[Guest]

Jaimito was doing a physics exam, but he did not study at all. He was good at mathematics, though. One of the question of the exam was:

What's the binding energy of two quarks whatever and so so blah blah (he never heard of that)?

a) 1.43E-27 eV

b) 5.63E-18 eV

c) 8.41E-24 eV

Then Jaimito asked the teacher 'How did you get the other two numbers, I mean, the wrong ones?'

'I just invented them, digit by digit, randomly'.

He said 'Thanks, that actually helps!'

What option did Jaimito pick and why? What are the odds for him in that question?

[Guest]

Jaimito was doing a physics exam, but he did not study at all. He was good at mathematics, though. One of the question of the exam was:

What's the binding energy of two quarks whatever and so so blah blah (he never heard of that)?

a) 1.43E-27 eV

b) 5.63E-18 eV

c) 8.41E-24 eV

Then Jaimito asked the teacher 'How did you get the other two numbers, I mean, the wrong ones?'

'I just invented them, digit by digit, randomly'.

He said 'Thanks, that actually helps!'

What option did Jaimito pick and why? What are the odds for him in that question?

By Benford's Law and Bayes' Theorem, the probability should be about 70% that a (1.43x10^-27 eV) is correct.

[Guest]

Jaimito was doing a physics exam, but he did not study at all. He was good at mathematics, though. One of the question of the exam was:

What's the binding energy of two quarks whatever and so so blah blah (he never heard of that)?

a) 1.43E-27 eV

b) 5.63E-18 eV

c) 8.41E-24 eV

Then Jaimito asked the teacher 'How did you get the other two numbers, I mean, the wrong ones?'

'I just invented them, digit by digit, randomly'.

He said 'Thanks, that actually helps!'

What option did Jaimito pick and why? What are the odds for him in that question?

I'm guessing c) since it's the only one with a repeating digit, something that humans tend to be biased against when manually generating a series of random numbers. However, I'll leave it to any physicists to settle the correct answer.

Edited September 12, 2008 by JDewey

[unreality]

CR: does Benford's Law apply in this situation though? I had the understanding that it only applies to certain (usually human-activity-based) numbers, not necessarily things like atomic-level physics

[Guest]

CR: does Benford's Law apply in this situation though? I had the understanding that it only applies to certain (usually human-activity-based) numbers, not necessarily things like atomic-level physics

I wasn't sure either, so I (of course) went to Wikipedia, the font of all knowledge. From http://en.wikipedia.org/wiki/Benford%27s_law: "This counter-intuitive result has been found to apply to a wide variety of data sets, including ... physical and mathematical constants..."

The most obvious explanation for something like this is that humans use units which will tend to produce that sort of distribution in common situations. Wikipedia seems to disagree, though, and who am I to argue?

[Guest]

I wasn't sure either, so I (of course) went to Wikipedia, the font of all knowledge. From http://en.wikipedia.org/wiki/Benford%27s_law: "This counter-intuitive result has been found to apply to a wide variety of data sets, including ... physical and mathematical constants..."

The most obvious explanation for something like this is that humans use units which will tend to produce that sort of distribution in common situations. Wikipedia seems to disagree, though, and who am I to argue?

I should point out that the teacher for circumvent this by using a random number generator that picks numbers according to Benford frequencies.

You could argue that such a generator would not meet the OP statement of being "completely random," but I think one reasonable requirement of complete randomness might be indistinguishability between the psuedo-random and naturally occurring numbers.

[Guest]

Jaimito was doing a physics exam, but he did not study at all. He was good at mathematics, though. One of the question of the exam was:

What's the binding energy of two quarks whatever and so so blah blah (he never heard of that)?

a) 1.43E-27 eV

b) 5.63E-18 eV

c) 8.41E-24 eV

Then Jaimito asked the teacher 'How did you get the other two numbers, I mean, the wrong ones?'

'I just invented them, digit by digit, randomly'.

He said 'Thanks, that actually helps!'

What option did Jaimito pick and why? What are the odds for him in that question?

hmm...

Well it starts with a 33.3 chance for each... but genaraly humans creating a random awnser chose not to use an awnser as B)or C) because it is general to not use the first answer so my guess is A

I hope this spoiler works...

[Guest]

By Benford's Law and Bayes' Theorem, the probability should be about 70% that a (1.43x10^-27 eV) is correct.

Yep, that's the right answer.

Benford's law can be applied to any distribution of numbers than can vary among different orders of magnitude. If we distribute these numbers on a logarithmic scale, there's 30% probability that the first number is a 1, 17.6% of being a 2, etc, and only 4.6% of being a 9.

Physical constants have a huge varying range, thus they fit perfectly to the distribution.

The teacher generated the other two answers randomly digit by digit, so that implies that the first digit has the same chance to be a 1 or a 9.

Jaimito had 70% chances of guessing because dividing 30 by the sum of the probabilities of having a 1, a 5 or a 8, you get 0.7.

People actually use this law to try to spot human invented numbers in a table of quantities, for example, to find fraudulent accounting data.

Check "Benford's law" in Wikipedia to find out more about this distribution.

[Guest]

Jaimito was doing a physics exam, but he did not study at all. He was good at mathematics, though. One of the question of the exam was:

What's the binding energy of two quarks whatever and so so blah blah (he never heard of that)?

a) 1.43E-27 eV

b) 5.63E-18 eV

c) 8.41E-24 eV

Then Jaimito asked the teacher 'How did you get the other two numbers, I mean, the wrong ones?'

'I just invented them, digit by digit, randomly'.

He said 'Thanks, that actually helps!'

What option did Jaimito pick and why? What are the odds for him in that question?

He picked option C) as the answer. The A) and B) fell into the laws of random choice, including every number except 9.

[Guest]

Most probably C) because,it has a repeating number.

I know when I create a random number I always try not to repeat the digits... That's a big mistake.

[unreality]

So Benford's Law does fit for this? Cool