Comments by "\/" (@joebazooks) on "TED-Ed"
channel.
-
281
-
105
-
35
-
29
-
15
-
8
-
8
-
8
-
7
-
7
-
6
-
6
-
6
-
5
-
4
-
4
-
4
-
4
-
3
-
3
-
3
-
3
-
3
-
3
-
3
-
3
-
2
-
2
-
2
-
2
-
2
-
2
-
2
-
2
-
2
-
2
-
2
-
2
-
2
-
2
-
2
-
Adam Thornton
if you are deliberately stuck somewhere--say, on an island--with 99 other people, all of whom have green eyes, you know that at the very least 99/100 have green eyes.
now, since we can't be sure of our own eye color, let's simply exclude ourself from the equation; if we exclude ourself from the equation for a moment, we know that 99 other people--all of whom have green eyes--know for certain that at the very least 98/99 people have green eyes since they can't see their own eyes.
98/99 is what each of them perceive.
99/99 is the reality for each of them.
bearing that in mind, if i know for certain that at the very least 99/100 have green eyes since i can't see my own eyes, what are the chances i myself have green eyes?
99/100 is what i perceive.
100/100 is most certainly the reality.
i think the chance of you not having green eyes is 0.0001% or something similar, but i could be wrong
but it should never be that complex of a process to begin with anyway. if you are deliberately stuck somewhere with 99 other people, all of whom have green eyes, the chances you also have green eyes is through the roof
2
-
2
-
2
-
2
-
2
-
2
-
2
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
Eddie no, man. you can disregard one of the frogs in the clearing altogether because you already know that 1 out of 2 are male. the probability of the 2nd frog being female or male is 50/50 and this is independent from from 1 of the frogs being male. just because we don't know which of the 2 frogs is male, doesn't skew the probability of the 2nd frog towards female.
the only time the following possibilities and probabilities (MM25%FF25%FM25%MF25%) come in to play is if you are calculating the probabilities of 2 unknown frogs in a row.
for instance, it's like having two die. in order to survive you need two 6s, but we know already that one of the die is 6, so you're chance of rolling 6 and surviving is 1/6, not 1/36. NOW, if you had to roll two consecutive 6s, then the chance of that happening is 1/36, but we already know one of the die is a 6, so we are only rolling once and the probability and results of that roll are independent from the predetermined roll...
1
-
Eddie Fair enough that you think it's a problem of conditional probability, and if the problem was intended to be an example of conditional probability, it's a terrible example at that, because it's not in fact conditional probability in the way that you imagine.
Further, conditional probability is no different than statistical probability, insofar as with conditional probability you're simply taking into account foreknowledge of one event (A) that effects the probability of another event (B).
Yes, the Monty Hall problem is a problem of conditional probability because knowing that the host has to reveal a door with a goat behind it (event B), after the contestant has already chosen one of three a doors (event A), influences the probability of the contestants second choice (event C). In this case, the knowledge concerning event B is a condition that effects the probability of event C.
Let's look at the conditions and events of the frog problem...
(condition A) knowing of the species 50% are male, 50% are female
(condition B) only female frogs possess the chemical antidote
(event A) spotting a frog on a stump
(event B) hearing a male croak from a group of two frogs
(event C) choosing which to go
None of these events or conditions effect the probability in the way that you imagine, nor in the way that the video proposes--so don't feel bad about yourself for screwing up because the creators screwed up too.
Let me illustrate this for you with a simplified analogous experiment for the sake of clarity and your understanding.
a. Get 4 pennies
(the 4 of which will represent the entire species of frog, which is analogous to condition A earlier in my comment because in order for the fact that 50% of the species is male and 50% of the species is female to be true, the species must contain an even number of frogs or pennies)
b. Place 2 Heads-up and the other 2 Tails-up
(this is analogous to condition B earlier in my comment because we know that 50% of the frogs are male and 50% are female)
c. Remove 1 Heads-up penny from the group (which will be your Male in the group of two)
d. Put on a blindfold
e. Mix up or have somebody else mix up the remaining 3 (2T and 1H) pennies that are leftover after step c.
d. Remove 1 penny from the leftover group of 3 while blindfolded
(the penny that you remove blindly is 66% likely to be a Tails-up penny because in the leftover group of three pennies is 2 Tails-up and 1 Heads-up, which leaves you with a group of 1T and 1H.)
e. Distribute 1 of the 2 pennies that remain in the game to the left
(50% likely to be T and 50% likely to be H)
f. Distribute the last penny to the right
(also 50% likely to be T and 50% likely to be H)
g. Remove your blindfold
h. record result
i. Repeat steps A to H indefinitely 100,000 times
The frog problem is conditional probability, but not in the way you believe it is.
1
-
1
-
1
-
1
-
1
-
Alkaski yes, i have heard of conditional probability, but the "possibilities" that you're accounting for in your calculation are not the actual possibilities for the frog scenario. the actual possibilities for the frog scenario are as follows: DM, MD, DF, FD; whereby D represents the given male.
as to whether or not there is a female frog on one side and or the other, so that you would be able to survive:
(in the clearing) DM, MD, DF, FD - 2/4 50%
(on the stump) F, M - 1/2 50%
1
-
1
-
1
-
1
-
1
-
1
-
Leo Smith you're wrong. flipping a coin once does not change the probability if you were to flip the coin again. if the condition was to flip two consecutive heads or two consecutive tails, only then does the probability lessen. let's use dice as an example. if i were to use only one die, and i rolled a 6, re-rolling this die does not increase the likelihood that i will roll a 1, 2, 3, 4, or 5, on the next roll. this is known as the gambler's fallacy. if we had two die, however, and the condition for our survival was rolling a 6 with each die, this would be more unlikely. BUT, we already know that one of the die has been rolled and it's a 6, therefore the roll of the next die becoming any of the six numbers is equally likely. it is not all of a sudden more likely to be a 1, 2, 3, 4, or 5.
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
i live in canada and always use the oxford comma if practicing good grammar. from my experience, it usually avoids more confusion than it creates. the oxford comma makes sense, period.
i.e.
a) 'he had stolen, bought and sold, and squeezed lemons.'
b) 'he had stolen, bought, sold, and squeezed lemons.'
c) 'he had stolen, bought, sold and squeezed lemons.'
personally, i believe a) and b) express two different notions, if only slightly; whereas c) is just confusing and borderline nonsensical.
1
-
1
-
1
-
icemd24 In short, the method they use treats effectively identical outcomes as different possibilities, and it uses these additional possibilities, which are irrelevant to the outcome, in its calculations of the probability. Likewise, they disregard relevant information, which in turn has generated an inclination to consider irrelevant information as relevant information in their calculations. In other words, it would be no different from declaring:
(1) buses travel to only two different destinations, Destination A (DA) and Destination Z (DZ);
(2) there are as many buses travelling to DA as there are travelling to DZ;
(3) in order to survive, you must get to DZ;
(4) you notice that there is 1 bus at the bus stop on the right, and 2 buses at the bus stop on the left;
(5) you know that 1 of the 2 buses at the bus stop on the left is travelling to DA;
and, after asking 'What are your odds of survival if you go right?' and 'What are your odds of survival if you go left?', then claiming:
(1) that because you do not know which bus at the bus stop on the left is travelling to DA, even though 1 of the 2 buses is indeed travelling to DA, there are more unique possibilities, and therefore more effectively unique outcomes, and for this reason your odds of getting to DZ in order to survive are 33.33% better than if you were to go to the bus stop on right whereby there is also only 1 bus with an unknown destination.
I hope that this is a clear description. Let me know if you have any more questions!
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
David Williams Well, if there an equal probability of choosing, say, a male frog at random, then the population must be split evenly, otherwise there would not be an equal probability. This is why, for instance, there cannot be an equal probability of choosing a male or female frog at random from an odd number of frogs, even if the sample from which you are selecting a frog is substantial, say 1000 frogs; if there are 501 males and 499 females, there is not an equal probability of selecting one or the other, as it is slightly more probable that you will select a male frog at random, however insubstantial this difference may be and despite variance. I'm sorry to break it to you but if you have an equal probability of selecting heads-up or tails-up coins from a massive sample, you're no more likely to pick one over the other; which means even if you are to select just 2 coins from 500 coins, probability dictates that you'll end up with 1 heads-up coin and 1 tails-up coin. I get what you're saying, and I agree with what you've said, but your conclusion is simply wrong.
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
*****
you kind of lost me about half-way through your third paragraph.
likewise, you said, "you think it's imminently important that the word 'mind' is not necessarily the initial product of the brain." however, i feel as if the word itself certainly is a product of--in addition to the lips, the vocal cords, et cetera--the brain, insofar as the word is basically a particular form of information that was deliberately chosen and or "produced" by the brain to serve a function that is similar to any given sign (a street sign, stop sign, etc.), that purpose being to refer to, point to or at, and or represent another more elaborate body of information (as opposed to a material body/object/thing), specifically 'cerebral activity' to keep it simple.
further, because this particular word, 'mind', represents an activity, it is necessarily abstract, unlike a material object such as a tree that indefinitely possesses a definite form or at least a form that can be indefinitely perceived as definite.
i guess what i'm trying to get at it is whether or not the word's utilization is practical, whether or not its functionality stretches beyond the exchange of hollow information, beyond the production of noise? does the word itself, 'mind', foster and facilitate practical progress in one way or another to warrant its continual, somewhat prevalent use? even, does its use hinder or prevent practical progress in one way or another? does the use of abstract words in general create more confusion and disagreement than understanding? does the cost outweigh the rewards?
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
*****
That's untrue. You have to think about it. Hence, the only difference between one clue and the other—'The person next...' and 'At least 1...'—is the degree of immediacy at which new information is induced.
It might be easier for you guys to understand this if we the change the clue slightly: 'The person beside the person who is beside you has green eyes.' Or even, 'The person beside the person who is beside the person next to you has green eyes'.
It might also help to consider the actual clue—'At least 1...'—and change that slightly: 'At least 99 of you have green eyes'; with which each of them will necessarily induce the information that 'If anybody has brown eyes, it must be me'.
What new information does the statement 'At least 99 of you have green eyes' have that the statement 'At least 1 of you has green eyes' does not? Nothing, yet the prisoners can leave a whole day or a whole ninety-nine days earlier. The only difference is the degree of immediacy at which new information is induced. '99' is just as arbitrary as '1' or '87' or '13' or '25', which in turn is also no different from any other clue that does not explicitly state that you have green eyes yourself.
To further illustrate my point, consider the same problem but with only two prisoners on the island. The clue the prisoners are given is: 'The person next to you has green eyes'. Well, this clue can be interpreted in one of two ways: (1) The person next to you (plural) has green eyes; (2) The person next to you (singular) has green eyes. In order for the prisoners to actually know which interpretation is the correct interpretation, they first have to determine that there is nobody else beside the two prisoners—"Nobody else is around. It's only us two prisoners on this island, so then the clue must be interpreted as 'The person next to me has green eyes'." Only after they've first determined that, they are able to subsequently determine that, if the clue must be true, "I too have green eyes".
In the beginning the only information that each of them are lacking is whether or not they themselves have green eyes. If we told 100 prisoners that 'The person next to you has green eyes', though they would leave almost immediately (or much more immediately than in some other cases), nobody would actually leave immediately upon hearing that statement because the statement does not contain the information 'You personally/All of you have green eyes', which would be new information.
You also have to bear in mind that, even if they were standing in neat, orderly rows, there would be more than just 1 person standing next to you at all times...
1
-
1
-
*****
Foremost, I am going to modify my clue slightly: '[A] prisoner next to you has green eyes'.
Secondly, it is a stretch of the imagination to claim "the [creator] of the [thought] experiment" agrees with you and not with me on this matter, but this is beside the point.
Third of all, one of the conditions is not "the statement must refer to everyone", and this is also beside the point. Nonetheless, the original clue does indeed refer to everyone—'At least one of you (plural) has green eyes'—whereas the second clue does not refer to everyone—'A prisoner next to you (singular) has green eyes'.
Fourth, I understand that you do not agree with my definition of new information. However, your definition of new information applies to the original clue, 'At least one of you has green eyes'. The original clue is "information or data that allows [the prisoners] to reach [the] correct conclusion [eventually]; The very content of the information [alone allows the prisoners] to logically derive [the correct conclusion]"; if this were not the case, the prisoners would have left either long before you showed up to give them the clue or not at all.
'All of you have green eyes' > I know immediately that I have green eyes.
'A prisoner next to you has green eyes' > I do not know immediately that I have green eyes.
'All of you have green eyes' ≠ 'A prisoner next to you has green eyes'
Lastly, Remember that space, by definition, is three-dimensional and not linear, and therefore "[each prisoner] at the morning meeting must be [standing] next to [not only] someone", but more than one prisoner at a time. This is the crucial piece of information that you are neglecting. For instance, imagine a scenario with only three prisoners in a triangular formation: P1 is standing next to P2 and P3, whereas P2 is standing next to P1 and P3 and P3 is standing next to P1 and P2; if somebody told them 'A prisoner next to you has green eyes', it does not follow from this necessarily that P1 has green eyes because P1 is not standing next to only one prisoner, but standing next to P2 and P3; therefore, the prisoner with green eyes next to P2 might be P3 and not P1, and the prisoner with green eyes next to P3 might be P2 and not P1.
Again, there is no new information in the statement 'A prisoner next to you has green eyes', none whatsoever. "The statement itself has not presented any [new] information. This information is already available to everyone. As a prisoner with 99 visible green-eyed mates, you know that literally everyone on the island has knowledge of at least one green eyed inmate" next to them.
1
-
1
-
*****
As a reminder--the only two conditions, as explicitly stated in the video, are: (1) You can only make one statement; (2) You cannot tell them any new information. Yet, again, this is beside the point.
Furthermore, I find it quite ironic and incredibly telling that you've dismissed all of the valid points that I've brought forth as wrong without even addressing them, while addressing the only point that was beside the point, which I'm not sure why you brought that up in the first place... LOL
I suggest rereading my comment, or, if it still doesn't make sense, rereading your comment and then my response. As it is often the case on YT, you're misconstruing aspects of my comment; though I forgive you, for it has become beyond apparent that English is likely your second language. If you are incapable of basic comprehension--no shame in that--I bid you adieu
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
David Williams So you have 2 frogs... FrogA and FrogB. You know one of them is male. However, not only must one of them be female, but FrogB must be female in order to survive.
If this were the case, then necessarily the sequence/order/position in relation to sex would matter, and [ F (FrogA) M (FrogB) ] and [ M (FrogA) F (FrogB) ] can be considered in conjunction with one another as unique possibilities because they represent two different outcomes. They otherwise do not represent two meaningfully different outcomes and therefore should not be considered as such, as meaningful. It's pretty fucking straight-forward shit man...
We shouldn't even be discussing this, though; We are unable to determine whether or not the sex of one frog effects the sex of another frog, even though we know 50% of the population is male whereas the other 50% is female, since the quantity of individuals from which the sample was taken is unknown. If the entire population was only 4 frogs, then all of a sudden with 1 male exposed, the chance that the next frog is female becomes 66.%. This is the only situation in which the chance of the next frog being female is 66.6%
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1