Khan Academy Labs · YouTube · 5:53
This 120-second introductory segment explains one way to increase communication-system capacity: increase the number of distinguishable signaling events. It first uses Alice and Bob’s string system, where hard, medium, soft, high-pitch, and low-pitch plucks create more signal types. It then presents Thomas Edison’s quadruplex telegraph as an electrical application, combining forward/reverse current with two intensities to produce four levels shown as +3, +1, -1, and -3. The clip states that this let Western Union send more messages without building new lines. Finally, it introduces the limitation: using a thousand or a million voltage levels per pulse becomes difficult because electrical noise limits the receiver’s resolution, illustrated with a SIGNAL meter and an oscilloscope probe/trace demonstration. This video segment introduces the concept of channel capacity in communication systems. It begins by illustrating the unavoidable presence of noise, such as thermal noise, using an oscilloscope, emphasizing that signal differences must be large enough to overcome this noise. The narrator then defines two fundamental parameters for calculating capacity: the symbol rate (n), measured in baud, which is the number of symbol transfers per second; and the number of differences per symbol (s), which represents the size of the symbol space or alphabet. Using animated decision trees, the video demonstrates how these two parameters combine to determine the total size of the message space, which is calculated as s raised to the power of . Examples with binary () and ternary () trees show the exponential growth of possible messages as the sequence length increases. This 113-second clip introduces channel capacity through the idea of message space. It uses physical examples (hard/soft and hard/medium/soft plucks, two-letter written notes) and animated branching trees to show that if a system has S distinguishable symbols per position and sends N positions, the number of possible messages is . Specific values shown include , , , , and briefly . The narration then stresses that capacity concerns how many different messages could be sent, not their semantic meaning, illustrated by binary waveforms, match signals labeled ATTACK/NO ATTACK, jellyfish footage, and unfamiliar script. It closes by saying this counting idea forms the basis for later definitions in modern information theory.
Use the learning inspector for key ideas and moments, or open the reading tabs for the complete notes.
Generated from the video's visuals and explanation; not verbatim speech.
The segment opens by naming a second route to higher communication capacity: enlarge the alphabet of distinguishable signaling events. The visuals move through devices and displays with multiple settings, treating “different signaling events” as different receiver-distinguishable states rather than merely faster pulses.
The Alice-and-Bob string example makes the idea concrete. A vibrating string is paired with labels HARD, MED, and SOFT, while the narration also mentions high-pitch versus low-pitch plucks produced by tightening the cable. Mathematically, each reliably distinguishable pluck type adds another possible symbol in the communication alphabet.
The same principle is then transferred to electrical telegraphy through Thomas Edison’s quadruplex system. The narration combines two binary distinctions—forward versus reverse current and weak versus strong intensity—to obtain four levels. The displayed values , , , and are the clip’s concrete representation of that four-symbol electrical alphabet.
The practical consequence is stated historically: Western Union could send more messages without building new lines. The schematic labeled The Quadruplex supplies visual context for the engineering system, although the clip does not perform a circuit derivation or quantify the message-rate increase.
The segment then introduces the limiting factor. If one tries to send a thousand or a million voltage levels per pulse, adjacent levels become very close together. The narration says these fine-grain differences create receiving-end difficulties, and for electrical systems the resolution is limited by electrical noise. The SIGNAL meter with scale 1–5 functions as an analog visual for the difficulty of reading closely spaced levels.
Finally, the clip moves to measurement hardware. The oscilloscope panel shows PROBE COMP ~ 5V and channel inputs CH 1 and CH 2, then the screen displays CH1 with 100V and M 1.00ms alongside a visibly irregular horizontal trace. This demonstration connects the abstract noise limitation to an observable electrical-line display, though the supplied clip ends before a full quantitative explanation of the trace.
The video opens with a close-up of an oscilloscope. A hand adjusts the VOLTS/DIV knob. Initially, the screen shows a relatively clean, flat horizontal line. As the sensitivity increases, the line becomes visibly thick and fuzzy, representing background noise. The narrator explains that minute, undesired currents are always present due to natural processes like heat and geomagnetic storms.
A distinct, spiky signal is then superimposed onto the noisy baseline. The narrator emphasizes that for a communication system to work reliably, the differences between signaling events (the height of the spikes) must be large enough so that random noise cannot accidentally push a signal from one state to another.
The scene transitions to a black screen with the word "CAPACITY" in glowing green text. The narrator introduces the goal of defining the capacity of a communication system using two simple ideas.
The first idea appears: "SYMBOL RATE" in orange text, with the variable "n" in yellow below it. The narrator defines this as the number of symbol transfers per second, noting that it is commonly known today as "baud".
The second idea appears: "DIFFERENCE" in teal text, with the variable "s" in yellow below it. The narrator defines this as the number of differences per symbol, which can be thought of as the size of the symbol space—how many distinct symbols are available to choose from at each step.
The video shifts to an animation of a decision tree. The narrator explains that the parameters n and s can be visualized as a tree of possibilities. Each symbol transmitted is a decision point, and the number of branches at each point is determined by s, the number of differences.
The animation shows a binary tree () growing level by level. After 4 levels (), the base is labeled "Message space ". The narrator states that after n symbols, the tree has s to the power of n leaves. Since each path from the root to a leaf represents a unique message, the number of leaves is the total size of the message space.
The animation resets and shows a ternary tree () growing. After 4 levels (), the base is labeled "Message space ". The narrator reiterates that the message space is the width of the base of the tree, defining the total number of possible messages that can be sent in a sequence of n symbols.
The video transitions to a physical demonstration with small white blocks on a black surface, setting up a concrete example of sending a message, though the specific mechanics are not detailed in this segment.
The clip opens with a physical binary alphabet: two cards labeled HARD and SOFT. The narration identifies these as the two possible differences in a pluck-based communication system, setting .
An animated tree replaces the cards. With one symbol position there are two branches, and with a second symbol position each branch splits again. The bottom label changes from Message space to Message space , matching the spoken claim that two plucks allow one of four possible messages.
A third card labeled MED is placed between HARD and SOFT, changing the example to . The next animation is a ternary tree: one level gives 3 messages, two levels give , and three levels give . The narration explicitly states these values.
The example shifts from plucks to written notes. Hands write green letters on paper while the narration describes Alice and Bob exchanging notes containing only two letters. The following 26-way tree first shows Message space for one character, then expands to Message space for two characters, because .
The video then separates counting from interpretation. A green grid shows binary digits and waveform traces while the narration says we no longer care about the meaning applied to chains of differences, only how many different messages are possible. Split-screen matches labeled ATTACK and NO ATTACK, jellyfish footage, and unfamiliar script illustrate that the same sequences could represent commands, feelings, music, or an unknown alphabet.
The tree interface returns briefly with a four-branch example labeled Message space , then cycles through earlier message-space values. The narration defines capacity intuitively as how many different things you could say and says the message space defines exactly how many differences are possible in any situation.
Two dice roll on a dark surface as the narration calls this the final step bringing the discussion to modern information theory and places that development in the early twentieth century. The remaining seconds are a black screen with no additional mathematical content.
A communication system can increase capacity by increasing the number of different signaling events, meaning the number of distinguishable symbols or states the receiver can interpret. The clip presents this as an alternative or complement to simply sending pulses faster.
In the Alice-and-Bob string example, different physical pluck types create different signal events. Hard, medium, and soft plucks vary strength, while high-pitch and low-pitch plucks vary cable tension. Each distinguishable pluck type enlarges the signaling alphabet.
Edison’s quadruplex telegraph is described as using two current directions and two intensities. Combining these binary choices gives four distinguishable levels, displayed as , , , and . The narration calls these four different current values while also naming the displayed quantities in volts.
The quadruplex telegraph is presented as letting Western Union greatly increase the number of messages sent without building new lines. The capacity gain is qualitative in the clip; no numerical throughput increase is given.
Adding many voltage levels per pulse eventually becomes impractical because adjacent levels differ by smaller amounts. The clip states that fine-grain differences cause receiving-end difficulties and that electrical noise limits resolution in electrical systems.
The clip shows an oscilloscope with PROBE COMP ~ 5V, CH 1, and CH 2, then a CH1 trace labeled with 100V and M 1.00ms. The visible irregular trace supports the idea that real electrical lines must be inspected under noise-limited conditions.
All physical communication channels are subject to unavoidable noise, such as thermal noise from heat or interference from geomagnetic storms. To ensure reliable transmission, the differences between valid signal states must be significantly larger than the amplitude of the background noise, preventing random fluctuations from causing errors.
The symbol rate, denoted as n, is the number of distinct symbol transfers that occur per second in a communication system. In modern terminology, this rate is often referred to as baud.
Denoted as s, this parameter represents the number of distinct symbols available to be chosen at each time step. It defines the size of the symbol space or alphabet used by the communication system.
The total number of unique messages that can be transmitted in a sequence of n symbols using an alphabet of size s is given by s raised to the power of n. This can be visualized as the number of leaves in a decision tree where each node has s branches and the tree has n levels.
For a communication system with S distinguishable choices per symbol and N symbol positions, the number of possible ordered messages is . The video visualizes this as a branching tree whose leaves are the possible messages.
With HARD and SOFT as the only two pluck types, one pluck gives 2 possibilities and two plucks give possible messages. The animated binary tree ends with four red leaves and the label Message space .
Adding MED creates three distinguishable pluck types. The ternary tree shows 3 possibilities for one pluck, for two plucks, and for three plucks.
If each written position can be one of 26 letters and a note contains two letters, the number of possible ordered notes is . The 26-way branching animation first labels the one-symbol space as 26 and the two-symbol space as 676.
The clip stresses that capacity is initially about how many different messages could be sent, not what those messages mean. Binary waveforms, match signals, jellyfish imagery, and unfamiliar script are used to show that the same counting framework applies across different interpretations.
The narration presents message-space counting as the foundation for later definitions of information and modern information theory. Capacity is framed as the number of different things a communication system could say.
Explore conditions, steps and evidence. Supplementary explanations are labeled separately from content shown in the video.
Yellow text on a black background lists four values vertically: +3, +1, -1, -3.
The narrator says, “So he had plus 3 volts, plus 1 volt, minus 1 volt, and minus 3 volt.”
+3, +1, -1, -3
Four discrete voltage/current levels used as distinct signaling states in the quadruplex telegraph example.
Discrete signal levels; units stated in audio as volts.
An analog meter labeled SIGNAL has a curved scale marked 1, 2, 3, 4, 5.
The needle moves across the scale while the narration discusses fine-grained differences and receiving-end difficulty.
The physical quantity measured by the SIGNAL meter is not explicitly named in the clip.
SIGNAL meter scale 1–5
Visual analog display used to represent signal level or received signal strength; exact measured quantity is not stated in the clip.
Displayed numeric scale from 1 to 5.
Oscilloscope screen shows CH1 at lower left and CH1 again at lower right.
Lower-left label reads 100V.
CH1
Channel 1 input trace on the oscilloscope display.
Oscilloscope channel identifier.
The oscilloscope lower-left readout displays 100V next to CH1.
Whether 100V is volts per division or another displayed scale setting is not explicitly spoken in the clip.
100V
Voltage-related oscilloscope scale/readout shown for CH1.
Voltage scale on an oscilloscope display.
The oscilloscope bottom-center readout displays M 1.00ms.
M 1.00ms
Time-base setting shown on the oscilloscope, indicating milliseconds per horizontal division.
Time scale on an oscilloscope display.
Oscilloscope front panel label reads PROBE COMP with ~ 5V and a square-wave symbol.
A probe tip is placed against the PROBE COMP terminal area.
PROBE COMP ~ 5V
Oscilloscope probe compensation test output labeled approximately 5 volts with a square-wave symbol.
Test signal output on oscilloscope hardware.
The narrator says, 'we can define this as n where it's n symbol transfers per second'.
The letter 'n' appears in yellow below the text 'SYMBOL RATE'.
n
Symbol rate, defined as the number of symbol transfers per second.
Positive integer representing a rate.
The narrator says, 'And we can call this s'.
The letter 's' appears in yellow below the text 'DIFFERENCE'.
s
Number of differences per symbol, also referred to as the symbol space.
Positive integer representing the size of the alphabet.
Top-left panel shows "Differences/symbol" with ", 3, 4, 26".
Narration uses the number of possible messages for systems with 2, 3, and 26 differences per symbol.
S
Number of distinguishable differences or symbols available per transmitted symbol.
Positive integer values shown in this clip: 2, 3, 4, and 26.
Top-right panel shows "Symbols/sec" with ", 2, 3, 4".
Narration counts messages after two plucks and three plucks, matching the displayed symbol count.
N
Number of transmitted symbols, plucks, or written characters in one message sequence.
Positive integer values shown in this clip: 1, 2, 3, and 4.
Bottom label reads "Message space = ..." with values 2, 4, 3, 9, 27, 26, 676, and 16 at different times.
Narration states that two plucks give four possible messages, three-symbol systems give and , and two letters give .
The on-screen formula uses lowercase while the legend uses uppercase S; the clip does not explicitly explain the case difference.
Size of the message space, i.e. the total number of distinct length-N sequences that can be formed from S possible symbols per position.
Bottom text repeatedly labels the tree result as "Message space".
Narration says the message space defines exactly how many differences are possible in any situation.
Message space
Set of all possible messages representable by a communication system for a given number of symbols per message and number of choices per symbol.
Narrator: “It also became clear that there was one other way to increase the capacity of a communication system. We can increase the number of different signaling events.”
Opening visuals show a telegraph key, numbered paint swatches, and a washing-machine dial as examples of multiple distinguishable settings or states.
The clip defines one way to increase the capacity of a communication system: use more different signaling events. The surrounding examples visually suggest that a system’s alphabet of distinguishable states can be enlarged beyond a simple binary choice.
Applies to a communication system where receiver can distinguish the added signaling events.
The clip does not state a formal capacity formula in this interval.
Narrator describes Alice and Bob’s string communication system and says varying the type of plucks allowed them to send messages faster.
Examples given are hard, medium versus soft plucks, and high pitch versus low pitch plucks by tightening the cable different amounts.
A vibrating string/cable is shown, followed by labels HARD, MED, SOFT being arranged as categories.
In the Alice-and-Bob string example, the method is to encode information using physically different pluck events. The video distinguishes amplitude/force categories such as hard, medium, and soft, and also pitch categories produced by changing cable tension.
The communication medium is a string or cable.
Different pluck types must remain distinguishable at the receiver.
This is an illustrative example, not a formal theorem.
Narrator says the idea was implemented by Thomas Edison and applied to the Morse code system.
Narrator says it was based on using weak and strong batteries to produce signals of different strengths.
Narrator says Edison also used two directions, forward versus reverse current, and two intensities.
Yellow text lists +3, +1, -1, -3.
Narrator names plus 3 volts, plus 1 volt, minus 1 volt, and minus 3 volt, then says these are four different current values which could be exchanged.
The clip uses both “signals,” “current values,” and “volts” in close succession; the exact electrical variable represented by each displayed number is not fully separated in the narration.
The clip presents Edison’s quadruplex telegraph idea as expanding the Morse-code signaling alphabet by combining current direction and current intensity. Two directions and two intensities yield four distinguishable levels, illustrated as +3, +1, -1, and -3.
Applied to an electrical telegraph/Morse-code communication system.
Requires the receiver to distinguish both sign/direction and magnitude/intensity.
The historical mechanism is described qualitatively rather than derived mathematically.
Narrator says it enabled Western Union to save money by greatly increasing the number of messages the company could send without building new lines.
Narrator says this is known as the quadruplex telegraph and continued to be used into the twentieth century.
A schematic labeled The Quadruplex appears with component legend text including D.T., S.T., P., C.R., C, G, and 1 and 2 Batteries.
The schematic’s detailed circuit operation is visible but not explained step-by-step in the clip.
The quadruplex telegraph is presented as a historical multiplexing method that increased message throughput on existing telegraph lines. The claimed benefit is economic: more messages could be sent without constructing new lines.
Refers to Western Union’s telegraph infrastructure.
The capacity increase is stated qualitatively; no numerical capacity gain is given in the clip.
Narrator asks why not send a thousand or a million different voltage levels per pulse.
Narrator answers that fine-grain differences lead to difficulties on the receiving end.
Narrator states that with electrical systems, the resolution of these differences is always limited by electrical noise.
An analog SIGNAL meter with scale 1–5 is shown while the narration discusses receiving-end difficulty.
The SIGNAL meter is used visually, but the clip does not explicitly define its calibration or the exact noise model.
The clip explains a limitation on increasing signaling events: if voltage levels are made too finely spaced, the receiver has difficulty distinguishing them. For electrical systems, the resolution limit is attributed to electrical noise.
Applies to electrical communication systems.
Assumes signals are distinguished by voltage level or similar continuous amplitude quantities.
The statement is qualitative; no probability model or noise equation is shown.
Narrator says, “If we attach a probe to any electrical line.”
Oscilloscope front panel shows PROBE COMP ~ 5V, CH 1, and CH 2.
A probe is attached/touched to the oscilloscope test area and wires are shown.
Oscilloscope screen displays CH1 100V, M 1.00ms, and a noisy horizontal trace.
The final spoken phrase after “any electrical line” is not fully recoverable within the supplied clip; the visual demonstration continues to an oscilloscope trace.
The clip introduces an oscilloscope probe as a way to inspect an electrical line. The visual sequence moves from the probe-compensation terminal and channel inputs to an oscilloscope display with a noisy trace, supporting the preceding claim that real electrical signals have noise-limited resolution.
Uses an oscilloscope and probe.
The displayed trace is on CH1 with visible scale labels 100V and M 1.00ms.
The clip does not complete a quantitative analysis of the trace.
The narrator defines the first parameter: 'how many symbol transfers per second, which we called symbol rate and today it's known simply as baud'.
The text 'SYMBOL RATE' appears on screen.
The symbol rate is the number of symbol transfers that occur per second in a communication system. It is also known as baud.
Applies to discrete-time communication systems.
The narrator defines the second parameter: 'how many differences per symbol, which we can think of as the symbol space, how many symbols can we select from at each point'.
The text 'DIFFERENCE' appears on screen.
This parameter represents the number of distinct symbols available to be chosen at each time step, effectively the size of the alphabet or symbol space.
Applies to discrete-time communication systems.
Animated trees display "Message space ", "= 4", "= 3", "= 9", "= 27", "= 26", "= 676", and "= 16".
Narration explains that with two choices and two plucks there are four messages, with three choices there are and messages, and with 26 letters there are messages.
For a communication system with S possible differences per symbol and N symbols in a message, the number of distinct messages is obtained by multiplying the choices at each position, giving . The video visualizes this as a branching tree whose leaves are the possible messages.
Each symbol position has the same number S of distinguishable choices.
There are N independent symbol positions in the message.
Different sequences are counted as different messages regardless of their meaning.
Narration says that when looking at a communication system, its capacity can be thought of as how many different things you could say.
The preceding tree examples quantify possible messages as values.
The clip defines an intuitive notion of communication-system capacity: instead of asking what a message means, ask how many different messages the system can represent. The message space size gives that count for a specified number of symbols per message.
Applies to a described communication system with a fixed alphabet size and message length.
The definition here is counting-based and does not yet introduce units such as bits.
Narration states that we no longer care about the meaning applied to these chains of differences, merely how many different messages are possible.
Binary waveforms, match signals, jellyfish footage, and alien writing are shown as examples of different possible meanings.
The video emphasizes that the relevant quantity is the number of distinguishable message sequences, not the interpretation attached to them. The same counting framework applies whether the sequences encode numbers, names, feelings, music, or an unknown alphabet.
The communication system must have distinguishable symbols or differences.
Meaning may vary or be unknown without changing the count of possible messages.
Narrator states there was one other way to increase the capacity of a communication system: increase the number of different signaling events.
No formal definition of communication-system capacity is given in this interval.
A communication system’s capacity can be increased by increasing the number of different signaling events.
The communication system can support additional distinguishable signaling events.
The receiver can distinguish the added events.
Existential: there is at least one other way to increase capacity.
Narrator attributes the implementation to Thomas Edison and says it was applied to the Morse code system.
Narrator says weak and strong batteries produce signals of different strengths.
Narrator says Edison used two directions, forward versus reverse current, and two intensities.
The four displayed values are +3, +1, -1, -3.
The clip does not provide primary-source details or a circuit-level proof of how the four levels were generated and detected.
Thomas Edison applied the idea of increasing signaling events to the Morse code system by using forward versus reverse current and two intensities, giving four current values: +3 volts, +1 volt, minus 1 volt, and minus 3 volts.
The system is an electrical telegraph/Morse-code system.
Current direction and intensity can be distinguished by the receiving apparatus.
Historical existential claim about Edison’s implementation.
Narrator says it enabled Western Union to save money by greatly increasing the number of messages the company could send without building new lines.
Narrator identifies this as the quadruplex telegraph.
No numerical message-rate increase or cost calculation is shown.
The quadruplex telegraph enabled Western Union to greatly increase the number of messages it could send without building new lines, thereby saving money.
Western Union used the quadruplex telegraph on existing lines.
The increased signaling alphabet could be exploited in operation.
Historical qualitative claim; “greatly” is not quantified in the clip.
Narrator asks why not send a thousand or a million different voltage levels per pulse.
Narrator says fine-grain differences lead to difficulties on the receiving end.
Narrator says with electrical systems, the resolution of these differences is always limited by electrical noise.
The word “always” is spoken as a broad qualitative assertion; the clip gives no formal noise model or inequality.
In electrical systems, the resolution of fine-grained differences among many voltage levels per pulse is limited by electrical noise.
Signals are represented by distinguishable voltage levels.
The communication system is electrical.
Noise is present on the line or receiver.
Universal within the stated class: with electrical systems, resolution is always limited by electrical noise.
Narration says that with hard versus soft pluck, two plucks allow one of four possible messages to Bob.
A binary branching tree expands to two levels and the bottom label reads "Message space ".
If a communication system has possible differences per symbol and symbols, then the number of possible messages is .
There are exactly two distinguishable choices per symbol.
The message consists of two symbols.
Sequences differing in position or choice are distinct.
For the specific binary two-symbol system shown.
Narration says that with hard, medium, and soft plucks, two plucks give messages and three plucks give 27 messages.
A ternary branching tree is labeled first "Message space ", then "= 9", then "= 27".
If a communication system has possible differences per symbol, then , 2, and 3 symbols produce 3, , and possible messages respectively.
There are exactly three distinguishable choices per symbol.
Messages are sequences of length N over those choices.
For the specific three-symbol alphabet shown and message lengths 1, 2, and 3.
Narration says that if Alice and Bob exchange written notes containing only two letters, a single note contains one of possible messages.
A 26-way branching tree is labeled "Message space " and then expands to "Message space ".
If a written communication system has possible letters per position and positions, then the number of possible notes is .
Each written position can be one of 26 distinguishable letters.
The note contains exactly two letters.
Different ordered pairs count as different messages.
For the specific 26-letter two-character written-note example.
A four-branching tree appears briefly with the bottom label "Message space ".
The legend shows and among the selectable values.
The narration during this brief interval is not clearly tied to the 16 example, so the spoken explanation for this exact frame is uncertain.
If a communication system has possible differences per symbol and symbols, then the number of possible messages is .
There are exactly four distinguishable choices per symbol.
The message length is two symbols.
For the specific four-symbol two-position tree shown briefly.
Narration says this simple idea forms the basis for how information will be later defined and brings us to modern information theory.
The message-space counting idea introduced in the clip is presented as the basis for later formal definitions in information theory.
The communication system can be described by distinguishable differences per symbol and a number of symbols.
Capacity is being considered in terms of how many different messages could be sent.
Stated as a conceptual claim for the development of information theory in the video.
Narrator says Edison used two directions and two intensities.
Narrator then lists plus 3 volts, plus 1 volt, minus 1 volt, and minus 3 volt.
Four yellow values appear vertically: +3, +1, -1, -3.
Narrator calls them four different current values.
The clip does not explicitly write the multiplication expression; the count is inferred from the stated two directions and two intensities.
The narration identifies forward versus reverse current as two possible directions.
Directly stated in the audio.
The narration identifies weak and strong battery-produced signals as two possible intensities.
Directly stated in the audio.
Combining two independent choices, direction and intensity, yields four distinguishable combinations.
Combinatorial counting of independent binary choices; this multiplication is an analyst-made explicit form of the video’s stated count.
The video displays the four resulting levels as signed voltage values.
Visible diagram and matching narration.
The quadruplex example uses four distinguishable signaling levels, obtained by combining two current directions with two intensities.
Narrator proposes sending a thousand or a million different voltage levels per pulse.
Narrator says fine-grain differences lead to difficulties on the receiving end.
Narrator says electrical-system resolution is limited by electrical noise.
A SIGNAL meter needle moves over a 1–5 scale, visually suggesting uncertainty in reading closely spaced levels.
The clip does not quantify noise variance, signal spacing, error probability, or a capacity bound.
Start from the hypothetical idea of using a thousand or a million voltage levels per pulse.
Stated as a rhetorical question in the narration.
Increasing the number of levels within a voltage range makes adjacent level differences finer.
Implicit in the phrase “fine-grain differences”; no formula is shown.
The narration states that fine-grain differences lead to difficulties on the receiving end.
Directly stated in the audio.
For electrical systems, the ability to resolve those small differences is limited by electrical noise.
Directly stated in the audio.
The clip’s intuitive derivation is that adding more voltage levels eventually fails because the receiver cannot reliably distinguish noise-corrupted, closely spaced levels.
The narrator explains that the parameters form a decision tree where each symbol is a decision with branches depending on the number of differences. After n symbols, there are leaves, representing the message space.
An animation shows a binary tree expanding over 4 levels, with the base labeled 'Message space '. It then shows a ternary tree expanding over 4 levels, with the base labeled 'Message space '.
Model the transmission of a sequence of symbols as a decision tree.
Each symbol choice represents a branching point in the tree.
At each branch, the number of possible choices is equal to the number of differences per symbol, s.
Definition of the symbol space.
For a sequence of n symbols, the tree has n levels of branching.
Definition of the symbol rate and sequence length.
The total number of leaves in the tree is s multiplied by itself n times, which is .
Basic combinatorics of a tree structure.
Each path from the root to a leaf represents a unique message.
Definition of a message as a sequence of symbols.
Therefore, the size of the message space is .
Conclusion from the tree model.
The total number of possible messages of length n using an alphabet of size s is .
A root node branches into two nodes, then each branches into two leaves.
The bottom label changes from "Message space " to "Message space ".
Narration says the hard-versus-soft system with two plucks defines one of four possible messages.
Start with one symbol position having two possible differences, represented by two branches from the root.
The displayed legend sets for differences per symbol.
Add a second symbol position by branching each first-level node into two more nodes.
The animation selects symbols/sec and expands the tree one level deeper.
Count the final leaves of the two-level binary tree.
Each of the 2 first choices is paired with 2 second choices, giving 4 distinct sequences.
A binary communication system sending two symbols has message space size 4.
A three-branching tree is shown with labels "Message space ", then "= 9", then "= 27".
Narration explicitly says and that with three plucks it jumps to 27 messages.
With one symbol position and three possible differences, there are three leaves.
The tree first shows a single level of three branches under .
With two symbol positions, each of the 3 first choices branches into 3 second choices.
The animation expands to two levels and labels the message space as 9.
With three symbol positions, each of the 9 two-symbol sequences branches into 3 more choices.
The animation expands to three levels and labels the message space as 27.
For three possible differences per symbol, message-space sizes are 3, 9, and 27 for one, two, and three symbols.
A 26-way branching tree is labeled "Message space " and then expands to "Message space ".
Narration says a two-letter note has possible messages.
One written character can be any of 26 letters, giving 26 possible one-symbol messages.
The first-level fan-out tree is labeled with message space 26.
A two-character note pairs each of the 26 first letters with each of the 26 second letters.
The animation adds a second level and the narration states .
A two-letter written message over a 26-symbol alphabet has 676 possible messages.
Narrator introduces Alice and Bob’s string communication system.
Narrator says varying the type of plucks allowed them to send messages faster.
A vibrating string/cable is shown.
Labels HARD, MED, SOFT are placed as categories.
Narrator mentions high pitch versus low pitch plucks by tightening the cable different amounts.
No explicit message alphabet, bit count, or capacity calculation is given for the string example.
Use a string communication system and increase message speed by making the signaling events more varied.
Alice and Bob communicate using a string or cable.
Plucks can differ in force: hard, medium, soft.
Plucks can differ in pitch by tightening the cable different amounts.
Show how increasing the number of distinguishable pluck types increases signaling capacity.
Use different strengths of pluck, labeled HARD, MED, and SOFT in the visuals.
Stated in narration and shown by labels.
Use high-pitch versus low-pitch plucks by tightening the cable different amounts.
Stated in narration and accompanied by string vibration imagery.
Each reliably distinguishable pluck type adds another possible signal event.
Connects the example to the earlier proposition about increasing signaling events.
The string example demonstrates that messages can be sent faster by enlarging the set of distinguishable physical pluck events.
The verification is conceptual: the clip ties the example to the stated principle that increasing different signaling events increases communication-system capacity; no numerical check is provided.
Narrator describes Thomas Edison applying the idea to the Morse code system.
Narrator names weak and strong batteries, forward versus reverse current, and two intensities.
The values +3, +1, -1, -3 are displayed.
A schematic titled The Quadruplex is shown with legend text for transmitters, relays, condenser, ground, and batteries.
Narrator says this enabled Western Union to send more messages without building new lines.
The schematic contains many components, but the clip does not trace current paths or prove the four-channel operation from the circuit diagram.
Apply the idea of more signaling events to an electrical Morse-code telegraph system.
Use weak and strong batteries to create different signal strengths.
Use forward and reverse current directions.
The displayed levels are +3, +1, -1, -3.
The system is called the quadruplex telegraph.
Explain how four distinguishable electrical signal levels can increase telegraph message capacity on existing lines.
Produce signals of different strengths.
Stated in narration.
Add a second binary distinction, current direction.
Stated in narration.
Represent the four resulting distinguishable signed levels.
Shown as yellow text and named in narration.
Identify the historical system using these four levels.
Stated in narration and supported by the schematic labeled The Quadruplex.
Conclude that Western Union could increase message throughput on existing infrastructure.
Stated in narration.
The quadruplex telegraph example uses four electrical signaling levels, allowing more messages to be sent over existing telegraph lines.
The clip verifies the idea historically and qualitatively through narration and the quadruplex schematic; it does not provide a numerical capacity calculation.
Oscilloscope panel labels include PROBE COMP ~ 5V, CH 1, and CH 2.
A probe is placed against the oscilloscope test area and wires are shown.
Narrator says, “If we attach a probe to any electrical line.”
Oscilloscope screen shows CH1 100V, M 1.00ms, and a horizontal trace with visible jitter/noise.
The clip ends before a completed spoken explanation of the oscilloscope trace; the exact intended measurement conclusion after “zoom in closely enough” is not fully available in the supplied interval.
Inspect an electrical line with an oscilloscope probe to visualize signal behavior relevant to noise-limited resolution.
An oscilloscope has PROBE COMP ~ 5V and channels CH 1 and CH 2.
A probe is attached/touched to the test area.
The oscilloscope display shows CH1, 100V, and M 1.00ms.
Connect the physical probe/electrical-line setup to a visible oscilloscope trace.
The narration introduces attaching a probe to any electrical line.
Directly stated in audio.
The display is labeled CH1, indicating the traced signal is shown on channel 1.
Visible oscilloscope label.
The screen shows a horizontal line with visible irregularity/jitter.
Visible diagram/animation.
The oscilloscope demonstration visually supports the preceding claim that real electrical lines show noise-limited signal behavior.
Verification is visual: the displayed trace is not perfectly clean. The clip does not provide a numerical noise measurement before the interval ends.
A binary tree is shown expanding level by level. The text 'Message space ', then '= 4', then '= 8', and finally '= 16' appears at the base.
Visualize the message space for a system with 2 differences per symbol and a sequence of 4 symbols.
Determine the size of the message space.
Observe the tree branching into 2 paths at each level.
differences per symbol.
Count the number of levels, which corresponds to n.
symbols.
Count the total number of leaves at the bottom.
Each leaf represents a unique message.
The message space size is .
The animation explicitly labels the base as 'Message space '.
A ternary tree is shown expanding level by level. The text 'Message space ', then '= 9', then '= 27', and finally '= 81' appears at the base.
Visualize the message space for a system with 3 differences per symbol and a sequence of 4 symbols.
Determine the size of the message space.
Observe the tree branching into 3 paths at each level.
differences per symbol.
Count the number of levels, which corresponds to n.
symbols.
Count the total number of leaves at the bottom.
Each leaf represents a unique message.
The message space size is .
The animation explicitly labels the base as 'Message space '.
Physical cards labeled "HARD" and "SOFT" appear beside a small white block.
A binary tree is shown with "Message space " after two levels.
Narration says they are using a hard versus soft pluck as their communication system and that two plucks define one of four possible messages.
Alice communicates to Bob using a pluck system with two possible differences per pluck.
Possible differences per symbol: HARD and SOFT.
.
Message length in the counted example: .
Determine how many different two-pluck messages are possible.
Identify the alphabet size from the physical labels and legend.
The clip shows two distinguishable pluck types and sets .
Raise the alphabet size to the number of plucks.
The binary tree expands to two levels and the message-space label becomes 4.
4 possible messages.
The animated tree has four leaves and the narration explicitly states one of four possible messages.
A third card labeled "MED" is added between "HARD" and "SOFT".
A ternary tree is labeled "Message space ", then "= 9", then "= 27".
Narration says hard versus medium versus soft plucks give messages with two plucks and 27 messages with three plucks.
Replace the two-pluck-type system with three pluck types and count messages for two and three plucks.
Possible differences per symbol: HARD, MED, SOFT.
.
Message lengths considered: and .
Determine the number of possible messages for two plucks and for three plucks.
Count the leaves after expanding the ternary tree to two levels.
The narration states 3 to the power of 2 equals 9 and the screen label reads 9.
Count the leaves after expanding the ternary tree to three levels.
The narration states that with three plucks the number jumps to 27 and the screen label reads 27.
9 possible messages with two plucks; 27 possible messages with three plucks.
Both values are spoken and displayed as message-space labels on the ternary tree.
Hands write green letters on paper, including visible letters B, L, F, and A.
A 26-way tree is labeled "Message space " and then "Message space ".
Narration says written notes containing only two letters on a piece of paper have possible messages.
The handwritten letters shown are illustrative; the clip does not state that these specific letters form the counted examples.
Alice and Bob exchange written notes containing only two letters.
Each written position can be one of 26 letters.
.
Message length: .
Determine how many different two-letter notes are possible.
Count the possibilities for a single written letter.
The first-level 26-way tree is labeled with message space 26.
Count ordered pairs of letters.
The narration states 26 to the power of 2 equals 676 and the expanded tree label reads 676.
676 possible notes.
The value is both spoken and shown on the 26-symbol branching animation.
A green grid shows binary digits above square-wave and noisy waveform traces.
Narration says the resulting sequences could represent numbers, names, feelings, music, or perhaps an alien alphabet.
The exact binary string is not consistently legible across the sampled frames, so no specific sequence value is recorded.
Show that the same counting approach applies to signal sequences without assigning them semantic meaning.
A binary-style signal representation is displayed.
The preceding message-space framework counts possible sequences.
Illustrate that sequences can carry many kinds of meaning while the count of possible sequences remains the relevant quantity.
Display binary digits and corresponding waveforms as a communication signal.
The animation shows sequences above waveform traces.
State that meaning is not needed for counting possible messages.
The narration explicitly says we no longer care about the meaning applied to these chains of differences.
The example supports meaning-independent counting of signal sequences.
The visual binary signal is paired with narration listing possible interpretations such as numbers, names, feelings, music, or an alien alphabet.
A split-screen shows a match being lit and an unlit match, labeled "ATTACK" and "NO ATTACK".
Narration continues discussing how resulting sequences could represent different meanings.
Use a simple physical signal to show that a communication sequence can encode a decision.
Two match states are shown visually.
Labels assign meanings ATTACK and NO ATTACK.
Illustrate that message sequences can represent meaningful commands even though capacity counting ignores meaning.
Show two distinguishable physical signal states.
The lit and unlit match provide two observable alternatives.
Attach semantic labels to the alternatives.
The on-screen text reads ATTACK and NO ATTACK.
The example shows a binary signal can encode a command, while the capacity discussion counts distinguishable sequences rather than meanings.
The labels are visible on the split-screen match animation.
Jellyfish footage is followed by close-ups of non-Latin writing on wood.
Narration says sequences could represent feelings, music, or perhaps even some alien alphabet we could never understand.
The exact language or script in the wooden writing is not identified in the clip.
Demonstrate that unknown or nonhuman meanings do not affect the counting of possible message sequences.
Jellyfish footage is shown as an example of feelings or natural signals.
Non-Latin writing is shown as an example of an unfamiliar alphabet.
Support the claim that information capacity concerns possible differences, not understood semantics.
Show biological or natural signal imagery while narration mentions feelings and music.
The jellyfish footage accompanies the list of possible meanings.
Show unfamiliar writing while narration mentions an alien alphabet we could never understand.
The wooden script appears during the statement about an unknown alphabet.
The examples reinforce that message-space counting is independent of whether humans understand the encoded meaning.
The narration explicitly lists meanings including an alien alphabet we could never understand while these visuals appear.
A hand operates a telegraph key.
Numbered paint swatches such as 8418, 8417, 8416, 8415, and 8414 appear.
A washing-machine dial shows settings including Off, Spin, Rinse, Extra Light, Light, Normal, Heavy, Delicates, and Wrinkle Free Fabrics.
The exact semantic mapping from paint swatches and washing-machine settings to signaling events is visual analogy rather than explicitly stated for each object.
Telegraph key
Numbered paint swatches
Washing-machine dial
Cuts move from one device or display with multiple settings to another.
Each visual example presents multiple selectable or distinguishable states.
The montage illustrates the narration’s idea that communication capacity can be increased by having more different signaling events.
A thin string or cable vibrates in a dark setting.
Labels HARD, MED, and SOFT are placed as categories on a dark surface.
The precise physical displacement differences corresponding to HARD, MED, and SOFT are not measured on screen.
Vibrating string/cable
HARD label
MED label
SOFT label
The string vibrates; labels are arranged to name different pluck types.
The communication medium remains a string/cable.
The labels represent categories of pluck type.
The visual sequence supports the Alice-and-Bob example that different pluck strengths and pitches create more distinguishable signal events.
A historical photograph of Thomas Edison with equipment appears.
Electrodes in liquid produce bubbles.
Hands connect wires to a small switchboard-like device.
Yellow text lists +3, +1, -1, -3.
A schematic labeled The Quadruplex appears with legend text including D.T., S.T., P., C.R., C, G, and 1 and 2 Batteries.
The liquid-electrode footage is illustrative; the clip does not explicitly explain its relation to the quadruplex circuit.
Thomas Edison photograph
Electrodes in liquid
Switchboard/wiring device
Voltage-level text
The Quadruplex schematic
The video moves from historical figure to electrical demonstrations, then to discrete level labels and a circuit schematic.
The topic remains electrical signaling with multiple distinguishable states.
These visuals connect Edison’s historical quadruplex telegraph to the idea of using signed, multi-level electrical signals.
An analog meter labeled SIGNAL has scale marks 1, 2, 3, 4, 5.
The needle moves across the scale.
The meter’s exact measured quantity and calibration are not stated.
SIGNAL meter
Needle
Scale marks 1–5
The needle sweeps or shifts across the numbered scale.
The display remains an analog signal-level meter with five marked positions.
The moving needle visually suggests difficulty in reading closely spaced signal levels, matching the narration about fine-grain differences and receiving-end problems.
Oscilloscope front panel shows PROBE COMP ~ 5V, CH 1, and CH 2.
A probe is placed against the test terminal area.
Bare wires are shown against a dark background.
Oscilloscope screen shows CH1 100V, M 1.00ms, and a noisy horizontal trace.
The final spoken explanation is incomplete within the supplied clip, so the intended quantitative interpretation of the trace is not fully established.
PROBE COMP terminal
CH 1 input
CH 2 input
Probe
Wires
Oscilloscope grid
CH1 trace
The view moves from oscilloscope controls to probe/wire connection to the displayed waveform.
The displayed trace is associated with CH1.
The screen retains scale labels 100V and M 1.00ms during the final display.
The sequence demonstrates how an electrical line is inspected with an oscilloscope and visually introduces noise as a limitation on resolving signal levels.
A hand turns a knob on an oscilloscope. The screen shows a flat line that becomes noisy, and then a signal with spikes is superimposed on the noise.
The narrator discusses minute undesired currents caused by natural processes like heat and geomagnetic storms, and how signal differences must be large enough to avoid noise interference.
Oscilloscope screen
Signal trace
Noise
The signal trace changes from a clean flat line to a noisy flat line, and then to a noisy signal with distinct spikes.
The presence of noise is constant once introduced.
Visualizes the concept of noise in a communication channel and the need for sufficient signal amplitude to distinguish events.
Animated decision trees expand downwards, showing branching based on the number of differences per symbol (s) and the number of symbols (n).
Tree nodes
Branches
Leaves
Text labels for s and n
The trees grow level by level, increasing the number of leaves exponentially.
The branching factor at each node remains constant for a given tree.
Illustrates how the message space size () is derived from the combinatorics of sequential symbol choices.
Black background with a small white block and two folded cards labeled HARD and SOFT.
Narration introduces a hard versus soft pluck communication system.
Small white block
Card labeled HARD
Card labeled SOFT
Black background
The scene establishes two distinguishable physical signal types before the animated tree appears.
Only two symbol types are visible in this setup.
The cards represent possible differences per symbol for the first communication example.
A white root node branches into red leaf nodes; the bottom label changes from Message space to Message space .
Legend shows Differences/symbol , 3, 4, 26 and Symbols/sec , 2, 3, 4.
Root node
Branching lines
Red leaf nodes
S and N legends
Message space label
The tree grows from one level to two levels.
The message-space label changes from 2 to 4.
The branching factor remains 2 throughout this interval.
The animation visualizes possible messages, reaching for two symbols.
Hands place a third folded card labeled MED between HARD and SOFT.
Narration introduces hard versus medium versus soft plucks.
Card labeled HARD
Card labeled MED
Card labeled SOFT
Hands
A third distinguishable symbol type is added to the physical demonstration.
The symbols remain discrete and visually separated on cards.
The scene changes the alphabet size from to .
A three-branching tree appears with labels Message space , then = 9, then = 27.
Narration states and 27 messages with three plucks.
Root node
Three-way branches
White intermediate nodes
Red leaf nodes
Message space label
The tree expands from one level to two levels and then to three levels.
The message-space label changes from 3 to 9 to 27.
Each node branches into three choices.
The animation visualizes possible messages for , 2, and 3.
Hands use a green marker to write letters on white paper; visible letters include B, L, F, and A.
Narration shifts to Alice and Bob exchanging written notes containing only two letters.
The paper orientation changes and not every written character is fully legible.
White paper
Green marker
Handwritten letters
The demonstration moves from pluck cards to written characters on paper.
The example concerns discrete written symbols rather than continuous sound.
The handwritten letters illustrate that a written alphabet can be treated as a set of distinguishable symbols for message counting.
Narrator asks why not send a thousand or a million different voltage levels per pulse, then explains that fine-grain differences cause receiving difficulties.
Narrator states that electrical noise limits resolution.
One might think a communication system can simply keep adding more voltage levels per pulse to increase capacity indefinitely.
The clip states that fine-grained differences become difficult on the receiving end, and in electrical systems the resolution of those differences is limited by electrical noise.
Narrator says there was one other way to increase capacity: increase the number of different signaling events.
The string example shows HARD, MED, SOFT and pitch variation rather than only two signal types.
A learner may assume communication capacity is improved only by increasing pulse rate or by using a fixed binary on/off alphabet.
The clip emphasizes enlarging the alphabet of distinguishable signaling events, such as multiple pluck types or multiple signed current/voltage levels.
Narration explicitly says we no longer care about the meaning applied to these chains of differences, merely how many different messages are possible.
Binary waveforms, match commands, jellyfish, and alien writing are shown as different possible meanings.
One might think that understanding or defining the semantic content of a message is necessary to determine a communication system's capacity.
The clip states that capacity is first treated as the number of different messages that could be sent; meaning may be numbers, names, feelings, music, or an unknown alphabet without changing the counting framework.
Changing S from 2 to 3 to 26 produces message-space values 4, 9, 27, and 676 for comparable message lengths.
Narration contrasts hard/soft, hard/medium/soft, and 26-letter written notes.
One might assume that the number of possible messages is determined only by how many symbols are sent.
Editorial clarification based on the video examples: the count depends on both the number of choices per symbol S and the number of symbols N, through . Increasing either factor changes the message space.
The string example follows the narration’s statement that capacity can be increased by increasing different signaling events.
The Alice-and-Bob string example applies the general principle that more distinguishable signaling events can increase communication-system capacity.
Narrator says Edison implemented the idea and applied it to the Morse code system.
The quadruplex telegraph is presented as a historical electrical application of increasing the number of signaling events.
Narrator connects the four current values to Western Union sending more messages without building new lines.
The practical Western Union benefit depends on the quadruplex system’s four distinguishable signaling levels.
Narrator contrasts adding many voltage levels with the limitation caused by electrical noise.
Noise limits the strategy of increasing signaling events by adding many closely spaced voltage levels, contrasting with the successful use of a small number of well-separated quadruplex levels.
The oscilloscope trace appears after the narration about electrical noise limiting resolution.
The clip does not explicitly label the visible trace as a noise measurement.
The oscilloscope/probe demonstration provides a visual instance of inspecting an electrical line where noise-limited resolution matters.
The narrator transitions from discussing noise to defining the capacity of a communication system.
Understanding the impact of noise is a prerequisite for defining system capacity, as capacity must account for reliable transmission despite noise.
The narrator states, 'these parameters can be thought of as a decision tree of possibilities'.
The parameters n and s are applied to construct the decision tree model used to derive the message space size.
Narration says we can use the message space to define exactly how many differences are possible and frames capacity as how many different things you could say.
The message-space formula is used to quantify the intuitive capacity notion introduced in the narration.
Narration says the important realization is that we no longer care about meaning, merely how many different messages are possible.
The counting framework contrasts with semantic interpretation: message space counts distinguishable sequences rather than understood meanings.
The binary tree label changes to Message space .
Narration states four possible messages for two plucks in a hard-versus-soft system.
The hard-versus-soft two-pluck example is the special case , of the general message-space formula.
The ternary tree labels show 3, 9, and 27.
Narration states and 27 messages with three plucks.
The hard/medium/soft pluck example applies the general formula with and , 2, 3.
The 26-way tree expands to Message space .
Narration states possible messages for two-letter notes.
The written-note example applies the general formula with and .
Narrator states that increasing the number of different signaling events is another way to increase communication-system capacity.
Narrator gives hard, medium, soft, high-pitch, and low-pitch plucks as examples.
Labels HARD, MED, SOFT appear.
Narrator says two directions and two intensities give four different current values.
The values +3, +1, -1, -3 are displayed.
Narrator says Western Union could send more messages without building new lines.
Narrator asks why not send a thousand or a million voltage levels and answers that electrical noise limits resolution.
Narrator says if we attach a probe to any electrical line.
Oscilloscope labels PROBE COMP ~ 5V, CH 1, CH 2, CH1 100V, and M 1.00ms are visible.
The final spoken explanation is incomplete in the supplied clip.
Discussion of noise sources and signal amplitude.
Definition of symbol rate and baud.
Derivation of message space size using a tree model.
Repeated on-screen label "Message space ".
Narration defines capacity using how many different things could be said.
Narration states possible messages for two-letter notes.
Tree label changes from 26 to 676.
Narration says we no longer care about meaning, merely how many different messages are possible.
Waveforms, matches, jellyfish, and alien writing illustrate different meanings.
Covered · Narration states that increasing the number of different signaling events is another way to increase communication-system capacity, with montage visuals of multiple selectable states.
Covered · Alice and Bob string example: hard/medium/soft plucks and high/low pitch plucks by changing cable tension.
Covered · Edison/Morse-code quadruplex principle: weak and strong batteries, forward and reverse current, and displayed levels +3, +1, -1, -3.
Covered · Western Union benefit and identification of the quadruplex telegraph, accompanied by historical footage and The Quadruplex schematic.
Covered · Narration explains why many closely spaced voltage levels are difficult to receive and attributes the limit to electrical noise; SIGNAL meter visual supports the point.
Covered · Oscilloscope probe and CH1 display with labels PROBE COMP ~ 5V, CH 1, CH 2, 100V, and M 1.00ms; visible noisy trace illustrates electrical-line inspection.
Covered · Final one-second continuation of the oscilloscope/noise visual context; no additional distinct mathematical event is identifiable beyond the already covered probe-and-trace demonstration.
Covered · Oscilloscope demonstration of noise and signal amplitude.
Covered · Definition of the two key parameters: symbol rate (n) and differences per symbol (s).
Covered · Derivation and visualization of the message space size () using decision trees.
Covered · Transition to a physical example with blocks, no new mathematical concepts introduced in this short segment.
Covered · Physical HARD and SOFT cards introduce a binary communication alphabet.
Covered · Binary tree expands to two levels and shows message space 4.
Covered · A MED card is added, changing the physical alphabet to three choices.
Covered · Ternary tree shows message spaces 3, 9, and 27.
Covered · Handwritten letters introduce a written-note communication example.
Covered · 26-way tree expands to message space 676.
Covered · Binary waveform grid illustrates meaning-independent signal sequences.
Covered · Match split-screen labels ATTACK and NO ATTACK as possible meanings.
Covered · Jellyfish and unfamiliar script support the claim that meanings can vary or be unknown.
Covered · Brief four-branch tree displays message space 16.
Covered · Tree recap accompanies the definition of capacity as the number of different things that could be said.
Covered · Rolling dice accompany the transition to modern information theory.
Covered · Screen is black with no additional mathematical content.
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