I HATE RELATED RATES

Here is the link to this weeks Car Talk Puzzler: "Row, Row, Row, Your Boat"


Here is what I have so far: 


(note: I got no where, which was not surprising.):

From Random Graphic Images

Here is the SHORT VERSION of the puzzle: You put your boat in and row up river for one mile.  Your hat flies off.  You continue rowing for 10 minutes then decide to go back for your hat.  You catch up to the hat at the same place you started rowing.  You row at the same pace going down river as you did going up river.


My cheat was to 'google-search-hat-floats-downstream' for how to do related-rates, (and a big hint for this particular one, hopefully) and apply it to this problem.  I wind up doing this about once a year and then because the mind tends to forget painful memories I forget how to do related rates until the next time I have to do one.


Of course since this is the 'Car Talk Puzzler' then there must be some nice way to conceptualize this puzzle that does not require a lot of algebra.


And there is and here it is: What It Means To "Understand" Something!. (This was one of the 'let-me-google-that-for-you' hits from above.  


The whole article is well worth reading, in its entirety, but for the purposes of this post the bit about the hat floating down stream is of most concern here.


A key to understanding this problem (as pointed out in the link above) is to not think about rowing against the current or rowing with the current but instead think of walking along one of those 'glide-ways' that they have in airports. 


You are walking along the glide way and you drop your hat and continue to walk for however long until you decide to turn around and walk back and pick up your hat.  It will take exactly the same amount of time to walk away from the hat as it will to walk back to the hat.  So if you decided to turn around after 15 seconds then it will take you 15 seconds to walk back for your hat. (another way to say this is to say that: THE HAT DID NOT GO ANYWHERE WITH RESPECT TO THE SURFACE OF THE GLIDE WAY YOU WALKED AWAY FROM IT (on the surface of the glide way) THEN WALKED BACK TO IT).


Notice, however one of three cases applies:


[CASE-A] If you pay attention to the art work on the walls then you will notice when you are walking the 'correct' way along the slide way if things go by faster than normal walking.


[CASE-B] Or you will notice that you are walking the 'wrong' way along the slide way if things go by slower than normal walking.


[CASE-C] Or if the slide way is stopped then you will notice that the art work on the walls changes as if you were not even ON the slide way, things will going by at normal walking speed.  


However, and this is the punch line, in all three cases it will take the SAME amount of time to go back and pickup your hat as you spent walking away from it, because the hat just lay there on the slide way. 


NOTE: This does assume if you are walking the 'wrong' way on a moving slide way that the hat does not arrive at the end before you get back to it.  If it does then you would catch up to it more quickly than otherwise. 


The reason the time to get back to your hat is the same in all three cases is that your motion with respect to the surface of the slide way is due ONLY to your walking motion.  


If you walk the 'correct' way then it is as if you are paddling 'downstream-with-the-current'.  


If you walk the 'wrong' way then it is as if you are paddling 'upstream-against-the-current'.  


If the glide way is stopped, or you are not walking on the glide way it is as if you are paddling 'in-a-zero-current-stream'. 


Still another way to say things is to say: You and your hat are NOT being carried along the glide way, the glide way itself is the thing that is moving and you and your hat are being carried along (or not) the 'bank' of the glide way.


So in terms of the original puzzle:  


How fast was the current if you notice; when you grab your hat out of the water, (which we now understand will take exactly 10 minutes to get to) you and the hat are right back where you started (the dock)? 


And you also notice this an interesting coincidence, that you grab your hat right at the dock, and probably think that this coincidence allows you to actually compute the current rate. Well, really, if you just grabbed your hat and noted where you were you were you would probably say, "Man, the current must be really fast for me to travel all this way in 10 minutes!" 


Now here is the math.


The rate of change of the distance between you and the 'DOCK' when traveling 'upstream' is r-c (where r is the rate you row, and c is the rate of the current).  This is because you are rowing against the current and it is slowing you down, relative to the bank.


The rate of change of the distance between you and the 'starting-point' when traveling 'downstream' in the current is r+c. Likewise this is because you are rowing with the current and it is speeding you up, relative to the bank.


Assume everything is miles per hour so (10 minutes is written as 1/6 of an hour).  


Also notice that when miles per hour is multiplied by time (hours) then distance results (in other words (m/h)*h = m. (And miles per hour means miles divided by hours). 


So now:  


If d = distance traveled along the bank in the 10 minutes after loosing your hat. 
then d = (r-c)/6.


And the total distance traveled from the starting point before turning around is 1+(r-c)/6. Because we traveled one mile from the dock before our hat flew off.


And also:


We have the case that it takes 10 minutes (1/6 hour) when traveling at r+c to travel all the way back to the starting point which is 1+(r-c)/6 miles away from where we turned around (as we figured out above). 


Also notice that when distance traveled (miles) is divided by time (hours) then miles per hour results: the formula is m/h.


So we now get the following formula for miles per hour down stream when we divide total distance paddled down stream by total time:


[1+(r-c)/6]/(1/6) = 6 + r-c 


That formula is the speed traveling downstream.


However:  From just thinking about traveling downstream we already know the speed is just the rowing rate plus the current rate.  The formula is r+c.


Setting these two formulas equal to each other we get:


6 + (r-c) = r+c
    6 - c = c
        6 = 2c
        3 = c


And the answer to the question of whether or not the speed of the current can be computed is: Yes! And the rate of the current is 3 miles per hour.

The Next Great Adventure?

As I wander through blog posts on a Saturday Morning ...

• ORIGINAL POST: "Psychopathic Killer Robots, AI, and The Singularity"
• LATEST POST IN A LINK FROM ABOVE: "Why is death bad?"
• REFERENCED POST:"Is death bad for your?" Puzzles Remain ... this blog post is how I resolve the puzzle.
• QUOTE FROM A HARRY POTTER NOVEL: "After all, to the well-organized mind, death is but the next great adventure" Dumbledore speaking to Harry about the coming death of Nicolas Flamel.

So the question remains: Why are we afraid of, so concerned with death. The answer is connected to how the human mind emerged, from the perspective of natural selection.

Natural Selection is the 'law-of-evolution'.  That is if you can persist and pass along your gene sequences to coming generations then you (your gene sequences) are 'Selected In Favor'.  If you do not persist and thus do not pass along your gene sequences to coming generations then you (your gene sequences) are 'Selected Against'. Organisms evolve because they persist.

This seems very simplistic, and it is.  There is no grand design, other than the wonder we all feel when considering our surroundings whether immediate or cosmic.  That wonder is confined to the inside of our heads.  That wonder, by the extension of our ability to communicate with others, is also inside the heads of our fellow creatures.

It comes back to the mind, or consciousness the thing that seems to distinguish between motile and non motile organisms.  If an organism is motile at a level that is higher than chemical like a plant responding to nutrients in the soil or light from the sun or a virus or bacterium then there exist a sensory feedback mechanism that allows the motile organism to move around its environment.

This sensory feedback mechanism is what allows motile organisms to keep from falling off cliffs or banging into trees or even avoid being eaten prematurely by its predators.

The sensory feedback mechanism has evolved in organisms that do the most moving around to be the conscious mind.  This mind is at its very least a mechanism that takes in the sensory inputs of the organism and then does a short term prediction of the future in order to react to its environment.  The success of its ability to predict the future determines if it can persist.  If the mind makes a mistake then failure cause it to be 'Selected Against' since it does not persist.  This means that the avoidance of 'fatal-mistakes' is hard wired into the minds of motile organisms.

At least one motile organism, humans, have a mind that seems to be able to 'talk-to-itself' or 'think-about-itself' or 'model itself'.  And further, this ability has been 'Selected In Favor Of'.  This ability to contemplate itself combined with the emergence of very nuanced communication methods between humans resulted in the emergence of what humans call, intelligence.

Getting back to death:  The avoidance death which is necessarily hard wired into our minds combined with another very important attribute of the mind (the no-crash-attribute) explain why death is such a big deal for humans.

The no crash attribute of the mind of a motile organism is what keeps it from seizing up when confronted with two conflicting models of the future.  If an organism with a mind, in doing it's short term prediction of the future has a choice, "fight or flight" as an example must make the choice that has the highest probability of resulting in a 'false-negative'.

In other words if the organism senses a rustle in the grass and decides on flight and it turns out to be the wind then no problem, but if it decides to not flee and the rustle is not the wind and results in the organism being lunch for another then that is 'Selected Against'.

In either case the mind can not freeze up or sieze. It has to 'do-something'.  This feature of the mind is hard wired. This combined with the hard wired attribute to avoid death combines to make death one of the most complex, for a human mind, events that can be contemplated.

Such a concept, one with a built in paradox, still must be dealt with by the mind.  This hard wired ability to deal with paradox allows the human mind to come up with ideas that completely and totally fly in the face of the scientific method.  Such ideas, because they arise at such basic levels of the mind are clung to with a tenaciousness that defies reason.

The statement that an idea (or belief) defies reason is used as a pejorative.  If reason, or the scientific method itself is examined it is seen to be at least a deliberative process. A deliberative (slow) process violates the hard wired behavior of the mind that demands snap judgments based on bad data.

Another way to say this is that reason and the scientific method are luxuries that an organism can not enjoy unless it finds itself in a state of easy living.  Human civilization has provided just such an environment and allowed these mental processes to emerge.

These mental processes emerge because they work.  The one thing that organisms do at the expense of all others is engage in behaviors that, work!  Where, work, is synonymous with increase the ability to persist.

The emergence of such high level processes does not give an organism the ability to override, at will, the hard wired processes that evolved as basic artifacts of its mind.

For this reason the human mind: Invents religion, fears death, believes in Gods, and rejects out of hand scientific evidence for things it finds uncomfortable (or paradoxical), and generally clings to ideas and concepts that have nothing to do with reason and the scientific method.

That humans can do an analysis of their own minds is an accomplishment that is totally coupled with intelligence which is in turn totally coupled with the ability of one human to communicate with another.  This behavior is a very satisfying one whether or not it us used to contemplate itself or the universe as perceived by its senses.  This contemplation can be accomplished using the scientific method or any other belief system that emerges from the inner workings of the mind.

Second Ride of the Year

A really nice ride.  I left the house and rode down Yadkin drive to Crabtree Creek then along Allegheny to the Greenway.  Once on the Greenway I rode up to Shelly Lake then on north up Lead Mine Creek to Longstreet.  Longstreet comes out at Sawmill Road which turns into Morning Dove Drive when it crosses Six Forks Road.  Morning Dove winds around within a block or so of Falls of the Neuse Road.  I then rode down Falls of the Neuse to Sandy Forks which cuts across to Six Forks Road.  Then down Six Forks, Cranbrook, Manchester, Rampart then back on Yadkin.  Once on Yadkin I rode back to Allegheny and instead of turning right I turned left and rode up by the Golf Course and onto Lassister Mill Road.  The Greenway starts up again just after you cross Crabtree Creek and continues on down to cross Anderson, then on down the creek crossing Old Wake Forest, Atlantic, Capitol Blvd.  The Greenway continues almost to Wake Medical Center, dead-ending on Milburnie.  That is the turn around and then it is back to Yadkin and up the hill to Davidson Street.


Here are the stats:


43 Kilometers
17 Kilometers per hour
2.5 Hours


Here is a picture as you cross the 'Swamp-At-Raleigh-Road-And-Crabtree-Creek'

From Random Graphic Images

Here is a map of the ride:

From Random Graphic Images

Here is a link to the 'Map-My-Ride' map:
http://www.mapmyride.com/routes/view/94518823

First Ride of the Year

This morning when I collected my bike from the storage shed in the back yard I noticed that the pedels were missing!  Then I remembered, the last time I rode my bike was in October of 2011 about seven months ago.  And that ride was the 2011 Cycle North Carolina Bike Tour.  When you put your bike on the truck for the ride back to Raleigh you have to take the pedels off.

I decided to not only put the pedels back on but also to replace my new 'Moon-Saddle' with Evelyn's saddle that she used before she got her moon-saddle.  And I found that saddle very nice.  I'm not sure if I am going to try that moon saddle again.

Since this is my first bike ride in seven months I decided to just do a greenway ride.  The ride wound up going around 30 kilometers and took 1:45.  Here is a link to the ride if I had not had to turn around a ride back down the hill then up the hill to Ridge Road: "http://www.mapmyride.com/routes/view/92066445".  Here is a screen shot of the route:

From Random Graphic Images

I left the house and rode down to Crabtree Creek, along Yadkin Drive.  I then turned onto Allegheny and rode to the greenway.  Once on the greenway I rode to Lead Mine Creek and got on the Crabtree Creek Trail.  I followed the Crabtree Creek trail to the end and turned around and rode back to the McDonalds at the corner of Blue Ridge Road and Crabtree Blvd.  Then on to the new greenway that parallels the beltway up to Glen Eden Drive.

This new part is now being landscaped and is very nice.  Once at Glen Eden I rode across the beltway and looped down under Glen Eden on the new greenway.  I followed the new path and crossed under Lake Boon Trail.  The new greenway then parallels the street until you get to the road that climbs up to Martin Middle School and Ridge Road.  I crossed this street and kept on the new greenway until it ended very near the beltway bike bridge.  At that end point there are pilings that look like there will be a elevated part that spans a ravine just before you get to the bridge.  I turned around rode back to the road then up the hill to Ridge Road then on down past All Star Bike Shop at Ridge Road Shopping Center.  I then too the new greenway beside Wade Avenue to the bike bridge to the NC Art Museum.  Once at the Museum I got on Blue Ridge road and rode back down to Crabtree Creek, taking Edwards Mill Road that goes past the Crabtree Creek Tavern and it was then back on the greenway and back home.

It was a nice ride that probably took around 30k, my bicycle trip computer has a dead battery so I can not give the exact milage.

Here is a picture of the end of the greenway and the poles that will be the base of the bike trestle over the ravine:

From Random Graphic Images

Here is another picture of the bridge to the Art Museum. If standing where this picture is taken you look to your left you will see where the new greenway will come out.

From Random Graphic Images