karl-j
I have been thinking about trying a one-handed layout lately, the one you link is intriguing!
Stockholm - 0.8 unicorns per 100,000
Silicon Valley - 1.4 unicorns per 100,000
"[Modern heuristic and approximation algorithms] can find solutions for extremely large problems (millions of cities) within a reasonable time which are with a high probability just 2–3% away from the optimal solution." [0]
When close enough is enough, NP problems can often be solved in P time, and I suspect this is one of those cases. For crypto however, close enough is not enough.
[0] https://en.wikipedia.org/wiki/Travelling_salesman_problem#He...
And given that the list being sorted is a one in n! chance, often enormously less likely than than hardware malfunction, wouldn’t the algorithm mostly produce malfunctions rather than sorted lists?
(Genuinely curious if I’ve got the right understanding of the CS and potential physics.)
The minute inherent value of the answer is not why it was done. Finding the answer became personally valuable to people for a few reasons:
The unavailability made it seem more valuable. The idea of making something seemingly unknowable known is enticing. Making headway on a problem makes the solution personally valuable. The production, rhetoric, and appeals to nostalgia in Sal's first video about the project made it seem more valuable to many. Being part of a group who share an objective that matter to them is inherently valuable to humans.
I believe the project added value to the lives of everyone involved, and the experience gained and the connections made will add value to the rest of the world.
All of this could have been true for a project that actually matters, yes, but those projects tend to have high barriers to entry, consequences for failure, and distant horizons of success. I think this project replaced time and computing power that would have been spent on games and youtube, not on important problems.
I'm writing out the basics of the solution below, but the physical reason for the non-impossibility is that the problem statement assumes the lowest possible amount of noise to overcome, long symbol durations, and high gain antennas.
For learning resources to recommend I'm lacking a little, since I mainly relied on lectures etc, but if you're interested in terrestrial wireless communications you could check out Stanford's class by Andrea Goldsmith. [1] There's very little about antennas, satellites, long distance communications and all that, but a draft of her book is available and all the lectures, so it's very comprehensive even though it's only tangentially related. You can also check out the link budget Wikipedia page [2] for an overview of things affecting these kinds of transmissions, as well as many links to interesting related topics, like the voyager program and their unique struggles (300+dB path loss and still hanging in there!)
The path loss is L = (4 * pi * d/lambda)^2, where lambda is wavelength. At 1.5GHz carrier frequency this results in L = 1.41e38 = 382dB, which definitely is a monstrous number, and with no antenna gain and terrestrial noise powers this would be practically impossible to overcome.
But with an equivalent receiver noise temperature of 5K (meaning the noise we are receiving is only the faint radio noise from space [3]) and a bandwidth of 100Hz the signal is only competing with noise with power N_0 = kBT = 6.90e-21W = -202dBW giving us some hope of establishing communications.
The gain of the 300m diameter antenna is G = 4 * pi * Area/lambda^2 = 2.2e7 = 74dB, and we have one transmitting and one receiving so we can double that dB gain.
Given the Eb/N0 = 10dB requirement and the rate of R = 48bps we can figure out the necessary received power after the antenna gain. Energy per bit is N_0 * 10, so the received power has to be Pr = N_0 * 10 * R = 3.3e-18W = -175dBW.
The transmit power plus gains minus loss has to be greater than the receive power limit, so it should be Pt >= Pr - 2G + L = -175dBW -(2 * 74)dB + 382dB = 59dBW = 800kW
I'm getting a different answer here because the exam had some additional pointing/polarization loss, which I apparently flipped the sign on in my solution. So the correct answer for my problem should be in the low MW, but still not outlandish. I have not received the corrected exam yet, so there might be other errors too.
[1] https://web.stanford.edu/class/ee359/courseinfo.html
[2] https://en.wikipedia.org/wiki/Link_budget
[3] I'm a little unclear on how this would be achieved, since the earth antenna is, well, earth based and at some 290K. This is however what the problem assumed, so maybe they're counting on cooled space based antennas.
[1] https://www.amazon.com/4G-LTE-Advanced-Pro-Road-5G/dp/012804...
I had a problem like this on my wireless systems exam recently, where the setup was two Arecibo style antennas with a reasonable 20ly distance, a low 48bps, an Eb/N0 of at least 10dB, and a few other reasonable assumptions. The transmit power needed turned out to be less than 250kW.
5G aims to allow for completely new applications that were not possible before, and hoping that's where the money will come from. Ultra-reliable and low latency, and massive machine type communications are two new areas 5G is pushing into. The first will allow applications like self driving cars, remote control with immediate feedback, and combined with the increased speeds, augmented and virtual reality. The second area is for the smart city/home type of applications.
This is all from my digital communications professor with ties to Ericsson, but on a personal note I'd be hype to explore distant places in real time by wearing a vr headset and controlling a drone with a 360° camera and <10ms latency. You could be anywhere in the world and actually interact with the environment with just a 5G enabled headset and a 5G-drone renting app. Racing through an abandoned mall! Drone laser tag in a redwood forest!
> There is no single thing named "electricity." We must accept the fact that, while several different things do exist inside wires, people wrongly call all of them by a single name.
I wonder what the medium would have to be like to be useful for instant messaging, since not all things being said need to endure or benefit from linking. Maybe the ink fades unless new things are written nearby, proving its relevance?
[1] https://hapgood.us/2015/10/17/the-garden-and-the-stream-a-te...
Just to curb peoples expectations a bit, I started the process of getting diagnosed about two years ago, got the diagnosis less than a year ago, and I'm having the first meeting with a doctor who can actually prescribe meds next week. No part of it has been simple or quick. So I guess YMMV.