- Definition of “coin” revised exactly while flip is in progress, e.g. physical money is abolished and coins are now officially called “dwarf coins”
– whoops, sorry, this is almost the same as Baal_Houtham’s above - coin discovered to be something other than a coin
#19. The coin is tossed, then both contestants have fatal heart attacks before it lands. Much later someone finds the bodies & pockets the coin, never noticing or caring which face is up.
If a coin flips in a forest and no one is there to observe the result, is there a result? Well Mr. Feynman … is there?
Real world coincidence: Some time in the last week I saw a coin lying on the sidewalk. Was that the aftermath of a coin toss? We’ll never know. With COVID about I didn’t bother to pick up that nickel.
I picked up a quarter and a dime today. I’m messing with fate!
Numberphile (https://www.youtube.com/user/numberphile/videos) has some videos of coin tossing and that guy tossed real coins.
Can’t remeber the professors name who did it but I remember how he described how to make five sided die:
Take a object shaped like a Toblerone packet. It’s a rod with unilateral triangle as its cross section. When you throw it there’s clearly three equal probabilities it to land on one of the sides. But imagine flattening it lengthwise and in the end you’d have a triangle disk that has two sides that are equaly probable it to land if tossed. So there must be a sweet spot in the flattening where it’s equally likely to land on a side or on an end. There’s your d5.
You mean like Derren Brown in his TV special The System?
The coin tossing:
ISTR reading in a magazine (Discover, maybe), many years ago, about an actual computer-controlled coin tossing machine. The coin started face-up in a holder, and the machine controlled two variables:
-
The height of the toss
-
The rotation rate of the coin
The article included an X-Y plot showing the result of the toss for a range of height/rotation pairs. At low heights and rotation rates, the result was very predictable: the plot was dominated by large area (ranges of height/rotation) where you had either heads or tails. But as you got to greater heights or rotation rates, the areas of constant result grew smaller and more irregular. This was believed to be due to several factors:
-
The limited ability of the machine to perfectly/repeatably apply a desired height or rotation rate, which caused the coin to sometimes deliver one result when you might have expected the other. Certainly you could build a higher quality machine, but even then you’d still reach its limit at some point.
-
The bouncing of the coin on landing was chaotic, especially when starting with high energies. As it was a real coin, the edge was not “perfect” (neither was the landing surface), i.e. tiny imperfections came into play.
-
Air currents don’t matter for low height/spin tosses, but for tosses with greater hang time, they could have an effect.
If the coin is made with plutonium and it has a flux capacitor and is flipped at the speed of 88 MPH and lightning strikes giving 121 gigawatts of power it will time travel. I assume this will go to the year on the coin.
A Boltzmann Brain spontaneously forms in the vicinity of the flip; the coin is incorporated as a nose ring.
I think a better version of this is a box with the coin suspended and spun by magnetic field (pulsed and modulated). In the box is a radioactive element and a detector, wired to the power supply of the magnetic field generator such that the magnetic field is turned off when a decay is detected. Close the box. Until the box is opened, the coin is neither heads not tails, but in a mixed state of heads and tails. Schrödinger’s coin.
That was what I was getting at. The coin would therefore be in a superposition until you opened the box.
But you’re right to postulate a different setup… The way I put it, the coin would start in a position and then the flipper might flip it back into that position. Better that the coin starts in the heads position with a flipper that simply turns the coin over to tails if it’s activated.
I’m pretty sure the plot I’m thinking of was from the '80s or '90s, but here’s a similar study that was published in 2004 (PDF):
There’s a plot at the top of page 6 that’s similar to the one I’m remembering. The difference is that this plot appears to be based on theoretical equations rather than the actual, imperfect results of the real coin-tossing machine that I’m remembering; in the latter case, the plot got messier and messier the farther you moved from the origin.
Yeah, that might be better. In your first gedanken experiment, the superposition was flipped/unflipped, not heads/tails. I tried to remedy that by creating a flipped, but unresolved state at the start. I think your second experiment also creates a mixed heads/tails state.
We’ve had threads and threads on how to make n-sided dies.
My approach is simple. A Toblerone package is an example of a triangular prism AKA 3-prism. That can be generalized to any integer number of sides. A 4-prism might be a box for a single fluorescent tube lamp. A 5-, 13-, or 100-prism is equally simple to manufacture.
As long as it’s long enough, or has slanted ends, so it will always fall so the long axis is parallel to the table, you have a Dn. Whether it’s fair is entirely a matter of manufacturing tolerances. Which is certainly a well-understood domain.