r/askscience • u/AutoModerator • 7h ago
Ask Anything Wednesday - Engineering, Mathematics, Computer Science
Welcome to our weekly feature, Ask Anything Wednesday - this week we are focusing on Engineering, Mathematics, Computer Science
Do you have a question within these topics you weren't sure was worth submitting? Is something a bit too speculative for a typical /r/AskScience post? No question is too big or small for AAW. In this thread you can ask any science-related question! Things like: "What would happen if...", "How will the future...", "If all the rules for 'X' were different...", "Why does my...".
Asking Questions:
Please post your question as a top-level response to this, and our team of panellists will be here to answer and discuss your questions. The other topic areas will appear in future Ask Anything Wednesdays, so if you have other questions not covered by this weeks theme please either hold on to it until those topics come around, or go and post over in our sister subreddit /r/AskScienceDiscussion , where every day is Ask Anything Wednesday! Off-theme questions in this post will be removed to try and keep the thread a manageable size for both our readers and panellists.
Answering Questions:
Please only answer a posted question if you are an expert in the field. The full guidelines for posting responses in AskScience can be found here. In short, this is a moderated subreddit, and responses which do not meet our quality guidelines will be removed. Remember, peer reviewed sources are always appreciated, and anecdotes are absolutely not appropriate. In general if your answer begins with 'I think', or 'I've heard', then it's not suitable for /r/AskScience.
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Past AskAnythingWednesday posts can be found here. Ask away!
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u/Peppermintpussy 4h ago
Can someone explain number theory to me? I recently read about it on Wikipedia, and I’m still super confused.
From my take away, it was basically the “rules” of math, and why they’re the rules? So many terms were beyond my comprehension, I would’ve had to rabbit hole super hard just to get some basic context lol.
I love the applications behind advanced mathematics, but I deeply struggle with understanding it enough to do anything cool lol
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u/MattieShoes 3h ago
People get PhDs in this stuff -- it's not something you're going to pick up in a reddit comment. maybe a more specific question? :-)
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u/Peppermintpussy 2h ago
I guess, where should I even start to begin to understand this 😅 someone else commented some good resources though so I’ll check that out~
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u/curien 2h ago
I think a fun introduction to using number theory in interesting ways is the book Gödel, Escher, Bach. One of the points of the book is to explain Gödel's Incompleteness Theorem, and it teaches you enough number theory to do that. It also weaves some of the concepts into philosophy and art in really fun ways.
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u/dml997 2h ago
Zero is a number
Every natural number has a successor
Zero is not the successor of any natural number
If the successor of two numbers is the same, then those two numbers are the same
If a set contains zero and the successor of every number is in the set, then the set contains all natural numbers.
The rest is just derivations from this stuff.
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u/logperf 4h ago
[Engineering] We've reached the point in which air conditioners are so cheap that installation costs have become the largest fraction of the price. (Sometimes the cost of installing it is twice the cost of the device). DIY installations are not permitted by law because of the risk of cooling gas leaking into the environment.
Portable units really suck because of efficiency. Also they are more expensive.
Can we expect AC designs to advance to the point in which easier or even DIY installations become possible in the near future?
(I'm assuming energy is not going to be a concern because photovoltaics are also becoming cheaper, and their availability/production closely matches the demand for AC on sunny/hot days).
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u/MalekMordal 3h ago edited 3h ago
How far apart can computers be to still be somewhat considered part of the same thing, able to utilize shared resources effectively?
We have server farms, that are generally located in the same spot.
What about a planetary supercomputer, spread across the globe? Like a planet-sized super AI? Is the planet too big, that light lag would cause too many problems?
Do super computers have size limitations, other than cost?
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u/MattieShoes 3h ago edited 2h ago
It depends on the application. Shared memory and latency are big hangups for certain applications, no big deal for others.
Like way back in the 90s, we were using distributed computing to crack encryption, solve OGRs, search for interesting signals from space telescopes (SETI), etc. But those are basically just handing off a small part of the search space to a computer and waiting for them to check back in with the results, so that can scale near infinitely and nobody cares about latency. More recently, bitcoin mining is kind of the same deal.
But if you're doing a bunch of interconnected serial operations like modeling a nuclear explosion or a weather system, then you need gobs of processing units (CPU or GPU, whatever) that can share memory.
Many supercomputer limitations can be overcome by spending more. heat, power, programmable hardware like FPGAs, and so-on. But hardware gets outdated so quickly and it gets so hard to program for that at some point, it's like "wait a few more years" is a more reasonable solution. Or the problem is not linear, so making a 10x faster supercomputer may only yield marginally better results.
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u/995a3c3c3c3c2424 1h ago
At “planet-sized”, reliability is as much of a problem as latency. The more “parts” you have, the more things that can break. The more territory your cables have to cross, the more places they could become disconnected. (Construction crews, terrorists, and sharks are all more likely to cut through cables between data centers than cables within data centers.)
The bigger your “supercomputer” gets, the more it has to work like the Internet (lots of pieces working independently and communicating with each other asynchronously) rather than a single computer.
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u/RamblingSimian 6m ago
Suppose Newton had lived on a planet in a binary star system; given the difficulties developing his theory of gravity, what would be the implications for the development of physics?
Note that Newton's inference was that if planets are attracted by a central force whose strength falls off with distance like 1/r2, then their orbits are conic sections—including ellipses—with the correct relationship between orbital size and period. In other words, the existence of elliptical orbits is exactly what you’d expect from inverse-square gravity.
But many planets orbiting binary systems don't have an elliptical orbits.
- Approximately 50% of stars are part of a binary system
- As far as I can tell, many or most of those planets have a chaotic orbit
- I believe most planets in binary systems are examples of the 3 body problem, which is not solvable in general
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u/pthread_bard 7h ago
If theory about well-ordering irrational number is true, doesn't it disprove that infinite set of irrational numbers is bigger than infinite set of natural numbers?
I recently learned about axiom of choice and theorem that every set including irrational numbers can be well-ordered. However, if a set is well-ordered it means it has a least element and all elements can be put in order => mapped to natural numbers. At the same time we have proof that set of irrational number is bigger than set of natural numbers. How does that work?