## The pee versus in-pee question

Greetings from America’s fourth-best city, Seattle, where I’m attending the STOC’2006 conference. I arrived here yesterday from America’s third-best city, Boston, where I visited MIT for a week and gave a talk about The Learnability of Quantum States. (I’ll leave the best and second-best cities as exercises for the reader.)

Since tomorrow’s my birthday, I’ll consider myself free to blog about whatever I feel like today (as opposed to most days, when I blog about whatever the invisible space antelopes tell me to). So without further ado, here’s a question that bugged me for years: why do we need to urinate on a regular basis?

I mean, I understand solid waste perfectly well, and I also understand the need to get rid of urea and the other waste products in urine. But why constantly excrete water, something that humans and other animals regularly die from not having enough of? Why not store the water in the body until the next time it’s needed? From a Darwinian perspective, a regularly-vacating bladder would seem to make as little sense as a toothless vagina.

And yet, after minutes of diligent Wikipedia research, I’ve pieced together what I believe is a complete solution to this pee versus in-pee puzzle.

The short answer is that conserving water, rather than just pissing it away (so to speak), is exactly what our bodies try to do. But one needs to remember that, while feces comes directly from the digestive tract, urine is collected from waste products in the bloodstream. In particular, the kidneys contain permeable membranes whose job is to let wastes like urea through, while keeping the useful stuff (like red blood cells) out. However, as with any other filtration process, it’s difficult or impossible to keep all the water on one side of the barrier.

So what the body does instead is to let the water through, then slowly absorb it back into the bloodstream as needed. That’s why your urine is darker (more concentrated) if you’re dehydrated than if you aren’t. At some point, though, it presumably becomes infeasible to extract more water from the bladder without also letting the toxic wastes back into the bloodstream.

Now, I know what you’re thinking. You’re thinking, “why isn’t my urine always dark? In other words, why don’t I always absorb as much water as possible back into my bloodstream, whether I’m dehydrated or not? Why not save the water for a (non) rainy day?”

Aha, I’ve got an answer to that one too. Besides excreting wastes, another function of urine is to maintain a homeostatic balance between water and sodium in the blood. If there’s too much water (say, because you just drank six beers), your blood will be too thin, which can cause brain damage (completely apart from the other effects of the beer). Ideally, your body would store the excess water separately from the blood — and again, that’s exactly what it tries to do, but your bladder is only so big.

In summary, if you think through what my “in-pee” solution would actually entail, it turns out to be almost identical to the “pee” solution that Nature actually adopted. One might even say that pee = in-pee.

[Note for harping relatives: now do you understand why I didn’t go to medical school?]

### 36 Responses to “The pee versus in-pee question”

1. Jack William Bell Says:

Hey Scott! Welcome to the center of the universe. And, happy birthday!

How long are you going to be in Seattle? Long enough we can get together and experiment with your beer/homeostatic balance thesis some night this week? (I’m leaving for a conference in Madison on Wednesday night.)

jackb (at symbol here) sff (dot here) net

2. Scott Says:

Jack: I’m staying at the Red Lion on 5th Avenue. If you want to meet me here for a beer, email me (scott at scottaaronson dot com) and we’ll fix a time. Same goes for any other readers from Seattle.

3. Anonymous Says:

Too bad, I’m still in Water-loo. But I’ll celebrate your birthday tomorrow!

4. Anonymous Says:

Here in Israel we celebrate Scott-day twice a year. Once in regular cities and once in cities surrounded by walls.

5. Anonymous Says:

I found that last comment hilarious, but that’s probably because I didn’t get the real joke. For some reason, jokes that just don’t make any sense can be very funny sometimes.

Oh, and happy birthday Scott.

6. John Sidles Says:

Scott, please consider yourself (and any of complexity theorists who are interested) to be invited to our Quantum System Engineering Lab on the UW Campus — just call 206 543 1720, anytime Monday, for directions.

Our QSE Lab is in the Mechanical Engineering Building, Room 119. Knock loudly, because the vaccuum pumps are noisy! Our QSE Group meeting runs at 1:00 pm on Mondays, and this is a very good itme to visit, but please feel free to come by anytime that is convenient for you.

On the docket at Monday’s QSE Group Meeting is our recent realization that the manifolds on which we do quantum model order reduction (MOR) are Kahler manifolds, and in particular that quantum MOR Kahler manifolds have much in common with the Calabi-Yau manifolds of string theory.

This realization has been a considerable morale boost for us quantum engineers. Until a couple of weeks ago, we had been feeling kind of dumb for being unable to, e.g., draw good pictures of our quantum MOR manifolds, or calculate their curvature tensors and global topological characteristics.

Now we are beginning to appreciate that everyone (meaning, quantum system engineers, differential geometers, complexity theorists, cryptographers, and string theorists) finds the differential geometry of Kahler manifolds to be a tough subject that touches many fields of inquiry. (Remark: this emerging conceptual unification is what we Seattle folks hypothesize that Mike Nielsen is up to during his present non-blogging haitus).

Now to discuss Scott’s thread topic, which we engineers think is truly of planetary consequence: pee-pee.

As our UW medical students know, it’s not so easy to keep water in while letting wastes out! Gerbils and other desert mammals excrete nitrogen wastes in the form of (solid) uric acid instead of (dissolved) urea; this conserves water.

Oddly, terrestrial plants have never learned to inspire CO2 without losing water. They do their gaseous exchange through “stoma” (microscopic mouths on leaves).

If this CO2 exchange process were redesigned from scratch to avoid water loss, then “make the deserts bloom” could become a literal reality.

So let’s do a simple “Fermi calculation” on whether our entire global civilization could, without violating physical law, run wholly on photosynthetic energy derived from this ultimate version of dry-land farming.

The practical physical limits to photosynthetic thermodynamic efficiency are between one percent and ten percent. Taking three percent efficiency as the geometric mean, taking the solar flux as averaging 100 watts / meter^2 (much higher at noon, much lower at midnight), and assuming the six billion human beings on the planet each need five kilowatts of CW power to be happy (which just my wild-ass guess; 5 kW being enough power to brew coffee, run a laptop, keep the Internet powered up, and drive a small car for couple of hours a day, with some power left over — gee, what else does a civilized person require?), then the required land area is about (3200 km)^2.

This is about the size of the Greater Sahara Desert.

So yes, the presently-blighted nations of northern Africa could potentially be the OPEC of the 21st Century. Also, this would partially address the global warming problem (I say “partially” because the albedo of northern Africa would be darkened).

Therefore, as far as us quantum system engineers are concerned, there is a fairly obvious progression between the geometry of Kahler manifolds, global warming, energy production, and “pee peee”, as follows:

Kahler manifolds (in all their manifestations)
-> reliable spin imaging design engineering
-> desktop-scale atomic imaging technologies
-> a global-scale molecular biome survey
-> the advent of ab initio system biology
-> dry-land biomass production

Needless to say, this technology chain is not what we discuss at our QSE Group meetings!

To the uninitiated. the engineering topics that our group meetings focus upon can seem staggeringly mundane and obscure. E.g., discovering that there is an accidental resonance of the seventh harmonic of our turbopump with our cantilever frequency has been a big breakthrough for us!

Like the infamous “pogo” instability of the Saturn V booster, this accidental resonance (and innumerable similar engineering challenges) is not a fundamental physics issue, but these engineering-type issues are not any less showstoppers for not being fundamental.

So if you don’t mind our QSE Group’s Toyota-style obsession with the “unrelenting pursuit of engineering perfection”, please feel welcome to visit!

Sincerely … John Sidles

7. Scott Says:

I found that last comment hilarious, but that’s probably because I didn’t get the real joke.

Nor did I. If it’s a religious reference, it was too obscure for me.

Oh, and happy birthday Scott.

Thank you!

8. Anonymous Says:

Here in Israel we celebrate Scott-day twice a year. Once in regular cities and once in cities surrounded by walls.

cities surrounded by walls makes me think of fortified settlements, but I don’t see the relation to you, Scott. Happy Birthday.

Happy birthday Scott.

10. John Sidles Says:

PS: upon checking the above Fermi estimate against actual US energy consumption, we find that total as-delivered energy consumption in the US, including all economic sectors (transportation, industrial, residential, and commercial), is about 70 quadrillion BTUs.

The equivalent per-capita CW power is 8 kW, which is not wildly different from 5 kW Fermi estimate of the previous post.

So, that’s how much energy it takes to run a civilization that is rich enough to support complexity theorists … seemingly a useful number to know.

But gosh-golly, if running even one Beowulf cluster pushes you over your per-capita energy quota … then maybe the time is foreseeably arriving, when the energy costs of the computation sector will be comparable to the traditional four sectors of transportation, industrial, residential, and commercial?

To say nothing of home entertainment systems with 72-inch plasma displays, driven by quad-processor cpus! How much power do these things require, anyway?

Hopefully, it will turn out that P==NP, for reasons of energy-saving. :;

11. Mom Says:

Happy 25th Birthday, Scott!I seem to remember when you were a toddler you wanted to be an “eye doctor!” And all the harping relatives have been satisfied now that you have the Dr. in front of your name, even if it’s not a medical doctor. By the way, I don’t think you ever took a biology class in your two years of high school. Did you take one in college?

12. Scott Says:

By the way, I don’t think you ever took a biology class in your two years of high school. Did you take one in college?

No.

Do you plan on writing any books like autobiography or your experience with computer science etc.? Or is it too early?

14. Scott Says:

Nagesh: Yes, I’m currently putting the finishing touches on my autobiography. Perhaps you can help me choose a title. I’ve narrowed it down to the following three —

SCOTT: Straight From The Lymph Nodes

SCOTT: The Extremely Nerdy Years (1989-2005)

SCOTT: More Than A Paper Towel

If you are really serious,

among the three I would suggest.
SCOTT: The Extremely Nerdy Years (1989-2005)

Life is extremely time dependent and those were probably the crucial years in making what you are.

The other two did not quite make sense to me:)

16. Scott Says:

Nagesh:

1. I was not serious.

2. Dude.

Cool! What do you mean by your point 2?

18. Who Says:

Just happened to see this on arxiv
and it sounded nice, so I wanted to let someone know about it:

http://arxiv.org/abs/quant-ph/0605181
The BQP-hardness of approximating the Jones Polynomial
28 pages, 6 figures, comments are welcome!
Following the work by Kitaev, Freedman and Wang, Aharonov, Jones and Landau recently gave an explicit and efficient quantum algorithm for approximating the Jones polynomial of the plat closure of a braid, at the $k$th root of unity, for constant $k$. The universality proof of Freedman, Larsen and Wang implies that the problem which these algorithms solve is BQP-hard. The fact that this is the only non-trivial BQP-complete problem known today motivates a deep investigation of this topic.
A natural question which was raised in Aharonov et al is the following. …[snip]… To do this we introduce some new techniques for analyzing universality in quantum computation, which enable us to apply Solovay-Kitaev indirectly. As a side benefit, we reprove the density theorem of Freedman, Larsen and Wang, using quite elementary arguments; this hopefully sheds light on the reason that these problems are indeed quantum-hard.”

of course it would drive you crazy if everybody did this all the time. but this is meant to be friendly. it sounds good and I dont know anybody else to tell about it====and I dont usually bug you with stuff.

19. Scott Says:

Yeah, we heard about that paper in Dorit’s talk at STOC today.

20. Anonymous Says:

I think we have by now successfully concluded that Nagesh is not a rabid Scott fan, but rather one of the most ingenuous trolls in the admittedly short history of blogging.

Cities Surrounded by Walls:

Purim is celebrated annually on the 14th of the Hebrew month of Adar. (In cities that were walled in the time of Joshua, including Jerusalem, Purim is celebrated on the 15th of the month, known as Shushan Purim).

(from purim in wikipedia)

The description in Hebrew Wikipedia is funnier: [my translation — e.v.]
“in ancient cities where there is doubt if there was a wall since the days of Yehushua Ben Nun Purim is celebrated in both days, due to doubt. And one does not cless on reading the scroll except on the 14th, since this is the time of reading for most towns. Tiberius is a special case, since the doubt about it is not about its being surrounded by a wall since the days of Yehushua, but if the Kinneret [Israel’s sweet-water sea — e.v.] counts as a wall of the town. There is a detailed discussion and different views about he who travels in the days of Purim from a town which is not surrounded by a wall to a town that is, and vice-versa. He who does so should ask how to behave”

Now we’re truely Shtetl-Optimized.

22. Scott Says:

23. Dr. Vector Says:

Glad to see you’re once again dipping into the ‘dirty parts’ of biology. This could get to be a second career for you. One of my favorites along these lines is: why do we have thick hair only on our heads, in our armpits, and around our dangly bits?

24. L Says:

Camels do a better job of storing water in their blood and cellular fluids than humans. Apparently, they can tolerate 30% fluid loss (or so I just read on the web somewhere).

But what about the possibility of a water-only tank, separate from the bladder, in the in-pee solution? Is it clear that that is not feasible, Dr. Aaronson?

25. John Sidles Says:

Dr. Vector said: “Glad to see you’re once again dipping into the ‘dirty parts’ of biology. This could get to be a second career for you.

I second Dr. Vector’s motion! Because, where else, other than systems biology, are new jobs for complexity theorists going to be created?

The following Fermi estimate (which is admittedly somewhat tongue-in-cheek) is instructive.

Let’s hypothesize that one person in one ten thousand is called to be a complexity theorist, and that each complexity theorist publishes three articles per year. On a planet with six billion people, this will yield about six hundred thousand practicing complexity theorists, who will publish about 1.8 million scholarly articles per year.

The net planetary output of complexity theory, therefore, is destined to stabilize at about five thousand new theory articles each day. Hey, reading the arxiv servers obviously will be a full-time job! (and thank goodness, Sunday is a day of rest).

Now, only about one percent of global scientists and engineers will be complexity theorists. So in this same Fermi scenario, the net yield of science and technology articles will be about five hundred thousand new articles per day.

That’s a lot of reading … about seven new articles per second. As far as I can tell, the current rate of publication of new science and engineering articles is ‘only’ about ten thousand articles per day … about one every seven seconds.

Of course, all this research will require a massive increase in research investment. Assuming each new article costs about \$25,000, the required annual planetary R&D budget works out to be about five trillion dollars. And assuming this is about 1% of planetary GNP, the planetary GNP will have to be about five hundred trillion dollars.

For comparison, the present planetary GNP is about thirty trillion dollars, so basically, we are talking about growing the planetary GNP by a factor of about fifteen.

As Crocodile Dundee would say … “Call that a planetary budget? Now this is a planetary budget!”

Now, what kind of science and technology endeavor could sustain and unify this stupendous informatic rate and its equally stupendous requirements for global economic investment and growth?

Complexity theorists have the answer! Namely, there are exponentially many “natural” problems in NP, each of which is surely worthy of a scholarly article.

And system biology is, of course, an unbounded source of NP problems that–by definition—are natural.

Gee, the numbers that our Fermi calculation are producing are undeniably scary, but then, maybe all numbers are scary that describe a planet that has six billion people on it.

And yet, to a complexity theorist, these same Fermi numbers become less scary upon reflection. They suggest that complexity theory will provide a primary avenue for forestalling the forty-five year-long “flattening” that the physics community has been struggling. The possibility of flattening is something every young scientist and engineer should think about, IMHO … because it can happen to any field.

Now, there is a perception that biology problems are inelegant, but as a professor of medicine myself, let me assure you that, to the contrary, elegant problems are everywhere in medicine and biology.

E.g., yesterday afternoon our Quantum System Engineering Group held our first “Applied String Theory” seminar.

As a background, it turns out that the quantum state space associated with our imaging simulations of the spin state of the anti-HIV drug nevirapine has a Kahler-type metric structure.

This reminds us engineers of the following historical precedent: back in the late fifties and early sixties, the largest single use of computer cycles was (according to my system engineering colleagues) Dantzig’s simplex algorithm — people were spending all their computer cycles wandering around the edges and vertices of convex hulls, solving natural practical optimization problems. Researchers either published these solutions, or used them to make money, or both.

Today, and for similar reasons, we quantum system engineers are beginning to perceive that during the next few years, a geometrically increasing fraction of computer cycles will be spent travelling along the natural geodesics of Kahler manifolds, in order to efficiently simulate broad classes of quantum systems.

Thus, we quantum system engineers are beginning to perceive — but as yet, only dimly — that Kahler manifolds are to quantum simulation what convex hulls are to classical optimization theory, namely, a natural mathematical arena in which both fundamental and applied work by many science and engineering disciplines is consilient. So it is good news that these Kahler manifolds have a complexity sufficient to sustain enterprises of the above scale.

The above Fermi goals amount to an overall planetary goal of creating a billion new jobs. … surely a daunting and elusive goal. And yet, isn’t this the scale on which planetary circumstances require that we all be thinking?

Hmmm … I set out to write a humorous post, in tribute to Scott’s wonderful mix of humor and elegant mathematics in The learnability of quantum states. But I have to confess, and apologize, that maintaining a sense of humor on a crowded planet gets tougher as you get older! Optimism, however, does survive … you young folks can take comfort in that.

26. Scott Says:

But what about the possibility of a water-only tank, separate from the bladder, in the in-pee solution? Is it clear that that is not feasible, Dr. Aaronson?

Well, no — you mentioned camels, and that’s exactly what they do. But I guess for primates the Darwinian costs of a back hump would outweigh the benefits.

27. Scott Says:

John: Could I ask you to keep your comments either shorter, more relevant to my posts, or both?

Thanks!

28. Anonymous Says:

So Scott, Jack, how was your date?

29. John Sidles Says:

Scott, you are quite correct, and I do apologize for that lengthy post … perhaps my wife made the coffee too strong this morning. I’ve considered starting my own blog, but then, does the world really need another blog?

Your “Shtetl-Optimized” is IMHO an outstanding creative effort, in reflection of its consistent quality, humor, and not least, durability. Thank you very much.

30. Anonymous Says:

Your “Shtetl-Optimized” is IMHO an outstanding creative effort

What it is with Scott that inspires this bizarre fanboyism? Maybe this place is better than the norm, but I mean, let’s try to keep things in perspective. Painting the Sistine chapel was an “outstanding creative effort.” Writing a decent blog entry on some random topic every other week is, well, you figure it out.

31. Scott Says:

So Scott, Jack, how was your date?

32. John Sidles Says:

How tough is it to write a regular blog? Darn tough … Mark Twain wrote eloquently about this struggle. I’m sure that some weeks, Scott feels the same as Twain. Which is why he deserves our thanks and appreciation.

33. Anonymous Says:

And what could that be? I guess that’s a prohibited question.

34. L Says:

Sorry, I thought you knew that (apparently, according to multiple sources on the web) camels don’t store water in their humps (except for what is part of the fat, which is what is stored there). It’s blood and (not fat-cell) cellular fluid that stores most of the water.

35. Scott Says:

Sorry, I thought you knew that (apparently, according to multiple sources on the web) camels don’t store water in their humps (except for what is part of the fat, which is what is stored there).

Interesting! The obvious next question is: why don’t they store just water in their humps? Is the fat more useful to them, or is there something evolutionarily infeasible about a water hump?

36. Lloyd Says:

It’s clearly apparent that you’re a doctor of real science rather than that biological rubbish!
Nah, I’m just kidding, but seriously, even I could explain the need for regular urinating, and I’ve only been forced to take biology at a basic level since I was 3. (I’m now 16, and have just taken my final Biology exam, and will thankfully never be touching the subject with a 50 foot pole ever again).