Believing in the value of conceptual labor

Ideas are funny things. It can take hours or days or months of noodling on a concept before you’re even able to start putting your thoughts into a shape that others will understand. And by then, you’ve explored the contours of the problem space enough that the end result of your noodling doesn’t seem interesting anymore: it seems obvious.

It’s a lot easier to feel like you’re doing real work when you’re writing code or collecting data or fixing firewall rules. These are tasks with a visible, concrete output that correlates roughly with the amount of time you put into them. When you finish writing a script, you can hold it up to your colleagues and they can see how much effort you put into it.

But as you get into more senior-type engineering roles, your most valuable contributions start to take the form not of concrete labor, but of conceptual labor. You’re able to draw on a rich mental library of abstractions, synthesizing and analyzing concepts in a way that only someone with your experience can do.

One of the central challenges in growing into a senior engineer consists in recognizing and acknowledging the value of the conceptual labor. We have to learn to identify and discard discouraging self-talk, like:

  • Time spent thinking is time spent not doing. When you’re a senior engineer, thinking is often the most valuable kind of doing you can do.
  • It’s not worth telling anyone about this connection I thought of. As a senior engineer, you will make conceptual connections that no one else will make. If they seem worthwhile to you, then why shouldn’t it be worthwhile to communicate them to others?
  • My coworkers are all grinding through difficult work and I’m just over here ruminating. Working with concepts is difficult work, and it’s work whose outcome can be immensely beneficial to your team and your org, but only if you follow through with it. Don’t talk yourself down from it.

Perhaps for the first time in your career, one of the skills you have to develop is faith: faith in the value of your conceptual labor. When an idea looks important to you, have faith that your experience is leading you down a fruitful path. Find that idea’s shape, see how it fits into your cosmos, and put that new knowledge – knowledge that you created by the sweat of your own brow – out into the world.

The paradox of the bloated backlog

I want to point out a paradox you may not have noticed.

A team of software engineers or SREs invariably has more good ideas than time. We know this very well. Pick any system we own, and we’ll come up with a list of 10 things we could do to make it better. Off the top of our head.

On the other hand, when our team is confronted with the opportunity to purge some old features or enhancements out of the backlog, there’s resistance. We say, “we might get around to this some day,” or “this still needs to get done.”

These two beliefs, taken together, reveal a deep lack of team self-confidence.

If our team always has more good ideas than time, then we’re never going to implement all the good ideas in our backlog. If we add more people, we’ll just get more good ideas, and the backlog will just get more bloated.

Why are we reluctant to ruthlessly remove old tickets, then? We know that we’re constantly generating good ideas. In fact, the ideas we’re generating today are necessarily (on average) better than most of the ideas in the backlog:

  1. We have more information about the system now then we used to, so our new ideas are more aligned with real-world facts, and
  2. We have more experience as engineers now, so we have developed better intuition about what kind of interventions will create the most value.

Seen in this light, a hesitance to let go of old ideas is revealed as a symptom of a deep pathology. It means we don’t believe in our own creativity and agency. If we did, we would have easy answers to the questions we always ask when we consider closing old tickets:

  • What if we forget about this idea? That’s okay. We’ll have plenty of other, better, more relevant ideas. We never stop generating them.
  • What if this problem gets worse over time? If the risk is enough that we should prioritize this ticket over our other work, then let’s do that now. Otherwise, we can cross that bridge if we ever get to it.
  • Will the reporter of this ticket even let us close it? Nobody owns our backlog but us. When we decide to close a ticket, all we owe the reporter is an honest explanation of why.

Leave behind the paradox of the bloated backlog and start believing in your team’s own agency and creativity. Hell, maybe even cap your backlog. A team with faith in its competence is a team unleashed.

Latency- and Throughput-Optimized Clusters Under Load

It’s good to have accurate and thorough metrics for our systems. But that’s only where observability starts. In order to get value out of metrics, we have to focus on the right ones: the ones that tell us about outcomes that matter to our users.

In The Latency/Throughput Tradeoff, we talked about why a given cluster can’t be optimized for low latency and high throughput at the same time. In conclusion, we decided that separate clusters should be provisioned for latency-centric use cases and throughput-centric use cases. And since these different clusters are optimized to provide different outcomes, we’ll need to interpret their metrics in accordingly different ways.

Let’s consider an imaginary graph dashboard for each type of cluster. We’ll walk through the relationships between metrics in each cluster, both under normal conditions and under excessive load. And then we’ll wrap up with some ideas about evaluating the capacity of each cluster over the longer term.

Metrics for comparison

In order to contrast our two types of clusters, we’ll need some common metrics. I like to employ the USE metrics at the top of my graph dashboards (more on that in a future post). So let’s use those:

  • Utilization: The total CPU usage for all hosts in the cluster.
  • Saturation: The number of queued requests.
  • Error rate: The rate at which lines are being added to hosts’ error logs across the cluster.

In addition to these three metrics, we want to see a fourth metric. For the latency-optimized cluster, we want to see latency. And for the throughput-optimized cluster, we want to see throughput.

One of the best things about splitting out latency-optimized and throughput-optimized clusters is that the relationships between metrics become much clearer. It’s hard to tell when something’s wrong if you’re not sure what kind of work your cluster is supposed to be doing at any given moment. But separation of concerns allows us to develop intuition about our systems’ behavior and stop groping around in the dark.

Latency-optimized cluster

Let’s look at the relationships between these four important metrics in a latency-optimized cluster under normal, healthy conditions:

2019-03-11 blog charts latency-oriented healthyUtilization will vary over time depending on how many requests are in flight. Saturation, however, should stay at zero. Any time a request is queued, we take a latency hit.\

Error rate would ideally be zero, but come on. We should expect it to be correlated to utilization, following the mental model that all requests carry the same probability of throwing an error.

Latency, then – the metric this cluster is optimized for – should be constant. It should not be affected by utilization. If latency is correlated to utilization, then that’s a bug. There will always be some wiggle in the long tail (the high percentiles), but for a large enough workload, the median and the 10th percentile should pretty much stay put.

Now let’s see what happens when the cluster is overloaded:

2019-03-12 blog charts latency-oriented loaded

We start to see plateaus in utilization, or at least wider, flatter peaks. This means that the system is low on “slack”: the idle resources that it should always have available to serve new requests. When all resources are busy, saturation rises above zero.

Error rate may still be correlated with utilization, or it may start to do wacky things. That depends on the specifics of our application. In a latency-optimized cluster, saturation is always pathological, so it shouldn’t be surprising to see error rates climb or spike when saturation rises above zero.

Finally, we start to see consistent upward trends in latency. The higher percentiles are affected first and most dramatically. Then, as saturation rises even higher, we can see the median rise too.

Throughput-optimized cluster

The behavior of our throughput-optimized cluster, on the other hand, is pretty different. When it’s healthy, it looks like this:

2019-03-22 blog charts throughput-oriented healthy.png

Utilization – which, remember, we’re measuring via CPU usage – is no longer a fluffy cloud. Instead, it’s a series of trapezoids. When no job is in progress, utilization is at zero. When a job starts, utilization climbs up to 100% (or as close to 100% as reality allows it to get), and then stays there until the job is almost done. Eventually, the number of active tasks drops below the number of available processors, and utilization trails off back to zero.

Saturation (the number of queued tasks) follows more of a sawtooth pattern. A client puts a ton of jobs into the system, bringing utilization up to its plateau, and then as we grind through jobs, we see saturation slowly decline. When saturation reaches zero, utilization starts to drop.

Unlike that of a latency-optimized cluster, the error rate in a throughput-optimized cluster shouldn’t be sensitive to saturation. Nonzero saturation is an expected and desired condition here. Error rate is, however, expected to be follow utilization. If it bumps around at all, it should plateau, not sawtooth.

And finally, in the spot where the other cluster’s dashboard had a latency graph, we now have throughput. This we should measure in requests per second per job queued! What our customers really care about is not how many requests per second our cluster is processing, but how many of their requests per second. We’ll see why this matters so much in a bit, when we talk about this cluster’s behavior under excessive load.

Throughput should be tightly correlated to utilization and nothing else. If it also seems to exhibit a negative correlation to saturation, then that’s worth looking into: it could mean that queue management is inappropriately coupled to job processing.

Now what if our throughput-optimized cluster starts to get too loaded? What does that look like?

2019-03-23 blog charts throughput-oriented loaded

Utilization by itself doesn’t tell us anything about the cluster’s health. Qualitatively, it looks just like before: big wide trapezoids. Sure, there a bit wider than they were before, but we probably won’t notice that – especially since it’s only on average that they’re wider.

Saturation is where we really start to see the cracks. Instead of the sawtooth pattern we had before, we start to get more sawteeth-upon-sawteeth. These are jobs starting up on top of jobs that are already running. A few of these are to be expected even under healthy circumstances, but if they become more frequent, it’s an indication that there may be too much work for the cluster to handle without violating throughput SLOs.

Error rate may not budge much in the face of higher load. After all, this cluster is supposed to hold on to big queues of requests. As far as it’s concerned, nothing is wrong with that.

And that’s why we need to measure throughput in requests per second per job queued. If all we looked at was requests per second, everything would look hunky dory. But when there are two jobs queued and they’re constrained to use the same pool of processors, somebody’s throughput is going to suffer. On this throughput graph, we can see that happen right before our eyes.

Longer-term metrics

Already, we’ve seen how decoupling these two clusters gives us a much clearer mental model of their expected behavior. As we get used to the relationships between the metrics we’ve surfaced, we’ll start to build intuition. That’s huge.

But we don’t have to stop there! Having a theory (which is what we built above) also allows us to reason about long-term changes in the observable properties of these clusters as their workloads shift.

Take the throughput-optimized cluster, for instance. As our customers place more and more demand on it, we expect to see more sawteeth-upon sawtooth and longer intervals between periods of zero saturation. This latter observation is key, since wait times grow asymptotically as utilization approaches 100%. So, if we’re going to want to do evaluate the capacity needs of our throughput-optimized cluster, we should start producing these metrics on day one and put them on a dashboard:

  • Number of jobs started when another job was already running, aggregated by day. This is the “sawteeth-upon-sawteeth” number.
  • Proportion of time spent with zero saturation, aggregated by day.
  • Median (or 90th percentile) time-to-first-execution for jobs, aggregated by day. By this I mean: for each customer job, how much time passed between the first request being enqueued and the first request starting to be processed. This, especially compared with the previous metric, will show us how much our system is allowing jobs to interfere with one another.

An analogous thought process will yield useful capacity evaluation metrics for the latency-optimized cluster.

TL;DR

UnsteadyBlueAardvark-size_restricted

Separating latency- and throughput-optimized workloads doesn’t just make it easier to optimize each. It carries the added benefit of making it easier to develop a theory about our system’s behavior. And when you have a theory that’s consistent with the signal and a signal that’s interpretable within your theory, you have observability.

The Latency/Throughput Tradeoff: Why Fast Services Are Slow And Vice Versa

Special thanks to the graceful and cunning Ben Ng for consulting on this post.

I’m finally getting around to reading that DevOps* book everybody’s been raving about, Site Reliability Engineering: How Google Runs Production Systems. My verdict so far: it’s pretty good.

Here’s one of the first passages to jump out to me, from Chapter 3: Embracing Risk:

The low-latency user wants Bigtable’s request queues to be (almost always) empty so that the system can process each outstanding request immediately upon arrival. (Indeed, inefficient queuing is often a cause of high tail latency.) The user concerned with offline analysis is more interested in system throughput, so that user wants request queues to never be empty. To optimize for throughput, the Bigtable system should never need to idle while waiting for its next request.

This is a profound and general insight. When I read this passage, my last decade of abject suffering suddenly came into focus for me.

When I say “abject suffering,” I’m of course talking about ElasticSearch administration. When a storage system like ElasticSearch has to serve both high-latency and high-throughput workloads, it is guaranteed to get ugly. This fact is super important, which is why I’m devoting this blog post to exploring the relationships among latency, throughput, and capacity from a queueing perspective. I hope I can make these relationships stick in your mind like they’ve stuck in mine.

* Go ahead. Tell me DevOps and SRE aren’t the same thing. I dare you.

The tradeoff between throughput and latency

Consider a service that responds to requests. As an example, let’s say it’s a service that takes as input a picture of a dog and returns a picture of that dog wearing a silly hat.

2019-02-25 dog wearing hat
Artist’s rendering

Like almost any service (exception: Tourbillon), our service can only handle a certan number of requests per second [to put hats on dogs (RPSTPHOD)]. We’ll call this number its capacity. If we have 200 processes devoted to dog-hatting, and dogs take on average 400 milliseconds to haberdash, then the theoretical capacity of the system is

(200) / (0.4s) = 500 hats per second

Now let’s consider the two types of users that depend on our service:

  • On-the-spot dog hatters. At any given time, these users have a single dog picture that requires a hat as soon as possible. Perhaps they’re using our service to support a website that generates a single dog-hat picture per page load, and they want their page to load quickly. These users are interested primarily in how quickly they can get a hat on a dog. In a word: latency.
  • Bulk dog-hatters. These users tend to have massive data sets that they want processed as quickly as possible. The most obvious example would be a law enforcement agency wanting to compare their large database of pet photos to surveillance footage of a particular dog robbing a bank while wearing a hat. Bulk dog-hatters care not about the latency of any individual dog-hatting, but about the throughput they can achieve. In other words: how close they can get to our service’s theoretical capacity of 500 hats per second.

But here’s the problem: no single cluster of dog-hatting servers can be optimal for both types of users. And the better we make the service for one kind of user, the worse we make it for the other.

The needs of on-the-spot users

In order to minimize latency for our on-the-spot users (without dropping any of their requests), we need to make sure that there’s always a processor idle when their request comes in. If we fail to make sure of this, then new requests will have to be queued while we wait for a spot to open up, thus inflating latency. The system needs some “slack.”

2019-02-25 blog charts low-latency

Since we need slack, we don’t ever want throughput to approach capacity. The closer we get to our system’s capacity, the more drastically latencies will balloon, like I talked about in this post.

The needs of bulk users

Our bulk dog-hatters, on the other hand, don’t care so much about request latency. Some of their individual requests might take seconds, or minutes, or even hours to complete. What they care about is how quickly our service can process their entire data set. In other words, they care about getting throughput as close as possible to capacity.

This means that, whenever a job is running, bulk dog-hatters want there to be (virtually) zero slack. Every processor should be active at all times. Consequently, our queue sizes will explode as soon as the job starts, and our queues will stay occupied until the job is almost done.

2019-02-25 blog charts high-throughput

In this case, we want our queues to be full whenever there’s a bulk job running. Anything else would give sub-optimal throughput.

Splitting the cluster up

The needs of on-the-spot and bulk users are incompatible. One group needs minimal latency, while the other group needs maximal throughput.

If both of these groups are using the same cluster, we’re going to have serious problems. On-the-spot users’ latencies will vary widely depending on whether there’s currently a bulk job in progress, and bulk users’ job times will vary depending on the number of on-the-spot users currently using the system. No matter how much we scale or tweak tuning parameters, neither group will get what they need. And what’s worse, we’ll be stuck in a perpetual tug-of-war between the priorities of these two groups.

So let’s split our cluster in two: a “low latency” cluster and a “high throughput” cluster. And let’s let our users pick the right one for their use case. This way, we’ll have much clearer expectations about the performance and scaling characteristics of our service, and we’ll avoid the frustrating priority tug-of-war that characterized our mixed-use cluster.

The split doesn’t have to be complete. Instead of having two wholly separate clusters, we could have some kind of load balancer that reserves a certain portion of our fleet for low-latency traffic and slots bulk jobs onto dedicated segments of the cluster. The details of every solution will vary. What matters is that on-the-spot and bulk dog-hatters aren’t drawing on the same pool of resources.

Once we do split up our cluster, then, what should we expect the performance characteristics of the new clusters to be? What will their graph dashboards look like when they’re healthy, or near capacity, or over capacity? In an upcoming post, I’ll use some more queueing reasoning to answer these questions. So get hype for that!

[UPDATE: It’s here!]

Let’s Stop Pretending Estimates Are Exact

Some days I feel like estimates and plans are worthless. Other days I find myself idly speculating that if only we were better at planning and estimating, everything would be beautiful.

In an engineering organization, we want realistic plans. Realistic plans and roadmaps will hypothetically help us utilize our capacity effectively and avoid overcommitting. And our plans are usually built on estimates; that’s why we believe that “correct” estimates are more likely to generate a realistic plan. Therefore, we believe that correct estimates are useful for planning.

On the other hand, if you’ve ever worked with engineers, you also believe that estimates are never correct. Something always gets in the way, or we pad the estimate out to avoid being held responsible for missing a deadline, or (occasionally) the task ends up being much simpler than we expected. The time we estimate is never the time it actually takes to do the job.C7ofJ_scaled

These two statements seem to be in contradiction, but they are not. There is a key to holding both these beliefs in your head at once. And I believe that if an entire engineering org were to grasp this key together, it would unlock enormous potential.

The key is to treat uncertainty as a first-class citizen.

Why This Is Hard

Developing organizational intuition in about estimates is really hard. It is in fact so hard that I’m not aware of any organization that has done it. I see two big reasons for this:

  1. We don’t have good awareness of the amount of uncertainty in our estimates.
  2. We pay lip service to the idea that estimates aren’t perfect, but we plan as if they are.

1. Uncalibrated estimates

When we give estimates, those estimates aren’t calibrated to a particular uncertainty level. Everybody has different levels of confidence in their estimates, and those levels are neither discussed nor adjusted. As a result, engineers and project managers find it impossible to turn estimates into meaningful plans.

2. Planning with incorrect use of uncertainty

You’ve surely noticed uncertainty being ignored. It usually goes something like this:

PM: How soon do you think you can have the power converters re-triangulated?
ENG: I’m not sure. It could take a day, or it could take five.
PM: I understand. What do you think is most likely? Can we say three days?
ENG: Sure, three or four.
PM: Okay. I’ll put it down for four days, just to be safe.

Both sides acknowledge that there is a great deal of uncertainty in this estimate. But a number needs to get written down, so they write down 4. In this step, information about uncertainty is lost. So it shouldn’t be a surprise later when re-triangulating the power converters takes 7 days and the whole plan gets thrown off.

Example

Suppose 5 teams are working independently on different parts of a project. Each team has said they’re 80% confident that their part will be done by the end of the year. The project manager will want to know how likely is it that all five parts will be done by the end of the year?

When we answer questions like this, we don’t usually think in terms of probability. And even if we do think in terms of probability, it’s easy to get it wrong. If you ask non-mathy people this question (and most project managers I’ve worked with are not mathy), their intuition will be: 80%.

DreidelsBut that intuition is extremely misleading. What we’re dealing with is a set of 5 independent events, each with 80% probability. Imagine rolling five 5-sided dice. Or, since 5-sided dice are not really a thing, imagine spinning five 5-sided dreidels (which are also not really a thing, but are at least geometrically possible). You spin your five dreidels and if any of them comes up ש‎, the project fails to meet its end-of-year deadline. The probability of success, then, is:

(80%)⁵ = 80% ⋅ 80% ⋅ 80% ⋅ 80% ⋅ 80% = 32.8%

Awareness of the probabilistic nature of estimates makes it obvious that a bunch of high-confidence estimates do not add up to a high-confidence estimate.

To make matters even worse, most organizations don’t even talk about how confident they are. In real life, we wouldn’t even know the uncertainties associated with our teams’ estimates (this is problem 1: uncalibrated estimates). Nobody would even be talking about probabilities. They’d be saying “All five teams said they’re pretty sure they can be done by the end of the year, so we can be pretty sure we’ll hit an end-of-year target for the project.” But they’d be dead wrong.

Why This Is Worth Fixing

I believe that poor handling of uncertainty is a major antagonist not just of technical collaboration, but of social cohesion at large. When uncertainty is not understood:

  • Project managers feel let down. Day in and day out they ask for reasonable estimates, and they’re left explaining to management why the estimates were all incorrect and the project is going to be late.
  • Engineers feel held to unreasonable expectations. They have to commit to a single number, and when that number is too low they have to work extra hard to hit it anyway. It feels like being punished for something that’s no one’s fault.
  • Managers feel responsible for failures. Managers are supposed to help their teams collaborate and plan, but planning without respect for uncertainty leads to failure every time. And what’s worse, if you don’t understand the role of uncertainty, you can’t learn from the failure.
  • Leadership makes bad investments. Plans may look certain when they’re not at all. Return on an investment often degrades quickly with delays, making what looked like a good investment on paper turn out to be a dud.

Fostering an intuition for uncertainty in an organization could help fix all these problems. I think it would be crazy not to at least try.

How To Fix It

Okay, here’s the part where I admit that I don’t quite know what to do about this problem. But I’ve got a couple ideas.

1. Uncalibrated estimates

To solve the problem of uncalibrated estimates (estimates whose uncertainty is wrong or never acknowledged), what’s needed is practice. Teams need to make 80%-confidence estimates for everything – big and small – and record those estimates somewhere. Then when the work is actually done, they can review their estimates and compare to the real-world completion time. If they didn’t get about 80% of their estimates correct, they can learn to adjust their confidence.

Estimating with a certain level of confidence is a skill that can be learned through practice. But practice, as always, takes a while and it needs to be consistent. I’m not sure how one would get an organization to put in the work, but I do believe it would pay off if they did.

2. Planning with incorrect use of uncertainty

Managers and project managers should get some training in how to manipulate estimates with uncertainty values attached.

Things get tricky when tasks need to be done one after the other instead of in parallel. But I like to think we’re not adding complexity to the process of planning; rather we’re just revealing the ways in which the current process is broken. And recognizing the limits of our knowledge is a great way to keep our batch sizes small and our planning horizons close.

I think we need to get used to calibrating estimates before we can see our way clear to address the planning challenges.

Can It Be Fixed?

It strikes me as super hard to fix the problems I’ve outlined here in a company that already has its old habits. Perhaps a company needs to be built from the ground up with a culture of uncertainty awareness. But I hope not.

If there is a way to make uncertainty a first-class citizen, I truly believe that engineering teams will benefit hugely from it.

Falsifiability: why you rule things out, not in

This June, I had the honor of speaking at O’Reilly Velocity 2016 in Santa Clara. My topic was Troubleshooting Without Losing Common Ground, which I’ve written about and written about before that too.

I was pretty happy with my talk, especially the Star Trek: The Next Generation vignette in the middle. It was a lot of ideas to pack into a single talk, but I think a lot of people got the point. However, I did give a really unsatisfactory answer (30m46s) to the first question I received. The question was:

In the differential diagnosis steps, you listed performing tests to falsify assumptions. Are you borrowing that from medicine? In tech are we only trying to falsify assumptions, or are we sometimes trying to validate them?

I didn’t have a real answer at the time, so I spouted some bullshit and moved on. But it’s a good question, and I’ve thought more about it, and I’ve come up with two (related) answers: a common-sense answer and a pretentious philosophical answer.

The Common Sense Answer

My favorite thing about differential diagnosis is that it keeps the problem-solving effort moving. There’s always something to do. If you’re out of hypotheses, you come up with new ones. If you finish a test, you update the symptoms list. It may not always be easy to make progress, but you always have a direction to go, and everybody stays on the same page.

But when you seek to confirm your hypotheses, rather than to falsify others, it’s easy to fall victim to tunnel vision. That’s when you fixate on a single idea about what could be wrong with the system. That single idea is all you can see, as if you’re looking at it through a tunnel whose walls block everything else from view.

Tunnel vision takes that benefit of differential diagnosis – the constant presence of a path forward – and negates it. You keep running tests to try to confirm your hypothesis, but you may never prove it. You may just keep getting tests results that are consistent with what you believe, but that are also consistent with an infinite number of hypotheses you haven’t thought of.

A focus on falsification instead of verification can be seen as a guard against tunnel vision. You can’t get stuck on a single hypothesis if you’re constrained to falsify other ones. The more alternate hypotheses you manage to falsify, the more confident you get that you should be treating for the hypotheses that might still be right.

Now, of course, there are times when it’s possible to verify your hunch. If you have a highly specific test for a problem, then by all means try it. But in general it’s helpful to focus on knocking down hypotheses rather than propping them up.

The Pretentious Philosophical Answer

I just finished Karl Popper’s ridiculously influential book The Logic of Scientific Discovery. If you can stomach a dense philosophical tract, I would highly recommend it.

karl-popper-4.jpg
Karl “Choke Right On It, Logical Positivism” Popper

Published in 1959 – but based on Popper’s earlier book Logik der Forschung from 1934 – The Logic Of Scientific Discovery makes a then-controversial [now widely accepted (but not universally accepted, because philosophers make cats look like sheep, herdability-wise)] claim. I’ll paraphrase the claim like so:

Science does not produce knowledge by generalizing from individual experiences to theories. Rather, science is founded on the establishment of theories that prohibit classes of events, such that the reproducible occurrence of such events may falsify the theory.

Popper was primarily arguing against a school of thought called logical positivism, whose subscribers assert that a statement is meaningful if and only if it is empirically testable. But what matters to our understanding of differential diagnosis isn’t so much Popper’s absolutely brutal takedown of logical positivism (and damn is it brutal), as it is his arguments in favor of falsifiability as the central criterion of science.

I find one particular argument enlightening on the topic of falsification in differential diagnosis. It hinges on the concept of self-contradictory statements.

There’s an important logical precept named – a little hyperbolically – the Principle of Explosion. It asserts that any statement that contradicts itself (for example, “my eyes are brown and my eyes are not brown”) implies all possible statements. In other words: if you assume that a statement and its negation are both true, then you can deduce any other statement you like. Here’s how:

  1. Assume that the following two statements are true:
    1. “All cats are assholes”
    2. “There exists at least one cat that is not an asshole”
  2. Therefore the statement “Either all cats are assholes, or 9/11 was an inside job” (we’ll call this Statement A) is true, since the part about the asshole cats is true.
  3. However, if the statement “there exists at least one cat that is not an asshole” is true too (which we’ve assumed it is) and 9/11 were not an inside job, then Statement A would be false, since neither of its two parts would be true.
  4. So the only way left for Statement A to be true is for “9/11 was an inside job” to be a true statement. Therefore, 9/11 was an inside job.
  5. Wake up, sheeple.

plhpico

The Principle of Explosion is the crux of one of Popper’s most convincing arguments against the Principle of Induction as the basis for scientific knowledge.

It was assumed by many philosophers of science before Popper that science relied on some undefined Principle of Induction which allowed one to generalize from a finite list of experiences to a general rule about the universe. For example, the Principle of Induction would allow one to deduce from enough statements like “I dropped a ball and it fell” and “My friend dropped a wrench and it fell” to “When things are dropped, they fall.” But Popper argued against the existence of the Principle of Induction. In particular, he pointed out that:

If there were some way to prove a general rule by demonstrating the truth of a finite number of examples of its consequences, then we would be able to deduce anything from such a set of true statements.

Right? By the Principle of Explosion, a self-contradictory statement implies the truth of all statements. If we accepted the Principle of Induction, then the same evidence that proves “When things are dropped, they fall” would also prove “All cats are assholes and there exists at least one cat that is not an asshole,” which would prove every statement we can imagine.

So what does this have to do with falsification in differential diagnosis? Well, imagine you’ve come up with these hypotheses to explain some API slowness you’re troubleshooting:

Hypothesis Alpha: contention on the table cache is too high, so extra latency is introduced for each new table opened

Hypothesis Bravo: we’re hitting our IOPS limit on the EBS volume attached to the database server

There are many test results that would be compatible with Hypothesis Alpha. But unless you craft your tests very carefully, those same results will also be compatible with Hypothesis Bravo. Without a highly specific test for table cache contention, you can’t prove Hypothesis Alpha through a series of observations that agree with it.

What you can do, however, is try to quickly falsify Hypothesis Bravo by checking some graphs against some AWS configuration data. And if you do that, then Hypothesis Alpha is the your best remaining guess. Now you can start treating for table cache contention on the one hand, and attempting the more time-consuming process (especially if it’s correct!) of falsifying Hypothesis Alpha.

Isn’t this kind of abstract?

Haha OMG yes. It’s the most abstract. But that doesn’t mean it’s not a useful idea.

If it’s your job to troubleshoot problems, you know that tunnel vision is very real. If you focus on generating alternate hypotheses and falsifying them, you can resist tunnel vision’s allure.

A Moral Thought Experiment That Breaks My Brain

Note: This blog post is not about computers or math or DevOps. I like those things, and I write about them usually. But not today.

Sometimes I read something and I’m like “that can’t be right,” but then I think about it for a while and I can’t figure out why it’s not right. This happens to me especially often with arguments about moral intuition.

We humans make moral judgements and decisions all day, every day, without even thinking about it. It’s a central part of what makes us us.

Try this: pick a moral belief that you hold very firmly. For example, I went with, “It’s wrong to treat people with less respect because of their sexual orientation.” Now, try to imagine no longer believing that thing. Imagine that everything about your mind is the same, except you no longer hold to that one belief or its consequences. It’s hard, isn’t it? It really feels like you wouldn’t be the same person.

We know that our moral beliefs change over the course of our lives, and so that feeling of our selves being tightly coupled to those beliefs must be an illusion. But still, it’s very disturbing when a well constructed thought experiment forces us to reevaluate our basic moral intuitions.

What follows is a thought experiment that has such a brain-breaking effect on me. We can’t all be moral geniuses who cut right through the Trolley Problem like this kid:

Making People Happy, or Making Happy People?

On this week’s episode of Sam Harris’s Waking Up podcast, the Scottish moral philosopher and effective altruism wunderkind Will MacAskill gave a very brief but very brain-breaking argument. It’s had me scratching my chin intensely for a couple days now.

It seems intuitive to me that we, as humans, have no moral obligation to make sure that more humans come into existence in the future. After all, it’s not like you owe anything to hypothetical people who will never come into existence. There seems to me to be no way that such a moral obligation could arise. I think a lot of people would agree with this intuition.

Will MacAskill’s argument (and I’m not sure it’s his originally, but I heard it from him) goes like this. Imagine what we’ll call World A. World A has some number of people in it, living their lives. And let’s also imagine World B, which has all the same people as World A, plus another person named Harry. Everybody in World B is exactly as well-off as their counterparts in World A, and Harry’s well-being is at a 6 out of 10. He’s moderately well-off.

blog_world_a_b
Photo credit: Brett Swanson

According to my intuition that there is no moral reason to prefer World B, in which Harry exists, to World A, in which Harry never came into being. If we say the total moral value of World A is a and the moral value of World B is b, I believe that a = b.

Alright, MacAskill says, now let’s introduce World C. This world is identical to World A, except it includes a person named Harry whose well-being is an 8 out of 10. He’s very happy almost all the time!

blog_world_c.png

Now, by the same logic I used before, letting World C’s total moral value equal c, I have to say that a = c. This world with a Harry at well-being level 8 is not preferable to a world in which Harry never existed.

This puts me in a bit of a pickle. Because, by straight-up math, we know that if a = b and a = c then b = c. In other words, there’s no moral reason to prefer World C to World B. But come on! World C is exactly like World B except that Harry is better off. Obviously it’s an objectively preferable world.

I feel reductio ad absurdum‘d and it makes me very uncomfortable. Does this mean I have an obligation to have kids if I think I can give them happy lives? I don’t believe that, but I’m not sure what to believe now.