I should also point out that when I said: " Assuming your not trying to create collisions...", I was referring to the fact that md5 has been compromised. My point is that 128 bits is enough bits to ensure you will not get a random collision due to chance if you are using a good hashing algorithm.
I should also point out that the convention for UUIDs (universally unique identifiers) is also 128bits. Meaning that the chances of randomly getting the same 128 bit number is so low that experts have determined it's ok to just assume it never happens for purposes of computing.
OK so I wrote a quick little python script (I just remember python has bignumber support) to do it on a smaller numbers.
If we assume md5 was only 64 bits, even with 100 million files, your chances fo hitting an md5 collision are 0.03% (i.e. a 0.0003 chance).
When you bump up the md5 to 128 bits 100 million files has a 0.000000 (rounded to 6 decimal places) chance of happening.
maybe I will let my program run overnight and see how far it gets. It's programmed to count how many files it will take before the probability of a collision is 50%. Who knows, maybe it will take millions of years to finish. We'll see tomorrow morning.
md5 is a 128bit hash. Assuming your not trying to create collisions, the odds of you getting a collision in n files is:
p = 1 - (2^128)! / ((2^128 - n)! * (2^128)^n)
This is an expression that starts at 0 and gradually goes to 1 as n goes to infinity.
These numbers are so big, I have no idea how to even solve for n to get something like p = 0.0001%, without using a bignumber package, but I imagine n would have to be *REALLY* big in order to get a p significantly above 0
Instead of rewarding people for innovating, we incentivize people/companies to patent trivially simple ideas to lock their potential competitors out of new markets and actually stifle innovation.
Patents are supposed to drive people to come up with ideas that would be cost prohibitive if they were not given some kind of incentive like a temporary government enforced monopoly. Giving out these monopolies in exchange for for such obvious ideas (i,.e. they would be invented regardless) is a shitty deal for society.
Well I don't know what to say. I know the source of the problem with NFS and large files is in vxworks. I also have this problem in Linux, but I think it's for a different reason. Lots of people on the internet have similar problems, but the answers tend to be "I used a different OS (on client or server) and it started working, I don't know what exactly fixed it".
Maybe A newer version of the NFS client/server, or a better default setting fixes this issue, but I haven;t been able to figure out what it was.
At least in vxworks the problem was that the nfs server was reopening the file on each packet, and seeking to the beginning of the file to open it, and then seeking to the end of the file to continue the read/write. For small files this seek delay was usually small. On very large files, the nfs server would spend all it's time seeking and throughput would slow to a crawl. Sadly knowing this key piece of information doesn't help me. Maybe I'll just try again one day with a brand new linux OS and it will magically be working.
When you do an experiment, if your hypothesis is proven true then the null hypothesis is disproven. If you don't actually do an experiment, then you haven't done anything to prove the null hypothesis.
I don't know what you consider "special protection", but I am claiming that you need to actually do an experiment to conclude a null hypothesis in a scientifically rigorous way.
When we assume that lion roars don't cause earthquakes because it's a stupid hypothesis. We haven't actually proven the null hypothesis, we are just assuming on intuition and not on evidence.
If we actually did an experiment and can not show a link between lion roars and earthquakes, then you can conclude the null hypothesis by default. But you have to at least try before arriving at this conclusion.
But in science we don't protect a hypothesis, when it is contraindicated by the evidence, by inventing unknown unrecorded unexplained confounding factors.
You don't need to invent them. But you can and should assume that there are some, and take appropriate steps to mitigate the effect of possible confounding factors you may be unaware of.
If you study two things, and there is no measurable correlation between them, then it is only reasonable to conclude that there is no link between them. Although it is technically slimly possible that the two things are linked, but some confounding factor precisely counteracts the link such that the measured correlation is zero, that cannot be reasonably proposed without some evidence.
If you have already taken appropriate steps to eliminate confounding factors, and there is no measurable correlation then it is reasonable to conclude that there is no link. If you haven;t taken the appropriate steps to eliminate confounding factors, then it doesn't really matter what you measured because it's not really useful.
Speculation isn't good enough, which is what you did when you said this:
It could be that marijuana increase schizophrenia, and some other factor decreases schizophrenia fore than marijuana increases it.
I also said I wasn't suggesting this was true or even likely to be true. I was saying that it is important to take steps to eliminate confounding factors because things like this can and do happen. This is why we have statistical methods to mitigate confounding factors
Concluding that there is no link between schizophrenia and marijuana from the fact that schizophrenia went down during a time when marijuana usage went up, is not scientifically or statistically rigorous. You need more data to make such a conclusion. For example a double blind study with a simple random sampling, etc.
This is the crux of the issue. They don't have the same visual information. The 1080 resolution is a bigger space to fill (it has more pixels remember?) If you down scale that to 720 you can get away with reducing the bitrate because you are removing information by downscaling. If you keep it at 1080 you will want a higher bitrate than you would at 720.
This is the crux of the issue, and you seem to be thinking that the same amount of information goes into each pixel. This is true for lossless encoding (which is completely impractical for 1080p video), and not true for lossy video encoding (which included compression algorithms like h.264 and vp8).
The "citation" you provides a policy on minimum, maximum and recommended bitrates for various resolutions. This is not a statement of fact about all videos, but guidelines used by youtube.
But if we ignore that for a second, it actually is evidence towards what I am saying, Notice how the maximum 720 bitrate (4000 kbps) is higher than the minimum 1080p bitrate (3000 kbps).
Even the chart you provided clearly shows that you can have higher bitrate videos at lower resolution, and vice versa
I really don't know why you can't just admit you are wrong. If it's because I made fun of you and called you names, then fine, that was a bit childish of me, but it was in response to your arrogant attitude despite clearly being misinformed.
When someone says "I want 1080p" they do not mean they want to see what looks like a 640×360 video upresed to 1920x1080. They want to see a crisp "HD" picture.
This was illustrating a point, not saying that anybody should do this in practice.
It was an experiment you could do
A 720p video has 921600 pixels. A 1080p video has 2073600 pixels just over twice as many as a 720p video.
Take a 720p video source and encode it at the google recommended bitrate of 2500kpbs. Then take that same source, upscale it to 1080p and encode it at 2500kpbs.
According to you the video should look more than twice as bad because the same amount of data needs to be split among more than twice as many pixels. If you actually did it though, you'd find that it does not look significantly worse if you use a good lossy compression algorithm like h.264. If you used no compression at all, then there would be less than have the data in each pixel and it would look bad.
Another way to put it is that video typically has a lot of redundant information. In video compression lingo this is referred to as spatial redundancy and temporal redundancy. When you compress information you are removing redundant information. When you are performing lossy compression, you can remove information that is "almost redundant", and the quality of the video will be based on your threshold of what you consider "almost redundant".
Some video has lots of redundant information (e.g. south park episodes), and some video has less redundant information (like an action movie) The resolution of the video determines an upperbound for the amount of information a video can contain, but this does not mean that higher resolution videos have more information, just that they *can* and *usually* do have more information. But as I said this is a correlation. The higher resolution doesn't *cause* the video to have more non-redundant information. This is only true of uncompressed video.
I think producing the encryption key probably is incriminating in a lot of circumstances, because it proves you had the ability to access the data, and strong evidence of ownership.
If you already admitted to owning and encrypting the data, then I guess it doesn;t matter. But if your defense is that the usb key isn't yours and you don't know the password, then providing the password does kind of screw up your story.
Probably, but I don't think there is proof of that. How do you prove what someone is thinking. Clearly he knew the password, because he produced it eventually, but that doesn't prove that he didn't forget it then remember it, as he claimed.
It can only lower the bitrate while increasing the resolution by removing visual information! Are you daft? It's math not magic.
Have you ever encoded a video? No one is ever going to recommend you to use the same bitrate to encode a video to 1080P as they would to 720P.
Hundreds if not thousands
No one is ever going to recommend you to use the same bitrate to encode a video to 1080P as they would to 720P.
Have you actually ever tried this? If you did, you would find that under most circumstances, The quality will only be a little lower for the 1080p video. That's because, even though there is a lot of visual information removed from the 1080p video, the 720p video started with less visual information, and they end up around the same quality. There is some additional overhead in a 1080p video over a 720p video (e.g. more macroblocks), but this is what causes the 1080p video to be slightly worse quality)
And this is assuming that you are using a bitrate that is more suitable to 720p over 1080p (for this particular video). If you used a bitrate that was more suitable to 1080p, and you encoded the 720 version at this same bitrate will the 720p video always be higher quality because it is lower resolution? Obviously not, because if this were true every one would encode at super high bitrate at low resolution. There is diminishing returns when increasing bitrate, depending on the source video.
Sure people don't always use a higher bitrate but if they don't it is almost always not the right choice. If they are aiming for a lower filesize they should just go with a lower resolution because making a high resolution with the bitrate too low will cause it to look terrible!
This was my whole point to begin with. I said that your streaming capacity is related to the bitrate. This accounts for all videos rather than only the videos where the people encoding it made good choices (which is actually a minority of people). And no it doesn;t look terrible. It just looks a little worse than it could if it was done correctly, which is why people get away with it.
You are still wrong about it being correlated. More visual information requires more data there is no way around that. There are many factors that contribute to bitrate and resolution but when you account for the differences it is straight causation. I will repeat: math not magic.
So by your own logic, 2 videos with the same bitrate, a 720p and a 1080p, have the same visual information, so why would one look like crap?
Have you ever resized an image to be a higher resolution (up sampling), and then zoomed into the original to make them the same visual size? They look about the same quality, and they end up being about the same number of bits (if they are compressed). This is because the amount visual information is about the same.
I will reiterate that you don't know what correlation means. The term correlation describes exactly this kind of scenario, where it is not just a coincidence that higher resolution videos are higher bitrate, but it is not the direct cause.
You are right that it's math and not magic. The problem is that you don't know how that math works. You seem to think you do. But you don't.
I think it's also true that a larger percentage of people are going to university, so the average "intelligence" of people in university in terms of natural ability is probably lower now than when it was just the very best students attending.
Most of the mediocre students today would have simply not gone to university in the past. I think the same principle holds when it comes to things like blogs. The fact that public discourse can sometimes make it seem as if people are getting dumber, when it is really just that more and more people know how to read and write and can now even be published, whereas in the past, there was a higher cost to publishing, and you were more likely to have something important to say before being willing to incur that cost.
Not bashing modern life, it's great, but it isn't making many "great thinkers" in the mold of the 19th century mathematicians. We do more, with less understanding of how, or why.
The easier math problems are lower hanging fruit. As time goes on, the problems that are left become increasingly hard. Even when they get solved, average people can't understand what it means, and that makes it hard to care about, and hward for newspapers to make money covering that story.
Also when you read about the history of mathematics, it's easy to feel like these breakthroughs were happening all the time, compared with now, when in fact they were very slowly, and the pace of discovery is probably higher now than at any point in the past.
It's easy to say music was better in the 70's than now when you condense the 70's down to 100 truly great songs, forgetting all the crap, and compare it to whats playing on the radio today.
Resolution and bitrate are more than "just" correlated.
The fact that you said this, makes me think you don't know what "correlation" means.
It is causative.
You also don't know what "causative" means.
This means that in the vast majority of useful cases higher resolution will need a higher bitrate.
You don't know what the fuck you are talking about.
Let me break this down into a car analogy for you. This is what you did:
Accelerating a car to a faster velocity requires more energy.
No it doesn't! A race car can accelerate to 250kmph going down a hill using less energy than an Astro van to get to 150kmph going up a hill! Herp derp!
You also don't know shit about physics.
A car going a certain velocity has the same kinetic energy whether this energy was converted from chemical energy in a fuel or from potential energy of going down a hill.
A better example is this:
You say "A car that is going faster has more energy." I say actually the mass of the car also matters as it's kinetic energy is equal to 0.5*m*v^2". You say "Stop being obtuse", "everyone agrees with me", "I can never admit when I am wrong or when someone else is right", "Herp derp, I'm a fucking idiot"
do you know of anybody that builds their media library to have their 1080p files be lower quality than their 720p?
I do not know anybody who does this intentionally, but most people I know do not encode their own videos. If they get their videos from many different sources that have different standards of quality, it is likely that they will have some videos that are both higher resolution and lower bitrate than other videos in their collection.
Furthermore, you are assuming that all these files are encoded with the same compression algorithm. Some compression algorithms have better performance. It is very possible for a 1080p video that is encoded with an efficient algorithm (e.g. h264) to be both better quality and lower bitrate than that same video encoded at 720p with a lower performing algorithm (e.g. cinepak)
The point is that the the ability to stream a video is directly dependent on the bitrate of the video. The fact that higher resolution videos tend to have a higher bitrate is just a correlation.
Slashdot Mirror
OK so it's morning and my program has calculated the probability of getting a collision with 50 billion files at 0.000000
I wouldn't call creating 2^128 files easy. Also, you are likely to get collisions way before you get close to reaching 2^128 files.
I should also point out that when I said: " Assuming your not trying to create collisions...", I was referring to the fact that md5 has been compromised. My point is that 128 bits is enough bits to ensure you will not get a random collision due to chance if you are using a good hashing algorithm.
I should also point out that the convention for UUIDs (universally unique identifiers) is also 128bits. Meaning that the chances of randomly getting the same 128 bit number is so low that experts have determined it's ok to just assume it never happens for purposes of computing.
http://en.wikipedia.org/wiki/Universally_unique_identifier
BTW I am at 500 million files, and the odds of getting a 128bit md5 collision are still 0.000000
OK so I wrote a quick little python script (I just remember python has bignumber support) to do it on a smaller numbers.
If we assume md5 was only 64 bits, even with 100 million files, your chances fo hitting an md5 collision are 0.03% (i.e. a 0.0003 chance).
When you bump up the md5 to 128 bits 100 million files has a 0.000000 (rounded to 6 decimal places) chance of happening.
maybe I will let my program run overnight and see how far it gets. It's programmed to count how many files it will take before the probability of a collision is 50%. Who knows, maybe it will take millions of years to finish. We'll see tomorrow morning.
md5 is a 128bit hash. Assuming your not trying to create collisions, the odds of you getting a collision in n files is:
p = 1 - (2^128)! / ((2^128 - n)! * (2^128)^n)
This is an expression that starts at 0 and gradually goes to 1 as n goes to infinity.
These numbers are so big, I have no idea how to even solve for n to get something like p = 0.0001%, without using a bignumber package, but I imagine n would have to be *REALLY* big in order to get a p significantly above 0
O(n^2) vs O(2^n) is a huge difference eve for very small datasets (hundreds of pictures).
Hopefully it's actually something like O(p * 2^n) vs O(p * n^2) where n is the thumbnail size and p is the number of images.
Instead of rewarding people for innovating, we incentivize people/companies to patent trivially simple ideas to lock their potential competitors out of new markets and actually stifle innovation.
Patents are supposed to drive people to come up with ideas that would be cost prohibitive if they were not given some kind of incentive like a temporary government enforced monopoly. Giving out these monopolies in exchange for for such obvious ideas (i,.e. they would be invented regardless) is a shitty deal for society.
And sue king for infringing
I don't think embiggen is a cromulent word.
Well I don't know what to say. I know the source of the problem with NFS and large files is in vxworks. I also have this problem in Linux, but I think it's for a different reason. Lots of people on the internet have similar problems, but the answers tend to be "I used a different OS (on client or server) and it started working, I don't know what exactly fixed it".
Maybe A newer version of the NFS client/server, or a better default setting fixes this issue, but I haven;t been able to figure out what it was.
At least in vxworks the problem was that the nfs server was reopening the file on each packet, and seeking to the beginning of the file to open it, and then seeking to the end of the file to continue the read/write. For small files this seek delay was usually small. On very large files, the nfs server would spend all it's time seeking and throughput would slow to a crawl. Sadly knowing this key piece of information doesn't help me. Maybe I'll just try again one day with a brand new linux OS and it will magically be working.
When you do an experiment, if your hypothesis is proven true then the null hypothesis is disproven. If you don't actually do an experiment, then you haven't done anything to prove the null hypothesis.
I don't know what you consider "special protection", but I am claiming that you need to actually do an experiment to conclude a null hypothesis in a scientifically rigorous way.
When we assume that lion roars don't cause earthquakes because it's a stupid hypothesis. We haven't actually proven the null hypothesis, we are just assuming on intuition and not on evidence.
If we actually did an experiment and can not show a link between lion roars and earthquakes, then you can conclude the null hypothesis by default. But you have to at least try before arriving at this conclusion.
But in science we don't protect a hypothesis, when it is contraindicated by the evidence, by inventing unknown unrecorded unexplained confounding factors.
You don't need to invent them. But you can and should assume that there are some, and take appropriate steps to mitigate the effect of possible confounding factors you may be unaware of.
If you study two things, and there is no measurable correlation between them, then it is only reasonable to conclude that there is no link between them. Although it is technically slimly possible that the two things are linked, but some confounding factor precisely counteracts the link such that the measured correlation is zero, that cannot be reasonably proposed without some evidence.
If you have already taken appropriate steps to eliminate confounding factors, and there is no measurable correlation then it is reasonable to conclude that there is no link. If you haven;t taken the appropriate steps to eliminate confounding factors, then it doesn't really matter what you measured because it's not really useful.
Speculation isn't good enough, which is what you did when you said this:
It could be that marijuana increase schizophrenia, and some other factor decreases schizophrenia fore than marijuana increases it.
I also said I wasn't suggesting this was true or even likely to be true. I was saying that it is important to take steps to eliminate confounding factors because things like this can and do happen. This is why we have statistical methods to mitigate confounding factors
Concluding that there is no link between schizophrenia and marijuana from the fact that schizophrenia went down during a time when marijuana usage went up, is not scientifically or statistically rigorous. You need more data to make such a conclusion. For example a double blind study with a simple random sampling, etc.
This is the crux of the issue. They don't have the same visual information. The 1080 resolution is a bigger space to fill (it has more pixels remember?) If you down scale that to 720 you can get away with reducing the bitrate because you are removing information by downscaling. If you keep it at 1080 you will want a higher bitrate than you would at 720.
This is the crux of the issue, and you seem to be thinking that the same amount of information goes into each pixel. This is true for lossless encoding (which is completely impractical for 1080p video), and not true for lossy video encoding (which included compression algorithms like h.264 and vp8).
The "citation" you provides a policy on minimum, maximum and recommended bitrates for various resolutions. This is not a statement of fact about all videos, but guidelines used by youtube.
But if we ignore that for a second, it actually is evidence towards what I am saying, Notice how the maximum 720 bitrate (4000 kbps) is higher than the minimum 1080p bitrate (3000 kbps).
Even the chart you provided clearly shows that you can have higher bitrate videos at lower resolution, and vice versa
I really don't know why you can't just admit you are wrong. If it's because I made fun of you and called you names, then fine, that was a bit childish of me, but it was in response to your arrogant attitude despite clearly being misinformed.
When someone says "I want 1080p" they do not mean they want to see what looks like a 640×360 video upresed to 1920x1080. They want to see a crisp "HD" picture.
This was illustrating a point, not saying that anybody should do this in practice.
It was an experiment you could do
A 720p video has 921600 pixels. A 1080p video has 2073600 pixels just over twice as many as a 720p video.
Take a 720p video source and encode it at the google recommended bitrate of 2500kpbs. Then take that same source, upscale it to 1080p and encode it at 2500kpbs.
According to you the video should look more than twice as bad because the same amount of data needs to be split among more than twice as many pixels. If you actually did it though, you'd find that it does not look significantly worse if you use a good lossy compression algorithm like h.264. If you used no compression at all, then there would be less than have the data in each pixel and it would look bad.
Another way to put it is that video typically has a lot of redundant information. In video compression lingo this is referred to as spatial redundancy and temporal redundancy. When you compress information you are removing redundant information. When you are performing lossy compression, you can remove information that is "almost redundant", and the quality of the video will be based on your threshold of what you consider "almost redundant".
Some video has lots of redundant information (e.g. south park episodes), and some video has less redundant information (like an action movie) The resolution of the video determines an upperbound for the amount of information a video can contain, but this does not mean that higher resolution videos have more information, just that they *can* and *usually* do have more information. But as I said this is a correlation. The higher resolution doesn't *cause* the video to have more non-redundant information. This is only true of uncompressed video.
Reading or writing? And how big are the files you are accessing?
I think producing the encryption key probably is incriminating in a lot of circumstances, because it proves you had the ability to access the data, and strong evidence of ownership.
If you already admitted to owning and encrypting the data, then I guess it doesn;t matter. But if your defense is that the usb key isn't yours and you don't know the password, then providing the password does kind of screw up your story.
Probably, but I don't think there is proof of that. How do you prove what someone is thinking. Clearly he knew the password, because he produced it eventually, but that doesn't prove that he didn't forget it then remember it, as he claimed.
So you have the burden to prove your innocence in Great Britain?
It can only lower the bitrate while increasing the resolution by removing visual information! Are you daft? It's math not magic.
Have you ever encoded a video? No one is ever going to recommend you to use the same bitrate to encode a video to 1080P as they would to 720P.
Hundreds if not thousands
No one is ever going to recommend you to use the same bitrate to encode a video to 1080P as they would to 720P.
Have you actually ever tried this? If you did, you would find that under most circumstances, The quality will only be a little lower for the 1080p video. That's because, even though there is a lot of visual information removed from the 1080p video, the 720p video started with less visual information, and they end up around the same quality. There is some additional overhead in a 1080p video over a 720p video (e.g. more macroblocks), but this is what causes the 1080p video to be slightly worse quality)
And this is assuming that you are using a bitrate that is more suitable to 720p over 1080p (for this particular video). If you used a bitrate that was more suitable to 1080p, and you encoded the 720 version at this same bitrate will the 720p video always be higher quality because it is lower resolution? Obviously not, because if this were true every one would encode at super high bitrate at low resolution. There is diminishing returns when increasing bitrate, depending on the source video.
Sure people don't always use a higher bitrate but if they don't it is almost always not the right choice. If they are aiming for a lower filesize they should just go with a lower resolution because making a high resolution with the bitrate too low will cause it to look terrible!
This was my whole point to begin with. I said that your streaming capacity is related to the bitrate. This accounts for all videos rather than only the videos where the people encoding it made good choices (which is actually a minority of people). And no it doesn;t look terrible. It just looks a little worse than it could if it was done correctly, which is why people get away with it.
You are still wrong about it being correlated. More visual information requires more data there is no way around that. There are many factors that contribute to bitrate and resolution but when you account for the differences it is straight causation. I will repeat: math not magic.
So by your own logic, 2 videos with the same bitrate, a 720p and a 1080p, have the same visual information, so why would one look like crap?
Have you ever resized an image to be a higher resolution (up sampling), and then zoomed into the original to make them the same visual size? They look about the same quality, and they end up being about the same number of bits (if they are compressed). This is because the amount visual information is about the same.
I will reiterate that you don't know what correlation means. The term correlation describes exactly this kind of scenario, where it is not just a coincidence that higher resolution videos are higher bitrate, but it is not the direct cause.
You are right that it's math and not magic. The problem is that you don't know how that math works. You seem to think you do. But you don't.
A higher resolution causes a higher bitrate (this is why it is causative).
A person selecting the bitrate they encode a video with causes the bitrate to be whatever is selected.
People usually (but not always) select higher bitrates for higher resolution videos, which results in a CORRELATION between resolution and bitrate.
But when everything else is the same for a video file if you increase the resolution you will increase the bitrate.
Have you ever encoded a video? You can select whatever bitrate you want and it is independent of the resolution
I think it's also true that a larger percentage of people are going to university, so the average "intelligence" of people in university in terms of natural ability is probably lower now than when it was just the very best students attending.
Most of the mediocre students today would have simply not gone to university in the past. I think the same principle holds when it comes to things like blogs. The fact that public discourse can sometimes make it seem as if people are getting dumber, when it is really just that more and more people know how to read and write and can now even be published, whereas in the past, there was a higher cost to publishing, and you were more likely to have something important to say before being willing to incur that cost.
Not bashing modern life, it's great, but it isn't making many "great thinkers" in the mold of the 19th century mathematicians. We do more, with less understanding of how, or why.
The easier math problems are lower hanging fruit. As time goes on, the problems that are left become increasingly hard. Even when they get solved, average people can't understand what it means, and that makes it hard to care about, and hward for newspapers to make money covering that story.
Also when you read about the history of mathematics, it's easy to feel like these breakthroughs were happening all the time, compared with now, when in fact they were very slowly, and the pace of discovery is probably higher now than at any point in the past.
It's easy to say music was better in the 70's than now when you condense the 70's down to 100 truly great songs, forgetting all the crap, and compare it to whats playing on the radio today.
All you need to know is SOCATOA, whatever the fuck that means.
What everyone else seems to see except you,
Now you speak for everyone?
Resolution and bitrate are more than "just" correlated.
The fact that you said this, makes me think you don't know what "correlation" means.
It is causative.
You also don't know what "causative" means.
This means that in the vast majority of useful cases higher resolution will need a higher bitrate.
You don't know what the fuck you are talking about.
Let me break this down into a car analogy for you. This is what you did:
Accelerating a car to a faster velocity requires more energy.
No it doesn't! A race car can accelerate to 250kmph going down a hill using less energy than an Astro van to get to 150kmph going up a hill! Herp derp!
You also don't know shit about physics.
A car going a certain velocity has the same kinetic energy whether this energy was converted from chemical energy in a fuel or from potential energy of going down a hill.
A better example is this:
You say "A car that is going faster has more energy." I say actually the mass of the car also matters as it's kinetic energy is equal to 0.5*m*v^2". You say "Stop being obtuse", "everyone agrees with me", "I can never admit when I am wrong or when someone else is right", "Herp derp, I'm a fucking idiot"
I never said it required a higher bitrate
You literally said:
higher resolution requires a higher bitrate
do you know of anybody that builds their media library to have their 1080p files be lower quality than their 720p?
I do not know anybody who does this intentionally, but most people I know do not encode their own videos. If they get their videos from many different sources that have different standards of quality, it is likely that they will have some videos that are both higher resolution and lower bitrate than other videos in their collection.
Furthermore, you are assuming that all these files are encoded with the same compression algorithm. Some compression algorithms have better performance. It is very possible for a 1080p video that is encoded with an efficient algorithm (e.g. h264) to be both better quality and lower bitrate than that same video encoded at 720p with a lower performing algorithm (e.g. cinepak)
The point is that the the ability to stream a video is directly dependent on the bitrate of the video. The fact that higher resolution videos tend to have a higher bitrate is just a correlation.