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I absolutely love the Ellenberg quote: > Mathematician Jordan Ellenberg argues that Simpson's paradox is misnamed as "there's no contradiction involved, just t

by kromem 3y ago

I absolutely love the Ellenberg quote: > Mathematician Jordan Ellenberg argues that Simpson's paradox is misnamed as "there's no contradiction involved, just two different ways to think about the same data" and suggests that its lesson "isn't really to tell us which viewpoint to take but to insist that we keep both the parts and the whole in mind at once." Keeping multiple possibilities in mind at once was what allowed the Epicureans to determine survival of the fittest, trait inheritance from each parent, that light was made of discrete units that weighed very little and were moving very fast, and that in order for free will to exist the quanta making up matter had to have multiple possible results under the same governing physical laws and conditions - all several millennia before the scientific method independently found the same results. It's a great analytical method, especially in data analysis as suggested here.

biomcgary 3y ago
Interesting list of Epicurean theories. Any good starting point that addresses them together and how multiple possibility thinking is related?
- kromem 3y ago
  I can't recommend enough straight up reading Lucretius'sNature of Things. But one of the examples in there of how their methodology ends up successful is when he's discussing the possible reasons lighting and thunder occur at different times. One possibility thrown out is that they are actually occurring at different times. But another is that they occur at the same time but one takes longer to reach the viewer than the other. On its own, these two ideas don't indicate the correct answer. But then Lucretius ties the latter to another observation - that this seems similar to how a drummer in the distance can be seen to beat the drums before you would hear the drums. Essentially in an age without the methodology of testable predictions, they circumvented that shortcoming by considering multiple hypotheses for multiple naturally occurring observations and looking for overlaps between them. This seems to have pointed them in the correct direction on a number of major topics, especially relative to their contemporaries who were generally arguing for a particular hypothesis with various appeals to rhetoric or principle (like Aristotle claiming the leader of a bee hive couldn't be female because it had a stinger and "the gods don't give women weapons"). The times the Epicureans completely miss the mark is generally when they disregarded their principle of avoiding false negatives and discounted things with insufficient observational evidence (for example, they had pretty bad cosmology and they rejected the Stoic pre-gravity due to their incorrect base assumption of infinite amounts of matter). The times they kept an open mind and considered how concepts overlapped, even when they were wrong about the 'why' of an initial assumption they were often correct in secondary assumptions when tying it into multiple other systems and observations.
brabel 3y ago
Sorry to nitpick, but "light was made of discrete units that weighed very little and were moving very fast" is not really correct. First of all, light has exactly zero weight (only a massless particle can travel at exactly the speed of light, and at no other speed for that matter). Secondly, you're leaving out the wave/particle duality of light, which sort of reminds the Simpson's paradox description of "just two different ways to think about the same data", without which you simply can't fully understand the behaviour of light (or of the statistical system you're looking at).
- kromem 3y ago
  This was written in 50 BCE, nearly two thousand years before Einstein's Nobel winning work proving the discrete qualities of photons. I'm well aware it's at best a partial description of light. But it's leagues ahead of Plato's tiny triangles of fire in Timaeus or any other contemporary descriptions. Also, technically zero mass is very little weight (the least, in fact). And the speed of light is very fast (the fastest). So Lucretius was correct in his statements, if just conservative in the degree to which he stated them (which was in line with the Epicurean commitment to the avoidance of false negatives). Wave particle duality doesn't really get discussed in Western antiquity outside of a single tangent describing the beliefs of the Peratae who claim the universe has a threefold nature, with the first being continuous and infinitely divisible, the second being a near infinite number of potentialities, and the third being a formal instance. There's a bit of an Everettian quality to their thinking, but outside of its quite broad scope of thought I'm unaware of anyone saying "yeah, reality is both continuous and discrete at the same time" until physicists grappling with contradictory experimental results in the 20th century. The closest in antiquity outside of this group was arguably Plato's theory of forms where the forms were continuous and their physical manifestations discrete, though this is materially different from the idea they are both simultaneously occurring in what's around us (even if Plato's paradigm most likely influenced the much later Peratae).
- lupusreal 3y ago
  Weight isn't mass; weight is the force acting on something due to gravity. Gravity effects light, albeit only by a little, so in this sense light has a small but nonzero weight.
lukas099 3y ago
I'm having trouble making the connection between Simpson's paradox and the Epicureans. Can you help me out?
- kromem 3y ago
  Ellenberg says the way to avoid falling into Simpson's paradox is to keep multiple views of the data in mind when doing analyses. Let's say you were in ancient Greece, and you separately observe a drummer on a hill bang a drum before you hear it. Then on another day you see lightning before you hear thunder. If you consider each event on its own, a perfectly logical explanation is that there's something unique to drums that slows down the sound from them so it takes longer to reach you, and that lighting and thunder occur at different points in time. But if you consider the set of both events together, a hypothesis that solves both at the same time is that things you hear take longer to reach you over long distances than things you see. This was actually one of the examples directly from Lucretius, who in discussing the multiple hypotheses for why lightning and thunder occur at different times tied his suggestion that they occur at the same time but have different travel speeds to his observations of drummers on hills. It's less specifically Simpson's paradox and more the general value of Ellenberg's analytical advice on avoiding the Simpson's paradox as having been at the root of the success (in hindsight) of one of the wiser philosophy schools in antiquity.
  - lukas099 3y ago
    Good explanation, thanks!
saghm 3y ago
> Mathematician Jordan Ellenberg argues that Simpson's paradox is misnamed as "there's no contradiction involved, just two different ways to think about the same data" Isn't this a bit of a misunderstanding on their part on the meaning of the word "paradox"? The fact that they're called paradoxes is that they go against initial intuition and _seem_ contradictory, not that they necessarily are. If anything, I'd guess that most of the named paradoxes turn out to not actually be contradictory because when something seems incorrect and actually is incorrect, it's a lot less likely to be interesting enough to give a name.
- klodolph 3y ago
  There are various categories of paradoxes and different ways people have categorized them. Quine calls this one a “veridical paradox”, where it seems false but is true. Example of a different types of paradox are: any proof that 1=0, Russell’s Paradox, and Zeno’s paradox. These are either false in some sense or used to illustrate fallacious reasoning.
  - missingrib 3y ago
    I don't think Zeno's paradoxes have truly been proven false.
    - shawabawa3 3y ago
      > I don't think Zeno's paradoxes have truly been proven false. Are you suggesting that there's a chance motion doesn't exist?
      - klodolph 3y ago
        It also has not been proven that real, correct proofs for 1=0 do not exist. Paradoxes are not all about proofs.
        edanm 3y ago
        I'm fairly sure it has actually, under some axiom schemas.
edanm 3y ago
> that in order for free will to exist the quanta making up matter had to have multiple possible results under the same governing physical laws and conditions That seems like a strange and out-of-place statement, unless I'm misunderstanding it. I assume this is talking about Quantum mechanics, but I don't think this represents Quantum mechanics or free will correctly, and I doubt the Epicureans knew anything about QM at all.

by kromem 3y ago

biomcgary 3y ago

Interesting list of Epicurean theories. Any good starting point that addresses them together and how multiple possibility thinking is related?

kromem 3y ago
I can't recommend enough straight up reading Lucretius'sNature of Things. But one of the examples in there of how their methodology ends up successful is when he's discussing the possible reasons lighting and thunder occur at different times. One possibility thrown out is that they are actually occurring at different times. But another is that they occur at the same time but one takes longer to reach the viewer than the other. On its own, these two ideas don't indicate the correct answer. But then Lucretius ties the latter to another observation - that this seems similar to how a drummer in the distance can be seen to beat the drums before you would hear the drums. Essentially in an age without the methodology of testable predictions, they circumvented that shortcoming by considering multiple hypotheses for multiple naturally occurring observations and looking for overlaps between them. This seems to have pointed them in the correct direction on a number of major topics, especially relative to their contemporaries who were generally arguing for a particular hypothesis with various appeals to rhetoric or principle (like Aristotle claiming the leader of a bee hive couldn't be female because it had a stinger and "the gods don't give women weapons"). The times the Epicureans completely miss the mark is generally when they disregarded their principle of avoiding false negatives and discounted things with insufficient observational evidence (for example, they had pretty bad cosmology and they rejected the Stoic pre-gravity due to their incorrect base assumption of infinite amounts of matter). The times they kept an open mind and considered how concepts overlapped, even when they were wrong about the 'why' of an initial assumption they were often correct in secondary assumptions when tying it into multiple other systems and observations.

brabel 3y ago

Sorry to nitpick, but "light was made of discrete units that weighed very little and were moving very fast" is not really correct. First of all, light has exactly zero weight (only a massless particle can travel at exactly the speed of light, and at no other speed for that matter). Secondly, you're leaving out the wave/particle duality of light, which sort of reminds the Simpson's paradox description of "just two different ways to think about the same data", without which you simply can't fully understand the behaviour of light (or of the statistical system you're looking at).

kromem 3y ago
This was written in 50 BCE, nearly two thousand years before Einstein's Nobel winning work proving the discrete qualities of photons. I'm well aware it's at best a partial description of light. But it's leagues ahead of Plato's tiny triangles of fire in Timaeus or any other contemporary descriptions. Also, technically zero mass is very little weight (the least, in fact). And the speed of light is very fast (the fastest). So Lucretius was correct in his statements, if just conservative in the degree to which he stated them (which was in line with the Epicurean commitment to the avoidance of false negatives). Wave particle duality doesn't really get discussed in Western antiquity outside of a single tangent describing the beliefs of the Peratae who claim the universe has a threefold nature, with the first being continuous and infinitely divisible, the second being a near infinite number of potentialities, and the third being a formal instance. There's a bit of an Everettian quality to their thinking, but outside of its quite broad scope of thought I'm unaware of anyone saying "yeah, reality is both continuous and discrete at the same time" until physicists grappling with contradictory experimental results in the 20th century. The closest in antiquity outside of this group was arguably Plato's theory of forms where the forms were continuous and their physical manifestations discrete, though this is materially different from the idea they are both simultaneously occurring in what's around us (even if Plato's paradigm most likely influenced the much later Peratae).
lupusreal 3y ago
Weight isn't mass; weight is the force acting on something due to gravity. Gravity effects light, albeit only by a little, so in this sense light has a small but nonzero weight.

lukas099 3y ago

I'm having trouble making the connection between Simpson's paradox and the Epicureans. Can you help me out?

kromem 3y ago
Ellenberg says the way to avoid falling into Simpson's paradox is to keep multiple views of the data in mind when doing analyses. Let's say you were in ancient Greece, and you separately observe a drummer on a hill bang a drum before you hear it. Then on another day you see lightning before you hear thunder. If you consider each event on its own, a perfectly logical explanation is that there's something unique to drums that slows down the sound from them so it takes longer to reach you, and that lighting and thunder occur at different points in time. But if you consider the set of both events together, a hypothesis that solves both at the same time is that things you hear take longer to reach you over long distances than things you see. This was actually one of the examples directly from Lucretius, who in discussing the multiple hypotheses for why lightning and thunder occur at different times tied his suggestion that they occur at the same time but have different travel speeds to his observations of drummers on hills. It's less specifically Simpson's paradox and more the general value of Ellenberg's analytical advice on avoiding the Simpson's paradox as having been at the root of the success (in hindsight) of one of the wiser philosophy schools in antiquity.
- lukas099 3y ago
  Good explanation, thanks!

saghm 3y ago

> Mathematician Jordan Ellenberg argues that Simpson's paradox is misnamed as "there's no contradiction involved, just two different ways to think about the same data" Isn't this a bit of a misunderstanding on their part on the meaning of the word "paradox"? The fact that they're called paradoxes is that they go against initial intuition and _seem_ contradictory, not that they necessarily are. If anything, I'd guess that most of the named paradoxes turn out to not actually be contradictory because when something seems incorrect and actually is incorrect, it's a lot less likely to be interesting enough to give a name.

klodolph 3y ago
There are various categories of paradoxes and different ways people have categorized them. Quine calls this one a “veridical paradox”, where it seems false but is true. Example of a different types of paradox are: any proof that 1=0, Russell’s Paradox, and Zeno’s paradox. These are either false in some sense or used to illustrate fallacious reasoning.
- missingrib 3y ago
  I don't think Zeno's paradoxes have truly been proven false.
  - shawabawa3 3y ago
    > I don't think Zeno's paradoxes have truly been proven false. Are you suggesting that there's a chance motion doesn't exist?
    - klodolph 3y ago
      It also has not been proven that real, correct proofs for 1=0 do not exist. Paradoxes are not all about proofs.
      - edanm 3y ago
        I'm fairly sure it has actually, under some axiom schemas.

edanm 3y ago

> that in order for free will to exist the quanta making up matter had to have multiple possible results under the same governing physical laws and conditions That seems like a strange and out-of-place statement, unless I'm misunderstanding it. I assume this is talking about Quantum mechanics, but I don't think this represents Quantum mechanics or free will correctly, and I doubt the Epicureans knew anything about QM at all.