Coincidence comes from gravity. Gravity comes from moon and sun. Moon and sun come from perfect balance. “I am” come from creating the best balance possibilities from the law of physics for every living cells.
Why do we need to estimate probabilities? Largely because we make observations on samples but want to make/test claims about populations. Inferential statistical procedures are used to estimate the amount of sampling error in our samples and use it to determine the probability that our results are due to random chance. The logic of inferential statistics is to estimate the probability of getting particular outcomes and make decisions based on these probabilities.
A Diamond is a clear transparent precious gemstone made totally of Carbon atoms (Chemical Composition ‘C’) crystallized in a cubic (isometric) arrangement which has been highly compressed over millions of years.
NOV 29, 2011 12:05 PM
The process works a little something like this. Sussman takes
a big old beam of science a laser and fires a several-trillo second burst through a diamond. In the process of going through the diamond, the laser fundamentally changes in completely random ways, providing those true random numbers everyone craves. That’s right. Ben Sussman makes random numbers by shooting lasers at diamonds, for science. This is exactly the kind of experiment I imagined scientists doing when I was about 6 years old. The only way this could be cooler is if it were all going down in space.
At this point, you’re probably thinking, “So what’s so random about this? After all, if dice rolls aren’t random because we theoretically could predict them, what makes this laser-diamond stuff any different?” Well, we theoretically can’t predict these numbers. It’s not that we don’t know how the light changes inside the diamond. It’s that we can’t know. It is unknowable. To know would defy the very laws of physics.
As you can probably guess, quantum physics is to blame for this one. While traveling through the diamond, the laser experiences a quantum fluctuation, and according to the Heisenberg uncertainty principle, it is literally impossible to figure out what happened in there; all we can do is take a look at what’s coming out the other side. Basically, when you shoot a laser through a diamond, quantum physics does a whole bunch of stuff that is literally impossible to know, ever. Are you getting this?!
It may seem like an arbitrary pursuit to go so far to get truly random numbers. Maybe dice rolls are good enough for you. Maybe you don’t see the fun in shooting lasers at diamonds. Be that as it may, pseudo-random numbers, especially computer generated ones, are not good enough for one particular, important field: Cryptography. The ability to generate truly random numbers, in the quantity I might add, could revolutionize the field of cryptography by finally allowing access to encryption keys that literally can’t be reverse-engineered. The only way to unlock data encrypted with a truly random number is brute force, and that can be an impossibly time-consuming endeavor.
With digital data transmission becoming ever more the norm and information theft becoming more and more of a serious threat, true random number encryption stands to be a huge game changer and would require any hacking attempt to have the absurd processing power and even more absurd luck. Also, these numbers are the product of shooting lasers at diamonds. Can’t forget about that.
You already know that the probability of an outcome is:
number of ways an outcome can happen ÷ total number of possible outcomes
However, finding the total number of possible outcomes is not always straightforward – especially when we have more than one event.
The answer is 4. 1d4 means a range from 1 to 4, and although the dice differ in the number being on the top or bottom of the pyramid, the answer will always be between these.
Dice Rolls are Not Completely Random
Scientists used new theoretical models and high-speed movies of dice rolls to illustrate findings.
Ben P. Stein, Contributor
Dungeons and Dragons, Yahtzee, and a huge number of other games all rely on throwing dice–from the 4-sided pyramid shape to the familiar 6-sided cube and the monster 20-sided variety. The dice are meant to introduce an element of chance to these games; we expect that the outcomes of the rolls will be truly random.
However, new theoretical models and high-speed movies of dice rolls of numerous shapes and sizes confirm this is not strictly the case. They show that dice thrown with a 1 on the top are slightly more likely to land as a 1 than as the other values for every type of the various kinds of dice they studied. But at the same time, it’s usually too hard for someone to predict the outcome of the throw of a single die–you’d have to know the starting conditions of the throw and its environment so precisely that for all practical purposes, the result could be considered random.
Exploring a question that was debated in the 17th century by scientists and mathematicians Blaise Pascal and Pierre de Fermat, and many others before and since, doctoral student Marcin Kapitaniak at the University of Aberdeen, Scotland and his co-authors created a sophisticated theoretical model of the die throw in three dimensions. They considered how the effects of gravity, air resistance, the friction of the table, and other factors influence the outcome of the roll. In addition, they observed the fall of the die with a high-speed camera that could capture the die’s trajectory at a rate of 1500 frames per second. What did they find to be the most important factor?
“The initial position of the die,” Tomasz Kapitaniak, of the University of Lodz in Poland, wrote to me in an email. Small changes in the position can significantly affect the outcome. Other factors are less significant. “The air resistance can be neglected,” he said.
However, he quickly added, “friction is important.”
With a high-friction table, in which the dice can’t slide across very easily, the dice tend to bounce around more times, tumbling and twirling, and making the results harder to predict. With a smooth, low-friction, or soft table, the dice tend to bounce fewer times.
Even bouncing doesn’t always mix things up. The high-speed video showed that dice frequently did not change their face even after a bounce.
Could gamblers use the knowledge from this paper to their advantage, by placing the desired value of their roll as the highest-lying face of their die?
“I don’t know how to use it practically in a casino,” Kapitaniak wrote. Players would have to know everything so precisely–most importantly, the exact position of the die–to be able to predict the results with certainty.
On the other hand, casino operators won’t ever be able to achieve 100% random rolls with dice. They often drill the pips–the little dots in dice–and fill it with the uniformly weighted material in efforts to make all sides of the dice equally probable to come up in a roll.
“Drilling the pips…gives the symmetry in the die but symmetry is not enough” to make it random, he said. “[The] top face will always be more probable.”
If not random, is the die roll chaotic–the popular concept that originated in the second half of the 20th century, in which small differences in starting conditions can lead to large differences in end results? The most common example is the hypothetical picture of a butterfly flapping its wings in South America changing air circulation patterns to influence the weather halfway around the globe. The end result is knowable only if you have precise knowledge of the starting conditions of the world’s weather.
A die roll is chaotic only if it bounces on the table an infinite number of times, according to Kapitaniak. But this is far from attainable, due to the fact that the die loses energy with each bounce due to friction.
With the high-speed camera images and the new theoretical treatment, this paper provides a new contribution to the question of the true randomness of dice throws and coin tosses. It contributes to an increasingly sophisticated understanding of what can be considered fully random in everyday life.
And in a more practical vein, if you’re playing Dungeons and Dragons tonight, it probably wouldn’t hurt to start your roll with the coveted 20 on top–it may occasionally give you the desired results, while Dungeon Masters could insist on playing on the roughest, highest-friction table they can find.
The work will appear in an upcoming issue of the journal Chaos.