The Hyperbolic Lens

My interest in photography has led me off into some research into lens design. Why are camera lenses so darn complicated?

There are lots of issues, but the one I'd like to focus on is the shape of the lens. The shape of two objects rubbed against each other gradually becomes a sphere and a spherical hollow to match it. Most lens grinding is based on this, and so the surfaces of lens elements is a composite lens design are either flat, convex, or concave parts of a sphere.

Unfortunately, a sphere is not the perfect shape to focus light. That shape is a hyperbola. This has been known since the 17th century, and several great thinkers have tried to come up with ways to  create hyperbolic surfaces on lenses.

A wonderful monograph on the subject is "Descartes And The Hyperbolic Quest", by D. Graham Burnett. (http://books.google.com/books?id=oAYNAAAAIAAJ&lpg=PP1&pg=PA93) I've linked to a page showing the solution of Christopher Wren, the great architect. I really like this image!

Now some of you might be thinking that this solution is cheating. Sure, you can create a hyperbolic surface if you've already got one handy, in the form of the hyperboloid. All you've done is push off the problem one step. But creating the hyperboloid is easy, as one of the other illustrations shows. If you have two skew lines, and rotate one around the other, you trace out the surface of a hyperboloid.

Even today, manufacturing costs dictate that most lens elements are spherical. Hyperbolic lenses are used in specialty applications such as copying machines. Aspherical elements are incorporated into sophisticated lens designs for cameras, but they are not to my knowledge hyperbolic.

Talisman: the Game

When my son Daniel was 9 or 10, we played the board game Talisman with his friends. It was a lot of fun, and I was sad when I found out that it was no longer in print.

Well, I am sad no longer!

While browsing the ever enlarging Games section at Barnes and Noble, I noticed that Talisman is back on the shelves in a handsome new edition. Yay! As with the version we played, there are several add-ons for it as well. I didn't see Talisman Dungeon on the shelf, but it is available through Amazon.

According to reviews on Amazon, the rules have been tweaked slightly from the classic 2nd edition. For example, the mighty Prophetess no longer dominates the game as a character. Looks like a new generation is going to get hooked by this game.

Review: First Life, by David Deamer

Just finished David Deamer's First Life.

The main point of the book is to expound on Deamer's theory that lipid based vesicles were important to the Origin Of Life (OOL). Lipids are the oils and fatty acids we use today as cell walls in our bodies. They are 'polar' molecules, with a different charge at each end of the chain of atoms. This makes one end attracted to water and the other end repelled by water (hydrophobic). When dispersed in water, the hydrophobic ends wind up crowded together, while the hydrophillic ends stick out, so the lipid molecules naturally form surfaces that are two molecules thick. Under the natural physical forces found in water, the most stable shape for these layers is a sphere -a vesicle or bubble.

A key property of these vesicles is that small molecules can work through the layer separating the inside from the environment, but a large molecule inside can't get out. Therefore, a chemical reaction that built up large molecules from small ones inside the vesicle would build up a concentration of large molecules far faster than the same reaction happening in the open, where the reaction products would get mixed and diluted quickly. It just so happens that life is full of these kind of reactions.

Having read a lot of pop sci literature (Zimmer, Ridley, etc.) it shows that Deamer is a working scientist, not a professional writer. At times the book felt padded by reviews of everything from the Big Bang onward, and an explanation of what name comes first in an article reference. And there was a fair bit of chemistry porn, in which the author gives a bit too much detail on lab procedures.

Deamer's take home message is that OOL requires some minimum complexity, and most scientists are not willing to attempt the messy experiments necessary. In a football analogy, grant funded science is a "three yards and down" ground game, and OOL needs some Hail Mary passing. 

His last chapter describes his ideal update of the famous Miller-Urey experiment, which showed that a combination of small molecules and energy could lead to biologically important molecules such as amino acids. It's big, throws a lot into the mix, and would cost a couple million dollars to run. At the same time, he acknowledges that it would have to run over and over, with multiple changes in atmosphere, temperature, pressure, etc. which would increase the cost. But at the same same time, he mentions that robotic experimentation runs hundreds of experiments at the same time. However, the two ideas never connect - that you have to reduce OOL experiments to something that can be done on a microfluidics chip in large batches.

Recommended. 

Vaclav Havel, RIP

Vaclav Havel was one of the great men of the 20th Century. Like Nelson Mandela, he was jailed by the regime that he eventually replaced. He cared deeply for his country and the world.

Last night, I went with Blanka to light candles for Havel at Narodni Trida, the memorial to the Velvet Revolution that toppled Communism in Czechoslovakia. We walked around the old part of the city, and enjoyed the sites of the Christmas Market in Old Town Square. We eventually wound up in Wenceslas Square, another important site in the history of Havel and the Velvet Revolution. There, the statue of St. Vaclav had been turned into another candle draped memorial. I tried to explain to some French tourists what was going on, why students were reading from Havel's essays to the crowd. We lit another candle and returned home.

Remember him. He mattered.

Public reading by SFABC Writers of the Weird at The Fine Grind

Congratulations to the Science Fiction Association of Bergen County's Writers of the Weird! Thanks to the organizational energies of Phil DeParto, the group of published and aspiring writers held a group reading at The Fine Grind (http://www.thefinegrindcoffeebar.com/) this past Sunday afternoon.

The Fine Grind gave us a warm welcome, with a space reserved for the expected group of writers and cheering section. We had six authors present seven short stories, tied together with introductions by Phil, and a pitch by John Adamus for the North Jersey Writer's Meetup group. John made his group sound awesome, I might check it out since it meets in my favorite Barnes and Noble in Paramus!

I enjoyed reading my own story, Molybdenum, for the group. I hope others enjoyed listening as much as I enjoyed reading!

If we repeat the experience (perhaps at a public library), I'll try to blog it in advance.

World's Best Computer Chair

Staples Varretta high back mesh chair. SKU 865004. 'Nuf said.

The Facepalm of Compensation

Readers here and elsewhere will know that Dr Granville Sewell thinks there is a problem with biology and the Second Law of Thermodynamics. He has written several versions of an argument claiming that the Second Law poses a problem for biology, especially the origin and development of life on Earth.

Dr Sewell is not alone in this concern. Generations of creationists have had this concern. However, the answer given is so obvious that even creationist bastions such as the Institute of Creation Research no longer recommend using this issue in debates. That answer is that SLoT only applies in closed systems, and the Earth is not a closed system. The surface of the planet receives energy from the Sun, energy from its core (from radioactive decay and residual heat of friction) and these sources overcome the trend towards higher entropy.

Dr Sewell has attempted to avoid this answer by arguing in several ways. One is to try to apply SLoT to an open system. Another is to attack the idea of compensation that appears in some elaborations of the answer given above.

Dr Sewell's argument is that even an open system MUST rely on passage through the boundary of anything that that is going to increase inside the system.

If an increase in order is extremely improbable when a system is closed, it is still extremely improbable when the system is open, unless something is entering which makes it NOT extremely improbable.

The above quote is from Dr Sewell's Can ANYTHING Happen in an Open System?

One of the biggest problems with this argument, which Dr Sewell has called his controversial tautology, is that it expands SLoT to cover any diffusion problem at all. We can break this down into two sub-problems, expanding SLoT and treating the issue as a diffusion problem.

Can SLoT be expanded to cover anything beyond thermal entropy? Obviously, Dr Sewell says yes here, and in his invocation of "X-order" in the AML paper. At the same time, in a later article he criticizes Dr Dan Styer for allegedly applying SLoT broadly. He has perhaps learned something, since most scientists would agree that you can't, willy nilly, go applying conservation laws wherever and whenever you feel like it.

Secondly, not all of the universe is a diffusion problem. Let's say that my open system of choice is a crowded bar, and I'm interested in the amount of whiskey in the bar as whiskey diffuses across the boundary I've drawn around the bar. Is the amount of whiskey in the bar solely dependent on the amount crossing the boundary? Obviously not, it also depends on the rate at which it is consumed within the bar, the rate at which sober customers (who are not, themselves, made of whiskey) arrive, and the rate at which inebriated customers (partially made of metabolized whiskey) exit.

What is true of whiskey is also true of cosmic rays, high energy photons, radioactive atoms, and many other things. They can enter through a boundary around an open system, but there are significant transformational processes that can occur within the system as well. So Dr Sewell's controversial tautology is neither controversial nor a tautology. It is simply wrong.

This is why Dr Sewell's argument fails at explaining photosynthesis. Similar to the crowded bar, we draw the boundary around the cell wall of a cyanobacteria. Light enters at one frequency, strikes various molecules, is absorbed, its energy is changed into thermal motion and the potential state of various electrons, sugars are produced and eventually a low energy infra-red photon exits the boundary. Sugar did not enter across the boundary. A low energy photon did not enter across the boundary. The quantity of high energy photons inside the boundary has not increased.

This brings us to compensation. We can say that the exit of the low energy photon "compensates for" the sugar. There is an energy difference between the high energy photon that came in through the boundary, and the sugar molecule. If we add in all the thermal motions and escaped photons, we should be able to make the energy equation balance.

But not the order equation. Even though the sugar molecule has lower entropy, the universe as a whole is worse off.

Dr Sewell seems to think that compensation can happen at a distance. It doesn't. Dr Styer says in his article:

Presumably the entropy of the Earth’s biosphere is indeed decreasing by a tiny amount due to evolution, and the entropy of the cosmic microwave background is increasing by an even greater amount to compensate for that decrease.

Does this mean that Dr Styer is engaged in some magical thinking that life here makes the CMB colder via some spooky action at a distance? No. Dr Styer previously wrote:

The Sun heats the Earth through electromagnetic radiation  largely in the visible and near-infrared bands . The Earth radiates electromagnetic radiation largely in the far-infrared band into outer space, where it eventually joins the cosmic microwave background.

So it is clear that the CMB effect Dr Styer is referring to is based entirely on the passage of sunlight through the biosphere of the Earth. Yes, the CMB observed by someone distant from the Earth will have higher entropy than if the same sunlight had struck a dead planet of the same size and location.

Compensation is not action at a distance. You can always trace the interactions back to the point where one high entropy and one low entropy component were created, and see how the high entropy component escaped the open system. In considering the overall accounting for entropy in the closed system (the Universe) within which our open system is embedded, the escaped component is compensation for the low entropy component it left behind. It is only in this overall perspective that we need to worry about compensation, since it is only in this closed system that we need to be concerned with SLoT.

These misunderstandings and logical fallacies have led Dr Sewell to embarrass himself once again, by writing to the journal that published Dr Styer's article, the American Journal of Physics. In a blog entry on Uncommon Descent, Dr Sewell calls AJP a "major physics journal". In fact, it is a journal for articles related to teaching physics to high school and college students. The rejection message he received makes that clear, as well as making clear the overall high crank science level of his writing.