# 2073: Kilogram

Kilogram |

Title text: I'm glad to hear they're finally redefining the meter to be exactly three feet. |

## Explanation[edit]

Standard units such as the kilogram, metre, and second are redefined from time to time as measurement technologies improve. These redefinitions are generally done to improve the precision to which the various units can be known or reproduced, without changing their actual value. The joke here is that redefining the kilogram to equal one pound sounds like an incredible idea to Americans who never use the kilogram. It would not only fail to improve on its precision, but would also significantly change the value of what a kilogram is, making all things already measured for science and in the rest of the world impossible to correctly understand the mass of.

On the day of this comic, the General Conference on Weights and Measures (which Randall confuses with the International Committee for Weights and Measures) voted to redefine the kilogram by fixing it to the value of Planck's Constant. This is measured using a Kibble balance, which involves passing a measured current through an electromagnet to exert a force to balance 1 kg. The change took effect on May 20, 2019, when the platinum cylinder International Prototype Kilogram that defines the unit was retired. This means that the mass of a kilogram is no longer tied to a physical object, but to the fundamental properties of the universe. By fixing the value of Planck constant to 6.62607015×10^{-34} kg⋅m^{2}⋅s^{−1}, the kilogram is defined in terms of the second and the speed of light via the metre.

The previous method of confirming that a kilogram is accurate is to use physical metal weights measuring exactly one kilogram, periodically transporting them around the world to an official weight lab to confirm they still weigh the same. Over time these physical objects have changed very slightly in their mass making them unreliable in the long run -- thus running into the issue that a kilogram did not stay a constant measure of mass. Note that these weights and comparisons are so precise that a fingerprint on one of the weights could throw them off.

The new method of confirming that a kilogram is accurate relies upon an extremely precise knowledge of local gravitational effects & an absence (or counteraction) of electromagnetic interference. On a traditional scale, two units of equal weight will balance, regardless of local gravitational levels; whereas the new method requires that the gravitational force be determined precisely for every site, meaning an additional measurement has to take place. This involves a high-precision gravimeter such as the FG5 absolute gravimeter.

In this comic, Black Hat announces that the kilogram has been redefined as equal to one pound. Ponytail and Cueball seem to think this makes things simpler, but Megan is alarmed. The metric system of measurement is the one used by most of the world and is the standard system used in science. Redefining the kilogram to be equal to the pound would be very disruptive and outrage supporters of the metric system. Redefining the kilogram as being a completely different size from before will create a lot of confusion, since now when people read a mass in kilograms they need to work out whether it was written in old kilograms or new (pound-sized) kilograms.

The pound is officially defined as 0.45359237 kilograms, or less than half a kilogram. This makes defining a kilogram as one pound even more impossible as they are then stuck in a loop, as 0.45359237 kilograms must have the same mass as 1 kilogram, meaning the value of the kilogram would be equal to zero.

The title text continues the joke by saying that the metre has been defined as exactly three feet. The yard, the closest US measurement to the metre, is three feet. However, a metre is about 9 centimetres longer than a yard. As with the pound, the metric system is used to define the yard as it is officially defined as 0.9144 metres. This joke recreates the comic in the real world, with Randall playing as Black Hat, and the reader responding. Those who fall for the claim will either be excited that things are simpler, or devastated at what the result will be.

## Transcript[edit]

- [Black Hat talking to Ponytail, Cueball, and Megan while all stand in a row. Megan's hands are raised emphatically.]
- Black Hat: To end many years of confusion, the International Committee for Weights and Measures has just voted to redefine the kilogram.
- Black Hat: As of next May, it will equal exactly one pound.
- Ponytail: Oh, cool.
- Cueball: That
*does*make things simpler. - Megan:
**No!!**

## Trivia[edit]

To further expand on this, the classic definitions of all our various units of time, length, mass, and temperature are based on phenomena that are neither convenient to measure precisely nor in fact consistently reproducible. The duration of an Earth day and year vary unpredictably, the circumference of the Earth varies, the International Prototype Kilogram gains or loses mass any time it is handled (and in fact just sitting there it and its reference copies diverge from each other), and the value of baseline temperatures such as the freezing point of water depend on which isotopes of hydrogen are in the water molecules.

Nevertheless, there really are constants of nature. For example, one of them is ‘*c*’, the speed of light in a vacuum. The expressed value of *c* depends on your choice of the unit of distance and the unit of time, but it’s a constant in those units. Now just suppose we all had a reproducible way to define a specific unit of time, which just for fun we call a ‘second’. You might not know the length of a ‘metre’, but if I told you that measured in metres per second the universal constant value of *c* is exactly 299792458 metres per second, then I would have fixed the length of a metre to be exactly the distance light travels in a vacuum in 1/299792458 seconds. And in fact this is what the international body responsible for defining our SI units has done.

One second is defined to be a specific number of periods of the radiation emitted in a certain transition of a cesium 133 atom. The specific number was set in the year 1967, so as to match a previous astronomical standard called ephemeris time to the limit of human measuring ability at the time. The 1967 definition didn’t change the actual duration of a second, but it did make its measurement forever reproducible.

In 1983 the value of *c* was fixed to the value noted above. Prior to that it had been measured with respect to existing definitions of a metre, and had to be expressed with a measure of uncertainty. For example in 1973 a team at the US National Bureau of Standards refined *c* to 299,792,457.4 m/s ± 1 m/s. But from 1983 onwards, with an exact integer value for *c* that is quite close to that Bureau measurement, the length of a metre is now fixed with no plus/minus uncertainty. Furthermore, both the second and the metre match their predecessor definitions for all intents and purposes.

Similar redefinitions of units of mass and of temperature in terms of universal constants have been agreed to, mass with regard to the Planck constant *h*, and temperature with regard to the Boltzmann constant *k*. The constants *h* and *k* had previously been measured quantities, complete with uncertainties. The SI body fixed both of them to exact values, resulting in exact, no-uncertainty values for a kilogram of mass and a kelvin of thermodynamic temperature. As with the second and the metre, these new definitions match their predecessor definitions for all intents and purposes.

To expand on this even further, three additional universal constants that were previously measured and that had uncertainty values have been assigned fixed values, resulting in exact definitions of three corresponding units of measurement without affecting their applicability. Fixing the unit of elementary charge, *e*, serves to define the unit of electric current, the Ampere. Fixing the unit of luminous efficacy *K _{cd}* serves to define the unit of luminous intensity, the candela. And fixing the Avogadro constant

*N*serves to define the unit of amount of substance, the mole.

_{A}A Wikipedia article about redefining the SI units of measure in terms of newly fixed values of things taken to be universal constants is 2019 redefinition of the SI base units.

Additionally, it might be worth noting the pound has multiple different types and definitions. The most common definition today is the international avoirdupois pound (lb), which is defined (discarding the semantics) as a unit of mass equal to 0.45359237 kilograms. However the pound is commonly used as to describe force, defined as the force an avoirdupois pound exerts on the Earth (lbf). These definitions however are identical in practical terms, such that an item with 0.45359237 kilograms of mass exerts one avoirdupois pound of force on the Earth. In the SI, the derived unit of force is the newton.

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# Discussion

It's nothing short of a miracle that the US made it to the moon when the imperial system's so ingrained into our culture. Oh, wait, it was a bunch of German scientists who made that possible. Nevermind... Alex

I didn't know that weights and currencies could be converted 1:1, that's cool! Fabian42 (talk) 16:37, 16 November 2018 (UTC)

I wish they *had* redefined the kilogram a little bit. It would have been neat if 1 kg was exactly the weight of 1 dm^3 (1 litre) of water under one atmosphere of pressure. Right now it's soooo close. It's a good enough estimate for simple maths, but whenever you tell people that a litre of water weighs one kilogram the pedants comes out of the woodworks... Kapten-N (talk) 16:50, 16 November 2018 (UTC)

- Having thought about it, therein lies much of the joke. Originally a kg was 1 dm^3 of water at stp. But it's no longer that, so it is essentially now an arbitrary value. And being an arbitrary value, there's really no principled argument not to just redefine it as a pound. The only argument against redefining it as a pound is practical, and sentimental.Nccsa186 (talk) 19:29, 8 April 2019 (UTC)

- You'll get pedants whenever you refer to a kilogram as weight; it's a mass. The difference is that stuff weighs less on the Moon - or on tall mountains - although the mass is the same. I think the article as I just read it gets away with this. And, sure, what is the standard kilogram but a weight, that you take and weigh... [email protected] 162.158.91.59 23:57, 16 November 2018 (UTC)

- It
*used*to be a mass. Now it's a ratio of the local gravitational strength versus the efficiency of an EM field. Kibble scales require EM shielding & an environment of*precisely*1g, in order to be accurate. Since gravity isn't equal everywhere, our measurements of kilograms will now vary accordingly. ProphetZarquon (talk) 08:36, 17 November 2018 (UTC)

- It

- No, it doesn't require an environment of precisely 1g, it relies on the fact that the effect of local gravity is well understood, can be measured precisely, and compensated for. It's a fundamental aspect of the Kibble balance and you can rest assured that it hasn't been overlooked by the physicists designing it! 162.158.134.34 16:38, 17 November 2018 (UTC)
- Oh really?
*How*would one precisely measure the local gravity? In kilograms of force? No, sorry. This is a bad method. It leads to an insoluble quandary & clearly either*hasn't*been thought through by its supporters, or is an intentional exploit.*Actually*fixing it to Planck's constant would be great, but a Kibble scale can't do that. Weighing mass against anything but another mass is foolish.ProphetZarquon (talk) 22:15, 19 November 2018 (UTC)- Local gravity is measured with a gravimeter, which is a kind of accelerometer that also compensates for tidal effects. You can read about it here: https://en.wikipedia.org/wiki/Gravimeter 162.158.94.2 15:32, 9 December 2018 (UTC)

- Oh really?

- No, it doesn't require an environment of precisely 1g, it relies on the fact that the effect of local gravity is well understood, can be measured precisely, and compensated for. It's a fundamental aspect of the Kibble balance and you can rest assured that it hasn't been overlooked by the physicists designing it! 162.158.134.34 16:38, 17 November 2018 (UTC)

- I'm very happy that measuring a kilogram accurately now may require EM shielding. EM shielding is far too rare nowadays, in this modern world of far-beyond-van-eck-phreaking. Anything that makes shielding more prevalent and widely understood is sorely needed. 172.68.65.84 23:19, 20 November 2018 (UTC)
- Amen to that! -
*Originally sent from inside a Faraday cage, but for some reason it didn't work until I stepped out.* - ProphetZarquon (talk) 20:08, 28 November 2018 (UTC)

- Amen to that! -

- I'm very happy that measuring a kilogram accurately now may require EM shielding. EM shielding is far too rare nowadays, in this modern world of far-beyond-van-eck-phreaking. Anything that makes shielding more prevalent and widely understood is sorely needed. 172.68.65.84 23:19, 20 November 2018 (UTC)

Up until 1964 a litre (and therefore actually the metre too) used to be defined as the volume that water with mass 1kg takes. But this is not good for exact measurements not only because you need exactly reproducable temperature, pressure (not so problematic, because you can measure them and then calculate the divergence) and gravity (not so easy to measure, because you need an exact mass and exact masses are impossible to keep the same), but also because you need pure water free of any polutions of other stuff (hard and expensive) and even free of tiny amounts of isotopes which are deuterium and tritium (even way more expensive). Because the water that was used then was never close to pure the actual weight of water nowadays is 0.99997kg at 4°C and 1.013bar and I don't know which value for g. There is also another definition which I like, but is hard to measure in real life scenarios: E=mc². A kilogramm should be 1/c² of the mass which anything becomes heavier that you accelerate by the energy of one Joule. --162.158.90.150 17:11, 16 November 2018 (UTC)

- But how do you define/measure a Joule then? Fabian42 (talk) 18:19, 16 November 2018 (UTC)
- No, until 1964, meter and litre were totally independent, a meter has never been defined directly or indirectly in relation to a mass of water. It is only since 1964 that the liter is defined as a cubic decimeter.162.158.90.36 18:36, 16 November 2018 (UTC)
- The original proposition for a reproducible unit of mass (after the french Revolution, by Talleyrand) was that of the pound being the mass of a cubic foot of distilled water, Also the
*Grave*(equal to our kilogram) was defined by the cubic decimetre of water by the French Commission of weights and measures in 1793. ("Le poid du pied cube d'eau étant ainsi connu, on a conclu celui du décimètre cube, ou la nouvelle unité de poids" https://books.google.nl/books?id=FufDNJHvgFEC p.274). So length and mass *were* interlinked by water.

- The original proposition for a reproducible unit of mass (after the french Revolution, by Talleyrand) was that of the pound being the mass of a cubic foot of distilled water, Also the
- Also, in E=mc², E is the energy
**at rest**(for a stationary object of mass m), so your definition using the acceleration makes no sense.162.158.88.254 18:47, 16 November 2018 (UTC)- That's not the original intent of that formula though. The modern formula is E=γmc², where m is the rest mass. But when Einstein wrote m in E=mc², he meant mass as in the measure of how much gravitational force you exert and experience... which in modern terms is γm . These days, E=mc² is only valid if γ=1, which translates to a body at rest. But that's due to the convention regarding what is meant by mass (rest mass or effective mass) changing since that formula was written, not the E being intended to neglect relativistic effects. 172.69.55.112 22:56, 11 September 2019 (UTC)

Actually, for the new definition of the kilo using the Kibble balance you need to measure the gravity... 162.158.134.16 17:34, 16 November 2018 (UTC)

Welp, looks like 1 kg, a.k.a. 1 lb, a.k.a 2.2 lb, is now officially defined to have zero mass.
172.69.50.28 16:56, 16 November 2018 (UTC)

- …or infinite. Fabian42 (talk) 16:59, 16 November 2018 (UTC)
- What I understand: the joke is not (only) about 1 (old) kg = 1 (old) lb, but (also) about 1 new kg = 1 old lb... or 1 new lb = 1 old kg :^) Or about a ring of positive characteristic --188.114.102.94 17:08, 16 November 2018 (UTC)

- I'm so glad other people see the problem with this supposed "official" definition. We've gone from a unit of measure problematically prone to contamination error, to a unit of measure that changes depending on where you measure it! ProphetZarquon (talk) 08:36, 17 November 2018 (UTC)

what about the ambiguity of the pound? would they reference an Avoirdupois bound or a Troy lb? --wonderkatn 172.69.50.16 (talk) *(please sign your comments with ~~~~)*

I don't believe the Imperial system is "no longer used". Gills have been retired, but yards and even chains are still in use, not to mention the Imperial ~~lb~~ pint. Yngvadottir (talk) 18:49, 16 November 2018 (UTC)

- The imperial system has some good things about it. Feet are divisible by 12, and Fahrenheit is much nicer for human temperatures. Linker (talk) 18:55, 16 November 2018 (UTC)
- Yeah, coz it's so easier to divide by 12 than to divide by 10! 162.158.89.61 (talk)
*(please sign your comments with ~~~~)*- No it is easier to divide by 2, 3, 4, and 6, and yes, I can divide the number of feet by 10 easily in my head. SDSpivey (talk) 19:15, 16 November 2018 (UTC)
- The idea is that with twelve parts, you can have 1/2, 1/3, 1/4, 1/6, and 1/12 all be integer number of parts. This is why these types of systems developed in the past, and why so many systems also had multiples of 60 (you can do the math here.). They were easy to divide by merchants without access to any sort of calculation method. The base-10 system is great if you're only ever dealing with halves or tenths. But if you want a quarter or a third of something, you have to split the base units. It's no longer necessary in modern life, but it had a real advantage in ancient times. Cgrimes85 (talk) 19:18, 16 November 2018 (UTC)
- No longer necessary in modern life... Which is why we should all switch to base-10 units of time! ProphetZarquon (talk) 08:36, 17 November 2018 (UTC)
- Or we could change everything else to base 12... (I can dream, can't I?) Linker (talk) 18:45, 17 November 2018 (UTC)
- I would love a base-10 time system. Especially since time=money, and money is base-10. Color me surprised a while back when my research led me to find out this had been tried in the past. They had a whole calendar system designed to renumber minutes, hours, days and weeks. I think they went to a 10 day week. Would have worked, too, except for religion. Under the new system, too many people had problems keeping track of every seventh day. SO it was scrapped. --ElectroDFW-- 108.162.238.59 08:06, 22 November 2018 (UTC)
- "Swatch time" was dangerously close to a sensible set of increments. Agreed that base-10 would be better than what we use now. ProphetZarquon (talk) 20:08, 28 November 2018 (UTC)

- I would love a base-10 time system. Especially since time=money, and money is base-10. Color me surprised a while back when my research led me to find out this had been tried in the past. They had a whole calendar system designed to renumber minutes, hours, days and weeks. I think they went to a 10 day week. Would have worked, too, except for religion. Under the new system, too many people had problems keeping track of every seventh day. SO it was scrapped. --ElectroDFW-- 108.162.238.59 08:06, 22 November 2018 (UTC)

- Or we could change everything else to base 12... (I can dream, can't I?) Linker (talk) 18:45, 17 November 2018 (UTC)

- No longer necessary in modern life... Which is why we should all switch to base-10 units of time! ProphetZarquon (talk) 08:36, 17 November 2018 (UTC)

- Yeah, coz it's so easier to divide by 12 than to divide by 10! 162.158.89.61 (talk)

Ok, I'm going to point out something. What's a meter? 1000 milimeters. What's a milimeter? .....skipping the questions all the way to the end, the answer is "the wavelength of the color orange". Or at least that's what I read. So my question is: why orange? What's so special about orange? What as a species or as a solar system or as universe does the color orange have to do with anything? 172.68.90.10 21:50, 16 November 2018 (UTC) SiliconWolf

- Orange is my favorite color. Enough said. Alex

- "The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole." That's why orange. Think of those lines from equator to pole... and how an orange is divided in segments beneath the peel. This is why the "Terry's Chocolate Orange" is so called, because it resembles the fruit orange. [email protected] 162.158.91.59 23:51, 16 November 2018 (UTC)

- The wavelength definition of the meter is not in use anymore either. Since 1983, the meter is defined as the distance the light (any light) travel in the vacuum in 1/299792458 seconds. Of course, all units have a part of arbitrary, and the value it is used to calculate the meter (the orange color, the 1/299792458 seconds...) are basically chosen because they are close to and more precise than the previous definition that existed, in order to not have to recalibrate things that don't need high precision. 103.22.200.210 08:03, 17 November 2018 (UTC)

- I feel like we're starting to compare angstroms & millitrumps, here. ProphetZarquon (talk) 08:36, 17 November 2018 (UTC)
- I don't think we need to bring politics in here. -boB (talk) 15:16, 19 November 2018 (UTC)
- Agreed, but all this talk of "orange" makes it very hard not to relate the entire conversation to politics, for some of us who are particularly affected. Hopefully someday it'll just be another color that's hard to rhyme, again.

- I don't think we need to bring politics in here. -boB (talk) 15:16, 19 November 2018 (UTC)

**Be very careful**

An announcement to a new definition of the kilogram is published wildly (I mean what I'm saying) today. Please do not present this issue as a final fact, I'm still missing an official statement -- it's just press hype. And there are two possible definitions taken account, not only the one from the US. The final decision right now looks like some of Randall's compromises. Just sayin... --Dgbrt (talk) 20:01, 16 November 2018 (UTC)

- OK then, here's an after-the-vote November 16 web page from NIST, the National Institute of Standards and Technology, within the US Department of Commerce. It says it's a done deal. historic-vote-ties-kilogram-and-other-units-natural-constants. --JohnB 162.158.79.89 21:58, 16 November 2018 (UTC)
- Thanks, but my German sources still preset something like counting atoms Kilogram and MOL, counting atoms, just meaning I'm not sure what will be true in May 2019, do we know the truth??? And in fact it looks like Europeans are fighting against US scientists, or vice versa. This is far of a standard I would prefer. --Dgbrt (talk) 22:29, 16 November 2018 (UTC)
- I'm
*extremely*skeptical of the Kibble scale definition. It won't maintain constant mass at different locations. ProphetZarquon (talk) 08:36, 17 November 2018 (UTC)

- I'm

- Thanks, but my German sources still preset something like counting atoms Kilogram and MOL, counting atoms, just meaning I'm not sure what will be true in May 2019, do we know the truth??? And in fact it looks like Europeans are fighting against US scientists, or vice versa. This is far of a standard I would prefer. --Dgbrt (talk) 22:29, 16 November 2018 (UTC)

It will be very funny when we find out one of those constants is not really constant ... sure, planck length is less likely to change than physical object, but it MIGHT. Like, maybe it gets longer the older the universe is ... -- Hkmaly (talk) 23:17, 16 November 2018 (UTC)

- The definition of units is always dependent on our knowledge of physics. Perhaps the best example of this is the confusion about whether the pound is a unit of mass or weight. The lb predates the distinction and the definition bifurcated when the distinction became clear.
- If Planck's constant isn't constant then we get two functionally different concepts of mass and we have to decide if we stick with the new definition or go back to (some equivalent of) the older one.
- By the way the confusion over the definition of a lb was settled long ago. The lb is defined in terms of the kg and is a unit of mass. The claim that the lb is a unit of force is a deliberate obfuscation perpetuated by bad physics teachers who understand neither physics nor the history of physics. 108.162.219.58 19:52, 19 November 2018 (UTC)
- Since they're proposing to measure the gravitational force exerted on a unit of mass against the force exerted by an electromagnetic field (instead of comparing the downward force exerted on two masses), the new definition
*isn't*a constant. For instance, on the moon such a scale would define 1kg as about 13.3lbs! The "new official definition" is a bad one. ProphetZarquon (talk) 08:36, 17 November 2018 (UTC)

You could not define the kilogram in terms of electric force when you defined the Amp in terms of the current that creates a given force. But by defining the amp in terms of numbers of elementary charges per second and setting Avogadro and other constants by fiat, you break the circle. 162.158.38.190 23:54, 16 November 2018 (UTC)

In the Netherlands, we use the metric system. We also use the term "pond" to mean pound. However, we use metric pounds. Those are 0.500 kilogram, so it is actually easy to use. 162.158.89.61 (talk) *(please sign your comments with ~~~~)*

US weight and length units definition is strictly based on metric system: "Standards for the exact length of an inch have varied in the past, but since the adoption of the international yard during the 1950s and 1960s it has been based on the metric system and defined as exactly 2.54 cm."{https://en.wikipedia.org/wiki/Inch} "the most common today is the international avoirdupois pound, which is legally defined as exactly 0.45359237 kilograms" {https://en.wikipedia.org/wiki/Pound_(mass)} Therefore the conversion proposed sounds recursive. Also, https://www.youtube.com/watch?v=SmSJXC6_qQ8 172.68.51.178 13:49, 17 November 2018 (UTC)

While it would be nice if the meter were equal to a yard, it would certainly be better if the meter were defined as 5.28 feet, so that kilometers and miles are the same.Mathmannix (talk) 13:54, 17 November 2018 (UTC)

- Not to mention, why are highway sign distances measured in quarter-miles, but our car odometers are tenths? Grrr... --ElectroDFW-- 108.162.238.59 08:06, 22 November 2018 (UTC)

I'm guessing that they'll get around the varying g problem by defining the kg in terms of some standard acceleration equal to 9.81 m/s^2. Then when measuring an object's mass you would account for the difference between the local value of g and the standard one. This isnt a problem because we can measure gravitational acceleration quite precisely and it depends only on the units of length and time. 108.162.216.190Carl108.162.216.190

- The varying g problem is already compensated for in the way you describe (otherwise the Kibble balance wouldn't be useful), ProphetZarquon is just spreading misinformation. Arcorann (talk) 07:55, 18 November 2018 (UTC)

In the What If "A Mole of Moles," Randall states in his estimates, "Anything I can throw weighs one pound. One pound is one kilogram." [1] 162.158.75.178 (talk) *(please sign your comments with ~~~~)*

Let's see... All the things this proposed change would mess up. (even assuming that Black Hat meant 1 Kilogram = 1 mass-pound) .... The newton just changed, but only in relation to the KG, so I guess the force required to lift 1 KG in 1 G is still technically about 10 newtons, only it's a DIFFERENT newton now... atmospheric pressure is no longer ~= to 100 kilopascals, because the pascal just changed. 1 liter of water is no longer ~= to 1 KG. Metric and imperial Tons are no longer anywhere close to each other. 1 mole of carbon-12 no longer masses 12 grams. There must be other ways the common rules-of-thumb of the metric system just got broken, any suggestions? 108.162.216.82 19:44, 18 November 2018 (UTC)

There is already one link to a Veritasium video on this subject a few coments above, and there was a new video out just before this vote, about the new units: The kg is dead, long live the kg. --Kynde (talk) 15:57, 19 November 2018 (UTC)

The title text actually made me scream in existential horror. 162.158.79.89Somebody who probably has an account here but can't be bothered to log in.