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Topic: Simple random number generator?
Replies: 24   Last Post: Jan 7, 2013 10:52 AM

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Existential Angst

Posts: 28
Registered: 11/13/11
Re: Simple random number generator?
Posted: Nov 27, 2012 10:36 PM
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"Ben Bacarisse" <ben.usenet@bsb.me.uk> wrote in message
news:0.ef56b5652decd19bb478.20121128013501GMT.87k3t6v7ay.fsf@bsb.me.uk...
> "Existential Angst" <fitcat@optonline.net> writes:
>

>> "Ben Bacarisse" <ben.usenet@bsb.me.uk> wrote in message
>> news:0.e12037e9d116e6e9081a.20121127131802GMT.878v9nw5f9.fsf@bsb.me.uk...

>>> Clark Smith <noaddress@nowhere.net> writes:
>>>

>>>> On Mon, 26 Nov 2012 15:08:17 -0500, Existential Angst wrote:
>>>>

>>>>> Would be the digits of e, pi, et al?
>>>>> If that's the case, no need for fancy pyooter algorithms?
>>>>>
>>>>> Inneresting article on pi, randomness, chaos.
>>>>> http://www.lbl.gov/Science-Articles/Archive/pi-random.html

>>>>
>>>> Is it not the case that the digits of e, pi et al. can't strictly
>>>> be random, if it is only because they are highly compressible? I.e.
>>>> because there small, compact formulas that spit out as many digits as
>>>> you
>>>> want in a completely deterministic way?

>>>
>>> Absolutely.

>>
>> Well, as I responded above, Bailey/Crandall would most certainly
>> disagree.

>
> No they don't. They use random, quite properly, in a slightly informal,
> statistical sense:
>
> It is of course a long-standing open question whether the digits of
> and various other fundamental constants are "random" in an appropriate
> statistical sense.
>
> Note the quotes and the fact that the term is immediately qualified.
>

>>> Of course, that's also the case for the "fancy pyooter algorithms" that
>>> Existential Angst wants to replace, so he or she is not really talking
>>> about random but about pseudo-random sequences.

>>
>> Well, ackshooly I am talking about true random. Bailey and Crandall are
>> hypothesizing that e, pi et al are true random (I like "intrinsically
>> random"), but you and others are apparently arguing that because pi can
>> be
>> calc'd or generated, it cannot be random. Bailey/Crandall would clearly
>> disagree with this.

>
> No, they don't. I am sure they accept the information theoretic
> meaning of the word, just as I accept the statistical sense of the term
> (especially what in "scare quotes").


What is the diffeence between "random" in the information-theoretic context
vs. the statistical context?
Wouldn't the two be correlatable or translatable in some way?


>
>> Calculating the digits
>>> of pi or e etc (and, presumably, some simple combinations thereof) is
>>> harder than the super fast "fancy" algorithms already used, so I don't
>>> see the benefit.

>>
>> Hasn't pi been calc'd to billions of places already? Seems to me that's
>> enough random numbers to last people for a while.... lol

>
> Does the lol mean you are joking?


Well actually, the wiki article I linked says pi has been calc'd to a
*trillion* digits.
The point being, if you need a random sequence, for whatever purpose, you
can just sort of pull them "off the shelf", from anywhere in the sequence.
A trillion numbers oughtta do ya....

>
> <snip>

>> I think "intrinsic experiments", like single-photon slit/diffraction
>> experiments would be an elegant way to generate true random numbers --
>> but
>> even that is then dependent on the "legitimacy" of the experimental
>> setup.

>
> Good quality, hardware-generated random number sequences (if our current
> understanding of quantum effects is correct) are random in a different
> way to the digits of pi. It helps if the terminology is be able to
> distinguish between them.


Which harks back to the above.
Couldn't you take a single photon slit experiment, sample the results
"byte-wise", ie, record every diffraction result in groups of 5, and let
those five zero's/one's represent a base 10 digit? Then, you'd have the
photon slit experiment generate irrational-number-like randomness.

In that sense, information-theoretic randomness (if you would charactize the
photon exp as "informational") and statistical randomness could be
translatable?
--
EA




>
> <snip>
> --
> Ben.






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