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FQXi FORUM

February 22, 2018

From the article: "Imagine you flip a coin 100 times. You can‚Äôt predict whether the coin will land heads or tails on any particular toss‚Äîonly that, if you keep flipping for a long time, the coin should come up heads just as often as tails."

But then if one flips a coin 25 times, all heads say, then your chances of predicting either heads or tails should increase? If at the 96th flip, you look at the recorded data: 48 heads and 48 tails, what are the probability of your guestimation of the remaining 4 flips?

There is an interesting "coin-toss" experiment that involves the predictability of data recorders and the probability of experiment outcomes, that has a relational time paramiter, which can be intepreted as a "cause" effect.

I will put together my thought experiment and post it here later, but for now a question:If the first coin flipped lands tails, what baring (if any?), does this have on the remaining coins being flipped, is the first coin flipped responsable for the outcome of the following tossed coins, and does this increase exponentially, ie..the fourth coin..fifth, twentyfourth....nintysixth?

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But then if one flips a coin 25 times, all heads say, then your chances of predicting either heads or tails should increase? If at the 96th flip, you look at the recorded data: 48 heads and 48 tails, what are the probability of your guestimation of the remaining 4 flips?

There is an interesting "coin-toss" experiment that involves the predictability of data recorders and the probability of experiment outcomes, that has a relational time paramiter, which can be intepreted as a "cause" effect.

I will put together my thought experiment and post it here later, but for now a question:If the first coin flipped lands tails, what baring (if any?), does this have on the remaining coins being flipped, is the first coin flipped responsable for the outcome of the following tossed coins, and does this increase exponentially, ie..the fourth coin..fifth, twentyfourth....nintysixth?

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It does seem like, if your coin lands on heads 25 times in a row, you're "due" for a tails. But assuming that your coins are fair (and that is something you might start to doubt if it came up heads 25 times in a row), each toss still has identical 50-50 odds. No toss is affected by the outcome of the previous tosses.

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This is really quite amazing, without me actually putting down, what I thoguht was a loophole in the probability of outcomes, youve answered a puzzling question I had been pondering on, and thus saved me trying to oversimplify an obvious straightforward process!

What I was going to try and demonstrate (apart from maybe my simplistic reasoning to try and understand), was just making 2 flips of paired coins,(2 tosses are one unit of data?) recording the data as a heads or tails, and making 100 "paired" flips (200 actual coins), and then repeating the process a number of times, with an actual "time" log to the flips?..ie 2 coins flipped by devise at same instant taking 1 second, waiting for one second, then flip again..waiting for 2 seconds..then 3 seconds..up to a gap of 99 seconds between flips?

More to follow!

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What I was going to try and demonstrate (apart from maybe my simplistic reasoning to try and understand), was just making 2 flips of paired coins,(2 tosses are one unit of data?) recording the data as a heads or tails, and making 100 "paired" flips (200 actual coins), and then repeating the process a number of times, with an actual "time" log to the flips?..ie 2 coins flipped by devise at same instant taking 1 second, waiting for one second, then flip again..waiting for 2 seconds..then 3 seconds..up to a gap of 99 seconds between flips?

More to follow!

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100 fair coins are placed upon 100 levers that will flip them to a specific height. At this height, a camera is activated to take a picture of the coins, either heads or tails. The photos are then examined, the first photo shows Heads, without looking at the remaining photo's, what is your guestimation of the remaining 99 photo's ?

Assume the experiment is performed as true and precise as physical possible.

"It does seem like, if your coin lands on heads 25 times in a row, you're "due" for a tails. But assuming that your coins are fair (and that is something you might start to doubt if it came up heads 25 times in a row), each toss still has identical 50-50 odds. No toss is affected by the outcome of the previous tosses."

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Assume the experiment is performed as true and precise as physical possible.

"It does seem like, if your coin lands on heads 25 times in a row, you're "due" for a tails. But assuming that your coins are fair (and that is something you might start to doubt if it came up heads 25 times in a row), each toss still has identical 50-50 odds. No toss is affected by the outcome of the previous tosses."

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Obviously, if the experiment is set up as a "pure" and precise system, the analytic value is biased towards initial conditions, ie the exactness will produce a contiueous and repetative result based on the very first recorded data.

If the coins are true, and the initial states of all coins being placed exactly as possible upon the levers, and they attain an exact height for the detector/camera, than all 100 coins will show the exact same face! there can be no random distribution, does this precision constitute "unfairness" ?

How much immprecision needs to be added to the experiment in order to attain a result that for all intensive purpose is deemed "random" but fair?

As an example, lets have 100 levers that have intermitent Heads-Tails-Heads-Tails... placed upon the levers at rest before they are all activated. Will this then produce 50 Heads + 50 Tails? Even leaving the coins fall to the ground, at the instant they hit the ground, they should all have equal values, all coins that started from rest with Heads face up, should all end up recorded with the same resultant values.

The fact there is only two possible outcomes, can be replaced with geometric structures, say with different colour or numbered sides, for instance any cubic form?

"No toss is affected by the outcome of the previous tosses.", but if the setup is true and precise, then what falls first, or what is detected initially, will always follow, there can be no deviation from all coins obeying initial conditions, what ever law governs the first recorded data, if it remains true and constant, will impose the same effects upon all following recorded data.

If one could confirm that a single spin factor of say an Electron is "spin up", out of two possible states 'up or down', then one can always make the logical assumption that in entanglement experiment, the 2nd electron, split from the first, must be identical, spin up too!..The reason one assumes the "other" entangled electron is also "spin up", is based on the premise of the temr "EITHER" it cannot possibly be spin up + down at two different locations?

A two spin state SINGLE Electron, will always be assigned one-or-the-other spin state. One can never detect a single electron, at TWO separate locations, with TWO opposite spin-states!

One can FIP make the statement that every single electron in existence, will follow identical spin states, EITHER up or down, simplified I defy anyone to present an argument against the following statement:If I detect an electron in a spin-up state, then at that very instant, all non-detected electrons in existence are also in the same identical state. Conversly if I detect an electron spin-down state, the at that same instance, all non-detected electrons have the same spin-state value.

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If the coins are true, and the initial states of all coins being placed exactly as possible upon the levers, and they attain an exact height for the detector/camera, than all 100 coins will show the exact same face! there can be no random distribution, does this precision constitute "unfairness" ?

How much immprecision needs to be added to the experiment in order to attain a result that for all intensive purpose is deemed "random" but fair?

As an example, lets have 100 levers that have intermitent Heads-Tails-Heads-Tails... placed upon the levers at rest before they are all activated. Will this then produce 50 Heads + 50 Tails? Even leaving the coins fall to the ground, at the instant they hit the ground, they should all have equal values, all coins that started from rest with Heads face up, should all end up recorded with the same resultant values.

The fact there is only two possible outcomes, can be replaced with geometric structures, say with different colour or numbered sides, for instance any cubic form?

"No toss is affected by the outcome of the previous tosses.", but if the setup is true and precise, then what falls first, or what is detected initially, will always follow, there can be no deviation from all coins obeying initial conditions, what ever law governs the first recorded data, if it remains true and constant, will impose the same effects upon all following recorded data.

If one could confirm that a single spin factor of say an Electron is "spin up", out of two possible states 'up or down', then one can always make the logical assumption that in entanglement experiment, the 2nd electron, split from the first, must be identical, spin up too!..The reason one assumes the "other" entangled electron is also "spin up", is based on the premise of the temr "EITHER" it cannot possibly be spin up + down at two different locations?

A two spin state SINGLE Electron, will always be assigned one-or-the-other spin state. One can never detect a single electron, at TWO separate locations, with TWO opposite spin-states!

One can FIP make the statement that every single electron in existence, will follow identical spin states, EITHER up or down, simplified I defy anyone to present an argument against the following statement:If I detect an electron in a spin-up state, then at that very instant, all non-detected electrons in existence are also in the same identical state. Conversly if I detect an electron spin-down state, the at that same instance, all non-detected electrons have the same spin-state value.

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