411–420 of 839 posts
How does large scale randomness result in such complicated and intelligent systems, while after decades of research and all the computing power we have today, we still struggle to model and reproduce the intelligence of an insect.
Fourier Transforms. I'd wish I had a intuitive understanding of how they work. Until then I'm stuck with just believing that the magic works out.
If you see any signal, it can be represented as a value at each time, x(0) = 1, x(1) = 2 .. x(100) = 5 etc. We can visualize them as you shouting 1 at time 0, 2 at time 1 and 5 at time 100. Alternatively we can also do the same with a larger number of persons.
Representation using dirac delta
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Lets say that you have 100 persons at your disposal. You ask first person to shout 1 at time 0, second person to shout 2 at time 1 and person to shout 5 at time 100. Other times they will be silent. So with these 100 people you can represent the signal X. We call each of these person as bases. Mathematically they are delta functions of time, ie they get activated only at their specified time. Other times they are silent, ie 0. The advantage of this representation is that you have fine control on the signal. If you want to modify value at time=5, you can just inform the 5th guy.
Introduction to bases
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Dirac delta is not the only bases. You can ask multiple guys to shout at multiple times. They can even tell negative numbers. All you have to ensure is that they add up to the value of X. The guys should be able tell any number that can come as a part of X. This we name the property "SPAN".
Instead of 100 guys, we can have 200 guys too, ie 2 guys for each time and they tell half of the original value. However, this is wasteful since you have to pay for extra guys with no use. Hence we say that the bases should be orthogonal, ie they should not have correlation with others in the group. So as we have uncorrelated and spanning guys, we can represent any signal using them.
Fourier transform
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In case of Fourier transform, each guy will shout according to a sinusoidal wave. Lets say sine wave. ie guy 1 at time 0 will tell the value of sine(f0 t). Second guy will shout value of sine(f1t) and so on. The f0, f1 etc are the frequencies for each guy. Now it comes out that these guys will be orthogonal to each other, and they can span all the signals. Thus we have Fourier transform. Hence instead of representing signal as value at each step, we can represent it as value at each frequency.
Why Fourier transform
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We have seen that as long as bases span and and are orthogonal, they can define a transformation. But why is Fourier transform so famous. This comes from the systems we use. The most common systems we use are LTI(Linear time invariant) systems. A property of the said system is that they work on sinusoidal waves. Ie if a sinusoidal wave of frequency f is passed through an LTI system, all it can do is to multiply with a scalar. Any other wave will have a more complex effect. Hence if we can represent signals as a sum of sinusoids, we can represent our system as just a amplifier at each frequency. This makes whole of system analysis into a set of linear equations which we are good at solving. So we love Fourier transform
Earlier quoted context omitted.
Yes. It's interesting how powerful and clarifying this model of its-all-just-atoms-bumping-into-atoms is. It's interesting how many people take science courses, but don't really get this. In the context of Covid19, I see so many people wearing PPE, but failing to act as though they understand that the actual goal is to prevent this tiny virion dust from entering your orifices. Like wearing gloves and a mask, but then…
Masks are for keeping your own particles from spreading far, not the other way around.
Masks are for keeping your own particles from spreading far AND for lowering the probability of virions found in the environment from entering your respiratory system.
Masks lower the probability when all other variables are held constant. If someone thinks wearing a mask grants invincibility and in turn chooses to increase their exposure to high viral load individuals or environments, they're putting themselves at risk.
Double slit experiment. There's a lot out there detailing what happens but relatively few explanations go into why observing the state of a photon results in it "choosing" one slit over the other. I suspect many come away with the impression that it's magic despite there being a reasonably simple explanation for what's going on.
Fourier Transforms. I'd wish I had a intuitive understanding of how they work. Until then I'm stuck with just believing that the magic works out.
Ok, my time If you see any signal, it can be represented as a value at each time, x(0) = 1, x(1) = 2 .. x(100) = 5 etc. We can visualize them as you shouting 1 at time 0, 2 at time 1 and 5 at time 100. Alternatively we can also do the same with a larger number of persons. Representation using dirac delta -------------------------------------- Lets say that you have 100 persons at your disposal. You ask first person t…
Quantum Computers. Not like I'm five, but like I'm a software engineer who has a pretty decent understanding of how a classical turing machine works. I can't tell you how many times I've heard someone say "qubits are like bits except they don't have to be just 1 or 0" without providing any coherent explanation of how that's useful. I've also heard that they can try every possible solution to a problem. What I don't u…
But it could have some bleeding edge new applications from the TCP/IP space for urgent point, new methods for cryptography, or speeding up algorithms for searching. ¯\_(ツ)_/¯
Evolution. How does large scale randomness result in such complicated and intelligent systems, while after decades of research and all the computing power we have today, we still struggle to model and reproduce the intelligence of an insect.
Earlier quoted context omitted.
I had an aha moment with quantum computers a few months ago when reading an article that explained it as probability distributions. I don't think I have the complete understanding in my mind anymore and I wish I had saved the article, but looking into how quantum computers essentially serve as probability distribution crunching machines might help with your understanding.
So can they still do traditional deterministic(?) calculations? Or would that be somewhat akin to using machine learning to do your taxes; possible but just overkill? I've often heard it said that Quantum Computers can crack cryptographic keys by trying all the possible inputs for a hashing algorithm or something handwavey like that. Are they just spitting out "probable" solutions then? Do you still have to try a han…
I am not a quantum person but i once saw a geometric explanation for grover's algorithm which kind of made it all make sense to me. (grover's algorithm is the quantum algo you use for problems where you dont know any approach better than brute force. It can bruteforce stuff in O(sqrt(n)) guesses instead of O(n) like a normal computer). Basically, the geometric version was that you start with all possibilities being of equal probability (i.e. an even superposition of all possible states), negate the amplitude of the correct answer, then reflect the amplitudes around a line that is the mean of the amplitudes (do that sqrt(n)) times. The end result is the correct answer has a higher probability than the other answers. I unfortunately can't find the thing where i originally saw this, but they visualized it basically as a bar graph (of the amplitudes of possible states) and it seemed much clearer to me than other explanations i have come across
I consider that there are 4 levels of scientific writing. 1) news articles/lay press - basically terrible and typically get things wrong 2) scientific lay press (scientific american, discover, science news) - get things right, but generally no data/citations or nuance 3) journal summaries - get things right, citations and data for everything. Good summary of the latest scientific thought on a topic. Tend to push a po…
What exactly do you mean by journal summaries? For something between 2 and 4, the best I can come up with would be textbooks or seminars, both being extremely spotty in terms of quality and understandability. In any case, a big problem you get is a cliff of information content going from 4 down to whatever the next step is. The incentive structure substantially motivates putting out new material, which must have some…
For the other poster one nice source is of course The Annual Review journals. Arxiv of course too. The bibliographies in undergraduate/beginning graduate textbooks or syllabi are good sources too.
Why does my bread last for a while and then go bad? Or is it constantly going bad and I just haven't hit critical mass of mold for me to notice?