11 ms·

Averaging is a convenient fiction of neuroscience

110 points by domofutu 2y ago

fat_cantor 2y ago
Another convenient fiction is that neuronal communication is all spikes, 1's and 0's. In this fiction, neuromodulators are ignored. Glial cells are ignored. The immune system is ignored. The first neurons in the brain that select for different auditory frequencies are ignored - auditory hair cells release a steady stream of vesicles packed with glutamate, and postsynaptic glutamate receptors compute something like a moving average of the glutamate concentration in the synaptic cleft. But it's much, much more complicated than that. Sounds like something is holding back the field, but averaging is a pretty lousy description of what it might be.
Log_out_ 2y ago
The universe wants you to save energy so every intelligent life form allover runs flat copies of others, of which avg is just the scientific version thereof. Thus neuro science is bad everywhere in the Universe.
deleted 2y ago
[deleted]
glial 2y 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.
- sroussey 2y 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 2y 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 2y 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!
- heyitsguay 2y 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 2y ago
    By “low level” do you mean in the thalamus or cortex or something else. Live a citation. I initially thought that “low level” meant at the level of receptors and the first few synapses. But to the best of my knowledge gamma oscillations will not play a roll in the periphery. It would be great if you had a citation. I have been reading Karl Friston’s work all day.
    - glial 2y ago
      Here's an example[1] examining the functional role of gamma oscillations in the hippocampus: [1] https://www.jneurosci.org/content/15/1/47 https://www.jneurosci.org/content/15/1/47
- jtrueb 2y 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-book/dsp_book_Ch15.pdf https://www.analog.com/media/en/technical-documentation/dsp-...
  - etrautmann 2y 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.
- datameta 2y 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.
- ggm 2y 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 2y 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 https://en.wikipedia.org/wiki/Streetlight_effect
    - ggm 2y ago
      Good point.
- etrautmann 2y 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/S0896627319308943 https://www.sciencedirect.com/science/article/pii/S089662731...
_yb2s 2y 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.
- KK7NIL 2y ago
  I think you'd enjoy this video on different types of means and their applications: https://youtube.com/watch?v=V1_4nNm8a6w https://youtube.com/watch?v=V1_4nNm8a6w
- mcmoor 2y 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.
  - Jweb_Guru 2y ago
    While it is true that not all distributions are normal, many distributions are approximately normal (or at least, normal in some sensible space that maps onto the actual collected data). IMO the amount of ink spilled on the idea that science is fundamentally flawed because distributions aren't always normal is probably too high (especially among non-statisticians), and frankly that's not where statistical analyses usually go wrong. A much larger problem (that has nothing to do with the ultimate shape of the distribution) is stuff like postselecting from a set of plausible models until you find one that finds significant results, and claiming that was what you intended to measure all along (this is why it's important to consider stuff like hyperpriors, much moreso than lack of normality).
KK7NIL 2y 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?
robwwilliams 2y 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 2y 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.
  - robwwilliams 2y ago
    That is uncertain. They must be a product of underlying processes, but the mechanisms are still opaque. 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.
hinkley 2y 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'.
- stonethrowaway 2y ago
  They used those original average measurements to design seats for passengers instead.
robertclaus 2y 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.
- a_c 2y ago
  Human neural network build and trim connections constantly [1]. I imagine we will get much closer to AGI if we can update models dynamically, instead of just adding more neurons and more training. After all human didn't need reading billions of articles before writing an average one. [1] https://en.wikipedia.org/wiki/Neuroplasticity https://en.wikipedia.org/wiki/Neuroplasticity
- dilawar 2y 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.
  - llm_trw 2y ago
    Put another way, there is a reason why FM radio sounds much better than AM radio. https://www.youtube.com/watch?v=AzvxefRDT84 https://www.youtube.com/watch?v=AzvxefRDT84
- lamename 2y 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.
lamename 2y ago
There's even an artist that made this point: Cartoon Neuron https://www.redbubble.com/shop/ap/6229477 https://www.redbubble.com/shop/ap/6229477 https://x.com/Cartoon_Neuron https://x.com/Cartoon_Neuron
personjerry 2y ago
Reminds me of "When U.S. air force discovered the flaw of averages" [0] [0]: https://www.thestar.com/news/insight/when-u-s-air-force-discovered-the-flaw-of-averages/article_e3231734-e5da-5bf5-9496-a34e52d60bd9.html https://www.thestar.com/news/insight/when-u-s-air-force-disc...
richrichie 2y 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.
- bashtable 2y ago
  Is the book titled "Brainwashed: The Seductive Appeal of Mindless Neuroscience"? The writers are apparently not neuroscientists.
  - richrichie 2y ago
    No this was written by a neuroscientist.
1659447091 2y ago
Somewhat related book on how the concept of average can be misleading and/or detrimental, The End of Average https://search.worldcat.org/title/The-end-of-average-:-how-we-succeed-in-a-world-that-values-sameness/oclc/926105728 https://search.worldcat.org/title/The-end-of-average-:-how-w...
ithkuil 2y ago
There are three kinds of lies: lies, damned lies, and fake quotes.

110 points by domofutu 2y ago

Another convenient fiction is that neuronal communication is all spikes, 1's and 0's. In this fiction, neuromodulators are ignored. Glial cells are ignored. The immune system is ignored. The first neurons in the brain that select for different auditory frequencies are ignored - auditory hair cells release a steady stream of vesicles packed with glutamate, and postsynaptic glutamate receptors compute something like a moving average of the glutamate concentration in the synaptic cleft. But it's much, much more complicated than that. Sounds like something is holding back the field, but averaging is a pretty lousy description of what it might be.

Log_out_ 2y ago

The universe wants you to save energy so every intelligent life form allover runs flat copies of others, of which avg is just the scientific version thereof. Thus neuro science is bad everywhere in the Universe.

deleted 2y ago

[deleted]

glial 2y 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.

sroussey 2y 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 2y 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 2y 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!
heyitsguay 2y 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 2y ago
  By “low level” do you mean in the thalamus or cortex or something else. Live a citation. I initially thought that “low level” meant at the level of receptors and the first few synapses. But to the best of my knowledge gamma oscillations will not play a roll in the periphery. It would be great if you had a citation. I have been reading Karl Friston’s work all day.
  - glial 2y ago
    Here's an example[1] examining the functional role of gamma oscillations in the hippocampus: [1] https://www.jneurosci.org/content/15/1/47 https://www.jneurosci.org/content/15/1/47
jtrueb 2y 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-book/dsp_book_Ch15.pdf https://www.analog.com/media/en/technical-documentation/dsp-...
- etrautmann 2y 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.
datameta 2y 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.
ggm 2y 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 2y 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 https://en.wikipedia.org/wiki/Streetlight_effect
  - ggm 2y ago
    Good point.
etrautmann 2y 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/S0896627319308943 https://www.sciencedirect.com/science/article/pii/S089662731...

_yb2s 2y 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.

KK7NIL 2y ago
I think you'd enjoy this video on different types of means and their applications: https://youtube.com/watch?v=V1_4nNm8a6w https://youtube.com/watch?v=V1_4nNm8a6w
mcmoor 2y 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.
- Jweb_Guru 2y ago
  While it is true that not all distributions are normal, many distributions are approximately normal (or at least, normal in some sensible space that maps onto the actual collected data). IMO the amount of ink spilled on the idea that science is fundamentally flawed because distributions aren't always normal is probably too high (especially among non-statisticians), and frankly that's not where statistical analyses usually go wrong. A much larger problem (that has nothing to do with the ultimate shape of the distribution) is stuff like postselecting from a set of plausible models until you find one that finds significant results, and claiming that was what you intended to measure all along (this is why it's important to consider stuff like hyperpriors, much moreso than lack of normality).

KK7NIL 2y 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?

robwwilliams 2y 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 2y 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.
- robwwilliams 2y ago
  That is uncertain. They must be a product of underlying processes, but the mechanisms are still opaque. 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.

hinkley 2y 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'.

stonethrowaway 2y ago
They used those original average measurements to design seats for passengers instead.

robertclaus 2y 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.

a_c 2y ago
Human neural network build and trim connections constantly [1]. I imagine we will get much closer to AGI if we can update models dynamically, instead of just adding more neurons and more training. After all human didn't need reading billions of articles before writing an average one. [1] https://en.wikipedia.org/wiki/Neuroplasticity https://en.wikipedia.org/wiki/Neuroplasticity
dilawar 2y 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.
- llm_trw 2y ago
  Put another way, there is a reason why FM radio sounds much better than AM radio. https://www.youtube.com/watch?v=AzvxefRDT84 https://www.youtube.com/watch?v=AzvxefRDT84
lamename 2y 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.

lamename 2y ago

There's even an artist that made this point: Cartoon Neuron https://www.redbubble.com/shop/ap/6229477 https://www.redbubble.com/shop/ap/6229477 https://x.com/Cartoon_Neuron https://x.com/Cartoon_Neuron

personjerry 2y ago

Reminds me of "When U.S. air force discovered the flaw of averages" [0] [0]: https://www.thestar.com/news/insight/when-u-s-air-force-discovered-the-flaw-of-averages/article_e3231734-e5da-5bf5-9496-a34e52d60bd9.html https://www.thestar.com/news/insight/when-u-s-air-force-disc...

richrichie 2y 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.

bashtable 2y ago
Is the book titled "Brainwashed: The Seductive Appeal of Mindless Neuroscience"? The writers are apparently not neuroscientists.
- richrichie 2y ago
  No this was written by a neuroscientist.

1659447091 2y ago

Somewhat related book on how the concept of average can be misleading and/or detrimental, The End of Average https://search.worldcat.org/title/The-end-of-average-:-how-we-succeed-in-a-world-that-values-sameness/oclc/926105728 https://search.worldcat.org/title/The-end-of-average-:-how-w...

ithkuil 2y ago

There are three kinds of lies: lies, damned lies, and fake quotes.