A Theory of Medicine?
As it’s practiced today, medicine is almost always about particulars: “this has gone wrong; this is how to fix it”. But might it also be possible to talk about medicine in a more general, more abstract way—and perhaps to create a framework in which one can study its essential features without engaging with all of its details?
My goal here is to take the first steps towards such a framework. And in a sense my central result is that there are many broad phenomena in medicine that seem at their core to be fundamentally computational—and to be captured by remarkably simple computational models that are readily amenable to study by computer experiment.
I should make it clear at the outset that I’m not trying to set up a specific model for any particular aspect or component of biological systems. Rather, my goal is to “zoom out” and create what one can think of as a “metamodel” for studying and formalizing the abstract foundations of medicine.
What I’ll be doing builds on my recent work on using the computational paradigm to study the foundations of biological evolution. And indeed in constructing idealized organisms we’ll be using the very same class of basic computational models. But now, instead of considering idealized genetic mutations and asking what types of idealized organisms they produce, we’re going to be looking at specific evolved idealized organisms, and seeing what effect perturbations have on them. Roughly, the idea is that an idealized organism operates in its normal “healthy” way if there are no perturbations—but perturbations can “derail” its operation and introduce what we can think of as “disease”. And with this setup we can then think of the “fundamental problem of medicine” as being the identification of additional perturbations that can “treat the disease” and put the organism at least approximately back on its normal “healthy” track.
As we’ll see, most perturbations lead to lots of detailed changes in our idealized organism, much as perturbations in biological organisms normally lead to vast numbers of effects, say at a molecular level. But as in medicine, we can imagine that all we can observe (and perhaps all we care about) are certain coarse-grained features or “symptoms”. And the fundamental problem of medicine is then to work out from these symptoms what “treatment” (if any) will end up being useful. (By the way, when I say “symptoms” I mean the whole cluster of signs, symptoms, tests, etc. that one might in practice use, say for diagnosis.)
It’s worth emphasizing again that I’m not trying here to derive specific, actionable, medical conclusions. Rather, my goal is to build a conceptual framework in which, for example, it becomes conceivable for general phenomena in medicine that in the past have seemed at best vague and anecdotal to begin to be formalized and studied in a systematic way. At some level, what I’m trying to do is a bit like what Darwinism did for biological evolution. But in modern times there’s a critical new element: the computational paradigm, which not only introduces all sorts of new, powerful theoretical concepts, but also leads us to the practical methodology of computer experimentation. And indeed much of what follows is based on the (often surprising) results of computer experiments I’ve recently done that give us raw material to build our intuition—and structure our thinking—about fundamental phenomena in medicine.
A Minimal Metamodel
How can we make a metamodel of medicine? We need an idealization of biological organisms and their behavior and development. We need an idealization of the concept of disease for such organisms. And we need an idealization of the concept of treatment.
For our idealization of biological organisms we’ll use a class of simple computational systems called cellular automata (that I happen to have studied since the early 1980s). Here’s a specific example:
What’s going on here is that we’re progressively constructing the pattern on the left (representing the development and behavior of our organism) by repeatedly applying cases of the rules on the right (representing the idealized genome—and other biochemical, etc. rules—of our organism). Roughly we can think of the pattern on the left as corresponding to the “life history” of our organism—growing, developing and eventually dying as it goes down the page. And even though there’s a rather organic look to the pattern, remember that the system we’ve set up isn’t intended to provide a model for any particular real-world biological system. Rather, the goal is just for it to capture enough of the foundations of biology that it can serve as a successful metamodel to let us explore our questions about the foundations of medicine.
Looking at our model in more detail, we see that it involves a grid of squares—or “cells” (computational, not biological)—each having one of 4 possible colors (white and three others). We start from a single red “seed” cell on the top row of the grid, then compute the colors of cells on subsequent steps (i.e. on subsequent rows down the page) by successively applying the rules on the right. The rules here are basically very simple. But we can see that when we run them they lead to a fairly complicated pattern—which in this case happens to “die out” (i.e. all cells become white) after exactly 101 steps.
So what happens if we perturb this system? On the left here we’re showing the system as above, without perturbation. But on the right we’re introducing a perturbation by changing the color of a particular cell (on step 16)—leading to a rather different (if qualitatively similar) pattern:
Here are the results of some other perturbations to our system:
Some perturbations (like the one in the second panel here) quickly disappear; in essence the system quickly “heals itself”. But in most cases even single-cell perturbations like the ones here have a long-term effect. Sometimes they can “increase the lifetime” of the organism; often they will decrease it. And sometimes—like in the last case shown here—they will lead to essentially unbounded “tumor-like” growth.
In biological or medical terms, the perturbations we’re introducing are minimal idealizations of “things that can happen to an organism” in the course of its life. Sometimes the perturbations will have little or no effect on the organism. Or at least they won’t “really hurt it”—and the organism will “live out its natural life” (or even extend it a bit). But in other cases, a perturbation can somehow “destabilize” the organism, in effect “making it develop a disease”, and often making it “die before its time”.
But now we can formulate what we can think of as the “fundamental problem of medicine”: given that perturbations have had a deleterious effect on an organism, can we find subsequent perturbations to apply that will serve as a “treatment” to overcome the deleterious effect?
The first panel here shows a particular perturbation that makes our idealized organism die after 47 steps. The subsequent panels then show various “treatments” (i.e. additional perturbations) that serve at least to “keep the organism alive”:
In the later panels here the “life history” of the organism gets closer to the “healthy” unperturbed form shown in the final panel. And if our criterion is restoring overall lifetime, we can reasonably say that the “treatment has been successful”. But it’s notable that the detailed “life history” (and perhaps “quality of life”) of the organism will essentially never be the same as before: as we’ll see in more detail later, it’s almost inevitably the case that there’ll be at least some (and often many) long-term effects of the perturbation+treatment even if they’re not considered deleterious.
So now that we’ve got an idealized model of the “problem of medicine”, what can we say about solving it? Well, the main thing is that we can get a sense of why it’s fundamentally hard. And beyond anything else, the central issue is a fundamentally computational one: the phenomenon of computational irreducibility.
Given any particular cellular automaton rule, with any particular initial condition, one can always explicitly run the rule, step by step, from that initial condition, to see what will happen. But can one do better? Experience with mathematical science might make one imagine that as soon as one knows the underlying rule for a system, one should in principle immediately be able to “solve the equations” and jump ahead to work out everything about what the system does, without explicitly tracing through all the steps. But one of the central things I discovered in studying simple programs back in the early 1980s is that it’s common for such systems to show what I called computational irreducibility, which means that the only way to work out their detailed behavior is essentially just to run their rules step by step and see what happens.
So what about biology? One might imagine that with its incremental optimization, biological evolution would produce systems that somehow avoid computational irreducibility, and (like simple machinery) have obvious easy-to-understand mechanisms by which they operate. But in fact that’s not what biological evolution typically seems to produce. And instead—as I’ve recently argued—what it seems to do is basically just to put together randomly found “lumps of irreducible computation” that happen to satisfy its fitness criterion. And the result is that biological systems are full of computational irreducibility, and mostly aren’t straightforwardly “mechanically explainable”. (The presence of computational irreducibility is presumably also why theoretical biology based on mathematical models has always been so challenging.)
But, OK, given all this computational irreducibility, how is it that medicine is even possible? How is it that we can know enough about what a biological system will do to be able to determine what treatment to use on it? Well, computational irreducibility makes it hard. But it’s a fundamental feature of computational irreducibility that within any computationally irreducible process there must always be pockets of computational reducibility. And if we’re trying to achieve only some fairly coarse objective (like maximizing overall lifetime) it’s potentially possible to leverage some pocket of computational reducibility to do this.
(And indeed pockets of computational reducibility within computational irreducibility are what make many things possible—including having understandable laws of physics, doing higher mathematics, etc.)
The Diversity and Classification of Disease
With our simple idealization of disease as the effect of perturbations on the life history of our idealized organism, we can start asking questions like “What is the distribution of all possible diseases?”
And to begin exploring this, here are the patterns generated with a random sample of the 4383 possible single-point perturbations to the idealized organism we’ve discussed above:
Clearly there’s a lot of variation in these life histories—in effect a lot of different symptomologies. If we average them all together we lose the detail and we just get something close to the original:
But if we look at the distribution of lifetimes, we see that while it’s peaked at the original value, it nevertheless extends to both shorter and longer values:
In medicine (or at least Western medicine) it’s been traditional to classify “things that can go wrong” in terms of discrete diseases. And we can imagine also doing this in our simple model. But it’s already clear from the array of pictures above that this is not going to be a straightforward task. We’ve got a different detailed pattern for every different perturbation. So how should we group them together?
Well—much as in medicine—it depends on what we care about. In medicine we might talk about signs and symptoms, which in our idealized model we can basically identify with features of patterns. And as an example, we might decide that the only features that matter are ones associated with the boundary shape of our pattern:
So what happens to these boundary shapes with different perturbations? Here are the most frequent shapes found (together with their probabilities):
We might think of these as representing “common diseases” of our idealized organism. But what if we look at all possible “diseases”—at least all the ones produced by single-cell perturbations? Using boundary shape as our way to distinguish “diseases” we find that if we plot the frequency of diseases against their rank we get roughly a power law distribution (and, yes, it’s not clear why it’s a power law):
What are the “rare diseases” (i.e. ones with low frequency) like? Their boundary shapes can be quite diverse:
But, OK, can we somehow quantify all these “diseases”? For example, as a kind of “imitation medical test” we might look at how far to the left the boundary of each pattern goes. With single-point perturbations, 84% of the time it’s the same as in the unperturbed case—but there’s a distribution of other, “less healthy” results (here plotted on a log scale)
with extreme examples being:
And, yes, we could diagnose any pattern that goes further to the left than the unperturbed one as a case of, say, “leftiness syndrome”. And we might imagine that if we set up enough tests, we could begin to discriminate between many discrete “diseases”. But somehow this seems quite ad hoc.
So can we perhaps be more systematic by using machine learning? Let’s say we just look at each whole pattern, then try to place it in an image feature space, say a 2D one. Here’s an example of what we get:
The details of this depend on the particulars of the machine learning method we’ve used (here the default FeatureSpacePlot method in Wolfram Language). But it’s a fairly robust result that “visually different” patterns end up separated—so that in effect the machine learning is successfully automating some kind of “visual diagnosis”. And there’s at least a little evidence that the machine learning will identify separated clusters of patterns that we can reasonably identify as “truly distinct diseases”—even as the more common situation is that between any two patterns, there are intermediate ones that aren’t neatly classified as one disease or the other.
Somewhat in the style of the human “International Classification of Diseases” (ICD), we can try arranging all our patterns in a hierarchy—though it’s basically inevitable that we’ll always be able to subdivide further, and there’ll never be a clear point at which we can say “we’ve classified all the diseases”:
By the way, in addition to talking about possible diseases, we also need to discuss what counts as “healthy”. We could say that our organism is only “healthy” if its pattern is exactly what it would be without any perturbation (“the natural state”). But what probably better captures everyday medical thinking is to say that our organism should be considered “healthy” if it doesn’t have symptoms (or features) that we consider bad. And in particular, at least “after the fact” we might be able to say that it must have been healthy if its lifetime turned out to be long.
It’s worth noting that even in our simple model, while there are many perturbations that reduce lifetime, there are also perturbations that increase lifetime. In the course of biological evolution, genetic mutations of the overall underlying rules for our idealized organism might have managed to achieve a certain longevity. But the point is that nothing says “longevity perturbations” applied “during the life of the organism” can’t get further—and indeed here are some examples where they do:
And, actually, in a feature that’s not (at least yet) reflected in human medicine, there are perturbations than can make the lifetime very significantly longer. And for the particular idealized organism we’re studying here, the most extreme examples obtained with single-point perturbations are:
OK, but what happens if we consider perturbations at multiple points? There are immediately vastly more possibilities. Here are some examples of the 10 million or so possible configurations of two perturbations:
And here are examples with three perturbations:
Here are examples if we try to apply five perturbations (though sometimes the organism is “already dead” before we can apply later perturbations):
What happens to the overall distribution of lifetimes in these cases? Already with two perturbations, the distribution gets much broader, and with three or more, the peak at the original lifetime has all but disappeared, with a new peak appearing for organisms that in effect die almost immediately:
In other words, the particular idealized organism that we’re studying is fairly robust against one perturbation, and perhaps even two, but with more perturbations it’s increasingly likely to succumb to “infant mortality”. (And, yes, if one increases the number of perturbations the “life expectancy” progressively decreases.)
But what about the other way around? With multiple perturbations, can the organism in effect “live forever”? Here are some examples where it’s still “going strong” after 300 steps:
But after 500 steps most of these have died out:
As is typical in the computational universe (perhaps like in medicine) there are always surprises, courtesy of computational irreducibility. Like the sudden appearance of the obviously periodic case (with period 25):
As well as the much more complicated cases (where in the final pictures the pattern has been “rectified”):
So, yes, in these cases the organism does in effect “live forever”—though not in an “interesting” way. And indeed such cases might remind us of tumor-like behavior in biological organisms. But what about a case that not only lives forever, but also grows forever? Well, needless to say, lurking out in the computational universe, one can find an example:
The “incidence” of this behavior is about one in a million for 2 perturbations (or, more precisely, 7 out of 9.6 million possibilities), and one in 300,000 for 3 perturbations. And although there presumably are even more complicated behaviors out there to find, they don’t show up with 2 perturbations, and their incidence with 3 perturbations is below about one in 100 million.
Diagnosis & Prognosis
A fundamental objective in medicine is to predict from tests we do or symptoms and signs we observe what will happen. And, yes, we now know that computational irreducibility inevitably makes this in general hard. But also know from experience that a certain amount of prediction is possible—which we can now interpret as successfully managing to tap into pockets of computational reducibility.
So as an example, let’s ask what the prognosis is for our idealized organism based on the width of its pattern we measure at a certain step. So here, for example, is what happens to the original lifetime distribution (in green) if we consider only cases where the width of the measured pattern after 25 steps is less than its unperturbed (“healthy”) value (and where we’re dropping the 1% of cases when the organism was “already dead” before 25 steps):
Our “narrow” cases represent about 5% of the total. Their median lifetime is 57, as compared with the overall median of 106. But clearly the median alone does not tell the whole story. And nor do the two survival curves:
And, for example, here are the actual widths as a function of time for all the narrow cases, compared to the sequence of widths for the unperturbed case:
These pictures don’t make it look promising that one could predict lifetime from the single test of whether the pattern was narrow at step 25. Like in analogous medical situations, one needs more data. One approach in our case is to look at actual “narrow” patterns (up to step 25)—here sorted by ultimate lifetime—and then to try to identify useful predictive features (though, for example, to attempt any serious machine learning training would require a lot more examples):
But perhaps a simpler approach is not just to do a discrete “narrow or not” test, but rather to look at the actual width at step 25. So here are the lifetimes as a function of width at step 25
and here’s the distribution of outcomes, together with the median in each case:
The predictive power of our width measurement is obviously quite weak (though there’s doubtless a way to “hack p values” to get at least something out). And, unsurprisingly, machine learning doesn’t help. Like here’s a machine learning prediction (based on decision tree methods) for lifetime as a function of width (that, yes, is very close to just being the median):
Does it help if we use more history? In other words, what happens if we make our prediction not just from the width at a particular step, but from the history of all widths up to that point? As one approach, we can make a collection of “training examples” of what lifetimes particular “width histories” (say up to step 25) lead to:
There’s already something of an issue here, because a given width history—which, in a sense is a “coarse graining” of the detailed “microscopic” history—can lead to multiple different final lifetimes:
But we can still go ahead and try to use machine learning to predict lifetimes from width histories based on training on (say, half) of our training data—yielding less than impressive results (with the vertical line being associated with multiple lifetimes from a single width history in the training data):
So how can we do better? Well, given the underlying setup for our system, if we could determine not just the width but the whole precise sequence of values for all cells, even just at step 25, then in principle we could use this as an “initial condition” and run the system forward to see what it does. But regardless of it being “medically implausible” to do this, it isn’t much of a prediction anyway; it’s more just “watch and see what happens”. And the point is that insofar as there’s computational irreducibility, one can’t expect—at least in full generality—to do much better. (And, as we’ll argue later, there’s no reason to think that organisms produced by biological evolution will avoid computational irreducibility at this level.)
But still, within any computationally irreducible system, there are always pockets of computational reducibility. So we can expect that there will be some predictions that can be made. But the question is whether those predictions will be about things we care about (like lifetime) or even about things we can measure. Or, in other words, will they be predictions that speak to things like symptoms?
Our Physics Project, for example, involves all sorts of underlying processes that are computationally irreducible. But the key point there is that what physical observers like us perceive are aggregate constructs (like overall features of space) that show significant computational reducibility. And in a sense there’s an analogous issue here: there’s computational irreducibility underneath, but what do “medical observers” actually perceive, and are there computationally reducible features related to that? If we could find such things, then in a sense we’d have identified “general laws of medicine” much like we now have “general laws of physics”.
The Problem of Finding Treatments
We’ve talked a bit about giving a prognosis for what will happen to an idealized organism that’s suffered a perturbation. But what about trying to fix it? What about trying to intervene with another “treatment perturbation” that can “heal” the system, and give it a life history that’s at least close to what it would have had without the original perturbation?
Here’s our original idealized organism, together with how it behaves when it “suffers” a particular perturbation that significantly reduces its lifetime:
But what happens if we now try applying a second perturbation? Here are a few random examples:
None of these examples convincingly “heal” the system. But let’s (as we can in our idealized model) just enumerate all possible second perturbations (here 1554 of them). Then it turns out that a few of these do in fact successfully give us patterns that at least exactly reproduce the original lifetime:
Do these represent true examples of “healing”? Well, it depends on what we mean. Yes, they’ve managed to make the lifetime exactly what it would have been without the original “disease-inducing” perturbation. But in essentially all cases we see here that there are various “long-term side effects”—in the sense that the detailed patterns generated end up having obvious differences from the original unperturbed “healthy” form.
The one exception here is the very first case, in which the “disease was caught early enough” that the “treatment perturbation” manages to completely heal the effects of the “disease perturbation”:
We’ve been talking here about intervening with “treatment perturbations” to “heal” our “disease perturbation”. But actually it turns out that there are plenty of “disease perturbations” which automatically “heal themselves”, without any “treatment” intervention. In fact, of all possible 4383 single perturbations, 380 essentially heal themselves.
In many cases, the “healing” happens very locally, after one or two steps:
But there are also more complicated cases, where perturbations produce fairly large-scale changes in the pattern—that nevertheless “spontaneously heal themselves”:
(Needless to say, in cases where a perturbation “spontaneously heals itself”, adding a “treatment perturbation” will almost always lead to a worse outcome.)
So how should we think about perturbations that spontaneously heal themselves? They’re like seeds for diseases that never take hold, or like diseases that quickly burn themselves out. But from a theoretical point of view we can think of them as being where the unperturbed life history of our idealized organism is acting as attractor, to which certain perturbed states inexorably converge—a bit like how friction can dissipate perturbations to patterns of motion in a mechanical system.
But let’s say we have a perturbation that doesn’t “spontaneously heal itself”. Then to remediate it we have to “do the medical thing” and in our idealized model try to find a “treatment perturbation”. So how might we systematically set about doing that? Well, in general, computational irreducibility makes it difficult. And as one indication of this, this shows what lifetime is achieved by “treatment perturbations” made at each possible point in the pattern (after the initial perturbation):
We can think of this as providing a map of what the effects of different treatment perturbations will be. Here are some other examples, for different initial perturbations (or, in effect, different “diseases”):
There’s some regularity here. But the main observation is that different detailed choices of treatment perturbations will often have very different effects. In other words, even “nearby treatments” will often lead to very different outcomes. Given computational irreducibility, this isn’t surprising. But in a sense it underscores the difficulty of finding and applying “treatments”. By the way, cells indicated in dark red above are ones where treatment leads to a pattern that lives “excessively long”—or in effect shows tumor-like characteristics. And the fact that these are scattered so seemingly randomly reflects the difficulty of predicting whether such effects will occur as a result of treatment.
In what we’ve done so far here, our “treatment” has always consisted of just a single additional perturbation. But what about applying more perturbations? For example, let’s say we do a series of experiments where after our first “treatment perturbation” we progressively try other treatment perturbations. If a given additional perturbation doesn’t get further from the desired lifetime, we keep it. Otherwise we reject it, and try another perturbation. Here’s an example of what happens if we do this:
The highlighted panels represent perturbations we kept. An here’s how the overall lifetime “converges” over successive iterations in our experiment:
In what we just did, we allowed additional treatment perturbations to be added at any subsequent step. But what if we require treatment perturbations to always be added on successive steps—starting right after the “disease perturbation” occurred? Here’s an example of what happens in this case:
And here’s what we see zooming in at the beginning:
In a sense this corresponds to “doing aggressive treatment” as soon as the initial “disease perturbation” has occurred. And a notable feature of the particular example here is that when our succession of treatment perturbations have succeeded in “restoring the lifetime” (which happens fairly quickly), the life history they produce is similar (though not identical) to the original unperturbed case.
That definitely doesn’t always happen, as this example illustrates—but it’s fairly common:
It’s worth pointing out that if we allowed ourselves to do many single perturbations at the same time (i.e. on the same row of the pattern) we could effectively just “define new initial conditions” for the pattern, and, for example, perfectly “regenerate” the original unperturbed pattern after this “reset”. And in general we can imagine in effect “hot-wiring” the organism by applying large numbers of treatment perturbations that just repeatedly direct it back to its unperturbed form.
But such extensive and detailed “intervention”—that in effect replaces the whole state of the organism—seems far from what might be practical in typical (current) medicine (except perhaps in some kind of “regenerative treatment”). And indeed in actual (current) medicine one is normally operating in a situation where one does not have anything close to perfect “cell-by-cell” information on the state of an organism—and instead one has to figure out things like what treatment to give based on much coarser “symptom-level” information. (In some ways, though, the immune system does something closer to cell-by-cell “treatment”.)
So what can one do given coarse-grained information? As one example, let’s consider trying to predict what treatment perturbation will be best using the kind of pattern-width information we discussed above. Specifically, let’s say that we have the history of the overall width of a pattern up to a particular point, then from this we want to predict what treatment perturbation will lead to the best lifetime outcome for the system. There are a variety of ways we could approach this, but one is to make predictions of where to apply a treatment perturbation using machine learning trained on examples of optimal such perturbations.
This is analogous to what we did in the previous section in applying machine learning to predict lifetime from width history. But now we want to predict from width history what treatment perturbation to apply. To generate our training data we can search for treatment perturbations that lead to the unperturbed lifetime when starting from life histories with a given width history. Now we can use a simple neural net to create a predictor that tries to tell us from a width history what “treatment to give”. And here are comparisons between our earlier search results based on looking at complete life histories—and (shown with red arrows) the machine learning predictions based purely on width history before the original disease perturbation:
It’s clear that the machine learning is doing something—though it’s not as impressive as perhaps it looks, because a wide range of perturbations all in fact give rather similar life histories. So as a slightly more quantitative indication of what’s going on, here’s the distribution of lifetimes achieved by our machine-learning-based therapy:
Our “best treatment” was able to give lifetime 101 in all these cases. And while the distribution we’ve now achieved looks peaked around the unperturbed value, dividing this distribution by what we’d get without any treatment at all makes it clear that not so much was achieved by the machine learning we were able to do:
And in a sense this isn’t surprising; our machine learning—based, as it is, on coarse-grained features—is quite weak compared to the computational irreducibility of the underlying processes at work.
The Effect of Genetic Diversity
In what we’ve done so far, we’ve studied just a single idealized organism—with a single set of underlying “genetic rules”. But in analogy to the situation with humans, we can imagine a whole population of genetically slightly different idealized organisms, with different responses to perturbations, etc.
Many changes to the underlying rules for our idealized organism will lead to unrecognizably different patterns, that don’t, for example, have the kind of finite-but-long lifetimes we’ve been interested in. But it turns out that in the rules for our particular idealized organism there are some specific changes that actually don’t have any effect at all—at least on the unperturbed pattern of behavior. And the reason for this is that in generating the unperturbed pattern these particular cases in the rule happen never to be used:
And the result is that any one of the 43 = 64 possible choices of outcomes for those cases in the rule will still yield the same unperturbed pattern. If there’s a perturbation, however, different cases in the rule can be sampled—including these ones. It’s as if cases in the rule that are initially “non-coding” end up being “coding” when the path of behavior is changed by a perturbation. (Or, said differently, it’s like different genes being activated when conditions are different.)
So to make an idealized model of something like a population with genetic diversity, we can look at what happens with different choices of our (initially) “non-coding” rule outcomes:
Before the perturbation, all these inevitably show the same behavior, because they’re never sampling “non-coding” rule cases. But as soon as there’s a perturbation, the pattern is changed, and after varying numbers of steps, previously “non-coding” rule cases do get sampled—and can affect the outcome.
Here are the distinct cases of what happens in all 64 “genetic variants”—with the red arrow in each case indicating where the pattern first differs from what it is with our original idealized organism:
And here is then the distribution of lifetimes achieved—in effect showing the differing consequences of this particular “disease perturbation” on all our genetic variants:
What happens with other “disease perturbations”? Here’s a sample of distributions of lifetimes achieved (where “__” corresponds to cases where all 64 genetic variants yield the same lifetime):
OK, so what about the overall lifetime distribution across all (single) perturbations for each of the genetic variants? The detailed distribution we get is different for each variant. But their general shape is always remarkably similar
though taking differences from the case of our original idealized organism reveals some structure:
As another indication of the effect of genetic diversity, we can plot the survival curve averaged over all perturbations, and compare the case for our original idealized organism with what happens if we average equally over all 64 genetic variants. The difference is small, but there is a longer tail for the average of the genetic variants than for our specific original idealized organism:
We’ve seen how our idealized genetic variation affects “disease”. But how does it affect “treatment”? For the “disease” above, we already saw that there’s a particular “treatment perturbation” that successfully returns our original idealized organism to its “natural lifespan”. So what happens if we apply this same treatment across all the genetic variants? In effect this is like doing a very idealized “clinical trial” of our potential treatment. And what we see is that the results are quite diverse—and indeed more diverse than from the disease on it own:
In essence what we’re seeing is that, yes, there are some genetic variants for which the treatment still works. But there are many for which there are (often fairly dramatic) side effects.
Biological Evolution and Our Model Organism
So where did the particular rule for the “model organism” we’ve been studying come from? Well, we evolved it—using a slight generalization of the idealized model for biological evolution that I recently introduced. The goal of our evolutionary process was to find a rule that generates a pattern that lives as long as possible, but not infinitely long—and that does so robustly even in the presence of perturbations. In essence we used lifetime (or, more accurately, “lifetime under perturbation”) as our “fitness function”, then progressively evolved our rule (or “genome”) by random mutations to try to maximize this fitness function.
In more detail, we started from the null (“everything turns white”) rule, then successively made random changes to single cases in the rule (“point mutations”)—keeping the resulting rule whenever the pattern it generated had a lifetime (under perturbation) that wasn’t smaller (or infinite). And with this setup, here’s the particular (random) sequence of rules we got (showing for each rule the outcome for each of its 64 cases):
Many of these rules don’t “make progress” in the sense that they increase the lifetime under perturbation. But every so often there’s a “breakthrough”, and a rule with a longer lifetime under perturbation is reached:
And, as we see, the rule for the particular model organism we’ve been using is what’s reached at the end.
In studying my recent idealized model for biological evolution, I considered fitness functions like lifetime that can directly be computed just by running the underlying rule from a certain initial condition. But here I’m generalizing that a bit, and considering as a fitness function not just lifetime, but “lifetime under perturbation”, computed by taking a particular rule, and finding the minimum lifetime of all patterns produced by it with certain random perturbations applied.
So, for example, here the “lifetime under perturbation” would be considered to be the minimum of the lifetimes generated with no perturbation, and with certain random perturbations—or in this case 60:
This plot then illustrates how the (lifetime-under-perturbation) fitness (indicated by the blue line) behaves in the course of our adaptive evolution process, right around where the fitness-60 “breakthrough” above occurs:
What’s happening in this plot? At each adaptive step, we’re considering a new rule, obtained by a point mutation from the previous one. Running this rule we get a certain lifetime. If this lifetime is finite, we indicate it by a green dot. Then we apply a certain set of random perturbations—indicating the lifetimes we get by gray dots. (We could imagine using all sorts of schemes for picking the random perturbations; here what we’re doing is to perturb random points on about a tenth of the rows in the unperturbed pattern.)
Then the minimum lifetime for any given rule we indicate by a red dot—and this is the fitness we assign to that rule. So now we can see the whole progression of our adaptive evolution process:
One thing that’s notable is that the unperturbed lifetimes (green dots) are considerably larger than the final minimum lifetimes (red dots). And what this means is that our requirement of “robustness”, implemented by looking at lifetime under perturbation rather than just unperturbed lifetime, considerably reduces the lifetimes we can reach. In other words, if our idealized organism is going to be robust, it won’t tend to be able to have as long a lifetime as it could if it didn’t have to “worry about” random perturbations.
And to illustrate this, here’s a typical example of a much longer lifetime obtained by adaptive evolution with the same kind of rule we’ve been using (k = 4, r = 1 cellular automaton), but now with no perturbations and with fitness being given purely by the unperturbed lifetime (exactly as in my recent work on biological evolution):
OK, so given that we’re evolving with a lifetime-under-perturbation fitness function, what are some alternatives to our particular model organism? Here are a few examples:
At an overall level, these seem to react to perturbations much like our original model organism:
One notable feature here, though, is that there seems to be a tendency for simpler overall behavior to be less disrupted by perturbations. In other words, our idealized “diseases” seem to have less dramatic effects on “simpler” idealized organisms. And we can see a reflection of this phenomenon if we plot the overall (single-perturbation) lifetime distributions for the four rules above:
But despite detailed differences, the main conclusion seems to be that there’s nothing special about the particular model organism we’ve used—and that if we repeated our whole analysis for different model organisms (i.e. “different idealized species”) the results we’d get would be very much the same.
What It Means and Where to Go from Here
So what does all this mean? At the outset, it wasn’t clear there’d be a way to usefully capture anything about the foundations of medicine in a formalized theoretical way. But in fact what we’ve found is that even the very simple computational model we’ve studied seems to successfully reflect all sorts of features of what we see in medicine. Many of the fundamental effects and phenomena are, it seems, not the result of details of biomedicine, but instead are at their core purely abstract and computational—and therefore accessible to formalized theory and metamodeling. This kind of methodology is very different from what’s been traditional in medicine—and isn’t likely to lead directly to specific practical medicine. But what it can do is to help us develop powerful new general intuition and ways of reasoning—and ultimately an understanding of the conceptual foundations of what’s going on.
At the heart of much of what we’ve seen is the very fundamental—and ubiquitous—phenomenon of computational irreducibility. I’ve argued recently that computational irreducibility is central to what makes biological evolution work—and that it’s inevitably imprinted on the core “computational architecture” of biological organisms. And it’s this computational irreducibility that inexorably leads to much of the complexity we see so ubiquitously in medicine. Can we expect to find a simple narrative explanation for the consequences of some perturbation to an organism? In general, no—because of computational irreducibility. There are always pockets of computational reducibility, but in general we can have no expectation that, for example, we’ll be able to describe the effects of different perturbations by neatly classifying them into a certain set of distinct “diseases”.
To a large extent the core mission of medicine is about “treating diseases”, or in our terms, about remediating or reversing the effects of perturbations. And once again, computational irreducibility implies there’s inevitably a certain fundamental difficulty in doing this. It’s a bit like with the Second Law of thermodynamics, where there’s enough computational irreducibility in microscopic molecular dynamics that to seriously reverse—or outpredict—this dynamics is something that’s at least far out of range for computationally bounded observers like us. And in our medical setting the analog of that is that “computationally bounded interventions” can only systematically lead to medical successes insofar as they tap into pockets of computational reducibility. And insofar as they are exposed to overall computational irreducibility they will inevitably seem to show a certain amount of apparent randomness in their outcomes.
In traditional approaches to medicine one ultimately tends to “give in to the randomness” and go no further than to assign probabilities to things. But an important feature of what we’ve done here is that in our idealized computational models we can always explicitly see what’s happening inside. Often—largely as a consequence of computational irreducibility—it’s complicated. But the fact that we can see it gives us the opportunity to get much more clarity about the fundamental mechanisms involved. And if we end up summarizing what happens by giving probabilities and doing statistics it’s because this is something we’re choosing to do, not something we’re forced to do because of our lack of knowledge of the systems we’re studying.
There’s much to do in our effort to explore the computational foundations of medicine. But already there are some implications that are beginning to emerge. Much of the workflow of medicine today is based on classifying things that can go wrong into discrete diseases. But what we’ve seen here (which is hardly surprising given practical experience with medicine) is that when one looks at the details, a huge diversity of things can happen—whose characteristics and outcomes can’t really be binned neatly into discrete “diseases”.
And indeed when we try to figure out “treatments” the details matter. As a first approximation, we might base our treatments on coarse graining into discrete diseases. But—as the approach I’ve outlined here can potentially help us analyze—the more we can directly go from detailed measurements to detailed treatments (through computation, machine learning, etc.), the more promising it’s likely to be. Not that it’s easy. Because in a sense we’re trying to beat computational irreducibility—with computationally bounded measurements and interventions.
In principle one can imagine a future in which our efforts at treatment have much more computational sophistication (and indeed the immune system presumably already provides an example in nature). We can imagine things like algorithmic drugs and artificial cells that are capable of amounts of computation that are a closer match for the irreducible computation of an organism. And indeed the kind of formalized theory that I’ve outlined here is likely what one needs to begin to get an idea of how such an approach might work. (In the thermodynamic analogy, what we need to do is a bit like reversing entropy increase by sending in large numbers of “smart molecules”.)
(By the way, seeing how difficult it potentially is to reverse the effects of a perturbation provides all the more impetus to consider “starting from scratch”—as nature does in successive generations of organisms—and simply wholesale regenerating elements of organisms, rather than trying to “fix what’s there”. And, yes, in our models this is for example like starting to grow again from a new seed, and letting the resulting pattern knit itself into the existing one.)
One of the important features of operating at the level of computational foundations is that we can expect conclusions we draw to be very general. And we might wonder whether perhaps the framework we’ve described here could be applied outside of medicine. And to some extent I suspect it can—potentially to areas like robustness of large-scale technological and social systems and specifically things like computer security and computer system failures. (And, yes, much as in medicine one can imagine for example “classifying diseases” for computer systems.) But things likely won’t be quite the same in cases like these—because the underlying systems have much more human-determined mechanisms, and less “blind” adaptive evolution.
But when it comes to medicine, the very presence of computational irreducibility introduced by biological evolution is what potentially allows one to develop a robust framework in which one can draw conclusions purely on the basis of abstract computational phenomena. Here I’ve just begun to scratch the surface of what’s possible. But I think we’ve already seen enough that we can be confident that medicine is yet another field whose foundations can be seen as fundamentally rooted in the computational paradigm.
Thanks & Notes
Thanks to Wolfram Institute researcher Willem Nielsen for extensive help.
I’ve never written anything substantial about medicine before, though I’ve had many interactions with the medical research and biomedical communities over the years—that have gradually extended my knowledge and intuition about medicine. (Thanks particularly to Beatrice Golomb, who over the course of more than forty years has helped me understand more about medical reasoning, often emphasizing “Beatrice’s Law” that “Everything in medicine is more complicated than you can possibly imagine, even taking account of Beatrice’s Law”…)
