[HN Gopher] A wonderful coincidence or an expected connection: w...
___________________________________________________________________
A wonderful coincidence or an expected connection: why p2 [?] g
Author : signa11
Score : 335 points
Date : 2024-08-10 12:24 UTC (10 hours ago)
(HTM) web link (roitman.io)
(TXT) w3m dump (roitman.io)
| levzettelin wrote:
| He wouldn't be speaking like this if he was born on Mars.
| edflsafoiewq wrote:
| Sure he would, the meter would just be a different length.
| baxtr wrote:
| Finally an easy way to identify aliens!
| samstave wrote:
| How? Because they don't have a Venus?
| alfiedotwtf wrote:
| The pendulum from the Mars pole to Paris would be long indeed!
| Maxatar wrote:
| 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 wrote:
| 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 wrote:
| Actually no, the whole equation boils down to the definition of
| meter. Or rather, one of the earlier definitions.
| mistercow wrote:
| 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 wrote:
| Because the cubit is a measure of what a body can reach
| Bjartr wrote:
| How does that explain the relationship to the speed of
| sound?
| ValentinA23 wrote:
| A bit out of topic, however
|
| 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 wrote:
| 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 wrote:
| X^2 is a lot more interesting than x*0.0000743 or whatever
| it is
| satvikpendem wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| Ok, then by that thinking, you should find it _really_
| interesting that Earth escape velocity is almost exactly
| ph^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.
| Waterluvian wrote:
| Or the speed of light being almost a sweet 300 million m/s.
|
| Or after-atmosphere insolation being somewhat on average
| 1kw/m2.
| ta1243 wrote:
| 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: insolacion / aislamiento
|
| Chinese: Ri Zhao / Jue Yuan
|
| I guess coincidence
| mananaysiempre wrote:
| _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 ( _ile_
| 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_.
| mistercow wrote:
| > 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".
| nneonneo wrote:
| Usefully, the speed of light is extremely close to one
| foot per nanosecond. This makes reasoning about things
| like light propagation delays in circuits much easier.
| mistercow wrote:
| I really wish we had known this back before it was way
| too late to seriously change our units around. It would
| mean that our SI length units wouldn't have to have some
| absolutely ridiculous denominator to derive them from
| physical constants, and also the term "metric foot" is
| pretty fun.
| tomjakubowski wrote:
| Fun, and poetic too
| cozzyd wrote:
| I use the term "natural foot." It's very useful in
| simulations.
| kuschku wrote:
| See, the issue with "foot" is that different people use
| different body parts to measure length. Germany used the
| "Elle", which is the distance between wrist and elbow, or
| roughly one foot. Other regions used the foot or the
| cubit instead.
|
| The primary advantage of the SI system is that it has
| only ONE length unit that you add prefixes to.
| euroderf wrote:
| 32 meters is 35 yards, to within about an eighth of an
| inch. How's that grab you ?
| GoldenRacer wrote:
| My favorite is 1 mile = phi kilometers with <1% error
| baliex wrote:
| 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 wrote:
| 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 p*E7 = 31415926.5... , which
| is a <1% error from the number of seconds in a year.
| saalweachter wrote:
| 1 km = 5 furlong, with < 1% error.
| mistercow wrote:
| I wonder if this is related, but imperial measurements
| with a 5 in the numerator (and a power of two in the
| denominator) are generally just under a power of two
| number of millimeters.
|
| The reason is fun, and as far as I know, historically
| unintentional. To convert from 5/(2^n) inches to mm, we
| multiply by 25.4 mm/in. So we get 5*25.4/(2^n) mm, or
| 127/(2^n) mm. This is _just under_ (2^7) /(2^n) mm, which
| simplifies to 2^(7 - n) mm.
|
| This is actually super handy if you're a maker in North
| America, and you want to use metric in CAD, but source
| local hardware. Stock up on 5/16" and 5/8" bolts, and
| just slap 8 mm and 16 mm holes in your designs, and your
| bolts will fit with just a little bit of slop.
| dr_dshiv wrote:
| 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/arti
| cles/...
| jvanderbot wrote:
| Well, a second is also a pretty good approximate resting
| heart rate (60 bpm)
| saghm wrote:
| Reminds me of https://xkcd.com/687/
| panarky wrote:
| 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 wrote:
| 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 wrote:
| 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.
| _a_a_a_ wrote:
| I don't agree, I thought what he said was very
| interesting. It never occurred to me that pi might vary,
| and over a non-flat space I can see what they're saying.
| I think it's intrinsically interesting simply because it
| breaks one of my preconceptions, that pi is a constant.
| Talking about it being 'not very useful' just seems far
| too casually dismissive.
| mr_mitm wrote:
| Pi doesn't vary. The ratio of circumference to diameter
| of a circle may vary depending on the geometry. Clearly
| everyone means euclidean space unless specified
| otherwise. Any other interpretation will only lead to
| problems, which is why it's not useful. There is really
| no ambiguity about this in mathematics. Mathematicians
| still use the pi symbol as a constant when they compute
| the circumference of a circle in a given geometry as a
| function of the radius.
| TheRealPomax wrote:
| There is no "clearly" in Math. The fact that pi is a
| constant while at the same time not being "the same
| constant" in all spaces, and not even being "a single
| value, even if we alias it as the symbol pi" is what
| makes it a _fun_ fact.
|
| Heaven forbid people learn something about math that
| extends beyond the obvious, how dare they!
| withinboredom wrote:
| This whole conversation is painful to read:
|
| 1. Your parent was talking about projections from one
| space to another and getting it confused.
|
| 2. Pi is pi and their non-Euclidean pi is still pi
| (unless you want to argue that a circle drawn on the
| earth's surface has a different value of pi).
|
| The problem comes down to projections, then all bets are
| off.
| TheRealPomax wrote:
| Yes. That's what makes it a _fun_ fact. Most people never
| even learn about non-euclidean math, and this is the kind
| of "wow I never even thought about this" that _people
| should be able to learn about_ in a comment thread.
|
| Calling it painful to read is downright weird. Pi, the
| constant, has one value, everywhere. So now let's learn
| about what pi can _also_ be and how _that_ value is not
| universal.
| travisjungroth wrote:
| Just sounds like you've confused yourself. It's like
| spinning in circles and acting like no one else knows
| which way is up.
|
| That isn't a different pi. That's a different ratio. Your
| hint is that there are ways to calculate pi besides the
| ratio of a circle's circumference to its diameter. This
| constant folks have named pi shows up in situations
| besides Euclidean space.
| TheRealPomax wrote:
| Good job, you completely missed the point where I explain
| that pi, the constant, is a constant. And that "pi, if
| considered a ratio" (you know, that thing we did to
| originally discover pi) is _not_ the same as "pi, the
| constant".
|
| Language skills matter in Math just as much as they do in
| regular discourse. Arguably moreso: how you define
| something determines what you can then do with it, and
| that applies to everything from whether "parallel lines
| can cross" (what?) to whether divergent series can be
| mapped to a single number (what??) to what value the
| circle circumference ratio is and whether you can call
| that pi (you can) and whether that makes sense (less so,
| but still yes in some cases).
| stkdump wrote:
| My physics prof said g is actually a vector field.
| Because the acceleration has a direction and both
| magnitude and direction vary from point to point.
| jvanderbot wrote:
| Your physics Prof is correct of course, and so is GP.
| "Standard" values for g exist for these bodies, but it
| also varies everywhere.
| TheCleric wrote:
| I volunteer for the Mars mission as a weight loss tool.
| kevindamm wrote:
| Surviving on Mars will probably involve some mass loss,
| too.
| KeplerBoy wrote:
| It does not? Pi has nothing to do with our arbitrary unit
| system.
| eigenket wrote:
| pi is always just pi, but g may be defined in terms of the
| meter.
| KeplerBoy wrote:
| sure, that's the entire point.
|
| heck, g is not even a constant, it just happens to
| measure to roughly 9.8 m/s2 at most places around here.
| mikequinlan wrote:
| Pi is related to the circumference of a circle; the meter
| was originally defined as a portion of the circumference of
| the Earth, which can be approximated as a circle.
|
| "The meter was originally defined as one ten-millionth of
| the distance between the North Pole and the equator, along
| a line that passes through Paris."
| mistercow wrote:
| But that connection actually _is_ a coincidence. From
| what I can tell, when they standardized the meter, they
| were specifically going for something close to half of a
| toise, which was the unit defined as two pendulum
| seconds. So they searched about for something that could
| be measured repeatably and land on something close to a
| power of ten multiple of their target unit. The
| relationship to a circle there doesn't have anything to
| do with the pi^2 thing.
| mannykannot wrote:
| It was news to me, but that's what the article says, and
| it is supported by by Wikipedia, at least. [1]
|
| In addition, I feel the article glosses over the
| definition of the second. At the time, it was a
| subdivision of the rotational period of the earth
| (mostly, with about 1% contribution from the earth's
| orbital period, resulting in the sidereal and and solar
| days being slightly different.) Clearly, the Earth's
| rotational period can (and does) vary independently of
| the factors (mass and radius) determining the magnitude
| of g.
|
| The adoption of the current definition of the second in
| terms of cesium atom transitions looks like a parallel
| case of finding a standard that could be measured
| repeatably (with accuracy) and be close to the target
| unit - though it is, of course, a much more universal
| measure than is the meridional meter.
|
| [1] https://en.wikipedia.org/wiki/History_of_the_metre
| GuB-42 wrote:
| Not a coincidence. They defined the meter from the second
| using the pendulum formula, and the pandulum formula has
| a pi in it, so pi is going to appear somewhere. The
| reason there is pi is probably because a pendulum is
| defined by its length and follows a circular motion that
| has the length as its radius.
|
| We could imagine removing pi from the pendulum equation,
| but that would mean putting it back elsewhere, which
| would be inconvenient.
| mistercow wrote:
| Right, _that_ connection is not a coincidence. The
| connection the previous commenter drew between the meter,
| pi, and the circumference of the earth is a coincidence.
| hanche wrote:
| > The reason there is pi is probably because a pendulum
| is defined by its length and follows a circular motion
| that has the length as its radius.
|
| It's not quite that easy: For small excursions x the
| equation of motion boils down to x''+(g/L)x=0. There is
| not a p in sight there! But the solution has the form
| x=cos([?](g/L)t+ph), with a half period T=p[?](L/g), thus
| bringing p back in the picture. So indeed not a
| coincidence.
| mistercow wrote:
| Can you explain what you're taking issue with in the post,
| then? Because it specifically lays out how the historical
| relationship between the meter and the second does in fact
| involve pi^2 and the force of gravity on earth.
|
| (Granted, from what I can tell, it's waving away a few
| details. It was the toise which was based on the seconds
| pendulum, and then the meter was later defined to roughly
| fit half a toise.)
| nextaccountic wrote:
| It does, and the formula in the post explains the
| connection
| blablabla123 wrote:
| Changing units in Electrodynamics for instance comes with
| unexpected factors in formulas though, indeed containing p.
| (CGS <-> SI)
| HPsquared wrote:
| Isn't that just the change between rad/s and Hz?
| elashri wrote:
| It is more involving [1]
|
| [1] https://phys.libretexts.org/Bookshelves/Electricity_and
| _Magn...
| setopt wrote:
| It's more precisely the difference between "rationalized"
| and "unrationalized" units.
|
| You need a factor 4pi in either Gauss' law or Coulomb's law
| (because they are related by the area 4pi*r^2 of a sphere),
| and different unit systems picked different ones.
|
| It's more akin to how you need a factor 2pi in either the
| forward or backward Fourier transform and different fields
| picked different conventions.
| vitus wrote:
| > It's more akin to how you need a factor 2pi in either
| the forward or backward Fourier transform and different
| fields picked different conventions.
|
| Some fields even use the unitary transform -- they split
| the difference and just throw in a 1/sqrt(2pi) in both
| directions.
|
| https://en.wikipedia.org/wiki/Fourier_transform#Angular_f
| req...
| phkahler wrote:
| Doesn't the relationship hold if we change units? It seems like
| it must.
|
| When I worked with electric water pumps I loved that power can
| be easily calculates from electrical, mechanical, and fluid
| measurements in the same way if you use the right units. Volts
| _Amps, torque_ rad/sec, pressure*flow_rate all give watts.
| eigenket wrote:
| Nope, it completely vanishes in other units. If you do all
| your distance measurements in feet, for example, the value of
| pi is still about 3.14 but the acceleration due to gravity at
| the earth's surface is about 32 feet s^(-2). If you do your
| distance measurements in furlongs and your time measurements
| in hours then the acceleration due to gravity becomes about
| 630,000 furlongs per hour squared and pi (of course) doesn't
| change.
| ValentinA23 wrote:
| Only because you're using metric seconds instead of
| "imperial seconds" (the time it takes for a 1 foot long
| pendulum to complete a full oscillation).
| eigenket wrote:
| Sure, if you change either of the units you can always
| change the other one to fix the equation again.
| koolala wrote:
| But does it work when you use the right Imperial
| technique?
| usaar333 wrote:
| No, the equality requires the length of a 2 second period
| pendulum be g / pi^2. Change your definition of length - that
| no longer holds true.
|
| g in imperial units is 32 after all. g has units; pi does not
| lupire wrote:
| A more natural way to say it is that equality requires that
| the unit of length is the length of an arbitrary pendulum
| and the unit of time is the half-period of the same
| pendulum.
|
| The pendulum is a device that relates pi to gravity.
| koolala wrote:
| Sounds universal. Get a different value on the Moon? Of
| course... pi squares differently on the moon :)
| phkahler wrote:
| The equation holds in imperial units as well. The length of
| the 2 second pendulum needs to be in feet AND the value of
| g in ft/sec2.
| SAI_Peregrinus wrote:
| p^2 [?] 32 to you?
| koolala wrote:
| Replace s in your calculation with imperial s instead of
| metric s and it isn't imperial feet per metric seconds.
| phkahler wrote:
| Solving the equation for pi we get:
|
| PI = sqrt(g/L)
|
| g = 9.81. L=1
|
| or
|
| g = 32.174. L=3.174
|
| Either way works to approximately pi. There is a
| particular length where it works out exactly to pi which
| is about 3.2 feet, or about 1 meter. My point was that
| equations like that remain true regardless of units.
|
| The reason pi squared is approximately g is that the L
| required for a pendulum of 2 seconds period is
| approximately 1 meter.
| mannykannot wrote:
| This is not quite the same situation, as you are calculating
| a value having a dimension (that of power, or energy per
| second) three different ways using a single consistent system
| of units, and getting a result demonstrating / conforming to
| the conservation of energy. If you were to perform one of
| these calculations in British imperial units (such as from
| pressure in stones per square hand and rate of flow in slugs
| per fortnight) you would get a different numerical value (I
| think!) that nonetheless represents the same power expressed
| in different units. The article, however, is discussing a
| dimensionless ratio between a dimensionless constant and a
| physical measurement that is specific to one particular
| planet.
| glitchc wrote:
| Your quibble seems nitpicky and unwarranted. What the author is
| saying is that the relationship becomes evident if we consider
| the units of m/s^2 for gravity. They just didn't quite say it
| like that.
| mistercow wrote:
| Obviously it's nitpicky. That's what a quibble is. But I
| don't think it's unwarranted. How you reason your way to a
| conclusion is at least as important a lesson as the
| conclusion itself. And in this case, the part I quoted is a
| bad lesson.
| lupire wrote:
| The "magic" doesn't disappear in "any" other units.
|
| Period = 2p[?](length/g)
|
| So the "magic" holds in any units where the unit of time is the
| period of a pendulum with unit length.
| msteffen wrote:
| It's really the best and only way to find non-coincidences
| involving the definition of units, though. All such non-
| coincidences will have this property
| mistercow wrote:
| All coincidences involving the definition of units will also
| have this property. Once you've narrowed to that specific
| domain, invariance to change of units is completely
| uninformative.
| koolala wrote:
| Reading this gave me a chill. Please take my temperature and
| compare it to the norm temperature of humanity.
| arcastroe wrote:
| I'm surprised at the number of people disagreeing with your
| quibble. I had the exact same thought as you!
|
| If pi^2 were _exactly_ g, and the "magic" disappeared in
| different units, THEN we could say "so this is no coincidence"
| and we could conclude that it has to be related to the units
| themselves.
|
| But since pi^2 is only roughly equal to g, and the magic
| disappears in different units, I would likely attribute it to
| coincidence if I hadn't read the article.
| mjburgess wrote:
| It would be useful if people carried around some card with
| all the information that they understood on it, since
| opinions are largely symptoms of this.
|
| In almost all cases any apparent phenomenon specific to one
| system of measurement is clearly a coincidence, since reality
| is definable as that which is independent of measurement.
| twojacobtwo wrote:
| > since reality is definable as that which is independent
| of measurement.
|
| In terms of quantum mechanics, would that mean the wave
| function is real until it collapses due to measurement? Or
| am I misunderstanding your use of measurement there?
|
| Something about that is sticking in my mind in an odd way,
| but I can't put my finger on exactly what it is - which is
| intriguing.
| mjburgess wrote:
| Measurement can change what is measured, but it doesnt
| change it from illusion to reality.
|
| I cannot measure santa clause into existence. But I can
| change the temperature of some water by measuring it with
| a very hot thermometer.
|
| That measurement changes what is measured is the norm in
| almost all cases, except in classical physics which
| describes highly simplified highly controlled
| experiments. The only 'unusual' thing about QM is its a
| case in physics where measurement necessarily changes the
| system, but this is extremely common in every other area.
| It is more unusual that in classical physics, measurement
| doesn't change the system.
| john-aj wrote:
| I agree. But if you remove the "so", there is no contradiction.
| It is possible the author used "so" not to mean "in other
| words", but simply as a relatively meaningless discourse
| marker.
| mistercow wrote:
| Huh, interesting point. Writing unambiguously is ridiculously
| hard.
| anon457437 wrote:
| The comma differentiates. The comma indicates a short pause
| and a certain intonation in speech (the period means a
| longer pause and a different intonation). If you say that
| sentence with and without a pause/comma, you'll see (hear)
| that the sentence is correct. Reading unambiguously is also
| hard.
| mistercow wrote:
| The problem with that is that writers are not consistent
| with comma usage either, particularly when it comes to
| informal writing, where prescriptive rules are out the
| window anyway. And I would argue that it would be a bit
| of a norm violation even in informal writing to introduce
| this new point at the end of a paragraph rather than
| starting a new one, which makes me think that that was
| not the author's intent.
| gklitz wrote:
| What? The entire point is that it's no coincidence in this unit
| set. Saying that changing units indicates a coincidence is like
| saying that if we see Trump suddenly driving a Tesla after Elon
| stated throwing money at him, that must be just a coincidence
| because if we change the car model to a ford then there would
| be nothing odd about it.
| mistercow wrote:
| That analogy is so bizarre that I have no idea how to respond
| to it.
| koolala wrote:
| Truth feels like a coincidence when 1 small thing can make
| anything wrong.
| throwawayk7h wrote:
| you can rule that heuristic out immediately because pi is
| unitless, surely?
| yunohn wrote:
| I don't agree with this. You could literally redefine any unit
| (as we have done so multiple times in the past) and end up with
| zero coincidences.
|
| All measurement metrics are "fake" - nothing is truly
| universal, and can easily be correlated with another human made
| measure eg Pi.
| mistercow wrote:
| I seriously doubt you could define any system of units that
| has zero coincidences, even with significant computational
| effort. Some things in the real world are just going to
| happen to line up close to round numbers, or important
| mathematical constants, or powers or roots of mathematical
| constants, and then you'll have some coincidences.
|
| There are just too many physical quantities we find
| significant, and too many ways to mix numbers together to
| make expressions that look notable.
| thayne wrote:
| Not necessarily. One of the things I was taught when studying
| astronomy is that if you observe periodicity that is similar to
| a year or a day, that's probably not a coincidence, you
| probably failed to account for the earth's orbit or rotation.
| jvanderbot wrote:
| This is a good example, but actually this is exactly what GP
| was referring to. It is a coincidence that the thing you're
| observing is periodic with earth's rotation. Observing a
| similar thing from a satellite (allegorically the same as
| "changing bases") would remove the interesting periodicity.
|
| The earths rotation _coincides_ with the phenomenon, so it 's
| likely a _coincidence_.
| otabdeveloper4 wrote:
| > was actually proposed back in the 17th century
|
| Pretty sure it was done back in Sumer first.
| karmakurtisaani wrote:
| A standard free measure for distance? Sounds dubious.
| otabdeveloper4 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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.
| ValentinA23 wrote:
| https://www.ukbiblestudents.co.uk/Great%20Pyramid/chapter%20...
|
| >"It was contended," says Dr. Peacock, " by Paucton, in his
| Metrologie, that the side of the Great Pyramid was the exact
| 1/500th part of a degree of the meridian, and that the founders
| of that mighty monument designed it as an imperishable standard
| of measures of length.
|
| https://www.theguardian.com/science/2020/dec/06/revealed-isa...
|
| >Newton was trying to uncover the unit of measurement used by
| those constructing the pyramids. He thought it was likely that
| the ancient Egyptians had been able to measure the Earth and
| that, by unlocking the cubit of the Great Pyramid, he too would
| be able to measure the circumference of the Earth.
| BrandoElFollito wrote:
| 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 wrote:
| pi * 1e7
| radiator wrote:
| 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 wrote:
| 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 wrote:
| 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.
| CoastalCoder wrote:
| I assumed the pi / g connection was because cows that
| accelerate in a vacuum are _spherical_.
| openrisk wrote:
| I think it was Gauss who proved that any convex cow would
| work equally well. But we need to assume an infinitesimally
| thin and infinitely long tail as boundary condition.
| Sharlin wrote:
| According to the Banach-Tarski paradox, if you accept the
| Axiom of Choice, you can disassemble a spherical cow and put
| the parts back together such that you end up with two cows of
| the original size. How exactly this affects Cow Economics is
| not well-understood.
| fouronnes3 wrote:
| As a computer scientist this is not surprising either. After
| all there are only three numbers: 0 1 and n.
| 360MustangScope wrote:
| You mean the legendary "i". There is no n.
| de_nied wrote:
| Yea if you're some classical snob.
|
| - Posted by the quantum gang
| pansa2 wrote:
| Remember that `i` is also a number. As in `for i = 0 to n`.
|
| Don't believe those mathematicians when they tell you that
| `i` is "imaginary".
| Anarch157a wrote:
| All numbers are imaginary.
|
| sqrt(-1) should have been called w, for "weird".
| syockit wrote:
| I use w for the complex roots of 1 though, when rewriting
| FFT notes.
| HPsquared wrote:
| And int_max
| Maken wrote:
| That's a implementation detail.
| jeffwass wrote:
| One of my old physics professors said something similar -
| there are only three numbers in the world - 0, 1, and
| infinity. No wait, zero is just one divided by infinity, so
| there are only two numbers, zero and one. So if the answer is
| not zero, it must be one. (ie, how to justify dimensional
| analysis and ignore any dimensionaless constant).
|
| Hysterical, especially for the fact that he quotes 'two' and
| 'three' in the sentence itself.
| imoverclocked wrote:
| He already got rid of "three" and just needed a little help
| to get rid of "two." Since we already have 0 and (almost)
| everything else can just be "one more" than something else,
| we only need 0 and one more ... or 1.
|
| One and Done!
| klabb3 wrote:
| Another one would be philosophy: there's nothing, something
| and everything. Or logic: [?], ![?] and [?]. Just rambling
| here, but seems like universal concepts across fields.
| john-aj wrote:
| Chiming in from theoretical linguistics: it is impossible
| for natural languages to "count", i.e. make reference to
| numbers other than 0, 1 or infinity.
|
| As an example, there are languages where prenominal
| genitives are impossible (0).
|
| Then, there are languages, such as German, where only one
| prenominal genitive is possible (1):
|
| > Annas Haus
|
| > *Annas Hunds Haus
|
| Finally, there are languages, such as English, where an
| infinite number of prenominal genitives are possible
| (infinity).
|
| > Anna's house
|
| > Anna's dog's house
|
| > Anna's mother's dog's house
|
| > Anna's mother's sister's ... dog's house
|
| But there are no languages where only two or three
| prenominal genitives are possible.
|
| This property is taken to be part of Universal Grammar,
| i.e. the genetic/biological/mental system that makes
| human language possible.
| ithkuil wrote:
| And -0 and NaN
| hyperhello wrote:
| 3600 seconds per hour, times 3*8 is only about 80,000 seconds a
| day. You can't get to a billion from there.
| sa46 wrote:
| Pi seconds is a nano-century. So 1 year = pi*10^7 seconds
| remuskaos wrote:
| A year is pi 10^7, or pi 1e7.
|
| On the other hand, 10 e9 = 10 * 10^9.
| leoff wrote:
| as a mechanical engineer, can confirm. also, e [?] pi [?] 3
| winwang wrote:
| in fact, e = 2, made rather abundantly clear in "finite
| difference" calculus, and also that in computer science, the
| "natural" log base 2.
| Sharlin wrote:
| The pi in pi*10^9 seconds clearly comes from the fact that
| Earth's orbit is circular.
| maxnoe wrote:
| Nore sure if serious or not, but anyway:
|
| 1) it isn't circular, although just barely (it's an ellipse)
| 2) the length of the day is not really related to the length
| of a year, and the second was defined as 1 / (24 * 60 * 60) =
| 1 / 86400 of the mean solar day length
|
| So this is really just a coincidence, there is no
| mathematical or physical reason why this relationship (the
| year being close to an even power of 10 times pi seconds)
| would exist.
| Sharlin wrote:
| Definitely not serious :)
|
| But from the fact that an Earth year happens to be roughly
| pi*10^7 seconds long, it follows that in 10^7 seconds Earth
| travels about two radians, or one orbital diameter, and
| equivalently that the diameter of Earth's orbit is roughly
| 10^7 seconds times Earth's orbital speed.
| breck wrote:
| Very interesting!
|
| So if I understand correctly: the meter was defined using gravity
| and p as inputs (distance a pendulum travels in 1 cycle), so of
| course g and p would be connected.
| fweimer wrote:
| On the hand, g is about 32.2 ft/s2. So it's suddenly related to
| p3? 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 p that shouldn't be there, statistically
| speaking.
| cvoss wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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.
| vessenes wrote:
| 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 wrote:
| Sorry to ruin the party, but g is a quite random number, on other
| planets the corresponding acceleration is different. So p^2~g is
| a pure coincidence and not relevant. The Newtonian gravitational
| constant G is a real constant btw.
| gpvos wrote:
| 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 wrote:
| My intuitive assumption, then, is that on Mars they would
| have come up with a _different_ meter such that p2 [?] 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 wrote:
| 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.
| michaelrpeskin wrote:
| > A unit system is not just something that matches
| objective reality but something that has some cognitive
| ergonomy.
|
| Beautifully stated!
|
| And that's one reason why I like the US units of
| measurement better than SI. I mean, the divide-by-ten
| thing is nice and all. But _within a project_ how often
| are you converting between units of the same measurement
| (e.g, meters to centimeters)? You pick the right "size"
| unit for your work and then tend to stay there. So you
| don't get much benefit from the easy conversion in
| practice.
|
| But if you're doing real hands-on work, you often need to
| divide by 2, 3, 4, and so on. So, for example, having a
| foot easily divisible by those numbers works well. And
| even the silly fractional stuff make sense when you're
| subdividing while working and measuring.
|
| Of course it all finally breaks down when you get to
| super high precision (and that's probably why machinists
| go back to thousands of an inch and no longer fractions).
|
| I think there's a little bit of academic snobbery with
| the SI units (though, it is a good idea for cross-country
| collaboration), but for everyday hand-on work the US
| system works really well. I always love the meme: There
| are two kinds of countries in the world, those who use
| the metric system and those who've gone to the moon.
|
| I'm an AMO physicist by training and my choice of units
| are the "Atomic Units" where hbar, mass of the electron,
| charge of the electron, and permittivity are all 1. That
| makes writing many of the formulae really simple. Which
| is what you say: it has cognitive ergonomy (and makes all
| of the floating point calculations around the same
| magnitude). Then when we're all done we convert back to
| SI for reporting.
| bialpio wrote:
| One example where picking units within a project is still
| not saving you from cognitive load is e.g. when doing
| woodworking. Ymmv, but I can add decimals way faster than
| I can add 7 9/16" + 13 23/32" (numbers picked arbitrarily
| but close to a precision of 1mm so if you are ok w/ that
| precision, you don't even need fractions in SI).
| jds-67 wrote:
| I have to admit I only read half of the article. Even if
| there is some historical fact there (but it was not mentioned
| at the beginning of the article), from a physical standpoint
| this comparison is already dimensionally wrong and also
| coincidentally only correct if you choose appropriate units.
| That was the point I was trying to make. There is not
| anything "deep" here.
| shermantanktop wrote:
| I'd suggest fully reading the article.
| gpvos wrote:
| I admit I scanned the article first and wondered what it
| was all about. The actual argument is not very clearly
| presented.
| kbelder wrote:
| How strange.
|
| "I only ran the first half of the program, but it didn't
| seem to give the correct answer, so it's obviously broken."
|
| "I only read the first half of the proof, but the answer
| wasn't contained there, so I'm forced to conclude the proof
| is worthless."
|
| You simply gave up before encountering the mathematical
| reason the relationship exists, why the units are
| different, and so on. You just ran with your incorrect
| initial assumption.
| gpvos wrote:
| Not strange at all, most people do that most of the time.
| sidpatil wrote:
| 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.
| beardyw wrote:
| You are correct but the point is the way the meter is
| calculated, g in meters per second should come to pi squared.
| dweekly wrote:
| Link is broken for me?
|
| "[ErrorBoundary]: There was an error: {}"
| roitman wrote:
| Try refreshing the page
| shubhamjain wrote:
| 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 wrote:
| Arguably most humans can't do this either.
| avaldez_ wrote:
| > 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
| badgersnake wrote:
| The only thing with more bollocks in it than this article is
| your aibro comment.
| kwhitefoot wrote:
| 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.
| philzook wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| > 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 wrote:
| 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.
| stkdump wrote:
| A human is ~1 meter, 1e2 kilograms and 1e9 seconds.
| HuangYuSan wrote:
| Funnily Avogadro's constant is actually equal to 1: it's
| defined as Avogadro's number times mol, but mol is itself a
| dimensionless quantity equal to the inverse of Avogadro's
| number.
| aaaronic wrote:
| Multiplying by increasingly complicated expressions
| equivalent to "1" is what I remember doing for almost every
| problem in Quantum Mechanics.
| sycren wrote:
| If the definition of the meter is still wrong disallowing p2 = g,
| how might this affect other calculations like for example thrust
| and in aerospace engineering?
| kseistrup wrote:
| And what would all other natural constants look like, had the
| meter kept the value derived from the length of the pendulum?
| im3w1l wrote:
| I knew that historically meter was related to the size of the
| earth somehow, but I had never had about the pendulum definition!
| spacebacon wrote:
| I laughed 3 times reading this article while pondering the
| novelty of standardization.
|
| Is standardization the sans-serif of civilization?
| alberth wrote:
| 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 wrote:
| 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 wrote:
| Okay so this one has an explanation. But what about these ?
|
| https://en.wikipedia.org/wiki/Mathematical_coincidence
|
| See also this blog: https://martouf.ch/tag/coudee-royale-
| egyptienne/
|
| One french royal cubit [?] one egyptian cubit [?] about p/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#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-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 wrote:
| > 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 wrote:
| I find this comment delightfully ironic in a contemporary
| moment of blatant shrinkflation.
| karmakaze wrote:
| 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 wrote:
| 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 wrote:
| 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.
| julienchastang wrote:
| 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-Th...
| karmakaze wrote:
| Numerologists unite!
| xxmarkuski wrote:
| I remember in mechanical engineering class we would often use
| this for exercise sheets. On our calculator we could directly
| enter p and 2, thus it was equally as fast to entering 10.
| imoverclocked wrote:
| That's one way of setting up a standard deviation!
| rich_sasha wrote:
| 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 wrote:
| According to the article the 1/4e10 circumference definition
| came second
| rich_sasha wrote:
| 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 wrote:
| 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 wrote:
| I wonder if this is how astrology was born. You can draw
| arbitrary connections between things if you stare at them long
| enough.
| bravura wrote:
| 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 wrote:
| Personal preferences continue to exist. I don't see that
| happening.
| pclmulqdq wrote:
| More fun arithmetic coincidences:
| https://en.m.wikipedia.org/wiki/Almost_integer
|
| Some of these are test vectors for math systems.
| fireattack wrote:
| 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
| gpvos wrote:
| 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 wrote:
| 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.
| lutusp wrote:
| 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 wrote:
| The best is sum(1, 36)
| areyousure wrote:
| ln(5) ~ 1.6094379 is much closer, differing by about half of a
| percent of a percent.
| maxnoe wrote:
| A year is very close to pi * 1e7 seconds, better than half a
| percent.
| koolala wrote:
| Do miles connect to feet and feet vs. gravity connect to the
| Golden ratio? 6 feet is like 2 pi?
| renewiltord wrote:
| Hence the 2[?]l formula for the pendulum haha
| Ekaros wrote:
| 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 wrote:
| Another wonderful coincidence:
|
| - Speed of light: 299,792,458 m/s
|
| - Great Pyramid of Giza: 29.9792458degN
| frankus wrote:
| 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 wrote:
| 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.
| nyc111 wrote:
| 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.
| osigurdson wrote:
| 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.
| kaapipo wrote:
| If the length of a meter were defined as the length of a seconds
| pendulum [1], then g would equal exactly p2. From the pendulum
| equation:
|
| `T = 2p[?](L/g)`
|
| substitute T = 2 s and L = 1 m:
|
| `2 s = 2p[?](1 m / g)`
|
| solve for g:
|
| `g = p2 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 wrote:
| The article explains that Huygens proposed this in the 17th C,
| and gives the same derivation :)
| mro_name wrote:
| > And yet, no matter how you look at it, this can't just be a
| simple coincidence.
|
| why not?
| tdiff wrote:
| Regarding "Catholic meter": its definition depends on time
| measurement. How did they ensure that "seconds" of different
| clocks were equal?
| umanwizard wrote:
| 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.
| quasarj wrote:
| > this can't just be a simple coincidence.
|
| uhhhhhh yes it can?
| anigbrowl wrote:
| 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
___________________________________________________________________
(page generated 2024-08-10 23:00 UTC)