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You are walking back to your office in the rain and your path is lined by a row of trees. You could walk under the trees or you could walk in the open. Which will keep you drier?

If it just started raining you can stay dry by walking under the trees. On the other hand, when the rain stops you will be drier walking in the open. Because water will be falling off the leaves of the tree even though it has stopped raining. Indeed when the rain is tapering off you are better off out in the open. And when the rain is increasing you are better off under the tree.

What about in steady state? Suppose it has been raining steadily for some time, neither increasing nor tapering off. The rain that falls onto the top of the tree gets trapped by leaves. But the leaves can hold only so much water. When they reach capacity water begins to fall off the leaves onto you below. In equilibrium the rate at which water falls onto the top of the tree, which is the same rate it would fall on you if you were out in the open, equals the rate at which water falls off the leaves onto you.

Still you are not indifferent: you will stay drier out in the open. Under the tree the water that falls onto you, while constituting an equal total volume as the water that would hit you out in the open, is concentrated in larger drops. (The water pools as it sits on the leaves waiting to be pushed off onto you.) Your clothes will be dotted with fewer but larger water deposits and an equal volume of water spread over a smaller surface area will dry slower.

It is important in all this that you are walking along a line of trees and not just standing in one place. Because although the rain lands uniformly across the top of the tree, it is probably channeled outward away from the trunk as it falls from leaf to leaf and eventually below. (I have heard that this is true of Louisiana Oaks.) So the rainfall is uniform out in the open but not uniform under the tree. This means that no matter where you stand out in the open you will be equally wet, but there will be spots under the tree in which the rainfall will be greater than and less than that average. You can stand at the local minimum and be drier than you would out in the open.

Its 61F today in Chicago and its going to push 70 tomorrow.  According to my phone it will drop down to normal seasonal temperatures by the end of the week but according to my phone that downward trend has been expected for each of the last three weeks and it hasn’t happened.  My phone hasn’t identified the structural change yet.

That got me thinking about some indices of global warming that weather forecasters might want to start tracking.

1. The flipflop index:  How late in the season will I still be putting on flipflops to take out the recycling?  Current value:  Dec 2 and counting.
2. The Giro index:  How many times will I have to go back into the crawl space to get the kids bike helmets out because there is yet another day of bike-friendly temperatures?  Current value:  3.
3. The Christmas/tennis index:  How many days will I play tennis outside in view of christmas trees for sale in the neighboring lot?  Current value: 1 as of tomorrow morning.
4. Tulip index:  How many times will we have to buy another supply of tulip bulbs and not plant them because I threw away the last pile thinking that Winter had finally put a stop to that cycle of self-deception?  Current value:  I learned my lesson last year.

Any others?  These data will be updated as the season (supposedly) progresses.

If you got out a pencil and graphed my kids’ time outside, with the date on the horizontal axis and the number of hours spent outside (and not fraying their parents nerves alternately bickering with one another and submitting requests to play on the iPad or watch TV) on the vertical, you would find a dramatic and sustained upward spike beginning right after Labor Day.

What is the underlying structural change that explains this?  School has begun.  Indeed, just as the school year begins and forces them to stay inside half the day (thankfully under the care of somebody else), suddenly going outside and playing with their friends becomes their favorite way to pass the time.

It’s not because time outside has suddenly become more precious.  On any August day when they have already wasted half of it sitting around inside, the time has become equally scarce.  And it’s not because time outside is a way to escape homework because that doesn’t really start until the second or third week of school.

I think the reason is coordination failure.  Playing outside by yourself is not very much fun, you only want to go outside when everyone else is outside.  But when you have the luxury of the entire day, it becomes difficult to predict the precise time of day when all the neighborhood kids are going to be outside.  And since they all have the same problem there in fact is no time of the day when all the neighborhood kids are outside and therefore no time of day when any of the neighborhood kids are outside.

Uniformly robbing all children in the neighborhood of 6 hours of prime playtime leaves them with only a few hours left in the day in which to coordinate.  And releasing them all from captivity at exactly the same time synchronizes them and creates an ideal focal point.  You find your friends outside immediately after school is out.

Unfortunately, in September in Chicago the sun is going to set not long after that, the weather is getting cool, and we really have only a month or so before playing outside is not going to be feasible anymore.  And that’s why “Summer Vacation” is a badly misguided convention.  School should be in session through the entire summer so that kids can make the most out of its coordination benefits.  There would be no more “summer time blues.”

Since kids spend their vacation indoors anyway, the vacation should be in the Winter when going outside isn’t an option.  Then we can really put Winter Vacation to good use:  they can catch up on all of the homework they avoided during the Summer School year when they were instead outside playing.

Scott Ogawa has the floor:

Consider [a] heterogeneous group of people who have different internal temperatures. In the Summer, people who are really hot complain a lot to the building manager, since building is [the] only source of cool. People who are really cold do not complain so much since there is always the “outside option” (literally) as relief. Things switch in the Winter. A complaint-minimizing building manager will jack the heat up in the Winter, and the A/C in the Summer.
I have no data, and it is tough to trust how things “feel” since we are not the best judges of absolute temperature. Nevertheless, I have heard many folks say the temperature inside big buildings always seems negatively correlated with outside temperature, which is extra strange given this costs more than a positive correlation.

Scott’s solution is something like this:  since people differ in their hot/cold preferences you want some variation in the temperature inside.  Most buildings aim for uniformity.  If half of the building is warm and the other half is cool, people will pick their favorite side of the building.  Keeping the mean temperature constant but adding a mean-preserving spread raises overall welfare due to sorting.

Emperor penguins form a group huddle to share warmth as they wait for eggs to hatch.  How do they coordinate?

Emperor penguins are the only vertebrates that breed during the austral winter where they have to endure temperatures below −45°C and winds of up to 50 m/s while fasting. From their arrival at the colony until the eggs hatch and the return of their mates, the males, who solely incubate the eggs, fast for about 110–120 days [1][3]. To conserve energy and to maintain their body temperature[4], the penguins aggregate in huddles where ambient temperatures are above 0°C and can reach up to 37°C [1][3].

Huddling poses an interesting physical problem. If the huddle density is too low, the penguins lose too much energy. If the huddle density is too high, internal rearrangement becomes impossible, and peripheral penguins are prevented to reach the warmer huddle center. This problem is reminiscent of colloidal jamming during a fluid-to-solid transition [5]. In this paper we show that Emperor penguins prevent jamming by a recurring short-term coordination of their movements.

What are the individual incentives in the huddle?  It would seem that the dynamics would be governed by the need to prevent manipulation by a self-interested penguin.

Check out this video (unfortunately you have to click to download it, its about 30MB.  there is no streaming version.)

Two aspects of our taste for good weather are in force in the Spring.  First, we enjoy the warmer weather but we have diminishing marginal utility for higher and higher temperatures.  Second, we have reference-depenendence:  a 40F day feels balmy in March when its been below freezing for the past three months but the same 40F day gives you the chills in May on that day when Winter sends you its final parting gift from the grave.

Given those preferences, here’s how a benevolent Mother Nature would maximize the joy of Spring.  Each day raise the temperature by just a little bit.  Gobble up the steep part of our utility for warmth but stop before marginal utility declines too much.  Then, tomorrow when our reference point adjusts upward pushing the steep part back into play, gobble up those marginal utils again.  Repeat.  This steady but gradual transition from Winter to Summer would be the hallmark of a benevelont Mother Nature.

But woe is us, here in Chicago our Mother Nature is of a different sort than that. She seems well-acquainted with another aspect of our reference-dependent weather preferences:  loss aversion.  Drops in temperature hurt more than equal-sized jumps upward.  Our Mother has figured out how to exploit this to full effect and minimize the joy of Spring.  It all starts in late February when she lays on us a miraculous 60F day right out of nowhere.  Our reference points soar. But then we take the plunge back down on the steep side of the loss-aversion curve and the round trip is worse than if we just had another two days of plain old Winter.

And that pattern pretty much repeats until about June 1.  Instead of that gradual steady incline our Spring in Chicago is the classic sawtooth pattern, a series of tragicomic episodes in which our reference points are coaxed upward and then smashed back into place like some kind of meteorologic Moe-Curly routine. Thoughts of summer give us the hope to soldier on, but only if in the past year we were lucky enough to have forgotten whom she hands the baton to once the temperature finally settles down:  the mosquitos.

Thanks to everyone who suggested restaurants.  I went to three:

1. Rootdown Denver.  The clear favorite.  Loud, trendy, waitstaff heavily tattooed.  Small plates for under \$10 each.  I had beet gnocchi, carrot and thai red curry soup, some other stuff. All great.  I was lucky to find a seat at the bar otherwise I would have waited a long time.  So definitely you need reservations. The best part of my dinner was that I finally found a bar that serves a mythical cocktail:  The Aviation.  I have been looking for this for a decade.  It was fantastic.  Thanks for the pointer Dan!
2. Osteria Marco.  Fine but typical Italian.  I had pizza.  I’ve had worse. They served by the glass a blend of Dolcetto, Barbera, and Nebbiolo from Langhe. That was something new for me, and I liked it.
3. Tastes Wine Bar.  A little depressing because I was the only person there. But the food was somewhat adventurous and good.  The wine was fine, but not the kind of varied selection I would have expected from a place that calls itself a wine bar.  The menu listed a sauvignon blanc from the Loire and when I ordered it to start with, I was told that they were out and tonight they were substituting a Sauv Blanc from Colorado!!  I did taste it. Once.

Its a shame I didnt make it to the Fluid coffee bar that Jacob Grier suggested. I was going to stop there on Sunday before going to the airport but Denver got hit with a snow storm and so I got on standby and headed to the airport early to make sure I got out of there before the flights were cancelled.

You did take my advice didn’t you?  If you did, then because of the January effect, you bought the S&P500 at 1180.55 on November 30 and sold it on the first trading day of the new year, yesterday, at a price of 1271.87 and made a 7.5% return in a single month.

I don’t mean breaking and entering.  It’s New Years Eve — 2PM on New Years Eve — and after heading out for a quick lunch I return to find The Jacobs Center locked for the weekend.  There is a separate electronic key to the building and I have one somewhere but I never need it so I don’t carry it around with me.  So I have to stand in the cold and wait for somebody to enter or exit the building and let me in.

There are two entrances so the question is which one to stand by and wait.  I wait for a while at the main entrance and then decide to try my luck at the next one on the other side of the building, about a 2 minute walk.  Of course on the way I am imagining that someone must be leaving from the first entrance just as it passed out of sight. When I get to the other entrance I find that there’s just as little activity there as at the first one. After a while I give up again and go back to the first.

I have a sinking feeling as I am walking back that I am violating some basic rationality postulate to have dropped the first alternative only to switch back to it again.  But it’s not hard to rationalize switching, even indefinite switching with a simple model of uncertain arrival rates.

At each entrance there is a random arrival process, say Poisson, which produces a comer or goer with some given flow rate.  It’s random so even if the arrivals are frequent on average its still possible that there is a long wait just because of bad luck.  Because it’s an unusual day I don’t know for sure what the arrival rates are at the two entrances so the best I can do is form a subjective distribution.

As time passes I learn only about the door I am watching and what I am learning is that the arrival rate is slower than I thought. Every moment that passes and I am still out in the cold the current door’s expected arrival rate is continuously dropping. There comes a point in time when it drops low enough that I want to switch to the other door.  The expected arrival rate at the other door hasn’t changed becuase I haven’t learned anything about it. I give up and walk to the other door once the estimated rate at the current door drops far enough below that it is worth 2 minutes of walking (and no chance of getting in during that time.) In fact, this may happen before the current door’s expected arrival rate drops below that of the other door. (Due to option value. See below.)

Once at the other door I start to learn about it and I stop learning about the first door.  Again, as time passes its estimated arrival rate drops while that of the first door remains constant.  There is again another threshold after which I return to the first.  Etc.  Until I finally give up and throw a brick through the Kellogg student lounge window.

Observation: Consider the threshold at which I switch from door 1 to door 2.  That is based on a comparison of the value of staying put versus the value of switching. The value of switching has built into it the option value of being able to switch back.  You can see the role of this option value by considering a truncated problem where once I switch doors I am unable to switch back.  Relative to that problem, the option of switching back makes me switch more frequently.  Because without the option to switch back, I want to hold on to the current option until I am certain that it’s a loser before giving it up for good.

Made it to Brooklyn alive. I don’t see what the big deal is, some nice chap shoveled me a spot and even gave me a free chair!

From @TheWordAt.

Speaking of which, have you noticed the similarity between shovel-earned parking dibs and intellectual property law?  In both cases the incentive to create value is in-kind:  you get monopoly power over your creation.  The theory is that you should be rewarded in proportion to the value of the thing you create.  It’s impossible to objectively measure that and compensate you with cash so an elegant second-best solution is to just give it to you.

At least in theory.  But in both IP and parking dibs there is no way to net out the private benefit you would have earned anyway even in the absence of protection.  (Aren’t most people shoveling spaces because otherwise they wouldn’t have any place to put their car in the first instance? Isn’t that already enough incentive?)  And all of the social benefits are squandered anyway due to fighting ex post over property rights.

I wonder how many people who save parking spaces with chairs are also software/music pirates?

Finally, here is a free, open-source Industrial Organization textbook (dcd: marciano.)  This guy did a lot of digging and we all get to recline in his chair.

Jonathan Weinstein does a very good Dickens.  A fun read.

“There are many other purposes of charity, Uncle, but at the risk of my immortal soul, I shall debate you on your own coldhearted terms. Your logic concerning gifts appears infallible, but you have made what my dear old professor of economic philosophy would call an implicit assumption, and a most unwarranted one.”

You hear this a lot in Chicago.  “We are having a cold snap because there is a low-pressure system over the Midwest and a high-pressure system to the North.  This causes windy conditions which brings cold air down from Canada.”

This sounds better than just saying “it’s cold today” but I can’t tell if it really is saying anything more than that.  First of all, as I have said before the following two statements are equivalent, at least empirically:

1. The air is colder than usual
2. The air was blown here from some place colder than here.

So telling me that the air came from Canada isn’t telling me much more than I already knew, it’s cold.  But the extra bit here seems tautological at an even deeper level because these two statements:

1. The air is blowing from down Canada
2. There is high pressure in the North and low pressure here

appear to be literally the same thing.  Why else would the air move from position A to position B if it were not due to pressure imbalances?

Is meteorology really just like finance?  (“Stocks fell today because of bearish investors”)  Or is there a non-circular way of explaining my frozen toes that just doesn’t fit into a 30 second weather report?

(drawing: glooming from http://www.f1me.net)

As a SoCal transplant to the Midwest I have had two very different experiences with weather.  Growing up, I learned a few immutable climate axioms.

1. If there is sunshine its going to be warm, if it is cloudy it is going to be cold.
2. If there are clouds plus precipitation its going to be even colder.

The beauty of these principles is that you can look out your window and know how to dress.  The tragedy of these principles is that they are totally false.

In Chicago, sunshine means on average that it is going to be colder.  Especially in the winter.  Cloudy days are on average warmer than sunny days.  And precipitation, especially snow, means its going to be even warmer than if it was just cloudy.

Eventually I think I figured out why.  The true axioms of weather are instead

1. How warm or cold it will be depends almost entirely on where the air is coming from.
2. Whether there are clouds and how much precipitation there will be depends a lot on where the air is coming from.

#1 is obvious but would be completely lost on a SoCalian because the air pretty much comes from the same place all the time.  It blows in from over the Pacific.  This being constant, the only thing left to determine the tiny fluctuations in temperature is whether or not the Sun has yet to burn off the marine layer (essentially fog that comes along with water blowing over the ocean.)  Naturally therefore sunshine=warmer.

(A variation on this which still confounds the SoCalian is the occasional Santa Ana condition where the air is blowing offshore from the deserts.  This keeps the marine layer at bay (sunshine) and the desert air is of course warm.)

In Chicago, the air can be coming from just about anywhere Westish.  Air coming from Canada: cold.  Air coming from Missouri:  warmer.  Now, sunshine means that the excess moisture that would have been in the air to form clouds fell to the ground before the air arrived.  That is more likely to have happened if the air is coming from Canada because in Canada it is colder and that means the the air can hold less moisture.  Hence the correlation sunshine=cold.

Indeed, clouds indicate that the air has moved from some place warmer, where the air could hold moisture.  Finally, precipitation means that it was so warm wherever the air is coming from that there is so much moisture in the air that by the time it reaches cold Chicago, it has to fall out of the sky onto me.

File this one under Blogging Something I Know Nothing About, yes. But after the first few times I ran outside in shorts in January because the sky was crystal blue, I have come to depend heavily on this theory.  And its working pretty well, at least until I move to Hawaii.

A more appropriate name for DST is daylight consumption time.  Shifting the clock re-alloates daylight from an hour when most are sleeping to an hour when almost everyone is awake.  And unless our preference for daylight has a discrete jump in the Spring and the Fall, we should be smoothing out this consumption.

Apart from watches (and what is the point of wearing one of those anyway?) nearly all of our timepieces orient themselves relative to a central server.  This would enable us to coordinate a smooth addition of time to our clocks, say 1 minute per day over a 60 day period.

Getting out of bed 1 minute earlier each of 60 consecutive days will dramatically reduce the total level of morning grumpiness compared to the current system where it comes in one big, grumpy, lump.

In the old days when our clocks were not synchronized this would not only have been too much of a chore, it would have caused all kinds of mis-coordination due to lack of common knowledge of the current time.  (Does she worry that I worry that she forgot to add a minute?)  But that problem is gone.

True, there would be a new kind of asynchrony vis-a-vis other countries where consumption of daylight isn’t valued as highly.  Under the current system at least they know our local time modulo the little hand.  But again, their time servers are smart enough to tell them the right time at whatever locale they are interested in.

Then of course in the fall, we smoothly adjust our clocks back.

If this is all obvious, forgive me I came late to this (I grew up in Orange County, CA where it last snowed in December of Yeah Right.)

The first thing to do, obviously is to make a snowball.  Your enemy combatant will do the same.  You each now have one snowball in your stockpile.  What next?

If you throw your snowball you will be unarmed and certain to pay the consequences.  So you don’t.  Neither does she.  You are at a standoff, but very soon you figure out what to do while you wait for the standoff to resolve.  Make another snowball.  Of course she does the same.

Now you each have an arsenal of two snowballs.  Two is very different from one however because if you throw your snowball you still have one to defend yourself with.  But you will have one fewer than she.  This still puts her at an advantage because once you use your last snowball you are again unarmed.  So you will only throw your first snowball if you have a reasonable chance of landing it.

The alternative is to make another snowball.  Which of these is the better option depends on what she is expecting.  If she knows you will throw, she is prepared to dodge it and then press her advantage.  If she knows you will make another one she will wait for you to reach down into the snow when you are most vulnerable and she will draw first blood.

So you have to randomize.  So does she.  There are two possible outcomes of these independent randomizations.  First, one or two snowballs may fly resulting in a sequence of volleys which eventually deplete your stocks down to one or two snowballs left.  The second possibility is that both of you increase your stockpile by one snowball.

Thus, equilibrium of a well-played snowball fight gives rise to the following stochastic process.  At each stage, with a certain positive probability, the stockpiles both increase by one snowball.  This continues without bound until, with the complementary probability in each stage, a fight breaks out depleting both stockpiles and beginning the process again from zero.

Special mention should be made of a third strategy which is to be considered only in special circumstances.  Rather than standing and throwing, you can charge at her and take a shot from close range.  This has the obvious advantages but clearly leaves you defenseless ex post.  Running away should be ruled out because you will be giving up your entire store of snowballs and eventually you will have to come back.  No, the only option at this point is to tackle her, landing you both deep in the snow.  With the right adversary, this mutually assured destruction could be the best possible outcome.

It’s trendy to get your economist on around the holidays and complain about the inefficiency of gift exchange.  Giving money is a more efficient way to make the recipient better off.  But that’s a fallacy that only trips up poser-economists.  To a real economist, that’s like observing that eating an omelette is an inefficient way to get all of the nutrients we need in our breakfast.  Yeah, so?  That’s not why I ate it.

A real economist recognizes unregulated, voluntary exchange when he sees it.  He doesn’t bother inventing some hypothetical motivation for the exchange because he understands revealed preference. If they are doing it voluntarily then it is efficient, regardless of what they think they are getting out of it.  Indeed, the pure consumption value of buying a plaid sweater for somebody is a perfectly good motivation.  And since the recipient voluntarily accepts the gift, even better.  If there was a Pareto superior alternative they would have done that instead.

So this holiday, swat that poser economist in red off your left shoulder, hold hands with the real economist in white on your right shoulder and give to your hearts’ content.  (Oh and I am very easy to shop for.  Just don’t forget to include a gift receipt!)

Each Christmas my wife attends a party where a bunch of suburban erstwhile party-girls get together and A) drink and B) exchange ornaments. Looking for any excuse to get invited to hang out with a bunch of drunk soccer-moms, every year I express sincere scientific interest in their peculiar mechanism of matching porcelain trinket to plastered Patricia. Alas I am denied access to their data.

So theory will have to do. Here is the game they play. Each dame brings with her an ornament wrapped in a box. The ornaments are placed on a table and the ladies are randomly ordered. The first mover steps to the table, selects an ornament and unboxes it. The next in line has a choice. She can steal the ornament held by her predecessor or she can select a new box and open it. If she steals, then #1 opens another box from the table. This concludes round 2.

Lady #N has a similar choice. She can steal any of the ornaments currently held by Ladies 1 through N-1 or open a new box. Anyone whose ornament is stolen can steal another ornament (she cannot take back the one just taken from her) or return to the table. Round N ends when someone chooses to take a new box rather than steal.

The game continues until all of the boxes have been taken from the table. There is one special rule: if someone steals the same ornament on 3 different occasions (because it has been stolen from her in the interim) then she keeps that ornament and leaves the market (to devote her full attention to the eggnogg.)

Theoretical questions:

1. Does this mechanism produce a Pareto efficient allocation?
2. Since this is a perfect-information game (with chance moves) it can be solved by backward induction. What is the optimal strategy?
3. How can this possibly be more fun than quarters?

He tottered over to the thermostat and there it was: treachery. Despite a long-fought household compromise standard of 74 degrees, someone — Adler’s suspicions instantly centered on his wife — had nudged the temperature up to 78.

For the sleepy freelance writer, it was time to set things right . . . right at 65 degrees. “I just kept pushing that down arrow,” he said of his midnight retaliation. “It was a defensive maneuver.”

The article suggests that women generally prefer higher thermostat settings than men.  (It is the opposite in my household.) The focus is on air conditioning in the summer and I wonder whether this ranking reverses in the winter.  (My wife prefers more moderate temperatures:  cooler in the summer, warmer in the winter. )

Repeated game exam question:  will this make the climate wars better or worse? Give your answers and reasons in the comments. Ushanka Shake: Knowledge Problem.

Q: How do you prove the existence of Spring in Chicago?

A: By continuity.

In February it was zero Farenheit. Today it is muggy and approaching 90.  By continuity, Spring happened somewhere in between.  But note that this existence proof is not constructive.  It is of no help in telling us exactly when it was that Spring fluttered by.  I must have been sleeping at the time.

I have been trying to come up with a practical measure of the length of Chicago winters.  Here are a few.

• On Oct 4 I swapped out my summer clothes for winter clothes.  Tomorrow I will take the summer clothes back out of storage.  7 months of winter.
• On Nov 10 I wore my heavy winter coat for the first time.  I downgraded to my wool coat for the first time on March 27.  4.5 months of deep winter.
• Sep 9 was the first day I did not wear flipflops. I wore them for the first time last week. 4.5 months of non-winter.

This post suggests that data on suicide seasonality debunks the myth of “winter blues.”  Most studies show that suicide rates peak in the Spring suggesting that Spring is a more depressing season than Winter.  But to make this inference we need a model of the optimal timing of suicide.

Suppose that your emotional well-being is a stochastic process which is mixed with a seasonal trend.  If Winter makes everyone unhappy, then this transient shock confounds the movements in the underlying stochastic process. You are not able to uncover the realization of your emotional random walk until after Winter is over and the seasonal component has washed away.

So you are really depressed in the winter but you are willing to wait it out to find out how you feel in the Spring. If Spring arrives and you are still depressed, you know you are riding a permanent shock.  Thus, the spike in suicides in the Spring actually proves that Winter is indeed the most depressing season.

This is a beautiful post from Alinea at Home.  It is worth reading the whole thing, but this bit resonates with me.

And that’s why I think I was drawn to the Alinea cookbook above anything else.  Because it’s so not me, but represents traits and skills I admire in others, but had not yet been willing to take the risk to figure out how to adapt or embed in myself.  I don’t know if it’s possible for me to change in that way or explore the possibility of rewiring (or even just tinkering with) my brain in this manner, but I knew I needed to get better about breaking out of my comfort zone, and doing it with food seemed to me to be a path that would make me the most willing to learn.

There are people who inspire and there are people who are very good at getting inspired by others.  We need both.