Not always, since:
The average human has one breast and one testicle
Des McHale
In other words, the average of a distribution is not necessarily the most probable value.
Omegaile
Karma: 204
No, you can think on the rationals, for example.
Yes, that’s it! Thanks.
Maybe I didn’t express myself well, but this strategy should work regardless of the distribution I choose. For example, if I choose a distribution in which 1 has probability 0, than your strategy yield 1⁄2 chance.
Oh… I misunderstood you then.
Actually there are no uniform distribution in this set (an infinite enumerable set). You may select numbers from this set, but some of them will have higher probability than others.
There is another very cool puzzle that can be considered a followup which is:
There are two envelopes in which I, the host of the game, put two different natural numbers, chosen by any distribution I like, that you don’t have access. The two envelopes are indistinguishable. You pick one of them (and since they are indistinguishable, this can be considered a fair coin flip). After that you open the envelope and see the number. You have a chance to switch your number for the hidden number. Then, this number is revealed and if you choose the greater you win, let’s say a dollar, otherwise you pay a dollar.
Now, before everything I said happens, you must devise a strategy that guarantees that you have a greater than 1⁄2 chance of winning.
Some notes:
1- the problem may be extended for rational, or any set of constructive numbers. But if you want to think only in probabilities this is irrelevant, just an over formalism.
2- This may seem uncorrelated to the two envelopes puzzle at first, but it isn’t.
3- I saw this problem first on EDITthis post on xkcd blag. Thanks for Vaniver for pointing out.
On the other hand, perhaps you only want to think about distributions for which it seems the paradox still holds: ones in which that, regardless of how much money you find in envelope A, envelope B still has an equal chance of being twice as much or half as much
I don’t see your conclusion holding. I am inclined to say: Therefore there are no distributions which that, regardless of how much money you find in envelope A, envelope B still has an equal chance of being twice as much or half as much.
I used to be a frequentist, and say that the probability of the unfair coin landing heads is either 4⁄5 or 1⁄5, but I don’t know exactly which. But that is not to say that I saw probabilities on things instead of on information. I’ll explain.
If someone asked me if it will it rains tomorrow, I would ask which information am I supposed to use? If it rained in the past few days? Or would I consider tomorrow as a random day and pick the frequency of rainy days in the year? Or maybe I should consider the season we are in. Or am I supposed to use all available information I have? The latter I would call subjective probability. If someone instead passed me the children problem I would say 1⁄3 because this problem implicitly tells me to consider only the what tells the enunciate.
But simply asking for the probability without a context, I would say either that this is a no question, i.e. that the enunciate is imprecise and lacking information, or I would believe that the interrogator was asking for a intrinsic probability, in which case I would say either 0 or 1, but I don’t know which.
But I did believe in intrinsic probability, in some cases, like quantum mechanics.
This view of mine became hollow after I started inquiring myself about this intrinsic probability. Even if such a thing existed, it couldn’t be differentiated from what I called subjective probability. By Occam’s razor I shouldn’t create 2 kinds of probabilities that I cannot tell apart. This thought was partly inspired by reading lesswrong, not a particular post, but by seeing the ease in which what I called subjective probability was used in several occasions.
I think value was used meaning importance.
Just out of curiosity, how are you now, a little more than a year later? Taking out “3”, that seems harder to change, how much of these points still apply in your life?
The staring one works on others by intimidation, as you look confident in an odd therefore unpredictable manner; the routine itself trains you to uncritically accept what’s in the later, sillier material. That’s interesting… you cannot fish without a bait. Without knowing Scientology much, I’d say they must provide some good things in order to attract followers. Seems like lukeprog decided to grab this things and leave.
Is this “click” you mention epiphany)?
Is this “click” you mention epiphany?
You could ask: Was the Trojan War an actual historical event?
It is not actually an popular question, but it is a question about a popular subject. I wouldn’t say it’s important, but it fits all other criteria. You could fill the listener about the details.
For some reason this seems to be a fairly common dream. I myself have had similar versions where I had discovered a perfectly reasonable method for flying ( although I was never able to speak out loud the method, it made perfectly sense in my head). And I also had this idea of waking up and telling people this so obvious method.
I find dreams very fascinating and wonder how many people have similar dreams than mine.
The truth is that neither cristians believe in a talking snake nor evolutionists believe in humans coming from monkeys. That’s just a straw man falacy. Cristians believe that’s a metaphor and evolutionists believe they have common ancestors.
“If I agree, why should I bother saying it? Doesn’t my silence signal agreement enough?”
The fact is that there is a strong motive to disagree: either I change my opinion, or you do.
On the other hand, the motives for agreeing are much more subtle: there is an ego boost; and I can influence other people to conform. Unless I am a very influent person, these two reasons are important as a group, but not much individually.
Which lead us to think: There is a similar problem with elections, and why economists don´t vote .
Anyway there is a nice analogy with physics: eletromagnetic force are much stronger than gravitational, but at large scale gravity is much more influent. (which is kinda obvius and made me think why no one pointed this on this post before)
Interesting… it reminded me of this comic: http://xkcd.com/690/
I think you are 75% right.