Every picture is made of waves - Sixty Symbols
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- čas přidán 7. 06. 2024
- Randomness, Fourier analysis and pictures of Jesus from the Daily Mail.
See lost of links below in full description.
This video features Professor Phil Moriarty from the University of Nottingham.
Stephen Jay Gould's mentioned book: bit.ly/brontobook
A good blog on this topic: bit.ly/1rLoddL
Fourier analysis and the uncertainty principle: • Heisenberg's Microscop...
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This project features scientists from The University of Nottingham
www.nottingham.ac.uk/physics/i...
Sixty Symbols videos by Brady Haran
A run-down of Brady's channels: bit.ly/bradychannels - Věda a technologie
i lost it when i saw that they had photoshopped jesus face on the cosmic background radiation.
You're not alone.
that wasn't photoshop my friend, preach.
You saw it too? Its a sign
Same here.
@@mayankkr.246 textbook case of wishful thinking
weird, out of those two pictures, I thought the one with the groups was the random one because it's less uniform, less orderly... but it also depends on the method of extraction as well...
in fact, it actually reminds me of another video where two groups had to write down coin tosses, one fictional, one real, and an expert can immediately tell who's who, based on those clusters
I also picked the right one :}
beirirangu Well, I think you have a better-than-average understanding of what random actually is (or how it should be usefully defined), which is evident by your knowledge of that coin exercise.
When seeing a series of numbers, even if they're are all the same, as long as there is no correlation between any of them it is still considered random. 44444444444444444444... is still a random sequence.
Digi Random is not the same concept as chaos. In a chaotic system, each component has definite correlations with other components, but the relationships are such that variance of certain values (position, speed, etc.) as the system progresses in time (or some arbitrary dimension) grows at a rate which makes any tiny perturbations in the initial conditions affect the variance of conditions at any time in a very significant way. That is a lot of jargon, but chaos was aptly summarized by Edward Lorenz when he said:
"Chaos: When the present determines the future, but the approximate present does not approximately determine the future."
The issue of chaos is closely related to some very rudimentary concepts in analysis, namely uniform continuity and uniform convergence.
Brady should release Sixty Symbols videos every day so that every day will have that high point.
Computerphile should do something about this, and how it relates to image compression.
Rua Whitepaw They just have
Makes sense.
I would've much rather seen graphs from a fourier analysis of the supposedly random and actual random diagram thingie, tho.
I can't unhear "Furry analysis"
A picture is worth a thousand... waves?
Imagine the sound of a thousand waves.
I'm always excited when I see this particular professor is in a video- he's so enthusiastic and fun to watch :)
I actually picked the clustered image as the random one. The other one seemed too close to a grid.
Been laughing to myself like a twat for ages at Jesus's face appearing in the CMB.
3:06
I'm more amazed they know enough about how Jesus looks to say it is his face.
kas00078
Yes! I’ve often thought the same when some freak out when anyone draws a supposed likeness of Mohammed.
:-|
lol, dat little jesus at 5:50
5:47 :D
looks like irrefutable proof to me.
Yeah =)
LMAO!! Great!
"I need to go now. I have to appear on a tortilla in Mexico..." - The Simpsons
bkiffter Indeed. Half Life 3 confirmed.
_And here comes the question:_ Where I can find the code please?
I see Jesus in the microwave background radiation (at 5:49). Now that's random! ...and hilarious!
Jesus in the CMBR. Niiiice touch, my boy.
This video blew my mind thank you so much for making this, I deeply appreciate it.
This is one of the most impressive ways to show the relation of Fourier analysis to Image processing. Would like to have seen my professors taking that good of an aproach. :) Kudos!
Professor Moriarty gave us a lecture today on the relationship between heavy metal music and quantum physics, and he is a very friendly person, with a good taste on music! makes me really want to learn about the fourier analysis
In my first calculus class in college, I was staring my professor's hypnotic shining bald head and his equally hypnotic monotonous voice lecturing the text on the textbook line by line. I had the feeling that the stuff he was teaching was not only boring but utterly useless and detached from the world I live in, so I decided to play video game instead, then I got F and learned nothing at all. 10 years later, after a few videos like this, I'm likely, damn, math is sexy! I'm so pumped for picking up the calculus and linear algebra I failed to learn in College . Brilliant work Professor Phil and Sixty Symbol!
All mathematical functions can be decomposed into a set of waves, not just images.
I figured the clustered image was more random because it seemed to be random in more than a single scale. The other image just looked like somebody had a regular grid of dots and just moved then a little at random.
Wow, 2009 is ancient history on CZcams ;-)
I caught myself writing "any" and knew it probably wasn't true... Noncontinuous functions are an obvious counter-example.. Then again, maybe an infinite number of sin waves could add up to a discontinuity? I wouldn't be surprised
Well, strictly speaking not "all" functions. For example, non-integrable functions have no Fourier transform. But it works for such a broad class of functions that as far as "real-world" problems are concerned, it might as well be all functions.
i saw whitespace patterns in the left image (kind of hexagon-like structures), hence i chose right one as random
Agree wholeheartedly
BiologyTube it's fair to say I was wrong. I was just too lazy to hedge or look up which functions don't qualify.
I do think every function that could describe something real is a sum of waves. I mean, just look at particle/wave duality :)
awesome video! fourier analysis somehow keeps popping up everywhere
Best explanation of 2D Fourier Transforms I've seen :-)
Could you please make a part 2 for , how to work backwards from the image to the waves . Thanks for all your videos .
the backward, or more precisely, inverse, process is going back from the spectral dimension to the image, which is what they are doing in this video. The forward transform was actually to decompose the original image into several frequencies. They did not say in the that the fourrier transform was done first, before being able to reconstruct an image like that
@@HasinaHr /where I can find the code please?
I don't really understand what I really watched, but this made me want to learn this phenomenon properly! Thanks!
Excellent video. Being purposefully pedantic about the dots on the paper, there is a 2D correlation, they are coplaner, which is significant because perspective drawing or photos remove the 3rd dimension. (Although it seems as if there's only 3 dimensions, actually it's ×3 dominant aspects of the Quantum Number Sequence and reciprocals in the 1-0D interval)
If you carry out the same process of wave creation, modulation and integration from the symbol of connection, a point, then the eventual context of connection has the universal properties known, assembled from waves of time duration, ie probability in possibility.
So the resolution of details depends on the degree of certainty in the data occurrence; the observer is on the aspect-balance singularity VP between certainty and nothing, an infinite boundary of the "world of light" resonance - space of electron orbital, in which the picture is a printout of the coherent certainty of here and now, in infinite perspective. Ie Superimposed waves painted in with mathematics in the Universal wave-package.
_____
Reality is the probability in possibility potential, image projection of the "eternity in connection sum-statement now, singularity-origin, ie the big picture, the wave-particle sum of all histories.
Really Nice work you are doing!
From the US and I grew up with the Mr. Happy books as well. I never realized that the author was english. Very cool.
Good explanation of fourier anlaysis - Very visual, helped to understand the context
Where were all these videos on Fourier Analysis when I was taking EE 224 (Signals and Systems I) last semester?
Love how something like this comes in to my area of maths, my final year project is Cluster Analysis using Statistical techniques I'll show this to my supervisor see what he thinks
8:00 Now I understand why SETI@Home was having us do Fourier Analysis on all those data modules. Also you can see how SDR works A/D conversion. Very cool.
I would've chosen the true random sample first but that's probably because I watched the video on random number patterns. Clusters are a part of the true random process, great video.
I got the dot question right! My resasoning was, that the dots on the left figure appear to have a tendency to want to sit a certain distance away from eachother, wheras the one on the right has some clusters and lines, while also having large gaps. When you look at it like that, the one on the left appears to have some kind of force present between the dots, wheras the other does not.
Hello Brady,
After watching this video about Fourier analisys I started thinking about the SETI project. They use A LOT of Fourier analisys to process radio signals from space and look for patterns. Can you do a video about how they are doing it?
Also, maybe you can link this to Computerphile and explain why GPUs (video cards) are much faster in doing Fourier analisys.
Great video, and it was nice seeing prof. Moriarty again.
Dammit Brady! There were lots of questions unanswered here! For instance: Would Fourrier Analysis detect non-randomness in the way coffee grains were spread in the sheet of paper? And more importantly: What is randomness really? It seems like the distinction between random and non-random events isn’t as easy as we would think. For instance, the coffee grains don't influence each other much (they aren't sticky, for instance), but it's very unlikely that some will end on top of another; and their position depend on how grouped together they were before letting them fall. Think about this also: How much paper surface you are willing to analyze can affect your results, right? Maybe the grains seem somewhat randomly spread if you take, say 100 square cm of paper but not 100 square meters. What about the randomness in quantum mechanics? You can’t predict which individual atom of, say, uranium is going to decay at a given moment, but uranium (as any other radioactive element) has a distinctive half life, that makes you predict very precisely what percentage of atoms will decay at any given (not so short) span of time. Is that random? Random like a roulette is random or random in another way?
you are extremely stupid
Coffee beans: I think that FT would detect the coffee bean pattern - even if you don't 'zoom out to much', it is important to note that it could be random and still undetected, if the signal is to weak to be significant. This becomes obvious if you think about him dropping only two beans, even if they are next to each other you would probably need more than 2 sine waves to represent them, thus your parameter space is larger than your sample space.
radio activity: is in radioactive decay is random like a roulette, it is random after 1 'trial', waiting a long time is kinda the same as having 60000 playing roulette, you can be pretty sure that about 10000 dies become of regression towards the mean. But you don't know which 10000 that dies like you don't know which 10000 atoms that disappeared only that you expect 10000 on average.
(ignoring that roulette is a discrete phenomena where radioactivity is continues)
I believe you are talking about 2 kinds of random. Deterministic random is when there are too many variables. Undeterministic random is like quantum mechanics, it is true randomness, not because we can't handle the amount of variables. Actually because everything is made up of subatomic particles, and those are truely random, i think also the macroscopic world is not deterministic random.
No, the coffee granules pattern was essentially random, just like the true random dots' picture (which I did identify correctly as the most random one), so it would not detect non-randomness because it's basically random.
Going to be doing a course in computer vision & imaging next year, after watching this video I'm definitely looking forward to it. Had never thought about images this way before, very very interesting :) thanks
Not just images but any function, any physical phenomenon can be decomposed into sinusoidal waves and its extremely beautiful
I would have like to have seen the Fourier analyses of the two "random" images, with the dots. It would be interesting to compare the two.
Is there any way we can get the program/website that was used for the number of 'layers' in those last few parts?
I love how biologists get a picture of a zebra.
hi, the video was very informative, one doubt - if i were to record my voice (for a known duration) and then reproduce that signal on a paper, how do i get the function of this signal - i understand that this function is fed to fourier to get the individual sine waves which make up the original wave - appreciate your reply, thanks.
It's just like sound waves really, except with light. A wave (like a saw wave) is made up of hundreds/thousands/infinite harmonics, and every time you add the next harmonic on, the saw wave becomes more defined. Just like increasing the number of waves in the video.
White noise however, which is defined as random oscillations, has no pattern of harmonics being louder than others, so it is a random sound, unlike a saw wave, which has easily distinguishable points.
Thinking in sound waves really helped me understand this, but then I am an audio kinda person. ^.^
Great video, as usual!
Wow. Best explanation I've heard :) Thank you!
Here's something that could be a nice "bonus video" to this one: Do the fourier transform on an image, then re-render it, using 1, 2, 3 etc. waves. Then queue the images in an animated sequence with increasing number of waves, so we see the image "form itself" out of a sea of waves.
Almost spitted my Sprite at 5:48!
Please make a image sequence animation of adding one at a time. I would love to see one of these pictures morph
This is really cool stuff! Does anyone know where I can get the Matlab file that Professor Moriarty is using to simulate images? I would love to see the code behind that!
Very nice and easy to follow. Would have liked a bit more detail towards the end though. (Will the amplitude/frequency diagram for any non-random image only have a _single_ peak, for instance. If so why is that?)
I am currently doing my masters degree in mathematical statistics and have never seen this. Absolutely amazing! Thank you for a mind blowing video
Great stuff, I really enjoyed that.
The face of Jesus Easter egg in the cmb image was fucking hilarious! - love it Brady!
I can't help but to repeat myself...
... Professor Moriarty is my favourite physicist from this channel...
I think they use a similar trick in video compression too (for example in the h.264 codec).
I got excited when I saw they were using MATLAB. :)
Like others said, it's too bad this video doesn't show the reverse, but seeing as how Brady forced an ending, I assume we'll be getting a second part soon. :) I've used Fourier Analysis before but this brought up some things I wasn't aware of.
great work!
Wait is this wave thingie a particular compression method for image. We did some image compressing in matrix course, noticed that low quality images did have kind of weavy pattern.
Brady, would it be possible to get/post the MatLab file(s) Professor Phil Moriarty is using in this video!?!
The picture on the left is obviously almost evenly distributed. How could you possibly think that THAT'S the random one?
Totally right. I stopped the video and tried to define randomness to me...
Throw coffee beans 1000 times and you will see clusters every tiem but not once it would distribute evenly!
To me the video is pretty much useless b/c it bases on the assumption that people choose the wrong picture as "random". Well, I do not quite see why they would - are they dumb, impulsive or what?
Random number sequences with recurring numbers look like they have a preference for that number. If there are no recurring numbers, but the order is wrong, it's not as easy for people to see. The even distribution in the left picture is off enough for there not to be a visible grid or easy-to-see recurring section, so it looks more 'random' than the clusters in the right picture, which people can easily draw lots of little curved lines into, even if the lines don't make sense in the end.
It would have been nice to see the amp/freq graph of some of the images Prof. Moriarty was constructing
Just saw my professor clean an image using a Fourier transform, pretty cool stuff
I Love this channel !
What software (for a guy with basic programming skill) can be used to compose/decompose image from/to waves
cepi24 Matlab, that's what he was using
Cool! I'd like to see a video on Randomness! It should be interesting!
I picked the right one.
+Jan96106 Me too
Hello,
Is this applicable to 3d object with 3d voxels instead of 2d pixels.
How does the fourier analysis vary with the rotation of the image in 2d and a 3d object ?
thank you
Is there a connection between Fourier transform and principal component analysis?
Is the code for deconstructing an image into sine waves / - reconstructing sine waves into an image - available?
Very cool. I've been playing around with speech recognition and fourier transforms lately. It's a very outstanding technique couldn't help thinking what a clever man this Fourier guy was. I'd love to see more about it/him if you please.
What programs did you use?
Any chance you could post your matlab code for creating images out of sine waves so that we could play with it?
Very much pratically explained Fourier transform ! thumbs up !
Thanks :)
When he was adding more waves to make the images more recognizable, e.g. for the picture of Brady he started at 9, then 36, 64, and finally 144. All perfect squares (3 squared, 6 squared, etc.). Is there any particular reason for this?
Is the Fourier series related to "random pokemon curve"s on Wolfram|Alpha?
HAH! that image of Jesus at 5:49
Very funny Brady. Keep it up, Sixty Symbols is always interesting
Thank you so much!
can you provide me the code of that picture at 9:21 ?
Nice video! Can I get the code from somewhere? (It looks like Matlab.)
if i have an image,how can i break it down and tell its Fourier components? how to go backward of what is done in the video?
I would love to get my hands on that code if possible and check this out a bit more thoroughly. Thoughts Brady? :)
5:49
Very smooth.
sixty symbols' videos are playing without sound for me!! it has been a while now i tried many things but no matter what or when the video is, it plays without sound!! any help?
What code is it? Is it Matlab or something? How/Where can I get a hold of it?
Did you forget to show us an FFT of the random vs non-random particle distributions? I thought that would have been on of your main points; to show a spherical FFT vs one with a few lines or spots in it that indicates patterning.
What software did y'all use to simulate those images from waves ?
Nice video, Elvis!
Damn, this is very enlightening.
I imagine this is part of the technique behind reverse image search engines (like TinEye). Breaking down images into waves and comparing the waves against each other.
These videos really make me want to take a physics course at the University of Nottingham.
In 4th semester i was studying fourier transform of a 2D wave, and i thought "Wow, this is amazing", i lost my mind.. And now in 8th semester i found fourier transform analysis for an image.. World and human thinking is absolutly beautiful
I'd have liked to have seen the Amplitude v Frequency chart for the Brady image too :(
Wouldn't mind having access to that code, try this out for myself. Nice video.
When I first learned about this in image processing class, I was flabbergasted. Nature is just amazing. Don’t want to get too philosophical but it seems to me that the school of thought that argues that everything is nature including complex phenomena like human actions, is just a sum total of very simple component parts, is the right one.
It's curious, when it came to the two pictures, my first thought was that the ordered one was just *too* neat and tidy, that true randomness is normally messier. For example, try flipping a coin 50 times and tally up the number of heads and tails you get. You probably won't get 25/25, chances are it will be something between 15/35 and 35/15. And you might see 4 or 5 heads in a row. It would be really weird if you got a perfect pattern of head-tails-head-tails-head-tails and so on.
The CMB map represents an image based on the removal of strong x-ray sources from the earth and other sources. Strong signals prevent week signals from being received. This can be tested with any radio where the same frequency is being transmitted. The closer signal will prevail . Attempting to filter to out which has been done with the CMB shows a filtered representation of the filtering.
does the radom distribution of the stars in the sky follow as the bell curve if it does what force of physic applies to the bell curve?
1:40 - Anyone else go for the one on the right? I thought the one on the right was random because the dots on the left sheet were way too evenly spaced plus the dots on the right sheet formed occasional clusters which is what you'd expect to see in a sheet of truly randomly placed dots.
Is there any way you could send out the MATLAB code? I would be very interested in seeing how you created the images. I would love more than anything to play with this experiment on my own!
On your website the shrodinger link does not work, you might wanna know that :) Keep up
Thanks for the video... Can I get the MATLAB code? Plz
So you break your image into waves can you turn those waveforms back into the same image ? Can two images have the same wave form?