Averaging is a convenient fiction of neuroscience
thetransmitter.org
thetransmitter.org
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.
They are pretty smart animals but so are dogs who have way less neurons. The point here being that the number of neurons is just one of the many factors that determines intelligence (general or not)
it's unclear how much of what we call intelligence is involving the cerebellum as well, but it may be quite relevant.
Of course the main reason why it's hard to have these kinds of conversations is that we don't all use the same definition of what "intelligence" means.
I often see this take, but the apt comparison is between parameter and synapse count, not neuron count. You should be counting hidden units rather than weights if you want to compare to neuron counts.
Even this is far too simple.
1-Astrocytes have processes (extensions) with localized calcium wave signaling as well as global cell calcium wave signaling that is involved in computation of some types of sensory inputs
2-Astrocytes detect and produce neuro-transmitters as well as glial-transmitters (and generally control/influence the synapses between neurons)
3-Neurons have tunneling nanotubes that dynamically connect cells together (on short time scales) and can transfer proteins, calcium (action potentials), etc.
4-Some types of neurons have natural resonance properties which impacts their function and processing of inputs
5-Some types of neurons learn input patterns in isolation (purkinje cells), meaning one single neuron can learn a time series of input and respond appropriately when pattern detected
etc.
There is a long list of interesting and unknown capabilities, it's pretty difficult to compare neurons+cells to an ANN at this point, too much unknown.
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!
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.
It would be great if you had a citation. I have been reading Karl Friston’s work all day.
https://www.analog.com/media/en/technical-documentation/dsp-...
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.
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.
https://www.sciencedirect.com/science/article/pii/S089662731...
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.
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.
They're bad with multimodal distributions, generally, as well as any random process governed by a distribution with no mean, e.g. Cauchy [1].
(Neuronal firing appears to be non-Gaussian, possibly lognormal [2], which does have a mean [3], but it isn't equal to the simple average.)
[1] https://en.wikipedia.org/wiki/Cauchy_distribution#Properties
This isn't true: https://ourworldindata.org/its-not-just-about-child-mortalit...
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.
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].
> adult morality reductions
LOL
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.
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.
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.
I am partial to using unform priors over all possibilities, and then just adding in the actual evidence for which you can actually quantify its quality/strength. Your "prior" for a new situation is constructed by applying the data you already had previously to a uniform prior- not by fabricating it from whole cloth via your biases. In practice this may be impossible for humans to do in their heads, but computers certainly can!
It’s totally reasonable and statistically sound to use statistics from Victorian England as the sole proxy for the pre-modern human race. /s
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.
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 |
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.
Wouldn't it be 50 since the half-life is an interval?
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...
Neither would a world with 88 people with the following death schedule.
| Age | Deaths/Year |
|---------+-------------|
| 0 to 5 | 2 |
| 5 to 70 | 1 |
| 70 | 3 |
Deeper than that, I think there is a modern tendency to want to believe false claims about how awful life was in the past, and how much better we have it now… so there are a large number of such myths that are nearly ubiquitous but not accurate. Not to say that many aren’t also accurate, just that the inaccurate ones go largely unquestioned.
Modern times are very different from most of human history- better in many ways and worse in many others. If we romanticize how perfect the present is, we then lose the ability to make things still better.
I literally proved by demonstration why having a distribution with an absolute mode in the extreme most value means that 97% of people still died younger than that. There is nothing wrong with the assumption that basically no one made it to 70 because less than 0.5% of people actually did for any period where we have records.
>Deeper than that, I think there is a modern tendency to want to believe false claims about how awful life was in the past, and how much better we have it now… so there are a large number of such myths that are nearly ubiquitous but not accurate. Not to say that many aren’t also accurate, just that the inaccurate ones go largely unquestioned.
Again, you're wronger than the people who hold that view. I'm not sure what you're arguing against at this point other than sophistry.
What I am saying is important to me because I’m interested specifically in what health and life were like for those few people that made it to old age in ancient times - to see how it might provide ideas to improve our health today. For example, I have found that I need a huge amount of exercise and natural light or else I feel fatigued and depressed… I felt I “should not” need this, until I realized not getting this is some sort of anomaly in human history- and there is no reason to expect everyone to be able to handle low levels of light and activity.
Reading about “evolutionary medicine” theorizing was so fascinating it led me to get my doctorate and become an academic PI, although my research is not really in that area these days, I still find it interesting and useful as a hypothesis generator and not "anti science" as another person on here accused me of.
The replies to my original comment are basically mostly people making this same category of mistake and arguing which is "correct" - the average or the mode of the same distribution. Unfortunately, I chose a really bad example where people already hold strong almost religious or political opinions, rather than something generic that just illustrates the math.
Oldest age is set 80, mode is set to 75. We start by distribution one percentage point to each age. Then add an extra to the mode and all the remaining to zero.
We now have a distribution where the most common age of death, other than zero be in 70-80, and more than half the population die before they reach 40.
The growth in life expectancy from surviving early childhood makes sense, but the decline in life expectancy for crossing 20 feels too sharp.
https://aeon.co/ideas/think-everyone-died-young-in-ancient-s...
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.
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
Life spans were abnormally short in medieval Europe, even compared to ancient humans.
Most of the scientists are not scammers. So if you believe that all science disciplines other than engineering are wrong[1], you should use another word that doesn't suggest researcher malice.
[1]Which is a very strong statement, because you claim to be an expert in all science disciplines at once.
And no, one does not claim to be “an expert in all disciplines at once” by pointing out the objective fact that we lack concrete data in a lot of fields.
You have the courage to trust what you understand deeply even if other powerful authorities disagree- and take the responsibility to make sure you do actually understand deeply (the conspiracy theory crowd is missing the second bit). As a practicing academic scientist, I feel like the vast majority of my colleagues with research focused academic careers also see it this way.
Nearly everything called "science" in popular culture (including school science classes, pop science books, etc.) is actually a sort of dogmatic religion that idolizes science. One of the weirdest things for me, is coming on here and when I share the type of creative thinking that actually leads scientists to new hypotheses, I am insulted and accused of being an "idiot" or "anti-science" by mostly career programmers for whom science is a religion, and not a creative process. When they talk to a scientist, they see someone that doesn't align with their fixed dogmatic views, and label it as basically the opposite of what they are actually encountering- real science looks like "pseudoscience" to them. These people would even attack someone like Isaac Newton as an idiot for daring to discuss something new that seems "weird" and idolize, e.g. a medical doctor repeating some old official stance from an institution that has been thoroughly disproven by new research.
> I've become increasingly convinced that the idea of averaging is one of the biggest obstacles to understanding things.
I'd counter that it's easily one of the biggest assistants in understanding things. The Central Limit Theorem in particular has been enormously influential. Without averaging statistical mechanics and thermodynamics would have been impossible and with them would go the industrial revolution.
What you're noticing is one kind of mistake caused by lack of literacy in science. There are many many more similar mistakes. The solution isn't less literacy.
This.
It's interesting how a common instinct to seeing problems is way too often to "destroy and rebuild" instead of "correct and improve". "Institutions have failed us?" A) "Let's burn them down" vs B) "Let's have better institutions, keep what's good, fix what's bad"
I get it that sometimes, rarely, it's impossible to improve something because it's soo rotten and entrenched that you literally have to destroy and rebuild from scratch, but it's almost never the case.
Amazing how the replies to my initial comment range from angrily calling me an idiot for saying something so obviously and egregiously wrong, to claiming it is so trivial and obvious that I should not have needed to mention it.
> The solution isn't less literacy.
Indeed, I can see how what I wrote could be taken that way, I also don't think so. The problem is combining an inadequate amount of literacy, with an almost religious belief in its absolute correctness, e.g. scientism.
> "e.g. scientism"
Isn't this just an anti-science term adopted by religious people and postmodernists?
Not at all, as a scientist, I find scientism to be very common and the biggest obstacle to the general public understanding science- more so than religious people and postmodernists which are at least openly anti-science, rather than just confused about what it is. It is a fanatical religious like belief in the correctness, completeness, and finality of "what science has already discovered" and an aggressive dismissal of e.g. things like creative though experiments or anecdotal observations that question current understanding. To people practicing scientism, the regular practice of actual science looks like heresy and pseudo-science and they would get angry if they were present, e.g. when Isaac Newton or Charles Darwin first mentioned their now accepted but once controversial ideas. They will say things like you don't know (and shouldn't think or talk about) anything until it is confirmed in a large study- without considering how scientists come up with the designs and ideas (and funding) for such studies in the first place.
Science in popular media and schools is taught as a bunch of authoritarian facts to memorize and believe without deeply and intuitively understanding, rather than a creative process of trying to deeply understanding and question things for yourself. When I mention something interesting or counter-intuitive I encountered in my professional research, or something interesting I have been thinking about recently- especially among young intelligent "skeptical and science loving" non-scientist programmers on this forum, I am often met with angry derision, because the process of talking about and exploring weird ideas- e.g. the actual how the sausage is made by working scientists, is seen as extremely unacceptable if it conflicts with what they heard in school, media, etc. I’ve mentioned things I’ve personally discovered on here- and been called an idiot and sent the wikipedia link for a field I’ve studied for decades, and is actually citing my older papers and work, by someone that only heard the field existed when they read my comment.
The pseudo-science conspiracy theory people ironically get the creative independent thinking part more right than the "Scientism-ists", but then miss the important second part of actually taking the responsibility to deeply understand for yourself, and critically question things.
There is something very wrong with science education when the people that say they love it, respond negatively when they encounter the real thing- and this can be fixed by redesigning science education. As an academic PI I don’t teach regular classes, but put students directly in the lab working on a new problem nobody has solved before, where they can’t look up the answer, and then mentor them 1 on 1 if they get really stuck. I then have them actually write it up and submit it to a real peer reviewed journal.
I don't think I'd describe what you're talking about as "scientism", it's more just a confusion about what science is.
There are a lot of critiques of so-called "scientism" but they focus on the assertion that there are ways of "knowing" things that are inaccessible to the scientific process. This more or less directly implies the supernatural (since we have to leave naturalism to understand it) or trolling (which is basically what postmodernism is).
Part of what you're running into in this site is that there is a political dislike of education, knowledge, and science in some coding circles. Your original comment brought out a few of them.
I sympathize with the postmodernists and religious people here… and think we’re talking about the same thing- and literally to the same people. Someone is arrogantly dismissing something they’ve spent a lot of time on as nonsense, without really understanding what it is.
The “scientism-ist” says anything they don’t understand is nonsense or a lie, unless it comes from a “scientific authority.”
When I hear about a religious “truth” or similar idea, I don’t dismiss it, but try to understand what it means to them, and what its functional purpose might be. Religious truths are usually literally false- but they are not really factual claims about physical reality in the first place, but methods or psychological tools that are “true” if they work for the intended purpose. If you visualize God for prayer or meditation - you get to a certain internal state… arguing about if you can find physical evidence of this God misses the point entirely. The more intelligent religious people understand this, but don’t talk about it, because doing so makes it not work anymore for the people not able to understand it in a more nuanced way.
I don’t agree that what they are talking about cannot be understood scientifically in principle- but I may agree our current understanding is too primitive, and not yet able to do so in a useful way… whereas with scientism it is either already understood by an authority- or else there is nothing of value to be understood- anything new or different is just false. Scientism admits no limits to our current understanding, nor to any possibility of future discovery other than a hypocritical lip service to supporting “research funding” or whatever.
On a personal level I can accept that regular obnoxious religious zealots exist and just avoid them… but it really irks me when they are telling me that they are the real scientists and I am not, when it is what I have decided my life to.
> The brutal reality is you don't have the IQ to understand averages or statistics like most people.
> Most of our ancestors lucky enough to made it to 45 years old in human history did not make it to 70.
> Using mode is misleading with "age", and you quickly showed you didn't understand 'the con' when you accidently tried to apply it.
> This is a political, the "past was wonderful fantasy" which is anti-science. It's used by the Woke for instance."
In this case I am using an equally "wrong" model on purpose while being well aware of its limitations, just to make a specific point. It highlights a point where people are doing exactly what you are accusing me of- romanticizing the present, and not understanding the reality of how it actually differs from the past. E.g. what are the actual reasons people had shorter life spans in the past, and what their lives were actually like. One should not forget the limitations of such a simple model, which was basically my point in the first place.
I am fascinated by "evolutionary medicine" and using such ideas as a hypothesis generator to figure out ways to treat "modern diseases of civilization." I am in no way romanticizing the past, but trying to understand the specifics, to better figure out how to develop more effective modern day medical treatments, not to return to the past. In truth I despise political thinking altogether, and like to look at mechanisms and biological details.
Your post smacks of "scientism" which is incompatible with actual practice of science. The very idea that a certain line of thinking or theorizing is "anti science" or should be taboo for political reasons is itself incompatible with creative open minded problem solving.
I can see it was a mistake to use this specific example for discussing the problem with averages- ironically because it is so accurate. Since so many people on here hold the exact misunderstanding I was criticizing, they are getting angry and insulting me instead of my intent, which was to explain a phenomenon and have this click as a simple example of it. A less charged example, where people don't have strong opinions already would have been better.
I'm not saying anything for or against the ~33 years claim, just that I doubt that it comes from a precise estimate of expected lifespan at birth.
This is the bit that you're missing: antiquity is generally considered to extend all the way into the 500-600s AD, with the Roman empire dominating its center and 'late antiquity' covering the whole early period of the Byzantine empire. This means that even just in Europe we have extensive documents (e.g. in the Christian era, baptism and burial records), as well as a wealth of burial evidence from which to extrapolate lifespans. If you look into the sources for Rome you'll find Egypt in particular come up a lot, which isn't an accident: the dry climate and extensive use of papyrus means that the region preserved far more records (and bodies) than any other part of the empire.
https://www.gresham.ac.uk/watch-now/return-microbes-how-infe...
The video has a text with the words.
Look for
> So, your life expectancy at five, in England, as a male, in 1870 was slightly longer than it is now, which is an extraordinary statistic, slightly shorter then if you were a female.
1870s Britain is not "ancient", but as far as medicine is concerned much closer to that than to modern times. What medicine there was wasn't even available to most people. They were pretty good with "physical" things like broken bones by then, but anything concerning microbes probably wasn't much better than what was done a thousand years earlier.
Obviously, as you point out, we don't have statistics from ancient times, only some hints, but that is the same for people making the claim about the short average life spans (without the little detail about infant and women mortality).
There also is the question of how meaningful it is to average over vastly different sections of the population (what you did and how you lived and what you ate, access to good water, hygiene), or times of famine or war.
Some related discussion, reddit, but the heavily moderated AskHistorians subreddit: https://www.reddit.com/r/AskHistorians/comments/12o4py/what_...
There we see the lower life expectancy of early agricultural societies vs. hunter-gatherers (ignoring their high number of deaths due to violence).
I think all of this also serves to illustrate OPs point about the problem of averages :-) There's just too much important information that is lost.
Congratulations, you just rediscovered the health policy of the Third Reich.
You should also consider that those are not my words, you are arguing against that professor.
Until the last few-ish generations, pregnancy and childbirth have been leading causes of death for women in those in-between decades of their lives.
(And obviously War and Famine, too, for both genders.)
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?
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.
Brains waves drive synchronization of groups of neurons, lower frequencies broader, higher frequencies more localized.
Gamma oscillations only run at about 40 Hz. That is not fast enough to clock neuronal computations or integrations in the 1 to 10 msec range.
Oscillations may have role in binding at larger scales. And when we use the word “synchronize” we generally seem to mean “given wall-clock time”.
Two neural events separated by 20 msec can be functionally coherent but may neither be in a particular phase relation or concurrent from an observer’s wall-clock perspective. Neuronal activity may not care about the observer’s timebase.
https://search.worldcat.org/title/The-end-of-average-:-how-w...
[0]: https://www.thestar.com/news/insight/when-u-s-air-force-disc...
Thus neuro science is bad everywhere in the Universe.