UniverseHacker 4 hours ago

I've become increasingly convinced that the idea of averaging is one of the biggest obstacles to understanding things... it contains the insidious trap of feeling/sounding "rigorous" and "quantitative" while making huge assumptions that are extremely inappropriate for most real world situations.

Once I started noticing this I can't stop seeing this almost everywhere- almost every news article, scientific paper, etc. will make clearly inappropriate inferences about a phenomenon based on the exact same mistake of confusing the average for a complete description of a distribution, or a more nuanced context.

Just a simple common example, is the popular myth that ancient people died of old age in their 30s, based on an "average life span of ~33 years" or such. In reality the modal life expectancy of adults (most common age of death other than 0) has been pretty stable in the 70s-80s range for most of human history- the low average was almost entirely due to infant mortality.

The above example is a case where thinking in terms of averages causes you to grossly misunderstand simple things, in a way that would be impossible even with basic common sense in a person that had never encountered the idea of math... yet it is a mistake you can reliably expect people in modern times to make.

  • llm_trw 3 hours ago

    >In reality the modal life expectancy of adults (most common age of death other than 0) has been pretty stable in the 70s-80s range for most of human history- the low average was almost entirely due to infant mortality.

    This is even wronger than what you critique.

    For every period in history that we have good data for people had a half-life - a period in which you'd expect half of all people to die: https://batintheattic.blogspot.com/2011/07/medieval-populati...

    For example in medieval Germany it looked something like:

        |   Age | Half-life |
        |  0-10 |        10 |
        | 10-20 |        40 |
        | 20-40 |        20 |
        | 40-80 |        10 |
        
    
    It's called a population pyramid not a population column for a reason.

    The exact age varies by location, but even if we ignore everyone under 10, half of all people left would still die before they are 40.

    • UniverseHacker 32 minutes ago

      What you said in no way conflicts with what I said. For example, if people have dangerous lives in a way that is unconnected to age they will tend to not live long, yet the modal life expectancy due to the additional mortality of actual old age can still be quite old.

      What I was saying is in reference to this study I read long ago, which suggests a modal life span of about 72 years of age in the paleolithic: https://onlinelibrary.wiley.com/doi/10.1111/j.1728-4457.2007...

    • JumpCrisscross 3 hours ago

      > if we ignore everyone under 10, half of all people left would still die before they are 40

      Wouldn't it be 50 since the half-life is an interval?

      • llm_trw 2 hours ago

        No, the half life for age 10-20 is much higher than that for 20-40 and the exponential function is non-linear.

  • bosma 4 hours ago

    > In reality the modal life expectancy of adults (most common age of death other than 0) has been pretty stable in the 70s-80s range for most of human history- the low average was almost entirely due to infant mortality.

    This isn't true: https://ourworldindata.org/its-not-just-about-child-mortalit...

    • usednoise4sale 21 minutes ago

      Our world in data pushes a clear agenda, and it isn't really to be trusted.

      Consider: https://ourworldindata.org/child-mortality-in-the-past

      From this article: "Researchers also collected data about hunter-gatherer societies. The 17 different societies include paleolithic and modern-day hunter-gatherers and the mortality rate was high in all of them. On average, 49% of all children died.[5]"

      This is cited as coming from: https://www.sciencedirect.com/science/article/abs/pii/S10905...

      Which categorically states: "Unfortunately there simply is not enough direct paleodemographic archaeological data to make definite claims about the global patterns of infant and child mortality rates of our Paleolithic hunter–gatherer ancestors."

      The author of the Our World in Data piece seemingly intentionally conflates the proxy with actual archaeological evidence of the actual child mortality rates. Given the clear warning in the cited article about making definite claims, I cannot read the deception any other way.

      After seeing this error, I do not know how you could possibly trust anything they have to say on the matter.

    • Spooky23 3 hours ago

      It mostly is. The biggest gains are in childhood. Aldo consider that you’re looking at figures for England and Wales, which isn’t necessarily representative.

      The largest contribution to improving life expectancy is measured by reductions in child mortality. The factors that drove those improvements (infection control, improved hygienic practices, food quality, regulation of food and drug purity, medicine) benefited everyone, but had the biggest impact on the old and young. In the 1850s, 8,000 infants died annually from adulterated milk alone.

      I think of my own journey. In 1824, 200 year ago Spooky23 would have died 20 years ago, a half blind cripple. 2024 Spooky23 is healthy with no back issues and god willing a few more decades.

      • llm_trw 2 hours ago

        From the nice graph at: https://ourworldindata.org/images/published/Life-expectancy-...

        In 1850 a 0 year old would expect to live to 41.6 years. A 5 year old would expect to live to 55.2.

        If we waved a magic wand and let all infants survive past childhood with nothing else changed in 1850 life expectancy would still be 27 years lower than it is today. Or put another way you'd have the same life expectancy as someone in South Sudan or Somalia.

        • Spooky23 2 hours ago

          Sounds like we mostly agree, save some pedantry.

          Nobody waved a wand. The contaminated milk that killed infants killed adults too - alcohol and milk were alternatives to unsafe water. Public health, medicine and other factors improved things.

          We don’t really have great stats from before the 19th century. Was 1850 a nadir in life expectancy? I’m not sure - but I suspect it varied by region and rural/urban conditions. 1750 NYC wasn’t as gross as 1850.

          • llm_trw 2 hours ago

            >Sounds like we mostly agree, save some pedantry.

            If by pedantry you mean that I'm not ignoring the cause of 70% of the improvement in life expectancy in the last 200 years then sure.

      • JumpCrisscross 2 hours ago

        > It mostly is. The biggest gains are in childhood.

        The life expectancy of a 60-year old going from 74.4 to 84, or a 70-year old from 79.1 to 85.9, is significant and meaningful. Not as much as a newborn's LE going from 41.6 to 81.1. But far from "pretty stable in the 70s-80s range for most of human history."

        Also, recent life-expectancy increases have come from adult morality reductions [1].

        [1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3000019/

  • dalmo3 28 minutes ago

    I came to the same realisation about a decade ago, after being a "science" enthusiast growing up. As you said once you see it you can't unsee it. Most of science is just a scam. The exceptions are those fields backed up by real world engineering. All of social and most of biological sciences are worse than useless, they are outright dangerous.

  • ddfs123 2 hours ago

    > In reality the modal life expectancy of adults (most common age of death other than 0) has been pretty stable in the 70s-80s range for most of human history-

    I am pretty sure this is wrong. East Asian cultures celebrate 60th birthday as becoming very elderly, and if you live to the 70s it's almost as if you achieved Buddhahood.

  • JumpCrisscross an hour ago

    Your beef appears to be with simple averages, not averaging per se.

    The average for life expectancy is the mean of the Gompertz distribution [1]. Specifically, one that is "left skewed and with a flattened slope for ages under 50 years for men and 60 years for women," which proceeds to become "more right skewed and leptokurtic" as age increases [2].

    So a simple average in the <55 domain would underestimate the mean while in the >55 domain it would overestimate it. Which is almost comically problematic when comparing ancient societies that had a median age below that level to modern ones above it.

    > the modal life expectancy of adults (most common age of death other than 0) has been pretty stable in the 70s-80s range for most of human history

    Not quite. 63 in 1900 to 83 in 2000 (in Sweden). Bigger differences when you go further back.

    [1] https://en.wikipedia.org/wiki/Gompertz_distribution

    [2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2652977/

    [3] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3000019/ Figure 1

  • hinkley 4 hours ago

    Averages are very bad in bimodal distributions.

    And that includes issues of public policy, where going left sort of works, and going right sort of works, and going in the middle sucks for absolutely everyone.

  • mcmoor 4 hours ago

    It's just trying to assume normal distribution when it's not normal. Modern science rely so much on that distribution that i actually whether they have overestimated its ubiquity just because it's so damn convenient to use.

robertclaus 4 hours ago

As a computer scientist, I was blown away the first time my friend explained to me that his research focused on the timing of neuron spikes, not their magnitude. After talking about it for a while I realized that machine learning neural networks are much closer to simple early models of how neuron's work (averages and all), not how neuron's actually signal. Makes sense when you consider how the latest LLM models have almost as many parameters as we have neurons, but we still seem pretty far from AGI.

  • dilawar 3 hours ago

    In many, perhaps most, signalling pathways, amplitude doesn't matter much (it does at log-scale). Given how well we control temperature and therefore rate of the reaction, it makes sense to use timing to fight off the noise.

  • lamename 2 hours ago

    Yes and no. An alternate perspective is that the output of each neuron in an artificial neural net is analogous to an F-I curve in a real neuron (spike frequency-input DC current curve). In this way, different neurons have different slopes and intercepts in their FI curves, just as a network of ANN neurons effectively have their activation functions tweaked after applying weights.

    I usually only say this to other neuroscientists who have a background in electrophysiology. The analogy isn't perfect, and is unnecessary to understand what ANNs are doing, but the analogy still stands.

glial 5 hours ago

All models are convenient fictions. I heard a neuroscientist once describe averaging as a low-pass filter. People know it hides high-frequency dynamics. But unless you have a way to interpret the high-frequency signal, it looks an awful lot like noise.

  • etrautmann an hour ago

    This is broadly speaking not correct. If you average together a bunch of trials with variable timing, then the result can tend to wash out higher frequency components (which you might not have realized were in the data), but trial averaging is not a low pass filter at all. There are some nice methods to recover temporal structure that changes across trials prior to averaging, like:

    https://www.sciencedirect.com/science/article/pii/S089662731...

  • jtrueb 4 hours ago

    It is a low-pass filter in the frequency domain with a roll-off that is not smooth. I quite like [1] as a quick reference.

    https://www.analog.com/media/en/technical-documentation/dsp-...

    • etrautmann an hour ago

      Not the OP but we're talking about different things here. Much of the concern about averaging is about averaging across trials. Smoothing a spike train over time isn't really the issue that this thread is concerned with, since that's just averaging successive samples within some small window.

  • ggm 3 hours ago

    > But unless you have a way to interpret the high-frequency signal, it looks an awful lot like noise.

    In other words, they're looking for their lost keys under the lamp-post because it's easier there. If there is a signal in the HF, it's not yet understood. This feels like "junk DNA" -which is I believe receiving more attention than the name suggests.

    • JumpCrisscross 2 hours ago

      > they're looking for their lost keys under the lamp-post because it's easier there

      This is a strange criticism. If you're looking for your keys in the dead of night, and there is a lamp post where they might be, you should start there.

      The streelight effect criticises "only search[ing] for something where it is easiest to look" [1]. Not searching where it's easiest in all cases.

      In this case, we know averaging destroys information. But we don't know to what significance. As the author says, "we now have the tools we need to find out if averaging is showing us something about the brain’s signals or is a misleading historical accident." That neither confirms nor damns the preceding research--it may be that averaging is perfectly fine, hides some of the truth that we can now uncover or is entirely misleading.

      [1] https://en.wikipedia.org/wiki/Streetlight_effect

  • sroussey 5 hours ago

    I think of summaries as the text equivalent of averaging. Some high frequency stuff you don’t want to loose in that case are things like proper names, specific dates, etc. In the face of such signal, you don’t want to average it out to a “him” and a “Monday”.

    • datameta 4 hours ago

      That would be a median in your example no? A spurious average might be us thinking that the statistical mean word contains all vowels except for 'e', and that 'm' is twice as likely as the other most likely consonants.

    • bitwize 4 hours ago

      That makes a lot of sense. Thank you for this analogy.

      We use Conscrewence at work for internal documentation, and when I pull a page up it wants to recommend an AI-generated summary for me. Uh, no, Atlassian, I'm on this page because I want all the details!

  • datameta 4 hours ago

    In physics the model we choose is based on the scale - as in the macro sense all quantum effects average out over the several sextillion atoms in, say, a wood screw.

  • heyitsguay 5 hours ago

    My grad school research was with an NIH neuroscience lab studying low-level sensory processing that offered a fascinating perspective on what's really going on there! At least for the first few levels above the sense receptors in simpler animal models.

    To oversimplify, you can interpret gamma-frequency activity as chunking up temporal sensory inputs into windows. The specific dynamics between excitatory and inhibitory populations in a region of the brain create a gating mechanism where only a fraction of the most stimulated excitatory neurons are able to fire, and therefore pass along a signal downstream, before broadly-tuned inhibitory feedback silences the whole population and the next gamma cycle begins. Information is transmitted deeper into the brain based on the population-level patterns of excitatory activity per brief gamma window, rather than being a simple rate encoding over longer periods of time.

    Again, this is an oversimplification, not entirely correct, fails to take other activity into account etc etc, but I'm sharing it as an example of an extant model of brain activity that not only doesn't average out high-frequency dynamics, but explicitly relies on them in a complex nonlinear fashion to model neural activity at the population level at high temporal frequency in a natural way. And it's not completely abstract, you can relate it to observed population firing patterns in, e.g., insect olfactory processing, now the we have the hardware to make accurate high-frequency population recordings.

robwwilliams 4 hours ago

Great note Mark. I agree. Action potentials are noisy beasts but much may be hidden in spike time coding that is obscured by averaging.

There is an even lower level problem that deserves more thought. What timebase do we use to average, or not. There is no handy oscillator or clock embedded in the cortex or thalamus that allows a neuron or module or us to declare “these events are synchronous and in phase”.

Our notions of external wall-clock time have been reified and then causally imposed on brain activity. Since most higher order cognitive decisions take more than 20 to 200 milliseconds of wall clock time it is presumptuous to assume any neuron is necessarily working in a single network or module. There could be dozens or hundreds of temporally semi-independent modules spread out over wall clock-time that still manage to produce the right motor output.

  • RaftPeople an hour ago

    > There is no handy oscillator or clock embedded in the cortex or thalamus that allows a neuron or module or us to declare “these events are synchronous and in phase”.

    Brains waves drive synchronization of groups of neurons, lower frequencies broader, higher frequencies more localized.

KK7NIL 4 hours ago

Very interesting how measurement limitations drive scientific consensus.

The author portrays this as a major flaw in neuroscience, but it seems like a natural consequence of Newton's flaming laser sword; why theorize about something that you can't directly measure?

hinkley 4 hours ago

There's an old case study from aerospace that shows up sometimes in UX discussions, where the US military tried to design an airplane that fit the 'average' pilot and found that they made a plane that was not comfortable for any pilots. They had to go back in and add margins to a bunch of things, so they were adjustable within some number of std deviations of 'average'.

richrichie 3 hours ago

There are even bigger problems. For example, the common “this region lights up more if this is done” type of fMRI studies are suspect because what the fMRI tool does may have no bearing to actual brain function. I read a book by a neuroscientist lamenting the abuses of fMRI in papers a while ago. Unfortunately, unable to locate the reference.