The last example is actually pretty good, too bad that you didn't do the matching calculation in the video itself to show why possibility can matter *a lot* in compression: 1/2 of the time you send 0 = 0.5 * 1 = 0.5 bits 1/4 of the time you send 10 = 0.25 * 2 = 0.5 bits 1/8 of the time you send 110 = 0.125 * 3 = 0.375 bits 1/8 of the time you send 111 = 0.125 * 3 = 0.375 bits Which sums up to only 1.75 bits needed per state, saving 12.5% of bandwidth, and shows nicely how knowledge about the to-be-compressed data allows beating the standard approach of taking log(number of states) as the number of bits needed, which is pretty much always the worst case for compression.
This guy looks so incredibly passionate about what he is teaching. If he was at my Uni, I would not regret paying my tuition if I knew he was getting paid to teach me. Damn. Makes me wanna be a professor.
I have no idea how I passed my chemistry tests on entropy, the way those books explain those concepts is so terrible. I just remember memorizing something along the lines of "entropy is a measure of disorder, and it always increases" and I didn't have any freaking damn clue what that even meant or why that was significant. The state of education is so bad. it just a plug'n-chug system, no creativity. Absolutely no passion for teaching or in learning is instilled into people. Great video!
I found myself drawn into this video more than I usually do for these kind of videos. The topic was shown in a very interesting way and the professor's voice quite enjoyable to the ears.
PNG: each scanline is fed through a filter, which predicts the pixel value from the nearby pixels, and the best choice is encoded on a per-scanline basis. then the output is fed through Deflate, which may recognize patterns but more often does RLE, and which also applies the use of Huffman coding. for example, each pixel could be predicted by subtracting the value of the pixel to the left. if they are the same color, you get "0,0,0,0", and with a lot of this, the image compresses nicely.
I'm a CS major and this channel is teaching me more than my class so far. Okay, I'll admit I've already learned what this class is teaching from youtube as well, but that's beside the point.
It was a bit confusing, but the formula -(p*log(p)) is normally not used alone, but rather one sums over all events that are possible and so the p term is just to obtain a weighted sum since what one is really interested in is what the average number of bits is for an event. The -(log(2^-2)) formula comes from the summation formula and you get (-1/4*log(1/4)) + (-1/4*log(1/4)) + (-1/4*log(1/4)) + (-1/4*log(1/4)) = -log(1/4) but this only works since the events are equiprobable.
Getting closer to Huffman coding used by LZH / ZIP compression. I hope we'll see more about that. Also as long as we're looking at image compression it would be cool to see a demo in slow motion of a JPEG, GIF, and PNG decompressing into a visible buffer.
Yeah, he quickly gets to the point, he doesn't mess around when explaining and explains extremely well. On top of that he just seems so passionate about what he does, if that were my field of study, you couldn't ask for a better teacher.
You're actually correct. In this case your interpretation is very valid. As long as the receiver and the sender both sync up at a particular time to communicate, then you can use that scheme. However, what he described in the video is the precursor to large file compression. If you had to send weather data from many different cities, you can have a bit stream that starts like "000000...". The receiver would not be able to tell if that's 6 sunny or 3 rainy. The method here is Huffman Coding
Given context, you can compress 4 states to fewer than 2 bits. For example, you could say that if the weather is unchanged, only send one low bit. This requires the listener to be able to determine whether it is a 1 or 2 bit signal, which means either having metadata such as a length header, or a timeout to determine the end of the signal.
You should specify that entropy is reached only for statistical compression algorithms. With LZW for example you can go bellow that. You should do a video about it, because it's quite interesting. I was mesmerized the first time I learned about it.
in a real-life data-format, also typically the Huffman tables are sent prior to any globs of encoded data, so a single decoder can deal with multiple sets of data. in a format like Deflate, the tables are themselves entropy coded. some formats (such as MPEG) use fixed tables, but still send a synchronization code and basic headers (for each frame). (some others send tables only on I-Frames). the Huffman table basically tells how to map the particular symbols to the particular bit patterns.
Wow, I actually learned something new on this video. I had never thought about this in all of my time of programming and working with computers. Keep it coming computerphile. Also, I am glad I subed to this channel.
After this video, an introduction to Huffman encoding is an absolute must have. Once you know that you should give shorter codes to more probable events, then huffman coding is the next step to deciding which codes should be used. It's also dead simple to teach.
I want to say that practicaly you can send the LA wheater report in one byte if you use time differences. sunny - send 0 at 5 : 30, rainy - send 1 at 5 : 30, foggy send 0 at 6 : 00, cloudy send 1 at 6 : 00.
There are some underlying issues that are specific to network theory and confidence in the received data that they cover *very* briefly in the beginning when they discuss sending a zero for sunny in the Sahara "just to be certain". You need high confidence that you actually received the correct message, and treating null as a state ignores many other possibilities in this scenario (cut wire, building on fire, etc.).
ergo, it;d be ambiguous if it were automatically decoded. you are exactly right. the code has to be the expected length. but wen you;ve only got four conditions the supposition I took was that the telegraph operator would manually decode it. He was speaking to the fundamental elements of complete and unambiguous code -- I didn`t realise you were informed, while relating to you the simplest situation as I could, as an answer to your question.
in the video, yes, basically. they didn't talk about the (relative funkiness) that is arithmetic coding though, which can also use fractional bits, but is still limited by entropy limits. it typically compresses slightly better at a significant speed cost vs Huffman (Huffman is generally preferable as it is much faster, and the size difference is usually fairly minor).
This was the best computerphile yet :) You really can't separate computers and maths (if you are talking about the internal workings at least). Computers are logical systems... math is logic.
that's the storage vs. time thing I'm sure we'll get to eventually. The various notions of optimality in computer science sure will give some nice videos. Maybe even how various compressions and codings relate to temperatures in physics. I've recently read a paper on a basically 1:1 mapping between code complexity and thermodynamics.
True, that works. The drawback is performance - you can only send a very limited amount of data unless you can adjust the timings to make them more strict. If I wanted to send 2 unit of information, I would have to wait from 5 to 8 times the interval. This could be cut down to 3 to 4 times the interval by sending 0 during the same interval to mean another states (i.e. 0 from 1-15 means rainy).
I just didn't get this back when I was in my teens. I was sure there must be a way around it. Its only when i got older that it seemed obvious. Lossy compression is another story. There may be ways to improve that.
Time is information. You may physically send one bit, but the time is an implicit source of information no matter how precise you want to be. When we talk information theory, we're interested in all factors that may constitute "information". And it still ignores the various possible problems that may occur in transit, which can include unpredictable delays in timing, throwing off the system. As mentioned.
A "baud" is a physical link-level symbol that can have any number of states, not just two. Many modulation schemes allow for encoding multiple bits in a single baud/symbol - don't worry, this is widely known and used. Please go over to the wikipedia page on bauds and symbol rates and read up (and stop by the page on QAM as well). I can't repeat what's on there in 500 chars, and the articles address your questions quite exhaustively.
For this example he said that 0 equals a short pulse und 1 equals a longer puls. Also, the guy in reno is always awaiting 2 Bits from LA. Usually when using morse code you make a small pause with the same length as your short pulse called a "Dit" between letters and a pause of 3 "Dit" (also called a "Dah") between words. Other examples are the ASCII-Code and a CSV-File. ASCII has a fixed string-length and for a CSV-File you need to specify a separator.
The reason why prefix codes are used instead of what you propose is because a continuous sequence of such codes would be ambiguous. For instance in your proposed code the decoder can't distinguish whether "0001" means "foggy(00) sunny(0) cloudy(1)" or "sunny(0) sunny(0) rainy(01)" or any other valid combination. You'd have to waste more bits for a 'word length' prefix or some framing structure to allow you to detect word boundaries, and at that point you might as well use a prefix code.
right, I'm going to clear some stuff up about those who want to get around this problem. sending data at x mins past the hour christian wagener - " Send a "0" on the hour = weather A Send a "0" one min past the hour = weather B Send a "0" two min past the hour = weather C Send nothing = weather C Single bit at $750 on average:) " the problem is, what if the weather changes 30 from weather b to weather a 30 seconds after hour? you'd be left with a problem. even if you think "oh just give the data recorded on the hour", the problem is, I don't want to wait 2 mins to get the info, I don't want to wait any amount of time. time adds entropy, sure. but If I ask for the weather, I need it now. another problem is what if the connection break? then we think they have weather C constantly. MRAROCKERDUDE - " I don't know if this is just reading too much into the weather metaphor but could you not encode the different weather states as 1, 0, 00, 11? " the problem here is, it's not like speaking. you can't just stop half way through the sentence to add entropy like you can with speaking. think of it like a bunch of 1s and 0s going through a data line. say I have 4 weathers and I encode them as 0,10,111,110 this is good because I can do this: 01001000110 and I know what it means. with weather 1 being a and weather 2 being b and so on I can say that is: a ,b ,a ,b ,a ,a ,d however if it was 0,1,00,11 well... try decoding this: 01001010110010
I'm not saying a signal should be sent more than 1 time a day. For example, as the professor in the video stated, if we have an assigned time at which the signal should be sent (say, at 3pm), then one would send a beep in the first ten seconds after 3:00pm if the weather is cloudy, or one beep in the second decasecond after 3:00 to signal some other weather until you go to sending a signal in the 4th decasecond if necessary. All you need to do, then, is send one signal instead of 2 at any time.
One of the hardest things about client-server relationship in an environment that is time dependent is getting them both to "think" in the same frame of time. Have a read particularly at video game client-server synchronization techniques and you might understand just how complicated this issue is.
what you're describing is a lossy compression, where the exact moment the weather changes can be extrapolated from the data stream... yes, I do know weather changes gradually, but it's also never /just/ sunshine or /just/ fog, this however was /just/ an example of how compression works as I said, if you really wanna save on data report the weather once a week, the cost cutting would be huge!
Clock synchronization is a hard problem. Rather, you'd work with a different type of encoding. You don't encode your data bits directly to on/off, but rather you use the /change/ (on->off) to indicate a one, and the lack of change to indicate a zero (or the other way around). This also circumvents some other problems that are due to large sequences of ones (or zeroes). If you're interested, look up manchester encoding on wikipedia.
If you had more states you would have to sacrifice something else to make your message just as clear, less bits per second perhaps. There is a huge amount of science in making sure signals are transmitted or stored without data lose, data is added so bits can be reconstructed if they are lost, alternating bits are used to keep track of which bit number you are up to so binary words are mapped to longer words, so that some patterns that are hard to read aren't used.
like they mentioned later on, it cannot be a prefix of another code. in your example if you get a series of codes, like 1010 is that sunny, rainy, sunny, rainy or is that foggy foggy? i dont think they did the best job of describing this, but its in there!
No, I agree with you. I'm talking about a packet that is the same size. In terms of physical objects for example a piece of paper can only fold so many times while the same amount of string can fold and bend many times more. If you were for example able to send data via pure light you could hypothetically encode the same packet with many times the data due to being able to encode data via spectrum and have each part of the white light when split into a spectrum contain data
In addition to the length of the tone that others have mentioned, there are also other ways of differentiation high from low bits. For example, they could be at different amplitudes (volume) or different frequencies (pitch or even colour). This is known as modulation.
What you describe is a modulation scheme and there the units of transmission are not called "bits" but "symbols". There are plenty of link modulation schemes which encode more than a single bit in a single symbol (google: QAM or QPSK, etc.), but these do not alter the fact that to describe 4 states you need at least 2 bits. Also look at "symbol rate" on wikipedia, which explains a lot of the general ideas behind this as well.
You have to see this in the context of precursors to compression as well. Let's say you try to compress Sunny-Sunny-Cloudy-Cloudy, it would give you 0011, but then this also means Rainy-Stormy. Now if you take his Los Angeles code, you have 4 codes, 0, 10, 110 and 111. So no matter what other you put it in, it can always be read back, no matter what form you put it in. So let's say 1000 messages were sent using the 2 bit method vs this method for los angeles you get: 1750 vs 2000 messages.
That is an interesting idea. A comment thought is that you are in effect using two bits anyway since there is two different sending times which can be considered 0 and 1. Given the price/bit, you are ofcourse right though. This is known as a covet channel meaning that one communicates with more then just sending bits and might be an interesting topic for a video.
It would be nice to see an episode on gray code counters and their applications. I was intrigued by that when I learned about it in comp sci classes years ago. I imagine they're used in countdown timer circuits to avoid transient states associated with critical events.
It is possible to make a system that only needs to send 1 bit to send information about any weather. The only thing you need is that the receiver knows what the bit means. You could make a system based on the time it is received. Like if it is received in the first 10 minutes of an hour it means it is sunny, if it is recieved the 10 minute period after the first 10 minutes it is rainy etc. You can even make a system that is based on the lack any of bits in a specific time span.
It is amazing that you made such a simple and easily corrected mistake, but that you do not have enough intellectual humility to just understand where you've gone wrong, accept it, and move on.
Regarding the four states of climate in SF, examples like that one could be reduced even more. Information theory talks about how information only is the data that was previously unknown. Therefore, once we know the state at both ends of the communication line we can send the change in information instead of the whole state. So if we are at sunny we could send a 0 to move a state backwards, a 1 to move forward and a 10 to move two states forward and send nothing when there was no change. We are sending no bits for no change 1 bit for two possible changes and 2 bits for the other possible change. Probabilities could be taken into account to decide where it is lest costly to send the 2 bits.
there is still a limit for a given level of quality, and the way quality loss works in JPEG is fairly well controlled (apart from a few areas which traditionally admit round-off errors). but, yeah, in JPEG, colors are converted to YCbCr, where Y=brightness, and holds most of the information (Cb and Cr are color). the entropy-coded numbers are mostly related to things like the magnitude of DCT coefficients and similar (which are stored losslessly, post quantization).
the point is that the practical limitation Professor Brailsford mentioned (and taking into account sending a bit cost $1000 at the time!) can be avoided and we can save ourselves some money. About possible problems that may occur,that's not any different than the method the professor mentioned. Calibrating time is like calibrating instruments, and having the flexibility to send a message that says the same thing every minute sounds even better to me.
You're almost correct. Most serial communication system use a clock called "BAUD rate" but they use -volts for logic high, +volts for logic low and 0v for idle. Old RS232 used +-12v
I would like to see a three prat series on the transistor. one on Computerphile, one on Periodic Videos and one on Sixty Symbols. On Computerphile you can talk about how they are used in computers. On the other two channels you can talk about the chemistry and physics that make them work.
It could be done in one bit. If, as the guy says, the signal is transmitted at the same time every day (say 12:00), then a delay could be introduced that varies according to the weather: Sunny: Send one bit at 12:00 exactly. Cloudy: Send one bit at 12:00.00.01 Rainy: Send one bit at 12:00.00.02 Foggy: Send one bit at 12:00.00.03 Or a dot at ...01 or ...02, or a dash at ...01 or ...02, which would take the same time as sending the two bits in the example in the video.
In this case, 0 isn't the absence of a signal, but a slightly different signal, where 0 is a short signal and 1 is a long signal (like Morse code). It could also be arranged so that 0 is a low-pitch signal and 1 is a high-pitch signal or any other binary set of signals with neither corresponding to the lack of a signal (as a lack of a signal generally doesn't cost anything in order to be sent).
the best way would just be max 2 bit they come within 15 minutes apart. so you send 0 (short beep) for sunny a 1 for rainy , 01 cloudy and 11 for sunny. you can do this because you know that it need to come within the same time frame, its probably for the saving the data. the example can be used for saving.
No. I'm talking about the objects in the box. If I'm sending umbrellas and only 1 umbrella can fit in a box then I can only send 1 umbrella per box, but if I learn that you can close/fold up an umbrella then I can send more than 1 umbrella per box. If you say I always have to send 2 boxes and I can fit 3 folded umbrellas in a box then I can have 6 states as to the 2 previous way. More information same package. I could also lower cost by saying unfolded = 3 then as well.
Thanks for the excellent reply bud. I was being a bit more abstract though. I wasn't thinking of the 'data' being sent by computer, just coloured light. So, for example, if the weather was sunny, the colour is orange etc. It was only after I posted it that it dawned on me he meant 'bits' literally as binary digits. I was being a bit more analogue :)
Couldn't the weather in San Francisco be transmitted more cheaply if leading zeroes were omitted? 0 = $1000 1 = $1000 10=$2000 11=$2000 Average number of bits needed: 1.5 Average cost for transmission: $1,500 In fact, no weather report could be interpreted as sunny. = $0000 1 = $1000 10 = $2000 11 = $2000 Average number of bits needed: 1.25 Average cost for transmission: $1250 Now that we've freed up the zero, I suppose we can move all the values down by one. = $0000 0 = $1000 1 = $2000 10 = $2000 Average number of bits needed: 1 Average cost for transmission: $1000 Just saying. Of course, I'm probably breaking some cardinal rule of information theory with this. *EDIT:* Yes people, I understand why I'm wrong. You can stop telling me.
Nathan T Hi Nathan, I think this is happening because RUclips is showcasing your comment as a "Top Comment" but it does not show the countless replies that have been made so far -.- So now and then someone is going to see your comment, not realise it has already been replied to, and reply to it. It's not going to stop unfortunately I think.
You could send it lossy over the net, but use information on the other end to make it unlossy. Say you know that you got two watches on both ends which are syncronized. Say a simple 2-bit sequence which yields 4 unique: 00, 01, 10, 11 recieved at a specific say minute, (could be seconds or miliseconds etc...) could yield 4 * 9 = 36 unique sequences. If only one bit within that minute was received then max 2-bit would translate to 6 unique codes: 1, 0, 00, 01, 10, 11. Then 6*9 = 54 unique.
Yes, they need more info than that. It's called preamble and headers. For each packet sent on the network they attach some extra data to know what is what and where it goes, or if it's a packet in the first place (that's what preamble is for). Basically a preamble is a series of 0's and 1's alternating (010101010101010101) to synchronize the connection and to make sure it's not just random noise. The video here is just over simplified for others to understand.
to compress (and more pertinently decompress) you have to use a specified algorithm. each of your signals would have to contain two binary digits in order to be decoded correctly
The biggest issue with this is that the communication isnt "over" until the entire time is complete in order to check every possibility against the default via omission. As well, I have instead of removing bits, instead added an alternative bit system based on time and silence rather than communication. Still instead of sending data, by agreeing on sufficient parameters, I have limited the need to expend energy in sending, by increasing the time taken to send it.
It could be confuse between 0 and 01 but we suppose we don't send 2 different messages the same minute. Each weather is 25% chance, BUT maybe (surely) the sunny weather is more stable. The weather changes less often for sunny BUT sunny last longer. So if we put 01 for sunny it will use less 2bit info than 1 bit. Same idea for sunny. if cloudy is the most rare weather after sunny, we put 01 for cloudy for the sunny weather.
If you were to want to send a number of days you could say something like the first bit is the number of days to follow if more than 1 bit is sent 0 = 2, 1 =3, 2 = 4. If you wish to send more days another bit would be sent after that. The point is to send the most data in the smallest cost, this would always be cheaper than binary because to do the same in binary would require 8 bits/4 days while this trinary method would only require 5bits/4days or cheaper ^.^ since 1 state has no cost.
binary isn't usually used to transmit signals. it has a wide frequency spectrum wich is a problem. see, most transmission channels, like cables for example, have their own filtering characteristics, which means some frequencies get attenuated or even lost. that's why you have to convert a binary signal into something more suitable. you do it with this thing called modulation (remember modems?).
What you are asking is not strictly a question on information theory but rather about engineering and how to build a system with certain properties. The problems you describe are real and there are engineering solutions around them. As you guessed correctly, they require a bit of overhead, called "signalling". That's why e.g. your 54Mbps WiFi never goes at 54Mbps - it's the physical "line" signalling rate (also called "baud rate").
The last example is actually pretty good, too bad that you didn't do the matching calculation in the video itself to show why possibility can matter *a lot* in compression:
1/2 of the time you send 0 = 0.5 * 1 = 0.5 bits
1/4 of the time you send 10 = 0.25 * 2 = 0.5 bits
1/8 of the time you send 110 = 0.125 * 3 = 0.375 bits
1/8 of the time you send 111 = 0.125 * 3 = 0.375 bits
Which sums up to only 1.75 bits needed per state, saving 12.5% of bandwidth, and shows nicely how knowledge about the to-be-compressed data allows beating the standard approach of taking log(number of states) as the number of bits needed, which is pretty much always the worst case for compression.
This guy looks so incredibly passionate about what he is teaching. If he was at my Uni, I would not regret paying my tuition if I knew he was getting paid to teach me.
Damn. Makes me wanna be a professor.
His voice is so relaxing. I would love to hear an audiobook read by him haha.
I love that on your channels you only find talented enthusiasts that not only explain stuff very clearly but also make it sound fun. Good job, Brady.
I have no idea how I passed my chemistry tests on entropy, the way those books explain those concepts is so terrible. I just remember memorizing something along the lines of "entropy is a measure of disorder, and it always increases" and I didn't have any freaking damn clue what that even meant or why that was significant. The state of education is so bad. it just a plug'n-chug system, no creativity. Absolutely no passion for teaching or in learning is instilled into people.
Great video!
That professor is such a badass :)
Once again Bradey asks the perfect questions. I think he has a great gift to help get the information across to viewers.
Annotation added for absolute clarity (though the Prof says it almost in his next breath) >Sean
What a pleasure it is to hear somebody who knows what he is talking about answering sensible questions.
You should have uploaded this video in 144p
"We edit nothing out of you" and everything befor and after that is pure gold.
Do steganography one of these times pls.
A big part of the greatness comes from the questions asked by the student.
I found myself drawn into this video more than I usually do for these kind of videos. The topic was shown in a very interesting way and the professor's voice quite enjoyable to the ears.
This guy has an amazing way of holding my attention for long videos.
PNG: each scanline is fed through a filter, which predicts the pixel value from the nearby pixels, and the best choice is encoded on a per-scanline basis. then the output is fed through Deflate, which may recognize patterns but more often does RLE, and which also applies the use of Huffman coding.
for example, each pixel could be predicted by subtracting the value of the pixel to the left. if they are the same color, you get "0,0,0,0", and with a lot of this, the image compresses nicely.
This professor is awesome... He seems like a GREAT teacher, if allowed to teach
I'm a CS major and this channel is teaching me more than my class so far.
Okay, I'll admit I've already learned what this class is teaching from youtube as well, but that's beside the point.
I have spent the last 3 years of mathematics thinking logs were useless now. Thank you for proving me wrong.
I love Brady's incisive, curious and critical style of interviewing.
It was a bit confusing, but the formula -(p*log(p)) is normally not used alone, but rather one sums over all events that are possible and so the p term is just to obtain a weighted sum since what one is really interested in is what the average number of bits is for an event.
The -(log(2^-2)) formula comes from the summation formula and you get (-1/4*log(1/4)) + (-1/4*log(1/4)) + (-1/4*log(1/4)) + (-1/4*log(1/4)) = -log(1/4) but this only works since the events are equiprobable.
Great video. FYI the encoding method he is referring to for encoding varied probability symbols (7:38) is called Huffman encoding.
Imagine having him as a lecturer, he's definitely one of the best!
Getting closer to Huffman coding used by LZH / ZIP compression. I hope we'll see more about that. Also as long as we're looking at image compression it would be cool to see a demo in slow motion of a JPEG, GIF, and PNG decompressing into a visible buffer.
This is precisely the type of content this channel needs.
Probably the best one Computerphile has done so far. This covered so much ground clearly and in only 12 minutes.
Yeah, he quickly gets to the point, he doesn't mess around when explaining and explains extremely well. On top of that he just seems so passionate about what he does, if that were my field of study, you couldn't ask for a better teacher.
You're actually correct. In this case your interpretation is very valid. As long as the receiver and the sender both sync up at a particular time to communicate, then you can use that scheme. However, what he described in the video is the precursor to large file compression. If you had to send weather data from many different cities, you can have a bit stream that starts like "000000...". The receiver would not be able to tell if that's 6 sunny or 3 rainy. The method here is Huffman Coding
Given context, you can compress 4 states to fewer than 2 bits.
For example, you could say that if the weather is unchanged, only send one low bit. This requires the listener to be able to determine whether it is a 1 or 2 bit signal, which means either having metadata such as a length header, or a timeout to determine the end of the signal.
You should specify that entropy is reached only for statistical compression algorithms. With LZW for example you can go bellow that. You should do a video about it, because it's quite interesting. I was mesmerized the first time I learned about it.
in a real-life data-format, also typically the Huffman tables are sent prior to any globs of encoded data, so a single decoder can deal with multiple sets of data. in a format like Deflate, the tables are themselves entropy coded.
some formats (such as MPEG) use fixed tables, but still send a synchronization code and basic headers (for each frame).
(some others send tables only on I-Frames).
the Huffman table basically tells how to map the particular symbols to the particular bit patterns.
This is a good one. Don't shy away from the details!
I loved the style of this video. It's great seeing the professor talk to Brady. It brings another level of humanity to the conveyance of the topic.
Wow, I actually learned something new on this video. I had never thought about this in all of my time of programming and working with computers. Keep it coming computerphile. Also, I am glad I subed to this channel.
I would pay anything to get a class with this guy. So inspiring!
the limit of Brady's channels as it approaches infinity = an intellectual society.
This is my favorite phile site!
Great job delivering educational and fun material,
thanks guys
Very nice explanation indeed. These concepts are so important these days for machine learning algorithms :)KD
After this video, an introduction to Huffman encoding is an absolute must have. Once you know that you should give shorter codes to more probable events, then huffman coding is the next step to deciding which codes should be used. It's also dead simple to teach.
I want to say that practicaly you can send the LA wheater report in one byte if you use time differences. sunny - send 0 at 5 : 30, rainy - send 1 at 5 : 30, foggy send 0 at 6 : 00, cloudy send 1 at 6 : 00.
This guy is awesome.
He should have his own TV show or movie documentary.
I'm really enjoying these computerphile videos.
There are some underlying issues that are specific to network theory and confidence in the received data that they cover *very* briefly in the beginning when they discuss sending a zero for sunny in the Sahara "just to be certain". You need high confidence that you actually received the correct message, and treating null as a state ignores many other possibilities in this scenario (cut wire, building on fire, etc.).
ergo, it;d be ambiguous if it were automatically decoded. you are exactly right. the code has to be the expected length. but wen you;ve only got four conditions the supposition I took was that the telegraph operator would manually decode it. He was speaking to the fundamental elements of complete and unambiguous code -- I didn`t realise you were informed, while relating to you the simplest situation as I could, as an answer to your question.
in the video, yes, basically.
they didn't talk about the (relative funkiness) that is arithmetic coding though, which can also use fractional bits, but is still limited by entropy limits. it typically compresses slightly better at a significant speed cost vs Huffman (Huffman is generally preferable as it is much faster, and the size difference is usually fairly minor).
This was the best computerphile yet :) You really can't separate computers and maths (if you are talking about the internal workings at least). Computers are logical systems... math is logic.
I hope we get much more from Professor Brailsford, he's great.
Its great to see videos about entropy, I hope to see more on information theory which is exiting and unfortunately underrated....
that's the storage vs. time thing I'm sure we'll get to eventually.
The various notions of optimality in computer science sure will give some nice videos.
Maybe even how various compressions and codings relate to temperatures in physics. I've recently read a paper on a basically 1:1 mapping between code complexity and thermodynamics.
True, that works. The drawback is performance - you can only send a very limited amount of data unless you can adjust the timings to make them more strict. If I wanted to send 2 unit of information, I would have to wait from 5 to 8 times the interval. This could be cut down to 3 to 4 times the interval by sending 0 during the same interval to mean another states (i.e. 0 from 1-15 means rainy).
Awesome video! It gives an interesting insight to the statistical meaning of entropy
I just didn't get this back when I was in my teens. I was sure there must be a way around it. Its only when i got older that it seemed obvious. Lossy compression is another story. There may be ways to improve that.
Time is information. You may physically send one bit, but the time is an implicit source of information no matter how precise you want to be. When we talk information theory, we're interested in all factors that may constitute "information".
And it still ignores the various possible problems that may occur in transit, which can include unpredictable delays in timing, throwing off the system. As mentioned.
A "baud" is a physical link-level symbol that can have any number of states, not just two. Many modulation schemes allow for encoding multiple bits in a single baud/symbol - don't worry, this is widely known and used.
Please go over to the wikipedia page on bauds and symbol rates and read up (and stop by the page on QAM as well). I can't repeat what's on there in 500 chars, and the articles address your questions quite exhaustively.
For this example he said that 0 equals a short pulse und 1 equals a longer puls. Also, the guy in reno is always awaiting 2 Bits from LA. Usually when using morse code you make a small pause with the same length as your short pulse called a "Dit" between letters and a pause of 3 "Dit" (also called a "Dah") between words. Other examples are the ASCII-Code and a CSV-File. ASCII has a fixed string-length and for a CSV-File you need to specify a separator.
The reason why prefix codes are used instead of what you propose is because a continuous sequence of such codes would be ambiguous. For instance in your proposed code the decoder can't distinguish whether "0001" means "foggy(00) sunny(0) cloudy(1)" or "sunny(0) sunny(0) rainy(01)" or any other valid combination. You'd have to waste more bits for a 'word length' prefix or some framing structure to allow you to detect word boundaries, and at that point you might as well use a prefix code.
I hope to see more from this gentelman. I is mindblowing how one's passion to anything can transfer to others through a youtube video. inspiring!
right, I'm going to clear some stuff up about those who want to get around this problem.
sending data at x mins past the hour
christian wagener -
"
Send a "0" on the hour = weather A
Send a "0" one min past the hour = weather B
Send a "0" two min past the hour = weather C
Send nothing = weather C
Single bit at $750 on average:)
"
the problem is, what if the weather changes 30 from weather b to weather a 30 seconds after hour? you'd be left with a problem. even if you think "oh just give the data recorded on the hour", the problem is, I don't want to wait 2 mins to get the info, I don't want to wait any amount of time. time adds entropy, sure. but If I ask for the weather, I need it now.
another problem is what if the connection break? then we think they have weather C constantly.
MRAROCKERDUDE -
"
I don't know if this is just reading too much into the weather metaphor but could you not encode the different weather states as 1, 0, 00, 11?
"
the problem here is, it's not like speaking. you can't just stop half way through the sentence to add entropy like you can with speaking. think of it like a bunch of 1s and 0s going through a data line.
say I have 4 weathers and I encode them as 0,10,111,110 this is good because I can do this: 01001000110 and I know what it means. with weather 1 being a and weather 2 being b and so on I can say that is: a ,b ,a ,b ,a ,a ,d
however if it was 0,1,00,11 well... try decoding this: 01001010110010
I'm not saying a signal should be sent more than 1 time a day. For example, as the professor in the video stated, if we have an assigned time at which the signal should be sent (say, at 3pm), then one would send a beep in the first ten seconds after 3:00pm if the weather is cloudy, or one beep in the second decasecond after 3:00 to signal some other weather until you go to sending a signal in the 4th decasecond if necessary. All you need to do, then, is send one signal instead of 2 at any time.
This is awesome!! I always wanted to know how this worked! What a great guest!!
One of the hardest things about client-server relationship in an environment that is time dependent is getting them both to "think" in the same frame of time. Have a read particularly at video game client-server synchronization techniques and you might understand just how complicated this issue is.
what you're describing is a lossy compression, where the exact moment the weather changes can be extrapolated from the data stream... yes, I do know weather changes gradually, but it's also never /just/ sunshine or /just/ fog, this however was /just/ an example of how compression works
as I said, if you really wanna save on data report the weather once a week, the cost cutting would be huge!
Clock synchronization is a hard problem. Rather, you'd work with a different type of encoding. You don't encode your data bits directly to on/off, but rather you use the /change/ (on->off) to indicate a one, and the lack of change to indicate a zero (or the other way around). This also circumvents some other problems that are due to large sequences of ones (or zeroes). If you're interested, look up manchester encoding on wikipedia.
If you had more states you would have to sacrifice something else to make your message just as clear, less bits per second perhaps. There is a huge amount of science in making sure signals are transmitted or stored without data lose, data is added so bits can be reconstructed if they are lost, alternating bits are used to keep track of which bit number you are up to so binary words are mapped to longer words, so that some patterns that are hard to read aren't used.
like they mentioned later on, it cannot be a prefix of another code. in your example if you get a series of codes, like 1010 is that sunny, rainy, sunny, rainy or is that foggy foggy? i dont think they did the best job of describing this, but its in there!
No, I agree with you. I'm talking about a packet that is the same size. In terms of physical objects for example a piece of paper can only fold so many times while the same amount of string can fold and bend many times more.
If you were for example able to send data via pure light you could hypothetically encode the same packet with many times the data due to being able to encode data via spectrum and have each part of the white light when split into a spectrum contain data
In addition to the length of the tone that others have mentioned, there are also other ways of differentiation high from low bits. For example, they could be at different amplitudes (volume) or different frequencies (pitch or even colour). This is known as modulation.
What you describe is a modulation scheme and there the units of transmission are not called "bits" but "symbols". There are plenty of link modulation schemes which encode more than a single bit in a single symbol (google: QAM or QPSK, etc.), but these do not alter the fact that to describe 4 states you need at least 2 bits. Also look at "symbol rate" on wikipedia, which explains a lot of the general ideas behind this as well.
You have to see this in the context of precursors to compression as well. Let's say you try to compress Sunny-Sunny-Cloudy-Cloudy, it would give you 0011, but then this also means Rainy-Stormy.
Now if you take his Los Angeles code, you have 4 codes, 0, 10, 110 and 111. So no matter what other you put it in, it can always be read back, no matter what form you put it in.
So let's say 1000 messages were sent using the 2 bit method vs this method for los angeles you get: 1750 vs 2000 messages.
That is an interesting idea. A comment thought is that you are in effect using two bits anyway since there is two different sending times which can be considered 0 and 1. Given the price/bit, you are ofcourse right though. This is known as a covet channel meaning that one communicates with more then just sending bits and might be an interesting topic for a video.
It would be nice to see an episode on gray code counters and their applications. I was intrigued by that when I learned about it in comp sci classes years ago. I imagine they're used in countdown timer circuits to avoid transient states associated with critical events.
Insane video for these guys, for their memory. I wonder how their life changed since then.
He's not dumb, he represents the common man, that's why he always talks to experts on all of his channels and asks probing questions.
It is possible to make a system that only needs to send 1 bit to send information about any weather. The only thing you need is that the receiver knows what the bit means. You could make a system based on the time it is received. Like if it is received in the first 10 minutes of an hour it means it is sunny, if it is recieved the 10 minute period after the first 10 minutes it is rainy etc. You can even make a system that is based on the lack any of bits in a specific time span.
It is amazing that you made such a simple and easily corrected mistake, but that you do not have enough intellectual humility to just understand where you've gone wrong, accept it, and move on.
Regarding the four states of climate in SF, examples like that one could be reduced even more. Information theory talks about how information only is the data that was previously unknown. Therefore, once we know the state at both ends of the communication line we can send the change in information instead of the whole state. So if we are at sunny we could send a 0 to move a state backwards, a 1 to move forward and a 10 to move two states forward and send nothing when there was no change. We are sending no bits for no change 1 bit for two possible changes and 2 bits for the other possible change. Probabilities could be taken into account to decide where it is lest costly to send the 2 bits.
there is still a limit for a given level of quality, and the way quality loss works in JPEG is fairly well controlled (apart from a few areas which traditionally admit round-off errors).
but, yeah, in JPEG, colors are converted to YCbCr, where Y=brightness, and holds most of the information (Cb and Cr are color).
the entropy-coded numbers are mostly related to things like the magnitude of DCT coefficients and similar (which are stored losslessly, post quantization).
the point is that the practical limitation Professor Brailsford mentioned (and taking into account sending a bit cost $1000 at the time!) can be avoided and we can save ourselves some money. About possible problems that may occur,that's not any different than the method the professor mentioned. Calibrating time is like calibrating instruments, and having the flexibility to send a message that says the same thing every minute sounds even better to me.
You're almost correct. Most serial communication system use a clock called "BAUD rate" but they use -volts for logic high, +volts for logic low and 0v for idle. Old RS232 used +-12v
Ahhh... My Information Theory course is all coming flooding back to me. My favourite course at Uni, too... Claude Shannon was a badass.
I would like to see a three prat series on the transistor.
one on Computerphile, one on Periodic Videos and one on Sixty Symbols.
On Computerphile you can talk about how they are used in computers.
On the other two channels you can talk about the chemistry and physics that make them work.
It could be done in one bit.
If, as the guy says, the signal is transmitted at the same time every day (say 12:00), then a delay could be introduced that varies according to the weather:
Sunny: Send one bit at 12:00 exactly.
Cloudy: Send one bit at 12:00.00.01
Rainy: Send one bit at 12:00.00.02
Foggy: Send one bit at 12:00.00.03
Or a dot at ...01 or ...02, or a dash at ...01 or ...02, which would take the same time as sending the two bits in the example in the video.
In this case, 0 isn't the absence of a signal, but a slightly different signal, where 0 is a short signal and 1 is a long signal (like Morse code).
It could also be arranged so that 0 is a low-pitch signal and 1 is a high-pitch signal or any other binary set of signals with neither corresponding to the lack of a signal (as a lack of a signal generally doesn't cost anything in order to be sent).
the best way would just be max 2 bit they come within 15 minutes apart. so you send 0 (short beep) for sunny a 1 for rainy , 01 cloudy and 11 for sunny. you can do this because you know that it need to come within the same time frame, its probably for the saving the data. the example can be used for saving.
No. I'm talking about the objects in the box. If I'm sending umbrellas and only 1 umbrella can fit in a box then I can only send 1 umbrella per box, but if I learn that you can close/fold up an umbrella then I can send more than 1 umbrella per box.
If you say I always have to send 2 boxes and I can fit 3 folded umbrellas in a box then I can have 6 states as to the 2 previous way. More information same package. I could also lower cost by saying unfolded = 3 then as well.
Thanks for the excellent reply bud.
I was being a bit more abstract though. I wasn't thinking of the 'data' being sent by computer, just coloured light. So, for example, if the weather was sunny, the colour is orange etc.
It was only after I posted it that it dawned on me he meant 'bits' literally as binary digits. I was being a bit more analogue :)
Couldn't the weather in San Francisco be transmitted more cheaply if leading zeroes were omitted?
0 = $1000
1 = $1000
10=$2000
11=$2000
Average number of bits needed: 1.5
Average cost for transmission: $1,500
In fact, no weather report could be interpreted as sunny.
= $0000
1 = $1000
10 = $2000
11 = $2000
Average number of bits needed: 1.25
Average cost for transmission: $1250
Now that we've freed up the zero, I suppose we can move all the values down by one.
= $0000
0 = $1000
1 = $2000
10 = $2000
Average number of bits needed: 1
Average cost for transmission: $1000
Just saying.
Of course, I'm probably breaking some cardinal rule of information theory with this.
*EDIT:* Yes people, I understand why I'm wrong. You can stop telling me.
Nathan T Hi Nathan, I think this is happening because RUclips is showcasing your comment as a "Top Comment" but it does not show the countless replies that have been made so far -.- So now and then someone is going to see your comment, not realise it has already been replied to, and reply to it. It's not going to stop unfortunately I think.
Quanxiang Loo
Oh.
I think I'll edit the comment, actually. That should work.
You could send it lossy over the net, but use information on the other end to make it unlossy. Say you know that you got two watches on both ends which are syncronized.
Say a simple 2-bit sequence which yields 4 unique: 00, 01, 10, 11 recieved at a specific say minute, (could be seconds or miliseconds etc...) could yield 4 * 9 = 36 unique sequences.
If only one bit within that minute was received then max 2-bit would translate to 6 unique codes:
1, 0, 00, 01, 10, 11. Then 6*9 = 54 unique.
Damn it Brady, where do you find these amazing people?
This video goes quite nice with the most recent Crash Course Chemistry video
I wish I had such a professor in my college
For those of you curious about the generation of unique codes for elements based on their probability, I suggest reading up on "Huffman Coding."
I love seeing these compression and data videos
Yes, they need more info than that. It's called preamble and headers. For each packet sent on the network they attach some extra data to know what is what and where it goes, or if it's a packet in the first place (that's what preamble is for). Basically a preamble is a series of 0's and 1's alternating (010101010101010101) to synchronize the connection and to make sure it's not just random noise. The video here is just over simplified for others to understand.
to compress (and more pertinently decompress) you have to use a specified algorithm. each of your signals would have to contain two binary digits in order to be decoded correctly
The biggest issue with this is that the communication isnt "over" until the entire time is complete in order to check every possibility against the default via omission. As well, I have instead of removing bits, instead added an alternative bit system based on time and silence rather than communication. Still instead of sending data, by agreeing on sufficient parameters, I have limited the need to expend energy in sending, by increasing the time taken to send it.
The presenter always asks good questions
It could be confuse between 0 and 01 but we suppose we don't send 2 different messages the same minute.
Each weather is 25% chance, BUT maybe (surely) the sunny weather is more stable. The weather changes less often for sunny BUT sunny last longer. So if we put 01 for sunny it will use less 2bit info than 1 bit. Same idea for sunny. if cloudy is the most rare weather after sunny, we put 01 for cloudy for the sunny weather.
If you were to want to send a number of days you could say something like the first bit is the number of days to follow if more than 1 bit is sent 0 = 2, 1 =3, 2 = 4. If you wish to send more days another bit would be sent after that.
The point is to send the most data in the smallest cost, this would always be cheaper than binary because to do the same in binary would require 8 bits/4 days while this trinary method would only require 5bits/4days or cheaper ^.^ since 1 state has no cost.
binary isn't usually used to transmit signals. it has a wide frequency spectrum wich is a problem. see, most transmission channels, like cables for example, have their own filtering characteristics, which means some frequencies get attenuated or even lost. that's why you have to convert a binary signal into something more suitable. you do it with this thing called modulation (remember modems?).
What you are asking is not strictly a question on information theory but rather about engineering and how to build a system with certain properties. The problems you describe are real and there are engineering solutions around them. As you guessed correctly, they require a bit of overhead, called "signalling". That's why e.g. your 54Mbps WiFi never goes at 54Mbps - it's the physical "line" signalling rate (also called "baud rate").