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Some Thoughts on Finding Fenn's Treasure…
I still remember assembling my first IKEA purchase. It ended up looking more like a chair than a coffee table. My neighbor, who had some experience with IKEA, took a look at the art-piece (cause that's all it was at that point) and then the instructions and quickly pointed out that I'd put a couple of dowels where screws were supposed to go and I'd put in one panel upside-down and backwards. He showed me the instructions and pointed to a dot, that's this hole here, pointing to the panel, you've got it on the top, and it should be on the bottom. And so it went, through three or four places where I'd misread the drawings.
The problem is that instructions work best if you already know what you're doing. If you have that expertise, if you already know where you're going, instructions are a great help, a reminder of the correct steps to follow. But to the novice it all looks like Greek.
I'm not trying to pick on IKEA, I'm sure they have a team of assembly engineers and testers that diligently work through the build process instruction repeatedly, refining it, working out the kinks. The problem is that the more experience and knowledge one has, the more difficult it becomes to provide adequate explanation or instruction to a novice. The difficulty of providing directions that anyone can follow is so well understood by IKEA that they have an assembly issue hot line. If you're having problems you can call up the hot line and they'll help you figure out why your coffee table looks like a chair.
And so it is with Mr. Fenn and his treasure poem.
To recap, for those who aren't familiar with Mr. Fenn's treasure…
Forrest Fenn, a wealthy business man, hid a box of treasure estimated to be worth approximately a million dollars somewhere in the Rocky Mountains. He wrote a poem that includes nine clues that guide the searcher to the treasure. Here's the poem.
As I have gone alone in there
And with my treasures bold,
I can keep my secret where,
And hint of riches new and old.

Begin it where warm waters halt
And take it in the canyon down,
Not far, but too far to walk.
Put in below the home of Brown.

From there it's no place for the meek,
The end is ever drawing nigh;
There'll be no paddle up your creek,
Just heavy loads and water high.

If you've been wise and found the blaze,
Look quickly down, your quest to cease,
But tarry scant with marvel gaze,
Just take the chest and go in peace.

So why is it that I must go
And leave my trove for all to seek?
The answers I already know,
I've done it tired and now I'm weak.

So hear me all and listen good,
Your effort will be worth the cold.
If you are brave and in the wood
I give you title to the gold.

It is estimated that there are several hundred thousand people searching for the treasure chest. I suppose I'm one of them.
As I've thought about the poem and quest I've come up with several thoughts that I'd like to share about the futility of the search. Yes, 'futility'. Here's why…
Let's do a quick analysis of such a quest. For simplicity, let's assume that each of the clues is a binary choice, like a fork in a road; we can either go left or right. So, from the start we walk down the road and come to the first clue where we go right, at the second clue we again go right, at the third clue we go left, and so on through all nine clues. The whole scenario, if drawn on a page, might look like a tree. At each junction, or clue, we have one of two choices which mathematically doubles the number of branches on the decision tree. So at the start, we have one option, at the first junction we have two options (1 x 2 = 2), at the second junction we have four options (2 x 2 = 4), at the third junction we have eight options (4 x 2 = 8), and so on. After nine junctions (or branches) we have 512 (or 2^9) end-points or leaves.
Let's assume a worst case scenario as an upper limit to our search. In this scenario we have no information that allows us to eliminate any of the branches of the tree so we must try them all. This type of search is called a brute force attack. So we walk down the road, taking every right branch until we get to the leaf at the end. Is the treasure there? No? Okay, backtrack to the last junction and take the other fork, a left. Is the treasure there? No? Okay, back track through two junctions, take the left, then the right fork and look for the treasure. Not there? Okay, backtrack… you get the idea. In this scenario we'll check each leaf of the tree until we find the treasure.
Too easy! With only 512 leaves we should have it done in no time at all.
But is it really that easy? Are there only 512 leaves that we have to explore? No. It would seem that there are quite a few more than that.
How many? Well there are nine clues, we know that, and we know the first one is 'where warm waters halt'. Let's start off with the common assumption that 'warm waters' has something to do with a hot spring (or warm spring). How many hot springs are there in the Rocky Mountains between Santa Fe and Canada? Well, I looked it up and there are 294. How does that change our branched tree? If we continue with the assumption that all the other clues have binary choices (only left or right) then there are 256 leaves below every first-level option. With 294 first-level options we calculate that there are now (294 x 256) 75,264 leaves. Yikes, that's a few more than 512.
Let's move on to clue number two. Wait. What's clue number two? Is it 'take it in the canyon down', or 'too far to walk', or 'home of Brown'? It seems we really don't have much consensus on which phrases or words are clues. How many options are there for 'too far to walk'? Some searchers put the distance at a couple of miles, others 10, some push it to 20 miles. How many possibilities are there for 'home of Brown'? Could he be referring to brown trout, Grafton Tyler Brown (the artist), monks (who dress in brown habits), brown bears, etc.? That's four options right there. Clearly, limiting each clue to two choices is too restrictive.
If we alter our initial assumption, that each of the last eight clues has a binary solution, with something a bit more realistic, like each clue has five options; then our calculation is changed from 294 x 256 (remember that 256 = 2^8 and the '2' represents the number of options) to 294 x 5^8 which calculates out to 114,843,750.
115 million possibilities! Yikes!
So, how can we attack this? Mr. Fenn has stated that the successful hunter will have seriously studied the poem. By this we might assume that the words in the poem have some non-obvious meaning. Perhaps he's used a word that has more than one definition and he's using one of the little-known or not-frequently-used meanings.
Regarding the writing of the poem Mr. Fenn said "I changed it over--I don't know how many times. I looked up the meaning of words. You know we really don't know what some of our words mean. For instance, what does the word 'several' mean? S-E-V-E-R-A-L, what does that mean?"
(I looked it up; it means 'more than two but not many'.)
So let's follow his lead. What does the word 'warm' mean? Here are the definitions from Google:
• of or at a fairly or comfortably high temperature
• (of clothes or coverings) made of a material that helps the body to retain heat; suitable for cold weather
• (of a color) containing red, yellow, or orange tones
• (of a scent or trail) fresh; strong(of a scent or trail) fresh; strong
• having, showing, or expressive of enthusiasm, affection, or kindness
• characterized by lively or heated disagreement
• sexually explicit or titillating
• (especially in children's games) close to discovering something or guessing the correct answer
Some of these obviously have little to do with water (sexually explicit or titillating) but others COULD be taken to address water (containing red, yellow, or orange tones). Should we be searching for colored water not hot water?
Further expanding our understanding of 'warm' as it relates to 'water' by searching on Mirriam-Webster we find that 'warm water' is 'an ocean or sea not in the arctic or Antarctic regions'. It follows then that a 'warm water' port is one that doesn't freeze in the winter.
These two definitions of temperature 'of or at a fairly or comfortably high temperature' and 'water that doesn't freeze' seem to be at odds. The Port of Seattle doesn't freeze in the winter but I don't think anyone would argue that the water there is 'warm'.
So, what if our previous assumption about the meaning of 'warm waters' is wrong? What if instead of referring to a hot spring, it has to do with non-freezing waters, or warm colors, or perhaps even warm names (warm creek, yellow creek), or etc. Has our careful study of the poem gotten us closer to a solution by eliminating any options? Oh, hell no, it's only expanded the realm of possibilities. It might have expanded our search to include the actual solution, which is a good thing, but it certainly hasn't eliminated any of the prior possibilities.
If we add these additional interpretations to the possible solutions for 'warm waters' the number of first-level options increases from 294 to… what? I don't know, but it's bigger. Let's just say 450. 450 x 5^8 is 175,781,250. That's a hell of a lot more than 512.
And what about the word 'halt'?
Where warm waters HALT
I read one solution that argued that where warm waters halt refers to the confluence of the Firehole and Madison rivers in Wyoming. Geyser basins upstream on both of these rivers keep them warm and as they flow downstream they cool. The author of this proposed solution somehow concluded that the confluence of these two streams was a halting of the warm-ness.
'Halt' is defined on Google as:
• bring or come to an abrupt stop
• a suspension of movement or activity, typically a temporary one
How is the gradual cooling of a flowing river a 'halt'? The water temperature 100 yards above the confluence of the Madison and Firehole rivers isn't appreciably different than that of the water 100 yards below the confluence.
Halt is defined as an abrupt stop. Where does water come to an abrupt stop? Well, if we consider a geyser, the water shoots out of the hole in the ground heading upwards and then stops momentarily before it starts coming down. The point at the apogee is an abrupt stop. It could be argued that when it hits the ground it again, momentarily, comes to a stop. Could the bottom of a water fall be considered a 'halt', an abrupt stop?
What about 'a suspension of movement or activity'? Water flowing into a lake or dam has a suspension of movement but Mr. Fenn has said that 'where warm waters halt is not related to any dam'. (Note, he specifically said 'dam', does that mean that a natural lake could still be the 'halting'?)
How much weight can we place on Mr. Fenn's use of the words in the poem? Well, we know that Mr. Fenn chose his words carefully, but we also know that he was constrained by the requirements of poetry. When asked 'Is there a specific reason that 'halt' and 'walk' are the only words that do not follow the rhyme scheme?' he said 'Yes, I was limited by my ability.' So, perhaps 'halt' doesn't really mean 'an abrupt stop' but really does refer to a fading. Can we be assured that his chosen words really mean the definition in the dictionary or did he use them just to fill a need in the rhyming scheme of the poem?
So what has all this 'studying' of the poem got us? Are we closer to solving the puzzle? The answer is 'maybe'. It is possible that our original thoughts were right, that 'warm waters' refers to a hot spring. If that's the case then all this studying has just muddied the waters and expanded the number of possible solutions so that the needle is now in an even bigger haystack, implying that we're farther than ever from a successful solution. On the other hand maybe our original ideas didn't include the solution; in that case we are closer to solving the puzzle because even though the haystack is bigger, now there's actually a needle in it.
If we include these new possibilities in our realm-of-solutions calculation where does the number end up? 200 million? 500 million? I don't know but it's a huge number.
What we need is a way to definitively eliminate branches of the solutions universe. Mr. Fenn has provided some details that can be used to narrow the search. He's clarified that the treasure is located within a specific altitude range. That helps. If we're working under the assumption that 'warm waters' refers to a hot spring and we know the location of all 294 within the geographical search area, we can easily eliminate those that are lower or higher than the target altitude range. But, the altitude specification is somewhat of an anomaly in that Mr. Fenn hasn't provided much information that allows the solutions universe to be narrowed. Using what he has revealed about altitude only eliminates about a dozen of the hot springs. Not much help really.
If we can't definitively eliminate any of the possible solutions can we probabilistically eliminate any? Maybe. For example we could map the hot springs in the Rocky Mountains and eliminate any that are more than say 10 miles from a significant road. This probabilistically eliminates some of the hot springs as being too remote for Mr. Fenn to have used them as the hunt starting point. If we reduce the distance to two miles we could eliminate even more hot springs but only at the risk of possibly removing the true solution from our realm of options.
We could extend this idea and recognize that Mr. Fenn has spent far more time in Santa Fe, NM and West Yellowstone, MT than he has in say, Colorado. Is it statistically more likely that he hid the treasure somewhere near one of these locations where he's spent time? Probably. We could use this idea to create a ranking or rating system with our estimations of how likely each solution might be. For example we might decide that any location within 5 miles of West Yellowstone would be assigned a likelihood of 75% while eastern Colorado might have a value of 20%. Boiling Duck hot spring is 4.5 miles from the nearest road so we'll assign a likelihood of 15% while Bath Water warm springs are 100 yards from a parking area so we'll assign that a likelihood of 90%.
Combining these various estimates using some appropriate mathematical formula would give us overall likelihood values. Bath Water warm springs are in eastern Colorado so the combined likelihood might be less than Boiling Duck hot springs which is in the hills just outside of West Yellowstone. (Note: these are fictitious springs, don't try and look them up and please don't ask me where they are.)
We could even take this farther and create a community ranking system. So instead of the likelihood ratings coming from just one person they could be aggregated from everyone in the TTOTC community. This would vastly improve their value and we could all occupy our non-boots-on-the-ground time arguing whether Boiling Duck hot springs should be ranked as 15% or 20%.
So we go to the effort of creating this massive ranking system and then what? Even if we collectively agree that it is highly likely that the treasure is hidden near West Yellowstone, can we be certain enough that we can completely eliminate other locations, like Colorado. Can we cross Colorado off the list just because we don't think it's very likely that Mr. Fenn hid the treasure there? I think we'll all agree that we can't. It may be less likely that the treasure is there but there is still some, small probability. So Colorado remains on the list.
So what are we left with? What's our best bet for solving the puzzle and finding the treasure? It seems that in the absence of data that can eliminate one or more of the branches we're left with the brute force attack described above which requires that we must try them all. Ugh! With somewhere in the neighborhood of 200 million possible solutions that's a lot of hunting.
But let's soldier on, stiff upper lip and all, and get to it. Off we go down the first branch, searching at each leaf, backtracking to the next branch, the next leaf and so forth. What if we get to the last branch, the last leaf and still haven't found the treasure? Does arriving at each leaf and NOT finding the treasure ensure that we can eliminate that branch/leaf from the search? I would argue that it doesn't. Just because I didn't see/find the treasure doesn't mean that it's not there. It just means that, well… that I just didn't find it.
This is actually WORSE than a brute force attack.
In a true brute force methodology we can eliminate each leaf after an attempt. If I'm trying to brute force my boss's computer password and I try her birthdate and it doesn't work the computer responds with 'failed login' and I can cross it off the list of possible solutions. But in this treasure hunt we can't eliminate any of the leaves because none of them have posted signs that say 'nope, not here, thanks for playing, try again'. After an exhaustive search of the entire tree save one branch, we're still no closer to finding the treasure.
It's feeling kind of futile to me.
Let's get back to my IKEA chair/table.
Mr. Fenn is like the IKEA assembly engineer. He knows each clue. He knows the path. He knows the blaze that marks the spot. He wrote the poem and labored over every word. To him the solution is as obvious as the nose on his face. It's as if he is looking at the solutions tree and the one true path is lit up in flashing, bright, pink neon. Every time he reads someone's solution that includes part of the one true path I'm sure he thinks oh my, they've got it, the treasure will be found tomorrow.
Mr. Fenn has stated that he knows for certain that some searchers have solved the first two clues and gotten close, within hundreds of yards, of the treasure. He knows they've solved the first two clues but do they? And, does knowing that someone else has solved the first two clues help the rest of us hunters? No, not one little bit. It doesn't help the searchers who were within a hundred yards nor it does it help the rest of us!
Because no one, except Mr. Fenn, knows where they were, when they were there, or who they are.
If he revealed that Janet had been close, but didn't tell us when or where, we could query Janet and ask 'where have you been?' and then eliminate everywhere else from the list of solutions. Even if she didn't respond to us, at least she'd know where she had been and she could cross everywhere else off her list. On the other hand, if he told us when someone had been close we could query everyone searching and ask 'where were you at such-and-such a time?' and cross everything else off the list. And of course if he told us where, it would save us all a lot of time (this one has my vote).
Without knowing who, when or where, telling us someone was close is telling us nothing at all. Even the people who were close don't know it, they're still looking at a plain tree, no neon highlights; and every branch still looks just as promising as the next. Even for the searchers who have been within a hundred yards of the treasure, the search is still a brute force attack without elimination.
Yes, futile.
The reward for finding Mr. Fenn's treasure is approximately one million dollars with the odds at several hundred million to one. By comparison the Texas Lottery has a scratch-off game called Texas Lottery Black which also has a million dollar prize. The odds of winning Texas Lottery Black are 1 in 1,029,683. Maybe we're barking up the wrong tree. If getting rich, or at least getting a million dollars, is our goal maybe we should be playing the lottery; or heading to Las Vegas.
But then again, this little hunt is a hell of an excuse to get outside and see some very pretty country. Maybe I'll see you out there.