Understanding Randomness
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Today's entry was written by Kathryn Applegate. Kathryn Applegate is Program Director at The BioLogos Foundation. She received her PhD in computational cell biology at The Scripps Research Institute in La Jolla, Calif. At Scripps, she developed computer vision software tools for analyzing the cell's infrastructure, the cytoskeleton.
Christians often equate randomness with an atheistic worldview, but randomness is an essential feature of many God-ordained biological processes, from the union of egg and sperm during reproduction to the generation of antibodies by the immune system. In fact, based on its prevalence in the natural world, one might conclude that randomness is one of God’s favorite mechanisms for creating life!
In my last post, I suggested that a good definition of randomness is extreme unpredictability. Here I want to clarify a few misconceptions about randomness before moving on, in future posts, to describing other biological processes that make use of it.
Misconception #1
Randomness is like “God of the Gaps”. With time, advancements in science will allow us to make accurate predictions in previously “random” systems.
Isaac Newton’s famous three laws of motion, described in his 1687 classic Principia Mathematica, have empowered physics students for centuries. Using these and Newton’s universal law of gravitation, you can predict the trajectory of everything from pool balls to planets. By the early nineteenth century, the idea of a “clockwork universe” was firmly established, and scientists believed that with time, science would be unlimited in its predictive power.
Although it could be true that we live in a “clockwork universe,”1 two developments in the twentieth century shattered our hopes of having a fully predictable universe. The first was quantum mechanics, which describes how things work at an extremely small scale. One of the major discoveries in quantum mechanics was Werner Heisenberg’s “uncertainty principle,” which holds that the more certain one is about the location of a particle, the less certain in principle one can be about its momentum, and vice versa. At the quantum level, then, our predictive powers are ultimately limited.
Another discovery that destroyed all hope for a fully predictable universe was chaos. Mathematically chaotic systems are those which are extremely sensitive to changes in their initial conditions. Even fully deterministic systems can exhibit chaotic behavior and act in unpredictable ways. Consider a famous function, the logistic map2:
I know equations make people nervous, but stay with me! This one does some fascinating things. Here’s how it works: start with some initial value for x at time t = 0, and plug that in for x(t). Let’s start with 
= 0.2. R is just some constant value; let it be 2. Now we use the function to calculate the outcome in the next time step, t = 1:
We can use this value as input for the next step, and repeat this process over and over to find the output at each time point.
What happens? The answer is plotted in the figure below on the left. If we follow along the x-axis, which represents time, we see that the value of x goes toward 0.5 and stays there forever.
What if we start with the same , but increase R to 3.1? Following the same process as before, we get a very different result! The middle graph shows that the outcome oscillates between two values over time.
If you make R = 4, the function does something very strange. In the right-most plot, the function still fluctuates up and down, but it begins to look irregular. And if we change the initial condition, , just slightly, from 2.0 (blue solid line) to 0.2000000001 (red dotted line), we see they are virtually the same until somewhere around t = 14. After that point, they exhibit completely different behavior.
Several observations can be made here. First, the same equation can produce three different classes of behavior, simply by changing R and . These classes are called fixed-point (left), periodic (middle), and chaotic (right). Below the values of R that lead to chaos, the system is not sensitive to the initial value of . Over time, the system will either become a flat line or oscillate.
When R is greater than approximately 3.569946, however, the system becomes chaotic, and the outcome is extremely sensitive to changes in the initial value of . What this means is you would have to know the value of to infinity to predict its long term behavior. Since this is impossible in any kind of real-world application, the detailed behavior of a chaotic system is impossible to predict.
If this is true even for a simple, completely deterministic equation, how much more difficult is it to predict the behavior of a more complicated chaotic system, like a hurricane! Even the poor weathermen here in San Diego get it wrong sometimes, and the weather here doesn’t change very much.
So, between the uncertainty principle in quantum mechanics, and the sensitivity of chaotic systems, we now know that we are fundamentally limited in our predictive power––not just temporarily. Whether the systems we study are truly indeterministic is another (interesting) question, which of course has implications for divine action.
Misconception #2
Randomness means anything can happen, and all possibilities are equally likely.
People often think randomness means the outcome is completely open-ended, but you can’t roll a 7 on a 6-sided dice, nor draw a red marble from a bag of blue ones. Even random processes function according to rules. (The logistic map in the last section is another good example.)
Sometimes, the word random is used to mean unbiased. If you want to know who will win a political election, you make sure to poll a random sample of people, not just those hanging around a Tea Party rally. But the word random doesn’t have to mean that all possibilities are equally likely. When maternal and paternal chromosomes get together during conception, they exchange long sequences of DNA in a process called recombination. We now know that recombination happens more often in some places of the genome than others, but the specific sites where it will occur in a given embryo are impossible to predict. So recombination is random in the sense that it is unpredictable, but not in the sense that all outcomes are equally likely.
Misconception #3
Randomness always leads to disorder.
On the contrary, randomness often leads to exquisitely ordered and complex outcomes. In my last post, we watched a simulation of viral self-assembly from individual proteins bouncing around in a jar. You could repeat the simulation a thousand times and always get the same result, even though the particular assembly pathway would look different each time. That is, if the starting materials are present and the conditions (temperature, pH, etc) are right, you will always get a beautiful, highly symmetric virus. Random motion is the mechanism used to search “solution space” for a favorable outcome.
Fractals provide another great example of patterns emerging from randomness. Fractals are chaotic patterns with the same basic property: no matter how much you “zoom in,” the overall structure is maintained. Clouds, trees, crystals, and snow flakes are naturally-occurring fractals.
You can construct a fractal like the Sierpinski triangle shown at left by rolling a die and following simple rules.3 If 100 people in a room independently rolled a die 100 times and followed the rules, they would all have different sequences of rolls, but all would end up with the same pattern!
Thus, for many random processes, the fine details may be unpredictable along the way, but the macro-level outcome is foreseeable.
Summary
“Randomness,” when taken to mean unconquerable unpredictability, is inherent in many processes created by God, from hurricanes to viral assembly to genetic recombination to antibody production. Randomness means that the details of the future are unpredictable, and will stay that way regardless of scientific progress. That said, randomness is constrained by rules and often leads to complex patterns and macro-level order. More misconceptions about randomness no doubt lurk in all our minds, leading to suspicion when we hear phrases like, “evolution is random.” But hopefully, this post can help to clarify some of the confusion.
Notes
- Philosophers of physics still debate whether there is some underlying deterministic structure to the universe, or whether events at the quantum level are indeterministic. See http://plato.stanford.edu/entries/determinism-causal/#QuaMec. In either case, we are fundamentally limited in our ability to make predictions about the outcomes of quantum events.
- The logistic map is one of the best-studied equations in dynamical systems theory. The particular values used in the figure were taken from Melanie Mitchell’s excellent book, Complexity: A Guided Tour, and were created using MATLAB.
- Thanks to Isaac Yonemoto for pointing this out.
May 3rd 2010
Penman:
A good answer, and I have no quarrel with your reasoning, but I would go further than you do. If God knows that a universe “characterized by PQR” will *certainly* (not just probably) “give rise to XYZ”, and God creates that PQR universe, then God has “set up” nature so that it *must” produce XYZ. The “randomness” of such a nature thus occurs within a framework which is not random, but directed. Often human science will be able to detect only the random aspect of creation, but the directive framework is there all the same. So if God creates through evolution, we should expect to see in nature a propensity for non-living matter, moving “randomly”, to come together into living matter, not just under the most wildly improbable of circumstances, but fairly often, and we should expect to find that single-celled creatures have a natural propensity to become multi-celled creatures, and that living forms have a tendency to mutate into more complex forms, etc. In other words, we should expect to see a tilted universe, i.e., a designed universe. Yet the hardcore Darwinists among the TEs (Miller, Ayala and others) will have no truck or trade with such tilting or design. I wonder why a Christian would object to it.
Reply to this commentMay 3rd 2010
*I meant to say I’m not a “theologian” not “theist”. Whoops.
Bilbo:
You ask some really great questions, and I’m not sure I can do them justice in this space, but the short answers are:
1) Antibodies are proteins (or more correctly, protein complexes, as they are composed of a few different protein chains, which are “strings” of amino acids bonded together, like a string of pearls), so the way they are assembled is identical.
Antibodies are unique because the DNA that encodes them (DNA serves as instructions for all proteins) can undergo rapid mutation that leads to dramatic change in these proteins on a rapid timescale (within days) to allow the body to defend fend off an infinite number of foreign objects (like viruses).
2) I think it is fair to discuss their evolution as a *type* of protein evolution. Novel proteins (like the kind that lead to new organisms), generally come about because of slower proceses (often taking many generations), so there *are* some big differences thought.
3) Antibodies are both released outside of the cell and kept attached to the cell, exposed to the environment. All the mutation happens within the cell though.
Hope that helps!
Reply to this commentMay 3rd 2010
“Unapologetic Catholic:
“I notice you didn’t answer my question in post #12042. Would you endorse the Schoenborn/Ratzinger statement about evolution and design in biological nature, or not? If not, why not?”
No. The particular off the cuff statements you are referring to are bilogically erroneosu based on an ignorance of the science. A good example of religous men spouting off on a subjec they know little about. That happens at one time or another to all of us. The official statements of the Church since then back off from those staements, especailly Cardinal Schonborn who was duped by the Discoveyr Institute. His measure words since then are significanty more cautious.
The thoughtful official statement of the Church I set ou abovet, taken from Imago Dei is biologically accurate and acords with Catholic theology.
Reply to this commentMay 4th 2010
Can you show, UC, how “official statements of the [RC] Church since then back off from those statements”, with links to more recent statements or speeches?
You sound pretty self-confident, frankly, rather ‘off the cuff’ yourself.
You think ‘morality evolved into existence.’ Obviously being orthodox Catholic is not important.
From your link: “the message of Pope John Paul II cannot be read as a blanket approbation of all theories of evolution, including those of a neo-Darwinian provenance which explicitly deny to divine providence any truly causal role in the development of life in the universe.”
“In the Catholic perspective, neo-Darwinians who adduce random genetic variation and natural selection as evidence that the process of evolution is absolutely unguided are straying beyond what can be demonstrated by science. Divine causality can be active in a process that is both contingent and guided.”
Rich quoted: “Any system of thought that denies or seeks to explain away the overwhelming evidence for design in biology is ideology, not science.”
You have simply not answered Rich’s question.
Reply to this commentMay 4th 2010
Ican’t let this one pass, either:
” I’m giving you “common ancestry”; I want to know why you’re so sure that a wholly natural mechanism exists, if you can’t provide a stepwise evolutionary pathway (even a hypothetical one will do) in even a single case.”
You’ rean’t “giving” anything. that’s a scitific fact, like concedign gravinty. Wearen’t bargainign here, we’re dealingin facts.
I’veactually provided very substaintial information (limited by 1250 characterrs and the inability to make horses drink despite beign led tot he creek) regarding evolutionary pathways, and you won’t do the homework.
Here’s the link again:
http://ocw.mit.edu/OcwWeb/Biology/7-012Fall-2004/CourseHome/index.htm
When you demostrate minimum competence in the field of study, we can have a meaningful conversation on the subjects discussed. Until then proably not.
Reply to this commentMay 4th 2010
Un. Catholic:
Despite the fact that you are Catholic, you clearly have not reviewed the entire history of Catholic statements on evolution, and you are cherry-picking the pro-evolution ones which please you. You remind me of Ken Miller, who knows zip about the theology of the Church he attends, and Francisco Ayala, who, if he ever learned any serious Catholic theology in seminary (which is dubious), has forgotten it all, because every time he opens his mouth he utters another heresy. So you are certainly following Catholic TE role models in picking and choosing what you like from Catholic teaching and ignoring the rest. I think you should change your handle to “Catholic with caveats”.
You are trying to project competence in biology, but you don’t appear to know the most basic epistemological distinctions within science, such as the difference between a fact and an inference. Gravity (or at least the set of mathematical relationships in nature associated with that word) is a demonstrated fact, whereas common descent is an inference based on homology and other circumstantial evidence. So it appears you have no more to teach me about science than about Catholic theology.
Reply to this commentMay 4th 2010
Rich, any thoughts on that cetacean evolution/development article I posted for you? It seems to me it fit what you were asking for.
Reply to this commentMay 4th 2010
Dennis:
I’ll get back to you when I’ve looked at it. If it makes a serious attempt to connect particular changes in identifiable sectors of the genome to particular morphological changes, and to specify how those morphological changes would give a selective example, then yes, it’s the sort of thing I’m looking for. In broad terms, I’m looking for something that attempts to deal with the very specific mechanical problems posed by Richard Sternberg in the video which I’ve already referenced.
Reply to this commentMay 5th 2010
Dennis:
I have looked at the article on cetacean hind-limb evolution.
Yes, this is the sort of detailed study that would be required to empirically sustain any naturalistic account of macroevolution. I like the way it attempts to get down to the nitty-gritty of genetic and developmental mechanisms.
While it is entirely reasonable that a scientific article should focus only on one aspect of whale evolution, and I don’t fault the writers for failing to deal with the other aspects (the blowhole, marine lactation, etc.), my original point was that *all* the changes (some of which are interconnected, from the point of view of selection) need to be explained, before we have a convincing evolutionary account of the land-to-sea transition. I would therefore say that this article represents respectable science, but that science is not yet in the position where it can claim to *know* that land mammals evolved into whales by entirely natural mechanisms.
Reply to this commentMay 5th 2010
I don’t mean to belittle the complexities or revelation in this information. From a survey kind of a position though I question if it is truly randomness in the end. For a sperm to reach an egg, I think of victory more than random chance. The victor is the best out of a million possibilities. If this concept is not a valid part of our natural processes, then instead of selecting Ph.D. candidates to mentor perhaps we should be casting lots? I think the misconceptions presented here speak to the validity of such an argument. What may seem random is in part due to our inability to truly see all impacting variables.
In regards to mutations it seems that the areas most likely to produce these variables that cause them may natural opportunities to expressing creativity. Life would seem a little too synthetic without a surprise element to things. Order doesn’t require uniformity. A defect could be an opportunity for life to demonstrate provision rather than to expose a limitation.
Reply to this commentMay 9th 2010
A bit late to jump back in with this, but here is an article by Stephen Barr, whom many of you will likely know from First Things, that deals quite well with the issue of ‘randomness’ and which I found helpful:
http://www.unav.es/cryf/english/designevolution.html
Reply to this commentMay 10th 2010
>The particular off the cuff statements you are referring to are bilogically erroneosu based on an ignorance of the science. A good example of religous men spouting off on a subjec they know little about.
I reply: Rather UC is spouting off on subjects he knows nothing about. The post-enlightenment belief we can only know material & efficient causes in nature & not formal & final ones is a philosophical belief not a scientific one. Schoenborn/Ratzinger where making a philosophical analysis not a scientific one. This is about Mechanistic Philosophy Vs Thomistic. Philosophy is the perennial science.
I suggest UC needs to educate himself by reading FROM ARISTOTLE TO DARWIN AND BACK AGAIN:A Journey in Final Causality, Species, & Evolution by Etienne Gilson (forward by Card Schonborn) IGNATIUS PRESS. Then he can repent of his insolence in thinking he knows better than either Schoenborn or Pope Benedict.
Reply to this commentMay 10th 2010
>When you demostrate minimum competence in the field of study, we can have a meaningful conversation on the subjects discussed.
I reply: Until you learn the most basic Thomistic philosophy and learn to see Evolution threw the eyes of that philosophy then YOU CANNOT defend the idea evolution and Christian theism are compatible. The “Random” vs “Design” dichotomy is only a conundrum if one postulate Philosophical Mechanism. If you hold to classic philosophy & Thomism the problem is non-existent. Here is a phrase for you to learn “Divine Providence”. BTW Catholicism accepts Evolution as compatible with Divine Revelation (as understood correctly by the Holy Church) but it doesn’t mandate it nor does that make Neo-Darwinism true. Neo-Darwinism could be true or false and some other unknown natural mechanism(or divine act) could be responsible for the teleology of living things.
Reply to this commentMay 10th 2010
Hi Ben,
Why do you persist in capitalising ‘evolution’?
Also, ‘threw’ is past tense for throwing. ‘Through’ signifies what you are meaning to say. (It has been about a dozen times spelled wrongly, so please excuse the pedantic correction.)
I agree with your criticism of UC and find his remarks misplaced.
*Although* I don’t see it as mechanistic philosophy vs. Thomistic philosophy. But rather, the appropriate opposite for mechanism is organism.
Thomas Aquinas was a person, not a philosophical deity. Catholic Christians, in order to move forward, *must* be able to go beyond Thomistic philosophy. I have already offered you one way to do it. Gilson is a good first step.
Reply to this commentMay 10th 2010
Gregory my spelling & Grammar are awful & I’m too old & set in my ways to bother correcting it for mere comment box postings.
>*Although* I don’t see it as mechanistic philosophy vs. Thomistic philosophy. But rather, the appropriate opposite for mechanism is organism.
I reply: Your entitled your opinion but after reading Feser, Conway and Oderberg I am convinced the problem is the post-enlightenment error that in nature there are only efficient and material causes. I absolutely accept Aristotelian/Thomistic metaphysics as essential and reject the myth that modern philosophy (Hume, Kant, Descartes etc) has refuted it. If in nature there are only those two causes then teleology is reduced to God acting directly as the efficient agent who specifically & immediately designs all living things as in creationism or God is a weak open theism deity who uses trial and error. OTOH if we accept the four causes then God can imbue certain matter & life with properties where they can provide teleology by mere natural means such as in evolution.
Reply to this commentMay 10th 2010
>Thomas Aquinas was a person, not a philosophical deity. Catholic Christians, in order to move forward, *must* be able to go beyond Thomistic philosophy.
I reply: That is an irrational & absolutely unnecessary either/or mentality that is alien to Catholic thinking. Methinks your (mis)understanding of Thomism is likely filtered through the likes of Anthony Kenny (who to put it politely didn’t know what he was talking about)? Thomism fills Catholicism that is like talking about Orthodox Judaism without Maimonides or Calvinism without Calvin. It’s absurd.
>I have already offered you one way to do it. Gilson is a good first step.
I reply: I don’t understand this statement. Gilson & Thomism are in conflict? Thomism would be a gutted non-existent philosophy without presupposing the metaphysics of Aristotle. Gilson’s arguments are based on Aristotelian metaphysics? Am I missing something guy?
Reply to this commentMay 10th 2010
Hi Ben,
I said move forward and go beyond, not forget. It would be absurd, as you say, for a Catholic Christian to do otherwise with Thomas and Aristotle.
No, Gilson is not the main issue. I offered you another. Thomas and Aristotle, plus what next?
We live in an electric-information age now, Ben. I am much on your side in highlighting formal and final causes. But what then?
Is teleology a big issue for you too?
Don’t you think teleology is a big issue that *must* be involved in any definition of ‘biologos’ that this Foundation would give?
Reply to this commentMay 11th 2010
>I said move forward and go beyond, not forget. It would be absurd, as you say, for a Catholic Christian to do otherwise with Thomas and Aristotle.
I reply: Sorry about that. Thanks for the clarification, sorry.
Reply to this commentMay 11th 2010
>Thomas and Aristotle, plus what next?
I reply: I’m not sure I understand the question?
>Is teleology a big issue for you too?
I Reply: Yes & I think the failure to distinguish the difference between teleology in a Mechanistic philosophical framework vs an AT (i.e. Aristotelian/Thomism ) one is what is dogging the whole debate between Atheism vs Theistic Evolution vs ID.
Reply to this commentMay 11th 2010
Hello BenYachov,
Aristotle lived over 2300 yrs ago, Aquinas over 700 yrs ago. Don’t you think a ‘new’ approach, combining with the ‘old,’ could help?
We are on the same page *against* mechanistic philosophies. This is partly what worries me about the IDM. They embrace the idea that ‘organisms’ are/contain ‘machines.’ Of course, it is an analogy, but Darth Vader is lurking behind their backs when they do it.
In my view, you and other Catholic Christians need an A+T+? option, i.e. something more. You haven’t found it yet. But perhaps it is already out there.
I have mentioned McLuhan as a way to discover more. Have you read his “Laws of Media: The New Science” (1988)? In it, he and his son outline the so-called ‘four effects’, which are meant to compliment Aristotle’s (and Aquinas’) ‘four causes.’ It is worth learning about in case you hadn’t heard of it before.
Was the question about why you capitalize ‘evolution’ unclear also? Just curious.
Thanks,
Reply to this commentGregory