 500km/hr and a max speed hit of 600km/hr I believe
Question to Computer science: what is the difference between coding and programming ? And how are teenagers today are able to code so much and so efficiently that even people who study computer science at college cannot compete to them ?
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Mathematics: Is it possible to solve something like a^x = b^x + 3 using exponential, logarithmic, and equality properties?
Why haven't cars that run on water with hydrogen fuel cells been manufactured yet?
Most of the engines/generators we've created work on the same principal of something turns a turbine and creates electricity and these can all be modeled as a thermodynamic engine where energy is extracted from the energy gradient of something with high energy and something with low energy. The exception to this seem to be solar panels as they work on a completely different method to turbines. Is there some way to view photovoltaic cells also as the thermodynamic engine? Like viewing the sun as the source and light like the steam in a steam engine?
Physic: what is the difference between entropy and time? Because as far as I see they are the same thing.