The Minecraft boat-drop mystery
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- čas přidán 29. 03. 2024
- Here is camman18's CZcams short about the mystery: • java edition moment
Huge thanks to Natalie for sending it to me!
This is the bug report Oliver found: bugs.mojang.com/browse/MC-119...
Explore floating point errors yourself using the IEEE-754 Floating Point Converter: www.h-schmidt.net/FloatConver...
My previous video about Minecraft: • How lucky is too lucky...
Thanks to my patreon supporters. They keep my this.status = IN_AIR. / standupmaths
CORRECTIONS
- None yet, let me know if you spot anything!
Filming by Matt Parker
Editing by Gus Melton
Minecraft footage by Oliver Dunk
Written and performed by Matt Parker
Produced by Nicole Jacobus
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
New book! mathsgear.co.uk/products/love... - Zábava
As a game dev, this is the level of bug-reporting quality we only dare hope for in our wildest fever dreams.
The reason Minecraft bug reports can be so datailed is because the Minecraft EULA allows end-user to decompile the game. So technically Minecraft is a source-available software.
finally, something more than "the game stopped working, please fix it :("
I agree its great but honestly not sure how i would fix that bug, without breaking anything else or have more computation and checks.
@@aladanor personally I would give the same tolerance for the onGround check, as the status has, so there wouldn't be a discrepancy between the two. But yeah... I'm not familiar with the rest of the code, so I don't know if this wouldn't break something else xP
@@aladanorI mean, the system (at least as explained here) is definitely a little clunky. Probably because Minecraft is approaching 15 years old after all.
I'd have to look at the actual code, but I imagine some cleaner logic for handling the fall would either eliminate this bug all together or at least make it easier to fix.
Floating point numbers causes boats to break. Makes sense, since boats need to float correctly.
11/10 comment
Extremely underrated comment. They should pin this. 😆
Gosh this is genius
@@abebuckingham8198 no worries; it has floated to the top
@@landru27 just because is a good point
Him: Warning math people they don't need to know anything about Minecraft to enjoy the video
Me: A Minecraft person, worried that I need to know anything about math to enjoy the video
haha
This video simplified:
Computers do not like numbers that are not multiples of 2^integer.
Oh, hello there)
and DID you need to know about maths to enjoy the video?
hi moggy swampy
Another fun fact: If a boat falls from 44970 blocks high, it will not break despite it being in the sequence calculated. This is because after falling for that long, the tiny difference between 0.0399999991059303 and 0.04 compounds enough to offset the boat by more than the 0.001 block margin to have the ON_LAND status.
This also means that boats are safe to fall from any height of 43543 or higher until you get all the way up to 1794944 blocks, at which point the boat is offset by the 0.04 blocks needed to wrap back around into the range where it can take damage, after falling for nearly 8 minutes.
Lovely fact!
❤
❤
That is far more than the maximum height....
@@reIONEre yeah but you can get mods that remove the build height limit. You can also just teleport the boat to that height.
The status of neither being in the air nor on the ground is what we in more basic speech call "Swimming".
And, specifically relevant to this, being in water negates all fall damage.
that could also possibly be the status of being on a ladder
in lava, yes. :)
Or cobweb, right?
I have a feeling that a lot of things that negate or reduce fall damage would be relevant here. I'm not in the air, I am actually:
in water, on a ladder, in a cobweb, in lava (it doesn't negate it then for some reason), in scaffolding, in powdered snow...
12:54 "famously, multiples of 5 are at least 5 apart"
But only if they're distinct!
Yes we all saw the video, mate
@@aurelia8028 Not necessarily. Every once in a while I will space out and miss a line like that. Regardless, this is a comment conveying appreciation for a good joke; it's positive feedback, and good for the algorithm. It has value, even if it has none directly for you.
To be fair, this makes more sense when you know how floating point numbers work. It's a reference to rounding errors that crop up all the time.
That was profound.
imagine being the mojang dev that receives the bug report containing a full stand-up maths video
examples of both on_ground and inair being false:
-climbing/descending ladders
-swimming
-falling through cobweb
-climbing/descending vines
-riding a boat/other entity 8:54
Also probably sinking through powdered snow or scaffolding. Maybe sliding on the side of a honey block. And potentially gliding with an elytra because the damage taken from crashing with an elytra is calculated separately from fall damage, so there's probably a different state specifically for that.
This makes me wonder if Matt has his explanation slightly off and it is the case that the boat’s in-air value is true but your in_air value is false when riding in the boat and usually means the boat bypasses its damage calculation except for the floating point cases and separately you bypass the damage calculation except for these floating point errors where maybe the boat has reached the ground; been destroyed; your in-air gets set to true; so in the next tic you don’t bypass the checkFallDamage method and instead die.
Actually, horses don’t count (unless it’s Bedrock version) if I recall correctly
Edit: I made a mistake. This is for fall damage when riding horses.
climbing was the first thing i thought of
9:42 The reason we need to check that fall damage was actually caused by falling is that Ender Pearls deal fall damage to the user when used.
This comment needs to be pinned! 😀
This suggests that if you use them while in the air you would be immune to that damage because your status would be IN_AIR. Is that correct?
@@petergerdes1094you take damage regardless 😅
@@petergerdes1094Ender pearls teleport the player, and I'm assuming that the position (and therefore the ON_GROUND status) happens before the damage check is done.
@@ShadowlessDeath47 ender pearls do not have this check, it simply deals 5.0 fall damage to the player
Last time I saw a gaming breakdown this specific it involved parallel universes.
Mario?
@@IcecalGamer M(a/2)rio
Matpat
i wonder how many half a presses was needed for this.
Super Mario 64 TAS Speedrun for anyone wondering.
Went to investigate. Turns out 198 will break the boat with a player in it (although it waits to do so until you leave the boat), but doesn't cause player damage, which is probably why it isn't in the short.
🙃 Minecraft physics
I was trying to figure out why no one was pointing out that there was a missing value in his list... several times.
12 and 13 also don't cause player damage, though, (and also don't break the boat when a player is in it), so I don't think that's the reason. I think people just repeat the "theoretical" values without testing them very thoroughly.
Something about "player in boat" is different from other cases, for both the rider and the boat itself.
I was thinking of that, though that was included in the bug report. The video that was documenting this though was specifically about the java edition, which I don't know if that's either significant, or that wouldn't make a difference and it was just overlooked when the short was published. Either way, the important issue is that this phenomenon was recorded through the bug report, which I'm more inclined to monitor.
@@BlueCyann There's about 2 kinds of negligence upon the short's inclusion of 12 and 13, as it's omission of 198. However, nothing about this is theoretical. It's in the bug report, and the report does mention that there are different conditions which the player does/doesn't survive (but never specified which). They simply used examples of the affected values to illustrate the point about the bug and how that's handled.
I would think that would've been beyond the point to include the player in the test used in this video when it's illustrating the fall damage to the boat with those values. When the boat is "destroyed" is a whole matter unto itself with the game's code in relation to the distance. That's already covered.
but then matt had a very good idea. he used f5. you see, using f5 gave him a whole new perspective and he was able to see a floating point error he couldn't have seen before.
OH NO THIS PHRASE IS GONNA HAUNT ME EVERYWHERE NOW THAT I'VE WATCHED THE HOPPER SAGA NOOOOOOO
"whatever floats your boat"
This is such a high quality pun it hurts. +1
genius
+2 moment
You win the internet for today.
pff, get real
Climbing on a ladder doesnt count as in the air, while also not being on the ground
swimming maybe too? (if you can swim in that game)
@@uu8217 You can swim in the game (properly only as of only a few years ago), and it has its own state.
doesn't*
You can also climb vines. And scaffolding, though that may be considered on the ground. You may also be in lava or falling though a cobweb. Or lying in a bed, or riding a horse. I'm not sure what any of those mean.
.
@@uu8217 There's boats, so obviously you can swim
A Camman18 Matt Parker crossover is NOT something I expected but I thoroughly enjoyed
"Multiples of 5, in my opinion, are at least 5 apart."
-Peggy Hill
Programming tip of the day: floating-point values that get repeatedly added should, whenever possible, be chosen to be exactly-representable numbers. Instead of 0.04, the acceleration should have been chosen to be 0.0390625 ( = 1/32 + 1/128 ); then the problem would not have arisen.
(In memory of the late Garry Tee, who taught me this many years ago. Rest in Peace.)
Great tip!
I did not expect to get this kind of wisdom from a youtube comment. Thanks.
This may solve the problem of repeated adds, however because of the use of the mantissa and exponent in IEEE floating point representations that is not guaranteed. This would produce deterministic results in fixed point arithmetic with 8 bits or more reserved for the fractional component. However, this bug is actually due to floating point/integer rounding errors and therefore your suggested improvement is not a solution.
My programming tip is only use floating points when absolutely unavoidable. If you are only using numbers with a fixed number of decimals, prefer switching the decimal point and using whole numbers for all the calculation. For example properly coded accounting applications use whole numbers to represent the value in cents, not floats to represent the value in dollars with a decimal part. And in modern languages, there is even a "decimal" type that is specifically designed to do that for you.
@@christianbarnay2499 Yeah no. Many times, fixed-point math can actually be *slower* than floating-point counterpart. Like multiply/divide across multiple orders of magnitude, trigonometry, exp/log, etc.
Point being (pun intended), modern computer are absolute beast when numbercrunching IEEE 754 floating-point, to it being a measure of power (FLOPS). I would dare to say the inverse, *don't* use fixed-point unless you absolutely sure:
1. All numbers fits, including intermediates.
2. Has sufficient precision that is more than standard floating-point.
3. You *really* need that extra precision, with trade-off of more memory/register/cache/etc.
4. Use good generic fixed-point library (don't try to manually implement, it's 100% not worth it).
I love how we’re all just accepting that the situations where falling from a great height whilst sitting in a boat kills you are the bugs and the ones where you survive with no repercussions are the game working as intended.
The case where the outcome is contrary to the intended logic is the bug. In this case, the intended logic is that being in a boat negates fall damage.
@@SnakebitSTI it clearly started life out as a bug which they've kept around because people like it's quirky/exploit nature.
@@TimSheehan
> a bug which they've kept around because people like it's quirky/exploit nature.
it is a feature then, not a bug
@@zocker1600 ... you know that "not a bug its a feature" phrase is from people making fun of buggy/ faulty things right?
E.g.
Oh the door handle has fallen off... Not a bug its a feature car is very secure against breakin now!
@@TimSheehan It becomes a feature once its presence becomes intentional. Your examples are different.
I wonder how related this is to Minecraft's weirdest death message: "death.fell.accident.water"?
That death message only happens when falling a specific number of blocks down onto a waterlogged slab (half block with water on top). Normally water cancels fall damage, but in this one case it doesn't and it gives a very unusual death message about dying by falling into water.
how is waterlogged counted? because i think it is, when you hit a solid piece of a block, that is also waterlogged
I do not know, but it seems possible that it's the same issue between the math and the conflicting status.
@@VoltisArt Maybe it's when you get a fall damage death (some kind of floating point issue) while the game is telling you you're in water.
I would bet nearly any amount of money that the death happens when your falling speed is such that after one "tick" you are exactly aligned with the top of the slab, having been outside of the water the previous tick.
I can think of several different code weirdnesses that could actually be responsible for the death, but I bet that's the edge case regardless of the specifics.
I think that message occurs because the developers didn't account for you dying in that specific way, and didn't assign a proper message to play when it happens.
An interesting thing is that the boat breaks into sticks and planks. And here's the thing, once upon a time boats were really fragile, they would break from crashing too hard, and they of course also break when you hit them, and in both of those instances they used to break into blocks and planks. Then in an update a long time ago they made it so that they don't break as easily (can't break by crashing) and if you break them by hitting them they drop themselves (or in other words a boat item).
But with that bug they still drop the old drops.
As a programmer, floating point imprecision has been cause for may hours of desperate debugging.
And why I avoid floats unless I'm _really_ certain I need them
@@adfaklsdjfI remember that once I actually created a class 'fraction' that had integer numerator and denominator to be able to compute some numbers exactly, I remember I needed it for something haha
I'm not a programmer, but I did some gauge stuff for Flight Sim back in the day. One involved some INT(float) operation that wouldn't work (iirc I was converting to octal for transponder), and I was completely unaware of the float rounding error. Obviously, my "programming" failed and I couldn't figure out why. So I set it up in Excel to see what was going on, and to my amusement even excel did it wrong. Only when I expanded number of decimals did it show i.e. 4.9999999543xxx instead of 5. I've been aware of it since, even if I've never had to deal with it again.
it helps when you understand that they are in fact precise, just inaccurate
@@adfaklsdjf Why would you be using any data structure that you aren't sure you need?
I like that, as soon as he told the numbers where that happened, my first instinct was to pause the video and put the sequence on OEIS. Next scene is he putting the sequence on OEIS and finding nothing.
I just wish he tried to find a pattern on his own for a bit longer, both before OEIS and especially after OEIS failed. That feels like a more rewarding way of doing things.
I am disappointed that as of the start of April 2024, it is still not in OEIS.
Now the "Minecraft Boat Fall Damage Sequence" will be introduced to OEIS.
I asked ChatGPT (not the best option, I know, but it was worth a shot)
It started strong (-ish?) and then started (convincingly/confidently) pulling stuff out of it's virtual arse.
:)
Same.
Finally, a video that combines three of my favorite things. Mathematics, floating point number tomfoolery and Minecraft.
People who code in Java must love this!
@@Vifnis I do 😅
Now go compute some inverse square roots :p
1:08 - looking at this offhand, there is some patterning here:
12 and 13 have a difference of 1
49 and 51 have a difference of 2
111 and 114 have a difference of 3
202 and a perhaps missing 206 would have a difference of 4
310 and 315 have a difference of 5
I'm not sure what is placing these pairs, but I hypothesize that 206 is also a height from which you would die, and that the next two heights would have a difference of 6 between them. If 206 doesn't work, perhaps that is for a significant reason?
edit- oof it was 198! so my hypothesis was actually not too far off then, nice!
Yeah the missing 198 is at least part of what kept me from seeing a pattern.
Yeah, I'm bad at maths but decent at pattern recognition and the pattern didn't take me long to see:
Along with what you said, the distance between each pair of numbers is:
- 36 = 12×3,
- 60 = 12x5,
- 84 = 12x7,
- 108 = 12x9,
Following the pattern, the next 10 numbers in the sequence would be: 447, 453, 609, 616, 796, 804, 1008, 1017, 1245, 1255...
Oh this is SO funny to see a video about this. Fun fact--since most players have no clue about this and use driving boats off ledges as a safe way to get down cliffs, you can often trick people into exploding if you measure out a drop that's exactly the right height.
It gets a bit into the weeds, but the historical reason for the "don't calculate fall damage if you're falling" stuff is that boats used to break if you rammed them into land. That got removed, but the fix was kinda a hack and accidentally left this method in.
Thank you for reminding me of this! I felt like i was missing one piece of information and i think this was it. Boats used to break and now they don't! Matt keeps talking about a fall damage calculation but I think a better name would be *collision* calculation. And to protect them against damage this is the code they added which in turn inadvertently also keeps the player from damage as well!
So the bug isn't really that the boat breaks at certain heights, but that the "avoid having the boat break all the time" workaround causes a bug where you _incorrectly_ don't receive fall damage while sitting in a boat _except_ with these rounding errors.
@@SteinGauslaaStrindhaug this is a good way to put it!
I remember boats breaking... I always hated that but maybe I should go back and play old minecraft
@@SteinGauslaaStrindhaugit used to be a bug, now it's a feature!
9:08 when you're under water, you can be neither in the air nor in the ground.
I mean, unless you're on the bottom
if you jumped into a cobweb or are sliding down honey as well
My first thought was that it might apply to ladders.
My first thought was "when you're swimming in lava". I guess that resembles my fortune, errr, skills, when playing Minecraft. :)
The tolerance for 'in air'
Was likely implemented due to something like a path block being very close to, but not quite a full block. If the game considered you airborne for that moment, it would feel clunky and not let you jump. Especially if you had one foot on the grass and another on the path (depending on where the ground check is measured from)
It could also be to ensure your character remains grounded during little rounding errors like that
Super cool break down!!
That's why we usually try to avoid floating numbers in programming! Excellent video, enjoyed every second of it.
Stand-up Maths is slowly becoming a Minecraft stan
Stan-up maths
Stand-Up Crafts
And the bad thing about this...
@@babilon6097 Is that nothing ever goes wrong with a bit of Math, right...
At this rate Matt will have to actually play it...
you can actually fall down non-integer heights, falling from different snow layers or from cakes, beds, enchanting tables, ....
has anyone looked that those?
it rounds to the nearest number of blocks fallen minus 3 (meaning first 3 blocks don’t deal damage, every block afterwards deals 1 point of damage). so if you fall 3.49 blocks, you take 0 damage. if you fall 3.5 blocks, you take 1 point, half a heart of damage.
@@davidbarroso1960 but would you take damage in a boat if you fall 12.5 blocks, for example?
@@davidbarroso1960That doesn't matter, because floating point inaccuracy could still occur and place you very slightly above the ground
@@yonaoismeI'm assuming it hasn't been tested yet because it isn't really necessary to fix the bug, but it could be really easily tested by spawning boats with command blocks, slowly travelling upwards by using an invisible armour stand
@@yonaoisme no. for you to take damage, the resulting position has to be “equal” to the floor position. but the resulting position never ends in .5, so it’ll never equal the floor position if the fall height ends in .5.
underwater would put you not ON_GROUND while neither IN_AIR
but more importantly these seperate values play different roles in applying gravity & using player's oxygen underwater
Since you covered Minecraft, maybe have a look at the famous overbounce bug in the Quake3 engine (idTech3). Here also when you drop from a certain height, you get an "overbounce". In short, all your falling velocity gets "bounced" in your direction of travel tangentially. Though even more special, when your horizontal speed is exactly zero when the overbounce happens, you would bounce back up to the start height. This can be used in some maps to gain additional speed or each certain places more easily.
Overbounce is kinda funny because there are several "variants". First of all the height above the ground is the most important factor. However you could always simply drop / walk off a ledge or jump off that ledge. Two different heights as a result. Furthermore your player could be in a "sticky" state as it's usually called. That state means your character is not perfectly on the ground but essentially hovers a tiny bit off the ground. You can get to this state either by stepping on a certain stair height and back off. So your falling velocity is just right that you get into the sticky state. Another common way is to use a single shot of the plasma gun to the ground you're standing on. The impact has a slight knockback and lifts you a tiny bit in the air (with the right angle against a wall you can actually climb walls). When you are sticky, the drop and jump heights for the overbounce to happen are different. Another way to get to a certain overbounce height is to do a rocketjump into the ceiling of the map. In some maps the distance from the ceiling to the ground is just right.
Some mods (like DeFRaG) had built-in indicators which can tell you if you are "sticky" and if the surface you're looking at would result in a drop or jump overbounce. It's quite handy for finding great trickjump spots in maps.
Q3 was and still is one of the best FPS shooters of all time. The physics and netcode are just perfect. Since the Q3 source code is released under the GPL (John Carmack, the hero) we can exactly see what the code does. The overbounce "bug" is also the result of a feature (specifically that you would slightly bounce of walls when you run into them at an angle) and a safety threshold (specifically you're considered on ground when you are less than 0.25 units off the ground. You player is 48 units in height). Here's a video that goes through the code to explain what happens: ( WmO2cdTU7EM ) and here's a defrag video from the 2017 world cub (round 6 is my personal favourite, but the final round is also sick ^^): ( cCO9QuV-cgM ). In Round 6 DeX reached about 1800 ups (units per second) with vanilla Q3 physics. Apart from VQ3 there's a modified version called CPM (Challenge Pro Mode which has some changes, especially more air control and fast weapon switching). "inder" reached almost 3000 ups in that map. The normal runspeed is 320 ups :)
I played a lot of defrag but never was even close to be considered a defragger :D Pro players are just crazy people.
2:50 You can use levels of snow for 1/8 of a block precision with some additional levels at 1/16 - carpet, 3/16 - trapdoor, 9/16 - bed, 15/16 - grass path (I could've forgotten something).
Bells, enchantment tables, cakes, are some more specific ones, but (and this is slightly cheating) there's also falling ANY distance up to 0.01 precision by falling sideways out of a water stream or honey blocks (or even technically off of vines/ladders/scaffolding but that's way harder to be precise ironically)
Are you actually lower than a block on soul sand or is that implemented differently? It's unlike grass paths because you can place rails and redstone.
@@fwiffo Yes, you are lower, which is why you can get effects from blocks below the soul sand, if ice for example is below the soul sand you will find it gets slippery, and this isn't hard coded, it's just the fact that the block your feet are in is the block above the ice. You can also see the Y coordinate in F3 go down when you step on soul sand.
@@fwiffo I'd guess that Soul Sand simply has a lower collision for the top part, so it isn't actually a full block, only visually represented as one.
@TheRenaSystem and different stages of amethyst shard growth, pitcher plants, and...
The rabbit hole for Minecraft gravity goes so much further! Turns out most different entities experience different accelerations due to gravity, and different drag forces too! Boats are the simplest, since they don't experience drag.
As an example, players and most mobs experience 0.08 b t^-2 of acceleration, or 0.01 b t^-2 if they have slow falling, and experience a vertical drag coefficient of *nearly* 0.02, and a horizontal drag coefficient of *nearly* 0.09 (just as in the video, these "nearly"s are due to floating point errors). Drag is calculated after applying acceleration.
Another example would be projectiles, all which experience ~0.01 drag in all directions, but in this case drag is calculated *before* acceleration! Every projectile experience different gravity though: the ones that stack to 16 like pearls, eggs and snowballs experience ~0.03, while potions, arrows and tridents experience ~0.05, llama spit experiences ~0.06 and xp bottles experience ~0.07.
I'm just surprised that SciCraft hasn't figured out how to hack Minecraft physics using this.
I was looking into horse jump heights a while back and found out that if you're riding a horse in moderately-recent versions, it experiences .02 vertical drag twice per tick, or around .0396 per tick. Do you know if other entities experience this sort of effect in any direction?
I was about to comment that I remember seeing somewhere some acceleration graphs for MC and they weren't constant and then the higher numbers in Matt's sequence prolly won't work but you pointed it out way more detailed *kudos*
@@Kirby703 As far as I'm aware no, but I haven't looked much into mobs riding other mobs like in this case. Maybe that could be something interesting to look at...
One time I was modding a monster that jumps in the air to land on the player and crush them, and I was having *so* much trouble until I discovered Minecraft has **different air resistance** for *vertical* and *horizontal* motion 🤨
Did not expect another Minecraft video, but I'm very glad to see you looking into this!
Never in my life did I think Camman18 would end up in a stand up maths video. We truly live in one of the times.
Didn’t realize there was an online encyclopedia of integer sequences, but thats pretty neat
You watch at Matt Parker not knowing numberphile's most featured website? Quite suspect
Neil Sloane
They have the founder of it -Neil Sloane on quite a few numberphile videos. He's pretty cool
I think Matt has a copy of the EIS (i.e. the printed version, before it was the OEIS).
@@nocturnomedieval They're probably new here - be gentle.
Stand-up Code Review
_[Agile/Scrum PTSD intensifies]_
oh god please no
8:48 the game does do a check for when your head is underwater, which divides your mining speed by 5 unless you have aqua affinity on your helmet, and the same occurs when "in the air" (including creative flight in survival mode, but that requires mods or server plugins), not sure if those affect anything in this case, but they do combine (atleast in 1.10.2 that i have open to afk)
in air and on ground are separate to allow for easily coding things like ladders, platforms, bouncy slime blocks, swimming, floating in lava, lots of stuff.
who is that guy
hello
cool
skibdi toilet
Hi camman
Hi
This also makes ROUNDING a number an actual nightmare, because XX.5 might actually be XX.49999999 or XX.500000001 and you just can't tell
Rounding floating point numbers is a legitimate nightmare that you should only do if you don't actually care about the result being consistent with anything else in your system.
Thankfully 0.5 is exactly representable in binary
@@jesselapides4390 yes, but should 0.1+0.4 round up or down? Should 0.1x5 round up or down? Should 0.05x10 round up or down? If you're dealing with precise numbers you usually don't need to round
@@jesselapides4390 Sure, but not all numbers with a .5 at the end are representable. For example, the number 65166464.5 is stored as 65166464, which means if you round 65166464.5, it will round down instead of up, like it should.
@@xanderh2404 You cannot store 65166464.5 in a 32-bit float. You can't store even 65166464 vs 65166463 in a float (ie, you'll get the same value (65166462 to 65166466 all "round" to 65166464))
Ladder is probably an example on "Not on ground" but "Not in air"
It is often done on platforming games, where the platforms actually extend a little further out than it looks, to account for input lag and so on. Developers found out, that if you don't add this compensation, it makes the game extremely hard (some of the early games known for being difficult were difficult exactly because of this ) My guess is, that this is to make jumping block to block easier.
I had watched a video about this a while ago, but I can't remember what it was called.
8:50 one example is having your upper body in the water (technically "swimming"), or in a cobweb.
14:40 The short stops at 315 because that's the longest drop you can achieve within the buildable height of a Minecraft world, which goes from y=-64 to 320 for a total height of 384 blocks.
While true, I feel like I should point out that data packs can change worldgen to go from -2032 to 2032
minecraft.wiki/w/Custom_noise_settings
Yeah you're right
8:53 I beleive if you are in water/lava/cobwebs you aint in the air but aint on the floor either
Very informative and interesting video, I love seeing Non-Minecrafters' takes and opinions on Minecraft, especially those of mathematicians and people of other professions.
Also, *8:48* There are quite a bit of cases in Minecraft where you're simultaniously not in the air but also not on the ground at the same time. ''Going for a swim'' as you mentioned is one of them, but there's also being in lava, sliding down the side of a honey block, falling into powdered snow, stuck falling on cobwebs... You name it.
With regard to the bit at 10:28, this is actually the normal, correct way to compare floating point numbers. The fudge factor even has a name, epsilon.
You _never_ do a strict equals comparison on floats, because it'll be false unless you're comparing something to itself or to zero. Instead you check if it's within some range, like above or below a target value. You add or subtract epsilon from the value as appropriate to account for the rounding errors.
So does that mean that when you use the standard == comparison operator in your code that under the hood the CPU is actually subtracting one from the other and checking that the result is within plus or minus epsilon of zero? So that in something like Java, that's a thing that's being done without the programmer necessarily knowing it?
@@AlRoderick I think it's something the programmers integrated (and OP just means it's common)? Because I definitely have been screwed over by this before
@@AlRoderick actually no! "==" does a direct comparison, which is why 0.1+0.2==0.3 (as floats, idk about doubles) returns false. There is probably some package for comparing floats somewhere :)
@@catmacopter8545 Yup, exactly this. The language can't make the == operator do this by default because somebody someday might actually want to do a true strict comparison of floats.
Math packages will usually have a way to do this, or you can just do it yourself. It's not exactly a common problem, most of the time you're working with integers (not necessarily the _datatype_ integer, the mathematical integer).
@@AlRoderick No, == does an exact comparison, which would cause you to fall through the ground unless you were clamping the value, because you would never exactly be at the same level as the ground. Clamping instead of comparing an approximate value may be a way to fix this bug though, like only comparing if you are at or below the ground and correcting the position to be exactly equal to ground level to avoid ever rounding in a way that causes fall damage.
I was surprised to hear absolutely no mention of terminal velocity in this video about acceleration due to falling, so I did a bit of my own investigation and it turns out that although Minecraft does have a terminal velocity, under these specific conditions the boat/player would not be falling long enough to achieve it. 🤓
When would it though? Considering the video deals with all the height values in MC
@@Baddabythere are ways to launch a boat upwards so it goes above build height, like hooking a bunch of fishing rods to it and pulling them up at the same time
@Baddaby Okay, this is an excellent question because my initial answer would have been: "Because of the build height limit in Survival worlds there is only enough height in Sandbox worlds to achieve terminal velocity so Matt must be testing in a Survival world... etc" BUT after reviewing the video again it does appear that Matt WAS indeed testing at heights above the Survival height limit (it makes sense that one would do certain tests in a Survival world) so in theory some of the higher tests should be reaching terminal velocity and no longer be subject to acceleration, so what's going on here? 🤔
I did a little more digging and my current theory is that he is testing on a Super Flat world that starts at Y=60 and bedrock is directly beneath one layer of Grass blocks, which would potentially reduce the maximum falling distance by 60 blocks e.g. a result from Y=300 is actually only falling 240 blocks.
Again I could be wrong, perhaps Matt is the only person who can answer this, I wonder if he considered terminal velocity at all or if it would even effect the results but I feel like it should, right?
@@Baddaby *deep breath* And just to complicate this further, terminal velocity in Minecraft is different for different entities! For a; Player=78.4m/s, Item or Block=40m/s, Arrow=100m/s
I don't know which of these is applicable for a player in a boat, your guess is as good as mine 😂
what's the point of the emoji?
Here is another one that relates to converting items into a bit string, this is useful in bulk storage selection, since its much faster to send redstone signals instead of items.
A minecraft double chest has 54 slots for different items, which means that any bit position can only be set by at most 54 different items for all codes. (there are also 27 slots for single chests, 9 slots for droppers/dispensers and 5 slots for hoppers). What are the most amount items you can encode in x bits, where each items has a unique code?
One idea would be to use only codes that have only 1 bit set and if those are all exhausted use codes with 2 bits set, and so on. Side question: How many codes are there for n bits where only k bits are 1. (Its the binomial coefficients)
Of course we could use we could use a very large number of bits and only encode 1 bit for each items, but that is very wasteful. So another question could be whats the optimal amount of bits to use?
If you are intrested in more minecraft meets maths related content take a look at WhiteStoneJazz youtube channel and the 'Encoding items in Minecraft' series where i got this idea from.
Been a Parker viewer since the domino computer (redstone irl) and a minecraft player for longer, so these random crossovers always make my day :D hoping for more in the future!
As a programmer working with geometric operations, I hate floating point numbers. They're the worst.
Wait until a work colleague wants to use floating point numbers with currency 😨
@@SushiElementalDo it and pull an Office Space 😂 (but unlike the movie, do your arithmetic correctly)
@@octopoDEEZ_NUTS Haha I'll think about it 🤓
@@SushiElemental There's an open source ERP (not super well known but actually used by some companies) that uses floating points for currency. ERP does inventory, accounting, etc. One of the many reasons that made me want to tear my hair out when working with it.
@@bobson_dugnutt It seems some people just want to lose money.
08:48 I think the reason for having the additional onGround variable is because you can swim in Minecraft too (i.e. not in air, and not on ground)
Which can be covered by the status "is_swimming" or something :P
yes. there can often be good reasons to have an enum status variable but also a bool that covers a specific case of that enum
@@Khantiathat would bloat the code and if you add enough stuff like this your performance will suffer
It's more efficient to cover all 3 options with just the two states
@@bilboswaggings first time I'm hearing of such practices... since when is it more optimal to check if (this.status == ON_GROUND && !isGrounded) instead of just (this.status = IN_WATER)? Computation-wise the latter option is more efficient. It makes little sense for this to be the reason for the existence of isGrounded :P
@@Khantia as shown in the example both are needed for the game to function as it's built
Adding a status for in water would also require you to add the code necessary for that check (how else would you know what the status is)
That connection between binary and how it changes the stored number due from 0.04 to 0.03999... was mind blowing and explained (i believe) a reoccurring issue I run into with ArcGIS and Field data. This was a great video and explanation!
11:16
I guess the most common example might be ender pearling (teleportation)... However, ender pearling is only 4 HP damage, so my guess is it *does* do damage because of the checkFallDamage() function, but it checks some other field or function to see how *much* you're falling.
Really interesting video!
8:56 While not on the ground but also not in the air, you could be swimming in water, swimming in lava, falling through packed snow, or falling through the Void (basically the out of bounds area). These are just what I could think of off the top of my head.
Stuck in a spider web…
perhaps falling inside of a non solid block like fire might not count as in the air? just a thought
Climbing a ladder
@@Halinn would you be in the air while climbing a ladder? or are you just "in" the ladder?
Both for this and the first Minecraft video, Matt specifies 'for those not familiar with Minecraft' that they shouldn't worry about not knowing.
Now I'm curious how big an overlap there is between the "knows about minecraft" and "watches Matt Parker videos" demographics.
I would guess that some of Matt's viewers play minecraft as it is probably popular in programers too. But most of the minecrafters are probably children who do not know Matt and math.
@@Neo-vz8nhnerdy 20 year olds likely make up a sizable chunk of his audience and I'd bet those people grew up on Minecraft (or were at least around it) and would have played Minecraft. Though I agree that obviously the majority of Minecraft players have never seen one of his videos
i watch(ed) ilmango on the scicraft server and i watch people like marcel vos in openrct2 and im also here, so theres at least one XD
Someone made a CPU in Minecraft. Like a .0000001 MHz 8086 or something.
@@BobCat0someone also made a 1 hz cpu in Minecraft. Most other ingame redstone computers run way slower though
Minecraft and stand up maths was a collab I never knew I needed.
There are so many amazing maths problems in Minecraft, I think everyone would enjoy them
I was curious why certain pairs (12,13 & 49,51) were so close to eachother, the algebra behind it really helps
11:00 The reason why the check has a tolerance on it is precisely because of those pesky binary floating point problems you tend to run into.
Since you can never be *quite* sure you end up at exactly a whole number when doing calculations, an easy workaround is to just check to be within a 0.001 margin of it.
Yes, we programmers are lazy and can't be bothered to do this properly 😎
Pretty sure that IS "doing it properly", given the context of the problem.
@@chrishillery I would argue it's not, because you're not getting the analytically correct answer for any given input. Floating point was designed to be a jack of all trades format; it's good enough at representing basically any kind of number, but not the proper way for anything specific.
In this case, a proper way to do it could have been to store postion as an integer multiple of 0.04 (essentially, a fixed-point format rather than floating point). This way you can get a proveable, exact algorithm.
@JochCool Sure, that's why financial apps don't use floating point. But that's what I meant by "the context of the problem". *Given that* you're working with floating point, the only valid implementation of "equals" is that kind of epsilon comparison.
@@chrishillery I still disagree: there already exists code that makes sure you don't fall through the ground - the code that checks for collisions. If you can detect for collisions, you can certainly check whether you have "finished falling" and are, in fact, on the ground, in the exact same way as the collision - this should hopefully eliminate the distinction of becoming "on ground" and touching the ground.
But hey, the margin is a neat trick that probably made for less code and fewer bugs than my idea, so I don't mind it.
@@JochCoolActually, your position isn't limited to 0.04 increments if there are forces other than gravity
as of this comment, the sequence is still not in the OEIS but I don't expect that to hold forever
This is entirely dependent on the 0.04 acceleration constant, so it doesn't really seem like something they would add. "Integers 1/25th of a triangle number" is pretty arbitrary.
@@cadekachelmeier7251 Methinks we need a way to search the OEIS for sequences that are offset or a multiple of some sequence then.
Because triangle numbers are probably in there and would come up.
"Block heights in Minecraft, from which being in a boat will not save you from fall damage"
@@cadekachelmeier7251as if they don't have completely arbitrary sequences
@@LethalChicken77 they do but they try to keep them to a minimum . . . however I think an exception will probably eventually be made for this sequence, just because it's in this video.
There is another topic similar to this without explanation: the nothing clutch. In Minecraft versions pre 1.19.2 you were able to hold space and shift right before you hit the ground to take no fall damage. It didn’t work at some heights though. I was wondering if you could explain it. There is a video by my friend Zoova on CZcams the nothing clutch if you need a better explanation
thats it not how vertical movement in minecraft is calculated at all
matt parker camman18 crossover is not what i expected today
I was NOT expecting such a good explanation from a non-minecraft channel
I got so excited when he showed the IEEE converter! That website used to be my bible!
9:00 i am not a minecraft player myself but just from your phrasing i can see an answer: you are not on the ground and not in_air when you are under water, for example :-)
The math and reasoning is sound all around , but i think there's a missunderstanding of the 'why', at around 09:00 , with the whole 'on ground on air' explination, i think that it's not about 'taking fall damage while not being on the air' The actual 'bug' is, when you are on a boat, since you are ON TOP of the boat, 'this.status' is never on_land, so the game basically ignores the 'on.ground' and asumes you are still falling. But in those numbers, the distance from the ground to your character (trough the boat), is so small, it correctly identifies that you did fall and should take damage. I think this reasoning makes more sense than 'taking fall damage when you are not falling'.
Thank you! I was confused his explanation here too
So, if they used the same method/formula to calculate when (this.status = ON_LAND) and when (onGround = TRUE), then this bug would be fixed, right? Or are they somewhat different things?
So this is a case where they decided that a bug was a feature, then got a "bug report" for cases where the game was working the way it was originally supposed to? I haven't the words to tell you how much I love this.
ETA: Apparently, the "no falling damage while on a boat" thingy was a by-product of fixing a different bug (boats broke when rammed into land or something). Dear gods, how I love it all.
Isn't the issue that the boat is breaking, and then the player falls through and hits the ground? The boat, without even having a player in it, breaks from certain fall heights.
This makes much more sense! I do hope this gets pinned!
onGround is mostly used for deciding if you should take fall damage or not. This is often used for quite a few fly cheats to prevent fall damage, especially older ones. However, it also prevents ladders, vines, and scaffolding from killing you when you fall onto them.
hi misspotato
wait, scaffolding stops fall damage?
@@endernightblade1958 I'm not certain actually. I just assumed so because they're just cube shaped ladders, but I haven't actually tested it.
@@misspotato813 i think i vaguely recall them stopping me when crouched at least, but as far as i know without that they’re practically a solid block
@@endernightblade1958 if you are holding shift when falling onto scaffolding you will not take any. If you're not holding shift you're taking full dmg
I was taught when I learned to code in the 1970s that all floating point checks need to use a precision check, and never a strict equality check for exactly this reason. The problem here is that they implemented the status check correctly, but the on ground Boolean incorrectly. I always thought that the equality operation on floating point variables should cause a compile-time error.
Boats are indeed famously sensitive to floating errors
the fact that the boat breaks into planks and sticks is incredibly interesting and likely due to vestigial code. Back in the day if you ran into a shoreline, your boat would break into sticks and planks but now, there are no circumstances in normal gameplay where that should happen, if you break one by hand, it drops the boat item itself so there must be something else going on that makes the boat shatter at those particular heights
They never removed it that you can break the boat. They made it way sturdier and able to pick up.
@@Systox25 but the code is vestigial because these bugged block heights are the only time breaking a boat drops sticks and planks now
@@ordanarymods4990 thought explosions would also destroy them into pieces.
@@Systox25 fun thing is, it always gives you oak planks no matter the wood type used, meaning you can use boats to convert any wood type into oak
@@Systox25 they don’t
8:44 Caption error here, “this is just boolean” became “this is just bullying” 😄
There were a _lot_ of caption errors. One of the few times I've turned off non-automatically generated captions other than because it was covering up parts of the video.
There's been plenty of caption errors in recent videos.
I'm almost inclined to volunteer to contribute to the subtitles myself.
Hey man, don't be boolean the captions.
There's also "12th" instead of "20th" when talking about ticks.
Voice-to-text seems to have quite a problem with uncommon words, nor does it judge well by context. That is also similar to why I do not trust auto-correct. I prefer it mark suspected misspelling and let me correct it myself. Those random word switcheroos are really annoying.
2 or so weeks ago, I finished my 3 month long school project on polygonal numbers in certain modulo. This is very close to what you were doing here :3
To answer the question at 8:50, you could be floating (or burning) in water or lava!
So the real bug is that status and onGround are not using same margin of error
or that they are not updated at the same time. either way, the real bug isn't floating point rounding, but de-sync of state.
you're not on the ground if you're IN the groud, suffocating
also void
also water and lava
also cobweb
If you're in the ground, you count as on the block beneath your feet, I think
If you're in the void, you count as in the air but just don't have anything to hit
Liquids shouldn't count as in the air or on the ground, and probably don't
Cobwebs shouldn't change if you're in the air or on the ground, and they'd just affect your falling speed/acceleration
The solution to avoid this type of errors is the single responsibility principle.
I have had some issues with bugs like this.
The solution is in fact very simple, whenever you have a condition such as ( bounds checking, threshold removal of data )
or any type of calculation like these. You should create one function/one class responsible for handling this operation everywhere you need it in your code.
In the video, we see the problem where two different status can be updated by two different bounds checking algorithms. Therefore, there is an opportunity for edge cases like these to exist.
3:25 Note: 0.04 is the gravity for boats. It varies from entity to entity and most have it be 0.08 if I recall correctly.
Finally tackling the big issues.
Minecraft has some really interesting quirks with the way it calculates fast moving entities. To prevent it going through a block when it's moving extremely quickly, it checks every block position between the entity's previous and current positions, but does this separately for the x, y, and z directions. So it can go through a block diagonally because it effectively moves to its new position along the x direction, then y, then z. Some crazy tnt cannons take advantage of this.
Moreover, blocks in unloaded chunks don't have collisions. If an entity is so fast, it moves into an unloaded chunk in one tick, it will go through all blocks it would otherwise collide with in that one tick (before also becoming unloaded)
So, a while back, on my channel (in my 2nd Hardcore World) I died and lost my world due to this "bug"; which led to me doing a ton of reasearch and testing on my own (I was able to find the same numbers mentioned here). This is a bug that has been quietly discovered, but the developers did not plan on patching it.
Additionally, for those that care, in the event that the player is in a boat, they will take damage at the same levels... unless the boat is stationary in the x&z directions; a stationary boat will not break, so I tend to just stay completly still when boating off ledges higher than 40 blocks. Good video. Have been waiting on this!
6:43 the h-schmidt float converter has been so useful to me in my reverse engineering work. i unironically enjoyed seeing it in this video. no clue who H. Schmidt even is but their converter is such a great tool
Minecraft!? Heck yeah!
YOOOOO!!!! My favorite math guy uploads a video on MATH AND MINECRAFT?!! While I'M playing Minecraft?!? And while I'm doing Minecraft math myself for Stronghold triangulation?! THIS IS A DREAM!
no dream was a different video
@@Nolys-bk4kd It's a joke. Matt Parker's other video about Minecraft was about the Dream controversy.
@@bronsoncarder2491 I get that, but what's the joke?
@@Nolys-bk4kd just a pun on how you said this is a dream because of this lining up with exactly what you're doing, and how Matt released a video about the youtuber Dream and the chances of the item drops of his legendary run. We know you definitely weren't talking about the youtuber, but the pun's still funny.
@@Nolys-bk4kd you said "THIS IS A DREAM!", hence dream.
9:00 when landing on water. You're neither in the air nor on the ground. Water would also negate fall damage, so both the ground check and in air check would probably be 0 and therefore no damage is dealt. But that's just my guess. Haven't checked the code.
Regarding "can you not be on the ground and not in the air at the same time", it all depends on what the code is doing really. On the face of it they are opposites. However if they are measuring slightly different things then both true or both false could be valid.
It reminds me of a place I used to work (details changed to protect the not-so-innocent), where we monitored stuff in our warehouse. An item had several flags including online and offline, and every newb to the code had the same question: why are there two flags? It turned out that when an item is known about but not in the warehouse, it's offline, and online can never be true. When an item is online it's in the warehouse and we know what it's doing, and offline can never be true. For the most part online and offline are opposites. HOWEVER, there is some temporary storage in the warehouse, and when we put something there we're not monitoring it, so online is false, but offline is also false. Both flags true was definitely invalid though.
That's an explanation but not an excuse. The fact was that an item could be in any of three states, but for whatever historical reason, it wasn't convenient to actually express it that way (as a choice between online/offline/unmonitored), so instead, a second boolean flag was added. And I'd argue that if you must use 2 flags, they should have been offline/online and monitored/unmonitored, rather than online/maybe-unmonitored and offline/maybe-unmonitored.
By the way if you ever find yourself in this situation in Minecraft (trapped exactly one of these numbers in the air with nothing but a boat) you can get in the boat and then, while you’re falling, quickly get out and then back in again. This will reset your momentum from the point you exited the boat, and prevent the bug.
You can also just exit the boat right before hitting the ground
@@thesurlywombat Yes, this is far easier. Getting back into a falling boat reliably is a little bit tricky, mechanically.
Camman18 in a stand up maths video is something I never expected
Matt Parker doing Minecraft videos is peak content
Seeing camman in a Standup Maths video feels like seeing your drug dealer selling to your teacher
What I found really surprising there is that for boats, Minecraft doesn't apply air resistance logic!
So in theory if you were to spawn a boat at an insane height and go into it, you could reach arbitrarily high speed. This is not at all how the rest of the game works. The player itself has a terminal velocity, because the game takes into account "air resistance"
Also Minecraft has different value for gravitational acceleration for different entity types.
Someone mentioned here that the boat has a maximum velocity but it needs to fall from higher than here shown
actually, when a player is sitting in a boat, air resistance is added. However this does not appear to be the case for mobs, so when you put a pig with a saddle in a boat it doesn't have air resistance. You can then hop on the pig and enjoy gravity freely
@@breznknedlwith enough Hermits with some fishing rods and you got yourself a space program 😂
I notice this when speedrunners launch a shulker riding boat high in the sky for transportation.
The boat comes down at such speed it looks like teleporting to the ground
9:00 as a games programmer and a minecrafter, there is one situation in game where you can be not on the ground and not in the air at the same time, and that's when swimming. In that case, onGround would evaluate to false, but status would be something like SWIMMING, and the game modifies the player physics based on status. onGround just determines if you can jump, start sprinting, and probably a few other things.
Ladders
I would guess OnGround is used to reduce your mining speed while it's false (ever tried mining something while on a ladder? It takes like twice as long)
ok longtime minecraft player here, i'm gonna need a second part with just 1 player inside the boat, 2 player inside the boat and also maybe mobs instead of players in an other test because they often impact the physics differently than the players.
i am VERY Curious behind the math in all of that because that answer some random instances i've had in the years!
I heard the opening line as "If you are named Natalie..." before the context based autocorrect kicked in.
You can actually test this hypothesis by testing to see what happens if you land on certain blocks. Some blocks in Minecraft are not exactly one block tall when it comes to entity collision (e.g. with boats and players), and this height can be measured and checked with regards to collision. (Alternatively, you can manually change the tick rate to check what happens when it changes).
I bet there's even more holes if you went from partial heights, such as using snow layers to add 1/8th of a block at a time
No, because 1/25 has no common divisors with 1/8. The closest you get is .125: 2 ticks in you're at y-0.12 leaving you 0.005 above the ground. You'd need an accumulated error of 0.004 to pass the check. The precision error is 0.0000000009, so you'd have to fall for 4.4 million ticks to accumulate enough errors to trigger the bug.
It rounds
I've fixed similar bugs in the past due to floating point errors.
The solution is normally to uniform the rounding function. E.g
going from int to round (in the case of python).
So that every evaluation of a block is the same
as a minecraft programmer, the OnGround tag only exists because it's accessible in datapacks (player status is in the source code, while OnGround can be changed with a console command)
It could be read for players or changed for other entities, but not changed for players, right?
@@thesurlywombat correct. you can't actually modify player data.