12 ms·

A wonderful coincidence or an expected connection: why π² ≈ g

• levzettelin 2y ago
  He wouldn't be speaking like this if he was born on Mars.
  • edflsafoiewq 2y ago
    Sure he would, the meter would just be a different length.
  • baxtr 2y ago
    Finally an easy way to identify aliens!
    • samstave 2y ago
      How? Because they don't have a Venus?
  • alfiedotwtf 2y ago
    The pendulum from the Mars pole to Paris would be long indeed!
  • Maxatar 2y ago
    I thought they key insight of this article was if he were born on Mars, then the meter would have been defined differently so that gravity would still be 9.8 m/s^2. I think what you meant to say was that he wouldn't be speaking like this if people were born with 3 fingers.
• mistercow 2y ago
  This is interesting, but I have to quibble with this: > If you express this value in any other units, the magic immediately disappears. So, this is no coincidence Ordinarily, this would be extremely indicative of a coincidence. If you’re looking for a heuristic for non-coincidences, “sticks around when you change units” is the one you want. This is just an unusual case where that heuristic fails.
  • karmakurtisaani 2y ago
    Actually no, the whole equation boils down to the definition of meter. Or rather, one of the earlier definitions.
    • mistercow 2y ago
      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.
• otabdeveloper4 2y ago
  > was actually proposed back in the 17th century Pretty sure it was done back in Sumer first.
  • karmakurtisaani 2y ago
    A standard free measure for distance? Sounds dubious.
    • otabdeveloper4 2y ago
      No. The other way around. Two seconds is the period of a pendulum with a length of two Sumerian cubits. (One meter is thus two Sumerian cubits, but that's an artifact due to us still using Sumerian time measurements.) P.S. I don't know why Sumerians used a factor of two. Americans still divide the day into two 12 hour spans, according to Sumerian fashion. P.P.S. One second is 1/(2*12*60*60) of a solar day. 12 and 60 were "round numbers" in Sumer; they used sexagesimal counting.
      • Maken 2y ago
        Probably because 12 is a much better base than 10. 12 can be divided by 2, 3, 4 and 6 and still results in whole numbers, which helps a lot when doing rounding and fraccional numbers. The only reason we use base 10 is because is much easier to count with our fingers.
        • jjk166 2y ago
          There's also a method of counting where you touch your thumb to the sections of your fingers on the same hand, which naturally lends itself to base 12. This can be extended by keeping track of how many times you've counted to 12 on the other hand, which lends itself to either base 60 or base 144. Interestingly, the Sumerians did not seem to employ this method, they would count 6 instances of counting to 10.
      • gavindean90 2y ago
        Because it traverses the distance twice would be my guess. If you show someone a pendulum going through 3 periods and asked a group of people a generic question like “how many times did it move” without clarifying what you meant I would bet maybe half the people would say 6 as long as everyone counted correctly.
• BrandoElFollito 2y ago
  As a physicist, this makes sense. Pi = 3, pi^2 = 10, which is g Not sure why everyone is surprised. Ah, and a year is pi*10e9 seconds (IIRC)
  • exe34 2y ago
    pi * 1e7
  • radiator 2y ago
    As a physicist? When we did physics at school, and we were solving problems, the answer was always a number together with its unit. pi² might be 10 because it is a pure number, but g can never be 10, because it is an acceleration, a physical quantity, so it must be 10 of some unit.
    • bmacho 2y ago
      Not if you define g as the real number before m/s^2, in the expression '10 m/s^2'. In middle school physics lessons this makes teachers to hate you (it's their job to ensure that you do not do this), but after that, this has advantages time to time. .. I remember hearing an anecdote that ancient Greeks did not know that numbers can be dimensionless, and when they tried to solve cubic equations, they always made sure that they add and substract cubic things. E.g. they didn't do x^3 - x, but only things like x^3 - 2*3*x. I don't think this is true (especially since terms can be padded with a bunch of 1s), but maybe it has some truth in it. It is plausible that they thought about numbers different ways than we do now, and they had different soft rules that what they can do with them.
    • BrandoElFollito 2y ago
      Oh, come on, it is inches / (day * "hold on"). Everyone knows this, this is physics for art majors 101. In guess it's a good thing I left physics after my PhD.
    • jrpt 2y ago
      I mean it is pretty common to set c=1 though.
• breck 2y ago
  Very interesting! So if I understand correctly: the meter was defined using gravity and π as inputs (distance a pendulum travels in 1 cycle), so of course g and π would be connected.
  • fweimer 2y ago
    On the hand, g is about 32.2 ft/s². So it's suddenly related to π³? I think there's no connection at all, it's just an accident. It would be really weird if some contemporary property of the earth were actually related to a fundamental mathematical constant. It's similar to finding a message among the digits of π that shouldn't be there, statistically speaking.
    • cvoss 2y ago
      The bulk of the article is devoted to explaining that g = pi^2 in m/s^2 units (under an old definition of meter) because (that definition of) the meter was not selected arbitrarily, but selected in a way that makes the equation hold on purpose.
• thaumasiotes 2y ago
  g is related to the radius of the earth; the meter is related to the circumference of the earth; and pi is the relationship between the radius and the circumference.
  • mistercow 2y ago
    Aside from the fact that the post already explained what the actual historical connection is, your explanation requires some serious hand-waving about the mass of the Earth and the gravitational constant, neither of which were known when the meter was first defined.
    • jjk166 2y ago
      Reasonably accurate values for both M_earth and G were known at the time the SI meter was defined. Also it's not too hard to extend this. M_earth is a function of Earth's radius which goes into the definition of the meter. G is a function of earth's orbital period, which goes into the definition of the second. Further our definition of mass is based on the density of water, which is chosen because it is a stable liquid at this particular orbital distance from a star of our sun's mass.
      • mistercow 2y ago
        As far as I can tell, the most recent experiment to measure the mass of the Earth by 1790, when they decided on the definition of the meter, was the 1772 Schiehallion experiment, which gave a value 20% below the actual value. So if pi^2 were to somehow fall out of that it would likely be so far off as to be unrecognizable. But even that doesn’t matter, because the mass of the Earth didn’t play a direct role in the definition of the meter. If you take out the whole thing about the meter’s definition targeting half a toise, then all you have is “related to the circumference of the Earth”, and it would be a monumental coincidence if the mass of the earth and gravitational constant just conspired to somehow drop an unadulterated pi^2 out of the math.
        • jjk166 2y ago
• vessenes 2y ago
  Awesome write up and a great surprise in the history of the definition of the meter. Reading this reminds me a little of mathematicians like Ramanujan who spent a fair amount of time just playing around with random numbers and finding connections, although in this case, I imagine the author knew the history from the beginning. Anyway, I feel like my math degree sort of killed some of that fun exploration of number relations — but I did like that kind of weird doodling / making connections as a kid. By the time I was done with the degree, I wanted to think about connections between much more abstract primitives I’d learned, but it seems to me there are still a lot of successful mathematicians that work this way — noticing some weird connection and then filling out theory as to why, which occasionally at least turns out to be really interesting.
• jds-67 2y ago
  Sorry to ruin the party, but g is a quite random number, on other planets the corresponding acceleration is different. So π^2~g is a pure coincidence and not relevant. The Newtonian gravitational constant G is a real constant btw.
  • sidpatil 2y ago
    It's not about the values, but the units of measurement. g is in units of meter/second^2. The article discusses the dependency of the meter's original definition on the value of pi.
  • gpvos 2y ago
    Have you read the article? The point is that the definition of the metre, which is used in g, originates from the length of a pendulum that swings once per second in the gravity field around Paris. So it is a matter of definitions, and the length of the metre originates from the duration of the second and the Earth's gravity field. The definitions of 1/40.000 of the Earth's circumference or ~1/300.000.000 of a light second came later.
    • ccvannorman 2y ago
      My intuitive assumption, then, is that on Mars they would have come up with a different meter such that π² ≈ 10 "mars meters" / s². Or alternatively stated, that the Mars meter would be much shorter than Earth's meter if they used the same approach to defining it (pendulums and seconds).
      • ValentinA23 2y ago
        A Martian meter defined by martians should relate their average size, the number of fingers they have on their hands and some basic measure of the planet. I mean, one meter is defined as 1/10^7 of the distance between the equator and the poles which leads to a round number in base 10. A unit system is not just something that matches objective reality but something that has some cognitive ergonomy.
• dweekly 2y ago
  Link is broken for me? "[ErrorBoundary]: There was an error: {}"
  • roitman 2y ago
    Try refreshing the page
• shubhamjain 2y ago
  What an amazing post! Such an interesting investigation. These kinds of write-ups make me realize how truly far we are from AGI. Sure, it can write amazing code, poems, songs, but can it draw interesting conclusions from first principles? I asked both ChatGPT and Claude, the same question, and both failed at pointing out the connection the author states. This is not to deride feats of AI today, and I am sure it will transform the world. But until it can show signs of human ingenuity in making unexpected and far-off connections like these, I won't be convinced we are nearing AGI.
  • air7 2y ago
    Arguably most humans can't do this either.
  • avaldez_ 2y ago
    > Sure, it can write amazing code, poems, songs, but can it draw interesting conclusions from first principles? Can you? https://youtu.be/KfAHbm7G2R0?si=oAPrNGylo7pUcRMZ https://youtu.be/KfAHbm7G2R0?si=oAPrNGylo7pUcRMZ
  • badgersnake 2y ago
    The only thing with more bollocks in it than this article is your aibro comment.
• kwhitefoot 2y ago
  It isn't equal to g even in SI units except at some very few spots on the surface of the earth. Change the units to any other system and it's not even roughly true. Edit: Now that i have read the article i see that it is no coincidence at all that it is close the pi squared. very interesting.
• ahmedfromtunis 2y ago
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  • drexlspivey 2y ago
    If you read the article you would see that it’s not a coincidence because the meter was defined such that pi^2 = g at the surface of the earth.
  • IHLayman 2y ago
    I disagree… the article talks about defining the meter using the pendulum and the second. Other planets would have their own definition of second, but not their own definition of pendulum. Since one meter is prescribed though a pendulum because of the oscillation formula and dependent on the frequency alone (in this case, 2 seconds), no matter what planet you are on, how strong gravity, is or how long a second is, the pendulum describes a relationship between seconds and meters such that if using this method a planet’s scientists would always define their units such that acceleration of gravity was eerily equal to pi^2. Makes me think of possible lunar scientists unwittingly making their meter 5/6th shorter(edit: english is hard) and then marveling at the same coincidence…
  • mjfisher 2y ago
    Nope, it's not a coincidence - it's an interesting exploration of the history of the definition of a metre. Read the article. As it says, at some point there was an attempt to standardise the length of a metre in terms of a pendulum's length; which related it directly to g through Pi.
  • jameshart 2y ago
    On any planet where you want to define a system of units, you can start by defining a fixed time period (maybe use a fraction of the planetary rotation cycle or something), then make a pendulum that swings with that frequency, and derive a unit of distance from its length. The local value of g will be roughly pi squared pendulum lengths per tick squared, in that system of measurement.
• philzook 2y ago
  I've got a related one I like. Why are the Avogadro's number and Boltzmann's constant inverses of each other N ~ 1/k? The statement doesn't make sense because the units don't work out, but it is true in mks. It's because they multiply to the gas constant which is ~1. They both are numbers to transfer from the microscopic to human scale units and they cancel for the gas constant, which is about human scale experience of gases.
  • bonzini 2y ago
    But it's a coincidence, right? N*k=8.31 is pressure*volume/temperature for a mole of gas. Temperature has a relatively small range (100-1000) and there's no reason why the range of P*V couldn't be far from that range, for example 0.01–0.1, with a different definition of meter, second or kilogram.
    • lupire 2y ago
      Meter, second, and kilogram were all chosen to be approximately the scale of a human, and the combined multiplicative units like Pascal, m^3, and Kelvin/Celsius are also numerically 1 in these units.
      • Someone 2y ago
        > Meter, second, and kilogram were all chosen to be approximately the scale of a human, “Approximately the scale of a human” leaves so much wiggle room that I don’t see how one can defend that claim. > and the combined multiplicative units like Pascal You don’t explicitly claim it, but I wouldn’t say the Pascal is “Approximately the scale of a human”. Atmospheric air pressure is about 10⁵ pascal, human blood pressure about 10⁴ pascal, and humans can very roughly produce about that pressure by blowing.
        • Ekaros 2y ago
          Which is why I have always kinda hated kilogram. Such an ugly unit for it having prefix. Grav should have been correct answer, but instead we ended up with something that is too small... That is in reality gram. For grams we could simply have milligravs or decigravs for 100g equivalents... Not that hard considering decilitres are used and decimetres are kinda tried in schools.
• sycren 2y ago
  If the definition of the meter is still wrong disallowing π² = g, how might this affect other calculations like for example thrust and in aerospace engineering?
  • kseistrup 2y ago
    And what would all other natural constants look like, had the meter kept the value derived from the length of the pendulum?
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• im3w1l 2y ago
  I knew that historically meter was related to the size of the earth somehow, but I had never had about the pendulum definition!
• spacebacon 2y ago
  I laughed 3 times reading this article while pondering the novelty of standardization. Is standardization the sans-serif of civilization?
• alberth 2y ago
  No mention of ‘meter’ being the unit of measurement, make this like saying 3:14pm is related to pi. There’s no correlation between a continuous number and a unit of measure. That’s truly apples to oranges comparison. g can easily be expressed in ‘feet’ as ~32.1 ft/s^2
  • mistercow 2y ago
    What do you mean by “no mention”? The entire article is about why this is specifically due to how the meter was first defined.
• ValentinA23 2y ago
  Okay so this one has an explanation. But what about these ? https://en.wikipedia.org/wiki/Mathematical_coincidence https://en.wikipedia.org/wiki/Mathematical_coincidence See also this blog: https://martouf.ch/tag/coudee-royale-egyptienne/ https://martouf.ch/tag/coudee-royale-egyptienne/ One french royal cubit ≈ one egyptian cubit ≈ about π/6 meters. One royal span ≈ 1/5 meter = 20cm. I'm wondering whether some of these coincidences could be explained by the anthropic principle, which deals with these quasi-equalities, for instance: >An excited state of the 12C nucleus exists a little (0.3193 MeV) above the energy level of 8Be + 4He. This is necessary because the ground state of 12C is 7.3367 MeV below the energy of 8Be + 4He; a 8Be nucleus and a 4He nucleus cannot reasonably fuse directly into a ground-state 12C nucleus. However, 8Be and 4He use the kinetic energy of their collision to fuse into the excited 12C (kinetic energy supplies the additional 0.3193 MeV necessary to reach the excited state), which can then transition to its stable ground state. According to one calculation, the energy level of this excited state must be between about 7.3 MeV and 7.9 MeV to produce sufficient carbon for life to exist, and must be further "fine-tuned" to between 7.596 MeV and 7.716 MeV in order to produce the abundant level of 12C observed in nature. Source: https://en.wikipedia.org/wiki/Triple-alpha_process#Improbability_and_fine-tuning https://en.wikipedia.org/wiki/Triple-alpha_process#Improbabi... The idea goes like this: 1. A more fundamental aspect under the anthropic principle which underpins the existence of complex life and intelligent observers is the quasi-alignment of values such as the fundamental constants in physics within a short margin. 2. If you consider the universe to be the product of a random sampling process over these constants (either real or virtual, it occurred many times or just once), and given the fact we exist, which implies an abundance of coincidences, the maths seem to tell us that we should expect to observe superfluous coincidences that are non-functional for the appearance of complex life, rather than the strictly minimal set of functional coincidences necessary for its emergence. 3. This implies that coincidences and pattern seeking are not just features (or bugs) of our complex minds but are present in the universe latently since it is not just fine-tuned for the emergence of complex life but for the presence of coincidences such as these https://medium.com/@sahil50/a-large-numbers-coincidence-299cb199e03d https://medium.com/@sahil50/a-large-numbers-coincidence-299c.... 4. It may be even testable by running computer experiments relying on genetic programming/symbolic regression to see whether there is something special about the value of physical constants in our universe when compared to the value they would have in other universes. I think such experiments should factor the fact that not all equations with the same mathematical complexity (number of operands and operators) have the same cognitive complexity. Indeed, if you look at the big equation in the link above, you'll remark that it can be further compressed into a/b = c/d (where a is the photon redshift radius for instance). So I guess you'd also have to throw into the mix Kolmogorov algorithmic complexity to assess this aspect (which is in fact used in some cognitive theories of relevance to tackle this kind of stuff to the tune of "simpler to describe than to generate") Thoughts ?
• EasyMark 2y ago
  > Sometimes that was even useful. If you needed to buy more cloth, you'd call the tallest person in the village and have them measure the fabric with their cubits. I highly doubt this bit of strategy would have worked with sellers of said fabric. They may have not had formal measurements but they weren't stupid either.
  • kthejoker2 2y ago
    I find this comment delightfully ironic in a contemporary moment of blatant shrinkflation.
• julienchastang 2y ago
  Relatedly, I recommend reading "The Measure of All Things" by Ken Alder about the origins of the metric system and the first scientific conference ever. It is a surprisingly gripping read. https://www.simonandschuster.com/books/The-Measure-of-All-Things/Ken-Alder/9780743216760 https://www.simonandschuster.com/books/The-Measure-of-All-Th...
• karmakaze 2y ago
  Might be interesting if were true in Planck units. But also 2Pi is fundamental, who defines a ratio of something to 2 of something (radius)?
  • rvbissell 2y ago
    No, Tau is fundamental. Pi only exists because someone mistakenly thought the formula for circumference involved diameter, when in fact it involves radius. ("Quit factoring a 2 out of Tau!" I tell them.)
    • mistercow 2y ago
      Eh, you can find plenty of cases where tau is just as awkward as pi is elsewhere. Right off the bat, the area of a circle becomes more awkward with tau, becoming (tau*r^2)/2, and in general, the volume of an n-ball gains weird powers and roots of two in its denominator as n increases if you switch to tau. In general, I don't think you can really claim either one is "more fundamental". It's just a matter of framing.
      • karmakaze 2y ago
        It's not really about being awkward (that's a tell not the motivation), it's about basing on a radius or diameter: which is more fundamental? Or the arc length of a unit circle or half a circle, which isn't an arbitray formula it's the definition.
      • rvbissell 2y ago
        Actually, no: that Tau-centric area formula you gave derives naturally from taking the integral. Your example actually fits the expectation you have from what you learned in Calculus I. You should _expect_ that 1/2 scaling to be there. If it seems awkward to you, it's only because of a lifetime of seeing it done in terms of pi.
        • mistercow 2y ago
          You can argue that having an extra number to juggle around is somehow less awkward because, under specific and subjective criteria, it’s “expected”, but given that the whole hook for tau is “we keep having to put a multiplier of two everywhere”, I don’t find it very compelling. I can also make arguments that pi/2 would have been a better constant from a teaching perspective. The pi/2 version of the Euler identity, for example, would give you all the tools you need to link complex multiplication to rotation. But at the end of the day, the choice of multiple used for the constant is a convention. None is going to be ideal in every case, and no math fundamentally changes because of a particular choice. Trying to argue for a change in convention at this point is just silly.
• karmakaze 2y ago
  Numerologists unite!
• xxmarkuski 2y ago
  I remember in mechanical engineering class we would often use this for exercise sheets. On our calculator we could directly enter π and ², thus it was equally as fast to entering 10.
  • imoverclocked 2y ago
    That's one way of setting up a standard deviation!
• rich_sasha 2y ago
  This is neat, but still something if a coincidence. It appears the first definition of a metre is in fact around 1/4e10 the circumference of Earth, and the further coincidence is that a 1m mathematical pendulum has a period of almost exactly 2 seconds. So there's still a neat relationship between mass/radius of Earth, its diurnal rotation period and the Babylonian division of it into 86,400 seconds.
  • owisd 2y ago
    According to the article the 1/4e10 circumference definition came second
    • rich_sasha 2y ago
      Wikipedia says the Earth circumference definition comes from around Copernican times. Also my reading of TFA is that the pendulum definition was in fact a redefinition that didn't catch on.
    • Ekaros 2y ago
      I wonder how many numbers they checked until they arrived on this one. As to me it seems picked as something close enough for committee work.
• textlapse 2y ago
  I wonder if this is how astrology was born. You can draw arbitrary connections between things if you stare at them long enough.
• deleted 2y ago
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• bravura 2y ago
  Philosophy time: Does this mean in 400 years it's possible we no longer disagree about how to evaluate things? i.e. we converge on one totalitarian utility function that everyone basically accept answers every possible trolley dilemma? In 1600, people just took the world as that: measurements are sloppy, and vary culturally and based upon location etc. But we eventually came upon tools and techniques that are broadly accepted as repeatable and standard. Would this sort of shift be possible? Or desirable?
  • kccqzy 2y ago
    Personal preferences continue to exist. I don't see that happening.
• pclmulqdq 2y ago
  More fun arithmetic coincidences: https://en.m.wikipedia.org/wiki/Almost_integer https://en.m.wikipedia.org/wiki/Almost_integer Some of these are test vectors for math systems.
• fireattack 2y ago
  Totally unrelated to the content, but about the website itself. The site completely breaks when I visit it. After some investigation, I found out that if I enable Stylus (a CSS injection extension) with any rules (even my global ones), the site becomes unusable. Since it's built using the React framework, it doesn't just glitch; it completely breaks. After submitting a ticket and getting a quick response from the Stylus dev, it turns out that this website (and any site built with caseme.io) will throw an error and break if it detects any node injected into `<html>`. [1] https://github.com/openstyles/stylus/issues/1803 https://github.com/openstyles/stylus/issues/1803
  • gpvos 2y ago
    I don't currently use Stylus, but it breaks for me too; it looks like CSS isn't applied at all: I get some big logo images, and the text uses standard fonts. Not sure which extension triggers it, probably Dark Reader. I could still read it, so no biggie.
• otterley 2y ago
  This post feels like one of those cork boards with photos and strings connected between them in some prepper’s basement, but in blog post form.
• nyc111 2y ago
  g is the distance an earth skimming satellite falls to earth in one second along the tangent. But I don't know how it is related to pi.
• lutusp 2y ago
  Another "wonderful coincidence" is that the conversion between miles and kilometers involves this constant of conversion : kilometers = miles * 1.609344. Let's call 1.609344 the "km" constant. As it happens, km is very close the the Golden Ratio (sqrt(5)+1)/2 = 1.618033989... (call this "gr"). In fact they only differ by about 1/2 of one percent (100 * (gr/km - 1) = 0.54%)! As the author of the original article says, "If you express this value in any other units, the magic immediately disappears. So, this is no coincidence ...". Yeah ... wait, what? Here's another one. Pi (3.141592654...) is nearly equal to 4 / sqrt(gr) (3.144605511...), call the latter number "ap" for "almost pi". This connects pi to the golden ratio, and they differ by only 0.096% (100 * (pi/ap - 1)). Surely this means something -- doesn't it? Finally, my favorite: 111111111^2 = 12345678987654321. This proves that ... umm ... wait ...
  • 29athrowaway 2y ago
    The best is sum(1, 36)
  • areyousure 2y ago
    ln(5) ~ 1.6094379 is much closer, differing by about half of a percent of a percent.
  • maxnoe 2y ago
    A year is very close to pi * 1e7 seconds, better than half a percent.
  • koolala 2y ago
    Do miles connect to feet and feet vs. gravity connect to the Golden ratio? 6 feet is like 2 pi?
    • kelnos 2y ago
      Not sure, but I am indeed often connected to the earth via gravity by my feet.
      • dennis_jeeves2 2y ago
• renewiltord 2y ago
  Hence the 2√l formula for the pendulum haha
• deleted 2y ago
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• Ekaros 2y ago
  Underlying idea of whole metric and SI system is the real start point. You want to define some units that you can easily replicate. Time is reasonable enough one, measure and track length of day and then length of second. Now based on this figure out way to come up with replicable definition for distance, pendulum is good enough gravity is constant enough. Thus linking gravity and meter arises. From here you can define lot of other units like mass and Volt and Ampere... Everything comes from second which is weird, but does make lot of sense.
• notfed 2y ago
  Another wonderful coincidence: - Speed of light: 299,792,458 m/s - Great Pyramid of Giza: 29.9792458°N
• frankus 2y ago
  Another interesting coincidence (or perhaps a decades-long dad-joke troll perpetrated by German-speaking scientists) is that 1 hertz is roughly equal to the frequency at which a human heart (“Herz” in german, with a nearly indistinguishable pronunciation to “Hertz”) beats.
  • Ekaros 2y ago
    That seems rather low rate. Regular rate in rest is 60 to 100. Which only lower bound is roughly 1Hz, while upper rate is quite far what I would understand German to understand as roughly.
    • jobigoud 2y ago
      80+ heart rate at rest seems very high to me. Is this based on averages from present-day people? Including lots of sedentary people with hyper tension, overweight and obese people, etc. So "normal" in the statistical sense but maybe not "normal" in the physiological sense? Athletes have much lower resting rate. So if we take feral humans from 50Ky ago their rest heart rate would have been much closer to the 60 bpm.
• osigurdson 2y ago
  Having pi^2 = g would annoy me a bit as g is fundamentally a measured value. Depending on the required accuracy of the calculation, you can't even use the idealized value.
  • muzika 2y ago
    We simply wouldn’t need “g” and would say that acceleration due to gravity on earth is sqrt(pi).
• kaapipo 2y ago
  If the length of a meter were defined as the length of a seconds pendulum [1], then g would equal exactly π². From the pendulum equation: `T = 2π√(L/g)` substitute T = 2 s and L = 1 m: `2 s = 2π√(1 m / g)` solve for g: `g = π² m/s²`. This holds up in any strength of gravity, but the length of a meter would be different depending on it. [1]. This actually was proposed by Talleyrand in 1790. Imagine the world if this were true!
  • n4r9 2y ago
    The article explains that Huygens proposed this in the 17th C, and gives the same derivation :)
• mro_name 2y ago
  > And yet, no matter how you look at it, this can’t just be a simple coincidence. why not?
• tdiff 2y ago
  Regarding "Catholic meter": its definition depends on time measurement. How did they ensure that "seconds" of different clocks were equal?
  • School-Cotton 2y ago
    The traditional definition of the second before modern timekeeping was 1/86400 of a day. I’m guessing that was precise enough for their purposes.
    • jobigoud 2y ago
      It must have been brutal to create the first clocks when your smallest external reference is a day long. You first make a huge hour glass or clepsydra and tweak it once per day until it's perfect. Very slow debugging loop.
      • tdiff 2y ago
        Well, defining seconds via "caesium frequency" is perhaps more brutal.
• quasarj 2y ago
  > this can’t just be a simple coincidence. uhhhhhh yes it can?
• anigbrowl 2y ago
  Can we do the same with 432Hz please 432: yes it's a super fun and interesting number 432 cycles per second: seconds are not in fact special
• anigbrowl 2y ago
  How do mathematicians handle it when there are tantalizingly close relationships between purely mathematical numbers? I fell down this particular rabbit hole through the musical entrance (just intonation intervals), but I mean look at all this, it's clearly a setup. https://en.wikipedia.org/wiki/Mathematical_coincidence https://en.wikipedia.org/wiki/Mathematical_coincidence
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• rat_on_the_run 2y ago
  There is nothing meaningful about this. I can change the unit system to make g any value I want (this is done all the time in research). I try really hard to ignore all the physics-related articles posted here but this one is too egregious. It's not the usual thing where the author know nothing about the nouns they are using (enter, quantum). In this case the concepts are fairly simple. The fact that units can be freely changed should be taught in middle school. Somehow I found programmers have a much higher probability of talking about physics than people in other professions. And unfortunately in all cases I've seen, they have no idea what they are talking about. Unlike programming, physics is hard enough that it needs to be studied in classes.
  • aaplok 2y ago
    This is addressed in the article, including the fact that you can change the unit system to change the value of g. The article explains that the coincidence comes from the fact that the meter, as a unit, was defined (by Huygens) based on g and π. It was later redefined several times and the link between the two values became anecdotal. In other words, on another planet the gravitational constant would still have had a value of (approximately) π², and what would have been different is our unit length.
    • rat_on_the_run 2y ago
      Yeah, I saw the author says it depends on the units. But like, why is this interesting? This is not physics, just some number coincidence in the metric unit system, and I'm sure one can find many more these kind of things by playing around with the constants. The fact the author calls this a "wonderful coincidence" is just... Like, a simple energy conservation or momentum conservation, taught in middle school, is infinitely worth being talked than this. One philosophy in physics, is that the world and its rules are independent of human. We actively try to eliminate and downplay historical and human factors in the theory, and try to talk about just "the physics", because those factors often obscure the real physics (mechanism) and complicate the calculation. I mean people can find a historical thing interesting, but I guess I just feel disappointed that people find such a trivial thing so interesting, and maybe think that this is what physics is about, while physics is about anything but those pure coincidences.
• nightlyherb 2y ago
  Would readers well-versed in physics be happier if the equation in the title were `g ≈ π² m/s²` instead of `π² ≈ g`?
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• trainyperson 2y ago
  This article reasons that it is not a coincidence because of the “seconds pendulum” definition of the meter, which would necessitate the values being equal because of the pendulum time period equation. That all makes sense to me, and I agree. But here’s what’s odd to me: We ended up not choosing the seconds pendulum approach (for reasons mentioned in the article). Instead they chose to use “1 ten-millionth of the Earth’s quadrant”. Now, how is it that that value is so close to the length of the seconds pendulum? Were they intentionally trying to get it close to seconds pendulum length, and it just happened to be a nice round power of ten? Is that a coincidence?
  • jdthedisciple 2y ago
    I seriously need an explanation for that too. Never understood how these genius folks just came up with the most outlandish definitions that somehow make perfect sense
• juped 2y ago
  Why is this comment section, specifically, such an embarrassing dumpster fire? It's a serious question; this is the sort of neat derivation that makes for a popular Youtube video, and despite Youtube comments being famously... variable in quality, the comment section on videos about things like this is vastly more literate than the threads here right now. Is it just a coincidence, the chaotic behavior of uninformed sneer comments (which exist on every post; I've certainly been guilty, to my shame) meaning that some post is going to end up being the one with no other type of comment? Or is there some surprising reason why?
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• asimpletune 2y ago
  If society were tasked one day with reinventing standards and units, it doesn't matter why, what do you think are some things they would change? For example, I think for human counting, base 12 is about as easy as base 10, but gives good ways to express division by 3, in addition to division by 2 or 4. It also fits better with how we count time, like how there are 60 seconds in a minute, 12 months in a year, etc... but I imagine those might be revised as well. Anyways, I'm curious to hear what others think.
  • dueyfinster 2y ago
    To be honest I'm not a fan, time is cumbersome to do any sort of addition or subtraction to get exact days/hours/minutes (not to mention timezones etc). Compare to metric units, always base 10 and always easy to convert mm to cm to m and so on. Now that we live in a digital world - why do we consistently reinvent date/time libraries? To me that's proof enough the concepts are just hard to work with and over a long span of time verify your calculation is correct.
    • cameronh90 2y ago
      None of those issues with date and time are anything to do with the base, they're to do with date and time as defined by humans being inherently complicated concepts. Specifically, trying to have a single measurement "fit" for a load of different purposes. If we had based our system around base 12, a base 12 version of the metric system would be just as easy to work with as metric is in decimal, with the added bonus that you can divide powers of the base (10, 100, 1000, etc.) into quarters, thirds and sixths without needing a decimal place, and thirds of 1 would be non-repeating.
  • cameronh90 2y ago
    I think there's an argument for base 16 over 12. It's very slightly worse than base 12 for purely human use, since it's only divisible into halves, quarters and eighths. However, each hex digit maps to an exact number of binary digits, which I think outweighs the benefit of thirds and sixths in a digital world. Of course, it's all theoretical, because there's no chance this would ever happen short of an apocalypse that takes us back to the stone age, and unless the radiation gives us 12 or 16 fingers, we'd probably just reinvent decimal.
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• OJFord 2y ago
  The pendulum equation isn't progress at all, it's just another observation of it? Driving it 'backwards' as it were with known values for the parameters it would determine, and seeing that pi squared is roughly g without having to know the actual values of those constants. And now I've finished the article, nothing more is really offered. Am I missing something? That doesn't explain it/answer the question at all afaict? All we've done is find an equation that uses both pi and g, which shows again the relationship we started from?
  • School-Cotton 2y ago
    The point is that the original definition of the meter was the length such that, when g is expressed in meters, pi^2 = g
• andrei-akopian 2y ago
  You could not have done a worse job explaining it. This is written for which audience. For a person who doesn't know physics this is a very long and confusing explanation. Explaining that some units depend on others, and the importance of the ability to reproduce the metric system on your own, is much more important than the whole pre-story of length standards. There are lots of unanswered questions. What was the second defined as? Don't you measure time using a pendulum? Why was the astronomical definition more reliable? For a person who does know physics you can write a much shorter and clearer explanation eg.: "For a universal definition of the meter you need a constant that appears in nature, such as gravity. You could measure the distance an object falls in some amount of time, but it is easier to use a pendulum. Pendulums swing consistently with a period approximately equal to 2pisqrt(string length/gravity). I you were to use pi^2 for gravity, than after the square root the pis would cancel out, leaving T = 2*sqrt(Length). This is useful because a 1 meter pendulum takes 2 seconds to swing back and forth (1 second per swing.) Clocks at that time were quite accurate, with the second being reproducible from astronomical measurements. So you could take a pendulum, fiddle with it's length until it does exactly one swing every second, and then use the string or stick to measure whatever you wanted. That was great so they changed gravitational constant so it would equal pi^2 (9.87 m/s^2). (If you decrease the meter, everything will become longer.) Then they found out that gravity differs along earth's surface and a perfect mathematical pendulum proved to be difficult to reproduce, so they switched to an astronomy based definition based on the size of earth. That turned out to be broken as well, so they held a physical meter long stick in Paris. A few years ago physicists started using the plank constant which is the smallest possible distance you can measure."
  • simpaticoder 2y ago
    The meter is now (as of 2019) defined as the distance light travels in vacuum during N cycles of an atomic clock[1]. Note that to take into account GR effects you'd need to specify where on Earth you do the measurement, since gravity affects the clock rate. The velocity of light is defined, not measured, now. This is actually quite profound, because our system of units is now based on the validity of special relativity. 1 - https://en.wikipedia.org/wiki/Metre https://en.wikipedia.org/wiki/Metre
• pif 2y ago
  Bullshit! One is a number, the other is an acceleration. Who cares that numeric values are similar for a given set of measurement units?
• rizzir 2y ago
  Our mechanics professor in university told us that Pi squared is ten and 6xPi=20. He said "engineers do not care for the fourth digit after the dot. If you want some number very precisely calculated just hire a mathematician instead because they are cheaper per hour"
  • sfink 2y ago
    Multiple people have brought this up and I just don't get it. When would you ever use Pi squared for anything, and if you'd never use it, who cares what its value is? The only thing I could come up with is marking out an area by rolling a wheel some number of times to measure each edge. Long ago, I memorized the square root of pi precisely because it seemed like the least useful number I could think of. (I was frustrated by something. Never mind.) But pi squared seems like it's pretty much the same in terms of usefulness. If you said pi is the square root of 10, then I could see the value. Maybe that is what is being implied?
• ThatUnknownDude 2y ago
  Pretty sure this is just a coincidence.. I mean pi literally appears everywhere if you look hard enough lol