Seeding a C++11 random

[razzle]

yes, I tototally agree on the fact that the mind of street-(and even not so street-)man is full of misconceptions about probability and randmness, but in more subtle ways.
indeed, the dice problem above could be reformulated in a way to let a genuine misconception to emerge; for example, one could ask the street man to bet some money on a sequence, choosen among either (1,2,3,4,5,6) or, say, (3,5,1,2,2,4) and observe that most people would choose mostly the latter, for no rational reason.

I don't agree with this. The man in the street is almost always on the spot. For example when asked which of 1,2,3,4,5,6 or 3,5,1,2,2,4 is the least random he will almost always pick the former with the argument that it's more regular and thus less likely to appear. This is totally in line with Kolmogorov complexity/randomness for sequences.

How come the man in the street instantly and intuitively comes up with the same result it took a genius like Kolmogorov to describe? And how come academically trained urn-gazers often get it so completely wrong and claim these sequences are equally random?

It's because the man in the street genetically still is walking the great plains of Africa like he has for the major part of the last 8 million years. In short he bases his decisions on evolutionary survival value, not urn-gazing.

So when urn-gazing (lazily playing with prior probabilities) make sure you're in the secure confinement of an ivory tower. When in the jungle watch out for unexpected movement (unlikely regular events) and keep your Kolmogorov rifle loaded (while constantly evaluating posterior probabilities so you know when to shoot).

[superbonzo]

I don't agree with this

did you read that post ( not just that line you quoted ) ?

we're saying more or less the same thing, that is that the street man intuition is more right than it could appear to a blind accademic view.
But, the example above do shows a genuine misconception, that has nothing to do with his intuition of likelyness, it has to do with his decision ( choosing a sequence to bet in ) that is in genuine contradiction with his own expectations ( that he will lose more money when betting on this or that sequence ). People mind is full of these misconceptions and do hurt them everyday, from people ruining themselves in (border-line)pathological gambling, non sensical financial strategies, irrational health fears, etc ... etc ... ( a very very long list follows ... ) .

[razzle]

Spot on...

When people ask for "random" they can mean very different things with that...
Throw a die 6 times even with an unloaded dice, you could end up with
5, 5, 5, 5, 5, 5
or
1, 2, 3, 4, 5, 6

so yes, those ARE sequences of values obtained from a random event.

Show that sequence to people on the street however, ask if it they are random, and 99% will say "no".
even though those 2 sequences are just as likely to occur in 6 rolls as any of the other 6⁶ possible sequences.

And there's a reason for this as I explained in my post #31.

When presented with a sequence and asked to assess how random it is the man in the street will evaluate it in the Kolmogorov complexity/random sense. That's what he's genetically hard-wired to do because it has survival value. In fact the ability to recognize and assign meaning to patterns is one of the major hallmarks of the humans species.

Even a notorious urn-gazer should be able to understand that. If he only accepts the Kolmogorov (and the man in the street) notion of regularity I'm sure he will find an urn for it.

[superbonzo]

we're saying more or less the same thing

... uh, unless you meant to say that it's really wise to *always* consider "regular" ( whatever that's supposed to mean ) events more unlikely, in that case, sure, we don't agree. Invoking Kolmogorov complexity or take-it-easy evolutionism it's non sense in this regard ... unless you prove that such innate aversion against "regularity" exists, and show a machanism by virtue of which such aversion would determine a survival comparative advantage; contrary to what many seem to think, evolutionism is not about blindly conjecturing that because something exists hic et nunc, it is so because a selection occurred ...

[razzle]

... uh, unless you meant to say that it's really wise to *always* consider "regular" ( whatever that's supposed to mean ) events more unlikely, in that case, sure, we don't agree. Invoking Kolmogorov complexity or take-it-easy evolutionism it's non sense in this regard ... unless you prove that such innate aversion against "regularity" exists, and show a machanism by virtue of which such aversion would determine a survival comparative advantage; contrary to what many seem to think, evolutionism is not about blindly conjecturing that because something exists hic et nunc, it is so because a selection occurred ...

I don't quite follow your argumentation but I know what I mean so I concentrate on that.

With a regular sequence I mean a sequence that has low Komogorov complexity. The man in the street recognises such a sequence immediately because it has high survival value. Three examples,

111111 vs. 132596
123456 vs. 509270
202020 vs. 226308

The left hand sequences have low Kolmogorov complexity and the man in the street intuitively finds them regular. There's a certain repetitiveness about them that makes them look intentional. They're easily separable from the right hand side sequences that appear much more random.

And contrary to what you claim the left hand sequences are less common by far than the right hand sequences. This is an important result of Kolmogorov theory.

---

This has huge evolutionary implications and that's why the man in the street beats the urn gazing professor.

Say you are the happy owner of 9999 sheep. Unfortunately there's a tiger among them and you know it. Suddenly an animal breaks out of the sheep heard and approaches you at great speed. What would you do?

1. The professor.

Since you are the proud holder of a PhD in Sheep Hearding and did quite well in probability (if you may say so ) you quickly calculate that with an overwhelming 9999/10000 probability the approaching animal surely must be a sheep. Glad you paid attention during the balls-in-urns class you relax and continue reading Sheep International.

2. The man in the street.

A long time ago your wise old grandfather took you aside and said. Listen carefully. When you tend to your sheep and there's an animal approaching, always check whether it's yellow and has stripes because if it does it's a tiger. Remembering this you grab your Kolmogorov rifle and start preparing for the worst.

Now who's most likely to pass on his genes?

[superbonzo]

1. The professor.

Since you are the proud holder of a PhD in Sheep Hearding and did quite well in probability (if you may say so ) you quickly calculate that with an overwhelming 9999/10000 probability the approaching animal surely must be a sheep. Glad you paid attention during the balls-in-urns class you relax and continue reading Sheep International.

totally wrong, you're confusing probability theory and inferential statistics ( aka deciding what's better to do or not to do given statistical data, may be called ( or at least strictly related to ) also utility theory in economical settings ), the two are obviously technically related but totally indipendent ...
and even ignoring the ( rather slippery ) relation between utility and probability, the latter has nothing to do with computing "fractions" like in your 9999/10000 example ... do you know the difference between an event and a configuration ?

With a regular sequence I mean a sequence that has low Komogorov complexity [...] This is an important result of Kolmogorov theory.

the problem is that Komogorov complexity is just one of infinitely many inequivalent ways of computing "regularity"(in some arbitrary sense) of strings, and no, that's not an "important" result of Kolmogorov theory, whose strict conceptual applications in probability is rather limited, if not pointless. At best, one could try to invoke the notion of entropy, but again, if one has at least a vague idea of what (physical) entropy really is ( it's not a measure of "randomness", it's a logarithmic measure of the phase space volume ) then one should realize that its probabilistical implications, albeit important, require a lot of care before drawing hasty conclusions ...

[razzle]

that's not an "important" result of Kolmogorov theory,

Then please explain why not. Why isn't it an important result of Kolmogorov theory that most sequences are close to random and the more regular the fewer they are? It's not only another example of what seems to be a fundamental law of nature. I find it important here because it could explain why humans are so accutely aware of patterns in their environment; It has survival value because it signals an exception. That's why the man in the street gets it right intuitively while the ivory tower urn gazing academic stumbles.

Sure, there may be "infinitely many inequivalent ways of computing "regularity"" but it was Kolmogorov who came up with the interesting one. If you have a better suggestion please feel free to challenge Kolmogorov but do it up front instead of vaguely insinuating that you are privvy to much deeper insights.

you're confusing probability theory and inferential statistics
...
do you know the difference between an event and a configuration

Definitions are not arguments.

Inferential statistics and probability theory are two sides of the same coin and you can discuss how the sides are defined and how they relate until kingdom come without ever getting any closer to the nature of the coin.

And that's the purpose isn't it? When you have no arguments left you can always throw in a couple of definitions you're familiar with in the hope the discussion will be about them instead.

I could pick you apart also in a definitions game but it's quite meaningless and I don't have time for it so I drop it here, thank you. I don't want another "waterfront" discussion.