explain xkcd - User contributions [en]

571: Can't Sleep

2024-04-29T16:14:04Z

Fiss: better sentencing (have 16 bits to be 16-bit)

{{comic
| number = 571
| date = April 20, 2009
| title = Can't Sleep
| image = cant sleep.png
| titletext = If androids someday DO dream of electric sheep, don't forget to declare sheepCount as a long int.
}}

==Explanation==
[[Cueball]] is in bed and is having trouble sleeping. He tries the old standby of {{w|counting sheep}} as they jump over a fence, but upon reaching 32,767 sheep, 65535 sheep jump back over the fence and start counting up again from -32,768. This is a reference to an integer overflow, when an increasing amount (sheep in this case) suddenly overflows and shows up as a negative value. This is because when a whole number or integer is represented in a digital form, such as on a computer, the number's range is limited by the amount of space used to store it. When the greatest possible number given the storage space is exceeded, an arithmetic overflow occurs, which may result (depending on the used language among other things) in starting over at the least possible number given the storage space, similar to a car's odometer. Imagine an odometer with six digits reaching 999999. Upon driving one more mile or km, the digits will roll back over to 000000. Causing or failing to prevent integer overflow is a common mistake by programmers that may have software security consequences. Some languages like C/C++ even leaves the signed integer overflow ''undefined behavior'', it may or may not wrap to the beginning, the instruction can be ignored or may cause the software to crash.

In this case, the least and greatest possible numbers are -32,768 and 32,767, which implies that Cueball's brain would only be 16-bit. In addition, it's clear that the number is designated as a signed number, meaning that it can be either positive or negative.

However, even if Cueball had this limitation, it would never actually pose a problem. By 32,767 sheep, at a rate of one sheep per second, Cueball has been counting for 9.101 hours (or about 9 hours 6 minutes). This would signify that he has extreme insomnia and probably needs treatment, and also that he has spent the entire night counting, and therefore would just get up and start the day rather than count sheep all over again from -32,768.

The title text refers to the 1968 Philip K. Dick science fiction novel ''{{w|Do Androids Dream of Electric Sheep?}}'', which was adapted into the perhaps more widely known Ridley Scott directed 1982 film ''Blade Runner''. The implication is that if we ever do create androids that dream of electric sheep, we should make sure to give them sufficient storage space to store numbers large enough such that an arithmetic overflow will be far less likely to occur, even if they count for a long time. A "long int" depends on machine architecture, but it typically consists of four bytes rather than two, so instead of being limited to a range from -32,768 to 32,767 the number will be capable of storing numbers from -2,147,483,648 to 2,147,483,647, which would take 68.1 years to exhaust (at the rate of 1 sheep/sec). "sheepCount" is a possible name for a variable to be used in a computer program. Declaring a variable tells the computer that it should allocate a portion of memory to be associated with the variable name given. No spaces are used because variables cannot contain spaces, for a reason that would take a little too long to properly explain here.

==Transcript==
:[Cueball is in bed, presumably trying to sleep. The top of each panel is a thought bubble showing sheep leaping over a fence and Cueball's counting and the sheeps baaing is written above the sheeps. Two sheep are jumping from left to right in the first panel.]
:1... 2...
:Sheep: Baaa

:[Two sheep are jumping from left to right. Cueball is holding his pillow.]
:... 1,306... 1,307...
:Sheep: Baaa

:[A whole flock of sheep (nine visible) is jumping over the fence from right to left; the first and last sheep is cut off at the edge of the frame. Cueball is now sitting up looking up at his thought bubble.]
:... 32,767 ...-32,768...
:Sheep: Baaa baaa baaaa baaa ba
:Cueball: ?

:[Two sheep are again jumping from left to right. Cueball is holding his pillow over his head.]
:...-32,767... -32,766...
:Sheep: Baaa

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Animals]]
[[Category:Dreams]]

571: Can't Sleep

2024-04-28T15:45:08Z

Fiss: clarified the text

{{comic
| number = 571
| date = April 20, 2009
| title = Can't Sleep
| image = cant sleep.png
| titletext = If androids someday DO dream of electric sheep, don't forget to declare sheepCount as a long int.
}}

==Explanation==
[[Cueball]] is in bed and is having trouble sleeping. He tries the old standby of {{w|counting sheep}} as they jump over a fence, but upon reaching 32,767 sheep, 65535 sheep jump back over the fence and start counting up again from -32,768. This is a reference to an integer overflow, when an increasing amount (sheep in this case) suddenly overflows and shows up as a negative value. This is because when a whole number or integer is represented in a digital form, such as on a computer, the number's range is limited by the amount of space used to store it. When the greatest possible number given the storage space is exceeded, an arithmetic overflow occurs, which may result (depending on the used language among other things) in starting over at the least possible number given the storage space, similar to a car's odometer. Imagine an odometer with six digits reaching 999999. Upon driving one more mile or km, the digits will roll back over to 000000. Causing or failing to prevent integer overflow is a common mistake by programmers that may have software security consequences. Some languages like C/C++ even leaves the signed integer overflow ''undefined behavior'', it may or may not wrap to the beginning, the instruction can be ignored or may cause the software to crash.

In this case, the least and greatest possible numbers are -32,768 and 32,767, which implies that Cueball's brain would only use 16 bits. In addition, it's clear that the number is designated as a signed number, meaning that it can be either positive or negative.

However, even if Cueball had this limitation, it would never actually pose a problem. By 32,767 sheep, at a rate of one sheep per second, Cueball has been counting for 9.101 hours (or about 9 hours 6 minutes). This would signify that he has extreme insomnia and probably needs treatment, and also that he has spent the entire night counting, and therefore would just get up and start the day rather than count sheep all over again from -32,768.

The title text refers to the 1968 Philip K. Dick science fiction novel ''{{w|Do Androids Dream of Electric Sheep?}}'', which was adapted into the perhaps more widely known Ridley Scott directed 1982 film ''Blade Runner''. The implication is that if we ever do create androids that dream of electric sheep, we should make sure to give them sufficient storage space to store numbers large enough such that an arithmetic overflow will be far less likely to occur, even if they count for a long time. A "long int" depends on machine architecture, but it typically consists of four bytes rather than two, so instead of being limited to a range from -32,768 to 32,767 the number will be capable of storing numbers from -2,147,483,648 to 2,147,483,647, which would take 68.1 years to exhaust (at the rate of 1 sheep/sec). "sheepCount" is a possible name for a variable to be used in a computer program. Declaring a variable tells the computer that it should allocate a portion of memory to be associated with the variable name given. No spaces are used because variables cannot contain spaces, for a reason that would take a little too long to properly explain here.

==Transcript==
:[Cueball is in bed, presumably trying to sleep. The top of each panel is a thought bubble showing sheep leaping over a fence and Cueball's counting and the sheeps baaing is written above the sheeps. Two sheep are jumping from left to right in the first panel.]
:1... 2...
:Sheep: Baaa

:[Two sheep are jumping from left to right. Cueball is holding his pillow.]
:... 1,306... 1,307...
:Sheep: Baaa

:[A whole flock of sheep (nine visible) is jumping over the fence from right to left; the first and last sheep is cut off at the edge of the frame. Cueball is now sitting up looking up at his thought bubble.]
:... 32,767 ...-32,768...
:Sheep: Baaa baaa baaaa baaa ba
:Cueball: ?

:[Two sheep are again jumping from left to right. Cueball is holding his pillow over his head.]
:...-32,767... -32,766...
:Sheep: Baaa

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Animals]]
[[Category:Dreams]]

2034: Equations

2024-04-23T17:36:41Z

Fiss: typo correction, possably to possibly

{{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 {{w|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) times <math>\rho{}</math> (density) 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 {{w|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 {{w|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 {{w|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 {{w|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, possibly the nonsensical helium-monastatide, 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 {{w|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.

:[[File:All gauge theory equations.png]]
;All {{w|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. However, almost none of the symbols used here are found or applicable to gauge theory.

:<math>H(t)+\Omega+G\!\cdot\!\Lambda...\begin{cases}...>0\mathrm{\ (Hubble\ model)}\\
...=0\mathrm{\ (Flat\ sphere\ model)}\\
...<0\mathrm{\ (Bright\ dark\ matter\ model)}
\end{cases}</math>
;All {{w|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}}.

:[[File:All truly deep physics equations.png]]
;All truly deep {{w|physics}} equations
The joke about the "truly deep physics equations" is that most of the universal physics equations are simple, almost exceedingly so. In general, many of these equations are types of [https://en.wikipedia.org/wiki/Conservation_law conservation law] equations, which reflect some of the basic truths of the universe. A hallmark of conservation laws is that the total amount of some physical value does not change, and so one side of the equation is zero, as shown in the example. One example is Einstein's ''E = mc²'', which shows conservation of mass-energy. Noether's theorem shows that conservation laws have a one-to-one correspondence with a symmetry of nature, making these equations truly 'deep'.

The title text is referencing the fact that the {{w|magnetic field|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.

==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:Cosmology]]