Is randomness real?

Jul 2008
18,573
12,309
Virginia Beach, VA
#82
Most likely roll for a pair of dice, 7
Repeated flipping of a coin will result heads half the time.
The half life of any identified radioactive substance.
All of those things are probabilities not predictions. There is no mathematical formula that predict the result of a single throw of two dice. You can calculate the probability of the different results but there is no way to calculate the actual result.
 
Apr 2013
37,215
25,391
La La Land North
#83
Most likely roll for a pair of dice, 7
Repeated flipping of a coin will result heads half the time.
You are conflagrating probability and randomness. Yes, the most likely roll for a pair of dice is 7. But you can not predict on which roll that 7 will appear.

Equally well, on the coin flip, you can't predict if it will be h,t,h,t or h,h,t,t and so on. Odds are (probability) that if you flip enough times, the outcomes will be equal. But you can't predict in what order that outcome will be achieved.
 
Jul 2008
18,573
12,309
Virginia Beach, VA
#84
The chances of flipping four tails in a row on a fair coin toss are 0.5^4 or 6.25%. If the first flip is tails then the odds of the next three flips all being tails is 12.5%.
 
Nov 2012
17,145
5,648
Michigan
#85
No, I don't like it. Just off the top of my head right now, without referencing any textbooks, I think more along the line of an event which can not be predicted with certainty or having the outcome defined mathematically.
Displaying results of “random” events on a graph displaying a bell curved distribution is mathematical definition and often used as a test for randomness.
 
Nov 2012
17,145
5,648
Michigan
#86
The half life of a radioactive method is actually using math to predict the amount of metal decayed into another state.
 
Apr 2013
37,215
25,391
La La Land North
#87
The half life of a radioactive method is actually using math to predict the amount of metal decayed into another state.
Again the two above address probability. In neither case can you predict the outcome of any one event. You can only estimate the results of a large number of events.
 
Jul 2008
18,573
12,309
Virginia Beach, VA
#88
Displaying results of “random” events on a graph displaying a bell curved distribution is mathematical definition and often used as a test for randomness.
No, it is not a test for “randomness”. It is a measure of how likely a single event is to end with a specific result.

For example, if two people were each given a pair of dice and are told to come up with a result. One person is told on each result he is to roll the dice, the other person is told that he can set the dice to any result he wants with the restriction that he cannot set the dice to a combination that was used in any of the previous 35 tests.

The first persons results will be random. It will be impossible to predict with 100% accuracy any result. The second persons results will be non random, you would be able to tell, with 100% assuracnce what the result of the of the 36th test (and all subsequent tests) will be.

Yet taking all of the results from both tests (and given enough tests) both will give a bell curve graph.
 
Nov 2012
17,145
5,648
Michigan
#89
No, it is not a test for “randomness”. It is a measure of how likely a single event is to end with a specific result.

For example, if two people were each given a pair of dice and are told to come up with a result. One person is told on each result he is to roll the dice, the other person is told that he can set the dice to any result he wants with the restriction that he cannot set the dice to a combination that was used in any of the previous 35 tests.

The first persons results will be random. It will be impossible to predict with 100% accuracy any result. The second persons results will be non random, you would be able to tell, with 100% assuracnce what the result of the of the 36th test (and all subsequent tests) will be.

Yet taking all of the results from both tests (and given enough tests) both will give a bell curve graph.
I didn’t say it was a perfect test, I said it was a test. There is no test that absolutely proves randomness.
 
Nov 2012
17,145
5,648
Michigan
#90
No, I don't like it. Just off the top of my head right now, without referencing any textbooks, I think more along the line of an event which can not be predicted with certainty or having the outcome defined mathematically.
“Can not be predicted”, is saying that random depends on point of view and mental capacities of the observer.
 

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