A response to Duane on the importance of bitcoin as a new, decentralized currency. (This has been a fun running debate among friends over the last couple weeks.)
I read his recent post as claiming "decentralized is better." My response: "sometimes, but not always." Here's my reasoning.
Point 1: Money is a figment of our shared imagination. It has value because we all collectively accept that it has value. There's nothing particularly special about green paper, or gold rocks, or any given set of bits, except for the common knowledge that other people will also accept those currencies in exchange for goods and services. In that sense, the valuation of any currency is already "democratic" -- its real value exists in the minds of a distributed network of people. People were using rare stones as currency long before governments got involved.
Point 2: Enlightened self-interest leads us to centralize some of the responsiblity for maintaining currencies. One of the main threats to any currency is counterfeiting, so it makes sense to centralize responsibility for preventing counterfeiting to mints and enforcement agencies like the secret service. Another threat is inflation (or deflation), which is why every modern state with a large economy uses a central bank to manage inflation via the money supply. A third "threat" is transaction costs, which is why we use credit cards for so many things -- the artificial "currencies" maintained by these corporations are so convenient that they have displaced state-authorized currency in many transactions*.
Point 3: As a side-effect of centralization, governments gain some power to regulate other uses of money. (Note that governments, like currencies, are also a figment of collective imagination. The Constitution is law because we all agree that it's the law.) Thus, the imposition of taxes, tariffs, and embargoes; and continuing efforts by organized criminals to circumvent the system by laundering money. These things are not necessarily good or bad. They depend on whether we approve of the use of government power in those areas. By and large, I imagine most people approve of governments shutting down mobsters and sex trafficking rings. Using the same suite of tools for defense spending, planned parenthood, agricultural subsidies, "bailouts," etc. is more controversial.
On the whole, I'd argue that people are better off because governments have these capabilities at their disposal -- especially people living in places where government is reasonably transparent and accountable to its citizens. We're better off because we've decided to pay taxes for roadways, police stations, and schools. We're better off because the value of a dollar is reasonably stable. We're better off because corporations (especially publically traded firms) are forced to keep a strict accounting of their transactions. We're better off because the FBI and CIA can use financial information to crack down on terrorists and organized criminals.
Putting that all together, I see bitcoin as an attempt to float an unregulateable currency using P2P technology and cryptography. By construction, such a currency would make it very difficult for government to intervene in the ways discussed in points two and three. Although I don't agree with everything our government does**, I don't see compelling reasons to deny ourselves the ability to use those tools as a society. Together, we're made better off by careful use of centralized financial regulation and lawmaking. That being the case, bitcoin seems partly radical, partly old hat, and partly a step backwards.
*Semantic question: are credit cards a centralized or decentralized currency? What about frequent flyer miles? What about Subway sandwich discount punch cards? At some level, the labels "centralized" and "decentralized" are too blunt to be really useful. This seems related to Duane's comments about needing both more and less regulation.
**Nobody does. That's the nature of compromise.
Showing posts with label complex systems. Show all posts
Showing posts with label complex systems. Show all posts
Tuesday, April 26, 2011
Thursday, December 2, 2010
Arsenic-based life and autocatalytic sets
NASA has just announced the discovery of a new kind of extremophile bacteria. If I'm reading the (sketchy) early release info correctly, these critters use arsenic in their DNA, instead of phosphorus. This is a biggish deal because every other known life form uses phosphorus.
How big a deal? Setting aside shades of the Andromeda Strain*, people seem pretty underwhelmed. Partly it's a bait-and-switch involving the NASA brand: the microbe in question, Gammaproteobacteria GFAJ-1, isn't an alien visitor. It's a mutant strain of a run-of-the-mill terrestrial bug.
So the real question is: How surprised should we be that little GFAJ-1 managed to assimilate arsenic into its DNA? Or the converse: if it's so easy, should we be surprised that no other life form bothered to do the same thing?
Taking a conversational step sideways, this seems like a good moment to put in a plug for a really fascinating theory on the origin of life: autocatalytic sets. This theory--which I find persuasive--argues that life isn't rare or unexpected -- it's virtually inevitable. I can't find a good non-technical description of this underappreciated set of ideas online, so I thought I'd take a crack at it here . (My explanation is based largely on the opening chapters of Kauffman's At Home in the Universe).
The puzzle: all forms of life we know of are pretty complicated. There are a couple hundred cell differentiations in a human body; thousands of enzymes in a working cell; millions of base pairs in even the simplest DNA. (Prions and viruses, which are often simpler, don't count because they can't replicate without hijacking a cell's machinery.) With these kinds of numbers, the odds of getting the just right combination for life are astronomical. Try flipping 220 million coins until they line up with the base pairs in a single human chromosome. Practically speaking, it will never happen.
For most explanations for the origins of life, complexity is a stumbling block. We just got lucky, or God intervened, or maybe an asteroid seeded the planet to produce something capable of self-replication. There's a leap in the logic at the point where we try to explain the incredibly low probability of life emerging spontaneously from a lifeless chemical soup.
The autocatalytic theory turns this logic around: it argues that life exists because of its chemical complexity, not in spite of it.
The theory builds from three simple assumptions. First, some chemicals react; most don't, with roughly constant odds for any given pair of chemicals reacting. Second, chemical reactions produce new chemicals. Third, the number of possible chemicals is very large.
Thought experiment: suppose you find yourself in front of chemistry set containing a rack of n beakers, each filled with an unknown chemicals. Channeling your inner mad scientist, you begin mixing them at random. Suppose 1 in 100 pairs creates a reaction. How many total reactions should you be able to get out of your chemistry set?
If you have two chemicals, the odds of a reaction are just 1 in 100.
If you have three chemicals, you have three potential pairs, and the odds of a reaction are about 3 in 100.
If you have four chemicals, you actually have six potential pairs, so the odds of a reaction are a little better than 6 in 100.
At this point, exponentials start working rapidly in your favor. With five chemicals, you have 10 potential pairs, for a 9.5% chance of at least one reaction. Twelve chemicals gets you 66 pairs with 48.4% odds of at least one reaction. The deluxe 30-chemical starter kit has 435 potential pairs, with 98.7% odds of at least one reaction.
What does this prove? The number of likely reactions in a pool increases faster than the number of chemicals in the pool.
It keeps going, too. With 1 in 100 odds, you would expect to get about 4 reactions out of your 30-chemical kit. If each reaction creates a new chemical, you now have 34 chemicals in your pool, with correspondingly greater odds of additional reactions. Eventually, you pass a tipping point, and the expected number of compounds becomes infinite. If I've got my math right, it happens around 80 chemicals in this scenario, because the expected number of new reactions exceeds the number of reactions in the existing set. The more you mix, the more potential mixtures you get.
A quick pause: when we talk about chemicals, we're not talking about atoms in the periodic table of the elements. Except during fission and fusion, atoms themselves don't combine and react. Instead, we're talking about molecules.
In particular, organic molecules -- the ones that ended up supporting life -- fit this model very well. Enzymes, RNA, and DNA are all organic molecules. Believe it or not, a strand of DNA is one enormous molecule. Organic molecules are all built mainly from the same base atoms: carbon, hydrogen, oxygen, nitrogen, phosphorus -- and now arsenic(!) These atoms happen to be good at linking to form long chains. Because of the way these chains fold, they react with each other in often unpredictable ways. Most organic molecules don't react with each other, but quite a few do. And because the chains can get very long, the set of potential molecules made of CHONP atoms is essentially infinite.
Now getting back to the main story... We're halfway through. We've shown how simple rules for reactions can get you from a small-ish starting set to an infinite variety of chemicals to play with. It seems very reasonable to suppose that the primordial organic soup included enough organic reactants to pass the tipping point into infinite variety. But that just means a more flavorful soup. How do we get to life?
Setting aside the transcendental, life is defined by sustainable reproduction. A cell is a bag of chemicals and reactions that keeps working long enough to make at least one copy of itself. As part of the deal, the cell has to be in the right sort of environment, with whatever energy sources and nutrients are necessary.
Our cells achieve sustainability by using enzymes to catalyze other reactions. It turns out that the same logic that applies to pairs of reactions also applies to catalyzers: the probability of catalysts in a pool increases faster than the number of chemicals in the pool. Once you get enough chemicals, it's virtually certain that you'll have quite a few catalyzed reactions.
Here's the really nifty bit. As the number of catalyzed reactions in the set increases, eventually some of them will form an autocatalytic set -- a loop of reactions catalyzing each other. Reaction A creates the catalyst that enables reaction B, creating the catalyst for C, and so on back to catalyst Z that enables reaction A.
Based on the same logic we saw earlier, these loops always appear once the pool of chemicals gets large enough. They are typically long and complicated, cycling through a seemingly random group of chemicals among a much larger set of nutrients and byproducts. They tap nutrients and energy sources in the environment, increasing themselves the longer they run. In other words, autocatalytic sets look a whole lot like life as we know it.
I find this theory compelling. It takes the biggest objection to prevailing theories -- the inherent complexity of life -- and makes it the cornerstone of a different approach.
And as a bonus, it makes arsenic-based life forms seem very plausible. Given NASA's results, it seems reasonable to say that arsenic-based DNA is another unexplored evolutionary path for viable autocatalytic sets. Bill Bryson says it well in A Short History of Nearly Everything:
PS: Autocatalytic sets don't have much to do with the evolution/intelligent design debate. They propose a mechanism that could be responsible for jumpstarting evolution. So if you're comfortable with the idea that God would choose cosmological constants and direct evolutionary processes with some goal in mind, it probably won't bother you to add the idea that he would use chemical soups and catalysis networks along the way.
PPS: The main difference between an autocatalytic set and life as we know it is the absence of a cell wall. It's not hard to close the gap conceptually. Once a catalytic loop gets started, other loops usually form as well. At this point, competition and natural selection between autocatalytic cycles can kick in. If one autocatalytic loop happened to produce a hydrophobic byproduct (like a fat or lipid), it could easily act as a primitive cell wall. This kind of barrier would enable the autocatalytic loop to increase its concentration, and therefore its reaction rate. This kind of pseudocell would reproduce faster and very likely evolve into more sophisticated organisms.
*A ten word review of the Andromeda Strain: Typical Crichton--some interesting ideas; mildly annoying narration; mostly plotless.
** A wonderful book for putting some color on the messy process of scientific discovery.
How big a deal? Setting aside shades of the Andromeda Strain*, people seem pretty underwhelmed. Partly it's a bait-and-switch involving the NASA brand: the microbe in question, Gammaproteobacteria GFAJ-1, isn't an alien visitor. It's a mutant strain of a run-of-the-mill terrestrial bug.
So the real question is: How surprised should we be that little GFAJ-1 managed to assimilate arsenic into its DNA? Or the converse: if it's so easy, should we be surprised that no other life form bothered to do the same thing?
Taking a conversational step sideways, this seems like a good moment to put in a plug for a really fascinating theory on the origin of life: autocatalytic sets. This theory--which I find persuasive--argues that life isn't rare or unexpected -- it's virtually inevitable. I can't find a good non-technical description of this underappreciated set of ideas online, so I thought I'd take a crack at it here . (My explanation is based largely on the opening chapters of Kauffman's At Home in the Universe).
The puzzle: all forms of life we know of are pretty complicated. There are a couple hundred cell differentiations in a human body; thousands of enzymes in a working cell; millions of base pairs in even the simplest DNA. (Prions and viruses, which are often simpler, don't count because they can't replicate without hijacking a cell's machinery.) With these kinds of numbers, the odds of getting the just right combination for life are astronomical. Try flipping 220 million coins until they line up with the base pairs in a single human chromosome. Practically speaking, it will never happen.
For most explanations for the origins of life, complexity is a stumbling block. We just got lucky, or God intervened, or maybe an asteroid seeded the planet to produce something capable of self-replication. There's a leap in the logic at the point where we try to explain the incredibly low probability of life emerging spontaneously from a lifeless chemical soup.
The autocatalytic theory turns this logic around: it argues that life exists because of its chemical complexity, not in spite of it.
The theory builds from three simple assumptions. First, some chemicals react; most don't, with roughly constant odds for any given pair of chemicals reacting. Second, chemical reactions produce new chemicals. Third, the number of possible chemicals is very large.
Thought experiment: suppose you find yourself in front of chemistry set containing a rack of n beakers, each filled with an unknown chemicals. Channeling your inner mad scientist, you begin mixing them at random. Suppose 1 in 100 pairs creates a reaction. How many total reactions should you be able to get out of your chemistry set?
If you have two chemicals, the odds of a reaction are just 1 in 100.
If you have three chemicals, you have three potential pairs, and the odds of a reaction are about 3 in 100.
If you have four chemicals, you actually have six potential pairs, so the odds of a reaction are a little better than 6 in 100.
At this point, exponentials start working rapidly in your favor. With five chemicals, you have 10 potential pairs, for a 9.5% chance of at least one reaction. Twelve chemicals gets you 66 pairs with 48.4% odds of at least one reaction. The deluxe 30-chemical starter kit has 435 potential pairs, with 98.7% odds of at least one reaction.
What does this prove? The number of likely reactions in a pool increases faster than the number of chemicals in the pool.
It keeps going, too. With 1 in 100 odds, you would expect to get about 4 reactions out of your 30-chemical kit. If each reaction creates a new chemical, you now have 34 chemicals in your pool, with correspondingly greater odds of additional reactions. Eventually, you pass a tipping point, and the expected number of compounds becomes infinite. If I've got my math right, it happens around 80 chemicals in this scenario, because the expected number of new reactions exceeds the number of reactions in the existing set. The more you mix, the more potential mixtures you get.
A quick pause: when we talk about chemicals, we're not talking about atoms in the periodic table of the elements. Except during fission and fusion, atoms themselves don't combine and react. Instead, we're talking about molecules.
In particular, organic molecules -- the ones that ended up supporting life -- fit this model very well. Enzymes, RNA, and DNA are all organic molecules. Believe it or not, a strand of DNA is one enormous molecule. Organic molecules are all built mainly from the same base atoms: carbon, hydrogen, oxygen, nitrogen, phosphorus -- and now arsenic(!) These atoms happen to be good at linking to form long chains. Because of the way these chains fold, they react with each other in often unpredictable ways. Most organic molecules don't react with each other, but quite a few do. And because the chains can get very long, the set of potential molecules made of CHONP atoms is essentially infinite.
Now getting back to the main story... We're halfway through. We've shown how simple rules for reactions can get you from a small-ish starting set to an infinite variety of chemicals to play with. It seems very reasonable to suppose that the primordial organic soup included enough organic reactants to pass the tipping point into infinite variety. But that just means a more flavorful soup. How do we get to life?
Setting aside the transcendental, life is defined by sustainable reproduction. A cell is a bag of chemicals and reactions that keeps working long enough to make at least one copy of itself. As part of the deal, the cell has to be in the right sort of environment, with whatever energy sources and nutrients are necessary.
Our cells achieve sustainability by using enzymes to catalyze other reactions. It turns out that the same logic that applies to pairs of reactions also applies to catalyzers: the probability of catalysts in a pool increases faster than the number of chemicals in the pool. Once you get enough chemicals, it's virtually certain that you'll have quite a few catalyzed reactions.
Here's the really nifty bit. As the number of catalyzed reactions in the set increases, eventually some of them will form an autocatalytic set -- a loop of reactions catalyzing each other. Reaction A creates the catalyst that enables reaction B, creating the catalyst for C, and so on back to catalyst Z that enables reaction A.
Based on the same logic we saw earlier, these loops always appear once the pool of chemicals gets large enough. They are typically long and complicated, cycling through a seemingly random group of chemicals among a much larger set of nutrients and byproducts. They tap nutrients and energy sources in the environment, increasing themselves the longer they run. In other words, autocatalytic sets look a whole lot like life as we know it.
I find this theory compelling. It takes the biggest objection to prevailing theories -- the inherent complexity of life -- and makes it the cornerstone of a different approach.
And as a bonus, it makes arsenic-based life forms seem very plausible. Given NASA's results, it seems reasonable to say that arsenic-based DNA is another unexplored evolutionary path for viable autocatalytic sets. Bill Bryson says it well in A Short History of Nearly Everything:
"It may be that the things that make [Earth] so splendid to us---well-proportioned Sun, doting Moon, sociable carbon, more molten magma than you can shake a stick at and all the rest---seem splendid simply because they are what we were born no count on. No one can altogether say. ... Other worlds may harbor beings thankful for their silvery lakes of mercury and drifting clouds of ammonia."
PS: Autocatalytic sets don't have much to do with the evolution/intelligent design debate. They propose a mechanism that could be responsible for jumpstarting evolution. So if you're comfortable with the idea that God would choose cosmological constants and direct evolutionary processes with some goal in mind, it probably won't bother you to add the idea that he would use chemical soups and catalysis networks along the way.
PPS: The main difference between an autocatalytic set and life as we know it is the absence of a cell wall. It's not hard to close the gap conceptually. Once a catalytic loop gets started, other loops usually form as well. At this point, competition and natural selection between autocatalytic cycles can kick in. If one autocatalytic loop happened to produce a hydrophobic byproduct (like a fat or lipid), it could easily act as a primitive cell wall. This kind of barrier would enable the autocatalytic loop to increase its concentration, and therefore its reaction rate. This kind of pseudocell would reproduce faster and very likely evolve into more sophisticated organisms.
*A ten word review of the Andromeda Strain: Typical Crichton--some interesting ideas; mildly annoying narration; mostly plotless.
** A wonderful book for putting some color on the messy process of scientific discovery.
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