7 ms·

Yeah, I read the post. What I’m saying is “this relationship vanishes when you change units, so it must not be a coincidence” is a bad way to check for non-coin

Yeah, I read the post. What I’m saying is “this relationship vanishes when you change units, so it must not be a coincidence” is a bad way to check for non-coincidences in general. For example, the speed of sound is almost exactly 3/4 cubits per millisecond. Why is it such a nice fraction? The magic disappears if you change units… (of course, I just spammed units at wolfram alpha until I found something mildly interesting).

brians 2y ago
Because the cubit is a measure of what a body can reach
- Bjartr 2y ago
  How does that explain the relationship to the speed of sound?
  - ValentinA23 2y ago
    A bit out of topic, however https://www.youtube.com/watch?v=0xOGeZt71sg https://www.youtube.com/watch?v=0xOGeZt71sg Note: I'm more inclined to think this is a coincidence given that it establishes a link between the most commented text and the the most commented building in history. However I don't think these kind of relationships based on "magic thought" should be discarded right away just because they are coincidences, and I'd be very interested in an algorithm that automatically finds them.
- ants_everywhere 2y ago
  I never thought of the cubit this way. It's an interesting idea, but the cubit is the length of a forearm, whereas you can reach around yourself in a circle the length of your extended arm, from finger tip to shoulder. That would be somewhere between 1.5 to 2 cubits for people whose forearm is about a cubit long. I think the cubit is mainly a measure of one winding of rope around your forearm. That way you can count the number of windings as you're taking rope from the spool. This is the natural way a lot of us wind up electrical cables, and I'm sure it was natural back in the day when builders didn't have access to precise cubit sticks. I don't see the connection with the units and sound that you're making. But it is kind of interesting to know that sound travels about 3/4 of a forearm length per millisecond. That's something that's easy to estimate in a physical space.
jncfhnb 2y ago
X^2 is a lot more interesting than x*0.0000743 or whatever it is
- satvikpendem 2y ago
  Why is it more interesting? Is it just more interesting because we use such bases, or can it be interesting inherently? That is the question that is being asked, and why some say it's merely a coincidence.
  - jncfhnb 2y ago
    Well every number is the product of another number and some coefficient. If it’s a nice clean number then that implies it could be the result of some scaling unit conversion. But that should be sort of apparent. And it’s not super interesting if true. If a number is another number squared then that implies some sort of mechanistic relationship. Especially when the number is pi, which suggests there’s a geometric intuition to understanding the definition.
    - satvikpendem 2y ago
      In other bases, it does not actually imply much, even if it were squared. Maybe it really does make sense if it existed in base 10 but I cannot see much if it were part of other bases.
- mistercow 2y ago
  Ok, then by that thinking, you should find it really interesting that Earth escape velocity is almost exactly ϕ^4 miles per second. In fact, adding exponents here objectively makes it less interesting, because it increases the search space for coincidences. What makes the case in the post most interesting to me is that it looks at first glance like it must be a coincidence, and then it turns out not to be.
  - jncfhnb 2y ago
    You would need a compelling argument why x^4 is interesting. Especially something like the golden ratio. Not a long of things go to the fourth power in equations we need to use. Pi^2 directly features in periodicity
Waterluvian 2y ago
Or the speed of light being almost a sweet 300 million m/s. Or after-atmosphere insolation being somewhat on average 1kw/m2.
- ta1243 2y ago
  I always find insolation and insulation to be such an interesting pair of words I guess the equivelent of "change the units" is "change the language". French: insolation et isolation German: Sonneneinstrahlung / Isolierung Spanish: insolación / aislamiento Chinese: 日照 / 绝缘 I guess coincidence
  - mananaysiempre 2y ago
    insolation < Latin sol, solis m "sun" insulation < Latin insula, -ae f "island" (apparently nobody knows where this one comes from) isolation < French isolation < Italian isolare < isola < Vulgar Latin *isula < Latin insula, -ae f Spanish aislamiento < aislar < isla < Vulgar Latin *isula < Latin insula, -ae f Oh and the English island never had an s sound, but is spelled like that because of confusion with isle, which is an unrelated borrowing from Old French (île in modern French, with the diacritic signifying a lost s which was apparently already questionable at the time it was borrowed), ultimately also from Latin insula.
    - CRConrad 2y ago
      > Oh and the English island never had an s sound, but is spelled like that because of confusion with isle So the German cognate (I assume) Eiland probably hasn't had one either. Makes sense, since the Nordic Eya / Øy / Ö never felt like they should, and they must be just northern variants that lack the -land (literally the same in English) suffix.
- mistercow 2y ago
  > Or after-atmosphere insolation being somewhat on average 1kw/m2. I’m kind of inclined to say that this one isn’t so much of a coincidence as it is another implicit “unit” in the form of a rule of thumb. Peak insolation is so variable that giving a precise value isn’t really useful; you’re going to be using that in rough calculations anyway, so we might as well have a “unit” which cancels nicely. The only thing that’s missing is a catchy name for the derived unit. I propose “solatrons”.
euroderf 2y ago
32 meters is 35 yards, to within about an eighth of an inch. How's that grab you ?
- GoldenRacer 2y ago
  My favorite is 1 mile = phi kilometers with <1% error
  - baliex 2y ago
    That one’s useful too. If you know a few Fibonacci numbers you can convert miles to kilometres and vice versa with ease. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … 21 km is ~13 miles, 13 km is ~8 miles, etc. A 26 mile marathon? Must be ~42km. Same for speed limits too; 34 mph is ~55 kmh
  - eesmith 2y ago
    I use that approximation, via the Fibonacci sequence, to translate between miles and km. 13 miles ~ 21 km (actually 20.921470). My favorite approximation is π·E7 = 31415926.5... , which is a <1% error from the number of seconds in a year.
    - saalweachter 2y ago
      ... you all realize that phi is barely a better approximation than 8/5, right? 1.6 vs 1.609 (km in a mile) vs 1.618? (8/5)/(1 mile/1 km) = 0.9942; (1 mile/1 km)/phi = 0.9946. You're making things way harder on yourself for essentially no improvement in precision, especially when you're just rounding to the nearest whole number.
      - eesmith 2y ago
        That tells me you haven't memorized the first ten or twelve terms of the Fibonacci sequence.
  - saalweachter 2y ago
    1 km = 5 furlong, with < 1% error.
dr_dshiv 2y ago
Alpha brainwaves are almost exactly 10hz, in humans and mice. The typical walking frequency (for humans) is almost exactly 2hz (2 steps per second). And the best selling popular music rhythm is 2hz (120bpm) [1]. Perhaps seconds were originally defined by the duration of a human pace (i.e. 2 steps). These are determined by the oscillations of central pattern generators in the spinal cord. One might suspect that these are further harmonically linked to alpha wave generators. In any case, 120bpm music would resonate and entrain intrinsic walking pattern generators—this resonance appears to make us more likely to move and dance. Or it’s just a coincidence. [1] https://www.frontiersin.org/journals/neurorobotics/articles/10.3389/fnbot.2022.850489/full https://www.frontiersin.org/journals/neurorobotics/articles/...
- jvanderbot 2y ago
  Well, a second is also a pretty good approximate resting heart rate (60 bpm)
  - JadeNB 2y ago
    > Well, a second is also a pretty good approximate resting heart rate (60 bpm) I'm sorry to be the kind of person who feels compelled to make this comment, but you mean a Hertz, not a second.
    - aydyn 2y ago
      Youre right, you should be sorry. Dont be that guy.
    - xapata 2y ago
      You're right. Thanks for being that guy!
  - deleted 2y ago
    [deleted]
saghm 2y ago
Reminds me of https://xkcd.com/687/ https://xkcd.com/687/
panarky 2y ago
Another bad way to check for non-coincidences is to use a value like g which changes depending on your location. Pi is the same everywhere in the universe. g on Earth: 9.8 m/s² g on Earth's moon: 1.62 m/s² g on Mars: 3.71 m/s² g on Jupiter: 24.79 m/s² g on Pluto: 0.62 m/s² g on the Sun: 274 m/s² (Jupiter's estimate for g is at the cloud tops, and the Sun's is for the photosphere, as neither body has a solid surface.)
- TheRealPomax 2y ago
  Fun fact: pi is both the same, and not the same, in all of those places, too. Because geometry. If you consider pi to just be a convenient name for a fixed numerical constant based on a particular identity found in Euclidean space, then yes: by definition it's the same everywhere because pi is just an alias for a very specific number. And that sentence already tells us it's not really a "universal" constant: it's a mathematical constant so it's only constant given some very particular preconditions. In this case, it's only our trusty 3.1415etc given the precondition that we're working in Euclidean space. If someone is doing math based on non-Euclidean spaces they're probably not working with the same pi. In fact, rather than merely being a different value, the pi they're working with might not even be constant, even if in formulae it cancels out as if it were. As one of those "I got called by the principal because my kid talked back to the teacher, except my kid was right": draw a circle on a sphere. That circle has a curved diameter that is bigger than if you drew it on a flat sheet of paper. The ratio of the circle circumference to its diameter is less than 3.1415etc, so is that a different pi? You bet it is: that's the pi associated with that particular non-Euclidean, closed 2D plane. So is pi the same everywhere in the universe? Ehhhhhhhh it depends entirely on who's using it =D
  - mr_mitm 2y ago
    In non-euclidean spaces, your definition of pi wouldn't even be a value. It's not well defined because the ratio of circumference to diameter of a circle is dependent on the size of the circle and the curvature inside the circle. It's probably true that it's only well defined in euclidean space. Your relaxed definition, which I have never seen before, is not very useful.
antonvs 2y ago
> What I’m saying is “this relationship vanishes when you change units, so it must not be a coincidence” is a bad way to check for non-coincidences in general. Yeah, it was a strange claim, which makes me think that the author may have had his conclusion in mind when writing this. I.e. what he meant to say may have been something more like: "The relationship vanishes when you change units, which suggests the possibility that the relationship is a function of the unit definitions... and therefore not a coincidence."
ValentinA23 2y ago
There is relationship between the metric system and the French royal system. The units used in this system have a fibonacci-like relationship where unit n = unit n-1 + unit n-2. palm : 7,64 cm span : 12,36 cm handspan : 20 cm foot : 32,36 cm cubit: 52,36 cm cubit/foot =~ 1,618 =~ phi, el famoso Golden ratio. foot/handspan =~ phi too. And so on. From this it turns out that 1 meter = 1/5 of one handspan = 1/5 x cubit/phi^2 Another way to get at it is to define the cubit as π/6 meters (= 0.52359877559). From this we can tell that 1cbt = π/6m π meters = 6 cubits Source: https://martouf.ch/crac/index.php?title=Quine_des_b%C3%A2tisseurs https://martouf.ch/crac/index.php?title=Quine_des_b%C3%A2tis...

brians 2y ago

Because the cubit is a measure of what a body can reach

Bjartr 2y ago
How does that explain the relationship to the speed of sound?
- ValentinA23 2y ago
  A bit out of topic, however https://www.youtube.com/watch?v=0xOGeZt71sg https://www.youtube.com/watch?v=0xOGeZt71sg Note: I'm more inclined to think this is a coincidence given that it establishes a link between the most commented text and the the most commented building in history. However I don't think these kind of relationships based on "magic thought" should be discarded right away just because they are coincidences, and I'd be very interested in an algorithm that automatically finds them.
ants_everywhere 2y ago
I never thought of the cubit this way. It's an interesting idea, but the cubit is the length of a forearm, whereas you can reach around yourself in a circle the length of your extended arm, from finger tip to shoulder. That would be somewhere between 1.5 to 2 cubits for people whose forearm is about a cubit long. I think the cubit is mainly a measure of one winding of rope around your forearm. That way you can count the number of windings as you're taking rope from the spool. This is the natural way a lot of us wind up electrical cables, and I'm sure it was natural back in the day when builders didn't have access to precise cubit sticks. I don't see the connection with the units and sound that you're making. But it is kind of interesting to know that sound travels about 3/4 of a forearm length per millisecond. That's something that's easy to estimate in a physical space.

jncfhnb 2y ago

X^2 is a lot more interesting than x*0.0000743 or whatever it is

satvikpendem 2y ago
Why is it more interesting? Is it just more interesting because we use such bases, or can it be interesting inherently? That is the question that is being asked, and why some say it's merely a coincidence.
- jncfhnb 2y ago
  Well every number is the product of another number and some coefficient. If it’s a nice clean number then that implies it could be the result of some scaling unit conversion. But that should be sort of apparent. And it’s not super interesting if true. If a number is another number squared then that implies some sort of mechanistic relationship. Especially when the number is pi, which suggests there’s a geometric intuition to understanding the definition.
  - satvikpendem 2y ago
    In other bases, it does not actually imply much, even if it were squared. Maybe it really does make sense if it existed in base 10 but I cannot see much if it were part of other bases.
mistercow 2y ago
Ok, then by that thinking, you should find it really interesting that Earth escape velocity is almost exactly ϕ^4 miles per second. In fact, adding exponents here objectively makes it less interesting, because it increases the search space for coincidences. What makes the case in the post most interesting to me is that it looks at first glance like it must be a coincidence, and then it turns out not to be.
- jncfhnb 2y ago
  You would need a compelling argument why x^4 is interesting. Especially something like the golden ratio. Not a long of things go to the fourth power in equations we need to use. Pi^2 directly features in periodicity

Waterluvian 2y ago

Or the speed of light being almost a sweet 300 million m/s. Or after-atmosphere insolation being somewhat on average 1kw/m2.

ta1243 2y ago
I always find insolation and insulation to be such an interesting pair of words I guess the equivelent of "change the units" is "change the language". French: insolation et isolation German: Sonneneinstrahlung / Isolierung Spanish: insolación / aislamiento Chinese: 日照 / 绝缘 I guess coincidence
- mananaysiempre 2y ago
  insolation < Latin sol, solis m "sun" insulation < Latin insula, -ae f "island" (apparently nobody knows where this one comes from) isolation < French isolation < Italian isolare < isola < Vulgar Latin *isula < Latin insula, -ae f Spanish aislamiento < aislar < isla < Vulgar Latin *isula < Latin insula, -ae f Oh and the English island never had an s sound, but is spelled like that because of confusion with isle, which is an unrelated borrowing from Old French (île in modern French, with the diacritic signifying a lost s which was apparently already questionable at the time it was borrowed), ultimately also from Latin insula.
  - CRConrad 2y ago
    > Oh and the English island never had an s sound, but is spelled like that because of confusion with isle So the German cognate (I assume) Eiland probably hasn't had one either. Makes sense, since the Nordic Eya / Øy / Ö never felt like they should, and they must be just northern variants that lack the -land (literally the same in English) suffix.
mistercow 2y ago
> Or after-atmosphere insolation being somewhat on average 1kw/m2. I’m kind of inclined to say that this one isn’t so much of a coincidence as it is another implicit “unit” in the form of a rule of thumb. Peak insolation is so variable that giving a precise value isn’t really useful; you’re going to be using that in rough calculations anyway, so we might as well have a “unit” which cancels nicely. The only thing that’s missing is a catchy name for the derived unit. I propose “solatrons”.

euroderf 2y ago

32 meters is 35 yards, to within about an eighth of an inch. How's that grab you ?

GoldenRacer 2y ago
My favorite is 1 mile = phi kilometers with <1% error
- baliex 2y ago
  That one’s useful too. If you know a few Fibonacci numbers you can convert miles to kilometres and vice versa with ease. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … 21 km is ~13 miles, 13 km is ~8 miles, etc. A 26 mile marathon? Must be ~42km. Same for speed limits too; 34 mph is ~55 kmh
- eesmith 2y ago
  I use that approximation, via the Fibonacci sequence, to translate between miles and km. 13 miles ~ 21 km (actually 20.921470). My favorite approximation is π·E7 = 31415926.5... , which is a <1% error from the number of seconds in a year.
  - saalweachter 2y ago
    ... you all realize that phi is barely a better approximation than 8/5, right? 1.6 vs 1.609 (km in a mile) vs 1.618? (8/5)/(1 mile/1 km) = 0.9942; (1 mile/1 km)/phi = 0.9946. You're making things way harder on yourself for essentially no improvement in precision, especially when you're just rounding to the nearest whole number.
    - eesmith 2y ago
      That tells me you haven't memorized the first ten or twelve terms of the Fibonacci sequence.
- saalweachter 2y ago
  1 km = 5 furlong, with < 1% error.

dr_dshiv 2y ago

Alpha brainwaves are almost exactly 10hz, in humans and mice. The typical walking frequency (for humans) is almost exactly 2hz (2 steps per second). And the best selling popular music rhythm is 2hz (120bpm) [1]. Perhaps seconds were originally defined by the duration of a human pace (i.e. 2 steps). These are determined by the oscillations of central pattern generators in the spinal cord. One might suspect that these are further harmonically linked to alpha wave generators. In any case, 120bpm music would resonate and entrain intrinsic walking pattern generators—this resonance appears to make us more likely to move and dance. Or it’s just a coincidence. [1] https://www.frontiersin.org/journals/neurorobotics/articles/10.3389/fnbot.2022.850489/full https://www.frontiersin.org/journals/neurorobotics/articles/...

jvanderbot 2y ago
Well, a second is also a pretty good approximate resting heart rate (60 bpm)
- JadeNB 2y ago
  > Well, a second is also a pretty good approximate resting heart rate (60 bpm) I'm sorry to be the kind of person who feels compelled to make this comment, but you mean a Hertz, not a second.
  - aydyn 2y ago
    Youre right, you should be sorry. Dont be that guy.
  - xapata 2y ago
    You're right. Thanks for being that guy!
- deleted 2y ago
  [deleted]

saghm 2y ago

Reminds me of https://xkcd.com/687/ https://xkcd.com/687/

panarky 2y ago

Another bad way to check for non-coincidences is to use a value like g which changes depending on your location. Pi is the same everywhere in the universe. g on Earth: 9.8 m/s² g on Earth's moon: 1.62 m/s² g on Mars: 3.71 m/s² g on Jupiter: 24.79 m/s² g on Pluto: 0.62 m/s² g on the Sun: 274 m/s² (Jupiter's estimate for g is at the cloud tops, and the Sun's is for the photosphere, as neither body has a solid surface.)

TheRealPomax 2y ago
Fun fact: pi is both the same, and not the same, in all of those places, too. Because geometry. If you consider pi to just be a convenient name for a fixed numerical constant based on a particular identity found in Euclidean space, then yes: by definition it's the same everywhere because pi is just an alias for a very specific number. And that sentence already tells us it's not really a "universal" constant: it's a mathematical constant so it's only constant given some very particular preconditions. In this case, it's only our trusty 3.1415etc given the precondition that we're working in Euclidean space. If someone is doing math based on non-Euclidean spaces they're probably not working with the same pi. In fact, rather than merely being a different value, the pi they're working with might not even be constant, even if in formulae it cancels out as if it were. As one of those "I got called by the principal because my kid talked back to the teacher, except my kid was right": draw a circle on a sphere. That circle has a curved diameter that is bigger than if you drew it on a flat sheet of paper. The ratio of the circle circumference to its diameter is less than 3.1415etc, so is that a different pi? You bet it is: that's the pi associated with that particular non-Euclidean, closed 2D plane. So is pi the same everywhere in the universe? Ehhhhhhhh it depends entirely on who's using it =D
- mr_mitm 2y ago
  In non-euclidean spaces, your definition of pi wouldn't even be a value. It's not well defined because the ratio of circumference to diameter of a circle is dependent on the size of the circle and the curvature inside the circle. It's probably true that it's only well defined in euclidean space. Your relaxed definition, which I have never seen before, is not very useful.

antonvs 2y ago

> What I’m saying is “this relationship vanishes when you change units, so it must not be a coincidence” is a bad way to check for non-coincidences in general. Yeah, it was a strange claim, which makes me think that the author may have had his conclusion in mind when writing this. I.e. what he meant to say may have been something more like: "The relationship vanishes when you change units, which suggests the possibility that the relationship is a function of the unit definitions... and therefore not a coincidence."

ValentinA23 2y ago

There is relationship between the metric system and the French royal system. The units used in this system have a fibonacci-like relationship where unit n = unit n-1 + unit n-2. palm : 7,64 cm span : 12,36 cm handspan : 20 cm foot : 32,36 cm cubit: 52,36 cm cubit/foot =~ 1,618 =~ phi, el famoso Golden ratio. foot/handspan =~ phi too. And so on. From this it turns out that 1 meter = 1/5 of one handspan = 1/5 x cubit/phi^2 Another way to get at it is to define the cubit as π/6 meters (= 0.52359877559). From this we can tell that 1cbt = π/6m π meters = 6 cubits Source: https://martouf.ch/crac/index.php?title=Quine_des_b%C3%A2tisseurs https://martouf.ch/crac/index.php?title=Quine_des_b%C3%A2tis...