Timeline for Does the bias in a loaded die depend on gravity?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 12, 2023 at 12:46 | history | edited | AXensen | CC BY-SA 4.0 |
added 287 characters in body
|
| May 11, 2023 at 13:44 | comment | added | AXensen | @NuclearHoagie see the new edited answer. But this is not the correct interpretation of argument 1. In fact I had in mind a loaded dice that was loaded by putting more weight near the six-face. If it were loaded in another way (like with magnets) that's actually where argument 1 would fail. Because the forces that cause it to land on 6 more often would rescale with the rest of the motion of the dice if and only if those forces are gravitational. If the mechanism was magnetic, then the ratio of gravity to the loading mechanism would change and it would be more loaded on the moon. | |
| May 11, 2023 at 13:41 | history | edited | AXensen | CC BY-SA 4.0 |
added 963 characters in body
|
| May 11, 2023 at 13:20 | comment | added | AXensen | The currently most upvoted response (with a useful source!) makes it clear that the bouncing surface changes the way a dice is loaded. This argument clearly refutes the assumptions of arguments 1 and 3. I'm leaving this answer up because I think it has valid arguments for why changing gravity - and nothing else - under certain assumptions - should either change the result very little or not at all. But I think the caveats pointed out in the comments are an important part of understanding under what circumstances all three arguments may be wrong. | |
| May 11, 2023 at 12:56 | comment | added | Nuclear Hoagie | I don't buy argument #1 - I agree a die's outcome shouldn't depend on "how" you throw it, but that doesn't mean there can't be different outcomes when throwing it in different environments. Suppose the die-loading mechanism uses a magnet, you'd of course expect different outcomes when throwing it on a magnetized vs. non-magnetized table. Argument #1 implicitly assumes that the die-loading mechanism does not rely on gravity in any way, which I don't think is a fair assumption. | |
| May 11, 2023 at 8:44 | comment | added | Nadav Har'El | The air drag, initial velocity, die's plastic/elastic parameters, and other things, as well as the strength of gravity, obviously effect the outcome of a single throw. And in theory, if you throw the die with exactly same initial conditions, it will fall the same every time. But the question posed was whether result averaged over all slightly different initial conditions (with fixed gravity) will change if we change the fixed gravity. | |
| May 10, 2023 at 21:47 | comment | added | AXensen | I don't agree that drag and initial velocity are likely to matter. Air drag is a small contribution to the dice's motion (energy loss is in bounces). So it seems far-fetched to say it will affect P6. And saying the initial velocity matters feels like saying "if I hold the six facing up when I drop the dice, it is more likely to roll a six". The fundamental assumption of dice is that once you give it plenty of energy chaos erases any effect of the initial condition. I only meant to list highly relevant quantities. If I want small effects with units of s, I can include c because of relativity. | |
| May 10, 2023 at 21:37 | comment | added | Ján Lalinský | Regarding argument 3, also initial velocity of the die is relevant, and with the initial height above table, these two provide a time scale. | |
| May 10, 2023 at 21:22 | comment | added | Jeffrey | For argument 3, remember that the atmosphere viscosity is expressed in pascal-second. Changing the gravity changes the effect of viscosity. Viscosity is what slows the die down and allows it to settle on the loaded face. | |
| May 10, 2023 at 19:44 | comment | added | AXensen | @NadavHar'El Good point. But that implies something similar to argument 1 - that $P_6$ can only depend on $g$ if it also depends on things like the bounciness of the floor or the air density. | |
| May 10, 2023 at 19:41 | history | edited | AXensen | CC BY-SA 4.0 |
added 49 characters in body
|
| May 10, 2023 at 16:21 | comment | added | Nadav Har'El | In argument 3, I think you forgot something: Under your assumptions, the die would never stop jumping around (for the unit-analysis reason you explain, there can be no time when it stops jumping!), so for it to stop jumping, it needs something like air drag or plastic deformation - and those things have time in their units, which can explain when the die will stop jumping around, but can also theoretically make P6 depend on time. So I think argument 3 isn't useful. | |
| May 10, 2023 at 14:30 | history | edited | AXensen | CC BY-SA 4.0 |
added 451 characters in body
|
| May 10, 2023 at 14:21 | history | edited | AXensen | CC BY-SA 4.0 |
added 20 characters in body
|
| May 10, 2023 at 10:39 | history | edited | AXensen | CC BY-SA 4.0 |
added 128 characters in body
|
| May 10, 2023 at 10:31 | history | answered | AXensen | CC BY-SA 4.0 |