explain xkcd - User contributions [en]

2120: Brain Hemispheres

2019-03-06T23:32:21Z

Ethan:

{{comic
| number = 2120
| date = March 6, 2019
| title = Brain Hemispheres
| image = brain_hemispheres.png
| titletext = Neurologically speaking, the LEFT hand is actually the one at the end of the RIGHT arm.
}}

==Explanation==
{{incomplete|Created by an AUTONOMOUS LEG and a CHICKEN. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}
It is thought that the right half of the brain controls the left arm and left leg, and vice versa for the left half of the brain, [https://arxiv.org/pdf/1003.1872.pdf competing] [https://link.springer.com/article/10.1007%2FBF02972358 theories] exist for why this is the case. Also, many people incorrectly argue that different parts of the brain control logic and emotion, due to the importance of the [[https://www.sciencedirect.com/science/article/pii/S0028393211000285?via%3Dihub left]] brain for language processing. Randall joins and spoofs these by suggesting that the right brain instead controls the upper torso. This would suggest that your left leg moves independently of your brain. To explain the areas of the body controlled by both halves of the brain, Randall declares those sections "disputed," which suggests that the halves of your brain fight for control of the region.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[A stick figure with the left half of the brain colored orange and the right half colored blue. A blue box is overlaid over the left half of the body, and an orange box is overlaid over the top half. An arrow labeled:'DISPUTED/DUAL CONTROL' points towards the overlapping area.]
:'''Neuroscience Fact:'''
:The LEFT half of the brain actually controls the RIGHT half of the body... [Arrow pointing to blue rectangle]
:...while the RIGHT half of the brain actually controls the TOP half of the body. [Arrow pointing to orange rectangle]
:This leg is fully autonomous. [Arrow pointing to stick figure's left leg]

{{comic discussion}}

[[Category:Comics with color]]
[[Category:Comics featuring Cueball]]
[[Category:Biology]]

2091: Million, Billion, Trillion

2019-01-31T16:12:50Z

Ethan: /* Transcript */ Changed point things.

{{comic
| number = 2091
| date = December 28, 2018
| title = Million, Billion, Trillion
| image = million_billion_trillion.png
| titletext = You can tell most people don’t really assign an absolute meaning to these numbers because in some places and time periods, “billion” has meant 1,000x what it's meant in others, and a lot of us never even noticed.
}}

==Explanation==
{{incomplete|This needs about a thousand years of rewriting, and I assume we'll want to do a chart of X and Y positions as with most chart comics. Do NOT delete this tag too soon.}}
Much like [[558: 1000 Times|comic 558]], this comic addresses the difficulty ordinary people have with large numbers. Though most if not all people intuitively understand the difference between one object and two objects, or one object and ten objects, or even one object and a hundred objects, as numbers increase most people's ability to innately conceive of the numbers being discussed decreases remarkably quickly. When numbers reach the millions and the billions, and especially the trillions, most people don't truly process the numbers at all, and instead conceive of them as some version of a drastically-oversimplified concept such as "very big." Where comparing one to ten is simple, comparing "very big" to a different "very big" can prove extremely challenging, and will certainly require non-intuitive, conscious thinking.

The comic represents this challenge by providing a graph which represents [[Randall]]'s ''intuitive'' conception of the values of various very large numbers, and said conception's misalignment with reality. Though some trends reflect the real value of the numbers on the graph, i.e. 100 million larger than 10 million larger than 1 million and 1 billion larger than 1 million, the curve is far from the linear (exponential on the log-scaled axes) path it should take, with 1 billion being intuitively understood as less than 100 million, based, presumably, on the fact, easily comprehended on an intuitive level, that '''100 is larger than 1''', and therefore the presence of 100 in 100 million places it at a higher value than the 1 in 1 billion would place the latter. In reality, of course, 1 billion is ten times larger than 100 million, but the comic deals not with actual reality, but with the perception of reality of these numbers '''before conscious thought is applied'''.

The most interesting parts of the graph, and the parts where the disconnect between intuition and reality becomes clearest, are the dashed sections labeled with question marks, the one between 100 million and 1 billion, the other between 100 billion and 1 trillion. Here two competing intuitive understandings compete for dominance. On the one hand, the intuitive understanding described above, with 100 trumping 1, would see the curve taking a sharp downturn. On the other hand, the path from 100 million to 1 billion is paved with such numbers as 500 million, 700 million, and 900 million, all of which would theoretically be seen intuitively as larger than 100 million, thanks to the fact that 9 is greater than 7, and 7 greater than 5, and so on, bending the curve up rather than down. These two conflicting intuitions leave Randall with no single intuitive path for the two dashed sections, leading to their dashed and questioned state.

The comic's caption and title highlight another problem surrounding the intuitive grasping of large numbers: the flaws in the English words used for them. For instance, nothing about the word "million" suggests smallness relative to the word "billion" on an intuitive scale. This unintuitive language contributes greatly to the "100 trumps 1" intuitive fallacy described above.

=== Long scale and short scale ===

The title text references a highly relevant disconnect between the {{w|Long_and_short_scales|long and short scales of large numbers}}.

For all English speakers, and for most languages, 1 '''''million''''' constitutes 1,000 thousands, or, less ambiguously, 10^6. However, this is the last of the consensus numbers, and the definition of what should be the "next step" varies depending on how each country's language evolved.
* In many English-speaking countries, 1,000 millions equals 1 billion, or 1000*10^6=10^9; this convention is known as the '''short-scale'''.
* [https://en.oxforddictionaries.com/explore/how-many-is-a-billion/ In historical Britain] and many other countries with a language derived from French or Spanish, the "next step" may be named a thousand million, and 1 billion equals ''1 million'' millions, or 10^6*10^6=10^'''12''', with the base unit changing when you have a unit's worth multiple of the unit; this convention is known as the long-scale. (Note that this is no longer used in Britain since 1974.)
* In European languages where the '''long-scale''' system is used, 10^9 may be named a thousand million, or receive a name with a special suffix: the word milliard (meaning 1,000 million) is used in some form (e.g. milliard in French, Milliarde in German, milliard in Danish, milliárd in Hungarian, etc.), with the word billion defined as 1,000 milliard (or 1,000,000 million). In these languages, a billion never meant 1,000 million as it does in the short-scale system.
* Successive units, such as trillion, increase by the same multiple as one billion divided by one million - by 1,000 in the short-scale system and 1,000,000 in the long-scale system.

In other words, 1 billion objects in a country using the short-scale would be 1,000 million objects in a country using the long-scale; at the "next step", 1 trillion in the short-scale would be named 1 billion in the long-scale, despite the fact that the number of objects has remained the same. This difference between languages using the short-scale and the long-scale often causes confusion when translating articles with large numbers in them, as translators sometimes fail to change between short-scale and long-scale schemes, wrongly translating large numbers to incorrect values.

The fact that such a staggering difference of terminology was able to exist and be almost completely unknown to many supports Randall's point about the failure of human intuition in the discussion of extremely large numbers.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[A graph with Y-axis labeled “Perceived size of number” and X-axis labeled “Actual size of number (log scale)”.]
:[The line graph shows points that are labeled with the following numbers from “1 million” to “100 trillion”:]

{{incomplete|The "relative" coordinates are not relative, as the perceived size become smaller as the number grows. Please edit the coords to be "right"-ish. (To scale)}}
:['''Points on graph:''']
:[''Note: Coordinates are relative because the graph's y-axis has no shown scale.'']
:{| class="wikitable" style="text-align: center;"
|1 million
|[''(1, 1)'']
|-
|10 million
|[''(1, 2)'']
|-
|100 million
|[''(1, 3)'']
|-
|1 billion
|[''(1, 1.5)'']
|-
|10 billion
|[''(1, 3)'']
|-
|100 billion
|[''(1, 4)'']
|-
|1 trillion
|[''(1, 3)'']
|-
|10 trillion
|[''(1, 4)'']
|-
|100 trillion
|[''(1, 5)'']
|}
:[The perceived size increases between most numbers, but decreases between 100 million and 1 billion, and between 100 billion and 1 trillion. The decreases are shown as dashed lines labeled “?”, in contrast to the solid unlabeled lines between the increases. The increases and decreases in perceived size become smaller as the numbers grow in actual size.]
:[Caption below the panel:]
:Talking about large numbers is hard

{{comic discussion}}

[[Category:Line graphs]]

2034: Equations

2019-01-31T02:16:41Z

Ethan: /* Explanation */ E=mc² was breaking flow of text; fixed.

{{comic
| number = 2034
| date = August 17, 2018
| title = Equations
| image = equations.png
| titletext = All electromagnetic equations: The same as all fluid dynamics equations, but with the 8 and 23 replaced with the permittivity and permeability of free space, respectively.
}}
==Explanation==

This comic gives a set of mock equations. To anyone not familiar with the field in question they look pretty similar to what you might find in research papers or on the relevant Wikipedia pages. Most of the jokes are related to the symbols or "look" of most equations in the given field.

The comic makes jokes about the fields of kinematics, number theory, fluid dynamics, quantum mechanics, chemistry, quantum gravity, gauge theory, cosmology, and physics equations. Of course, all of the equations listed are not real equations (<math>\pi-\infty</math> and H2EAT are clearly jokes and making a mockery of the given field). As always, Randall is just having a laugh.

:<math>E=K_{0}t+\frac{1}{2}\rho{}vt^2</math>
;All kinematics equations
Most kinematics equations tend to make heavy use of constants, addition, powers, and multiplication. This specific equation resembles the actual kinematics equation d = vt + 1/2at^2, but replaces a (acceleration) with v (velocity) and replaces velocity with "K0", which is not a term used in kinematics.

:<math>K_{n}=\sum_{i=0}^{\infty}\sum_{\pi=0}^{\infty}(n-\pi)(i+e^{\pi-\infty})</math>
;All number theory equations
Randall jokes about how number theory often involves the use of summations. The use of ''π'' as an integer variable in the double summation is a joke, as ''π'' is essentially always used for the well-known constant 3.14159..., not a variable. The use of ''i'' as a summation variable '''is''' common, though it can also be confused with the imaginary unit √-1. The constants ''e'', ''i'', and ''π'', as well as the theoretical upper bound <math>\infty</math>, often appear in number theory equations.

:<math>\frac{\partial}{\partial{t}}\nabla\!\cdot\!\rho=\frac{8}{23}\int\!\!\!\!\int\!\!\!\!\!\!\!\!\!\subset\!\!\supset\rho\,{ds}\,{dt}\cdot{}\rho\frac{\partial}{\partial\nabla}</math>
;All fluid dynamics equations
Fluid dynamics equations often involve copious integrals, especially those over closed contours as done here, which are often the main telling factors of those equations to an outsider. The time derivative and gradient operator <math>\nabla</math> are common in fluid dynamics, mostly via the Navier-Stokes equation, and the fluid density <math>\rho</math> is one of the functions of central importance. The fraction 8/23 is a comically weird choice, but various unexpected fractions do pop up in fluid dynamics. The ds and dt go with the double contour integral (s is probably distance, t is time), but the derivative with respect to <math>\nabla</math> at the end is very much not allowed.

:<math>|\psi_{x,y}\rangle=A(\psi)A(|x\rangle\otimes|y\rangle)</math>
;All quantum mechanics equations
Quantum mechanics often involves some of the foreign-looking symbols listed, including {{w|Bra–ket notation|bra-ket notation}}, the {{w|Tensor product|tensor product}}, and the Greek letter Psi for a quantum state. Specifically, the left side of the equation is a ket state labeled Psi that depends on x and y (probably positions), while the right-hand side may be an operator A that depends on the state Psi (it is very unusual to have such a dependence) acting on what looks like another copy of that operator which depends on the outer product of states labeled by x and y (again strange). A charitable interpretation could be that the second A is the eigenfunction A of the operator A. Normally this is clearly indicated by giving the operator a “hat” (^ symbol) or making the eigenfunction into a ket eigenstate, but since the equation is intentionally nonsense both A’s are left ambiguous. Also note that the bra-ket math is inconsistent here, as the left side is a ket, but the right side is just two A’s, which are either operators or functions but are definitely not kets.

:<math>CH_4+OH+HEAT\rightarrow{}H_2O+CH_{2}+H_2EAT</math>
;All chemistry equations
Chemistry equations use formulas of chemical compounds to describe a chemical reaction. Such equations show the starting chemicals on the left side and the resulting products on the right side, as displayed. Sometimes such an equation might optionally indicate that an {{w|activation energy}} is required, for the reaction to take place in a sensible timeframe, e.g. by heating. A reaction requiring heating is usually indicated by a Greek capital letter Delta (''Δ'') or a specified temperature above the reaction arrow, however this comic uses the "+ HEAT" term on the left side instead. The joke is that Randall interprets "HEAT" to be another chemical, which reacts with Hydrogen (H) to H2EAT, which is nonsensical, as heat is transferred energy here, not added matter. Regardless of this, Randall gets the {{w|stoichiometry}} of this equation correct, with the same number of all types of 'atoms' on each side of the equation.

:<math>SU(2)U(1)\times{}SU(U(2))</math>
;All quantum gravity equations
Quantum gravity uses mathematical {{w|Group (mathematics)|groups}} denoted by uppercase letters, as shown. {{w|Special unitary group|SU(2)}}, {{w|Unitary group|U(1)}}, and {{w|Unitary group|U(2)}} are all well-studied groups, though 'SU(U(2))' makes no sense. The lack of relator means this expression isn't an equation. Here is a possible pun, on "Sue you too... you won"... "Sue you, you too", though it's unclear how it fits in here.

:Sg=(-1)/(2ε̄) ið(̂ ξ0 ⨢ pε ρvabc⋅η0)̂ f̵a0 λ(ξ) ψ(0a)
;All gauge theory equations
Gauge theory is a subset of field theory. Most gauge theory equations appear to have many strange-looking constants and variables with odd labels.

:<math>H(t)+\Omega+G\!\cdot\!\Lambda...\begin{cases}...>0\mathsf{\ (Hubble\ model)}\\
...=0\mathsf{\ (Flat\ sphere\ model)}\\
...<0\mathsf{\ (Bright\ dark\ matter\ model)}
\end{cases}</math>
;All cosmology equations
Cosmology is the science of the development and ultimate fate of the universe. The joke here may be pertaining to the different models accepted in the field of cosmology. H is the {{w|Hubble's law#Time-dependence of Hubble parameter|Hubble parameter}}, Ω is the universal {{w|Friedmann equations#Density parameter|density parameter}}, G is the {{w|gravitational constant}}, and Λ is the {{w|cosmological constant}}.

:Ĥ - u̧0 = 0
;All truly deep physics equations
The joke about the "truly deep physics equations" is that most of the universal physics equations are simple, almost exceedingly so. One example is Einstein's ''E = mc²''.

The title text is referencing the fact that the electric and magnetic fields are often explained to physics students using an analogy with fluid dynamics, as well as the fact that they do share some similarities (only in terms of mathematical description as three-dimensional vector fields) with fluids. The permittivity constant (represented with ''ε''0) and the permeability constant (represented with ''μ''0) are coefficients that relate the amount of charge required to cause a specific amount of electric flux in a vacuum and the ability of vacuum to support the formation of magnetic fields, respectively. They appear frequently in Maxwell's equations (the equations that define the electric and magnetic fields in classical mechanics), so Randall is making the joke that any surface integral with them in it automatically is an electromagnetism equation.

There is also the joke that because Ĥ - u̧0 = 0, one can simplify and find that Ĥ = u̧0. This obviously makes no sence as that means both symbols are equal, and therefore the equation is meaningless (which it is).

==Transcript==
:[Nine equations are listed, three in the top row and two in each of the next three rows. Below each equation there are labels:]

:E=K0t+1/2 ρvt2
:All kinematics equations

:Kn=∑∞i=0∑∞π=0(n-π)(i-eπ-∞) [K sub n = the summation from i = 0 to infinity of the sum from pi = 0 to infinity of (n - pi) * (i-e^(pi-infinity))]
:All number theory equations

:∂/∂t ∇⋅ρ=8/23 (∯ ρ ds dt ⋅ ρ ∂/∂∇)
:All fluid dynamics equations

:|ψx,y〉=A(ψ)A(|x〉⊗|y〉)
:All quantum mechanics equations

:CH4+OH+HEAT→H2O+CH2+H2EAT
:All chemistry equations

:SU(2)U(1)×SU(U(2))
:All quantum gravity equations

:Sg=(-1)/(2ε̄) ið(̂ ξ0 ⨢ pε ρvabc⋅η0)̂ f̵a0 λ(ξ) ψ(0a)
:All gauge theory equations

:H(t)+Ω+G⋅Λ ...
:[There is a brace linking the three cases together.]
:... > 0 (Hubble model)
:... = 0 (Flat sphere model)
:... < 0 (Bright dark matter model)
:All cosmology equations

:Ĥ - u̧0 = 0
:All truly deep physics equations

{{comic discussion}}

[[Category:Science]]
[[Category:Physics]]
[[Category:Math]]
[[Category:Chemistry]]
[[Category:Astronomy]]

2034: Equations

2019-01-31T02:14:51Z

Ethan: /* Explanation */ Added a bit to "All truly deep physics equations"

{{comic
| number = 2034
| date = August 17, 2018
| title = Equations
| image = equations.png
| titletext = All electromagnetic equations: The same as all fluid dynamics equations, but with the 8 and 23 replaced with the permittivity and permeability of free space, respectively.
}}
==Explanation==

This comic gives a set of mock equations. To anyone not familiar with the field in question they look pretty similar to what you might find in research papers or on the relevant Wikipedia pages. Most of the jokes are related to the symbols or "look" of most equations in the given field.

The comic makes jokes about the fields of kinematics, number theory, fluid dynamics, quantum mechanics, chemistry, quantum gravity, gauge theory, cosmology, and physics equations. Of course, all of the equations listed are not real equations (<math>\pi-\infty</math> and H2EAT are clearly jokes and making a mockery of the given field). As always, Randall is just having a laugh.

:<math>E=K_{0}t+\frac{1}{2}\rho{}vt^2</math>
;All kinematics equations
Most kinematics equations tend to make heavy use of constants, addition, powers, and multiplication. This specific equation resembles the actual kinematics equation d = vt + 1/2at^2, but replaces a (acceleration) with v (velocity) and replaces velocity with "K0", which is not a term used in kinematics.

:<math>K_{n}=\sum_{i=0}^{\infty}\sum_{\pi=0}^{\infty}(n-\pi)(i+e^{\pi-\infty})</math>
;All number theory equations
Randall jokes about how number theory often involves the use of summations. The use of ''π'' as an integer variable in the double summation is a joke, as ''π'' is essentially always used for the well-known constant 3.14159..., not a variable. The use of ''i'' as a summation variable '''is''' common, though it can also be confused with the imaginary unit √-1. The constants ''e'', ''i'', and ''π'', as well as the theoretical upper bound <math>\infty</math>, often appear in number theory equations.

:<math>\frac{\partial}{\partial{t}}\nabla\!\cdot\!\rho=\frac{8}{23}\int\!\!\!\!\int\!\!\!\!\!\!\!\!\!\subset\!\!\supset\rho\,{ds}\,{dt}\cdot{}\rho\frac{\partial}{\partial\nabla}</math>
;All fluid dynamics equations
Fluid dynamics equations often involve copious integrals, especially those over closed contours as done here, which are often the main telling factors of those equations to an outsider. The time derivative and gradient operator <math>\nabla</math> are common in fluid dynamics, mostly via the Navier-Stokes equation, and the fluid density <math>\rho</math> is one of the functions of central importance. The fraction 8/23 is a comically weird choice, but various unexpected fractions do pop up in fluid dynamics. The ds and dt go with the double contour integral (s is probably distance, t is time), but the derivative with respect to <math>\nabla</math> at the end is very much not allowed.

:<math>|\psi_{x,y}\rangle=A(\psi)A(|x\rangle\otimes|y\rangle)</math>
;All quantum mechanics equations
Quantum mechanics often involves some of the foreign-looking symbols listed, including {{w|Bra–ket notation|bra-ket notation}}, the {{w|Tensor product|tensor product}}, and the Greek letter Psi for a quantum state. Specifically, the left side of the equation is a ket state labeled Psi that depends on x and y (probably positions), while the right-hand side may be an operator A that depends on the state Psi (it is very unusual to have such a dependence) acting on what looks like another copy of that operator which depends on the outer product of states labeled by x and y (again strange). A charitable interpretation could be that the second A is the eigenfunction A of the operator A. Normally this is clearly indicated by giving the operator a “hat” (^ symbol) or making the eigenfunction into a ket eigenstate, but since the equation is intentionally nonsense both A’s are left ambiguous. Also note that the bra-ket math is inconsistent here, as the left side is a ket, but the right side is just two A’s, which are either operators or functions but are definitely not kets.

:<math>CH_4+OH+HEAT\rightarrow{}H_2O+CH_{2}+H_2EAT</math>
;All chemistry equations
Chemistry equations use formulas of chemical compounds to describe a chemical reaction. Such equations show the starting chemicals on the left side and the resulting products on the right side, as displayed. Sometimes such an equation might optionally indicate that an {{w|activation energy}} is required, for the reaction to take place in a sensible timeframe, e.g. by heating. A reaction requiring heating is usually indicated by a Greek capital letter Delta (''Δ'') or a specified temperature above the reaction arrow, however this comic uses the "+ HEAT" term on the left side instead. The joke is that Randall interprets "HEAT" to be another chemical, which reacts with Hydrogen (H) to H2EAT, which is nonsensical, as heat is transferred energy here, not added matter. Regardless of this, Randall gets the {{w|stoichiometry}} of this equation correct, with the same number of all types of 'atoms' on each side of the equation.

:<math>SU(2)U(1)\times{}SU(U(2))</math>
;All quantum gravity equations
Quantum gravity uses mathematical {{w|Group (mathematics)|groups}} denoted by uppercase letters, as shown. {{w|Special unitary group|SU(2)}}, {{w|Unitary group|U(1)}}, and {{w|Unitary group|U(2)}} are all well-studied groups, though 'SU(U(2))' makes no sense. The lack of relator means this expression isn't an equation. Here is a possible pun, on "Sue you too... you won"... "Sue you, you too", though it's unclear how it fits in here.

:Sg=(-1)/(2ε̄) ið(̂ ξ0 ⨢ pε ρvabc⋅η0)̂ f̵a0 λ(ξ) ψ(0a)
;All gauge theory equations
Gauge theory is a subset of field theory. Most gauge theory equations appear to have many strange-looking constants and variables with odd labels.

:<math>H(t)+\Omega+G\!\cdot\!\Lambda...\begin{cases}...>0\mathsf{\ (Hubble\ model)}\\
...=0\mathsf{\ (Flat\ sphere\ model)}\\
...<0\mathsf{\ (Bright\ dark\ matter\ model)}
\end{cases}</math>
;All cosmology equations
Cosmology is the science of the development and ultimate fate of the universe. The joke here may be pertaining to the different models accepted in the field of cosmology. H is the {{w|Hubble's law#Time-dependence of Hubble parameter|Hubble parameter}}, Ω is the universal {{w|Friedmann equations#Density parameter|density parameter}}, G is the {{w|gravitational constant}}, and Λ is the {{w|cosmological constant}}.

:Ĥ - u̧0 = 0
;All truly deep physics equations
The joke about the "truly deep physics equations" is that most of the universal physics equations are simple, almost exceedingly so. One example is Einstein's <math>E = mc^2</math>.

The title text is referencing the fact that the electric and magnetic fields are often explained to physics students using an analogy with fluid dynamics, as well as the fact that they do share some similarities (only in terms of mathematical description as three-dimensional vector fields) with fluids. The permittivity constant (represented with ''ε''0) and the permeability constant (represented with ''μ''0) are coefficients that relate the amount of charge required to cause a specific amount of electric flux in a vacuum and the ability of vacuum to support the formation of magnetic fields, respectively. They appear frequently in Maxwell's equations (the equations that define the electric and magnetic fields in classical mechanics), so Randall is making the joke that any surface integral with them in it automatically is an electromagnetism equation.

There is also the joke that because Ĥ - u̧0 = 0, one can simplify and find that Ĥ = u̧0. This obviously makes no sence as that means both symbols are equal, and therefore the equation is meaningless (which it is).

==Transcript==
:[Nine equations are listed, three in the top row and two in each of the next three rows. Below each equation there are labels:]

:E=K0t+1/2 ρvt2
:All kinematics equations

:Kn=∑∞i=0∑∞π=0(n-π)(i-eπ-∞) [K sub n = the summation from i = 0 to infinity of the sum from pi = 0 to infinity of (n - pi) * (i-e^(pi-infinity))]
:All number theory equations

:∂/∂t ∇⋅ρ=8/23 (∯ ρ ds dt ⋅ ρ ∂/∂∇)
:All fluid dynamics equations

:|ψx,y〉=A(ψ)A(|x〉⊗|y〉)
:All quantum mechanics equations

:CH4+OH+HEAT→H2O+CH2+H2EAT
:All chemistry equations

:SU(2)U(1)×SU(U(2))
:All quantum gravity equations

:Sg=(-1)/(2ε̄) ið(̂ ξ0 ⨢ pε ρvabc⋅η0)̂ f̵a0 λ(ξ) ψ(0a)
:All gauge theory equations

:H(t)+Ω+G⋅Λ ...
:[There is a brace linking the three cases together.]
:... > 0 (Hubble model)
:... = 0 (Flat sphere model)
:... < 0 (Bright dark matter model)
:All cosmology equations

:Ĥ - u̧0 = 0
:All truly deep physics equations

{{comic discussion}}

[[Category:Science]]
[[Category:Physics]]
[[Category:Math]]
[[Category:Chemistry]]
[[Category:Astronomy]]

2091: Million, Billion, Trillion

2019-01-30T02:34:27Z

Ethan:

{{comic
| number = 2091
| date = December 28, 2018
| title = Million, Billion, Trillion
| image = million_billion_trillion.png
| titletext = You can tell most people don’t really assign an absolute meaning to these numbers because in some places and time periods, “billion” has meant 1,000x what it's meant in others, and a lot of us never even noticed.
}}

==Explanation==
{{incomplete|This needs about a thousand years of rewriting, and I assume we'll want to do a chart of X and Y positions as with most chart comics. Do NOT delete this tag too soon.}}
Much like [[558: 1000 Times|comic 558]], this comic addresses the difficulty ordinary people have with large numbers. Though most if not all people intuitively understand the difference between one object and two objects, or one object and ten objects, or even one object and a hundred objects, as numbers increase most people's ability to innately conceive of the numbers being discussed decreases remarkably quickly. When numbers reach the millions and the billions, and especially the trillions, most people don't truly process the numbers at all, and instead conceive of them as some version of a drastically-oversimplified concept such as "very big." Where comparing one to ten is simple, comparing "very big" to a different "very big" can prove extremely challenging, and will certainly require non-intuitive, conscious thinking.

The comic represents this challenge by providing a graph which represents [[Randall]]'s ''intuitive'' conception of the values of various very large numbers, and said conception's misalignment with reality. Though some trends reflect the real value of the numbers on the graph, i.e. 100 million larger than 10 million larger than 1 million and 1 billion larger than 1 million, the curve is far from the linear (exponential on the log-scaled axes) path it should take, with 1 billion being intuitively understood as less than 100 million, based, presumably, on the fact, easily comprehended on an intuitive level, that '''100 is larger than 1''', and therefore the presence of 100 in 100 million places it at a higher value than the 1 in 1 billion would place the latter. In reality, of course, 1 billion is ten times larger than 100 million, but the comic deals not with actual reality, but with the perception of reality of these numbers '''before conscious thought is applied'''.

The most interesting parts of the graph, and the parts where the disconnect between intuition and reality becomes clearest, are the dashed sections labeled with question marks, the one between 100 million and 1 billion, the other between 100 billion and 1 trillion. Here two competing intuitive understandings compete for dominance. On the one hand, the intuitive understanding described above, with 100 trumping 1, would see the curve taking a sharp downturn. On the other hand, the path from 100 million to 1 billion is paved with such numbers as 500 million, 700 million, and 900 million, all of which would theoretically be seen intuitively as larger than 100 million, thanks to the fact that 9 is greater than 7, and 7 greater than 5, and so on, bending the curve up rather than down. These two conflicting intuitions leave Randall with no single intuitive path for the two dashed sections, leading to their dashed and questioned state.

The comic's caption and title highlight another problem surrounding the intuitive grasping of large numbers: the flaws in the English words used for them. For instance, nothing about the word "million" suggests smallness relative to the word "billion" on an intuitive scale. This unintuitive language contributes greatly to the "100 trumps 1" intuitive fallacy described above.

=== Long scale and short scale ===

The title text references a highly relevant disconnect between the {{w|Long_and_short_scales|long and short scales of large numbers}}.

For all English speakers, and for most languages, 1 '''''million''''' constitutes 1,000 thousands, or, less ambiguously, 10^6. However, this is the last of the consensus numbers, and the definition of what should be the "next step" varies depending on how each country's language evolved.
* In many English-speaking countries, 1,000 millions equals 1 billion, or 1000*10^6=10^9; this convention is known as the '''short-scale'''.
* [https://en.oxforddictionaries.com/explore/how-many-is-a-billion/ In historical Britain] and many other countries with a language derived from French or Spanish, the "next step" may be named a thousand million, and 1 billion equals ''1 million'' millions, or 10^6*10^6=10^'''12''', with the base unit changing when you have a unit's worth multiple of the unit; this convention is known as the long-scale. (Note that this is no longer used in Britain since 1974.)
* In European languages where the '''long-scale''' system is used, 10^9 may be named a thousand million, or receive a name with a special suffix: the word milliard (meaning 1,000 million) is used in some form (e.g. milliard in French, Milliarde in German, milliard in Danish, milliárd in Hungarian, etc.), with the word billion defined as 1,000 milliard (or 1,000,000 million). In these languages, a billion never meant 1,000 million as it does in the short-scale system.
* Successive units, such as trillion, increase by the same multiple as one billion divided by one million - by 1,000 in the short-scale system and 1,000,000 in the long-scale system.

In other words, 1 billion objects in a country using the short-scale would be 1,000 million objects in a country using the long-scale; at the "next step", 1 trillion in the short-scale would be named 1 billion in the long-scale, despite the fact that the number of objects has remained the same. This difference between languages using the short-scale and the long-scale often causes confusion when translating articles with large numbers in them, as translators sometimes fail to change between short-scale and long-scale schemes, wrongly translating large numbers to incorrect values.

The fact that such a staggering difference of terminology was able to exist and be almost completely unknown to many supports Randall's point about the failure of human intuition in the discussion of extremely large numbers.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[A graph with Y-axis labeled “Perceived size of number” and X-axis labeled “Actual size of number (log scale)”.]
:[The line graph shows points that are labeled with the following numbers from “1 million” to “100 trillion”:]

:'''Points on graph:'''
{{incomplete|The "relative" coordinates are not relative, as the perceived size become smaller as the number grows. Please edit the coords to be "right"-ish. (To scale)}}
:[''Note: Coordinates are relative because the graph's y-axis has no shown scale. Coordinates are in bold.'']
:{| class="wikitable" style="text-align: center;"
|1 million
|[''(1, 1)'']
|-
|10 million
|[''(1, 2)'']
|-
|100 million
|[''(1, 3)'']
|-
|1 billion
|[''(1, 1.5)'']
|-
|10 billion
|[''(1, 3)'']
|-
|100 billion
|[''(1, 4)'']
|-
|1 trillion
|[''(1, 3)'']
|-
|10 trillion
|[''(1, 4)'']
|-
|100 trillion
|[''(1, 5)'']
|}
:[The perceived size increases between most numbers, but decreases between 100 million and 1 billion, and between 100 billion and 1 trillion. The decreases are shown as dashed lines labeled “?”, in contrast to the solid unlabeled lines between the increases. The increases and decreases in perceived size become smaller as the numbers grow in actual size.]
:[Caption below the panel:]
:Talking about large numbers is hard

{{comic discussion}}

[[Category:Line graphs]]

2091: Million, Billion, Trillion

2019-01-30T02:30:26Z

Ethan:

{{comic
| number = 2091
| date = December 28, 2018
| title = Million, Billion, Trillion
| image = million_billion_trillion.png
| titletext = You can tell most people don’t really assign an absolute meaning to these numbers because in some places and time periods, “billion” has meant 1,000x what it's meant in others, and a lot of us never even noticed.
}}

==Explanation==
{{incomplete|This needs about a thousand years of rewriting, and I assume we'll want to do a chart of X and Y positions as with most chart comics. Do NOT delete this tag too soon.}}
Much like [[558: 1000 Times|comic 558]], this comic addresses the difficulty ordinary people have with large numbers. Though most if not all people intuitively understand the difference between one object and two objects, or one object and ten objects, or even one object and a hundred objects, as numbers increase most people's ability to innately conceive of the numbers being discussed decreases remarkably quickly. When numbers reach the millions and the billions, and especially the trillions, most people don't truly process the numbers at all, and instead conceive of them as some version of a drastically-oversimplified concept such as "very big." Where comparing one to ten is simple, comparing "very big" to a different "very big" can prove extremely challenging, and will certainly require non-intuitive, conscious thinking.

The comic represents this challenge by providing a graph which represents [[Randall]]'s ''intuitive'' conception of the values of various very large numbers, and said conception's misalignment with reality. Though some trends reflect the real value of the numbers on the graph, i.e. 100 million larger than 10 million larger than 1 million and 1 billion larger than 1 million, the curve is far from the linear (exponential on the log-scaled axes) path it should take, with 1 billion being intuitively understood as less than 100 million, based, presumably, on the fact, easily comprehended on an intuitive level, that '''100 is larger than 1''', and therefore the presence of 100 in 100 million places it at a higher value than the 1 in 1 billion would place the latter. In reality, of course, 1 billion is ten times larger than 100 million, but the comic deals not with actual reality, but with the perception of reality of these numbers '''before conscious thought is applied'''.

The most interesting parts of the graph, and the parts where the disconnect between intuition and reality becomes clearest, are the dashed sections labeled with question marks, the one between 100 million and 1 billion, the other between 100 billion and 1 trillion. Here two competing intuitive understandings compete for dominance. On the one hand, the intuitive understanding described above, with 100 trumping 1, would see the curve taking a sharp downturn. On the other hand, the path from 100 million to 1 billion is paved with such numbers as 500 million, 700 million, and 900 million, all of which would theoretically be seen intuitively as larger than 100 million, thanks to the fact that 9 is greater than 7, and 7 greater than 5, and so on, bending the curve up rather than down. These two conflicting intuitions leave Randall with no single intuitive path for the two dashed sections, leading to their dashed and questioned state.

The comic's caption and title highlight another problem surrounding the intuitive grasping of large numbers: the flaws in the English words used for them. For instance, nothing about the word "million" suggests smallness relative to the word "billion" on an intuitive scale. This unintuitive language contributes greatly to the "100 trumps 1" intuitive fallacy described above.

=== Long scale and short scale ===

The title text references a highly relevant disconnect between the {{w|Long_and_short_scales|long and short scales of large numbers}}.

For all English speakers, and for most languages, 1 '''''million''''' constitutes 1,000 thousands, or, less ambiguously, 10^6. However, this is the last of the consensus numbers, and the definition of what should be the "next step" varies depending on how each country's language evolved.
* In many English-speaking countries, 1,000 millions equals 1 billion, or 1000*10^6=10^9; this convention is known as the '''short-scale'''.
* [https://en.oxforddictionaries.com/explore/how-many-is-a-billion/ In historical Britain] and many other countries with a language derived from French or Spanish, the "next step" may be named a thousand million, and 1 billion equals ''1 million'' millions, or 10^6*10^6=10^'''12''', with the base unit changing when you have a unit's worth multiple of the unit; this convention is known as the long-scale. (Note that this is no longer used in Britain since 1974.)
* In European languages where the '''long-scale''' system is used, 10^9 may be named a thousand million, or receive a name with a special suffix: the word milliard (meaning 1,000 million) is used in some form (e.g. milliard in French, Milliarde in German, milliard in Danish, milliárd in Hungarian, etc.), with the word billion defined as 1,000 milliard (or 1,000,000 million). In these languages, a billion never meant 1,000 million as it does in the short-scale system.
* Successive units, such as trillion, increase by the same multiple as one billion divided by one million - by 1,000 in the short-scale system and 1,000,000 in the long-scale system.

In other words, 1 billion objects in a country using the short-scale would be 1,000 million objects in a country using the long-scale; at the "next step", 1 trillion in the short-scale would be named 1 billion in the long-scale, despite the fact that the number of objects has remained the same. This difference between languages using the short-scale and the long-scale often causes confusion when translating articles with large numbers in them, as translators sometimes fail to change between short-scale and long-scale schemes, wrongly translating large numbers to incorrect values.

The fact that such a staggering difference of terminology was able to exist and be almost completely unknown to many supports Randall's point about the failure of human intuition in the discussion of extremely large numbers.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[A graph with Y-axis labeled “Perceived size of number” and X-axis labeled “Actual size of number (log scale)”.]
:[The line graph shows points that are labeled with the following numbers from “1 million” to “100 trillion”:]

:'''Points on graph:'''
:[''Note: Coordinates are relative because the graph's y-axis has no shown scale. Coordinates are in bold.'']
:{| class="wikitable" style="text-align: center;"
|1 million
|[''(1, 1)'']
|-
|10 million
|[''(1, 2)'']
|-
|100 million
|[''(1, 3)'']
|-
|1 billion
|[''(1, 1.5)'']
|-
|10 billion
|[''(1, 3)'']
|-
|100 billion
|[''(1, 4)'']
|-
|1 trillion
|[''(1, 3)'']
|-
|10 trillion
|[''(1, 4)'']
|-
|100 trillion
|[''(1, 5)'']
|}
:[The perceived size increases between most numbers, but decreases between 100 million and 1 billion, and between 100 billion and 1 trillion. The decreases are shown as dashed lines labeled “?”, in contrast to the solid unlabeled lines between the increases. The increases and decreases in perceived size become smaller as the numbers grow in actual size.]
:[Caption below the panel:]
:Talking about large numbers is hard

{{comic discussion}}

[[Category:Line graphs]]

2091: Million, Billion, Trillion

2019-01-30T02:28:52Z

Ethan: Formatted into table.

{{comic
| number = 2091
| date = December 28, 2018
| title = Million, Billion, Trillion
| image = million_billion_trillion.png
| titletext = You can tell most people don’t really assign an absolute meaning to these numbers because in some places and time periods, “billion” has meant 1,000x what it's meant in others, and a lot of us never even noticed.
}}

==Explanation==
{{incomplete|This needs about a thousand years of rewriting, and I assume we'll want to do a chart of X and Y positions as with most chart comics. Do NOT delete this tag too soon.}}
Much like [[558: 1000 Times|comic 558]], this comic addresses the difficulty ordinary people have with large numbers. Though most if not all people intuitively understand the difference between one object and two objects, or one object and ten objects, or even one object and a hundred objects, as numbers increase most people's ability to innately conceive of the numbers being discussed decreases remarkably quickly. When numbers reach the millions and the billions, and especially the trillions, most people don't truly process the numbers at all, and instead conceive of them as some version of a drastically-oversimplified concept such as "very big." Where comparing one to ten is simple, comparing "very big" to a different "very big" can prove extremely challenging, and will certainly require non-intuitive, conscious thinking.

The comic represents this challenge by providing a graph which represents [[Randall]]'s ''intuitive'' conception of the values of various very large numbers, and said conception's misalignment with reality. Though some trends reflect the real value of the numbers on the graph, i.e. 100 million larger than 10 million larger than 1 million and 1 billion larger than 1 million, the curve is far from the linear (exponential on the log-scaled axes) path it should take, with 1 billion being intuitively understood as less than 100 million, based, presumably, on the fact, easily comprehended on an intuitive level, that '''100 is larger than 1''', and therefore the presence of 100 in 100 million places it at a higher value than the 1 in 1 billion would place the latter. In reality, of course, 1 billion is ten times larger than 100 million, but the comic deals not with actual reality, but with the perception of reality of these numbers '''before conscious thought is applied'''.

The most interesting parts of the graph, and the parts where the disconnect between intuition and reality becomes clearest, are the dashed sections labeled with question marks, the one between 100 million and 1 billion, the other between 100 billion and 1 trillion. Here two competing intuitive understandings compete for dominance. On the one hand, the intuitive understanding described above, with 100 trumping 1, would see the curve taking a sharp downturn. On the other hand, the path from 100 million to 1 billion is paved with such numbers as 500 million, 700 million, and 900 million, all of which would theoretically be seen intuitively as larger than 100 million, thanks to the fact that 9 is greater than 7, and 7 greater than 5, and so on, bending the curve up rather than down. These two conflicting intuitions leave Randall with no single intuitive path for the two dashed sections, leading to their dashed and questioned state.

The comic's caption and title highlight another problem surrounding the intuitive grasping of large numbers: the flaws in the English words used for them. For instance, nothing about the word "million" suggests smallness relative to the word "billion" on an intuitive scale. This unintuitive language contributes greatly to the "100 trumps 1" intuitive fallacy described above.

=== Long scale and short scale ===

The title text references a highly relevant disconnect between the {{w|Long_and_short_scales|long and short scales of large numbers}}.

For all English speakers, and for most languages, 1 '''''million''''' constitutes 1,000 thousands, or, less ambiguously, 10^6. However, this is the last of the consensus numbers, and the definition of what should be the "next step" varies depending on how each country's language evolved.
* In many English-speaking countries, 1,000 millions equals 1 billion, or 1000*10^6=10^9; this convention is known as the '''short-scale'''.
* [https://en.oxforddictionaries.com/explore/how-many-is-a-billion/ In historical Britain] and many other countries with a language derived from French or Spanish, the "next step" may be named a thousand million, and 1 billion equals ''1 million'' millions, or 10^6*10^6=10^'''12''', with the base unit changing when you have a unit's worth multiple of the unit; this convention is known as the long-scale. (Note that this is no longer used in Britain since 1974.)
* In European languages where the '''long-scale''' system is used, 10^9 may be named a thousand million, or receive a name with a special suffix: the word milliard (meaning 1,000 million) is used in some form (e.g. milliard in French, Milliarde in German, milliard in Danish, milliárd in Hungarian, etc.), with the word billion defined as 1,000 milliard (or 1,000,000 million). In these languages, a billion never meant 1,000 million as it does in the short-scale system.
* Successive units, such as trillion, increase by the same multiple as one billion divided by one million - by 1,000 in the short-scale system and 1,000,000 in the long-scale system.

In other words, 1 billion objects in a country using the short-scale would be 1,000 million objects in a country using the long-scale; at the "next step", 1 trillion in the short-scale would be named 1 billion in the long-scale, despite the fact that the number of objects has remained the same. This difference between languages using the short-scale and the long-scale often causes confusion when translating articles with large numbers in them, as translators sometimes fail to change between short-scale and long-scale schemes, wrongly translating large numbers to incorrect values.

The fact that such a staggering difference of terminology was able to exist and be almost completely unknown to many supports Randall's point about the failure of human intuition in the discussion of extremely large numbers.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[A graph with Y-axis labeled “Perceived size of number” and X-axis labeled “Actual size of number (log scale)”.]
:[The line graph shows points that are labeled with the following numbers from “1 million” to “100 trillion”:]

==== Points on graph: ====
::[''Note: Coordinates are relative because the graph's y-axis has no shown scale. Coordinates are in bold.'']
:{| class="wikitable" style="text-align: center;"
|1 million
|[''(1, 1)'']
|-
|10 million
|[''(1, 2)'']
|-
|100 million
|[''(1, 3)'']
|-
|1 billion
|[''(1, 1.5)'']
|-
|10 billion
|[''(1, 3)'']
|-
|100 billion
|[''(1, 4)'']
|-
|1 trillion
|[''(1, 3)'']
|-
|10 trillion
|[''(1, 4)'']
|-
|100 trillion
|[''(1, 5)'']
|}
:[The perceived size increases between most numbers, but decreases between 100 million and 1 billion, and between 100 billion and 1 trillion. The decreases are shown as dashed lines labeled “?”, in contrast to the solid unlabeled lines between the increases. The increases and decreases in perceived size become smaller as the numbers grow in actual size.]
:[Caption below the panel:]
:Talking about large numbers is hard

{{comic discussion}}

[[Category:Line graphs]]

2091: Million, Billion, Trillion

2019-01-30T02:22:00Z

Ethan:

{{comic
| number = 2091
| date = December 28, 2018
| title = Million, Billion, Trillion
| image = million_billion_trillion.png
| titletext = You can tell most people don’t really assign an absolute meaning to these numbers because in some places and time periods, “billion” has meant 1,000x what it's meant in others, and a lot of us never even noticed.
}}

==Explanation==
{{incomplete|This needs about a thousand years of rewriting, and I assume we'll want to do a chart of X and Y positions as with most chart comics. Do NOT delete this tag too soon.}}
Much like [[558: 1000 Times|comic 558]], this comic addresses the difficulty ordinary people have with large numbers. Though most if not all people intuitively understand the difference between one object and two objects, or one object and ten objects, or even one object and a hundred objects, as numbers increase most people's ability to innately conceive of the numbers being discussed decreases remarkably quickly. When numbers reach the millions and the billions, and especially the trillions, most people don't truly process the numbers at all, and instead conceive of them as some version of a drastically-oversimplified concept such as "very big." Where comparing one to ten is simple, comparing "very big" to a different "very big" can prove extremely challenging, and will certainly require non-intuitive, conscious thinking.

The comic represents this challenge by providing a graph which represents [[Randall]]'s ''intuitive'' conception of the values of various very large numbers, and said conception's misalignment with reality. Though some trends reflect the real value of the numbers on the graph, i.e. 100 million larger than 10 million larger than 1 million and 1 billion larger than 1 million, the curve is far from the linear (exponential on the log-scaled axes) path it should take, with 1 billion being intuitively understood as less than 100 million, based, presumably, on the fact, easily comprehended on an intuitive level, that '''100 is larger than 1''', and therefore the presence of 100 in 100 million places it at a higher value than the 1 in 1 billion would place the latter. In reality, of course, 1 billion is ten times larger than 100 million, but the comic deals not with actual reality, but with the perception of reality of these numbers '''before conscious thought is applied'''.

The most interesting parts of the graph, and the parts where the disconnect between intuition and reality becomes clearest, are the dashed sections labeled with question marks, the one between 100 million and 1 billion, the other between 100 billion and 1 trillion. Here two competing intuitive understandings compete for dominance. On the one hand, the intuitive understanding described above, with 100 trumping 1, would see the curve taking a sharp downturn. On the other hand, the path from 100 million to 1 billion is paved with such numbers as 500 million, 700 million, and 900 million, all of which would theoretically be seen intuitively as larger than 100 million, thanks to the fact that 9 is greater than 7, and 7 greater than 5, and so on, bending the curve up rather than down. These two conflicting intuitions leave Randall with no single intuitive path for the two dashed sections, leading to their dashed and questioned state.

The comic's caption and title highlight another problem surrounding the intuitive grasping of large numbers: the flaws in the English words used for them. For instance, nothing about the word "million" suggests smallness relative to the word "billion" on an intuitive scale. This unintuitive language contributes greatly to the "100 trumps 1" intuitive fallacy described above.

=== Long scale and short scale ===

The title text references a highly relevant disconnect between the {{w|Long_and_short_scales|long and short scales of large numbers}}.

For all English speakers, and for most languages, 1 '''''million''''' constitutes 1,000 thousands, or, less ambiguously, 10^6. However, this is the last of the consensus numbers, and the definition of what should be the "next step" varies depending on how each country's language evolved.
* In many English-speaking countries, 1,000 millions equals 1 billion, or 1000*10^6=10^9; this convention is known as the '''short-scale'''.
* [https://en.oxforddictionaries.com/explore/how-many-is-a-billion/ In historical Britain] and many other countries with a language derived from French or Spanish, the "next step" may be named a thousand million, and 1 billion equals ''1 million'' millions, or 10^6*10^6=10^'''12''', with the base unit changing when you have a unit's worth multiple of the unit; this convention is known as the long-scale. (Note that this is no longer used in Britain since 1974.)
* In European languages where the '''long-scale''' system is used, 10^9 may be named a thousand million, or receive a name with a special suffix: the word milliard (meaning 1,000 million) is used in some form (e.g. milliard in French, Milliarde in German, milliard in Danish, milliárd in Hungarian, etc.), with the word billion defined as 1,000 milliard (or 1,000,000 million). In these languages, a billion never meant 1,000 million as it does in the short-scale system.
* Successive units, such as trillion, increase by the same multiple as one billion divided by one million - by 1,000 in the short-scale system and 1,000,000 in the long-scale system.

In other words, 1 billion objects in a country using the short-scale would be 1,000 million objects in a country using the long-scale; at the "next step", 1 trillion in the short-scale would be named 1 billion in the long-scale, despite the fact that the number of objects has remained the same. This difference between languages using the short-scale and the long-scale often causes confusion when translating articles with large numbers in them, as translators sometimes fail to change between short-scale and long-scale schemes, wrongly translating large numbers to incorrect values.

The fact that such a staggering difference of terminology was able to exist and be almost completely unknown to many supports Randall's point about the failure of human intuition in the discussion of extremely large numbers.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[A graph with Y-axis labeled “Perceived size of number” and X-axis labeled “Actual size of number (log scale)”.]
:[The line graph shows points that are labeled with the following numbers from “1 million” to “100 trillion”:]

==== Points on graph: ====
::[''Note: Coordinates are relative because the graph's y-axis has no shown scale. Coordinates are in bold.'']
* 1 million ['''(1, 1)''']
* 10 million ['''(2, 2)''']
* 100 million ['''(3, 3)''']
* 1 billion ['''(4, 1.5)''']
* 10 billion ['''(5, 3)''']
* 100 billion ['''(6, 4)''']
* 1 trillion ['''(7, 3)''']
* 10 trillion ['''(8, 4)''']
* 100 trillion ['''(9, 5)''']
:[The perceived size increases between most numbers, but decreases between 100 million and 1 billion, and between 100 billion and 1 trillion. The decreases are shown as dashed lines labeled “?”, in contrast to the solid unlabeled lines between the increases. The increases and decreases in perceived size become smaller as the numbers grow in actual size.]
:[Caption below the panel:]
:Talking about large numbers is hard

{{comic discussion}}

[[Category:Line graphs]]

2091: Million, Billion, Trillion

2019-01-30T02:21:12Z

Ethan:

{{comic
| number = 2091
| date = December 28, 2018
| title = Million, Billion, Trillion
| image = million_billion_trillion.png
| titletext = You can tell most people don’t really assign an absolute meaning to these numbers because in some places and time periods, “billion” has meant 1,000x what it's meant in others, and a lot of us never even noticed.
}}

==Explanation==
{{incomplete|This needs about a thousand years of rewriting, and I assume we'll want to do a chart of X and Y positions as with most chart comics. Do NOT delete this tag too soon.}}
Much like [[558: 1000 Times|comic 558]], this comic addresses the difficulty ordinary people have with large numbers. Though most if not all people intuitively understand the difference between one object and two objects, or one object and ten objects, or even one object and a hundred objects, as numbers increase most people's ability to innately conceive of the numbers being discussed decreases remarkably quickly. When numbers reach the millions and the billions, and especially the trillions, most people don't truly process the numbers at all, and instead conceive of them as some version of a drastically-oversimplified concept such as "very big." Where comparing one to ten is simple, comparing "very big" to a different "very big" can prove extremely challenging, and will certainly require non-intuitive, conscious thinking.

The comic represents this challenge by providing a graph which represents [[Randall]]'s ''intuitive'' conception of the values of various very large numbers, and said conception's misalignment with reality. Though some trends reflect the real value of the numbers on the graph, i.e. 100 million larger than 10 million larger than 1 million and 1 billion larger than 1 million, the curve is far from the linear (exponential on the log-scaled axes) path it should take, with 1 billion being intuitively understood as less than 100 million, based, presumably, on the fact, easily comprehended on an intuitive level, that '''100 is larger than 1''', and therefore the presence of 100 in 100 million places it at a higher value than the 1 in 1 billion would place the latter. In reality, of course, 1 billion is ten times larger than 100 million, but the comic deals not with actual reality, but with the perception of reality of these numbers '''before conscious thought is applied'''.

The most interesting parts of the graph, and the parts where the disconnect between intuition and reality becomes clearest, are the dashed sections labeled with question marks, the one between 100 million and 1 billion, the other between 100 billion and 1 trillion. Here two competing intuitive understandings compete for dominance. On the one hand, the intuitive understanding described above, with 100 trumping 1, would see the curve taking a sharp downturn. On the other hand, the path from 100 million to 1 billion is paved with such numbers as 500 million, 700 million, and 900 million, all of which would theoretically be seen intuitively as larger than 100 million, thanks to the fact that 9 is greater than 7, and 7 greater than 5, and so on, bending the curve up rather than down. These two conflicting intuitions leave Randall with no single intuitive path for the two dashed sections, leading to their dashed and questioned state.

The comic's caption and title highlight another problem surrounding the intuitive grasping of large numbers: the flaws in the English words used for them. For instance, nothing about the word "million" suggests smallness relative to the word "billion" on an intuitive scale. This unintuitive language contributes greatly to the "100 trumps 1" intuitive fallacy described above.

=== Long scale and short scale ===

The title text references a highly relevant disconnect between the {{w|Long_and_short_scales|long and short scales of large numbers}}.

For all English speakers, and for most languages, 1 '''''million''''' constitutes 1,000 thousands, or, less ambiguously, 10^6. However, this is the last of the consensus numbers, and the definition of what should be the "next step" varies depending on how each country's language evolved.
* In many English-speaking countries, 1,000 millions equals 1 billion, or 1000*10^6=10^9; this convention is known as the '''short-scale'''.
* [https://en.oxforddictionaries.com/explore/how-many-is-a-billion/ In historical Britain] and many other countries with a language derived from French or Spanish, the "next step" may be named a thousand million, and 1 billion equals ''1 million'' millions, or 10^6*10^6=10^'''12''', with the base unit changing when you have a unit's worth multiple of the unit; this convention is known as the long-scale. (Note that this is no longer used in Britain since 1974.)
* In European languages where the '''long-scale''' system is used, 10^9 may be named a thousand million, or receive a name with a special suffix: the word milliard (meaning 1,000 million) is used in some form (e.g. milliard in French, Milliarde in German, milliard in Danish, milliárd in Hungarian, etc.), with the word billion defined as 1,000 milliard (or 1,000,000 million). In these languages, a billion never meant 1,000 million as it does in the short-scale system.
* Successive units, such as trillion, increase by the same multiple as one billion divided by one million - by 1,000 in the short-scale system and 1,000,000 in the long-scale system.

In other words, 1 billion objects in a country using the short-scale would be 1,000 million objects in a country using the long-scale; at the "next step", 1 trillion in the short-scale would be named 1 billion in the long-scale, despite the fact that the number of objects has remained the same. This difference between languages using the short-scale and the long-scale often causes confusion when translating articles with large numbers in them, as translators sometimes fail to change between short-scale and long-scale schemes, wrongly translating large numbers to incorrect values.

The fact that such a staggering difference of terminology was able to exist and be almost completely unknown to many supports Randall's point about the failure of human intuition in the discussion of extremely large numbers.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[A graph with Y-axis labeled “Perceived size of number” and X-axis labeled “Actual size of number (log scale)”.]
:[The line graph shows points that are labeled with the following numbers from “1 million” to “100 trillion”:]

==== Points on graph: ====
::[''Note: Coordinates are relative because the graph's y-axis has no shown scale. Coordinates are in bold.'']
* 1 million '''(1, 1)'''
* 10 million '''(2, 2)'''
* 100 million '''(3, 3)'''
* 1 billion '''(4, 1.5)'''
* 10 billion '''(5, 3)'''
* 100 billion '''(6, 4)'''
* 1 trillion '''(7, 3)'''
* 10 trillion '''(8, 4)'''
* 100 trillion '''(9, 5)'''
:[The perceived size increases between most numbers, but decreases between 100 million and 1 billion, and between 100 billion and 1 trillion. The decreases are shown as dashed lines labeled “?”, in contrast to the solid unlabeled lines between the increases. The increases and decreases in perceived size become smaller as the numbers grow in actual size.]
:[Caption below the panel:]
:Talking about large numbers is hard

{{comic discussion}}

[[Category:Line graphs]]

2091: Million, Billion, Trillion

2019-01-30T02:20:44Z

Ethan: Changed Transcript to be more clear.

{{comic
| number = 2091
| date = December 28, 2018
| title = Million, Billion, Trillion
| image = million_billion_trillion.png
| titletext = You can tell most people don’t really assign an absolute meaning to these numbers because in some places and time periods, “billion” has meant 1,000x what it's meant in others, and a lot of us never even noticed.
}}

==Explanation==
{{incomplete|This needs about a thousand years of rewriting, and I assume we'll want to do a chart of X and Y positions as with most chart comics. Do NOT delete this tag too soon.}}
Much like [[558: 1000 Times|comic 558]], this comic addresses the difficulty ordinary people have with large numbers. Though most if not all people intuitively understand the difference between one object and two objects, or one object and ten objects, or even one object and a hundred objects, as numbers increase most people's ability to innately conceive of the numbers being discussed decreases remarkably quickly. When numbers reach the millions and the billions, and especially the trillions, most people don't truly process the numbers at all, and instead conceive of them as some version of a drastically-oversimplified concept such as "very big." Where comparing one to ten is simple, comparing "very big" to a different "very big" can prove extremely challenging, and will certainly require non-intuitive, conscious thinking.

The comic represents this challenge by providing a graph which represents [[Randall]]'s ''intuitive'' conception of the values of various very large numbers, and said conception's misalignment with reality. Though some trends reflect the real value of the numbers on the graph, i.e. 100 million larger than 10 million larger than 1 million and 1 billion larger than 1 million, the curve is far from the linear (exponential on the log-scaled axes) path it should take, with 1 billion being intuitively understood as less than 100 million, based, presumably, on the fact, easily comprehended on an intuitive level, that '''100 is larger than 1''', and therefore the presence of 100 in 100 million places it at a higher value than the 1 in 1 billion would place the latter. In reality, of course, 1 billion is ten times larger than 100 million, but the comic deals not with actual reality, but with the perception of reality of these numbers '''before conscious thought is applied'''.

The most interesting parts of the graph, and the parts where the disconnect between intuition and reality becomes clearest, are the dashed sections labeled with question marks, the one between 100 million and 1 billion, the other between 100 billion and 1 trillion. Here two competing intuitive understandings compete for dominance. On the one hand, the intuitive understanding described above, with 100 trumping 1, would see the curve taking a sharp downturn. On the other hand, the path from 100 million to 1 billion is paved with such numbers as 500 million, 700 million, and 900 million, all of which would theoretically be seen intuitively as larger than 100 million, thanks to the fact that 9 is greater than 7, and 7 greater than 5, and so on, bending the curve up rather than down. These two conflicting intuitions leave Randall with no single intuitive path for the two dashed sections, leading to their dashed and questioned state.

The comic's caption and title highlight another problem surrounding the intuitive grasping of large numbers: the flaws in the English words used for them. For instance, nothing about the word "million" suggests smallness relative to the word "billion" on an intuitive scale. This unintuitive language contributes greatly to the "100 trumps 1" intuitive fallacy described above.

=== Long scale and short scale ===

The title text references a highly relevant disconnect between the {{w|Long_and_short_scales|long and short scales of large numbers}}.

For all English speakers, and for most languages, 1 '''''million''''' constitutes 1,000 thousands, or, less ambiguously, 10^6. However, this is the last of the consensus numbers, and the definition of what should be the "next step" varies depending on how each country's language evolved.
* In many English-speaking countries, 1,000 millions equals 1 billion, or 1000*10^6=10^9; this convention is known as the '''short-scale'''.
* [https://en.oxforddictionaries.com/explore/how-many-is-a-billion/ In historical Britain] and many other countries with a language derived from French or Spanish, the "next step" may be named a thousand million, and 1 billion equals ''1 million'' millions, or 10^6*10^6=10^'''12''', with the base unit changing when you have a unit's worth multiple of the unit; this convention is known as the long-scale. (Note that this is no longer used in Britain since 1974.)
* In European languages where the '''long-scale''' system is used, 10^9 may be named a thousand million, or receive a name with a special suffix: the word milliard (meaning 1,000 million) is used in some form (e.g. milliard in French, Milliarde in German, milliard in Danish, milliárd in Hungarian, etc.), with the word billion defined as 1,000 milliard (or 1,000,000 million). In these languages, a billion never meant 1,000 million as it does in the short-scale system.
* Successive units, such as trillion, increase by the same multiple as one billion divided by one million - by 1,000 in the short-scale system and 1,000,000 in the long-scale system.

In other words, 1 billion objects in a country using the short-scale would be 1,000 million objects in a country using the long-scale; at the "next step", 1 trillion in the short-scale would be named 1 billion in the long-scale, despite the fact that the number of objects has remained the same. This difference between languages using the short-scale and the long-scale often causes confusion when translating articles with large numbers in them, as translators sometimes fail to change between short-scale and long-scale schemes, wrongly translating large numbers to incorrect values.

The fact that such a staggering difference of terminology was able to exist and be almost completely unknown to many supports Randall's point about the failure of human intuition in the discussion of extremely large numbers.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[A graph with Y-axis labeled “Perceived size of number” and X-axis labeled “Actual size of number (log scale)”.]
:[The line graph shows points that are labeled with the following numbers from “1 million” to “100 trillion”:]

==== Points on graph: ====
::[''Note: Coordinates are relative because the graph's y-axis has no shown scale. Coordinates are in bold.'']
* 1 million '''(1, 1)'''
* 10 million '''(2, 2)'''
* 100 million '''(3, 3)'''
* 1 billion '''(4, 1.5)'''
* 10 billion '''(5, 3)'''
* 100 billion '''(6, 4)'''
* 1 trillion '''(7, 3)'''
* 10 trillion '''(8, 4)'''
* 100 trillion '''(9, 5)'''
:[The perceived size increases between most numbers, but decreases between 100 million and 1 billion, and between 100 billion and 1 trillion. The decreases are shown as dashed lines labeled “?”, in contrast to the solid unlabeled lines between the increases. The increases and decreases in perceived size become smaller as the numbers grow in actual size.]
:[Caption below the panel:]
:Talking about large numbers is hard

{{comic discussion}}

[[Category:Line graphs]]