explain xkcd - User contributions [en]

Talk:2585: Rounding

2025-03-20T15:57:57Z

172.69.59.147: Current bicycle speed record.

Wot no {{w|FFF system|furlongs per fortnight}}? [[Special:Contributions/172.70.91.126|172.70.91.126]] 23:14, 23 February 2022 (UTC)

: I, too, was initially surprised that Randall hadn't used the standard joke measure. But, then I realized that F/F is so outrageously large that rounding wouldn't offer much advantage. [[User:MAP|MAP]] ([[User talk:MAP|talk]]) 05:10, 24 February 2022 (UTC)

If we're using the table, can I suggest it be fully filled in, but mark "original (rounded)" value cells one key colour and the chosen conversion in another, so that scanning along (not necessarily adjacent/rightwards) then down (always next row) then along... you see the 'bounce around'. And we also get to appreciate what other fractional values ''could'' have been chosen, prior to rounding... Alternately, some flow-charty layout (perhaps contained within a nominally borderless version of the table?) with arrows leading across the width and filling in-between each down-step. Ideas only. I have others, but those seem the best bet to consider. [[Special:Contributions/172.70.85.113|172.70.85.113]] 01:32, 24 February 2022 (UTC)

Disagree with the current (as of 23:27 US Eastern, 23 February) explanation. According to this site (https://ilovebicycling.com/average-bike-speed/), average downhill bike speed is over 45 mph. Since Cueball doesn't specify "on flat terrain", he should have no problem going 45 without exploiting imprecise conversions. [[User:Nitpicking|Nitpicking]] ([[User talk:Nitpicking|talk]]) 04:30, 24 February 2022 (UTC)
:Huh? This does not say average downhill speed is > 45, it says "fastest". Also why would Cueball need to do this bizarre rounding if he can actually go 45mph? This is an exaggeration because he can only go a typical speed of 17mph.[[Special:Contributions/172.69.33.145|172.69.33.145]] 04:52, 24 February 2022 (UTC)
::Fastest for average cyclist. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 05:05, 24 February 2022 (UTC)
:As a cyclist of several decades experience, who has indeed attained such speeds on rare (reckless) occasions, I think that "fastest downhill speed for an average rider" is overstated. Maybe it is what average people are capable of on a well-surfaced, steep, straight, non-undulating road with sufficient vision (forward and of anything potentially moving into the road from the side) or at least confidence that you're not dealing with traffic/pedestrians/other unaware cyclists. Oh, and sufficient stopping distance for whatever brakes you have.
:Maybe everybody can do it ''once'', but a good bike-ride should be one you can walk away from at the end.
:(Also, that cycling-centric site might have a different idea of 'average' cyclist. The average person on a bike here can't even put their feet on the pedals correctly. If we're talking club-/competitive-cyclists (but still sub-pro) then I'd much more readily agree, but there are far more people these days who can't even ride on the roadway, it seems.)
:That bike, as drawn, looks like it'll be Okish (if kept well maintained) but not exactly set up as functional downhill racer, nor probably is the rider. I really think the machine probably could be ridden at 20+mph on the flat for as long as the rider can stand to, but the characterisation makes me not confident they're able to maintain that kind of average speed for a [https://www.cyclingtimetrials.org.uk/race-results/22059#anchor long ride], and I think they'd overbake a downhill speed-run too, or (sensibly) be more cautious. [[Special:Contributions/172.70.85.143|172.70.85.143]] 05:14, 24 February 2022 (UTC)
:: Yep - the speeds on that site are for road bikes. Cueball looks to be riding a hybrid (flat bars), which would tend to put him in a more upright position, creating a higher frontal area and air resistance, and so slowing his progress. That would have even more of an effect at higher speeds. [[Special:Contributions/162.158.159.43|162.158.159.43]] 11:14, 24 February 2022 (UTC)

Arguably, once you're up to numbers around 45, you're as likely, if not more so, to be rounding to the nearest 5 than the nearest unit (depending on context). So Cueball's initial statement could be taken as suggesting that he can ride at around 42.5 - 47.5mph (rather than 44.5 - 45.5mph). And if he could actually ride at over 45mph then he presumably wouldn't need to add the 'if you round' qualifier, so it could further be taken as just suggesting that he can exceed 42.5mph. [[Special:Contributions/162.158.159.43|162.158.159.43]] 11:22, 24 February 2022 (UTC)

Note I find it kind of disappointing that the insane "KPH" unit is used in the comic. Nobody uses that in places where speed is actually measured in km/h.
: yes, but we are talking about a US based comic, one of only 3 countries (Myanmar, Liberia, USA) that don't use the metric system for measurement...oh, except for money, but that isn't really metric, it is money ;o) [[Special:Contributions/108.162.250.190|108.162.250.190]] 00:50, 25 February 2022 (UTC)
:: Erm, I think you'll find the UK uses miles as well. And we're just putting ourselves through a massive political and economic upheaval so that we can have our old imperial weights and measures back (at least, I think that was the point of it all).[[Special:Contributions/141.101.77.24|141.101.77.24]] 16:30, 25 February 2022 (UTC)

Ironically, by the same standards it only takes one conversion to say that he can't move at all on a bike. he goes 0 parsecs, lightyears or AU (for example) per year, decade or century (for example).

Can we remove the rounding errors in the "exact" values in the tables? For instance, the final value should be "45.0000" not "45.0001". In fact, all three values ending with 0001 are rounding errors. (These were probably a result of converting to metric and back, using low precision conversion factors.) [[User:Divad27182|Divad27182]] ([[User talk:Divad27182|talk]]) 15:49, 24 February 2022 (UTC)
: Yeah, like fathoms/s and yards/s are by definition just a factor 2 apart. I recalculated the values without rounding at any step except the final step, so the rounding errors should be gone now. Also added vincula for repeating digits. [[User:Tharkon|Tharkon]] ([[User talk:Tharkon|talk]]) 19:25, 27 February 2022 (UTC)

Whoever decided to display that information in that table deserves an award. Gg. [[Special:Contributions/172.70.126.65|172.70.126.65]] 16:38, 24 February 2022 (UTC)

It's nice how the rounding of exact half-integers only ever has to deal with odd-numbers-and-a-half, so Cueball can't be charged with violating the "round to even" rule, nor with violating the "round away from zero" rule. [[Special:Contributions/172.70.131.122|172.70.131.122]] 18:06, 24 February 2022 (UTC)

It looks like Randall picked a starting speed (within a reasonable bike-riding range) to maximize his gain. Groups of starting speeds round to the same final speeds, and some groups have a higher maximum speed earlier in the rounding chain:
::{| class="wikitable"
! Start Speed
(mph)
! Max Speed
(rounded to mph)
! Final Speed
(mph)
|-
|1
|1
|0
|-
|2 to 9
|9
|8
|-
|10
|10
|8
|-
|11 to 16
|16
|15
|-
|17 to 45
|45
|45
|-
|46 to 54
|54
|53
|}[[Special:Contributions/172.70.131.122|172.70.131.122]] 21:24, 24 February 2022 (UTC)
:Are you assuming the exact same chain of conversions, just with different input values? Surely if he'd chosen to start at (say) 16, he'd have chosen whatever ''other'' chain of conversions would have sent him towards some decent high-value. Might have differed only by the initial conversions before it found itself landing on the same late-path, or could be completely different (to get to a different end) as the biased random-walk of choices hit a different useful stride pattern. [[Special:Contributions/141.101.99.20|141.101.99.20]] 22:39, 24 February 2022 (UTC)
::Yes, I put different starting speeds into the same conversion chain. Perhaps I should have said "He chose a reasonable starting speed and chain of conversions to maximize the gain." I was initially surprised that starting at 16mph ends at 15mph, then decided to plot it. The grouping of ending speeds also surprised me, but in hindsight that's to be expected with multiple round offs. [[Special:Contributions/162.158.75.17|162.158.75.17]] 23:02, 24 February 2022 (UTC)
:::Not surprising at all. Given any random (not selectively chosen) conversion-then-rounding function, you'd expect about half the time you get a lowered (absolute) value rather than a raised one, for the input number somewhere in the range 1 to infinity. For any pair of measures of unequal scales but sharing zero. (Possibly also viable in non-equal and dislocated scales, like °C and °F, but that's just a hunch that I've not emperically checked, and not applicable here anyway.)
:::The chain chosen was conspicuously optimal to get the starting value 17 to always rise. Possibly by the maximum possible amount, on each chosen step, from amongst all those considered conversions, but I haven't checked this. It even has a viable unit_A=>unit_B for one rounding rise then unit_B=>unit_A for yet another rounding rise, because it happily works like that at the respective points of each scale.
:::But when you start from a different value, you lose the initial upwards-bias in the same 'meshing' and on each subsequent Randall-chosen one. It's pretty much a random sequence, as far as the value that it wasn't designed for is concerned. Logic dictates that it will downplay the value about as often as it will up-play it, for most scenarios. Except maybe at resonant multiple/divisors of the original (which will still chaotically drift, as rounding up .6 for a value would mean rounding down .3 for value/2 or down from .2 for value*2, setting you up for the next function in the adopted sequence to fail), but then 17 is prime so you'd have to start with 34 for that to (sometimes) work.
:::And, assuming the sequence is chosen for maximising upwards, you've got the function at each stage that is selected precisely because ''for that exact state-value'' it is specifically upward-trending, so when you try that in a different context reversion-to-the-mean suggests you're perhaps more likely to hit one of the downward-trends in the relationship.
:::My theory is that for any given starting value, some convert-then-round (from a sufficiently diverse choice of options) will always maximise the resulting magnitude. And that result will always have its own maximal conversion. Although those two operations may be less maximising in combination than a submaximal first operation (maybe, in some cases, a slight ''reduction''?) that 'lands' on a better number for a differing secondary maximiser step to act upon. So a full search-path needs to consider an N-step look-ahead method rooted in a breadth-first trial of each step-1, etc, to optimise the maximiser-optimiser process. But I haven't the time to test it right now. Maybe later! [[Special:Contributions/172.70.162.77|172.70.162.77]] 00:53, 25 February 2022 (UTC)
::In fact, the starting value of 17 is most definitely optimal for these choices of units, assuming you want only one optimal choice of rounding (not having to choose between several equivalent values, and not end up non-rounding, like you get at 45 mph). A simple spreadsheet with the ablity to copy-paste an indefinite number of steps with error-checking is here: https://docs.google.com/spreadsheets/d/1ZUSbUmY2rz2JqJBfYIC2GQJucOJ71A0riTCm_OAE4VU/edit#gid=962607803 [[Special:Contributions/141.101.69.214|141.101.69.214]] 16:46, 9 March 2022 (UTC)

A note about the propulsion system in the mouseover text: This system is not entirely novel and was first proposed by Douglas Adams who suggested using the notebooks of waiters in bistros to achieve the desired precision loss. He suggested it should be possible to achieve speeds of round ∞kph (∞mph) [[Special:Contributions/162.158.202.247|162.158.202.247]]
:The books don't mention those details in their description of "bistromathics", and I don't recall them having been added to the radio adaptations. [[User:BunsenH|BunsenH]] ([[User talk:BunsenH|talk]]) 23:15, 24 February 2022 (UTC)
::To clarify: the book mentions the waiters' notebooks, but nothing about precision loss or achievable speeds. [[User:BunsenH|BunsenH]] ([[User talk:BunsenH|talk]]) 16:55, 25 February 2022 (UTC)
:The Improbability Drive (in the Hitchiker's Guide) also seems somewhat related.
:What relation can that have? I'm looking at {{link|https://hitchhikers.fandom.com/wiki/Bistromathics|this link}}. [[User:GcGYSF(asterisk)P(vertical line)e|GcGYSF(asterisk)P(vertical line)e]] ([[User talk:GcGYSF(asterisk)P(vertical line)e|talk]]) 03:32, 25 February 2022 (UTC)
:The various things that {{w|Hex (Discworld)|Discworld's "Hex"}} can do (including occasionally providing magical teportation) can rely upon it trying lots of 'impossible' things very quickly "before the universe notices". [[Special:Contributions/162.158.159.125|162.158.159.125]] 14:19, 25 February 2022 (UTC)
:My favorite "impossible" thing mentioned in the Hitchhiker's Guide is be able to fly by "learning how to throw yourself at the ground and miss". I have done this successfully while dreaming, but have never accomplished it while wide awake. But it is surely worth trying. [[Special:Contributions/108.162.219.49|108.162.219.49]] 15:13, 25 February 2022 (UTC)
::people on ISS miss the ground all day long, while falling at astounding speeds. [[User:Bmwiedemann|Bmwiedemann]] ([[User talk:Bmwiedemann|talk]]) 04:48, 5 March 2022 (UTC)
:Interestingly, it's impossible to get above 45 mph using any of the units Randall used: Converting 45 mph into any of those units always results in either an integral number or a number with fractional part below 0.5, which would result in rounding down. (I've used https://www.unitconverters.net/speed-converter.html for the more common units).--[[Special:Contributions/172.70.250.159|172.70.250.159]] 17:36, 25 February 2022 (UTC)
:It also reminds me of the Dungeons & Dragons "Peasant Railgun," which abuses a queue of readied actions to accelerate a projectile to relativistic velocities. [[Special:Contributions/172.70.110.163|172.70.110.163]] 19:59, 25 February 2022 (UTC)

"Normally, when you say you can ride a bike at 45 mph if you round, you mean that you can ride at a speed between 44.5 and 45.5, something most people are incapable of doing." When I was MUCH younger, in my late teens or early twenties, I decided to bicycle from a northern suburb of Philadelphia to my home in Hockessin, DE. It was a hot summer day and, only being in average shape, I underestimated my ability to hold up under the heat. A Delaware State Trooper wound up driving me and my bike to my destination. Halfway through my trip, I was going down a long hill on U.S. 1 in Media, PA and decided to see how fast I could go. The speed limit was 55 MPH. My speedometer didn't read that high, but I was passing cars going in the same direction. I estimate I was going at 5-10 MPH faster than the cars, and I'd guess they were going at least 55 MPH. So this statement may be true--most being more than 50%--but I suspect most young men of that age would be capable of 45 MPH and faster.
[[User:Hugh|Hugh]] ([[User talk:Hugh|talk]]) 15:20, 1 March 2022 (UTC)

I don't normally use this wiki so I don't know standard practices, but it might be worth pointing out somewhere on the explanations page that [https://mathoverflow.net/questions/416965/how-far-away-can-we-get-by-multiple-rounding-and-unit-change the question (implicitly raised in this comic) has been asked on MathOverflow] of whether it's possible to get to arbitrarily large (or small) values using conversion-and-rounding between a finite set of units, and [https://mathoverflow.net/questions/416965/how-far-away-can-we-get-by-multiple-rounding-and-unit-change/417018#417018 the answer is 'no']. So maybe one of y'all wants to add one of these links in the appropriate place, whitherever that may be. --[[Special:Contributions/141.101.69.46|141.101.69.46]] 08:59, 29 April 2022 (UTC)

The current speed record for a bicycle is 183.932 mph. Of course that was a special bicycle drafting behind a car.

Talk:2790: Heat Pump

2023-06-18T20:03:50Z

172.69.59.147:

woah! an xkcd with color what was the last one with color? (im kinda new to xkcd) [[Special:Contributions/172.71.122.48|172.71.122.48]] 21:17, 16 June 2023 (UTC)Erfaniom
:I guess the last one with a lot of color was [[2750]]. More at [[:Category:Comics with color]]. [[Special:Contributions/162.158.167.11|162.158.167.11]] 17:29, 17 June 2023 (UTC)

I suppose color was needed to show the air temperature. Odd, though, that in summer (in the northern hemisphere), the character is trying to increase the indoor temperature. [[User:Davidhbrown|Davidhbrown]] ([[User talk:Davidhbrown|talk]]) 21:27, 16 June 2023 (UTC)
:He's not. He's moving the hot air from inside to the cooler outside. [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 22:18, 16 June 2023 (UTC)
:::he's actually heating it, the comic is set in winter. It's a reference to the discussion about regulating heating systems in Germany. I added something about that in the explanation, but I don't think I made the citation right (I'm not to editing wikis) [[User:Marta]] ([[User talk:Marta|talk]]) 05:25, 17 June 2023 (UTC)
:::::The citation does not appear to strongly relate to the comic to me. I might be curious if Randall had a lot of comics queued and actually published a winter one in the summer, for example. [[Special:Contributions/172.69.59.112|172.69.59.112]] 00:19, 18 June 2023 (UTC)
::::::I agree, I think the Germany thing might probably be coincidental. Randall lives in North-Eastern America. It's unlikely, though quite possible, he was inspired enough by such foreign matters to base a comic on it. Still, you never know from whence inspiration may strike, in which case he published when he thought of it instead of when it'd be relevant... [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 04:40, 18 June 2023 (UTC)
:::::::News of this had not otherwise reached me over the German Ocean (i.e. North Sea), never mind where Randall is, way over the Pond (i.e. Atlantic). Not saying it wasn't a prominant bit of news, in his media feeds, but usually the problem is that something 'popularly heard about' state-side confuzzles anyone in (say) Europe/ex-Europe when used as inspiration for a comic without enough setup to it. Now, ''if'' say Penn./Mass. state legislature were being similarly proactive on such matters, I'd say it might be the cue for this. Otherwise, it might be better as an afterthough/Trivia instead of the lead-on paragraph. But I also don't know enough to know that it ''isn't'' worthy of such prominance, so this is just my thoughts, leaving others to alter it if they so wish... Anybody can do it, after all... [[Special:Contributions/162.158.74.96|162.158.74.96]] 09:55, 18 June 2023 (UTC)
::::Nearly right. Simple "insert URL" as a 'number' is single []s, or [<url><space>some text] to have it given linking text (preferable).
::::Plus you seem to have not used the four tildes, i.e. <code><nowiki>~~~~</nowiki></code> to sign the above comment (made it correct, for you), plus confusingly replied ''before'' another reply (so I indented you a bit more, as well as it now having that timestamp to make precedence clear).
::::But these are all things you'll pick up, I'm sure, if you're going to be getting [used] to wikis... Welcome! [[Special:Contributions/172.71.178.139|172.71.178.139]] 05:35, 17 June 2023 (UTC)
::I actully think he's warming the inside, already warmer than outside, by effectively (and literally!) squeezing the heat out of the cooler outdoors air.
::By compressing the cool outdoor air, he increases its temperature (p1v1/t1=p2v2/t2) to warmer than the warm indoor air, creating a squeezebox->room flow of heat energy, then returns to the outside before decompressing and lowering the temperature in his squeezebox below the cool-air temperature in order to create an outdoors->squeezebox flow of energy and repeat. (The comic has the cycle start at roughly half-way through that, and wraps round, but the heat-to-room seemed the most obvious starting place here.)
::Right now, I'd not wish to heat my indoors up (even at 11:30pm, like now), so I agree that it's a funny time of year show heat-adding (rather than heat removing), but it definitely is that. [[Special:Contributions/172.70.86.154|172.70.86.154]] 22:31, 16 June 2023 (UTC)
:::Assumption(?): Indoors is on the LHS and higher, outdoors on the RHS and lower, door opens outwards and steps down to "outside". He COULD instead be cooling a basement apartment with a door that opens inwards (like mine)... however he seems to make a noticeable difference to the red, not the blue, so... probably not. :-/ [[Special:Contributions/172.70.34.160|172.70.34.160]] 02:36, 17 June 2023 (UTC)
::: Since panel 3 shows it at its widest and bluest with "Release", I understand that to mean he's releasing the heat outside from inside - like an A/C does. The weird thing is then showing the reddest/smallest with "Radiate", that word means "make and release heat" to me. The thing is, past experience tells me Randall lives in roughly the same part of the world as me, same climate. That he's in the northern states (like, within a day's drive of the Canadian border), and the Eastern time zone, and it's summer for us. Only heat pumping people should want is pumping heat OUT of the house... [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 04:16, 18 June 2023 (UTC)
::::Releasing the spring. At that point, there's the same amount of heat within the device, but it's spread out more so that the temperature is lower (than it was, but also than the surrounding air, which is also ''negligibly'' compressed outwards of course). NB, it does ''not'' draw air into it.
::::Now he has a cool device, heat naturally flows into it until (sufficiently) equalised after a small wait. Take the outside-cool (and expanded) device inside and compress it (it does not expel air!) to have that amount of heat be in a smaller space and thus a higher temperature. High enough to (quite naturally) flow into the room. Thus low-temperature heat taken from outside and used to increase the higher-temperature heat inside, which is different to what happens if you trap and move cold ''air'' into a warm room. Though perhaps it looks like that on first appearance, except for the colour-cues going all screwy. [[Special:Contributions/162.158.74.96|162.158.74.96]] 09:55, 18 June 2023 (UTC)
Wasnt there a "My hobby is to open my refrigerator and when people tell me that doesnt help, I sneak into their house and use their AC?" Comic? I cant find it, but we should link it in the "how leaving a fridge open doesnt help" section [[Special:Contributions/172.71.142.158|172.71.142.158]] 23:36, 16 June 2023 (UTC)
:Sounds like Steven Wright, he has lots of those "my hobby is" jokes. [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 13:29, 17 June 2023 (UTC)

I think it's talking about leaving the door open in general i.e. forgetting to close it when getting groceries, not specifically when he's moving the heat pump [[User:Firestar233|Firestar233]] ([[User talk:Firestar233|talk]]) 23:40, 16 June 2023 (UTC)

I can't think of a good reason to say this, but my new fridge doesn't warm up on the back. It warms on the sides. A bad (and quite a PITA reason) is I had to get a new fridge. Protip: don't panic, and do put the sacks of ice into something that won't leak. First time I've met a fridge that doesn't warm on the back.
Btw, red hot blue cold. Pink? Light blue? A light blue a pink? Shrug. [[Special:Contributions/172.70.43.31|172.70.43.31]] 23:57, 16 June 2023 (UTC)

How many trips would this take? I'll leave the exact parameters of the calculation up to you. (Nerd sniping attempt.) ~ Megan she/her [[user talk:megan|talk]]/[[special:contribs/megan|contribs]] 00:20, 17 June 2023 (UTC)
: 42. But stick figures are just lines and have no surface area for heat transfer.
[[Special:Contributions/172.70.134.236|172.70.134.236]] 01:02, 17 June 2023 (UTC)

Currently, the explanation says you use a heat pump to "transfer heat from a relatively cold area to a relatively hot area". I don't know anything about the named "ideal gas law" in order to be sure enough to change this, but isn't that the wrong way around? If an area is ALREADY cold, why would anybody transfer heat FROM it? 04:49, 18 June 2023 (UTC)
:Let's say it's winter, and it's cold outside. It's warmer inside, but not as warm as you'd like it to be, so you need to warm it up. Where are you going to get the heat from? Traditionally you'd use a boiler to heat up water or electric coils, but these use lots of energy. A heat pump is more efficient, it moves some of the heat from the cold air outside to the inside. You need a pump because it won't move spontaneously -- heat always goes from warmer to colder areas. [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 09:49, 18 June 2023 (UTC)
:[edit conflict with the above reply, thus repetition, but as I was adding other stuff too...] It's fridge-logic! i.e., that's what fridges do... and if you're living in a cool climate, you can potentially heat your house above "too cold for indoors" temperatures by extracting heat from the "far too cold for indoors" air that is outside. [[Special:Contributions/162.158.74.96|162.158.74.96]] 09:55, 18 June 2023 (UTC)

Technically, it's not the ''ideal'' gas law in play, since air isn't an ideal gas, and the system would behave similarly for closer-to-reality gas behaviour models. But I can't think of a good way of modifying the article to reflect that. [[User:BunsenH|BunsenH]] ([[User talk:BunsenH|talk]]) 16:04, 18 June 2023 (UTC)

Noting you could make hand-crank manual heatpumps that are much easier to use than the one depicted. If it’s doable it’s of meaning because a heatpump can be a big electricity draw, and sometimes electricity is not available. You could also connect a horse, waterwheel, or windmill to it. Making homemade windmills out of bicycle parts is a thing. [[Special:Contributions/172.69.59.147|172.69.59.147]] 20:03, 18 June 2023 (UTC)