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Great, I feel like we're making good progress. (wisdom of the crowd..)

the standard deviation of the average of N guesses is proportional to 1/sqrt(N)

Yes, for example from here, if the standard deviation of the individual guesses is s, the standard deviation of the average of N guesses will be s / sqrt(N).

... And this represents the typical error of seven_and_sixes strategy, within one standard deviation.

Now -- to see if the strategy typically wins -- we just need the number for: given N guesses, what is the expected minimum error of the N guesses? (That is, the average minimum of the set of differences between each guess and the mean?)

endoself14y10

I would guess that this is proportional 1/N, whereas the average method gives 1/sqrt(N), so the probability that you win is O(1/sqrt(N)). In reality it would be worse, since, if you were not the last to go, you would only have the average of M guesses, with M < N. However, the average person has a probability of winning of 1/(N+1) so your probability of winning is sqrt(N) times better than the average person's, unless you can do even better with some other skill that you have. This analysis is complicated by exceptionally bad guessers and other average-takers, but not significantly. I accept your downvote because sixes was still lucky to win and did not acknowledge this.

See in context

51 Nonmagical Powers

by sixes_and_sevens

26th Apr 2011

1 min read

51

A couple of years ago my workplace was running one of those guess-the-number-of-jellybeans-in-the-jar competitions. I don't even like jellybeans all that much, but nonetheless, I held aloft my nonmagic calculator and said "by the power of Galton!" Taking the mean of all the previous guesses, I put that down as my answer. I was out by one bean, and won the jar. I don't think my colleagues have ever been so interested in statistics as they were that afternoon, and I doubt they ever will be again.

I'm going to admit something a bit silly and embarrassing now: that made me feel like a wizard. Not because of the scope of what I'd done, since it was an utterly trivial piece of arithmetic, but because of the reaction it got. I had drawn on arcane lore unknown to my colleagues, and used it to exercise power over the world.

Personally, I think something like solid state semiconductor technology is about as impressive a real-world miracle as one could ever want by way of demonstrating the whole Science Works/Rationality Is Systematised Winning/Maths Has Manifold Real-World Applications thing, but for most people it will never have the impact of intentionally winning a jar full of jellybeans.

So I ask you, LW-readership: what other impressive nonmagical powers do we have, that we can casually demonstrate to everyday people in everyday circumstances?

Cognitive ReframesGroup Rationality

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[-]Sniffnoy14y190

Older post, similar idea: http://lesswrong.com/lw/ve/mundane_magic/

[-]Larifari14y190

I am participating in a just-for-fun soccer prediction game with friends, where one gets awarded points for correctly predicted results or tendencies. In the beginning, I relied on gut feeling and information from soccer news sites like everyone else, and performed pretty badly. After a while, I implemented a simple script that takes quotes from betfair.com, a prediction market for sports, and calculates the prediction with highest expected points. Since then, I steadily climb the ladder.

[-]Miller14y20

I quite often go to find stock market proxies that might measure the significance of certain events. It helps to put bounds on things since the media generally places everything at Defcon 1 to attract attention. This rarely settles most or all questions you might have, and a lot of additional extrapolations are necessary, but can be of use.

Here is for instance, a Nuclear ETF. It might seemingly help to rule out the hypothesis of a substantial shift away from Nuclear to note that the value is in the range of just 6 months ago.

[-]KrisC14y180

There are gullible people. Here is a list of the powers I have had attributed to me by more than single individual or group and their mundane causes:

Flight. On occasion, I have arrived at destinations faster on foot faster than people in cars trying to arrive before me. This is simply a function of knowing my route and making accurate time estimates.
Raffle fixing. Several times I have manipulated raffles by waiting until the final opportunity and bidding on the under-valued prizes, or by calculating the value of the prizes and the number of tickets I would need to have a good chance at making a profit.
Jellybean counts. (as in original post)
Baby telepathy. Treat a baby like an adult or a friendly alien explorer who has yet to learn our language. Do not treat babies like dolls or inanimate objects. Babies have relatively few wants and needs and are easy to satisfy and teach.
Telepathy. Observation.
Fortune-telling. Accurate predictions.
Photographic memory. Not even close to true. Order your world according to relevant attributes and memories will be more easily accessed.
Speed reading. Nope. Practice and concentration.

Sadly, many observers would rather accept supernatural explanations.

[-]sixes_and_sevens14y100

Order your world according to relevant attributes and memories will be more easily accessed.

I would be very grateful if you could elaborate on this, or point to another explanatory resource.

[-]KrisC14y70

Memories are more easily accessed, in humans, when contextual information is brought to mind. When making observations that lead to memories, if the context is relevant to the questions that you will attempt to answer in the future, you will not have to artificially call forth the contextual info. The solution is to approach new situations critically.

So, if you explore a neighborhood, before you set out determine what you will look for. For instance, ask yourself: Are architectural features related to the relative affluence of the area at the time of each building's construction.

Or, in math classes, consider what the lessons build upon and where they may lead.

Consider new situations with conscious consideration of previous knowledge. "Blankness" is not appropriate when approaching an experience in which you have previous expertise. Calling to mind relevant experiences helps to ensure that memories attain relevant associations.

[-]virtualAdept14y20

[The solution is to approach new situations critically.]

This is a skill that can be honed in reading rather easily - I became explicitly aware of doing exactly as you've described when I began to have to offer up explanations and critiques of scholarly papers whose topics I wasn't innately familiar with on short notice. And it was just as surprising to my peers when I could come up with quick, cogent answers to complex questions about them on the spot.

Edit: Damnit, I fail at quote tags - is there a list somewhere of the tags the site uses?

[-]jwhendy14y20

Edit: Damnit, I fail at quote tags - is there a list somewhere of the tags the site uses?

Like how I quoted you?

If so, click the "Help" link to the bottom right of the text entry box after you clilck "Reply" and you'll see that it's the greater-than symbol.

[-]virtualAdept14y10

Like how I quoted you?

Wow. Yeah. My brain remembers looking for something like that, but I think it's only attempting to justify its embarrassment. Thanks!

[-]jwhendy14y30

Don't worry about it -- there have been many requests about changing that, making it more intuitive (like "markup formatting" vs. "help") -- I think the upcoming redesign will probably handle this and make it easier for folks.

[-]MinibearRex14y00

So basically, instead of just trying to collect facts, try to organize them in some way?

[-]KrisC14y10

Try to integrate new facts with old. "Update" your existing knowledge base.

[-]wedrifid14y10

Speed reading. Nope. Practice and concentration.

Speed reading doesn't seem to fit the supernatural pattern.

[-]ata14y30

It's not something that people would literally ascribe to supernatural agency, but it's still something that people see as happening "by magic" in a broader sense — it's associated with (e.g.) savants who have always been able to do it and don't really know how they do it.

[-]Jolly14y170

I was faced with a similar competition at Toorcon. I thought of three possible avenues:

1) Determine volume of the jar, calculate the number of potential pieces of candy corn in the jar. The downside is I expected everyone else to use the same method.

2) Find the same type jar and fill it with candy corn, and then count the number of pieces.

3) Execute option 2....and then swap it their jar, causing me to know the number of pieces in both the original and the replaced jar.

Rationality is powerful...rationality + being devious (or thinking orthogonally) is even better. P.S - Toorcon is a hacker con, so such behavior is considered acceptable O:-)

Edit: Option 3 was the one I executed :)

[-]falenas10814y150

Transfering data from one excel spreadsheet to something else: Control C, alt tab, control V, alt tab. Repeat.

I am now in charge of all data related things in my office, and I'm just a high school intern.

[-]Alicorn14y130

My mom had an office job of some sort a couple decades ago, and told me an anecdote in which she completely dumbfounded one of her co-workers by making use of various software capacities. My mother had learned of these capacities by reading the manual.

[-]nazgulnarsil14y110

RTFM/Googlefu is the defining superpwer of this generation.

[-]wedrifid14y70

I am now in charge of all data related things in my office, and I'm just a high school intern.

Special mention for the superpower of 'making people feel appreciated when given a task of data entry'.

[-]NihilCredo14y30

Control C, alt tab, control V, alt tab. Repeat.

Install AutoHotkey, write the one-line script RWin::Send ^c!{tab}^v!{tab}, and save seven keypresses out of eight :)

[-]falenas10814y00

I so want to use that. Sadly, NIH doesn't allow downloads from the internet.

[-]NihilCredo14y10

USB pens / optical discs?

[-][anonymous]14y90

what other impressive nonmagical powers do we have, that we can casually demonstrate to everyday people in everyday circumstances?

I can move my lips to create subtle vibrations in the air, which allows me to transmit my thoughts to other human beings. I think that's pretty darn impressive if you ask me.

[-]jwhendy14y80

Cool post. My thoughts:

Computer skills, to the unfamiliarized. I've written a script to do something and others have been amazed that I can do some task so quickly.
Complex Excel functions. People definitely have a "magic awe" response when Excel does something apparently amazing before their eyes and the formula doing it is longer than the cell text entry box.
Knowledge of how to use a terminal and command line tools.
The ability to empathize and "think in the shoes of another." I once asked someone if they believed in the flood and Noah's Ark. They were silent for a bit and then I asked, "Are you wondering what the Catholic Church's stance on it is?" They were somewhat blown away that I knew that's what they were wondering. This is a silly example, but it just comes from knowing that if a) I knew I needed to believe what the Catholic Church teaches, and b) I didn't know what they taught about the flood, and c) someone asked me what I thought about the flood... I'd be wondering what I was supposed to think about it.
Any repetition learned task. Seriously, anything that you're well-above average at that is either entertaining or useful can mesmerize. Guitar, dancing, stacking cups, some kind of tricks (card, zippo, magic, etc.)

Anyway, there's some of mine. I think the unifying key is that if someone can't figure it out and it's impressive or useful, they'll be slightly in awe, at least if they actually want that ability as well.

I add this last part, as I have been in awe of some skill X, but been pretty indifferent about Y because I didn't really care about Y.

Replace jelly bean predictions with predictions about some text-based mmorpg based on exactly the same arithmetic. Do you think anyone would have cared?

They probably saw "magic" because a) they wanted delicious jelly beans and b) they wanted the thrill that comes along with winning/impressing others. Had you shown them how to win some mmorpg by averaging numbers, they probably would have said "neat" and walked away.

[-]mutterc14y30

if someone can't figure it out and it's impressive or useful, they'll be slightly in awe

This causes me trouble in therapy. My therapist is enough in awe of what are (in my circles at least) ordinary skillz and intelligence levels, that she has trouble believing I can't just dazzle co-workers / managers / etc. on demand.

[-]Manfred14y70

Changing my mind is pretty cool, but maybe not impressive enough to those around me.

Maybe learning something new really quickly? But that's just a ordinary function of intelligence in certain situations, and is a very difficult power to pass on.

Ah, I know! Having lots of ideas. I occasionally have someone say something like "But how could X ever Y?" and I pull out a list from thin air, it's been fairly impressive. And this power is easy to pass on - some training in improv, working on seeing patterns for a few years, and not getting discouraged if you don't think of anything at first.

[-]D_Malik13y00

Ah, I know! Having lots of ideas. I occasionally have someone say something like "But how could X ever Y?" and I pull out a list from thin air, it's been fairly impressive. And this power is easy to pass on - some training in improv, working on seeing patterns for a few years, and not getting discouraged if you don't think of anything at first.

I would be grateful if you could say some more about this, for instance what one could do to train "seeing patterns".

[-]Manfred13y10

Seeing patterns means two things. The more mundane thing it means is building a bunch of connections between different concepts, either pairwise or by lumping things into categories. The less mundane thing it means is to see gradients and analogies among multiple things, and to be able to do it on the fly.

The mundane thing is (sensibly) easier to train. You have to establish these connections in the first place, for example by reading "how things work" books, or just by being curious, or by talking with other people about categories. And then you have to practice, which I recommend doing by playing a game. You take a thing, and then you take turns (assume you play with other people) naming other things this thing could be, if you squint your eyes a bit. For example, a tube of lipstick could be a tiny red mirror with a handle, or it could be the latest thing in paintball bullets, or it could be a melted eraser, or it could be a portable snack, or it could be a dotted-line-drawer for apprentice surgeons, or... the beginning of the game is easy, but the trick is knowing how many times to just keep going even after you think you're done (about 2, in my experience). This is a really good game for car rides. For example that thing with the tarp on top of the other guy's car could have been a smuggled alligator, or it could have been a heavy-duty tent, or a blue whale condom, or a defective parachute, or an inflatable robot, etc.

[-]D_Malik13y00

Thanks for clarifying. That sounds like a useful game, but I wonder how much you would have to practise it before you saw concrete gains.

I'm very interested in techniques for having more and better ideas, because I think most of the good things I've done in my life have been directly due to having a new idea or insight.

A model for winning by rationality is:

Decide on a goal.
Come up with ideas for achieving this goal. (creativity)
Identify the best idea or plan among those you've come up with. (epistemic rationality, general prediction ability)
Execute the best plan/idea. (willpower)

If you lack any of these steps you will fail. I'm surprised at how little discussion I've seen on LW about coming up with more and better ideas.

[-]Normal_Anomaly14y50

I spend much of every day in an environment with a lot of careless people, and I am above average at being observant. As such, I have a tendency to find a lot of spare change. I have had days where I've found over a dollar in nickels and dimes (last time that happened was this Tuesday). Whenever I want to buy something and I'm a little short on pocket change, I can reliably spend 5 minutes wandering around and find the few cents I need. My friends and I find this amusing.

[-]sixes_and_sevens14y50

On a somewhat-related note I've been thinking about what sort of events seem to have that magic-power quality to bystanders who don't know how they're accomplished.

My first thought was to consider the properties of explicit magic tricks, but they don't quite apply for a few reasons. Firstly, they're not real. Secondly, they're generally placed in a social context where spectators ultimately know they're not real. Thirdly, they're extremely contrived situations without a lot of practical value. It's generally the artificial sense of narrative impossibility that gives them the impact. If I could clear fallen debris with laser beams from my eyes, that would belong in a fundamentally different category to guessing a card someone thought of.

The only other skill I possess which seems to have the same sort of reaction is follow and lead in improvised partnered dance. Spectators often seem amazed that two people can coordinate their movements so well without talking to each other. The factual response is "we are talking to each other, just non-verbally".

[-]byrnema14y20

Down-voted for not acknowledging or not realizing that you were also lucky.

As people make their guesses, the mean of their guesses will fluctuate. This doesn't mean the number of jellybeans is fluctuating, of course. You were lucky that your well-educated guess happened to be closer than any other guess.

Suppose people's guesses were normally distributed about the true number of jellybeans with a specific standard deviation. Even with these ideal assumptions, the average of N guesses doesn't converge that quickly to the mean, and I don't suppose it converges faster than the probability that any one guess is closer to the true number than your mean.

[-]endoself14y40

Actually, with the assumptions you gave, as far as I can tell from memory and a quick look at wikipedia, the standard deviation of the average of N guesses is proportional to sqrt(N) so, whatever the average error of one guess is, the average error of the average of 16 guesses is 4 times less, making it a significantly better guess. This quantity is known as the standard error of the mean.

[-]byrnema14y10

Great, I feel like we're making good progress. (wisdom of the crowd..)

the standard deviation of the average of N guesses is proportional to 1/sqrt(N)

Yes, for example from here, if the standard deviation of the individual guesses is s, the standard deviation of the average of N guesses will be s / sqrt(N).

... And this represents the typical error of seven_and_sixes strategy, within one standard deviation.

[-]endoself14y10

[-]byrnema14y00

Oh wait. I think we've got some errors to fix. I won't have time immediately, but I'll edit my comment to reflect any changes you make. I knew what you meant, or you knew what I meant, but now it's confusing..

[-]endoself14y00

I'm not sure what you mean. Looking back I did make some errors in my analysis, but I'm not particularly motivated to correct them, since I doubt my conclusion will qualitatively change, though if I got the right probability of winning, it would be a coincidence. Maybe I'll feel more curious about the right answer another time.

[-]byrnema14y00

I fixed that the standard deviation of the average of N guesses is proportional to 1/sqrt(N) in this comment.

I don't think you should 'guess' that the minimum error is proportional 1/N, since its relationship with N is exactly what we need to know. Let's wait to see if someone knows.

... But do you realize that 1/N decreases faster than 1/sqrt(N), so that your guess would indicate that the average strategy would rarely win?

[-]endoself14y40

I don't think you should 'guess' that the minimum error is proportional 1/N, since its relationship with N is exactly what we need to know.

I mistakenly thought I had a qualitative argument that was too simple to bother spelling out. Unfortunately, it was also too simple to be correct. :-) However, see constant's comment; my intuition appeared to be probably right after all.

... But do you realize that 1/N decreases faster than 1/sqrt(N), so that your guess would indicate that the average strategy would rarely win?

Yes. If my analysis is correct, the method would be very unlikely to win, but it would be much better than using the same method as the other competitors, precisely because 1/N decreases faster than 1/sqrt(N).

[-][anonymous]14y20

As the minimum error approaches zero, the probability that the next guess will reduce the minimum error becomes proportional to the minimum error itself - that's because it's like trying to hit a target, and the probability of hitting the target is proportional to the size of the target. This only applies to the error close to zero, because that allows us to treat the probability distribution as essentially flat in that neighborhood, so we don't have to worry about the shape of the curve.

If the next guess does reduce the minimum error, then, on average, it will reduce the minimum error by half. As above, we're treating the probability distribution as essentially flat.

So, we expect that after some number n guesses, the minimum error is reduced by half. We expect that after 2n more guesses, the minimum error is reduced again by half. Assuming this is what happens, then we expect that after 4n more guesses, the minimum error is reduced by half again.

The reduction in error that we're seeing in this imagined playing out is approximately inversely proportional to the number of guesses. The total number of guesses goes from n to n+2n=3n, to n+2n+4n=7n, etc. If we keep going, the total number of guesses becomes 15n, 31n, etc. This approaches a doubling of total guesses. And the error after each approximate doubling is half what it was before.

This is far from a proof. This is crude, fallible reasoning. It's my best estimate, that's all.

[-]sixes_and_sevens14y20

Granted. I wasn't claiming it was a guaranteed winning strategy, and a fair element of luck was obviously involved.

[-]byrnema14y10

Now, I'm not sure that my comment was obvious or not. I thought that it would be.

Do people generally agree that this strategy should not be expected to win most of the time? (I would guess not even half the time, but this is just above where my estimate would be for large N.)

It seems appropriate to 'ask the crowd'..

Strategy shouldn't win contest most of the time.

Strategy should win contest most of the time.

Not obvious either way.

Karma balance.

per JoshuaZ'a request:

Strategy will win more frequently than trying to estimate but won't win most of the time

[-]byrnema14y40

Strategy will win more frequently than trying to estimate but won't win most of the time.

[-]JoshuaZ14y20

Can we have as an option "strategy will win more frequently than trying to estimate but won't win most of the time"?

[-]byrnema14y00

Sure..

[-]byrnema14y20

Strategy should win contest most of the time.

[-]byrnema14y10

Strategy shouldn't win contest most of the time.

[-]byrnema14y00

Not obvious either way.

[-]byrnema14y-40

Karma balance.

[-]torekp14y00

The guesses in most contests won't be normally distributed, period, so they won't be normally distributed around the true number. They'd be closer to log-normal or some such distribution, I would guess.

[-]byrnema14y00

Sounds reasonable. How do you know this / what do you base that on?

[-]torekp14y20

Long ago, I looked at some data on people's guesses in probability calibration exercises. Exercises like: how many eggs do Americans consume annually - write down a number such that you judge it X% probable the true number is less than or equal, and (100-X)% probable it is greater. I vaguely recall some such thing about the distribution of guesses. A very large number of guesses were many orders of magnitude too low, as well.

[-][anonymous]14y00

Are you aware of the wisdom of crowds phenomenon (Surowiecki) and correcting a lucky misapplication / hasty application of it, or are you simply unaware of it? I don't get a sense either way.

Also, I wonder whether the correct mean for this sort of wisdom of crowds averaging is arithmetic or geometric. I would be inclined to think that the geometric mean is the appropriate mean.

[-]byrnema14y10

I'm aware of the wisdom of crowds phenomenon -- I believe sixes_and_sevens used a good strategy. (Yes.) I haven't read about the corrections, but I wouldn't be surprised if there are some ways to optimize the process. (Why do you ask this second question?)

I wonder whether the correct mean for this sort of wisdom of crowds averaging is arithmetic or geometric.

I think this is an interesting question too. Perhaps someone knows the math for this; alternatively, it would take a few minutes to test it with some made-up guess distributions. (Any takers?)

[-]Swimmy14y20

The problem is that so many of our powers seem so mundane. For instance, I can predict your future tomorrow, the day after tomorrow, next month, next year, and even 100 years from now. (It starts like this: tomorrow you will have a normal day. It ends like this: a hundred years from now you'll be dead.) It may not be perfectly accurate, but it's at least as good if not better than any fortune teller. Yet in terms of what people want to know, that is incredibly boring.

[-]ata14y10

I'm good enough at intuiting and extrapolating software behaviours that I can fairly easily appear to make computers do things by magic, at least to people who aren't "good with computers" and can't see at a glance what I'm basically doing.

I'd like to learn actual (stage) magic; that would be useful for quick impressiveness.

[-]virtualAdept14y10

For whatever reason, I've always had a very strong memory for sounds - it's a relatively common occurrence for me to express knowledge of what a friend or family member had done on a particular day and time, based on hearing them bang about from another room. This tends to surprise them since I was not physically there to observe. The only other person I know who does this often is, fittingly, my mother.

More humorously, my office mates and I have jokingly accused our PI of teleportation; while it's usually extremely easy to hear someone coming down the hall long before they reach our door, he always manages to appear with no warning (even when someone's anticipating his arrival). He walks very quickly and wears quiet shoes, and is apparently the only person in the department who does the latter.

[-][anonymous]13y00

Unlike most Americans, I can eat until I'm full whenever I want and stay lean and fit... because I know that food reward modulates leptin sensitivity (http://pmid.us/22238401). Before this knowledge I spent most of my life obese and hungry.

In general, there is a lot of biological research out there that can potentially be applied to improving your own health, but is too new to have been synthesized into public health advice. Having access to, and the skills to critically read medical journals is a "superpower" because this knowledge can protect you from health problems that other people can't avoid.

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[-]jley14y00

Think about things you don't know how to do. :)

[-]ewang14y00

But next time one person, knowing what you did and figuring out your secret weakness, will put 3^^^3 or some other barely-finite-and-yet-nowhere-near-transfinite number to disrupt your 'powers'.

One amazing power we have is being able to use formulas to find equations that fit any data. Dangerously deceptive.

[-]JoshuaZ14y10

I've used this strategy before. A common way of dealing with this is simply to throw out any obvious outliers. Note that most people who do that sort of thing aren't doing it to disrupt the average, but rather just to be "funny" and so are more likely to just put down a 1 with a lot of zeros, or a long string of 9s.

[-]ewang14y00

Assuming you have enough entries, you can simulate a probability distribution way too far to either direction. However, assuming that same thing, you can also just guess everything and actually win.

[-]Armok_GoB14y00

Many aspects of art have this, especially those most people understand poorly, like 3d animation with dynamics.

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