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3228: Day Counter

2026-04-28T08:18:16Z

2A01:119F:2A5:8D00:1C5B:89A5:6E78:4C59:

{{comic
| number = 3228
| date = April 3, 2026
| title = Day Counter
| image = day_counter_2x.png
| imagesize = 319x287px
| noexpand = true
| titletext = It has been −2,147,483,648 days since our last integer overflow.
}}

==Explanation==

{{incomplete|The calculations by DL Draco Rex et al. in the Talk should be included in the explanation. Don't remove this notice too soon.}}

A common feature of an industrial setting is a prominent sign announcing how many days have elapsed since the last workplace accident. The sign is typically updated each day to a number one higher — or back to zero, if there ''has'' been an accident. Such signs are intended to foster a culture of safety among the workers in the facility, since presumably no one wants to suffer the embarrassment of being the one to have caused an accident that resets the number to 0. (However, it may also lead workers to cover up or conceal accidents, for the same reason, which would tend to increase future accidents, because they do not report the need to correct hazardous conditions that are causing accidents.)

Evidently, in the programming facility shown in the comic, a floating-point error has occurred today, and an attempt has been made to update the sign to say "It has been 0 days since...". But the number 0 is displayed incorrectly, as the very small negative value −0.00000000000000044. Perhaps the error that was made today was the very error that occurred in updating the sign! (This would of course violate {{w|causality}}, but in comedy, self-referential humor beats causality every time, and is at least self-consistent, like with [[363: Reset]])

Floating-point errors occur because computers can devote only a finite amount of storage for each {{w|Floating-point arithmetic|floating point number}} or other fraction. However, many {{w|real numbers}} and {{w|rational numbers}} theoretically require an infinite number of digits to represent them. For example, the ordinary fraction ⅓ is represented in decimal as 0.3333333333…, where the 3s repeat forever. When a number is truncated to fit in the finite amount of space, precision is inevitably lost, resulting in a slight rounding error. Unless carefully controlled, these rounding errors can accumulate, significantly degrading the accuracy of floating-point computations. For example, although ⅓ + ⅓ + ⅓ should obviously equal 1, a finite-precision calculation like 0.333 + 0.333 + 0.333 might show a misleading result of 0.999, which might not trigger the code to do what it should do when three thirds have been accumulated (it can be mitigated by allowing a match for a value which is within a suitably very small difference to the test value, but this must be considered carefully to not be over-/under-sensitive). The amount of required space for rational numbers is not universal, it depends on the base used (⅓ in base 3 requires just two digits: 0 as the units and 1 after the {{w|Decimal separator#Radix point|radix (ternary) point}}). Floating point arithmetic standards, like the popular IEEE 754, define how and when an approximation should take place, leading to predictable results, but they don't respect some basic properties of common arithmetic operations, which someone may take for granted, e.g. in floating point arithmetic addition and multiplication are commutative (a+b=b+a; a*b=b*a), but aren't guaranteed to be associative ((a+b)+c≈a+(b+c)); (a*b)*c≈a*(b*c)).

This issue is exacerbated on computers which use binary arithmetic (i.e., virtually all computers today), since in binary, the ordinary fraction 1/10 is represented as the infinitely-repeating base-2 fraction <tt>0.000110011001100110011</tt>…. A classic example is that, depending on circumstances, the calculation 0.1 + 0.2 might [https://stackoverflow.com/questions/588004/is-floating-point-math-broken seem to give an answer of 0.30000000000000004].

Floating point errors are particularly common in programming, especially in languages that implicitly convert decimal numbers to binary floating point, so an approximation is already made at conversion leading to unexpected results. The title text cites another common programming problem, integer overflow. When a value gets bigger than the biggest integer that can be represented in a certain format, it may "wrap around" to the smallest/most negative value (if the system is not instead set to catch this as an overflow error). In case of 32-bit signed integers it may wrap from 231−1 (2,147,483,647) to −231 (−2,147,483,648).

Integer overflow was the topic of [[571: Can't Sleep]], with yet another example of a 'days since' sign being [[3140: Biology Department]] (two examples, in both the comic and its title text).

It should be noted that computers displaying things like "-1 seconds until the next [blank]" is a glitch that actually happens.

==Transcript==
[White Hat, Ponytail, Cueball, and Megan are all below a large sign, which appears to be attached to the wall at its four corners. White Hat and Ponytail appear to be discussing something, while Cueball is sitting at his desk working on a laptop and Megan is walking away. The sign has text on it, as well as a large display presumably meant to show a number.]

:[Sign:] It has been
:[Display:] -0.00000000000000044
:[Sign:] days since our last floating point error

==Trivia==
As an example of how the number −0.00000000000000044 could have arisen when 0 was intended, consider this simple {{w|C (programming language)|C}} program:

#include <stdio.h>
int main()
{
double d = 19;
for(int i = 0; i < 10; i++) d -= 1.9;
printf("%.17f\n", d);
}

The program starts with the number 19, and subtracts 1.9 from it, ten times. Mathematically, we would expect the result to be 0. However, the number 1.9 cannot be represented exactly in binary, nor can the intermediate results 17.1, 15.2, 13.3, etc. The cascading roundoff errors conspire to produce a result of −0.00000000000000044 instead of the expected 0.

Another possibility is that the timestamps were rounded to an intermediate lower precision that ended up rounding above the actual time value:

#include <stdio.h>
float last_fp_error=0;
int main(){
double time = 0.00000000745058193;
int a=3; int b=-2; double f=10;
if(a/f+b/f!=(a+b)/f) last_fp_error=time;
printf("It has been %.17f days since our last floating point error",time-last_fp_error);
}

In the comic, such an error creates the ridiculous illusion that −0.00000000000000044 days have passed, which implies a 'negative' number of days, which is impossible{{cn}}. It also, even if it were a positive number, would mean that much less than a nanosecond had passed since the last error, which would be an unfeasably short amount of time. Of course, the joke is that in making the sign showing the amount of time since a floating point error was last made, they are creating a floating point error, meaning the sign maintains its own "error state" in a self-referential way. Also, if they tried to reset the sign, they might make the same error again, repeating the cycle over and over, which would not be ideal.

Coincidentally enough, [[Cueball]] is also floating — off his seat in this case, but this is an art style choice that ended up being apparent, as [[919|many]] [[1682|past]] [[1411|chair]] [[2362|sitters]] [[2382|are]] [[1088|shown]] [[1121|to]] [[3198|levitate]].


{{comic discussion}}<noinclude>[[Category:Interactive comics]][[Category:Dynamic comics]]
[[Category:Programming]]
[[Category:Math]]
[[Category:Comics featuring White Hat]]
[[Category:Comics featuring Ponytail]]
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]

3200: Chemical Formula

2026-04-28T07:23:24Z

2A01:119F:2A5:8D00:1C5B:89A5:6E78:4C59:

{{comic
| number = 3200
| date = January 28, 2026
| title = Chemical Formula
| image = chemical_formula_2x.png
| imagesize = 740x225px
| noexpand = true
| titletext = Some of the atoms in the molecule are very weakly bound.
}}

==Explanation==
{{incomplete|This page was created by all of the carbon in the universe. Don't remove this notice too soon.}}
This supposed "{{w|chemical formula}} for the universe" merely lists the numbers of atoms of each element that are [https://ptable.com/#Properties/Abundance/Universe thought to exist] in the observable universe. Usually, chemical formulae imply rather more of a discrete binding together of the atoms involved. They also represent a single {{w|molecule}} of the substance, rather than trying to cover the entire number of atoms in the whole quantity under consideration.

This may be poking some fun at the relative usefulness (or rather, uselessness) of chemical formulas for large organic molecules. While it is a useful concept for teaching people about chemistry and {{w|Chemical equation#Balancing chemical equations|balancing equations}}, and it was useful in the early days of chemistry to try to categorize and learn about molecules via {{w|stoichiometry}} - it does not give much useful information, such as its structure. For example, even the simple formula C11H15NO2 has [https://pubchem.ncbi.nlm.nih.gov/#query=C11H15NO2&input_type=formula over 300 registered isomers]. Many of them are [https://pubchem.ncbi.nlm.nih.gov/compound/17517#datasheet=LCSS NOT] {{w|MDMA#Side_effects|good to eat}}. For other purposes, formulae may group the components accordingly, such as {{w|1,1,1-Trichloroethane|CH3CCl3}} (simplifies to C2H3Cl3, as does {{w|1,1,2-Trichloroethane|an isomer}}) or {{w|ammonium carbonate|[NH4]2CO3}} (not usually identified as CH8O3N2, and not strictly an organic compound either).

As is common practice for real compounds that contain organic structures or substructures, the numbers of atoms of carbon and hydrogen are listed before all of the others; the others are listed in alphabetical order. There are estimated to be 1080 atoms of hydrogen (H), by far the most common element in the universe. The next most common element, helium (He), is a long way to the right in the list, and out of view, but would be about a twelfth as many as the hydrogens, or one order of magnitude using the Fermi approximations that pervade the formula.

In reality, there is not a fixed number of atoms of each element across the lifetime of the universe. The matter originally created in the {{w|Big Bang}} was unbound protons and neutrons. In the first few minutes, {{w|Big Bang nucleosynthesis|some of these combined to form lightweight nuclei}}, but most remained as {{w|proton}}s (i.e. the nuclei of hydrogen atoms). Other more complex atoms, up to {{w|atomic mass}} 56, formed later (and are still being formed) as a result of {{w|stellar nucleosynthesis}}. Still more massive nuclei have been and are being formed via {{w|supernova nucleosynthesis}}. Although the proportions of these atoms depend in a complex way on the fusion processes involved, and on the stabilities of those nuclei, the most massive atoms are generally both short-lived and less favored to form, so their elemental abundances in the universe are very small. As shown above, the number of americium (Am) atoms is much smaller than those of any other element in the visible part of the "formula". This indicates that there are slightly fewer atoms of americium in the entire universe than the total number of atoms of hydrogen and oxygen in 1.0 L of liquid water. However, [https://isis-online.org/uploads/isis-reports/documents/np_237_and_americium.pdf considerably more than that amount] (by orders of magnitude) is known to exist on Earth as a result of nuclear energy production, so it may be that the comic is based solely on natural abundances rather than taking human activity (or activity by hypothetical other beings) into account.

The title text is probably referencing {{w|gravity}}, because, for the most part, these atoms would be "held together" only by gravity, and it is a very weak bond indeed.

The numbers of atoms are large, but they are not nameless. Using the {{w|long and short scales}}, these numbers can be described as:
{| class="wikitable sortable"
!Pos!!Symb!!Name !!Quantity !!Short Scale name !!Long Scale name(s) !!Ranked quantity*
|-
| 1|| C ||Carbon ||data-sort-value="1e76"|1076 ||Ten quattuorvigintillion ||Ten thousand duodecillion Ten duodecilliard ||4
|-
| 2|| H ||Hydrogen ||data-sort-value="1e80"|1080 ||One hundred quinvigintillion ||One hundred tridecilllion ||1
|-
| 3|| Ac ||Actinium ||data-sort-value="1e67"|1067 ||Ten unvigintillion ||Ten undecillion ||data-sort-value="84"|≈84
|-
| 4|| Ag ||Silver ||data-sort-value="1e69"|1069 ||One duovigintillion ||One thousand undecillion One undecilliard ||data-sort-value="68"|≈68
|-
| 5|| Al ||Aluminium Aluminum||data-sort-value="1e75"|1075 ||One quattuorvigintillion ||One thousand duodecillion One duodecilliard ||14
|-
| 6|| Am ||Americium ||data-sort-value="1e26"|1026 ||One hundred septillion ||One hundred quadrillion ||data-sort-value="84"|≈84
|-
| 7|| Ar ||Argon ||data-sort-value="1e75"|1075 ||One quattuorvigintillion ||One thousand duodecillion One duodecilliard ||11
|-
| 8|| As ||Arsenic ||data-sort-value="1e70"|1070 ||Ten duovigintillion ||Ten thousand undecillion Ten undecilliard ||data-sort-value="40"|≈40
|-
| 9|| At ||Astatine ||data-sort-value="1e47"|1047 ||One hundred quattuordecillion||One hundred thousand septillion One hundred septilliard ||data-sort-value="84"|≈84
|-
| 10|| Au ||Gold ||data-sort-value="1e69"|1069 ||One duovigintillion ||One thousand undecillion One undecilliard ||data-sort-value="68"|≈68
|-
| 11|| B ||Boron ||data-sort-value="1e71"|1071 ||One hundred duovigintillion ||One hundred thousand undecillion One hundred undecilliard||data-sort-value="61"|≈61
|-
| 12|| Ba ||Barium ||data-sort-value="1e70"|1070 ||Ten duovigintillion ||Ten thousand undecillion Ten undecilliard ||data-sort-value="33"|≈33
|-
| 13|| Be ||Beryllium ||data-sort-value="1e71"|1071*||One hundred duovigintillion ||One hundred thousand undecillion One hundred undecilliard||data-sort-value="61"|≈61
|-
|data-sort-value="43"|43*||He||Helium||data-sort-value="3e79"|1079*||Ten quinvigintillion ||Ten tridecilllion ||2
|-
|data-sort-value="73"|73*||O ||Oxygen||data-sort-value="1e78"|1078*||One quinvigintillion ||One tridecilllion ||3
|}
:<nowiki>*</nowiki> - Information not provided by the comic; Source for ranked data, in particular, does not ''entirely'' agree with the quantities that are given in the comic.

The formula as it appears in the comic is truncated. The complete formula of the universe in this style (but arranged in decreasing order of abundance after carbon, which also happens to place hydrogen immediately after) would be
C₁₀⁷⁷ H₁₀⁸⁰
He₁₀⁷⁹
O₁₀⁷⁸
Ne₁₀⁷⁶ N₁₀⁷⁶ Fe₁₀⁷⁶ S₁₀⁷⁶
Mg₁₀⁷⁵ Si₁₀⁷⁵ Ar₁₀⁷⁵ Ni₁₀⁷⁵ Ca₁₀⁷⁵ Al₁₀⁷⁵ Na₁₀⁷⁵ Cr₁₀⁷⁵
Ti₁₀⁷⁴ Mn₁₀⁷⁴ P₁₀⁷⁴ K₁₀⁷⁴ V₁₀⁷⁴ Cl₁₀⁷⁴ Co₁₀⁷⁴
F₁₀⁷³ Zn₁₀⁷³ Ge₁₀⁷³
As₁₀⁷² Br₁₀⁷² Li₁₀⁷² Sc₁₀⁷² Cu₁₀⁷² Ga₁₀⁷² Se₁₀⁷² Kr₁₀⁷² Rb₁₀⁷² Sr₁₀⁷² Zr₁₀⁷² Te₁₀⁷² Xe₁₀⁷² Ba₁₀⁷² Ce₁₀⁷² Pb₁₀⁷²
B₁₀⁷¹ Be₁₀⁷¹ Y₁₀⁷¹ Nb₁₀⁷¹ Mo₁₀⁷¹ Ru₁₀⁷¹ Pd₁₀⁷¹ Cd₁₀⁷¹ Sn₁₀⁷¹ I₁₀⁷¹ La₁₀⁷¹ Pr₁₀⁷¹ Nd₁₀⁷² Sm₁₀⁷¹ Gd₁₀⁷¹ Dy₁₀⁷¹ Er₁₀⁷¹ Yb₁₀⁷¹ Os₁₀⁷¹ Ir₁₀⁷¹ Pt₁₀⁷¹ Hg₁₀⁷¹
Rh₁₀⁷⁰ Ag₁₀⁷⁰ In₁₀⁷⁰ Sb₁₀⁷⁰ Cs₁₀⁷⁰ Eu₁₀⁷⁰ Tb₁₀⁷⁰ Ho₁₀⁷⁰ Tm₁₀⁷⁰ Lu₁₀⁷⁰ Hf₁₀⁷⁰ Ta₁₀⁷⁰ W₁₀⁷⁰ Re₁₀⁷⁰ Au₁₀⁷⁰ Tl₁₀⁷⁰ Bi₁₀⁷⁰ Th₁₀⁷⁰ U₁₀⁷⁰
Tc₁₀⁰ Pm₁₀⁰ Po₁₀⁰ At₁₀⁰ Rn₁₀⁰ Fr₁₀⁰ Ra₁₀⁰ Ac₁₀⁰ Pa₁₀⁰ Np₁₀⁰ Pu₁₀⁰ Am₁₀⁰ Cm₁₀⁰ Bk₁₀⁰ Cf₁₀⁰ Es₁₀⁰ Fm₁₀⁰ Md₁₀⁰ No₁₀⁰ Lr₁₀⁰ Rf₁₀⁰ Db₁₀⁰ Sg₁₀⁰ Bh₁₀⁰ Hs₁₀⁰ Mt₁₀⁰ Ds₁₀⁰ Rg₁₀⁰ Cn₁₀⁰ Nh₁₀⁰ Fl₁₀⁰ Mc₁₀⁰ Lv₁₀⁰ Ts₁₀⁰ Og₁₀⁰ according to some broad stroke estimates of abundance.

==Transcript==
{{incomplete transcript|Don't remove this notice too soon.}}
:[A long panel with a chemical formula trailing off the right side halfway through the last symbol]
:C1076 H1080 Ac1067 Ag1069 Al1075 Am1026 Ar1075 As1070 At1047 Au1069 B1071 Ba1070 Be
:[Caption below the panel:] The approximate chemical formula for the universe

{{comic discussion}}<noinclude>
[[Category:Chemistry]]
[[Category:Cosmology]]