Does Water Flow Uphill?

My father related to me that he had discovered a paper by an uncle of his that proved that water flows uphill. The following is his transcription of that paper. It's a fun read -- and absolutely correct. Enjoy!

Does Water Ever Run Uphill?

In the days when it was still customary for pupils to learn through direct conference with their Tutors, we can imagine a Tutor as engaged in what was intended to be an instructive conversation with his pupil, somewhat to this effect:

Tutor: I heard you the other evening talking with some of your friends about the building of a canal, and I heard you say that the canal must have a continuous downward slope in its course, for, you insisted, water always runs down-hill. It then occurred to me that the next time I should meet you, I would ask you if you really meant to have your statement, that water always runs down-hill, to be taken seriously and literally, as an universal law as to the behavior of water on this earth.

Pupil: Of course I did, Sir, but I now see that I should have qualified my statement so as to make it apply to freely running water only. Certainly water which is contained in a water-pipe or in a hose, need not run all of its course in an uninterruptedly downwardly direction, for it is perfectly evident that through certain curved portions of the hose, and along certain bends and dips in the water-pipe, the water may momentarily run, shall I say, up-grade; but this will be brought about only through the superior pressure of the water on the proximal side of the bend in the hose or in the water-pipe, and does not contradict what every sense and all experience teaches us, namely, that free-running water, uncoerced by confinement within a pipe of some kind, always and invariably tends to run down-hill.

Nor, he continued, can the issuing of a jet from a hose-nozzle, when this may chance to be directed more or less vertically upward, be claimed as a contradiction to this general law of the behavior, under all circumstances, of free-running water. For here we are not, in truth, dealing with free-running water, but with water which has acquired an inertia of momentum by having been confined under a not inconsiderable pressure, previously to its issuing from the spout or nozzle. But as soon as this momentum has been expended, and the water has reached the ground, it is again in the condition of free-running water, and so far as I can see, it will, from then on, conform to what I am forced by all my observations, backed, I may say, by the general experience of all hydraulic engineers, to believe is an universal law of nature on this earth, that free-running water always tends to run down-hill.

If you could supply me, Sir, with an example of a body of water, when free to run, behaving in any other fashion, I should be very much interested to hear of any such body of water.

Tutor: It is just because I had bethought me of such a body of what you term "free-running water", and no inconsiderable body at that, that the remark I heard you make to your friends the other evening caught my attention.

But before we mention or describe this body of free-running water, let us be a little careful in defining our terms, so that we may fully understand each other, and may not be talking at cross purposes, or be merely quibbling over the proper definition of a word. For a great many arguments, as you must have observed, arise because the interlocutors have not taken this precaution; and when they think that they are arguing about facts of principles, their argument, as a fact, turns out to be merely one over their individual interpretation of some word or term, which had not been properly defined, beforehand, to their mutual satisfaction.

I shall ask you then, in the first place, exactly how you wish to interpret the terms which you have used in your enunciation of the dictum that free-running water always tends to run down-hill. You have already given a sufficiently accurate definition as to what you mean by free-running water; now I ask you for a similarly frank and exact definition of what you mean by the word or term "down-hill".

Pupil: Well, Sir, it never occurred to me that there could be any ambiguity in the term "down-hill"; for "up-hill and "down-hill" are such familiar conceptions that I can scarcely see how it would be possible for anyone to mistake or misapprehend their meaning. But since you ask me for a definition that I can abide by, I should like to contrast "up-hill' with "down-hill, and to say that, in these two terms the prefix "up" denotes a position which is more or less remote, vertically, from the surface of the earth; and that the prefix "down" denotes a position which is in greater proximity to the surface of the earth; and that when a body, as, let us say, a body of water, passes from the more elevated to the less elevated level, it may be said, how great so ever its lateral deviations, to make its way "down-hill". Do I make myself sufficiently clear, Sir?

Tutor: Sufficiently clear, indeed; but, my friend, I do not think that you have made your definition quite broad enough. For an accurate definition should continue to hold in all cases.

Now suppose that a stream of water should be flowing directly toward the mouth of the vertical shaft of a coal mine; and suppose that the miners had neglected to deflect the stream by digging for it proper deflecting channels, or that the embankment they had erected along such deflecting channels had been washed away, and the stream were actually to reach the brink of the vertical shaft. Now do you for one moment suppose that the water would be deterred from plunging down the shaft, because of your reference of "up-hill" and "down-hill" to stations more or less remote, vertically, from the surrounding level of the earth? You cannot but see that you must define what we may, if you please, call "up-ness" and "down-ness" in somewhat wider and more comprehensive terms. It is not with the clearness of your definition that I find myself inclined to take issue with you, but with its altogether too narrow limitations.

Pupil: I beg your pardon, Sir. I find that I was altogether too careless in limiting my definition by a reference to the surface of the earth; although, if you were not too exacting, we might consider the mine-shaft to be but a masked prolongation downward of the earth's general surface.

But without stopping to quibble over what shall be meant by the term, "the surface of the earth", let us refer what you call "up-ness" and "down-ness" to the center of the earth, and done with it.

Then by the term "up", or elevated, I rest content to have you believe that I mean a position a certain distance remote from the center of the earth; and that my the term "down", or less elevated, I mean a position less remote from the center of the earth; and that by the term "down-hill", I mean a passing from the more elevated to the less elevated position, both positions being referred to the center of the earth.

Tutor: Very well then, if you will abide by this definition, I am content to abide by it also. But I must ask you, in this connection, one more question, and that is: Why do you suppose that the water will flow "down-hill", which, I take it, you would define as toward the center of the earth?

Pupil: I see, Sir, that when you are questioning me, I must be very circumspect in my answers; but in this case I do not see that I need hesitate in saying that the water runs down-hill under the influence of gravity, for the attraction of gravitation tends to draw all things terrestrial toward the center of the earth.

Tutor: Do you feel sure of this?

Pupil: I do not see what other answer I can make, Sir. I feel very confident that it is the attraction of gravitation which causes the water to run down-hill.

Tutor: Do you feel prepared to say that free-running water, as you have defined it, is not to be found running "up-hill", under any circumstances, and do you still abide by your assertions that free-running water always runs, lateral deviations being left out of the account, toward the center of the earth, under the impelling influence of gravity?

Pupil: I think, Sir, that I am prepared to abide by that assertion, as covering all cases regarding free-running water.

Tutor: Well then, let the matter rest that way for the present. But you will doubtless permit me to ask you a few questions concerning geography.

Pupil: Certainly, Sir.

Tutor: I think I can take it for granted that you are familiar with the course of the Mississippi river; and I will first ask you what is the general direction of its course, from its source to its mouth, leaving out of the account, as was stipulated, any merely lateral deviations?

Pupil: Its general course is, within a very few degrees, about due north and south, across the whole breadth of the United States, from close to the Canadian border to the Gulf of Mexico.

Tutor: I will now ask you where is its source.

Pupil: I can answer you simply, as it were by rote, from the geography lessons of my grammar-school days. The source of the Mississippi is said to be in Lake Itasca, in the northwestern part of Minnesota.

Tutor: And do you happen to know the latitude of Lake Itasca?

Pupil: The latitude of Lake Itasca, as I remember it from my grammar-school days, is about 47 degrees 30 minutes N. Lat., and its longitude west from Greenwich is, as I remember, 95 degrees 20 minutes.

Tutor: Never mind the longitude. What we are interested in, at present, is only the latitude of Lake Itasca. Can you now tell me in what latitude lies the mouth of the Mississippi?

Pupil: The Mississippi has several mouths; but I think that about 29 degrees N. Lat, would be a fair answer.

Tutor: Now do you happen to know the elevation of Lake Itasca above the level of the sea?

Pupil: If my memory serves me, Lake Itasca lies some 1680 feet above the sea. This, at least, is given in the school-books as the elevation of the remotest springs of Lake Itasca.

Tutor: But one more question and I shall be through with my geographical inquiries. Do you know, perchance, the length of the Mississippi river?

Pupil: Its length is given in the books as 2900 miles.

Tutor: Yes. But this 2900 miles includes many curves or lateral deviations of the river-course, and these, we agreed, were to be left out of the account. What I wish to get at is the distance, in a straight line, from its source to its mouth. Any rough approximation of this straight-line distance will do. Would it seem reasonable to you to estimate its length, in these terms, at, say, 2,500 miles?

Pupil: I think, sir, that that would be a reasonable estimate.

Tutor: Then, gathering all these geographical data together, we may say, may we not, that the Mississippi is a river about 2,500 miles long, from its source to its mouth, and that it runs a course which is, practically, due north and south, from an elevation of some 1680 feet, at its source, to the sea-level, at its mouth, its source lying in 47 degrees 30 minutes N. Lat,. and its mouth in 29 degrees N. Lat.?

Pupil: As a basis for any argument you may have to make as to the Mississippi river, I should think that I can agree properly enough to that, as a statement correct in all essential particulars.

Tutor: I see, my friend, that you have an excellent memory for geographical details. If you have retained all these details in your mind since your grammar-school days, you should have little difficulty, with such an excellent memory, in recalling matters studied more recently. You have doubtless had some courses in solid geometry, have you not?

Pupil: I have, Sir, and that only last year.

Tutor: The earth, instead of being a perfectly spherical body, is actually an oblate spheroid, is it not?

Pupil: Yes, Sir, that is so.

Tutor: Will you tell me, then, just what is an oblate spheroid?

Pupil: An oblate spheroid is distinguished from a prolate spheroid in that while in a prolate spheroid any equatorial diameter is less than a diameter passing through the poles, in an oblate spheroid, on the other hand, the polar diameter is less than any equatorial diameter.

Each of the figures is a solid generated by the revolution of an ellipse, a so-called ellipsoid of revolution, But in the oblate spheroid, the generating ellipse is supposed to revolve about its minor axis; while in the prolate spheroid, the generating ellipse is supposed to revolve about its major axis.

An oblate spheroid is sometimes roughly described, rather than accurately defined, as a sphere flattened at the poles. I have, however, learned to be wary in answering your questions, and I fancy that it is more prudent to give you the more accurate definition of an oblate spheroid.

Tutor: Your definition is quite satisfactory. Now can you tell me what is the difference in length between the polar diameter of this oblate spheroid which we call the earth, and any one of its equatorial diameters?

Pupil: It is very nearly 27 miles.

Tutor: This implies, does it not, that the distance from, let us say, the north pole, to the center of the earth is some 13 1/2 miles shorter than is the distance from any point on the equator to the earth's center?

Pupil: It does, in deed, Sir.

Tutor: Now my friend, I would like you to follow my argument pretty closely, just here. You have said that the earth was an oblate spheroid, with and equatorial diameter longer, by some 27 miles, than the polar diameter. If now we were to trace a true circle, with a radius of the length of an equatorial radius, which is some 13 1/2 miles longer than a radius extending from the center of the earth to either of its poles, then this circle, from being coincident with the earth's surface at the equator, would diverge, as we traced it through the quadrant reaching from the equator to the north pole, more and more from such coincidence with the earth's surface, until, over the pole itself, the divergence would reach a maximum of 13 1/2 miles, would it not?

Pupil: Yes, Sir, and if we were to continue the circular arc, until we arrived once more at its origin, we should, as I understand it, have circumscribed a circle about our generating ellipse, which would touch the curve of the ellipse at either end of its major, or equatorial axis, and would transcend the miner, or bipolar axis by 13 1/2 miles at either end.

Tutor: You have grasped my idea completely, Now I ask you, is there any way to measure the divergence of the circumscribed circular arc from the actual surface of the earth at those two points in the northern quadrant, along the meridian of, I think you said, about 95 degrees west from Greenwich, in which we are particularly interested? These two points were at 47 degrees 30 minutes N. Lat., which is the latitude of the source of the Mississippi in Lake Itasca, and at 29 degrees N. Lat, which you gave as the approximate latitude of its mouth, in the Gulf of Mexico.

Pupil: Why, yes, Sir. We could determine, at each of these two points, the respective lengths of the radius vector of the ellipse, representing the surface of the earth, and of the circumscribed circular arc, which latter we indeed, already know, and by subtracting the former from the latter, for an angle of 47 degrees 30 minutes, we should have the amount of divergence at the source of the river; and by performing the same operation, for an angle of 29 degrees, we should have the measure of divergence of the river's mouth.

But this is a process that would involve some pretty complex mathematics, and I think that it would be much simpler to take advantage of the fact that we know that the rate of divergence of the circular arc from the actual surface of the earth is constant and uniform, and that anywhere along the quadrant of the meridian, irrespective of its position north or south, a given number of degrees of latitude would correspond to the same distance of divergence between the circumscribed arc and the actual surface of the earth.

Indeed, Sir, I think that, considered on this basis, the problem can readily be figured out as simply a problem in arithmetic, without resorting to the more complicated process of determining the divergence of a circumscribed circular arc from an elliptical arc at two given latitudes.

Tutor: By all means give the simplest solution of the problem you can. The method which you suggest will, I am sure, be quite adequate for the purpose.

Pupil: Very well, Sir, we shall know then, in a moment, just how much nearer the mouth of the river is to the circumscribed circular arc than is its source. For we know that the river runs south, from 47 degrees 30 minutes N. Lat. to 29 degrees N. Lat., and that it must therefore cross 47 degrees 30 minutes minus 29 degrees, which is 18 1/2 degrees of latitude in its course. The extreme divergence between the circumscribed circular arc and the actual surface of the earth is found at the pole, and this extreme divergence is 13 1/2 miles, while the pole is 90 degrees from the equator. Then, as the course of the river is across 18 1/2 degrees of latitude, the fraction

18.5/90, when multiplied by the amount of divergence at the pole, which is 13 1/2 miles, should give us the distance, in miles, by which the surface of the earth approaches the circumscribed circular arc throughout the whole north and south course of the river.

Now eighteen and one- half ninetieths of 13 1/2 miles is equal to 2.835 miles, and if these, as I presume, are statute miles, each of 5,280 feet, this represents an approach of the river of 5280 times 2.835, or 14,968.8 feet, during its entire north and south course, irrespective of its exact place north of the equator, along the meridian of approximately 95 degrees west from Greenwich, along which meridian the river runs.

But of these 14,968.8 feet, 1,680 feet are accounted for by the elevation of Lake Itasca above the sea-level. So the actual approach of the bed of the river to the circumscribed circular arc is 14,968.8 minus 1680 feet, or 13,288.8 feet.

Tutor: But, my friend, do you not see that you have just shown that the Mississippi river, in its course across 18 degrees 30 minutes of latitude, approaches closer and closer to the circumscribed circular arc with each degree of its north and south course; and does it not, as it approaches this circumscribed circular arc, get further and further away from the center of the earth?

Pupil: I see now, Sir, the dilemma into which I have brought myself. You can now, I perceive, force me to acknowledge that, according to my own definition of "down-hill" as being toward the center of the earth, the course of the Mississippi is "up-hill" throughout; for I now perceive that paradoxical as it may appear, the Mississippi flows away from, instead of flowing towards the center of the earth. I shall have to acknowledge that you have scored against me.

Tutor: But there is still another point which I feel that I am legitimately entitled to score against you, and it seems fair to approach it in this way.

All points on our circumscribed circular arc are equidistant, are they not, from the center of the earth?

Pupil: That, too, I must concede.

Tutor: Now you have stated that "free-running water" always tended to run "down-hill", being impelled thereto by the force of gravity, on account of which it always strives to run toward the center of the earth.

But on the other hand, you have just admitted that the actual flow of the Mississippi river was away from the center of the earth; that is, its flow is directly contrary to what it would be if the flow at the river were impelled by gravity. It must then be that some force other than gravity causes the Mississippi to flow in this apparently paradoxical manner, which you have admitted was actually "up-hill".

Pupil: I see, Sir, that you have fairly driven me out of both of the positions which I thought were impregnable. And I find myself obliged to admit, not only that the Mississippi river runs an "up-hill", instead of a "down-hill" course, but to admit also that the force which impels this flow is not the force of gravity, but that this force must be the centrifugal force, due to the rotation of the earth about its polar axis. The same force, indeed, which occasions the oblateness of the terrestrial spheroid.

Tutor: I am pleased that you so honestly own the force of my argument. You are quite right in your supposition that the flow of the Mississippi against gravity arises from the superior power, in this instance, of the centrifugal force due to the rotation of the earth. This superiority of the centrifugal force over the force of gravity is developed, however, owing solely to the fact that the course of the Mississippi lies practically along a meridian of longitude. In this case, the centrifugal force comes to transcend, by far, as you have seen, the force of gravitation. But this is decidedly not the case with a river which, like the Amazon, for instance, flows substantially along a parallel of latitude, from west to east.

The principal object I had in view, my friend, in leading you into this discussion, was to impress upon you how really slender is the support which our bodily sensations, though borne out by the bodily sensations and observations of millions of other men, some of whom may be of the utmost respectability for their scientific and their mathematical attainments, --- how really slender and tenuous a support our mere sensations afford used, for what might perhaps be dignified by the name of cosmic philosophizing.

So I trust, ,my boy, that you will not think me to be seeking merely to exult over your argumentative discomfiture, if I ask you to do a little more calculating for me, for the purpose of finding out just how great your error really was.

Pupil: Not for a moment, Sir, would I think of you as acting upon so ungenerous a motive. I shall truly be glad if I can be of any further service to you in this way.

Tutor: Well then. If you are so minded, let us proceed.

You have admitted that the Mississippi, in its north and south course across 18 degrees 30 minutes of latitude, ran an "up-hill" course, during which it ascended, in all, 13,288.8 feet. And we agreed, likewise, that the length of this course, leaving out of account all merely lateral deviations, should be considered to be approximately 2,500 miles. As you have paper and pencil handy, will you kindly figure out for me the average slope, per mile, of what you have admitted is an ascent, rather than, as you first argued, a drop.

Pupil: Certainly, Sir. The figure you ask for is simply the quotient obtained by dividing the 13,288.8 feet of ascent, by the 2,500-mile course of the stream; and this will give the number of feet per mile that the river, shall I say, "ascends", from its source to its mouth. This quotient is 5.37712, and this, therefore, is the number of feet, per mile, which the Mississippi runs "up-hill" throughout its course.

Tutor: But your original supposition was that in its 2,500-mile course, from north to south, the bed of the river really dropped 1,680 feet. Now I ask you to be kind enough to figure out for me what its downward slope would be, per mile, on the hypothesis that it really ran a "down-hill" course, For I think that we are entitled to know just how great is the actual discrepancy between your supposition and the reality. This we shall obtain only when we have added together the two slopes.

Pupil: If the river really descended, by force of gravity, as I supposed it did, from an elevation of 1.680 feet, to the sea-level, in a 2,500-mile course directly south, The slope per mile, would be the quotient obtained by dividing 1,680 by 2,500. This quotient is 0.672 feet, and this is the slope in each mile. The total discrepancy is then 5.37712 plus 0.672 which is 6.04912 feet to the mile.

I really am surprised, Sir, that I feel a little chagrined to have to admit that I have been worsted in the argument. But it is interesting to have you point out a case where I am obliged to admit that even free-running water must actually run, in a sense, "up-hill"; and that it runs "up-hill" at such an astonishing slope.

But this sets me to musing, and in my dreaming sets me to wondering whether or not there may be, somewhere on the earth, a free body of water, whose natural tendency to gravitational flow is quite annulled by having the two forces, that of gravitational attraction, and that of centrifugal force, so exactly counterbalanced as to prevent the occurrence of any natural flow at all.

Tutor: It is not inconceivable that there may be, on the surface of the earth, some free body of water, in exactly this singular predicament. But I do not, at this moment, recognize any particular free bode of water which would appear to stand in this delicately balanced situation. At all events, were such a free body of water to be discovered, this would constitute, as Mr. Kipling would say, "another story".

Mathematical analysis and narrative by:

Dr Roger Terry Bacon
New Haven, Conn
Circa March 1935

Copied from original by:
My Father

My Future Hideaway

I have been building this office in my attic for forever, it seems. The goal was and is to have my personal hideaway when the estrogen level gets too high in the rest of the house (a wife and two daughters do that occasionally). The delays are two-fold:

1. I tend to have a number of projects going on at once - so when the others get urgent, this one slips.
2. I decided to go with a pretty manually intensive design - as you can see -- loads of knotty pine panelling - all in 5 inch boards, and built-ins galore. The crazy angles don't help either.
   

Here is a view of the library area:
Now a view going the other way:

The dormer on the right, just in front of the table saw has a shed roof, so the lines are relatively straight-forward. The dormer on the left has a slanted roof, so I have slants going both ways. I'm not a professional carpenter by any means, so that was a bit of a challenge to get the cuts right.

I haven't been up there to do anything for too long, but I'll try to keep you'all posted as I make progress.

Most of the time, I find working on this to be fulfilling in a way that much of my other work (software engineering) is not. The act of constructing a physical space that can be touched and smelled reaches a core need of mine. Maybe it is because I grew up working side by side with my father on his furnature refinishing projects. I suspect more has to do with heritage. My grandfathers were a carpenter and a general contractor. They lived this business that I dabble in. Perhaps I have a little sawdust in my blood as a result.

Great post on Evangelicalism

Michael Lee has a solid post on why he is (still) an Evangelical. I really appreciate his reminders on the left / right boundaries of interpretation of Scripture. His emphasis on this being a 'big tent' is right on.

Aly Hawkins' suggestion that we find some other way of expressing 'infallibility' has real potential to open up some good discussion, too.

I get a taste of the Good Life and Meet a Monster

I had the good fortune to be invited to a special recognition event that IBM throws every year. It was quite a show. We were wined, dined, and entertained for three solid days in a first rate setting in Florida.

We drove up to the hotel in our rental car and three men approached the vehicle, opening doors and trunk, and whisking us and our possessions into the lobby. Our registration may have taken 30 seconds and after that, we had no more cares than to decide what to wear when. Everyone was, “How is your stay going? Is there anything I can get you?”

It was sweet! Really sweet! Not a care I the world besides, “What should I wear to the next event.”

Getting back to the airport at Miami was a bit of a shock – suddenly we were schlepping our own luggage through the lines and dealing with all our own logistics again. Yuck.

I realized just how easily I could become a creatures of the pampered culture that turns so many decent human beings in to monsters. Imagine living your life in a world in which you never worry about dragging luggage out of your car (or even driving it if you don’t want to). A world in which all of the logistical headaches we take for granted simply never happen unless someone screws up. Suddenly, the vicious lashing out at rude service personnel you hear about occasionally makes a little more sense – at least it’s feasible in light of what is defined as “normal” for these folks.

My pastor has been talking about the nature of God’s spirit recently – both mighty and holy. In other words, able to do anything and only wanting to do that which is good. The upper class has enormous power simply by virtue of the money that they command. Without the desire to do good all the time, they can end up becoming tyrants. And the slope is very slippery. My party had a couple of little logistical glitches while we were at this event, and we were pretty tough on our hosts about it. In our real world, we wouldn’t dream of such a reaction.

The place this slippery slope is most evident for me is parenthood. I have all the power and a lot less of the holiness than my daughters need. It is so easy to behave badly and justify it after the fact. I pray that God will transform me to more and more act and think for good.

the DaVinci Code dopiness

RLP has a great post on why the Church is completely missing the point by coming out against the DaVinci Code phenomenon here.

This silliness has a long history in the Church, and seems to have something to do with a fundamental loss of perspective. I remember that during my college days the riotous Monty Python movie, "Life of Brian" came out. I will never forget the little exchange after Brian wakes up to find a massive crowd of followers outside his bedroom:

Brian: "You are all individuals!"
Crowd: "Yes. We are all individuals!"
Some guy: "No, we're not!"
Crowd: "SHHHHHHHH!!!!"

But I digress. My church, and much of the Church at large, loudly protested that this movie was anti-Christian and picketed it. I ended up crossing my own church's picket line so I could find out what all the hoopla was about - and spent most of the movie rolling around in the aisle.

Mind you, the XXX version of Cinderella had been playing in the very same movie theatre a few weeks earlier, with no protestation from the church or the Church.

What is that about? (I am not advocating our drawing attention to all that other stuff by picketing it, just calling out the completely different response the same church had to these two movies.)

Perhaps it is because we take ourselves a little too seriously. If anything comes out that threatens our precious monopoly on the truth, we react vociferously. Perhaps we should read the prophets to figure out what we should be getting noisy about. They talk about righteousness as revealed by worship of the true God (not idols) and care for the poor and the stranger among us.

Today, the Church is as embroiled in the power politics of the day is it ever was while the Reformation was brewing. As a result, it has largely lost its prophetic voice -- the voice in the wilderness proclaiming, "The Kingdom of God is near!". Instead, we protest pop culture events like DaVinci.

The good news is that God's truth is so much bigger than our perception of it. We cannot own it, and at some level, defending God's truth is absurd, given that we can't even get our arms around it all. Instead of defending God, let's seek Him.