The book Redshift Rendezvous from 1990 explores this idea. (TBH the story is a little clunky, but if you like to see someone look at the physics in depth, it's pretty interesting.)
similarly, Einstein's Dreams is a collection of very short stories that explore different flavors of time. For example: time slows as you near the city center - those who approach it end up frozen forever like the event horizon of a black hole.
Too bad that it does not seem to work on mobile. I did not find any way to move around (add arrow buttons? Are we supposed to move around?) and if I double tap I change the direction in which I am looking but not very predictably. Maybe my phone is too slow.
Hmm, by some bug my back arrow first slows me down from approaching c, but then will sudddenly spead me back up (while going backwards), so I get stuck in a dark world. (Firefox on Linux).
Edit, maybe it's because the speed shift is so coarse I cross past 0 km/h from back to forwards and reverse too fast...
Other than this, very very nice. Love this kind of thing for developing intuiting outside the normal range in which we experience the laws of Physics. Well done.
classified 12 minutes ago [-]
> my back arrow first slows me down
That's exactly what would happen ins space.
teekert 8 minutes ago [-]
On some more testing, I don't seem to alter direction, just suddenly start to accelerate again. Ah well, it worked mostly.
tristanj 3 hours ago [-]
Velocity raptor is a free game that accurately simulates the effects of special relativity. It slows down the speed of light to 3m/s and you solve puzzles as a cute dinosaur. https://www.testtubegames.com/velocityraptor.html
There is also a helpful FAQ which explains all the strange things happening, such as length contraction, time dilation, and color shifting: https://testtubegames.com/srel101.html
My favorite levels are #18 (which demonstrates time dilation), #26 (which demonstrates space warping), and #42 (which demonstrates retarded time https://en.wikipedia.org/wiki/Retarded_time ). All the levels are unlocked and you can skip to any level.
koolala 2 hours ago [-]
Interesting this has the exact same controls with slidy movement + space bar to stop. It seems likely Claude based it off of it and the other MIT game.
> A Slower Speed of Light is a first-person game prototype in which players navigate a 3D space while picking up orbs that reduce the speed of light in increments. Custom-built, open-source relativistic graphics code allows the speed of light in the game to approach the player’s own maximum walking speed. Visual effects of special relativity gradually become apparent to the player, increasing the challenge of gameplay. These effects, rendered in realtime to vertex accuracy, include the Doppler effect (red- and blue-shifting of visible light, and the shifting of infrared and ultraviolet light into the visible spectrum); the searchlight effect (increased brightness in the direction of travel); time dilation (differences in the perceived passage of time from the player and the outside world); Lorentz transformation (warping of space at near-light speeds); and the runtime effect (the ability to see objects as they were in the past, due to the travel time of light). Players can choose to share their mastery and experience of the game through Twitter. A Slower Speed of Light combines accessible gameplay and a fantasy setting with theoretical and computational physics research to deliver an engaging and pedagogically rich experience.
fennec-posix 12 minutes ago [-]
This is what it's like with my new glasses
rootusrootus 2 hours ago [-]
Whenever I think about light speed being fast, I imagine myself standing at the edge of the solar system and watching a hypothetical photon travel from the Sun to the Earth and taking 8 minutes. Suddenly it doesn't feel like light is really all that fast except at human scales. 5 km/h would be fascinating though.
jbaber 57 minutes ago [-]
The globe here is, in my opinion, the best such visualization because I've personally travelled the distances depicted.
The speed of light is unbelievably slow, not even as a cosmic scale, but on earth.
We cannot play competitive multiplayer games globally, without 300ms ping. I dream of a world playing Black Ops 2 on a original PS3 in 2026 getting into a lobby because latency is low.
light is 186k miles per second, the other side of the globe is 12.5k miles away - so 67 ms / 130ms+ round trip in optimum conditions. Add more for network hops and consider that fiber is not quite as fast as vacuum.
300ms feels extremely optimistic coming from my perspective of someone living on an island in SE Asia
I ran into this a while back when I was trying to design an RTS with information delay.
chamomeal 3 hours ago [-]
Loved that game!! Blew my mind in my 1st year physics classes
TZubiri 2 hours ago [-]
It seems like it's open source, and that it splits the game from the actual engine, so if someone wants to vibecode something of their own, they can take this as a base rather than vibing the physics from scratch, with the risks of messing the core mechanic from scratch.
I feel like a rule of vibecoding would be that you shouldn't do it for the core of a product, the quality is just not there yet. Even if it is, your core contribution should be what LLMs would train on, rather than being their output.
Tostino 2 hours ago [-]
Played around with this one before. Very interesting. Thanks for linking it.
the-mitr 3 hours ago [-]
In the Three Body Problem Trilogy by Liu Cixin some of the more advanced civilisations have the ability to change the speed of light locally with very interesting consequences for the that local space
aaronbrethorst 3 hours ago [-]
I'm being vague to avoid spoilers, but I'll just say that it serves for a very interesting meditation on the concept of loss, and has stuck with me for the 5+ years since I read the trilogy.
er4hn 2 hours ago [-]
Same here, the quote on time passing stuck with me quite a bit.
divyekapoor 3 hours ago [-]
Pedantic note: The speed of light in glass, optical fiber and water is different from vacuum (much lower). On a certain scale, humanity also knows how to locally alter the speed of light though not to this extent.
walrus01 3 hours ago [-]
It's not actually that the speed of light in a singlemode fiber optic cable is slower, but that the photons aren't travelling in a direct path down the fiber like water down a pipe. They're bouncing off the interior walls of it at like a 45 degree angle billions/trillions of times before it reaches the other end of the cable.
Basically imagine like if you wanted to walk in a straight line between two points at both ends of a empty, long, narrow rectangular warehouse, and instead of walking in a straight line from A to B, you bounced off each wall at an angle (like a pool ball ricocheting off the bumpers) to get from one end to the other. Making your cumulative distance travelled on foot much greater.
vlyan 1 hours ago [-]
>the photons aren't travelling in a direct path down the fiber like water down a pipe. They're bouncing off the interior walls of it at like a 45 degree angle billions/trillions of times before it reaches the other end of the cable.
I know there are many other mundane technologies that can be described in sci-fi-ish way, but for some reason I'm particularly amazed by fiber transmitters being compact and cheap enough to be used in mass-produced killer drones.
walrus01 48 minutes ago [-]
Not just that but your average russian or ukrainian used expendable munition UAV that uses a singlemode fiber spool uses the cheapest and most mundane of fiber transceivers. There's no requirement for data rates above 1 Gbps, so ordinary SFP optics (not SFP+ or anything) are used, and the distances involved means it works fine with a extended range 1550nm to 1610nm reach thing that can nominally handle 40 to 80 km of fiber.
When I say data rates are way below 1 Gbps, it's because commonly you've got two things going on, a UART serial bridge from operator to flight controller board (same idea as what is implemented in RF with ExpressLRS, TBS Crossfire or similar), this is at most a Mbps or two. Then a possible live video feed over IP which will be easily under 50 Mbps.
The only thing a little bit out of the ordinary about them is that they're often bidirectional single strand optics with the prism built in, and tx/rx on different wavelengths (like 1550 and 1570, or 1550 and 1610, or whatever). Basically same thing that somebody lighting a very low cost metro dark fiber circuit might do to use only 1 strand for a gigabit or 10 Gbps link.
sampullman 21 minutes ago [-]
You can get a pretty good 1080p60 video at only 6mbps. Depends on how well the sender is encoding I guess, but it shouldn't be too much more than that.
rootusrootus 2 hours ago [-]
> They're bouncing off the interior walls of it at like a 45 degree angle billions/trillions of times before it reaches the other end of the cable
At the risk of exposing how little I remember from physics, doesn't light in a single mode fiber not bounce? (right about now I'm thinking that it's probably not great to think of photons bouncing because this is quantum level stuff, right? light is a wave, etc. gosh it's been a long time since I tried to really know any of this...)
walrus01 2 hours ago [-]
The bouncing is more a metaphor, the refraction of light bending at an angle is sort of like how if you as an exterior observer look at a person who is standing waist deep in a very calm and clear swimming pool, their legs appear to be at a different position than their torso. Now imagine that 'bending' repeating trillions of times.
Light’s still slower in glass than in a vacuum, though, or it wouldn’t refract at the transition between the two.
walrus01 2 hours ago [-]
Right, and it varies with what type of glass, google "refractive index of glass".
If you google image search "refraction fiber optics" you'll get some decent pictorial examples of what I meant by photons bouncing off the interior walls of a 9/125 SM fiber optic strand billions/trillions of times on its path, I guess I was trying to write an extremely simplified explanation of refraction in something like a typical SMF-28e / G.652.D fiber.
nearbuy 1 hours ago [-]
You're conflating two very different meanings of "the speed of light". Confusingly, "speed of light" can refer to the universal constant, c, which does not change in glass, or to the speed that light travels in a medium. Here, we're talking about c. Relativistic effects are based only on c. The Three Body Problem trilogy plot device is also about c.
nomilk 32 minutes ago [-]
Feels like W goes back (instead of forwards like in an FPS), and S goes forward. Is that intended or just my keyboard being weird?
EDIT: ah, by setting 'Speed of light' parameter to 40km/hr I find it a bit more intuitive
iceman_w 19 minutes ago [-]
What you are observing is relativistic aberration. W does make your velocity increase in the forward direction.
samplatt 26 minutes ago [-]
You're not controlling an FPS character walking, you're controlling the 'throttle' of how fast you're moving fwd or backward. Holding it down increases speed.
Forward means light is hitting your eyes faster, making it look like the distance the light had to cross is condensed, meaning it looks further away.
Moving backwards slights the light hitting your eyes, to the point where you're moving away from the light, so everything goes black.
aquafox 45 minutes ago [-]
FWIW, the best traveling speed is 147000km/h, because the Doppler effect makes a red light appear green. ;)
Vishal_Max 40 minutes ago [-]
This is awesome. I always think about this. As humans, we are very limited in what we can perceive and experience. A higher form of entity could have a completely different way of viewing nature and the world.
Just a thought experiment for you guys: imagine a bacteria that survives inside humans. It doesn't even know what a human is. For the bacteria, its entire world is simply the environment in which it lives. It doesn't know that we are living beings actively trying to maintain ourselves and survive.
Now, suppose a harmful bacteria enters our body, makes us sick, and we take medicine that kills all of them. From the bacteria's perspective, it could look like a natural disaster or some unexplained event in which they all suddenly get wiped out. They have no idea that a living being called a human actively tried to eliminate them using something called medicine, which was engineered specifically to kill them.
Similarly, what if our world, or nature itself, is part of some higher-level entity that we simply exist within? What if the reason for our deaths, natural calamities, and other events is something completely beyond our perception? Whatever we do, we may never be able to understand what is actually happening at that level, just as bacteria may never be able to understand that humans exist.
One thing that could potentially support this idea is self-regulation. We see self-regulating systems throughout nature, and these patterns seem to repeat at different scales. We ourselves are self-regulating organisms, and nature also has countless cycles and mechanisms that regulate themselves.
Maybe these patterns continue at scales we cannot perceive. We can observe certain things at the scale of humans, but we still don't fully understand what happens at the nano scale or on the scale of the universe. Perhaps there are higher levels of organization and self-regulation that we simply don't have the ability to perceive yet.
barrenko 34 minutes ago [-]
Cogito ergo sum is still the only "barrier" for self-awareness, aka real knowledge.
lolakutty 27 minutes ago [-]
Of course, this is what the end of Men in Black shows.
But let me tell you another possibility. What if there is no nature, but just our perception of it.
Yea, tree falling in the forest and all that...stated more explicitly..
Vishal_Max 25 minutes ago [-]
That is also very much possible, we can never know. Or maybe we can in the future. Only time can tell
aadyachinubhai 54 minutes ago [-]
Awesome, at 5 km/h it feels like I'm in a black hole. Time stops at the speed up light if I'm not wrong!
zrail 3 hours ago [-]
The first few Discworld books explore this a little bit too. I think pterry dropped the concept after that, I don't really remember it later in the series.
This only works on a desktop? Is there any way to interact with it on a phone?
emmelaich 49 minutes ago [-]
So weird, after visiting, my mouse icon disappears!
koolala 2 hours ago [-]
Which parts of this were ideas you came up with yourself?
Crowberry 1 hours ago [-]
It’s Astra ui and graphics. I recognise it after only having seen 3 examples…
dragonfax 3 hours ago [-]
Well I'm not a physicist, but we all travel through time at the speed of light. With a much smaller speed of light, I think relativistic speeds would be much easier to achieve. I.e. you could age noticeably differently than your family on a solo car drive to get groceries.
Kranar 3 hours ago [-]
The more accurate statement is that all objects have the same speed in spacetime. Time is just one dimension of spacetime and objects do not all travel along that dimension with the same speed. For example, an object travelling through space at close to the speed of light will have a speed along the time dimension close to zero.
Having said that... this is mostly a slogan and makes for good Youtube videos, but it falls apart the moment you subject it to even the most basic scrutiny. For one... it doesn't make sense to talk about a speed through time since speed is literally a measure of change with respect to time, so a change in time with respect to time doesn't make any sense.
But as a slogan, it captures the idea that motion through space and the rate of your own clock are tightly linked together.
pixl97 3 hours ago [-]
>it doesn't make sense to talk about a speed through time
Only if you're talking about other people's clocks and not your own. Your own clock is one second per second, but someone else's may be slower or faster relative.
Kranar 3 hours ago [-]
Once again, just subject your slogan to some basic scrutiny. Your own clock is one second per second, which is a pure number, 1... that's not a speed.
So then you say take someone else's clock and compare it to your own clock, but that is still just a pure number. A speed is not a number, it has units like meters per second. A ratio of two clocks has no units at all, the units cancel. Whatever number you get, 3 or 9, it's just a factor by which two clocks disagree. You can absolutely interpret this ratio as a rate, but that doesn't make it a speed.
And a speed is exactly what the slogan needs, because the diagram/geometry it's using involves a right angled triangle where on one side of the triangle is your speed through space, and on the other side of the triangle is your speed through time, and the hypotenuse of the triangle is fixed at c (since every object travels through spacetime at this fixed speed).
For that to mean anything both sides have to be the same kind of quantity. You can't put meters per second on one side and a bare number on the other and call it a triangle. Nor can you patch it by multiplying the ratio by c to give it units, because the thing you get then grows as you speed up instead of shrinking. Either it has the right units and the wrong behavior, or the right behavior and no units at all. There's no version of this geometry that produces a consistent picture.
bilekas 3 hours ago [-]
Are you trying to tell me time is relative?
qurren 2 hours ago [-]
As understood by general relativity, it actually is. There is no absolute time.
You can say the age of the universe is 14 billion years, but that's in our reference frame.
In another reference frame it may be a different number.
bilekas 2 hours ago [-]
I'm being flippant
eggn00dles 3 hours ago [-]
well the meter and the kilogram themselves are either completely or partially defined by the speed of light. its a fundamental constant that a large portion of nature depends on, so i doubt such surgical changes could be realized.
thesparks 2 hours ago [-]
What if the speed of light was 2c instead of c? Would that change anything for us?
BSTRhino 2 hours ago [-]
Less latency in multiplayer games or Zoom calls. Because light can travel around the Earth 7 times in one second, that means one roundtrip to a server on the other side of the world must take ~140 ms (1/7th of a second) which is a timescale you are able to feel. That's lag in multiplayer games. I'm constantly amazed that the reason why multiplayer client-side prediction strategies like rollback netcode exist is because light is slow enough on a human scale that we actually have to architect around it. Light is surprisingly slow in some ways.
Some of the details in the paper are super cool. Since the game pulls "c" down to near walking speed, you receive photons at different rates depending on their direction relative to your motion (relativistic aberration / searchlight effect) resulting in neat visual shifts.
I don't usually download games, but I might have to make an exception just to try it out.
inshard 54 minutes ago [-]
I don’t quite get the assumptions here. If c were actually 5 km/h, causal influences would propagate much more slowly. With G unchanged, planets and stars at their current masses and sizes would lie within their Schwarzschild radii. Any rock greater that 1.5km in radius is a blackhole. With c reduced to 5 km/h, the black-hole threshold would correspond to a surface escape speed of just 5 km/h. Holding the other relevant constants fixed would also radically alter atomic structure and chemistry. It seems like a lot would change before we could be around to observe the cool redshifts. Is the reduced c being applied only to the visual effects?
dares2573 3 hours ago [-]
Then we will never be able to see aliens again.
skulk 3 hours ago [-]
in the real world if the speed of light was 5 km, we'd probably be a lot smaller!
TZubiri 2 hours ago [-]
cool idea, but being vibe coded doesn't inspire much confidence on whether the math or author subject understanding is correct.
As such I wouldn't base my understanding on the subject on this as-is. Which is a shame as, if it was actually hand coded I might actually use this to learn relativity, something which would otherwise be out of my reach.
A note on source code, I think committing the actual javascript code and such is a mistake at the level of committing compiled binaries to a repo. It's more useful, correct and genuine to upload the prompts used, which are the source code that generates the target code, and upon which the author and others can study and modify the program.
"Here look." Her fingers started to fly on the DynaBook's keyboard, altering the program she had·written several weeks before .. You justact as though the ship is pointed towards the sun and add speed!· As she spoke her ship started to fall, but not towards the sun. Oh no!..·"
If we want to move closer to that ideal, of interactive education, I don't think we can just apply the old forms and use the LLM to aid one in being the allmighty program-creator, the LLM needs to be placed at the service of the user. I can't help but seeing the usage of LLMs to generate code as misplacing this power. It's as if a new powerful metal were discovered and smiths can only think about making hammers and foundries and casts with that metal, considering it too valuable to actually use it for the products being smithed.
nekusar 2 hours ago [-]
Would mean the biomolecular computers would be faster than electronics.
Electronics wouldnt work at all.
aghilmort 2 hours ago [-]
this is really great
fuzzfactor 3 hours ago [-]
Can't see your website but I would think everything you see would have so much latency it would be worse than today's internet with dialup using 2GB of RAM on an Atom CPU ;)
scotty79 3 hours ago [-]
Next step, taking into account effects of acceleration according to general relativity.
jrflowers 34 minutes ago [-]
You wouldn’t be able to see shit OP
Rendered at 05:55:07 GMT+0000 (Coordinated Universal Time) with Vercel.
https://www.goodreads.com/en/book/show/1382560.Redshift_Rend...
https://en.wikipedia.org/wiki/Einstein's_Dreams
Edit, maybe it's because the speed shift is so coarse I cross past 0 km/h from back to forwards and reverse too fast...
Other than this, very very nice. Love this kind of thing for developing intuiting outside the normal range in which we experience the laws of Physics. Well done.
That's exactly what would happen ins space.
There is also a helpful FAQ which explains all the strange things happening, such as length contraction, time dilation, and color shifting: https://testtubegames.com/srel101.html
My favorite levels are #18 (which demonstrates time dilation), #26 (which demonstrates space warping), and #42 (which demonstrates retarded time https://en.wikipedia.org/wiki/Retarded_time ). All the levels are unlocked and you can skip to any level.
> A Slower Speed of Light is a first-person game prototype in which players navigate a 3D space while picking up orbs that reduce the speed of light in increments. Custom-built, open-source relativistic graphics code allows the speed of light in the game to approach the player’s own maximum walking speed. Visual effects of special relativity gradually become apparent to the player, increasing the challenge of gameplay. These effects, rendered in realtime to vertex accuracy, include the Doppler effect (red- and blue-shifting of visible light, and the shifting of infrared and ultraviolet light into the visible spectrum); the searchlight effect (increased brightness in the direction of travel); time dilation (differences in the perceived passage of time from the player and the outside world); Lorentz transformation (warping of space at near-light speeds); and the runtime effect (the ability to see objects as they were in the past, due to the travel time of light). Players can choose to share their mastery and experience of the game through Twitter. A Slower Speed of Light combines accessible gameplay and a fantasy setting with theoretical and computational physics research to deliver an engaging and pedagogically rich experience.
https://www.reddit.com/r/educationalgifs/comments/qq5cw7/coo...
We cannot play competitive multiplayer games globally, without 300ms ping. I dream of a world playing Black Ops 2 on a original PS3 in 2026 getting into a lobby because latency is low.
https://wondernetwork.com/pings/Auckland
Your real world latency is going to be worse.
300ms feels extremely optimistic coming from my perspective of someone living on an island in SE Asia
https://gamelab.mit.edu/games/a-slower-speed-of-light/
A Slower Speed of Light (2012) - https://news.ycombinator.com/item?id=40332586 - May 2024 (59 comments)
What if we could reduce the speed of light - https://news.ycombinator.com/item?id=26309517 - March 2021 (1 comment)
A Slower Speed of Light (2012) - https://news.ycombinator.com/item?id=17169262 - May 2018 (15 comments)
A Slower Speed of Light - https://news.ycombinator.com/item?id=4731749 - Nov 2012 (105 comments)
"A Slower Speed of Light" Game Trailer - MIT Game Lab - https://news.ycombinator.com/item?id=4714779 - Oct 2012 (1 comment)
I feel like a rule of vibecoding would be that you shouldn't do it for the core of a product, the quality is just not there yet. Even if it is, your core contribution should be what LLMs would train on, rather than being their output.
Basically imagine like if you wanted to walk in a straight line between two points at both ends of a empty, long, narrow rectangular warehouse, and instead of walking in a straight line from A to B, you bounced off each wall at an angle (like a pool ball ricocheting off the bumpers) to get from one end to the other. Making your cumulative distance travelled on foot much greater.
I know there are many other mundane technologies that can be described in sci-fi-ish way, but for some reason I'm particularly amazed by fiber transmitters being compact and cheap enough to be used in mass-produced killer drones.
When I say data rates are way below 1 Gbps, it's because commonly you've got two things going on, a UART serial bridge from operator to flight controller board (same idea as what is implemented in RF with ExpressLRS, TBS Crossfire or similar), this is at most a Mbps or two. Then a possible live video feed over IP which will be easily under 50 Mbps.
The only thing a little bit out of the ordinary about them is that they're often bidirectional single strand optics with the prism built in, and tx/rx on different wavelengths (like 1550 and 1570, or 1550 and 1610, or whatever). Basically same thing that somebody lighting a very low cost metro dark fiber circuit might do to use only 1 strand for a gigabit or 10 Gbps link.
At the risk of exposing how little I remember from physics, doesn't light in a single mode fiber not bounce? (right about now I'm thinking that it's probably not great to think of photons bouncing because this is quantum level stuff, right? light is a wave, etc. gosh it's been a long time since I tried to really know any of this...)
https://www.aflhyperscale.com/articles/how-do-fiber-optics-w...
If you google image search "refraction fiber optics" you'll get some decent pictorial examples of what I meant by photons bouncing off the interior walls of a 9/125 SM fiber optic strand billions/trillions of times on its path, I guess I was trying to write an extremely simplified explanation of refraction in something like a typical SMF-28e / G.652.D fiber.
EDIT: ah, by setting 'Speed of light' parameter to 40km/hr I find it a bit more intuitive
Forward means light is hitting your eyes faster, making it look like the distance the light had to cross is condensed, meaning it looks further away.
Moving backwards slights the light hitting your eyes, to the point where you're moving away from the light, so everything goes black.
Just a thought experiment for you guys: imagine a bacteria that survives inside humans. It doesn't even know what a human is. For the bacteria, its entire world is simply the environment in which it lives. It doesn't know that we are living beings actively trying to maintain ourselves and survive.
Now, suppose a harmful bacteria enters our body, makes us sick, and we take medicine that kills all of them. From the bacteria's perspective, it could look like a natural disaster or some unexplained event in which they all suddenly get wiped out. They have no idea that a living being called a human actively tried to eliminate them using something called medicine, which was engineered specifically to kill them.
Similarly, what if our world, or nature itself, is part of some higher-level entity that we simply exist within? What if the reason for our deaths, natural calamities, and other events is something completely beyond our perception? Whatever we do, we may never be able to understand what is actually happening at that level, just as bacteria may never be able to understand that humans exist.
One thing that could potentially support this idea is self-regulation. We see self-regulating systems throughout nature, and these patterns seem to repeat at different scales. We ourselves are self-regulating organisms, and nature also has countless cycles and mechanisms that regulate themselves.
Maybe these patterns continue at scales we cannot perceive. We can observe certain things at the scale of humans, but we still don't fully understand what happens at the nano scale or on the scale of the universe. Perhaps there are higher levels of organization and self-regulation that we simply don't have the ability to perceive yet.
https://www.youtube.com/watch?v=OKnpPCQyUec
But let me tell you another possibility. What if there is no nature, but just our perception of it.
Yea, tree falling in the forest and all that...stated more explicitly..
https://en.wikipedia.org/wiki/A_Slower_Speed_of_Light
Having said that... this is mostly a slogan and makes for good Youtube videos, but it falls apart the moment you subject it to even the most basic scrutiny. For one... it doesn't make sense to talk about a speed through time since speed is literally a measure of change with respect to time, so a change in time with respect to time doesn't make any sense.
But as a slogan, it captures the idea that motion through space and the rate of your own clock are tightly linked together.
Only if you're talking about other people's clocks and not your own. Your own clock is one second per second, but someone else's may be slower or faster relative.
So then you say take someone else's clock and compare it to your own clock, but that is still just a pure number. A speed is not a number, it has units like meters per second. A ratio of two clocks has no units at all, the units cancel. Whatever number you get, 3 or 9, it's just a factor by which two clocks disagree. You can absolutely interpret this ratio as a rate, but that doesn't make it a speed.
And a speed is exactly what the slogan needs, because the diagram/geometry it's using involves a right angled triangle where on one side of the triangle is your speed through space, and on the other side of the triangle is your speed through time, and the hypotenuse of the triangle is fixed at c (since every object travels through spacetime at this fixed speed).
For that to mean anything both sides have to be the same kind of quantity. You can't put meters per second on one side and a bare number on the other and call it a triangle. Nor can you patch it by multiplying the ratio by c to give it units, because the thing you get then grows as you speed up instead of shrinking. Either it has the right units and the wrong behavior, or the right behavior and no units at all. There's no version of this geometry that produces a consistent picture.
You can say the age of the universe is 14 billion years, but that's in our reference frame.
In another reference frame it may be a different number.
https://youtu.be/uu7jA8EHi_0
Some of the details in the paper are super cool. Since the game pulls "c" down to near walking speed, you receive photons at different rates depending on their direction relative to your motion (relativistic aberration / searchlight effect) resulting in neat visual shifts.
I don't usually download games, but I might have to make an exception just to try it out.
As such I wouldn't base my understanding on the subject on this as-is. Which is a shame as, if it was actually hand coded I might actually use this to learn relativity, something which would otherwise be out of my reach.
A note on source code, I think committing the actual javascript code and such is a mistake at the level of committing compiled binaries to a repo. It's more useful, correct and genuine to upload the prompts used, which are the source code that generates the target code, and upon which the author and others can study and modify the program.
That said, as an idea, it reminds me of Kay's dynabook example ( https://dl.acm.org/doi/10.1145/800193.1971922 ) :
"Here look." Her fingers started to fly on the DynaBook's keyboard, altering the program she had·written several weeks before .. You justact as though the ship is pointed towards the sun and add speed!· As she spoke her ship started to fall, but not towards the sun. Oh no!..·"
If we want to move closer to that ideal, of interactive education, I don't think we can just apply the old forms and use the LLM to aid one in being the allmighty program-creator, the LLM needs to be placed at the service of the user. I can't help but seeing the usage of LLMs to generate code as misplacing this power. It's as if a new powerful metal were discovered and smiths can only think about making hammers and foundries and casts with that metal, considering it too valuable to actually use it for the products being smithed.
Electronics wouldnt work at all.